Biomechanics of the Eye [1 ed.] 9789062992508, 9789062998869

Citation preview

9 789062 992508 Copyright © 2018. Kugler Publications. All rights reserved.

ISBN 978-90-6299-250-8

Copyright © 2018. Kugler Publications. All rights reserved.

BIOMECHANICS OF THE EYE

Copyright © 2018. Kugler Publications. All rights reserved.

Biomechanics of the Eye Editors Cynthia J. Roberts William J. Dupps Jr.

Copyright © 2018. Kugler Publications. All rights reserved.

J. Crawford Downs

Kugler Publications/Amsterdam/The Netherlands

Copyright © 2018. Kugler Publications. All rights reserved.

ISBN 978-90-6299-250-8 Kugler Publications P.O. Box 20538 1001 NM Amsterdam, The Netherlands www.kuglerpublications.com © 2018 Kugler Publications, Amsterdam, The Netherlands All rights reserved. No part of this book may be translated or reproduced in any form by print, photoprint, microfilm, or any other means without prior written permission from the publisher. Kugler Publications is an imprint of SPB Academic Publishing bv, P.O. Box 20538, 1001 NM Amsterdam, The Netherlands Cover design by: Willem Driebergen, Rijnsburg, The Netherlands

Table of contents Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi About the editors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 1. Basics of biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Jesper Hjortdal 2. Corneal stroma: collagen ultrastructure and orientation in health and disease . . . . . . . . . . . . . 15 Keith M. Meek, Sally Hayes 3. Acoustic radiation force elastic microscopy and corneal structural correlation . . . . . . . . . . . . . 31 Eric Mikula, Donald J. Brown, Moritz Winkler, Elena Koudouna, Tibor Juhasz, James V. Jester 4. Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 W. Matthew Petroll, Miguel Miron Mendoza 5. The electrochemical basis of corneal hydration, swelling, and transparency . . . . . . . . . . . . . . . 63 Peter Pinsky, Xi Cheng 6. Material properties of the human cornea: anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Ashkan Eliasy, Zhou Dong, Harald Studer, Craig Boote, Ahmed Elsheikh 7. Inflation testing of the cornea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Thao D. Nguyen, Jun Liu 8. Optical coherence tomography principles and elastography . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Matthew R. Ford, Vinicius De Stefano, William J. Dupps Jr.

Copyright © 2018. Kugler Publications. All rights reserved.

9. Optical coherence elastography for ocular biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 Manmohan Singh, Michael D. Twa, Kirill V. Larin 10. Electronic speckle pattern interferometry and lateral shearing interferometry . . . . . . . . . . 147 Abby Wilson, John Marshall 11. Brillouin microscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Giuliano Scarcelli, Seok Hyun Yun 12. Deformation response to an air puff: clinical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Katie Hallahan, William J. Dupps Jr., Cynthia J. Roberts

vi

13. Factors contributing to air-puff derived corneal responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 Riccardo Vinciguerra, Renato Ambrósio Jr., Simone Donati, Claudio Azzolini, Paolo Vinciguerra 14. Biomechanics in ectasia detection: ORA and Corvis ST . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Renato Ambrósio Jr., Fernando Faria Correia, Bernardo T. Lopes, Rui Carneiro Freitas, Isaac Ramos, Marcella Q. Salomão, Allan Luz 15. Mechanisms of collagen crosslinking and implications on biomechanics . . . . . . . . . . . . . . . . 217 Eberhard Spoerl, David C. Paik 16. Crosslinking kinetics and alternative techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Michael Mrochen, Rebecca McQuaid, Nicole Lemanski, Bojan Pajic 17. Computational modeling of corneal refractive surgery, ectasia, and corneal crosslinking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Ibrahim Seven, Vinicius Silbiger De Stefano, William J. Dupps Jr. 18. Comparative biomechanics of intrastromal lenticule extraction and LASIK . . . . . . . . . . . . . . 261 Dan Z. Reinstein, Timothy J. Archer, Ibrahim Seven, Cynthia Roberts, William J Dupps Jr. 19. Iris biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281 Anup Dev Pant, Rouzbeh Amini 20. Accommodation and presbyopia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295 Matthew Reilly 21. Biomechanics of the lens and its role in accommodation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Noël M. Ziebarth, Vivian M. Sueiras, Vincent T. Moy, Fabrice Manns, Jean-Marie Parel 22. Biomechanics of the vitreous humor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 Rodolfo Repetto, Jennifer H. Tweedy 23. Introduction to posterior pole biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347 J. Crawford Downs, Vicky Nguyen

Copyright © 2018. Kugler Publications. All rights reserved.

24. Intraocular pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 Daniel C. Turner, Jessica V. Jasien, J. Crawford Downs 25. Collagen anisotropy in scleral mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 Neeraj Vij Jr., Jonathan Vande Geest 26. The dynamic response of the corneoscleral shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 Jun Liu, Keyton L. Clayson, Elias R. Pavlatos 27. Scleral remodeling in myopia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 Rafael Grytz

vii

28. The connective tissue phenotype of glaucomatous cupping in the monkey eye . . . . . . . . . . 405 Hongli Yang, Juan Reynaud, Howard Lockwood, Galen Williams, Christy Hardin, Luke Reyes, Cheri Stowell, Stuart K. Gardiner, Claude F. Burgoyne 29. Cellular mechanisms of lamina cribrosa remodeling in glaucoma . . . . . . . . . . . . . . . . . . . . . . 431 Reinold K. Goetz, Deborah Wallace, Tabitha Goetz, Colm O’Brien 30. Optic nerve head biomechanics in health, aging, and disease . . . . . . . . . . . . . . . . . . . . . . . . . 443 J. Crawford Downs 31. Cerebrospinal fluid pressure and the translaminar pressure gradient in optic nerve head biomechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Julia Raykin, Brian C. Samuels, Andrew J. Feola, C. Ross Ethier 32. Parametric analysis to identify biomechanical risk factors: taking control of population diversity and experiment variability . . . . . . . . . . . . . . . . . . . . . . . . . 479 Andrew P. Voorhees, Yi Hua, Ian A. Sigal 33. In-vivo characterization of optic nerve head biomechanics for improved glaucoma management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Xiaofei Wang, Meghna R. Beotra, Liang Zhang, Michaël J.A. Girard

Copyright © 2018. Kugler Publications. All rights reserved.

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

Foreword: Biomechanics of the eye To illustrate the explosive growth of biomechanical studies in ophthalmic science, I checked the 9th and 11th edition of Adler’s Physiology of the Eye, a veritable Bible of the field. The 1992 edition had not one indexed comment on “biomechanics”, while the 2011 version had two index entries for its nearly 1,000 pages! The cornea sections dealt with ultrastructure, light transmission, endothelial pumping, and neovascularization, but not bending forces, and the sclera was treated anatomically, but not physiologically. It is fortunate for us that a distinguished group of international experts contributed to the present volume, enlightening us on a series of vitally important issues that now occupy an important place in the understanding of how eyes work and don’t work. Seeing is believing: Inherent in many of the presentations to follow are new methods of viewing the ocular tissues. Advancing from the microcosmic window of transmission electron microscopy, we see the cornea and other ocular tissues clinically through the useful view of optical coherence tomography. Ex-vivo study methods now include a plethora of illuminating techniques that show the orientation of fibers, their composition, and their change in inflation studies: small angle light scattering, wide angle x-ray scattering, magnetic resonance imaging, and microscopy utilizing polarization, second harmonic generation, and two photon imaging. Many of these use unfixed tissue to avoid the major processing changes that alter tissue physiology. They permit in many cases the reconstruction of 3-D structure and its response as an in-vivo unit. Life in a bubble: While past studies put strips of cornea or sclera under uniaxial stretch, the ocular tissues behave as a 3-D globe, and the work to be presented moves to study ocular tissues in their situation in situ, at least insofar as is practical given the limitations of methods. From studies that began by speckling the scleral surface and inflating the globe, we now have microscopic methods of viewing the strain and fiber orientation of the full thickness of the cornea or sclera under stress. Furthermore, for many diseases, it is the process of aging or response to change in the tissue that determines whether abnormality is functionally important and how badly the eye is affected. Thus, disease-simulating experimental models of tissue change in animals are important. Pretty models: To understand how, and more importantly why, a tissue responds as it does, we benefit from the expertise of those who can construct model systems that simulate tissue reactions. These not only include all of the important elements as variables to weigh their relative importance, but permit systematic alteration in the magnitude of each variable to assess through sensitivity analysis its likely contribution. These models can be used most effectively when relevant data for each parameter is measured experimentally. Models in animals have begun to show us that looking only at baseline parameters is insufficient, as remodeling during disease may be more important than where the tissue started. This shows the value of teams of clinician-scientists and engineers working forceps to caliper. Who needs a disease: The book deals not only with diseases and their detrimental effect on quality of life, but also with more common features of the visual system that affect us: refractive error and presbyopia. Population-based studies now show that the most common causes of visual disability worldwide are the need for distance and reading glasses. If one wishes to start a career in vision science with the aim of having the maximum impact on the world, it would be to fix these two. The present book takes on aspects of these troubling problems and what biomechanics teaches about them. Softer mechanics: The eye has a variety of tissues that have biomechanical processes other than those that are classically considered part of the engineering repertoire (cornea and sclera). We are increasingly aware that collagenous fibers are one aspect of biomechanical response, but their accompanying matrix and cellular components play important roles as well. Recent research shows that we need to know more about the mechanics

x

of the trabecular meshwork (relevant to glaucoma and newer glaucoma surgeries), of the iris (for contributions to angle closure mechanisms), of the vitreous (for contribution to retinal detachment), and of the choroid (for relationships to myopia and age-related macular degeneration). Who cares? Basic knowledge leads to important future clues for both diagnosis and therapy. Important avenues for diagnostic biomarkers have been developed for the contributions of corneal hysteresis, central corneal thickness, iris volume loss on pupil dilation, and optic nerve head flexibility, among many others. The models point to potential treatments, and in the case of corneal ectasia, making the structure stiffer has shown promise for avoiding the need for replacement surgery of the cornea. For glaucoma, making the eye stiffer to limit strain has (at least in mice) made things worse, not better, so one size does not fit all. This volume has a huge collection of the best presentations by the sharpest minds in this field. Enjoy.

Copyright © 2018. Kugler Publications. All rights reserved.

Harry A. Quigley, MD A. Edward Maumenee Professor, Ophthalmology, Wilmer Institute, Johns Hopkins, Baltimore, MD, USA

Introduction

Copyright © 2018. Kugler Publications. All rights reserved.

J. Crawford Downs, William J. Dupps Jr., Cynthia J. Roberts Biomechanics is the study of the mechanical interaction of solids and/or fluids with internal and external forces in the context of biology. It has long been a mainstay in the cardiovascular and orthopedic fields, where it has been used to analyze and predict the mechanical and biological mechanisms underlying bone fractures, hard and soft tissue remodeling, and blood flow through arterial stents and aneurysms. Biomechanical techniques are critical in optimizing cardiac and orthopedic implant designs for maximum clinical efficacy and life. Ocular biomechanics has been primarily focused on diseases of the cornea, trabecular meshwork, sclera, and optic nerve head, with more limited application in the vitreous, lens, and iris. It has provided insight into disease processes and surgical outcomes in various eye disorders. For example, in glaucoma, ocular biomechanics has been used to analyze and predict the importance of the sclera in determining the biomechanics of the lamina cribrosa, the site of axonal damage in glaucoma. In the cornea, the science of biomechanics has been used to better understand the structural basis of corneal ectatic diseases and to develop biomechanically mediated treatments for keratoconus that have already resulted in a global reduction in the number of corneal transplants required for this disease. Biomechanical engineers use cutting-edge engineering-based computational and experimental techniques to investigate the interaction of ocular tissues with their surroundings, as well as the forces that are common in the eye: intraocular pressure, tensile and torsional muscle tractions, blood flow and vascular pressures, external traumatic forces, cerebrospinal fluid pressure, and tissue growth pressures. The tools bioengineers use include finite element modeling, a computational technique to split complex geometries into small regularly shaped elements, for which loading, mechanical stress (force distribution), and mechanical strain (local deformation) are calculated individually. The results of each of these simple elemental responses are then added up, or superposed, into the overall response of the structure. Measures of tissue deformation under load can now be obtained with imaging techniques, such as ultrasound biomicroscopy, optical coherence tomography, Scheimpflug tomography, infrared corneal reflection monitoring, and magnetic resonance imaging, and these observations can be used to generate various approximations of biomechanical properties and validate computational biomechanics simulations. Many of these measurement technologies are being developed (or are already available) for in vivo and clinical applications. The structural geometries in the human body are much more complex than typical engineered structures, such as bridges and airplane wings. Biological tissue stiffness is inherently complex in that it changes with orientation (anisotropy), the rate of loading (viscoelasticity), and the level of stretch or compression (hyperelasticity). Computational models require accurate representations of tissue geometry, loading and constraints on the modeled structure, and compliance or stiffness of the tissue constituents. Whereas certain elements of the ocular anatomy such as the cornea are very accessible to measurement, measurements are more difficult to obtain in very small structures and more posterior ocular components. Important factors such as fluid pressures or blood flow are nearly impossible to measure using current technology. When accurate representations of the model inputs are unavailable, simple representative geometries coupled with simplifying assumptions on the loading and tissue material properties can still be used to construct models that reveal fundamental relationships regarding the responses of tissues to load. The eye boasts one of nature’s most exquisite relationships between structure and function. Ocular function is a complex product of the eye’s constitutive elements, their mechanical properties, and a host of biological processes responsible for normal function, immunological defense, repair, and disease. This book introduces the eye as a biomechanical entity and surveys emerging efforts to apply biomechanical principles to understanding mechanisms of ocular disease, enhancing diagnosis, and optimizing treatment.

Copyright © 2018. Kugler Publications. All rights reserved.

About the editors Cynthia J. Roberts Dr. Roberts received a BS degree in Nursing with Distinction from the University of Iowa in 1979, and worked as a Registered Nurse for several years at the University of Iowa Hospitals and Clinics before enrolling in engineering. She received an MS degree in Electrical Engineering in 1986, and a PhD in Biomedical Engineering in 1989, both from The Ohio State University. Dr. Roberts is currently a Professor in Ophthalmology & Visual Science, and Biomedical Engineering at The Ohio State University, and holds the Martha G. and Milton Staub Chair for Research in Ophthalmology. Her research focus is ophthalmic engineering, or the application of engineering principles and problem-solving techniques to the maintenance and improvement of vision. Corneal topography was her first area of research within ophthalmology. Her other research interests include ocular biomechanics in refractive surgery, cornea and glaucoma; intraocular pressure measurement error; the in-vivo assessment of corneal biomechanical properties using ultrasonic and dynamic imaging techniques; ophthalmic imaging applications including intraoperative topography-guided surgery, Scheimpflug tomography, and optical coherence tomography with both corneal and retinal applications. She is well published in these areas and has many international collaborators. Dr. Roberts serves on the editorial boards of the Journal of Refractive Surgery, the Journal of Cataract and Refractive Surgery, and the International Journal of Keratoconus and Ectatic Corneal Diseases. She has given many invited lectures internationally, and multiple courses in corneal topography and corneal biomechanics, in both the United States and Europe. Dr. Roberts received the inaugural Barraquer Medal from the Brazilian Society of Refractive Surgery in 2008 with a lecture entitled ‘Biomechanical Customization: The Next Generation of Refractive Surgery.’ She was inducted as a Fellow in the American Institute for Medical and Biological Engineering in 2009, and was recognized by the American Academy of Ophthalmology with an Achievement Award in 2012.

Copyright © 2018. Kugler Publications. All rights reserved.

William J. Dupps Jr. William J. Dupps Jr., MD, PhD, a native of Catawba Island, Ohio, is Professor of Ophthalmology at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and Staff in Ophthalmology, Biomedical Engineering and Transplantation at Cleveland Clinic’s Cole Eye Institute and Lerner Research Institute. He is an Adjunct Professor of Biomedical Engineering at Case Western Reserve University and adjunct faculty in the Department of Chemical and Biomedical Engineering at Cleveland State University. After graduating with a BS in Chemical Engineering from Purdue University, he completed MS and PhD programs in Biomedical Engineering at The Ohio State University and earned a medical degree with honors in the Medical Scientist Training Program. He completed a residency in Ophthalmology at the University of Iowa Department of Ophthalmology and Visual Sciences and a two-year Cornea and Refractive Surgery Fellowship at the Cole Eye Institute, a program for which he now serves as Director. His clinical practice focuses on refractive surgery, corneal disease, and cataract surgery. With grant support that includes the National Institutes of Health, the Ohio Third Frontier program and Research

xiv

to Prevent Blindness, Dr. Dupps leads an interdisciplinary research team in translational corneal biomechanics. His research addresses the biomechanics of corneal refractive surgery and corneal ectatic disease as well as the development of novel approaches to optimizing corneal surgery through computational modeling and biomechanical measurement. Dr. Dupps’ has received the Achievement Award for service to the American Academy of Ophthalmology (AAO), the Kritzinger Award from the International Society of Refractive Surgery and a Distinguished Alumnus Award from The Ohio State University College of Engineering. He is currently chair of the AAO Practicing Ophthalmologist Curriculum Refractive Management & Intervention Panel. He is a member of the American Ophthalmological Society. Dr. Dupps serves as Associate Editor for the Journal of Cataract and Refractive Surgery and Translational Visual Science and Technology and served previously as an Executive Editor for Experimental Eye Research. He has published 120 journal articles and editorials and has delivered over 150 invited lectures. He holds several patents and received the Cleveland Clinic’s first Early Career Innovation Award in 2009 for founding OptoQuest, a Cleveland Clinic spin-off for commercializing systems to improve surgical planning through patient-specific computational simulation. He lives with his wife, Gretchen, and their three children in Bay Village, Ohio.

Copyright © 2018. Kugler Publications. All rights reserved.

J. Crawford Downs J. Crawford Downs received his PhD in Biomedical Engineering in 2002 from Tulane University in New Orleans, Louisiana, and is now Professor of Ophthalmology, Biomedical Engineering, and Computer Science at the University of Alabama at Birmingham (UAB) in Birmingham, Alabama, USA. He served as Vice Chair of Research in the Department of Ophthalmology during the department’s building phase (2013-2017) and as founding Director of the UAB Ocular Biomechanics and Mechanobiology Program. Prior to joining UAB, Dr. Downs held appointments as a Research Assistant Professor at the Louisiana State University Eye Center in New Orleans, Louisiana (2002-2005), and as an Associate Scientist at the Devers Eye Institute in Portland, Oregon (2005-2012). He has spent his career studying ocular biomechanics, focusing in particular on biomechanics and mechanobiology of the optic nerve head (ONH), sclera, and lamina cribrosa to better understand the pathophysiology of glaucoma, a leading cause of irreversible blindness worldwide. Dr. Downs uses the unilateral, inducible model of glaucoma in non-human primates, and has developed a novel wireless telemetry system that measures and records continuous intraocular pressure, arterial blood pressure, and intracranial pressures in both normal and glaucoma eyes. He uses these data, along with laser-based ocular inflation testing data and high-resolution 3-D reconstructions of the ONH geometry, as inputs to finite element models of ONH biomechanics. He also works in human donor eyes when possible. Dr. Downs’ laboratory is funded by R01 grants from the National Eye Institute of the National Institutes of Health, Bright-Focus Foundation, Research to Prevent Blindness (departmental support), and the EyeSight Foundation of Alabama. He has authored over 70 peer-reviewed research papers, 12 book chapters, and hundreds of conference abstracts, and he is a frequent invited lecturer at domestic and international meetings and institutions. Dr. Downs serves on the NASA Research and Clinical Advisory Panel for Space-associated Neuro-ocular Syndrome (SANS). He also serves on the editorial board of Current Eye Research and is a frequent reviewer and/or guest editor for a multitude of journals, including Investigative Ophthalmology and Visual Science, PLoS One, Nature Scientific Reports, Ophthalmology, and JAMA Ophthalmology. Dr. Downs is a frequent reviewer of grant proposals to NIH, domestic foundations, and foreign governments.

List of contributors Renato Ambrósio Jr. Department for Ophthalmology of the Federal University of The State of Rio de Janeiro (UniRIO) and Federal University of São Paulo (UNIFESP), Brazil; Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro, Brazil; Instituto de Olhos Renato Ambrósio and VisareRIO, Rio de Janeiro, Brazil Rouzbeh Amini Department of Biomedical Engineering, The University of Akron, Akron, OH, USA Tim Archer London Vision Clinic, London, UK Claudio Azzolini Department of Medicine and Surgery, University of Insubria, Varese, Italy Meghna R. Beotra Ophthalmic Engineering & Innovation Laboratory, Department of Biomedical Engineering, Faculty of Engineering, National University of Singapore, Singapore Craig Boote Structural Biophysics Group, School of Optometry and Vision Sciences, Cardiff University, Cardiff, UK Donald J. Brown Gavin Herbert Eye Institute, School of Medicine, University of California, Irvine, USA; Department of Biomedical Engineering, University of California, Irvine, USA Claude Burgoyne Devers Eye Institute, Optic Nerve Head Research Laboratory, Legacy Research Institute, Portland, OR, USA; Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA Xi Cheng Department of Mechanical Engineering, Stanford University, Stanford, California, USA

Copyright © 2018. Kugler Publications. All rights reserved.

Keyton L. Clayson Department of Biomedical Engineering, The Ohio State University, Columbus, OH, USA Fernando Faria Correia Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro, Brazil; Cornea and Refractive Department, Hospital de Braga, Braga, Portugal; Cornea and Refractive Department, Instituto CUF, Porto, Portugal; School of Health Sciences, University of Minho, Braga, Portugal Vinicius de Stefano Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA; Ophthalmology and Visual Sciences, Federal University of São Paulo, São Paulo, SP, Brazil

xvi

Simone Donati St. Paul’s Eye Unit, Royal Liverpool University Hospital, Liverpool, United Kingdom J. Crawford Downs Department of Ophthalmology, University of Alabama at Birmingham School of Medicine Birmingham, AL, USA William J. Dupps Jr. Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA; Department of Ophthalmology, Cleveland Clinic Lerner College of Medicine of Case Western Reserve University, Cleveland. OH, USA; Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA; Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH, USA Ashkan Eliasy School of Engineering, University of Liverpool, Liverpool, UK Ahmed Elsheik School of Engineering, University of Liverpool, Liverpool, UK; NIHR Biomedical Research Centre for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, London, UK; Institute of Ophthalmology, University College London, London, UK Ross Ethier Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA Andrew J. Feola Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA Matthew Ford Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA

Copyright © 2018. Kugler Publications. All rights reserved.

Rui Carneiro Freitas Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro, Brazil; Cornea and Refractive Department, Hospital de Braga, Braga, Portugal Stuart K. Gardiner Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA Michaël Girard Ophthalmic Engineering & Innovation Laboratory, Department of Biomedical Engineering, Faculty of Engineering, National University of Singapore, Singapore; Singapore Eye Research Institute, Singapore National Eye Centre, Singapore Tabitha Goetz Department of Ophthalmology, School of Medicine & Mater Misericordiae University Hospital, University College Dublin, Dublin, Ireland

xvii

Reinold K. Goetz Department of Ophthalmology, School of Medicine & Mater Misericordiae University Hospital, University College Dublin, Dublin, Ireland Rafael Grytz Department of Ophthalmology and Visual Sciences, University of Alabama at Birmingham, Birmingham, AL, USA Katie Hallahan Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA Christy Hardin Devers Eye Institute, Optic Nerve Head Research Laboratory, Legacy Research Institute, Portland, OR, USA; Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA Sally Hayes Structural Biophysics Research Group, School of Optometry and Vision Sciences, Cardiff University, Cardiff, UK Jesper Hjortdal Department of Ophthalmology, Aarhus University Hospital NBG, Aarhus, Denmark Yi Hua Department of Ophthalmology, University of Pittsburgh, Pittsburgh, PA, USA Jessica V. Jasien Department of Vision Sciences, School of Optometry, University of Alabama at Birmingham, Birmingham, AL, USA James Jester Gavin Herbert Eye Institute, School of Medicine, University of California, Irvine, USA; Department of Biomedical Engineering, University of California, Irvine, USA Tibor Juhasz Gavin Herbert Eye Institute, School of Medicine, University of California, Irvine, USA; Department of Biomedical Engineering, University of California, Irvine, USA

Copyright © 2018. Kugler Publications. All rights reserved.

Elena Koudouna Structural Biophysics Research Group, School of Optometry and Vision Sciences, Cardiff University, Cardiff, Wales, UK Kirill Larin Department of Biomedical Engineering, University of Houston, Houston, TX, USA; Department of Molecular Physiology and Biophysics, Baylor College of Medicine, Houston, TX, USA Nicole Lemanski Mabel Cheng MD PLLC, Albany, USA Jun Liu Department of Biomedical Engineering, The Ohio State University, Columbus, OH, USA

xviii

Howard Lockwood Devers Eye Institute, Optic Nerve Head Research Laboratory, Legacy Research Institute, Portland, OR, USA; Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA Bernardo T. Lopes Department for Ophthalmology of the Federal University of The State of Rio de Janeiro (UniRIO) and Federal University of São Paulo (UNIFESP), Brazil; Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro, Brazil; Instituto de Olhos Renato Ambrósio and VisareRIO, Rio de Janeiro, Brazil Alan Luz Department for Ophthalmology of the Federal University of The State of Rio de Janeiro (UniRIO) and Federal University of São Paulo (UNIFESP), Brazil; Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro, Brazil; Hospital de Olhos de Sergipe, Aracaju, Brazil Fabrice Manns Department of Biomedical Engineering, University of Miami College of Engineering, Miami, FL, USA; Ophthalmic Biophysics Center, Bascom Palmer Eye Institute, University of Miami Miller School of Medicine, Miami, FL, USA John Marshall Institute of Ophthalmology, University College London, London, UK Rebecca McQuaid University College of Dublin, Dublin, Ireland Keith Meek Structural Biophysics Research Group, School of Optometry and Vision Sciences, Cardiff University, Cardiff, UK Miguel Miron Mendoza Department of Ophthalmology, University of Texas Southwestern Medical Center, Dallas, TX, USA Eric Mikula Gavin Herbert Eye Institute, School of Medicine, University of California, Irvine, USA

Copyright © 2018. Kugler Publications. All rights reserved.

Vincent T. Moy Department of Physiology and Biophysics, University of Miami Miller School of Medicine, Miami, FL, USA Michael Mrochen IROC Science AG, Zürich, Switzerland; Swiss Eye Research Foundation, Reinach AG, Switzerland Vicki Nguyen Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA Colm O’Brien Department of Ophthalmology, School of Medicine & Mater Misericordiae University Hospital, University College Dublin, Dublin, Ireland

xix

David C. Paik Paik Laboratory for Tissue Cross-linking, Columbia University Medical Center, New York, NY, USA Bojan Pajic Orasis AG, Reinach, Switzerland; Swiss Eye Research Foundation, Reinach AG, Switzerland Arun Dev Pant Department of Biomedical Engineering, The University of Akron, Akron, OH, USA Jean Marie Parel Department of Biomedical Engineering, University of Miami College of Engineering, Miami, FL, USA; Ophthalmic Biophysics Center, Bascom Palmer Eye Institute, University of Miami Miller School of Medicine, Miami, FL, USA Elias R. Pavlatos Department of Biomedical Engineering, The Ohio State University, Columbus, OH, USA Matthew Petroll Department of Ophthalmology, University of Texas Southwestern Medical Center, Dallas, TX, USA; Biomedical Engineering Graduate Program, University of Texas Southwestern Medical Center, Dallas, TX, USA Peter Pinsky Department of Mechanical Engineering, Stanford University, Stanford, California, USA Isaac Ramos Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro, Brazil; Hospital de Olhos Santa Luzia, Maceió, Brazil Julia Raykin Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA

Copyright © 2018. Kugler Publications. All rights reserved.

Dan Reinstein London Vision Clinic, London, UK; Department of Ophthalmology, Columbia University Medical Center, New York, NY, USA; Centre Hospitalier National d’Ophtalmologie, Paris, France; Biomedical Science Research Institute, University of Ulster, Coleraine, Northern Ireland Matthew A. Reilly Department of Biomedical Engineering, Department of Ophthalmology & Visual Science, The Ohio State University, Columbus, OH, USA Rodolfo Repetto Department of Civil, Chemical and Environmental Engineering, University of Genoa, Genoa, Italy Luke Reyes Devers Eye Institute, Optic Nerve Head Research Laboratory, Legacy Research Institute, Portland, OR, USA; Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA

xx

Juan Reynaud Devers Eye Institute, Optic Nerve Head Research Laboratory, Legacy Research Institute, Portland, OR, USA; Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA Cynthia Roberts Department of Ophthalmology & Visual Science, Department of Biomedical Engineering, The Ohio State University, OH, USA Marcella Q. Salomão Department for Ophthalmology of the Federal University of The State of Rio de Janeiro (UniRIO) and Federal University of São Paulo (UNIFESP), Brazil; Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro, Brazil; Instituto de Olhos Renato Ambrósio and VisareRIO, Rio de Janeiro, Brazil Brian C. Samuels Department of Ophthalmology, University of Alabama at Birmingham, Birmingham, AL, USA Giuliano Scarcelli Fischell Department of Bioengineering, University of Maryland, College Park, MD, USA Ibrahim Seven Ocular Biomechanics & Imaging Lab, Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA Ian Sigal Department of Ophthalmology, University of Pittsburgh, Pittsburgh, PA, USA; Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, USA Manmohan Singh Department of Biomedical Engineering, University of Houston, Houston, TX, USA Eberhard Spoerll Carl Gustav Carus University Hospital, Department of Ophthalmology, Dresden, Germany

Copyright © 2018. Kugler Publications. All rights reserved.

Cheri Stowell Devers Eye Institute, Optic Nerve Head Research Laboratory, Legacy Research Institute, Portland, OR, USA; Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA Harald Studer Swiss Eye Research Foundation, Reinach, Switzerland; OCT Research Laboratory, Department of Ophthalmology, University of Basel, Switzerland Vivian M. Sueiras Department of Biomedical Engineering, University of Miami College of Engineering, Miami, FL, USA Michael Twa School of Optometry, University of Alabama at Birmingham, Birmingham, AL, USA

xxi

Daniel C. Turner Department of Vision Sciences, School of Optometry, University of Alabama at Birmingham, Birmingham, AL, USA Jennifer H. Tweedy Department of Bioengineering, Imperial College London, London, UK Jonathan Vande Geest Departments of Bioengineering and Ophthalmology, University of Pittsburgh, Pittsburgh, PA, USA Neeraj Vij Jr. Department of Biomedical Engineering, University of Arizona, Tucson, Arizona, USA Paolo Vinciguerra Humanitas University, Department of Biomedical Sciences, Milan, Italy; Humanitas Clinical and Research, Rozzano, Italy Riccardo Vinciguerra St. Paul’s Eye Unit, Royal Liverpool University Hospital, Liverpool, United Kingdom Andrew P. Voorhees Department of Ophthalmology, University of Pittsburgh, Pittsburgh, PA, USA Deborah Wallace Department of Ophthalmology, School of Medicine & Mater Misericordiae University Hospital, University College Dublin, Dublin, Ireland Xiaofei Wang Ophthalmic Engineering & Innovation Laboratory, Department of Biomedical Engineering, Faculty of Engineering, National University of Singapore, Singapore Galen Williams Devers Eye Institute, Optic Nerve Head Research Laboratory, Legacy Research Institute, Portland, OR, USA; Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA

Copyright © 2018. Kugler Publications. All rights reserved.

Abby Wilson Wolfson School of Mechanical, Manufacturing and Electrical Engineering, Loughborough, UK Moritz Winkler Department of Biomedical Engineering, University of California, Irvine, USA Hongli Yang Devers Eye Institute, Optic Nerve Head Research Laboratory, Legacy Research Institute, Portland, OR, USA; Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA Seok Hyun Yun Wellman Center for Photomedicine, Massachusetts General Hospital, Cambridge, MA, USA; Department of Dermatology, Harvard Medical School, Boston, MA, USA

xxii

Liang Zhang Ophthalmic Engineering & Innovation Laboratory, Department of Biomedical Engineering, Faculty of Engineering, National University of Singapore, Singapore Dong Zhou School of Engineering, University of Liverpool, Liverpool, UK

Copyright © 2018. Kugler Publications. All rights reserved.

Noël M. Ziebarth Department of Biomedical Engineering, University of Miami College of Engineering, Miami, FL, USA

Copyright © 2018. Kugler Publications. All rights reserved.

CORNEA

Copyright © 2018. Kugler Publications. All rights reserved.

1. Basics of biomechanics Jesper Hjortdal Department of Ophthalmology, Aarhus University Hospital NBG, Aarhus, Denmark

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction Biomechanics is mechanics applied to biology and seeks to understand the mechanics of living systems.1 The term biomechanics can thus be applied to the investigation of a variety of physical and chemical tissue properties. Having a basic understanding of the biomechanical properties of the eye has become increasingly important for clinicians working within the ophthalmological specialty. The anterior-most portion of the eye, the cornea, has unique biomechanical properties which are essential for preserving a stable refractive state. Corneal refractive procedures all disrupt the anatomical integrity of the cornea; due to the physical stress of intraocular pressure, this will result in a secondary deformation. The degree of deformation is dependent on the biomechanical properties of the cornea. The intrinsic biomechanical properties of the cornea can also be affected in diseases such as keratoconus and can today be modified using corneal crosslinking. In addition to the importance of corneal biomechanics in corneal optics, clinical methods for measurement of the intraocular pressure are based on deformation of the cornea. The degree of deformation will therefore not only depend on the magnitude of the intraocular pressure, but also on the specific biomechanical properties of the individual cornea. This chapter will give an introductory overview of the basic parameters used for characterizing the biomechanical properties of tissues. The main focus will be on in-vitro studies and in-vivo studies of the human cornea by means of an experimental approach, all taking into account the very special feature of the

cornea as a tissue, which easily imbibes water. Based on the author’s previous experience with experimental studies on corneal biomechanics and present position as an anterior segment surgeon, the aim is to keep the level basic, trying to ensure that the content is understandable for ophthalmology residents and clinicians working with refractive and other types of corneal surgery.

2. Elasticity The basic elements of elasticity are those of strain and stress, which are connected through the elastic properties of the material.2 When a force is applied to a fixed structure, it will deform to the point where the developed opposing force in the structure balances the applied force. For the same size of applied force, the extent of deformation will depend both on the size and shape of the unloaded structure and on the direction of the applied force. Consequently, absolute deformations are related to the original undeformed shape of the structure and quantified as strains, and forces are converted to stresses (force per unit area). Deformation and force can be decomposed into tensor components acting in parallel or perpendicular to each other, eventually giving rise to normal as well as shear stresses and strains. A Hookean elastic solid is a solid that obeys Hooke’s law, which states that the stress tensor is proportional to the strain tensor. The constants that determine how the tissue strains for a certain stress form together the consti-

Correspondence: Jesper Hjortdal, MD, PhD, DrMedSci, Department of Ophthalmology, Aarhus University Hospital NBG, Norrebrogade 44, 8000 Aarhus C, Denmark. E-mail: [email protected] Biomechanics of the Eye, pp. 3-13 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

4

J. Hjortdal

3. Measurement of the extensibility of the cornea In order to measure the in-plane, or tangential extensibility of the cornea, a force must stress the tissue. Two principles have been used in the past: either strip extensiometry or inflation tests based on pressure loading of the intact eye or the isolated anterior segment.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 1. A typical illustration of loading of a biological specimen. The relation between strain and stress is non-linear.

tutive properties of the material. A material without symmetry with respect to its mechanical properties is called anisotropic. On the other hand, in an isotropic material the elastic properties are independent of the orientation of the specimen. From the two constants (the Lamé constants) necessary to fully characterize an isotropic material, the more commonly used Young’s modulus of elasticity, the shear modulus, and Poisson’s ratio can be calculated.2 Few biological materials are linearly elastic and isotropic. In most cases, biological materials exhibit a non-linear relationship between the stress and the strain tensors, that is, the material is non-linearly elastic (Fig. 1). Biological materials typically show some sort of preferential orientation of their fibrillar micro-structural constituents causing anisotropic material properties, but also display symmetry in one or more planes. Various levels of symmetry thus exist between the two extremes of anisotropy and isotropy. Considering the microstructure of the cornea, with ground substance embedded collagen fibrils mainly running in lamellar sheets parallel to the corneal surface,3 it is apparent that the cornea is not an isotropic material. An orthotropic material exhibits symmetry of its elastic properties with respect to two orthogonal planes;2 such a model may, to some basic limits, be considered sufficient to describe the elastic behavior of the corneal stroma.

3.1. Strip extensiometry In strip extensiometry, strips of corneal tissue are excised and grasped by a dedicated biotester (Fig. 2). Typically, the tissue is cycled and stretched until the difference between loading and relaxation curves is reduced as a pre-conditioning procedure. The stress in the tissue is calculated from the force applied divided by the cross-sectional area of the tested strip. The strain is calculated as the relative elongation of the tissue strip from the non-stressed length. Finally, Young’s modulus of elasticity is calculated from the slope of the stressstrain curve. Several previous studies have investigated the in-plane membrane elasticity of the human cornea using strip extensiometry.4-9 Values for Young’s modulus range from 0.5 to 80 MPa, while those performed at physiological stress levels fall approximately between 0.5 and 5 MPa. The studies have all documented that corneal tissue shows stress-stiffening, as the deformation curve is non-linear. This means that Young’s modulus of elasticity becomes greater at higher levels of stress in the tissue.

Fig. 2. Strip extensiometry of a specimen.

Basics of biomechanics

When comparing results, it is of utmost importance to note which pre-stress level was used. Although this in principle should be zero, a small force is necessary to make the curved corneal tissue strip straight.10 As corneal tissue shows stress-stiffening, it is also essential to refer to a specific stress-level for the determined Young’s modulus. Quantitatively, the results from these studies vary one order of magnitude, possibly due to varying or uncontrolled experimental circumstances.

Copyright © 2018. Kugler Publications. All rights reserved.

3.2. Inflation tests To avoid the difficulties associated with strip extensiometry, whole-organ setups have also been used for in-vitro experiments. By studying the cornea in situ, application of physiological stresses becomes easier as the intraocular pressure can be used for setting up the stress in the tissue. Intraocular pressure gives rise to a wall tension in the cornea, which can be estimated from the corneal curvature and corneal thickness using the law of Laplace (Fig. 3). The whole-organ in-vitro setup is also advantageous for comparison of in-vitro and in-vivo experiments, as similar variables may be measured and compared. Whole-organ experiments require, however, application of more complex mechanical theories and additional assumptions, as loading inevitably becomes multi- rather than uni-directional as in strip extensiometry experiments.11 In the cornea, the in-plane meridional and circumferential corneal stresses may be estimated from the equations for a thin surface of revolution12 as mathematical derivatives of the law of Laplace.13,14 In testing, the corneal tissue is stress-loaded by varying the intraocular pressure and the resulting deformation strain of the cornea can be measured, allowing Young’s

Fig. 3. Inflation testing of the cornea. (A) Side view of the eye. (B) Frontal view of the eye. Strains in the circumferential and meridional direction can be measured and corresponding stresses can be calculated from (A).

5

moduli of elasticity to be calculated. Values around 5-10 MPa were measured in these studies. Alternatively, a more indirect approach can be used only if the cornea and surrounding limbal tissue is mounted and fixed in a test chamber. In such a model, changes in corneal apex position and corneal curvature can be measured, and Young’s moduli can be calculated.15 Values for Young’s modulus in these studies, however, were less than 1 MPa. It is not clear what caused this discrepancy, but fixation of the peripheral cornea may have affected the fibril organization within the tissue. In inflation tests, Young’s modulus of elasticity of the cornea has also been found to increase with increasing load, corresponding to non-linear elasticity.13-15 It has been suggested that folding of fibrils in the relaxed state is the structural basis for the observed non-linearity in mechanical testing of parallel-fibered structures such as tendons and ligaments.16 When the specimen is loaded, the folding will gradually disappear during the “toe-region” of the stress-strain curve, active load-bearing fibrils will be sequentially recruited, and in the linear part all fibrils will have straightened. Thus, sequential recruitment of fibrils may cause the observed non-linearity in stress-strain curves obtained in swollen corneas.13,14,17,18 The fibrils of the normo-hydrated human cornea have not been found to fold or crimp during unloading, whereas fibrils in the rabbit cornea do.19 Stromal striations have, however, been observed in the normal living human cornea.20 If the folded or crimped collagen fibrils are assumed to follow a sinusoidal course with an amplitude of a and a period of λ, the slack strain due to unfolding of the fibril will be (π a / λ)2.19 Thus, it can be calculated that for small slack strains, for example 1%, the ratio between amplitude and wave length will be 3%. It appears that such low amplitudes may easily escape detection using conventional morphometric techniques. Accordingly, low-amplitude crimp of the collagen fibrils might contribute to the observed non-linear elastic response of the normo-hydrated human cornea. Local reorientation of fibrils under stress may, however, also be responsible for the “toe-region” in stress-strain curves.21 Structural studies of the conformation of collagen molecules have also revealed axial regions of alternating “order” and “disorder”.22 Application of stress to a fibril may then result in preferential unraveling of the regions

6

of disorder, resulting in non-linear elasticity of the collagen fibril itself.

Copyright © 2018. Kugler Publications. All rights reserved.

4. Regional elastic differences in the cornea The regional corneal elasticity has been studied in whole-eye inflation tests.14 The studies revealed that the circumferential strain of the corneal limbus is fairly similar to the circumferential strain of the corneal regions during pressure loading. When calculated for the same intraocular pressure load intervals, the highest modulus of elasticity was found at the center and the para-central region in the meridional direction, and at the limbus in the circumferential direction. A higher modulus of elasticity in a certain direction and region corresponds to an increased resistance to deformation, and suggests that these particular regional directions behave like functional ligaments. In order to investigate whether these functional enhancements were due to higher stress levels or to localized higher elastic moduli, the stress-normalized elastic moduli were also evaluated. In the circumferential direction, the stress-controlled elastic modulus of the limbus was found to be significantly higher than that of the other regions, whereas the elasticity of the corneal periphery was not significantly different from that of the central or para-central regions. In the meridional direction, it was found that the stress-controlled elastic moduli of the center and para-center were higher than those of the periphery and the limbus. A similar tendency was observed by Shin et al.23 The fine microstructure of the human cornea has been studied using wide-angle X-ray scattering (WAXS), which has detailed the anisotropic arrangement of collagen fibrils in the human cornea and quantified typical characteristics, including: 1. a preferred orthogonal orientation in the central cornea in temporal–nasal (T–N) and superior– inferior (S–I) directions; 2. circumferentially arranged fibrils in the limbus and corneal periphery; 3. a transition zone between 1. and 2.; and 4. a greater total quantity of fibrils in the peripheral region compared to the central cornea.24-26 The variability in elastic moduli between the corneal

J. Hjortdal

regions must be caused by regional differences in the ultrastructural components responsible for the mechanical performance of the tissues. From this viewpoint, it can be considered useful to look on the cornea as a fiber-reinforced material27 in which the collagen forms the enhancing fibrillar structure and the ground substance forms the matrix.14 In this case, differences in the elastic modulus can be caused by variations in: 1. the elastic modulus of the fibrils; 2. the degree of reinforcement (mix-ratio of fibril to ground substance); 3. the efficacy factor (orientation of the fibrils); and 4. the sequential recruitment of fibrils. From considerations on the ultrastructure of the cornea, it can be hypothesized that the difference in elasticity in the meridional direction is possibly caused by a variable recruitment of collagen fibrils, whereas the circumferential limbal enhancement is caused by preferential circumferential orientation of fibrils in this region. Today, advanced studies on transverse depth collagen-fibril orientation and distribution28 combined with advanced mathematical models of the biomechanical properties of the cornea29,30 are used to refine our understanding of corneal elastic properties.

5. Shear-force resistance of the cornea The resistance of the human cornea to in-plane shear deformation is small,31 but little is known about its actual size due to methodological difficulties in measuring it (Fig. 4).31,32 In preliminary shearing experiments in rabbit31 and human corneas,32 the

Fig. 4. Shear testing of a cornea at a defined thickness, t.

Basics of biomechanics

shear modulus (shear stiffness) has been found to be in the order of 1 and 2 kPa, respectively. Petsche et al.33 measured the torsional shear throughout the stromal depth of the human cornea. They found the transversal, torsional shear modulus to be depth-dependent and its magnitude to be greatest in the anterior third stroma. Elsheikh et al.34 also measured the shear modulus of the human cornea, and found values in the range of 20 kPa. Further recent studies of the shear-force resistance of human corneas found values of 2 kPa and have also documented that the shear-resistance is higher in the anterior corneal stroma than in the posterior stroma.35 At low shear strain, the shear stiffness of an individual lamella is proposed to result from the gel properties of the interaction of stromal ground substance with the fixed charges of the glycosaminoglycans (GAG). The transverse shear modulus resulting from this interaction is expected to be small compared to the tensile modulus from direct testing of collagen fibrils on tension tests. A significant dependency of shear moduli on the axial compression of the tissue has also been observed. This agrees with the finding that increased compression results in the fixed charges of the GAG moving closer together. An increased fixed charge density may then result in increased shear modulus.35

Copyright © 2018. Kugler Publications. All rights reserved.

6. Swelling pressure The corneal stroma has an innate tendency to imbibe fluid and a swelling capacity that exceeds any other connective tissue in the body. This high swelling capacity and its transparency in vivo are both unusual properties for a connective tissue.36 The biophysical properties of the cornea therefore depend on precise maintenance of tissue hydration, and the heterogeneity of the stroma suggests that the swelling properties are not uniformly distributed. The less interwoven posterior stroma can swell more than the anterior stroma,37 and at a given swelling pressure, the posterior stroma is more hydrated than the anterior stroma.38 Maurice described the corneal stroma as a sponge, which behaves as if consisting of two separate phases: one rigid structural phase and one fluid phase. The gel pressure or swelling pressure (SP) of a tissue can be defined as: “the mechanical pressure applied to its surfaces which is needed to prevent swelling when

7

Fig. 5. Swelling pressure measurement of an excised cornea at a defined thickness, t.

the tissue has free access to a physiologic aqueous medium.” (Fig. 5).39,40 The swelling pressure depends on the degree of compression of the tissue,41 the ionic strength of the bathing medium,42 temperature,40 and pH.43 From experimental studies, differential swelling in different compartments of the corneal stroma have been described.44 The cornea swells predominantly in the anterior-posterior direction (orthogonal to its faces).45 However, the lattice of fibrils swells equally in all directions, whereas the tissue as a whole swells predominantly in one direction. This means that a rearrangement of the fibrils in two dimensions may occur as the cornea swells.46 From diffraction studies on highly swollen corneas, it was concluded that the swollen cornea is essentially a system of mutually repelling cylinders and the existence of interfibrillar crosslinking is unlikely.47 When swelling, however, the corneal stroma does not separate even when shear force is applied. Thus, the stroma possesses self-cohesion between corneal lamellae.48 The interweaving varies with depth, appearing maximally at the anterior surface and reducing posteriorly.49 Thus, corneal swelling and hydration can greatly influence the alignment of collagen fibrils in the stroma, and thereby influence the in-plane, tangential elastic properties of the cornea. Several investigators have measured the stromal swelling pressure in different mammalian species, but the swelling pressures of human corneas have only been scarcely investigated. At normal corneal thickness, the swelling pressure in humans has been measured as 84 mmHg.41

8

Fig. 6. (A) Stress relaxation at constant strain. (B) Creep at constant stress.

Copyright © 2018. Kugler Publications. All rights reserved.

7. Viscoelasticity If a material is suddenly strained to a constant level, the stresses induced in the material may decrease with time, that is, the material shows stress relaxation (Fig. 6A). Similarly, if a constant force suddenly stresses a material, the material may continue to deform with time, and the material is said to show creep (Fig. 6B). These phenomena are features of viscoelasticity.1 The cornea does show viscoelastic changes when tested in vitro. In swelling pressure experiments, it takes typically one to two hours before a steady state level is reached.41,50 In biological materials, the viscoelastic response is probably caused mainly by overall hydration changes of the tissue or by a redistribution of water within the tissue.1 Elsheikh et al.10 studied in detail creep and stress-relaxation behavior of the human cornea in pressure-chamber inflation and strip extensiometry tests, respectively, and found that creep and stress-relaxation went on for hours. In inflation tests of whole human eye globes, it has been shown that the creep observed in human corneas can be partly or fully explained by a change in corneal hydration.18 Corneas with increased thickness, corresponding to increased hydration, strained approximately 1% on the central epithelial side and 3% on the endothelial side when intraocular pressure was increased from 2 to 100 mmHg. In comparison, corneas which had been thinned in Dextran to normal hydration, strained approximately 0.5% on the epithelial as well as the endothelial side for the same pressure increment.13,14 Continuous pressure loading of a swollen cornea induced significant thinning of the

J. Hjortdal

corneal stroma, decreased epithelial surface strain, and increased endothelial surface strain.13,18 The observation of viscoelastic behavior in the intact human cornea may be explained by the influence of corneal hydration on the stress distribution between the corneal lamellae. In the swollen cornea, only the anterior corneal lamellae are able to take up tension, whereas the posterior lamellae will be slack. Clinically, this can be observed as folds in Descemet’s membrane. During the pressure-induced reduction in corneal volume, the posterior lamellae elongate and take up some of the corneal stress and the stress on the anterior lamellae will decrease. This is consistent with observations by Eliasson and Maurice,51 who after studying the displacement of the corneal surfaces induced by corneal thinning, concluded that the stress distribution across the corneal stroma is even in the normo-hydrated human cornea in vivo.31

8. Changes in corneal curvature induced by intraocular pressure The adult human cornea is very stable and fluctuations in intraocular pressure do not result in clinically significant changes in the radius of curvature of the cornea and the refractive state of the eye. In vitro, studies have revealed that in swollen corneas the change in central corneal radius of curvature parallel the change in central epithelial side corneal strain: when the corneal stroma stretched, the radius of curvature became larger, and vice versa.18 During corneal thinning and subsequent epithelial side shortening, the cornea thus became steeper. Other authors have found slight corneal steepening in association with corneal dehydration in vitro as well.52 Corneal hydration has also been found to influence corneal radius of curvature in vivo. Associated with an overnight 2.4% increase in corneal thickness, the radius of curvature increased 0.04 mm, and with eyelid opening, the cornea was found to thin and steepen slightly.53 The pressure-induced corneal curvature changes in normal human eyes have been found to be very small. In vivo, 0.2 diopters (0.04 mm) of central corneal flattening was observed when the pressure was increased from 14 to 30 mmHg.54 Previous in-vivo studies have similarly not been able to detect significant changes in kerato-

Basics of biomechanics

metric-measured corneal curvature during pressure loading.55 In studies of the corneal radius of curvature before and after treatment for acute glaucoma, Poinoosawmy and Roth56 found, however, that the keratometric measured corneal radius of curvature decreased 0.07 mm when the pressure was lowered from 27 to 20 mmHg. This change in curvature could, however, also be due to changes in corneal hydration. In summary, increasing intraocular pressure in the normal human eye changes the curvature of the cornea very little. It appears, however, that in vivo the cornea tends to flatten slightly when the pressure increases.

Copyright © 2018. Kugler Publications. All rights reserved.

9. Basic biomechanics in tonometry All types of clinical tonometry involve corneal bending. Factors which alter the bending rigidity of the cornea will therefore affect the readings of tonometry instruments. In normal subjects, there is a positive correlation between corneal thickness and intraocular pressure, as a thick cornea is more difficult to bend.57 The change in corneal radius of curvature may also affect tonometry readings. The necessary bending force is larger, and the displaced intraocular volume is larger in an eye with a steep cornea than in an eye with a flat cornea to achieve the same amount of corneal flattening. Both factors will tend to falsely increase the measured intraocular pressure.58,59 After refractive surgery for myopia, the cornea becomes thinner and flatter. Extrapolation from observations in normal corneas suggests that this will lead to artifactually low pressure measurements in eyes treated for myopia. Many clinical studies have documented that thinning and flattening keratorefractive procedures falsely lower the reading of tonometry instruments based on applanation and air-puff indentation.60 The clinical importance of the possible small errors in tonometry may become more important when the growing population of corneal refractive individuals becomes older and develops open-angle glaucoma. If the pressure is falsely measured as too low in these patients, the diagnosis may be missed or delayed. On the other hand, increased corneal thickness due to corneal edema results in inaccurately low readings of tonometers, possibly due to slack corneal fibrils

9

in the posterior layers of the cornea, which make the cornea easier to bend.61,62

10. Basic biomechanics in corneal disease The basic biomechanics of only few corneal diseases have been studied in vitro, as most corneal diseases are uncommon and tissue specimens typically can only be acquired post-mortem after donation from the deceased. Although keratoconus corneas are believed to be “softer” and more susceptible to deformation, the only two experimental studies based on strip extensiometry measurements could only show a difference between keratoconus and control corneal tissues at stress-levels much higher than those encountered in vivo.5,6 It may be that the mechanical characteristic of corneas with keratoconus may be a type of abnormal viscoelastic creep: a difference between normal corneas and corneas with keratoconus can be observed only over months or years.63

11. Basic biomechanics in refractive surgery 11.1. Radial keratotomy Although radial keratotomy for myopia is not performed any longer, earlier studies of incised corneas give some information about the basic biomechanics of corneal tissue. Inflation studies of the local deformation pattern of human corneas with a radial keratotomy have revealed that the mechanical behavior of the incised human cornea is a complex combination of tissue extension, tissue compression, and internal shear.64 Early microstructural studies only documented that radial keratotomy incisions gape during pressure loading.65-67 More detailed studies revealed that pressure loading of radially incised human corneas induced: 1. epithelial surface wound gape of 44 μm (2-100 mmHg pressure increment); 2. epithelial surface circumferential tissue compression between incisions; 3. considerable epithelial surface meridional tissue

10

Copyright © 2018. Kugler Publications. All rights reserved.

elongation at and between incisions; 4. little endothelial surface circumferential strain across incisions; and 5. little endothelial surface meridional strain at and between incisions.64 Thus, the peripheral “tissue addition” seen after radial keratotomy is a net result of wound gape and circumferential tissue compression. The negative circumferential strains between radial incision have also been confirmed using confocal microscopy in rabbit corneas.68 The presence of tissue compression between the four radial incisions can explain why additional incisions do not induce much additional corneal flattening.69 11.1.1. Pressure induced curvature changes after radial keratotomy In vitro, radial keratotomy results in considerable corneal flattening (2.3 diopters) even at very low loading pressures, and in the physiological pressure range the central cornea flattens around 0.05 diopters for each mmHg increment in intraocular pressure.64 Similar central curvature changes have been found in other in-vitro studies.70 In vivo, in studies of patients that have previously undergone radial keratotomy, increasing the intraocular pressure from 14 to 30 mmHg induced 0.5 diopters of central corneal flattening, corresponding to 0.03 diopters for each mmHg increment in intraocular pressure.54 Similar pressure-induced changes in central curvature have been found by Feldman et al.55 A significant proportion of patients previously operated on with radial keratotomy experience continued diurnal fluctuations in visual acuity, and these changes are associated with corneal steepening during the day.71,72 Corneal hydration and intraocular pressure also exhibit diurnal changes. In vitro, increased corneal hydration has been found to increase the flattening effect of a radial keratotomy;70 diurnal variations in corneal hydration have also been found to correlate with diurnal changes in corneal power.73 11.2. Surface ablation After photorefractive or phototherapeutic keratectomy, the corneal stroma is thinned and Bowman’s layer is removed. Overall, these changes in corneal structure should result in a biomechanical weakening. In in-vitro studies of excimer laser ablations in human cadaver

J. Hjortdal

eyes, a 7-mm diameter superficial central keratectomy induced central corneal strains 5-10% higher in corneas without Bowman’s layer compared with intact corneas.74 The epithelial surface tangential corneal strains in eyes with a 70% deep keratectomy increased twice as much as those of intact corneas, but the endothelial surface strains were similar. From considerations on the possible stress distribution in the keratectomized cornea, it can be argued that the difference between the epithelial surface strain and the endothelial surface strain is a function of the shear force resistance between the stromal lamellae.74 The differences in average corneal strains between the three groups could be explained by changes in central corneal thickness, as there were no statistically significant differences in the stress-normalized Young’s moduli of elasticity between the three groups. Corresponding with this, strip extensiometry studies of the cornea did not detect a statistically significant difference in elastic or viscoelastic properties between excised full-thickness corneal strip samples and paired samples with Bowman’s layer removed.75 When removed, the underlying lamellae of the otherwise unaltered corneal stroma possibly take up the mechanical functions of the outer limiting connective tissue layer. Measurements of the surface profile inside and outside the ablation zone of treated patients have documented that cutting of the anterior lamellae actually results in outward bulging of the cornea outside the ablated area.76 11.2.1. Pressure induced curvature changes after keratectomy After a keratectomy, corneal thickness decreases. The remaining corneal fibrils will therefore be exposed to higher levels of membrane stresses inducing some elongation of the fibrils. If the edge of the ablation zone is considered fixed it would be expected that the central cornea steepens in response to pressure loading. In vitro, it has been observed that the central radius of curvature does not change significantly with increasing pressure in intact eyes or in eyes without Bowman’s layer.74 In deeply ablated corneas, the corneal radius of curvature decreased in vitro approximately 1% when the intraocular pressure was increased from 2 to 100 mmHg.74 Similar central bulging has been reported in cadaver eyes when 150 μm or more of the outer

Basics of biomechanics

surface was excised with excimer laser.77 In patients who had undergone excimer laser ablation (approximately 70 μm ablation), no significant central corneal steepening or flattening was observed with increasing pressure, although normal control eyes flattened significantly due to pressure loading.54 In the study, a significant correlation between the pressure-induced change in central curvature and the postoperative time was, however, found. Patients investigated during the first months after surgery steepened more centrally than patients investigated one year or more after laser ablation. Thus, the wound healing response of the cornea somehow influences the corneal stability of excimer laser-ablated patients. It can be hypothesized that the recovery of stability is due to an increasing stromal shear force resistance, induced by scar tissue in the superficial cornea. 11. 3. Intrastromal procedures (LASIK, SMILE) Today, intrastromal corneal refractive procedures are increasingly used to correct refractive errors. Although a biomechanically mediated corneal protrusion (ectasia) can develop after any photoablative procedure, the procedures have only been scarcely evaluated in terms of basic biomechanical studies. The corneal biomechanical effects of varying laser-assisted in situ keratomileusis (LASIK) flap-depth and

References 1. 2.

Copyright © 2018. Kugler Publications. All rights reserved.

3. 4.

5.

6.

7.

Fung, YC. Biomechanics. Mechanical properties of living tissues. New York: Springer-Verlag 1981. Bisplinghoff RL, Marr JW, Pian THH. Statics of deformable solids. New York: Dover Publications Inc. 1965. Maurice DM. The cornea and sclera. In: Davson H (ed). The Eye, Vol 1B, pp. 303-351. New York: Academic Press:1984. Woo S L-Y, Kobayashi AS, Schlegel WA, Lawrence C. Nonlinear material properties of intact cornea and sclera. Exp Eye Res. 1972;14:29-39. Andreassen TT, Hjorth Simonsen A, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Exp Eye Res. 1980;31:435-441. Nash IS, Greene PR, Foster CS. Comparison of mechanical properties of keratoconus and normal corneas. Exp Eye Res. 1982;35:413-424. Hoeltzel DA, Altman P, Buzard K, Choe K. Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. J Biomech Eng. 1992;114:202-215.

11

side-cut angulations, and the relative contribution of the lamellar and side cuts have been evaluated using a femtosecond laser and radial shearing speckle pattern interferometry in human corneas in vitro.78 The study documented that vertical side cuts through corneal lamellae rather than horizontal delamination incisions contribute to the loss of structural integrity during LASIK flap creation. This finding supports the possible biomechanical advantage of the small incision lenticule extraction procedure (SMILE),79 although this has not been documented experimentally.80

12. Conclusion and perspectives Although simple in nature, the biomechanical properties of the human cornea are still a matter of debate. Recently, very advanced biomechanical models of the corneal tissue have been developed. The models are based on the microstructural composition of the tissue and mechanical properties of collagen fibrils and ground substance. These models will possibly further advance simulations of the corneal response to surgery and disease. However, further laboratory and clinical testing of human corneal tissue is necessary to provide valid empirical data for such models.

8.

9.

10. 11. 12. 13. 14. 15.

Zeng Y, Yang J, Huang K, Lee Z, Lee X. A comparison of biomechanical properties between human and porcine cornea. J Biomech. 2001;34:533–537 Wollensak G, Spoerl E, Seiler T. Stress-strain measurements of human and porcine corneas after riboflavin–ultraviolet-A-induced cross-linking. J Cataract Refract Surg. 2003;29:1780–1785. Elsheikh A, Anderson K. Comparative study of corneal strip extensiometry and inflation tests. J R Soc Interface. 2005;2:177-185. Jue B, Maurice DM. The mechanical properties of the rabbit and human cornea. J Biomech.anics 1986;19:847-853. Roark RJ. Formulas for stress and strain. New York: McGraw-Hill, Inc. 1965. Hjortdal J. Extensibility of the normo-hydrated human cornea. Acta Ophthal Scand. 1995;73:12-17. Hjortdal J. Regional elastic performance of the human cornea. J Biomech. 1996;29:931–942. Elsheik A, Wang D, Brown M, Rama P, Campanelli M, Pye D. Assessment of corneal biomechanical properties and their variabtion with age. Current Eye Research. 2007;32:11–19.

Copyright © 2018. Kugler Publications. All rights reserved.

12 16. Viidik AA. Functional properties of collagenous tissues. In: David A Hall & DS Jackson (eds.). International review of connective tissue research, Vol. 6, pp. 127-211 Academic Press: London 1973. 17. Hatami-Marbini H. Hydration dependent viscoelastic tensile behavior of cornea. Ann Biomech Eng. 2014;42:1740-1748. 18. Hjortdal JØ, Jensen PK. In vitro measurement of corneal strain, thickness, and curvature using digital image processing. Acta Ophthalmol Scand. 1995;73:5-11 19. Gallagher B, Maurice DM. Striations of light scattering in the corneal stroma. J Ultrastruc Res. 1977;61:100-114. 20. Bron AJ. Superficial fibrillary lines. A feature of the normal cornea. Brit J Ophthalmol. 1975;59:133-135. 21. Parry DAD, Craig AS. Collagen fibrils during development and maturation and their contribution to the mechanical attributes of connective tissue. In: Nimni ME (ed.): Collagen, Vol. II, pp 1-24. Boca Raton: CRC Press 1988. 22. Fraser RDB, MacRae TP, Miller A, Suzuki E. Molecular conformation and packing in collagen fibrils. J Mol Biol. 1983;167:497521. 23. Shin TJ, Vito RP, Johnson LW, McCarey BE. The distribution of strain in the human cornea. J Biomech. 1997;30:497-503. 24. Aghamohammadzadeh H, Newton RH, Meek KM. X-ray scattering used to map the preferred collagen orientation in the human cornea and limbus. Structure. 2004;2:249–256. 25. Meek KM, Boote C. The organization of collagen in the corneal stroma. Exp Eye Res. 2004;78:503–512. 26. Boote C, Hayes S, Abahussin M, Meek KM. Mapping collagen organization in the human cornea: left and right eyes are structurally distinct. Invest. Ophthalmol Vis Sci. 2006;47: 901–908. 27. Krenchel H. Fibre Reinforcement. Theoretical and practical investigations of the elasticity and strength of fibre-reinforced materials. Copenhagen: Akademisk Forlag 1964. 28. Abass A, Hayes S, White N, Sorensen T, Meek KM. Transverse depth-dependent changes in corneal collagen lamellar orientation and distribution. J R Soc Interface. 2015;12(104):20140717 29. Petsche SJ, Pinsky PM. The role of 3-D collagen organization in stromal elasticity: a model based on X-ray diffraction data and second harmonic-generated images. Biomech Model Mechanobiol. 2013;12:1101–1113. 30. Whitford C, Studer H, Boote, Meek KM, Elsheikh A. Biomechanical model of the human cornea: Considering shear stiffness and regional variation of collagen anisotropy and density. J Mech Beh Biomed Mat. 2015;42:76-87. 31. Maurice DM. Mechanics of the cornea. In: Cavanagh HD (ed). The Cornea: Transactions of the World Congress on the Cornea III. New York: Raven Press, Ltd. 1988. 32. Wollensak J, Ihme A, Seiler T. Neue Befunde bei Keratoconus. Fortschr Ophthalmol. 1987;84:28-32. 33. Petsche SJ, Chernyak D, Martiz J, Levenston ME, Pinsky PM. Depth-dependent transverse shear properties of the human corneal stroma. Invest Ophthalmol Vis Sci. 2012;53:873–880. 34. Elsheikh A, Ross S, Rama P, Alhasso D. Numerical study of the effect of corneal layered structure on ocular biomechanics. Curr Eye Res. 2009;34:26-35.

J. Hjortdal 35. Søndergaard AP, Ivarsen A, Hjortdal J. Corneal resistance to shear force after UVA-riboflavin cross-linking. Invest Ophthalmol Vis Sci. 2013;54:5059–5069. 36. Hart RW, Farrell RA. Structural theory of swelling pressure of corneal stroma in saline. Bull Math Biophys. 1971;33:165–186. 37. Kikkawa Y, Hirayama K. Uneven swelling of the corneal stroma. Invest Ophthalmol. 1970;9:735-741. 38. Lee D, Wilson G. Non-uniform swelling properties of the corneal stroma. Curr Eye Res. 1981;1:457-461. 39. Dohlman CH, Hedbys BO, Mishima S. The swelling pressure of the corneal stroma. Invest Ophthalmol. 1962;1:158–162. 40. Fatt I. The coefficient of thermal expansion of stroma. Exp Eye Res. 1971;12:254–260. 41. Olsen T, Sperling S. The swelling pressure of the human corneal stroma as determined by a new method. Exp Eye Res. 1987;44:481-490. 42. Huang Y, Meek KM. Swelling studies on the cornea and sclera: the effects of pH and ionic strength. Biophys J. 1999;77:1655-1665. 43. Ehlers N. Studies on hydration of cornea with special reference to acid hydration. Acta Ophthalmol (Copenh). 1966;44:924-931. 44. Wilson G, O’Leary DJ, Vaughan W. Differential swelling in compartments of the corneal stroma. Invest Ophthalmol Vis Sci. 1984;25:1105-1108. 45. Hedbys BO, Mishima S. Flow of water in the corneal stroma. Exp Eye Res. 1962;1:262–275. 46. Meek KM, Quantock AJ. The use of X-ray scattering techniques to determine corneal ultrastructure. Prog Retin Eye Res. 2001;20:95-137. 47. Elliott GF, Sayers Z, Timmins PA. Neutron diffraction studies of the corneal stroma. J Mol Biol. 1982;155:389-393. 48. Maurice DM. Some puzzles in the microscopic structure of the stroma. J Refract Surg. 1999;15: 692-694. 49. Smolek MK. Interlamellar cohesive strength in the vertical meridian of human eye bank corneas. Invest Ophthalmol Vis Sci. 1993;34:2962-2969. 50. Fatt I. Dynamics of water transport in the corneal stroma. Exp Eye Res. 1968;7:402-412. 51. Eliasson J, Maurice DM. Stress distribution across the in vivo human cornea. Invest Ophthalmol Vis Sci 20 (Suppl.) 1981;156. 52. Simon G, Ren Q. Biomechanical behavior of the cornea and its response to radial keratotomy. J Refract Corneal Surg. 1994;10:343-356. 53. Kiely PM, Carney LG, Smith G. Diurnal variations of corneal topography and thickness. Am J Optom Physiol Opt 1982;59:976982. 54. Hjortdal JØ, Böhm A, Kohlhaas M, et al. Mechanical stability of the cornea after radial keratotomy and photorefractive keratectomy. J Refract Surg 1996;12:459-466. 55. Feldman ST, Frucht-Perry J, Weinreb RN, Chayet A, Dreher AW, Brown SI. The effect of increased intraocular pressure on visual acuity and corneal curvature after radial keratotomy. Am J Ophthalmol. 1989;108:126-129. 56. Poinoosawmy D, Roth JA. Variations in visual acuity, refraction, and corneal curvature with changes in applanation tension. Br J Ophthalmol. 1974;58:523-528.

Basics of biomechanics

Copyright © 2018. Kugler Publications. All rights reserved.

57. Ehlers N, Bramsen T, Sperling S. Applanation tonometry and central corneal thickness. Acta Ophthalmol (Copenh.) 1975;53:34-43. 58. Whitacre MM, Stein R. Sources of error with use of Goldmann-type tonometers. Surv Ophthalmol 1993;38:1-30. 59. Kohlhaas M, Lerche R, Draeger J, et al. The influence of corneal thickness and corneal curvature on tonometry readings after corneal refractive surgery. Eur J Implant Ref Surg. 1995;7:84-88. 60. Yao WJ, Crossan AS. An update on post-refractive surgery intraocular pressure determination. Curr Opin Ophthalmol. 2014;25(4):258-263. 61. Ahearne M, Yang Y, Then KY, Liu K-K. An indentation technique to characterize the mechanical and viscoelastic properties of human and porcine corneas. Ann Biomech Eng. 2007;35:16081616. 62. Clemmensen K, Hjortdal J. Intraocular pressure and corneal biomechanics in Fuchs’ endothelial dystrophy and after posterior lamellar keratoplasty. Acta Ophthalmol. 2014;92:350-354. 63. Vellara HR, Patel DV. Biomechanical properties of the keratoconic cornea: a review. Clin Exp Optom. 2015;98:31–38 64. Hjortdal JØ, Ehlers N. Acute tissue deformation patterns of the human cornea after radial keratotomy. J Refract Surg. 1996;12:391-400. 65. Buzard KA, Ronk JF, Friedlander MH, Tepper DJ, Hoeltzel DA, Choe KI. Quantitative measurement of wound spreading in radial keratotomy. Refract Corneal Surg. 1992;8:217-223. 66. Petroll WM, New K, Sachdev M, Cavanagh HD, Jester JV. Radial keratotomy. III. Relationship between wound gape and corneal curvature in primate eyes. Invest Ophthalmol Vis Sci. 1992;33(12):3283-91. 67. Petroll WM, Roy P, Choung CJ, Hall B, Cavanagh HD, Jester JV. Measurement of surgically induced corneal deformations using three-dimensional confocal microscopy. Cornea. 1996;15:154164. 68. Henninghausen H, Feldman ST, Bille JF, McCulloch AD. Effect of swelling and refractive surgery on regional strains in the rabbit cornea. Invest Ophthalmol Vis Sci. 1996;37:S314. 69. Jester JV, Venet T, Lee J, Schanzlin DJ, Smith RE. A statistical analysis of radial keratotomy in human cadaver eyes. Am J Ophthalmol. 1981;92:172-177.

13 70. Maloney RK. Effect of corneal hydration and intraocular pressure on keratometric power after experimental radial keratotomy. Ophthalmology. 1990;97:927-933. 71. Santos VR, Waring GO, Lynn MJ, et al. Morning-to-evening change in refraction, corneal curvature, and visual acuity 2 to 4 years after radial keratotomy in the PERK Study. Ophthalmology. 1988;95:1487-1493. 72. Schanzlin DJ, Santos VR, Waring GO, et al. Diurnal change in refraction, corneal curvature, visual acuity, and intraocular pressure after radial keratotomy in the PERK Study. Ophthalmology. 1986;93:167-175. 73. MacRae S, Rich L, Phillips D, Bedrossian R. Diurnal variation in vision after radial keratotomy. Am J Ophthalmol. 1989;107:262267. 74. Hjortdal JØ, Ehlers N. Effect of excimer laser keratectomy on the mechanical performance of the human cornea. Acta Ophthalmol Scand. 1995;73:18-24. 75. Seiler T, Matallana M, Sendler S, Bende T. Does Bowman’s layer determine the biomechanical properties of the cornea? Refract Corneal Surg. 1992;8:139-142. 76. Dupps WJ Jr, Roberts C. Effect of acute biomechanical changes on corneal curvature after photokeratectomy. J Refract Surg. 2001;17:658-669. 77. Litwin K, Moreira H, Odahi C, McDonnell P. Changes in corneal curvature at different excimer laser ablative depths. Am J Ophthalmol. 1991;111:382-384. 78. Knox Cartwright NE, Tyrer JR, Jaycock PD, Marshall J. Effects of variation in depth and side cut angulations in LASIK and thinflap LASIK using a femtosecond laser: a biomechanical study. J Refract Surg. 2012;28:419-425. 79. Hjortdal JØ, Vestergaard AH, Ivarsen A, Ragunathan S, Asp S. Predictors for the outcome of small-incision lenticule extraction for Myopia. J Refract Surg. 2012;28:865-871. 80. Pedersen IB, Bak-Nielsen S, Vestergaard AH, Ivarsen A, Hjortdal J. Corneal biomechanical properties after LASIK, ReLEx flex, and ReLEx smile by Scheimpflug-based dynamic tonometry. Graefes Arch Clin Exp Ophthalmol. 2014;252:1329-1335.

Copyright © 2018. Kugler Publications. All rights reserved.

2. Corneal stroma: collagen ultrastructure and orientation in health and disease Keith M. Meek, Sally Hayes Structural Biophysics Research Group, School of Optometry and Vision Sciences, Cardiff University, Cardiff, UK

1. Introduction

Copyright © 2018. Kugler Publications. All rights reserved.

The cornea is the only connective tissue that must combine tensile strength with a perfectly defined shape and almost 100% transparency. For nearly a century, it has been known that these properties derive from the arrangement of the constituents of the stroma.1,2 The corneal stroma has a lamellar structure, with most layers running approximately parallel to the corneal surface, and lying at an angle to their neighbors. Therefore, throughout the full thickness of the 200 or so lamellae (in the central human cornea) all radial angles are occupied; this arrangement results in a high tensile strength within the plane of the tissue that can withstand the intraocular pressure. With the advent of electron microscopy, it was clear that each lamella contains parallel collagen fibrils which have a narrow diameter and a high degree of regularity in their lateral packing. It is these structural properties that confer strength and transparency to the tissue. In this chapter, we describe the structure of the corneal stroma in detail, discussing the hierarchical architecture of collagen from the molecules to the lamellae and showing how aspects of this can change in disease and following surgery.

2. Collagen hierarchical structure: molecules to fibrils Most of the collagen in the corneal stroma is types I, V, and VI, though numerous other collagen types such as XIII, XV, and XVIII are also present.3 Types I

and V co-localize within the fibrils, whereas type VI forms a random network of filaments that may help stabilize the fibrillar array, but may also prolong the life of corneal cells by preventing anti-beta 1 integrin-based cell apoptosis.4 Table 1 lists typical values for a number of structural,5-12 biomechanical,13,14 and optical properties5,15 of corneal collagen that have been obtained from the literature. 2.1. Collagen fibril structure Corneal collagen fibrils are the principal load-bearing constituents of the lamellae. The fibrils must resist the tensile forces due to the intraocular pressure and protect the inner ocular tissue from external trauma while, at the same time, remaining narrow to allow tissue transparency. These competing requirements are achieved by their rather complex structure. The basic unit of the collagen fibril is the triple helical collagen molecule containing two identical alpha 1 helices and one alpha 2 helix (each with left-handed coiling), in a right-handed supercoiled arrangement. The molecule contains over 3000 amino acids (>1000 in each alpha chain) and measures ~300 nm in length by about 1.6 nm in diameter (Table 1). The alpha chains are enzymatically crosslinked in the non-helical terminal regions.16 These molecules self-assemble in a staggered arrangement with a gap region between one molecule and the one in front (Fig. 1), which then gives the fibril an axial periodicity, D. The stagger is 234.2 amino acid residues,17 which leads to a value of D of close to 67 nm in most connective tissues. The immediate subunit of the fibril is the five-stranded microfibril.18 Within the microfibril constituent, molecules have a

Correspondence: Keith M. Meek, School of Optometry and Vision Sciences, Cardiff University, Maindy Road, Cardiff CF24 4HQ, UK. E-mail: [email protected] Biomechanics of the Eye, pp. 15-30 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

16

K.M. Meek and S. Hayes

Fig. 1. The hierarchical structure of collagen fibrils. Triple helical collagen molecules (top) assemble in an axially staggered array, with gaps between one molecule and the one in front to form five-stranded microfibrils (middle). The microfibrils aggregate in a coiled manner to produce the collagen fibril (bottom). The electron micrographs of the microfibrils are reproduced from Baldock et al.18 (bottom left) and Ottani et al.31 (bottom right) with permission of the copyright holders. Images are not shown to scale.

Misconception 1: There are other intermediate structures within the collagen fibril

Copyright © 2018. Kugler Publications. All rights reserved.

There have been reports over many years of larger subunits within collagen fibrils.19-21 At the time of writing, these larger subunit structures have not been universally accepted as their measured dimensions seem to be techniquespecific.

left-handed twist. These molecules are enzymatically crosslinked at several axial locations. In some tissues such as the cornea, these microfibrils also coil (with a right-handed twist),22 and this leads to a reduction in the axially-projected D-period to 65 nm (Table 1).12,23,24 This crosslinked rope-like structure, with an alternating twist at each hierarchical level, conveys considerable strength to the narrow corneal fibrils and is in contrast

to the fibrils in the adjacent sclera, which are wider and have a more parallel arrangement of microfibrils within them.24 At present, it is not certain if the collagen fibrils in the cornea are crimped in vivo as in other connective tissues, but recent publications claim there is a small crimp.25-27 This crimp would add another level of protection to the fibrils, allowing small extensions and distortion of lamellae without fibril sliding. Corneal collagen fibril diameters vary between species.7, 28 Electron microscopy showed the existence of an 8 nm step in diameter measurements from a number of corneal specimens belonging to different species,29 suggesting that fibrils grow by addition of discrete concentric radial shells of microfibrils.30,31 The variation of fibril diameter between species is accompanied by a similar variation in the center-to-center fibril spacings28 such that there is a constant collagen fibril area fraction.7 The fibril diameter in the center of the human cornea as determined by x-ray diffraction is approximately 31-34 nm, depending on age (Table 1).

Corneal stroma: collagen ultrastructure and orientation in health and disease

17

Table 1. Some properties of human corneal collagen fibrils Property37

Value

Data sources

Inter-molecular Bragg spacing

1.63 nm

Leonard and Meek7

Diameter of microfibrils*

4 nm

Holmes et al.6

Fibril diameter

31–34 nm

Meek and Leonard;7 Daxer et al.;8 Boote et al.9

Number of molecules in fibril cross-section

263

Meek and Leonard7

Number of microfibrils in fibril cross-section*

∼70 (64 type I and 6 type V)

Holmes and Kadler10

Tilt angle of microfibrils with respect to fibril axis* 15˚

Holmes et al.6

Collagen fibril D-periodicity

65 nm

Meek et al.12

Inter-fibrillar Bragg spacing

55–57 nm

Leonard and Meek;7 Boote et al.9

Fibril area fraction

0.34

Freund et al.11

Fibril cross-section number density

509 fibrils/µm2

Freund et al.11

Young’s modulus of collagen molecule

4.8 GPa

Gautieri et al.14

Young’s modulus of fibrils along fibril direction

∼ 1.0 GPa

Pinsky and Datye13

Form birefringence of fibrils

0.00218–0.0027

Worthington15

Fibril refractive index

1.411–1.454

Leonard and Meek;5 Worthington15

*Data from bovine corneas has been included where human data are not available.

Copyright © 2018. Kugler Publications. All rights reserved.

Misconception 2: The diameter of corneal collagen is about 24 nm The values close to 24 nm often found in the literature are obtained from electron microscopy, a technique which involves fixation and dehydration procedures that are likely to reduce the intermolecular spacing, and hence the fibril diameter. 20,32 Furthermore, it is believed that there is a fractal coating of proteoglycans surrounding each collagen fibril.33 The thickness of this coating is likely to be hydration sensitive,34 so it is possible that the diameters obtained from x-ray diffraction7 and low temperature electron microscopy processing35 are larger because they include the coating that is preserved in a hydrated state. Within the human cornea, fibril diameters are constant within the central 8 mm,9 do not vary with tissue depth,11,36 and increase rapidly toward the limbus.9,37 Average interfibrillar distances remain constant within the central 4 mm (horizontally) and 3 mm (vertically), and then start to rise in the periphery, increasing steeply at the limbus. These changes lead to

an increase in the fibril area fraction with position across the cornea.9 This, coupled with increasing peripheral corneal thickness, probably contributes to differences in the biomechanical properties between the center and the periphery of the human cornea.38,39 The area fraction of fibrils is proportional to the mechanical strength of connective tissues.9,40 For example, the ability to resist creep and crack propagation, as well as flexibility, are directly related to the amount of smaller diameter fibrils, but tensile strength is greater in wider fibrils.41 Thus, it is possible that the presence of smaller diameter fibrils near the visual axis requires closer packing in order to promote transparency and provide strength in a region where the cornea is thinner. These smaller fibrils in the center may also confer greater flexibility, maintaining tissue integrity while allowing deformation that may occur, for example, during eye rubbing. Several factors are involved in the control of fibril diameters, each one of them probably exerting an influence at a different hierarchical level.42 The presence of hydroxylysine-linked mono- and di-saccharides43 and covalent collagen crosslinking by transglutaminase-244 may be involved at the molecular level. The presence of type V collagen molecules, which have substantial globular domains, appears to limit the accretion of additional microfibrillar shells and thus

18

K.M. Meek and S. Hayes

Copyright © 2018. Kugler Publications. All rights reserved.

ultimately controls the diameter of individual fibrils.45,46 The association of proteoglycans with the surfaces of fibrils (see Section 2.2) has been shown to be essential to prevent adjacent fibrils from fusing together to form larger fibrillar structures.47-50 2.2. Fibril organization and the interfibrillar matrix When developing his theory of corneal transparency, Maurice51 assumed that the corneal collagen fibrils were packed in a crystalline lattice. This lattice was not observed in electron micrographs, and x-ray scattering confirmed that fibril packing was more “liquid-like”.52 The x-ray data indicated that fibril order extended to three fibril diameters from a given fibril, and this degree of order is sufficient for destructive interference of any scattered light so long as adjacent fibrils do not approach each other too closely.53 Reported values for the area fraction (and hence the volume fraction) occupied by the fibrils depends on the technique used, with x-ray studies yielding an average value close to 30% for many species.7 The lamellar structure of the cornea appears to derive from the stromal cells themselves,54,55 and may be directed by long cellular projections termed keratopodia.56 Recently, it has been shown that there is an early influence on lamellar stacking by the presence of covalent collagen crosslinking by lysyl oxidases.44 The control of fibril packing within the lamellae is provided by the interfibrillar proteoglycans (PGs) and their associated glycosaminoglycan chains (GAGs). Proteoglycans bind to collagen fibrils via their protein cores at specific axial locations.57,58 The proteoglycans and their GAGs form a fractal coating on the surface of the collagen fibrils33 and GAGs also extend out to associate with GAGs whose proteoglycans are attached to other fibrils (Fig. 2). The fractal coating limits aggregation if fibrils get too close by exerting a repulsive force due to the Donnan effect associated with their high negative charge.59 It was suggested that thermal motion of the GAG chains provides a counterbalancing attractive force, and these two opposing forces cause the fibrils to oscillate about their equilibrium positions.60 Alternatively, modelling has shown that the GAGs that connect adjacent fibrils can supply the necessary restoring force due to the constraining boundary conditions on the tissue as a whole. In other words, when a fibril moves further away from a neighbor, it moves closer to another

Fig. 2. Banded collagen fibrils are surrounded by a matrix containing two main proteoglycan types. Decorin consists of a protein core (green) that is attached to the collagen via hydrogen bonds at two possible sites within the gap region of the collagen fibrils. These core proteins tend to form duplexes. The associated dermatan sulphate glycosaminoglycans (red) appear to wrap around the surfaces of the fibrils and many interconnect, possibly via their glycosaminoglycan chains, to dermatan sulfate and keratan sulfate chains on adjacent fibrils. Keratan sulphate-containing proteoglycans such as lumican are attached via their protein cores at the gap/overlap boundaries. Up to three glycosaminoglycan chains (orange) are attached to their single protein cores (also in green). These appear to be shorter than the dermatan sulphate glycosaminoglycans and run either around or along the fibril axis or protrude into the interfibrillar space, sometimes forming links with other glycosaminoglycans attached to adjacent fibrils.

neighbor, which then provides an increased Donnan restoring force because the interstitial GAGs become more concentrated, and this pushes the displaced fibril back to its equilibrium position.59,61 These ideas are discussed in detail in Chapter 5. The interfibrillar matrix has an elastic modulus some 10,000 times lower than the collagen fibrils,62 and thus plays no significant role in the tensile properties of the mature cornea. However, interactions between decorin proteoglycan and type I collagen during fibrillogenesis increase the tensile strength of collagen gels63 so may be involved in the mechanical response by means of their influence on fibril aggregation. The hydrated proteoglycan matrix also plays a vital role in resisting tissue compression as well as in providing viscoelasticity to the cornea. It has been suggested that PGs in some tissues contribute to mechanical properties by allowing fiber sliding or by crosslinking collagen fibrils, thereby contributing to load sharing.64 The human cornea contains elastic fibers that are abundant in the limbus and peripheral posterior stroma65 and extend across the cornea above Descemet’s membrane.66 These fibers are present in the

Corneal stroma: collagen ultrastructure and orientation in health and disease

fetus and are thought to persist throughout life. They are elastin-rich at the limbus, but lose their elastin core as they progress across the cornea, becoming bundles of fibrillin rich microfibrils.66 Although their mechanical role in the adult cornea, if any, is not yet known, elastic fibers generally provide restoring forces when a tissue is extended, so they may be involved with restoring equilibrium when the cornea is distorted, for example by the intraocular pulse. Corneal stromal cells (keratocytes) reside between the collagen lamellae, and are responsible for secreting extracellular matrix components required to maintain normal corneal structure and function. From a mechanical standpoint, resting corneal keratocytes are considered quiescent; they do not express stress fibers or generate substantial contractile forces.67 However, they do interact with the extracellular matrix, and this is discussed in Chapter 4.

3. Collagen lamellar organization and distribution in the healthy cornea The microscopic organization of collagen in the cornea is in the form of lamellae that run roughly parallel to the surface of the eye like flattened fibers which, in the deeper layers, appear to cross the cornea from limbus to limbus.

19

With an average density of 456 fibrils per µm2 (Table 1), there are thus of the order of 200,000 fibrils within a typical lamella and of the order of 50 million throughout the whole central cornea. The anterior lamellae are interwoven and insert into Bowman’s layer, whereas the posterior lamellae are stacked rather like plywood (see Chapter 3). It is the arrangement of these lamellae, both within and out of plane, which ultimately determines the mechanical properties of the tissue. In 1938, Kokott71 observed stress lines in the cornea that suggested a preferential arrangement of lamellae in the vertical and horizontal directions. The existence of this arrangement was later confirmed using x-ray scattering — a powerful technique that allows quantitative measurements of collagen fibril parameters without the need for tissue processing.72 The x-ray beam is passed through a specific region of the cornea, from anterior to posterior, and the scatter is recorded and analyzed to provide data on several structural parameters (intermolecular spacing, fibril spacing, etc.). In this way, the observed scattered x-ray beam is the sum of the scattering from all of the 50 million or so collagen fibrils that it encounters. This technique has been used to obtain much of the numerical data presented in Table 1. In addition to the data shown in Table 1, the angular distribution of the scattered x-rays may be used to determine the angular distribu-

Copyright © 2018. Kugler Publications. All rights reserved.

Misconception 3: A structural unit exists between the fibril and the lamella Some techniques appear to reveal fibers that are much wider than those seen in electron micrographs. For example, the fibers seen within lamellae using second harmonic generation (SHG) non-linear microscopy are too wide to be the same as those seen using electron microscopy. However, the exact source of the signals generated using SHG is still not completely understood. In humans, the number of lamellae through the central stromal thickness is reported as 242 ± 4. In the more anterior region of the stroma, the density of the lamellae is 50% greater than in the posterior stroma.68 The lamellae are about 0.2 mm wide and 2 µm thick.69,70

Fig. 3. A vector plot map, created using x-ray scattering data, shows the predominant direction of collagen across the cornea, limbus, and sclera. In the montage display, the largest vector plots (which represent regions of greatest collagen alignment) have been scaled down by the factors shown in the color key.

20

K.M. Meek and S. Hayes

tion of lamellae at specific points in the tissue.73 The scatter intensity also allows the relative distribution of collagen mass to be mapped. By separating the scatter into isotropic and non-isotropic components, it is thus possible to separate out contributions from the lamellae that are, on average, equally populating all angles within the plane of the cornea, from the sub-population that have a preferred orientation.74 Observations of the angular scatter distribution across the human cornea and limbus confirmed that there is a preferred orientation of lamellae close to the vertical and horizontal directions (Fig. 3).74-76 On average, the two directions are equally populated, but there are significant differences between individuals that have been proposed to affect corneal shape.77 Misconception 4: Lamellae are orthogonally arranged in the human cornea

Copyright © 2018. Kugler Publications. All rights reserved.

The word “orthogonal” is used in many research papers to describe the vertical and horizontal preferred orientations of lamellae. In fact, lamellae make many different angles with their neighbours in the human cornea,78 so adjacent lamellae are not orthogonal.

The structural reinforcement provided by these preferentially aligned lamellae in the center of the cornea may help balance the stress exerted by the extraocular muscles,74 particularly in the horizontal direction.79 Moving the eyelids and squeezing the eyeball would exert stress principally in the vertical direction.77,80 A preferential alignment of lamellae in the central cornea is confined to the posterior two thirds of the stroma, with the anterior stroma possessing an essentially isotropic angular distribution of lamellae.75,81 This arrangement seems to be species-specific, with animals that require intermediate to high levels of visual acuity possessing an excess of collagen directed towards one or both sets of opposing rectus muscles.82 Studies of corneal birefringence have shown that the central human cornea acts as a birefringent retarder in the supero-temporal to infero-nasal direction.83 This information has often been interpreted as evidence of a preferred orientation of collagen in that direction, and therefore seen to be at odds with the x-ray scattering

studies described above. However, mathematically, the origin of corneal birefringence is more complicated than the origin of x-ray scatter, which arises only from the collagen fibrils or the molecules within them. The preferentially aligned vertical and horizontal lamellae identified by x-ray scattering studies may produce birefringence that tends to cancel out, resulting in only an excess of one fibril orientation being detected.84 In addition to this, it is not known what effect non-collagenous components, such as the extensive network of cell processes85 and the presence of elastic fibers within the cornea,86 may have on the overall birefringence. In the human cornea, this arrangement of lamellae changes within the peripheral couple of millimeters to a pseudo annulus at the limbus76,87,88 that appears to be necessary to support the change in curvature between the cornea and sclera.89 Such an annulus seems to occur in most mammalian species.82,90,91 The distribution of mass of the preferentially aligned collagen fibrils also suggested the presence of “anchoring lamellae” containing wider collagen fibrils that enter the cornea from the direction of the inferior, superior, medial, and lateral rectus muscles. These lamellae do not traverse the optical zone,37 and may insert into Bowman’s layer.92 X-ray scattering has also been used to quantify the out-of-plane angles made by lamellae at different depths in the tissue. This is an alternative approach to second harmonic generation non-linear microscopy (see Chapter 3). At the center of the cornea, the out-ofplane angle (inclination angle) falls from an average of 11˚ at the anterior surface to about 7.5˚ at the posterior surface.93 The current models of preferred lamella orientations within and through the depth of the cornea are schematically illustrated in Figure 4.

4. The role of collagen in keratoconus Keratoconus, first described by Nottingham in 1854,94 is an ocular disorder whereby the cornea thins and weakens to such an extent that it can no longer maintain its normal curvature. The progressive deterioration in tissue strength causes the cornea to bulge outward to assume a conical shape which results in severe, irregular astigmatism (Fig. 5). Although the effects of keratoconus on corneal tissue are well documented,95 its cause and the mechanism that leads to the progressive thinning

Corneal stroma: collagen ultrastructure and orientation in health and disease

21

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. A contour map showing the intensity of x-ray scatter (arbitrary units) from preferentially aligned collagen in a typical human cornea. The predominant direction of collagen has been superimposed using solid black lines (in the central and peripheral cornea) and a broken black line (limbus). In the peripheral stroma and limbus, anchoring lamellae (probably of scleral origin) are thought to reinforce the tissue in the mid-posterior layers without entering the central stroma. X-ray data from transverse sections show an increase in total scatter intensity between the central, peripheral and limbal regions (B) and a decrease in lamellar inclination angle between the anterior and posterior cornea (C). The presumed location of anchoring lamellae (solid black lines) and lamellae cut in cross-section (solid black circles) at the limbal pseudo annulus (broken black line) have been superimposed onto the contour plot in (B).

Fig. 5. Side profile of a normal cornea and a keratoconus cornea. Images courtesy of Ellen Hayes and Ken Pullum.

and weakening of the cornea remain uncertain.96 This uncertainty may be attributed in part to the lack of biomechanical and structural studies focused on the early stages of the disease and the possibility that keratoconus may be the end result, or final common

pathway, of many different pathological processes. Although changes in the epithelium and breaks in Bowman’s layer are a well-known occurrence in keratoconus,97 neither layer is considered to play a significant role in the strength of the cornea.98,99 The

22

K.M. Meek and S. Hayes

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 6. Vector plot maps showing the predominant orientation of stromal collagen in the central 7 mm of a normal and a keratoconic cornea have been superimposed onto videokeratography images taken from the same specimens prior to surgery. In the apical region of the keratoconic cornea, the normal preferred alignment of collagen in the vertical and horizontal directions is absent.

collagenous stroma, on the other hand, accounts for about 90% of total corneal thickness and is considered the primary load-carrying layer of the cornea. The role of basement membrane and stromal collagen in the pathogenesis is supported by reports of abnormalities in collagen types XIII, XV, an XVIII within keratoconic corneas100-102 and the association of keratoconus with certain connective tissue disorders, such as Marfan syndrome, osteogenesis imperfecta (brittle bone disease), mitral valve prolapse,103 and Ehlers-Danlos syndrome (hyper-mobility of joints and increased elasticity of skin).104 In this respect it is also interesting to note that advanced post-surgical keratoconus buttons show an abnormal elastic fiber network, which it has been postulated, may impede the recovery of the tissue following distortion and contribute to the pathogenesis of the disease.105 Although there is general agreement that the stromal thinning observed in keratoconus is caused by a reduction in the number of lamellae within the affected region106 and not by the compaction of collagen fibrils within individual lamellae,107 the precise mechanism by which the thinning occurs is not clear. Some have attributed the stromal thinning to collagen degradation instigated by the release of unspecific enzymes from a defective epithelium108 while others have favored a view that collagen is not lost, but simply redistributed within the cornea via a mechanism of lamellar slippage.104,109 Evidence supporting the involvement of collagen degradation in keratoconus progression has been provided by biochemical studies which have

shown heightened levels of proteolytic ­enzymes110-113 and decreased levels of proteinase inhibitors114 within the affected tissue. Similarly, a mechanism of lamellar slippage may be readily envisaged when one considers the reduced levels of inter-lamellar adhesion115 and lamellar interlacing in the apex of keratoconic corneas116,117 along with the diminished number of lamellar insertions into Bowman’s layer.116 Further strong evidence for a mechanism of lamellar slippage has been provided by X-ray scattering studies, which have shown gross lamellar rearrangement to occur in keratoconus corneas74,118 not only at the apex but also, in some cases, in the surrounding peripheral cornea (Fig. 6).119,120 Such a change in fibril orientation would be difficult to explain on the basis of tissue degradation alone, since collagen loss would be unlikely to give rise to a systematic realignment of fibrils. In addition to this, Edmund121 demonstrated that, except in advanced keratoconus, the cross-sectional area of corneas in optical section did not differ from that of normal corneas, implying that ectasia occurs by a redistribution of stromal mass rather than by a loss from extensive tissue degradation. However, more recent 3-D analyses of corneal volumes in normal and keratoconic eyes have demonstrated lower corneal volumes in earlier disease stages122,123 and suggest that some combination of tissue degradation and lamellar slippage may be required to explain the morphological features of keratoconus. One theory is that the loss of structural integrity in the keratoconus cornea is caused not only by the presence

Corneal stroma: collagen ultrastructure and orientation in health and disease

23

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 7. A background photograph of an 8 mm corneal button taken from a patient that underwent a re-graft due to corneal scarring six years after a 7.5 mm penetrating keratoplasty for keratoconus, has been superimposed with a vector plot map showing the predominant direction of collagen within the tissue. The color key shows the relative intensity of x-ray scatter from preferentially aligned collagen at each position (with red vector plots signifying the regions of greatest collagen alignment). The graft/host tissue boundary of the original keratoplasty (for keratoconus) can be seen clearly within the insets (red asterisks). Abnormalities in collagen orientation can be seen at both the graft/host tissue interface, where collagen alignment increases and most collagen lies tangentially to the interface, and also in the vascularized scarred region of the cornea where collagen orientation is disturbed. The predominant orientation of collagen in the non-scarred central region of the cornea appears to be rotated by 45° with respect to that of a normal cornea (in which collagen lies predominantly in the superior-inferior and nasal-temporal directions), which suggests that, in this case, the donor button was grafted obliquely. Photograph courtesy of Nicholas Hawksworth.

of abnormal keratocytes124 and matrix proteins,111,125,126 and the up-regulation of proteolytic enzymes,110,114 but also by an unravelling of lamellae along their length and from their limbal anchors, and a teasing apart at the points where lamellae bifurcate or insert into Bowman’s layer.120 Although Edmund127 found no direct evidence that lamellae are released from their limbal location, both Owens and Watters128 and Brautaset et al.129 were able to show that peripheral corneal thinning does occur in keratoconus, albeit to a much lesser extent than seen in the central region. Such alterations in stromal collagen architecture could result from the failure of a “locking mechanism” that may occur during normal childhood development to stabilize corneal and limbal lamellae, or from the effects of enzymatic digestion.120 Predictive multi-scale computational models of

keratoconus progression have been carried out at the University of Alabama at Birmingham130 using x-ray scattering measurements of corneal collagen architecture.119 The models have shown that once initiated, collagen sliding leads to the progressive conical shaped protrusion that is seen clinically, and increased collagen fibril degradation at the cone results in the disorganization of collagen architecture that is measured experimentally using x-rays. The model results further showed that: 1. the predominant directions of collagen fibril sliding and degradation were perpendicular to each other at the apex; and 2. the corneal thinning occurred around the apex of the cone and was primarily caused by the sliding mechanism (R. Grytz, personal communication, 2014).

24

K.M. Meek and S. Hayes

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 8. Scanning electron microscopy images of a post-mortem LASIK cornea. (A) The flap edge is clearly visible five years after LASIK surgery (yellow arrows). (B) At higher magnifications, the flap edge appears separated from the adjacent corneal tissue. (C) At the flap/stromal bed interface, collagen lamellae appear to be in disarray and there is no apparent reconnection between adjacent severed lamellae (blue arrows). (D) A vertical view of the flap edge shows a gap between the flap margin and the adjacent corneal tissue (white arrows). A few bridging fibers are seen to connect the flap to the stromal bed (green arrow). These images were reproduced from Abahussin et al.138

The good agreement between the computational model of keratoconus progression and clinical and experimental observations support the notion that the mechanism by which the cornea thins and steepens in keratoconus, is most likely a combination of collagen degradation and lamellar slippage. Furthermore, clinical findings of keratoconus stabilization following riboflavin/UVA crosslinking therapy131 support this theory, as the induced crosslinks have been shown to improve the resistance of the cornea to enzymatic digestion.132 Although the therapy does not appear to increase interlamellar cohesion,133 structural investigations have led us to believe that crosslinks formed at the fibril surface and in the protein network surrounding the collagen contribute to the increased tissue stiffness134 and stability131 observed following treatment.

5. Stromal collagen organization following surgery In-vitro and in-vivo studies of animal and human corneas subject to full-tissue thickness injuries have revealed changes in collagen architecture at all hierarchical levels, with alterations in lamellar organization,135-139 fibril diameter,140-142 spatial order,140,142 and the pattern of collagen intermolecular crosslinking135 being reported. Confocal microscopy and histological studies of the graft margin following penetrating keratoplasty have revealed abnormalities in the stroma at the graft-host interface that are indicative of a limited stromal healing response.143,144 More recently, x-ray scattering studies of lamellar orientation have revealed that a clear demarcation exists between the graft and recipient corneal tissue for up to 28 years post-surgery.138,139 Figure 7 shows the predominant orientation of stromal collagen at the graft-host tissue boundary of a cornea that underwent a 7.5 mm penetrating keratoplasty for keratoconus, followed by an 8.5 mm re-graft due to corneal scarring six years later. As has

Corneal stroma: collagen ultrastructure and orientation in health and disease

been noted in our previous work,138,139 the original graft margin remains clearly visible and structurally distinct for many years after penetrating keratoplasty, with lamellae in that region being increasingly aligned and lying predominantly tangential to the wound edge. Similarly, microscopical examination of a laser-assisted in situ keratomileusis (LASIK) treated cornea revealed that the hinged flap, which is created during the procedure to allow ablation of the exposed stromal bed, remained distinct from the rest of the cornea at five years post-surgery (Fig. 8).145 It is likely that some of the structural abnormalities, particularly those related to the organization of stromal collagen, may explain the reduced mechanical strength across the graft-host interface (even after the wound appears to be fully healed).146 They may also explain incidences of wound dehiscence up to 19 years after penetrating keratoplasty,147 and reports of relatively easy dislocation of LASIK corneal flaps many years after treatment.148,149 A further interesting point to note from Figure 7 is that the predominant orientation of collagen in the non-scarred central region of the cornea appears to be rotated by 45° with respect to that of a healthy, unoperated cornea in which collagen lies predominantly in the superior-inferior and nasal-temporal directions (Fig. 3). This suggests that in the original penetrating keratoplasty procedure, the donor button was likely grafted obliquely; such a situation is likely to be a

25

common occurrence in penetrating keratoplasty as the surgery is usually performed with no regard for the orientation of the donor tissue with respect to the host. As the superior-inferior and nasal-temporal preferred orientation of collagen in the central human cornea is thought to reflect a mechanical adaptation of the tissue to forces imposed by the extraocular muscles, a realignment of collagen might be expected with time. However, as indicated here and in a previous study,139 the predominant orientation of collagen remains oblique to the rectus muscles with no significant re-alignment occurring up to 28 years after an oblique penetrating keratoplasty. These findings likely reflect the extremely slow rates of collagen turnover in the quiescent stroma.150 Concerns about the effect of surgically induced lamellar alignment discontinuities on the optical and biomechanical properties of the cornea were raised by Meek and Newton in 1999;151 however, in the absence of published clinical trials it remains unknown whether variations in the degree of misalignment between the donor and host tissue may be a contributing factor to post-keratoplasty astigmatism. It is likely that improved knowledge about the impact of surgical procedures on stromal collagen arrangement and tissue biomechanics would help to determine the ultrastructural basis of post-operative complications, such as corneal instability and astigmatism.

References 1.

Copyright © 2018. Kugler Publications. All rights reserved.

2.

3.

4.

5.

Eisler P. Die Anatomie des meschlichen Auges. In: Schieck F and Brukner A (eds). Kurzes Handbuch der Ophthalmologie. Berlin: Verlag Von Julius Springer; 1930. Kolmer W. Ocular Development. In: Kolmer W, Lauber H (eds). Handbuch der mikroskopischen Anatomie des Menschen, Haut und Siinesorgane. Vol 2., pp. 623-76. Berlin: Verlag von Julius Springer;1936. Ihanamaki TT, Pelliniemi LJ, Vuorio E. Collagens and collagen-realted matrix components in the human and mouse eye. Prog Retin Eye Res. 2004;23(4):403-404. Howell S, Doane K. Type VI collagen increases cell survival and prevents anti-β1integrin-mediated apoptosis. Exp Cell Res. 1998;241(1):230-241. Leonard DW, Meek KM. Estimation of the refractive indices of collagen fibrils and ground substance of the corneal stroma using data from x-ray diffraction. Biophys J. 1997;72(3):1382-1387.

6.

Holmes DF, Gilpin CJ, Baldock C, Ziese U, Koster AJ, Kadler KE. Corneal collagen fibril structure in three dimensions: structural insights into fibril assembly, mechanical properties and tissue organization. Proc Natl Acad Sci USA. 2001;98(13):7307-7312. 7. Meek KM, Leonard DW. Ultrastructure of the corneal stroma - a comparative study. Biophys J. 1993;64(1):273-280. 8. Daxer A, Misof K, Grabner B, Ettl A, Fratzl P. Collagen fibrils in the human corneal stroma: structure and ageing. Invest Ophthalmol Vis Sci 1998;39:644-648. 9. Boote C, Dennis S, Newton RH, Puri H, Meek KM. Collagen fibrils appear more closely packed in the prepupilliary cornea- optical and biomechanical implications. Invest Ophthalmol Vis Sci. 2003;44(7):2941-2948. 10. Holmes D, Kadler K. The precision of lateral size control in the assembly of corneal collagen fibrils. J Mol Biol. 2005;345(4):773784.

Copyright © 2018. Kugler Publications. All rights reserved.

26 11. Freund DE, McCally RL, Farrell RA, Cristol SM, L’Hernault NL, Edelhauser HF. Ultrastructure in anterior and posterior stroma of perfused human and rabbit corneas. Relation to transparency. Invest Ophthalmol Vis Sci. 1995;36(8):1508-1523. 12. Meek KM, Elliot GF, Sayers Z, Whitburn SB, Koch MHJ. Interpretation of the meridional x-ray diffraction pattern from collagen fibrils in corneal stroma. J Mol Biol. 1981;149:477-488. 13. Pinsky P, Datye D. A microstructurally-based finite element model of the incised human cornea. J Biomech Eng. 1991;24(10):907-922. 14. Gautieri A, Vesentini S, Redaelli A, Buehler M. Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up. Nanoletters. 2011;11:758-766. 15. Worthington C. The structure of cornea. Quart Rev Biophys. 1984;17:423-451. 16. Yamauchi M, Chandler GS, Tanzawa H, Katz EP. Cross-linking and the molecular packing of corneal collagen. Biochem Biophys Res Commun. 1996;219(2):311-315. 17. Meek K, Chapman J, Hardcastle R. The staining pattern of collagen fibrils. J Biol Chem 1979;254:10711-10714. 18. Baldock C, Gilpin CJ, Koster AJ, et al. Three-dimensional reconstructions of extracellular matrix polymers using automated electron tomography. J Struct Biol. 2002;138:130-136. 19. Meller D, Peters K, Meller K. Human cornea and sclera studied by atomic force microscopy. Cell Tissue Res. 1997;288:111118. 20. Itoh T, Klein L, Geil H. Age dependence of collagen fibrils and subfibril diameters revealed by transverse freeze-facture and etching technique. J Microsc. 1981;125:343-357. 21. Yamamoto S, Hitomi J, Sawaguchi S, Abe H, Shigeno M, Ushiki T. Observation of human corneal and scleral collagen fibrils by atomic force microscopy. Jpn J Ophthalmol. 2002;46:496-501. 22. Orgel J, Irving T, Miller A, Wess T. Microfibrillar structure of type I collagen in situ. Proc Natl Acad Sci USA. 2006;103:9001-9005. 23. Marchini M, Morocutti M, Ruggeri A, Koch MHJ, Bigi A, Roveri N. Differences in the fibril structure of corneal and tendon collagen. An electron microscopy and x-ray diffraction investigation. Connect Tissue Res. 1986;15:269-281. 24. Yamamoto S, Hashizume H, Hitomi J, et al. The subfibrillar arrangement of corneal and scleral collagen fibrils as revealed by scanning electron and atomic force microscopy. Arch Histol Cytol. 2000;63(2):127-135. 25. Liu X, Wang L, Ji J, et al. A mechanical model of the cornea considering the crimping morphology of collagen fibrils. Invest Ophthalmol Vis Sci. 2014;55:2739-2746. 26. Grytz R, Meschke G. Constitutive modelling of crimped collagen fibrils in soft tissues. J Mech Behav Biomed Mater. 2009;2:522-533. 27. Mega Y, Robitaille M, Zareian R, McLean J, Ruberti J, DiMarzio C. Quantification of lamellar orientation in corneal collagen using second harmonic generation images. Optics Letters. 2012;37:3312-3314. 28. Gyi TJ, Meek KM, Elliot GF. Collagen interfibrillar distances in the corneal stroma using synchrotron x-ray diffraction: a species study. Int J Biol Macromol. 1988;10:265-269.

K.M. Meek and S. Hayes 29. Craig AS, Parry DAD. Collagen fibrils of the vertebrate corneal stroma. J Ultrastruct Mol Struct Res. 1981;74:232-239. 30. Hulmes D, Wess T, Prockop D, Fratzl P. Radial packing, order and disorder in collagen fibrils. Biophys J. 1995;68:1661-1670. 31. Ottani V, Martini D, Franchi M, Ruggeri A, Raspanti M. Hierarchial structures in fibrillar collagens. Micron. 2002;33(7-8):587596. 32. Fullwood NJ, Meek KM. A synchrotron X-ray study of the changes occurring in the corneal stroma during processing for Electron-microscopy. J Microsc. 1993;169:53-60. 33. Fratzl P, Daxer A. Structural transformation of collagen fibrils in the corneal stroma during drying: an X-ray scattering study. Biophys J. 1993;64:1210-1214. 34. Hayes S, White T, Boote C, et al. The structural response of the cornea to changes in stromal hydration. J R Soc Interface. 2017;14(131) 35. Craig AS, Robertson JG, Parry DA. Preservation of corneal fibril structure using low-temperature procedures for electron microscopy. J Ultrastruct Mol Struct Res. 1986;96:172-175. 36. Quantock A, Boote C, Young R, et al. Small-angle fibre diffraction studies of corneal matrix structure: a depth-profiled investigation of the human eye-bank cornea. J Appl Crystallogr. 2007;40:S335-340. 37. Boote C, Kamma-Lorger C, Hayes S, et al. Quantification of collagen organization in the peripheral human cornea at micron-scale resolution. Biophys J. 2011;101(1):33-42. 38. Jayasuriya A, Scheinbeim J, Lubkin VB, G, Kramer P. Pizoelectric and mechanical properties in bovine cornea. J Biomed Mater Res A. 2003;66A:260-265. 39. Meek KM. The cornea and sclera. In: Fratzl P, editor. Collagen Structure and Mechanics. New York: Springer 2008. 40. Goh K, Holmes D, Lu H-Y, et al. Ageing changes in the tensile properties of tendons: Influence of collagen fibril volume fraction. J Biomech Eng. 2008;130:1-8. 41. Parry D. The molecular and fibrillar structure of collagen and its relationship to the mechanical properties of connective tissue. Biophys Chem. 1988;29:195-209. 42. Meek K. Corneal collagen -its role in maintaining corneal shape and transparency. Biophys Rev. 2009;1:83-93. 43. Harding J, Crabbe M, Panjwani N. Corneal collagen. In: Robert L, Robert A (eds). Biochemistry of normal and pathological connective tissues. Colloques Internationaux du C.N.R.S; 1980; 287;51-64. 44. Wang L, Uhlig P, Eikenberry E, Robenek H, Bruckner P, Hansen U. Lateral growth limitation of corneal fibrils and their lamellar stacking depend on covalent collagen cross-linking by transglutaminase-2 and lysyl oxidases, respectively. J Biol Chem. 2014;289:921-929. 45. Lisenmayer T, Gibney E, Igoe F, et al. Type V collagen: molecular structure and fibrillar organization of the chicken alpha-1 (V) NH2-terminal domain, a putative regulator of corneal fibrillogenesis J Cell Biol. 1993;121:1181-1189. 46. Birk D. Type V collagen:heterotypic type I/V collagen interactions in the regulation of fibril assembly. Micron. 2001;32:223237.

Copyright © 2018. Kugler Publications. All rights reserved.

Corneal stroma: collagen ultrastructure and orientation in health and disease 47. Meek K, Holmes D. Interpretation of the electron microscopical appearance of collagen fibrils from corneal stroma. Int J Biol. Macromol 1983;5:17-25. 48. Chakravarti S, Magnuson T, Lass JH, Jespen KL, LaMantia C, Carroll H. Lumican regulates collagen fibril assembly. J Cell Biol. 1998;141:1277-1286. 49. Quantock AJ, Meek KM, Chakravarti S. An X-ray diffraction investigation of corneal structure in lumican-deficient mice. Invest Ophthalmol Vis Sci. 2001;42(8):1750-1756. 50. Kamma-Lorger CS, Pinali C, Martinez JC, Harris J, Young RD, Bedrup C, et al. Role of decorin core protein in collagen organisation in congenital stromal corneal dystrophy (CSCD). PLoS ONE 2016; 11: e0147948. 51. Maurice DM. The structure and transparency of the cornea. J Physiol. 1957;136:263-286. 52. Sayers Z, Koch MHJ, Whitburn SB, Meek KM, Elliott GF, Harmsen A. Synchrotron X-ray-diffraction study of corneal stroma. J Mol Biol. 1982;160(4):593-607. 53. Farrell R, McCally R. Corneal Transparency. In: DM A, FA J (eds). Principles and Practice of Ophthalmology, pp. 629-643. Philadelphia: WB Saunders 2000. 54. Guo X, Hucheon A, Melotti S, Trinkaus-Randall V, Zieske J, Ruberti J. Morphological characterization of organized extracellular matrix deposition by ascorbic acid stimulated human corneal fibroblasts. Invest Ophthalmol Vis Sci. 2007;48(9):40504060. 55. Ruberti J, Zieske J. Prelude to corneal tissue engineering Gaining control of collagen organization. Prog Retin Eye Res. 2008;27(5):549-577. 56. Young R, Knupp C, Pinali C, et al. Three-dimensional aspects of matrix assembly by cells in the developing cornea. Proc Natl Acad Sci USA. 2014;111(2):687-692. 57. Meek KM, Elliott GF, Nave C. A synchrotron X-ray-diffraction study of bovine cornea stained with cupromeronic blue. Coll Relat Res. 1986;6(2):203-218. 58. Scott J, Haigh M. Identification of specific binding sites for keratan sulphate proteoglycans and chondroitin-dermatan sulphate proteoglycans on collagen fibrils in cornea by the use of cupromeronic blue in ‘critical-electrolyte-concentration’ techniques. Biochem J. 1988;253(2):607-610. 59. Cheng X, Pinsky P. Mechanisms of self-organization for the collagen fibril lattice in the human cornea. J R Soc Interface. 2013;10(87):20130512. 60. Lewis P, Pinali C, Young R, Meek K, Quantock A, Knupp C. Structural interactions between collagen and proteoglycans are elucidated by three-dimensional electron tomography of bovine cornea. Structure. 2010;18(2):239-245. 61. Meek KM, Knupp C. Corneal structure and transparency. Prog Retin Eye Res. 2015;49:1-16. 62. Hjortdal JO. Regional elastic performance of the human cornea. J Biomech. 1996;29:931-942. 63. Reese SP, Underwood CJ, Weiss JA. Effects of decorin proteoglycan on fibrillogenesis, ultrastructure, and mechanics of type I collagen gels. Matrix biol. 2013;32(7-8):414423.

27

64. Comerford E, Geraghty B, Hamarashid R, Elsheikh A. The contribution of proteoglycans to the viscoelasticity of the canine anterior cruciate ligament. Osteoarthr Cartil. 2014;22:S313. 65. Kamma-Lorger C, Boote C, Hayes S, et al. Collagen and mature elastic fibre organisation as a function of depth in the human cornea and limbus. J Struct Biol. 2010;169(3):424-430. 66. Lewis PN and White TL, Young RD, Bell J, Winlove CP and Meek KM. Three-dimensional arrangement of elastic fibers in the human corneal stroma. Exp Eye Res 2017;146:43-53. 67. Petroll W, Lakshman N. Fibroblastic transformation of corneal keratocytes by rac inhibition is modulated by extracellular matrix structure and stiffness. J Funct Biomater. 2015;6(2):222240. 68. Bergmanson J, Horne J, Doughty M, Garcia M, Gondo M. Assessment of the number of lamellae in the central region of the normal human corneal stroma at the resolution of the transmission electron microscope. Eye Contact Lens. 2005;31(6):281-287. 69. Polack FM. Morphology of the cornea. Am J Ophthalmol. 1961;51:179-184. 70. Komai Y, Ushiki T. The three-dimensional organisation of collagen fibrils in the human cornea and sclera. Invest Ophthalmol Vis Sci. 1991;32(8):2244-2258. 71. Kokott W. Ubermechanisch-funktionelle strikturen des auges. Albrecht von Graefes. Arch Ophthalmol. 1938;138:424-485. 72. Meek KM, Quantock AJ. The use of X-ray scattering techniques to determine corneal ultrastructure. Prog Retin Eye Res. 2001;20(1):95-137. 73. Meek KM, Boote C. The use of x-ray scattering techniques to quantify the orientation and distribution of collagen in the corneal stroma. Prog Retin Eye Res. 2009;28(5):369-392. 74. Daxer A, Fratzl P. Collagen fibril orientation in the human corneal stroma and its implications in keratoconus. Invest Ophthalmol Vis Sci. 1997;38:121-129. 75. Meek K, Blamires T, Elliot G, Gyi TJ, Nave C. The organisation of collagen fibrils in the human corneal stroma: a synchrotron x-ray diffraction study. Curr Eye Res. 1987;6(7):841-846. 76. Aghamohammadzadeh H, Newton RH, Meek KM. X-ray scattering used to map the preferred collagen orientation in the human cornea and limbus. Structure. 2004;12:249-256. 77. Boote C, Dennis S, Huang Y, Meek K. Lamellar orientation in human cornea in relation to mechanical properties. J Struct Biol. 2005;149(1):1-6. 78. Radner W, Zehetmayer M, Aufreiter R, Mallinger R. Interlacing and cross-angle distribution of collagen lamellae in the human cornea. Cornea. 1998;17:537-543. 79. Lopping B, Weale R. Changes in corneal curvature following ocular convergence. Vision Res. 1965;5:207-215. 80. Marin-Amat M. Les variations physiologiques de la courbure de la cornee´pendant de vie. Leur importance et transcendance dans la refraction oculaire. Bull Soc Belge Ophthalmol Mol. 1956;113:251-293. 81. Abahussin M, Hayes S, Knox Cartwright N, et al. 3D collagen orientation study in human cornea using x-ray diffraction and femtosecond laser technology. Invest Ophthalmol Vis Sci. 2009;50(11):5159-5164

Copyright © 2018. Kugler Publications. All rights reserved.

28 82. Hayes S, Boote C, Lewis J, et al. Comparative study of fibrillar collagen arrangement in the corneas of primates and other mammals. Anat Rec. 2007;290:1542-1550. 83. Greenfield D, Knighton R, Huang X. Effect of corneal polarization axis on assessment of retinal nerve fiber layer thickness by scanning laser polarimetry. Am J Ophthalmol. 2000;129(6):715722. 84. Götzinger E, Pircher M, Dejaco-Ruhswurm I, Kaminski S, Skorpik C, Hitzenberger C. Imaging of birefringent properties of keratoconus corneas by polarization-sensitive optical coherence tomography. Invest Ophthalmol Vis Sci. 2007;48(8):3551-3558. 85. François J, Victoria-Troncoso V. The Cornea in Normal Condition and in Groenouw’s Macular Dystrophy. Springer Science & Business Media 2012. 86. Alexander R, Garner A. Elastic and precursor fibres in the normal human eye. Exp Eye Res. 1983;36:305-315. 87. Newton RH, Meek KM. The integration of the corneal and limbal fibrils in the human eye. Biophys J. 1998;75(5):2508-2512. 88. Newton RH, Meek KM. Circumcorneal annulus of collagen fibrils in the human limbus. Invest Ophthalmol Vis Sci. 1998;39(7):112534. 89. Boote C, Hayes S, Young R, et al. Ultrastructural changes in the retinopathy, globe enlarged (rge) chick cornea. J Struct Biol. 2009;166(2):195-204. 90. Quantock AJ, Dennis S, Adachi W, et al. An annulus of collagen fibrils in the mouse cornea and alterations in the form of hereditary keratoconus. Invest Ophthalmol Vis Sci. 2003;44(5):19061911. 91. Sheppard J, Hayes S, Boote C, Votruba M, Meek K. Changes in corneal collagen architecture during mouse postnatal development. Invest Ophthalmol Vis Sci. 2010;51(6):2936-2942. 92. Winkler M, Chai D, Kriling S, et al. Nonlinear optical macroscopic assessment of 3-D corneal collagen organization and axial biomechanics. Invest Ophthalmol Vis Sci. 2011;52(12):8818-8827. 93. Abass A, Hayes S, White N, Sorensen T, Meek K. Transverse depth-dependent changes in corneal collagen lamellar orientation and distribution. J R Soc Interface. 2015;12(104):20140717. 94. Nottingham J. Practical Observations on Conical Cornea, and on the Short Sight, and Other Defects of Vision Connected With It. London, UK: John Churchill 1854. 95. Romero-Jiméneza M, Santodomingo-Rubidob J, Wolffsohnc J. Keratoconus: A review. Cont Lens Anterior Eye. 2010;33(4):157166. 96. Davidson A, Hayes S, Hardcastle A, Tuft S. The pathogenesis of keratoconus. Eye. 2014;28:189-195. 97. Somodi S, Hahnel C, Slowik C, Richter A, Weiss DG, Guthoff RF. Confocal in vivo microscopy and confocal laser-scanning fluorescence microscopy in keratoconus. Ger J Ophthalmol. 1996;5(6):518-525. 98. Elsheikh A, Alhasso D, Rama P. Assessment of the epithelium’s contribution to corneal biomechanics. Exp Eye Res. 2008;86(2):445-451. 99. Seiler T, Matallana M, Sendler S, Bende T. Does Bowman’s layer determine the biomechanical properties of the cornea? Refract Corneal Surg. 1992;8:139-142.

K.M. Meek and S. Hayes 100. Määttä M, Heljasvaara R, Sormunen R, Pihlajaniemi T, Autio-Harmainen H, Tervo T. Differential expression of collagen types XVIII/endostatin and XV in normal, keratoconus, and scarred human corneas. Cornea. 2006;25:341-349. 101. Määttä M, Väisänen T, Väisänen M, Pihlajaniemi T, Tervo T. Altered expression of type XIII collagen in keratoconus and scarred human cornea; increased expression in scarred cornea is associated with myofibroblast transformation. Cornea. 2006;25:448-453. 102. Chaerkady R, Shao H, Scott S-G, Pandey A, Jun A, Chakravarti S. The keratoconus corneal proteome: Loss of epithelial integrity and stromal degeneration. J Proteomics. 2013;87:122-131. 103. Beardsley T, Foulks G. An association of keratoconus and mitral valve prolapse. Ophthalmol 1982;89(1):35-37. 104. Robertson I. Keratoconus and Ehlers-Danlos syndrome: a new aspect of keratoconus. Med J Aust 1975; 1: 571-573.99. 105. White TL, Lewis PN, Young RD, Kitzawa K, Inatomi T, Kinsoshita S, Meek KM. Elastic microfibril distribution in human keratoconic cornea. Exp Eye Res 2017; 159: 40-48. 106. Patey A, Savoldelli M, Pouliquen Y. Keratoconus and normal cornea: A comparative study of collagenous fibers of the corneal stroma by image analysis. Cornea. 1984;3:119-124. 107. Fullwood NJ, Tuft SJ, Malik NS, Meek KM, Ridgway AEA, Harrison RJ. Synchrotron x-ray diffraction studies of keratoconus corneal stroma. Invest Ophthalmol Vis Sci. 1992;33(5):1734-1741. 108. Teng CC. Electron microscope study of the pathology of keratoconus: part 1. Am J Ophthalmol. 1963;55:18-47. 109. Polack FM. Contributions of electron microscopy to the study of corneal pathology. Surv Ophthalmol. 1976;20:375-414. 110. Kenney M, Chwa M, Opbroek AJ, Brown DJ. Increased gelatinolytic activity in keratoconus cultures. A correlation to an altered matrix metalloproteinase-2/tissue inhibitor of metalloproteinase ratio. Cornea. 1994;13(2):114-124. 111. Sherwin T, Brookes NH, Loh IP, Poole CA, Clover GM. Cellular incursion into Bowman’s membrane in the peripheral cone of the keratoconic cornea. Exp Eye Res. 2002;74(4):473-482. 112. Rehany U, Lahav M, Shoshan S. Collagenolytic activity in keratoconus. Ann Ophthalmol. 1982;14(8):751-754. 113. Collier SA. Is the corneal degradation in Keratoconus caused by matrix-metalloproteinases? Clin Experiment Ophthalmol. 2001;29:340-344. 114. Zhou LL, Sawaguchi S, Twining SS, Sugar J, Feder RS, Yue BY. Expression of degradative enzymes and protease inhibitors in corneas with keratoconus. Invest Ophthalmol Vis Sci. 1998;39:1117-1124. 115. Bron AJ. Keratoconus. Cornea. 1988;7(3):16316-9. 116. Morshige N, Wahlert A, Kenney M, et al. Second harmonic imaging microscopy of normal and keratoconus cornea. Invest Ophthalmol Vis Sci. 2007;48(3):1087-1094. 117. Radner W, Zehetmayer M, Skorpik C, Mallinger R. Altered organization of collagen in the apex of keratoconus corneas. Ophthalmic Res. 1998;30(5):327-332. 118. Hayes S, Khan S, Boote C, et al. Depth profile study of abnormal collagen orientation in keratoconus corneas. Arch Ophthalmol. 2012;130(2):251-252.

Copyright © 2018. Kugler Publications. All rights reserved.

Corneal stroma: collagen ultrastructure and orientation in health and disease 119. Hayes S, Boote C, Tuft SJ, Quantock AJ, Meek KM. A study of corneal thickness, shape and collagen organisation in keratoconus using videokeratography and X-ray scattering techniques. Exp Eye Res. 2007;84(3):423-434. 120. Meek KM, Tuft SJ, Huang Y, et al. Changes in collagen orientation and distribution in keratoconus corneas. Invest Ophthalmol Vis Sci. 2005;46(6):1948-1956. 121. Edmund C. Corneal tissue mass in normal and keratoconic eyes. Acta Ophthal. 1988;66:305-308. 122. Ambrosio R, Alonso RS, Luz A, Velarde LGC. Corneal-thickness spatial profile and corneal-volume distribution: Tomographic indices to detect keratoconus. J Cataract Refract Surg 2006; 32: 1851-1859 123. Fontes BM, Ambrosio R, Jardim D, Verlarde GC, Nose W. Ophthalmology 2010; 117:673-679. 124. Akhtar S, Bron A, Salvi S, Hawksworth N, Tuft S, Meek K. Ultrastructural analysis of collagen fibrils and proteoglycans in keratoconus. Acta Ophthalmol. 2008;86(7):764-772. 125. Funderburgh JL, Panjwani N, Conrad GW, Baum J. Altered keratan sulphate epitopes in keratoconus. Invest Ophthalmol Vis Sci. 1989;30(10):2278-2281. 126. Dudakova L, Jirsova K. The impairment of lysyl oxidase in keratoconus and in keratoconus-associated disorders. J Neural Transm. 2013;120:977-982. 127. Edmund C. The corneo-limbal ring in normal and keratoconic eyes. Acta Ophthamol. 1988;66:376-380. 128. Owens H, Watters GA. Evaluation of keratoconic cornea using computerised corneal mapping and ultrasonic measurements of corneal thickness. Opthalmic Physiol Opt. 1996;16(2):115123. 129. Brautaset R, Nilsson M, Miller W, Leach N, Tukler J, Bergmanson J. Central and peripheral corneal thinning in keratoconus. Cornea. 2013;32(3):257-261. 130. Koster M, Boote C, Meek K, et al. Inter- and intra-lamellar slippage of collagen fibrils as a potential mechanism of keratoconus progression. Invest Ophthalmol Vis Sci. 2013;54(15):1642. 131. O’Brart D, Kwong T, Patel P, McDonald R, O’Brart N. Long-term follow-up of riboflavin/ultraviolet A (370 nm) corneal collagen cross-linking to halt the progression of keratoconus. Br J Ophthalmol. 2013;97(4):433-437. 132. Hayes S, Kamma-Lorger C, Boote C, et al. The effect of riboflavin/UVA collagen cross-linking therapy on the structure and hydrodynamic behaviour of the ungulate and rabbit corneal stroma. PLoS One. 2013;8:e52860. 133. Wollensak G, Spörl E, Mazzotta C, Kalinski T, Sel S. Interlamellar cohesion after corneal crosslinking using riboflavin and ultraviolet A light. Br J Ophthalmol. 2011;95:876-880. 134. Wollensak G, Spoerl E, Seiler T. Stress-strain measurements of human and porcine corneas after riboflavin-ultraviolet-A-induced cross-linking. J Cataract Refract Surg. 2003;29(9):17801785.

29

135. Cintron C, Hassinger L, Kublin C, Cannon D. Biochemical and ultratructural changes in collagen during corneal wound healing. J Ultrastruct Res. 1978;65:13-22. 136. Connon CJ, Meek KM. The structure and swelling of corneal scar tissue in penetrating full-thickness wounds. Cornea. 2004;23(2):165-171. 137. Kamma-Lorger C, Hayes S, Boote C, Burghammer M, Boulton M, Meek K. Effects on collagen orientation in the cornea after trephine injury. Mol Vis. 2009;15:378-385. 138. Hayes S, Young R, Boote C, Hawksworth N, Huang Y, Meek K. A structural investigation of corneal graft failure in suspected recurrent keratoconus. Eye. 2010;24:728-734. 139. Boote C, Dooley E, Gardner S, et al. Quantification of Collagen Ultrastructure after Penetrating Keratoplasty – Implications for Corneal Biomechanics. PLoS One. 2013;8(7): e68166. 140. Rawe IM, Meek KM, Leonard DW, Takahashi T, Cintron C. Structure of corneal scar tissue - an x-ray-diffraction study. Biophys J. 1994;67(4):1743-1748. 141. Kamma-Lorger C, Boote C, Hayes S, Albon J, Boulton M, Meek K. Collagen ultrastructural changes during stromal wound healing in organ cultured bovine corneas. Exp Eye Res. 2009;88:953959. 142. Cintron C, Schneider H, Kublin C. Corneal scar formation. Exp Eye Res. 1973;17:251-259. 143. Gerrit R, Melles J, Binder P. A Comparison of Wound Healing in Sutured and Unsutured Corneal Wounds. Arch Ophthalmol. 1990;108(10):1460-1469. 144. Morrison J, Swan K. Full-thickness lamellar keratoplasty. A histologic study in human eyes. Ophthalmol. 1982;89:715-719. 145. Abahussin M, Hayes S, Edelhauser H, Dawson D, Meek K. A microscopy study of the structural features of post-LASIK human corneas. PLoS One. 2013;8(5):e63268. 146. Calkins J, Hochheimer B, Stark W. Corneal wound healing: holographic stress-test analysis. Invest Ophthalmol Vis Sci. 1981;21:322-334. 147. Pettinelli D, Starr C, Stark WJ. Late traumatic corneal wound dehiscence after penetrating keratoplasty. Arch Ophthalmol. 2005;123:853-856. 148. Holt D, Sikder S, Mifflin M. Surgical management of traumatic LASIK flap dislocation with macrostriae and epithelial ingrowth 14 years postoperatively. J Cataract Refract Surg. 2012;38:357361. 149. Kim H, Silverman C. Traumatic dislocation of LASIK flaps 4 and 9 years after surgery. J Refract Surg. 2010;26:447-452. 150. Smelser G, Polack F, Ozanics V. Persistence of donor collagen in corneal transplants. Exp Eye Res. 1965;4:349-354. 151. Meek KM, Newton RH. Organization of collagen fibrils in the corneal stroma in relation to mechanical properties and surgical practice. J Refract Surg. 1999;15(6):695-699.

Copyright © 2018. Kugler Publications. All rights reserved.

3. Acoustic radiation force elastic microscopy and corneal structural correlation Eric Mikula1, Donald J. Brown1,2, Moritz Winkler2, Elena Koudouna3, Tibor Juhasz1,2, James V. Jester1,2 Gavin Herbert Eye Institute, School of Medicine, University of California, Irvine, USA; 2Department of Biomedical Engineering, University of California, Irvine, USA; 3Structural Biophysics Research Group, School of Optometry and Vision Sciences, Cardiff University, Cardiff, Wales, UK

1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction The human eye consists of two elements which focus light onto the retina, namely, the cornea and the crystalline lens. These two components provide the eye with an optical power of 60 diopters, D, with the cornea providing roughly two-thirds of the total power. Thus, the air-anterior cornea boundary is paramount to maintaining normal vision and even slight alterations to this surface can cause significant optical aberrations and reduce the quality of vision. The mechanical properties of the cornea are inextricably related to its physical structure, much in the same way as the mechanics of a bridge are tied to the spatial organization of the trusses and beams that it comprises. Understanding corneal biomechanics can provide valuable insight when considering disorders such as keratoconus as well as information regarding the response of the cornea to refractive surgeries or UVA corneal crosslinking. Numerous methods have been used to evaluate corneal elasticity, including strip testing, globe inflation, atomic force microscopy (AFM), Brillouin microscopy, optical coherence tomography (OCT) elastography, and various ultrasonic methods. Earlier methods, such as globe inflation and strip testing treated the cornea as a homogenous material, measuring a bulk material property, while latter methods such as AFM sought higher spatial ­resolution.1-9 The reported elastic moduli in these studies vary by several orders of magnitude

depending on the measurement modality. In addition to measurement methodology, this variation in corneal elasticity is attributed to the anisotropy in stromal architecture, and particularly in the collagen fibril organization, which greatly defines the mechanical properties of tissues. While there has been significant progress in the field, there is no consensus concerning corneal biomechanics, especially when considering the spatial distribution of mechanical properties both radially and along the optical axis. 1.1. Corneal biomechanics and structure review The unique collagen structure of the human cornea plays a pivotal role in the maintenance of corneal shape, biomechanics, and in turn, visual acuity. Briefly, collagen fibrils, 32-34 nm in diameter,10 are arranged into collagen lamellae which are 0.2-2.0 µm thick and 5-200 µm wide.11 The lamellae run limbus to limbus, where they merge with scleral fibers and are stacked in layers with approximately 240 lamellae in the central cornea.12 X-ray scattering has revealed that collagen lamellae have a bulk preferred orthogonal orientation with respect to one another in the nasal-temporal and inferior-superior directions.13 As these lamellae approach the limbus, they adapt a tangential orientation and merge with the circumferential fibril population of the limbal annulus.14 Second harmonic generation microscopy (SHG) has revealed that lamellae are randomly oriented in the sample plane, but show extensive branching and interweaving with one another in the anterior stroma

Correspondence: James V. Jester, 843 Health Sciences Road, Hewitt Hall, Room 2036, University of California, Irvine, Irvine, CA, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 31-43 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

Copyright © 2018. Kugler Publications. All rights reserved.

32

running at oblique angles relative to anterior limiting lamina (ALL, Bowman’s layer), while in the posterior cornea, lamellae run parallel to the anterior and posterior limiting lamina with minimal intertwining.15-17 Bow-spring like lamellae have also been observed by SHG, which extend from the ALL and intertwine with deeper fibers before reinserting back into the ALL.16,18,19 The varying structural properties in the cornea suggest that there are also varying mechanical properties spatially. Indeed, recent studies have found increased mechanical stiffness in the central anterior cornea twoto three-fold higher than the posterior cornea.16,20,21 An important difference exists between the lamellar structure of the anterior and posterior cornea. There is significant interweaving and bifurcation of stromal lamellae in the anterior cornea, with lamellae diverging from the parallel orientation and inserting upward into Bowman’s layer.11,22-24 Transmission electron microscopy shows that collagen fibril bundles in the anterior stroma branch and insert into the ALL at a density of 5.4 ± 0.8 insertions per 100 µm. Likewise, ALL originating fibril bundles appeared to insert into the anterior stroma at a rate of 29.8 bundles per 100 µm.24 Non-linear optical high-resolution macroscopy (NLO-HRMac) allows one to obtain a 3-D structural map of collagen structural organization from limbus to limbus. NLO-HRMac 3-D representations of the corneal collagen organization revealed that in the anterior corneal stroma collagen lamellae that insert into Bowman’s layer branch numerous times along their length and additionally they combine with other collagen lamellae that also insert into Bowman’s layer.15 It has been therefore speculated that a 3-D “leaf spring” is created that might have significant mechanical effects for the control of corneal shape.15 Furthermore, the degree of lamellar branching appears to be markedly higher in the anterior corneal stroma in contrast to mid and posterior stroma, which exhibited almost no branching at all.16,17 Figure 1 is an NLO-HRMac reconstruction illustrating anterior interweaving compared to the relative parallel orientation of collagen lamellae in the posterior cornea. In an effort to further quantify the interweaving of anterior stroma and the ALL, NLO-HRMac was used to measure lamellar branching point density (BPD). BPD is defined as the number of times a lamellae branches or bifurcates per millimeter, and is a measure of collagen fiber connectivity. It was found that BPD decreases

E. Mikula et al.

Fig. 1. NLO-HRMac reconstruction illustrating anterior interweaving compared to the relative parallel orientation of collagen lamellae in the posterior cornea.

from 26.6/mm just beneath the ALL to 8.7/mm halfway through the stroma.16 These findings suggest that not only do collagen fibers from the anterior stroma insert into the ALL, but actually intertwine with the ALL. Additionally, this study correlated BPD with elastic modulus at varying depths in the central cornea using needle indentation elastography. The anterior region with elevated branching density was found to be nearly twice as stiff as the mid and posterior regions. This finding was supported by earlier works which found that lamellar interweaving markedly increases interlamellar cohesive strength25,26 and protects the anterior region of the cornea against extreme swelling.27 As mentioned earlier, the biomechanical properties of the cornea are inherently linked to corneal structure; it should come as no surprise that methods to quantify these mechanical properties have been the subject of much research throughout the years. 1.2. Methods to measure corneal elasticity The reported values of corneal elasticity in the literature span several orders of magnitude, ranging from a few kilopascals to tens of megapascals.1-3,16,28 The reported values depend largely on the type of elastography methodology employed. Additionally, the type of elastic modulus varies in the reported values. Namely, the three most prominent are the tensile modulus, the compressive modulus, and the shear modulus. Whereas a traditional tensile strip test measures tissue strength along the direction of collagen fiber orientation, a compressive test evaluates the resistance of the cornea to compression along the

Copyright © 2018. Kugler Publications. All rights reserved.

Acoustic radiation force elastic microscopy and corneal structural correlation

optical axis through the corneal thickness. The shear modulus is a measure of the resistance of adjacent layers to ‘sliding’ past one another. In the classic approach of strip testing, a rectangular-shaped sample is excised from the cornea and is then mechanically stretched with increasing force to calculate stress-strain curves. Early strip testing determined the tensile elastic modulus of the human cornea to be roughly 4-14 MPa at a strain of 4%.1-3 Similarly, globe inflation methods yielded values of 1025 MPa to 17 MPa.4-8,29 Both methods lack the ability to measure the local spatial distribution of elastic properties, and essentially measure the bulk tensile strength of parallel collagen fibers without the potential for depth resolution in the measurements. AFM has been used to measure the depth dependence of the elastic modulus in the sectioned cornea.30 Reported values were in the tens of KPa. In a different study, the measurement of the transverse shear modulus at varying depths was described using torsional rheometry.31 Both these methods involved physically sectioning the corneal sample to access the different layers, also having limitations in depth and lateral resolution. However, interesting differences in mechanical properties between the anterior and posterior cornea were observed. Various ultrasonic methods have also been developed for probing the elastic properties of tissues. These methods involve a mechanical perturbation of the tissue and subsequent ultrasound imaging of the resultant tissue strain. Shear wave elasticity imaging uses a focused acoustic radiation force to generate shear waves within the cornea. The transverse strain generated by the shear waves is imaged and related to the shear elasticity of the tissue.32 The force is generated through a change in momentum of high intensity acoustic waves as they are partially absorbed within the focal volume. The amount of force generated is related to the acoustic intensity and the tissue absorption coefficient. Using focused ultrasound to generate body force within a tissue has the distinct advantage of being capable of palpating localized volumes within a tissue that would otherwise be inaccessible. Supersonic shear imaging also uses focused acoustic radiation force to generate shear waves within a tissue which are imaged and related to elasticity. The acoustic radiation force is sequentially focused at increasing depths within the sample at a rate that is faster than the speed of the shear

33

wave (i.e., supersonic), which typically has a velocity of just a few meters per second. The resultant shear waves constructively interfere and create high-amplitude plane-shear waves along the Mach cone.33,34 The shear wave is imaged via tracking the strain-induced speckle in the tissue, with shear wave velocity being related to elasticity. Supersonic shear imaging has been used to evaluate the efficacy of photodynamic Riboflavin/ UVA induced corneal crosslinking (CXL) and has shown an increase of roughly 460% in Young’s modulus as a result.34 Surface wave elastometry measures the speed of acoustic surface waves travelling parallel to the orientation of corneal collagen fibers and relates the propagation velocity to elasticity.35 Similarly, OCT has been used to measure shear wave speed in the cornea in response to mechanical perturbation of the corneal surface by a wire.36 A variation of this method used an acoustic radiation force to perturb the tissue while using OCT to image the tissue vibration.37,38 Acoustic radiation force impulse (ARFI) imaging uses high-intensity, focused ultrasound pulses to directly induce a displacement in the tissue. The displacement of the tissue is tracked using pulse-echoes and is related to the mechanical properties of the tissue.39 A similar method images corneal strain induced by a metal plate using an ultrasound elasticity microscope.40,41 The ultrasound elasticity imaging techniques described above rely on speckle-tracking methods to create the strain images. Elastic properties are calculated from the complex displacement field. Difficulties with these techniques arise from the cornea being a weak absorber of ultrasound. This results in small tissues displacements which must then be imaged via acoustic speckle tracking. Furthermore, the cornea is relatively anechoic and has limited ultrasonic speckle, further compounding the problem of imaging minute tissue strain. Brillouin microscopy has seen renewed interest in recent years due in part to non-conventional spectrometers with increased imaging speed and sensitivity in the GHz range.42 Brillouin scattering is an inelastic process where light interacts with thermally induced density fluctuations, also known as acoustic phonons.43,44 The phonons induce a frequency shift in the scattered light on the order of a few GHz. The frequency shift is related to the Brillouin elastic modulus of the material, which is typically measured in the gigapascal range for the cornea.

E. Mikula et al.

34

2. Acoustic radiation force elastic microscopy (ARFEM)

Copyright © 2018. Kugler Publications. All rights reserved.

ARFEM uses a low-frequency, high-intensity acoustic force to displace a femtosecond laser generated microbubble, while using a high-frequency, low-intensity ultrasound to monitor the position of the microbubble within the tissue.45 The method has been used to measure age-related elasticity changes in the human lens.46 The elastic modulus is related to the displacement of the microbubble within the cornea rather than tissue strain. Unlike other ultrasonic elasticity methods, ARFEM does not rely on the absorption of acoustic energy to induce tissue strains large enough to image. Rather, acoustic radiation is used to perturb a temporary microbubble within the cornea. This is especially useful since the cornea is relatively anechoic and a weak absorber of acoustic energy. The acoustic impedance mismatch between the cornea and gas bubble is sufficiently large, such that the bubble is essentially a perfect reflector of acoustic energy. Compared with a perfect absorber, a perfect reflector experiences two times the body force as the acoustic waves are not only stopped, but reversed as well. ARFEM has the advantage of improved depth resolution over other ultrasonic methods as the elasticity measurement is localized to the exact position of a microscopic bubble. This is in part due to the high transmission of visible and near infrared light in the cornea, which is well above 90% at 800 nm.46 The local elasticity is simply related to bubble displacement as opposed to a complex strain image. The location of the elasticity measurement depends solely on the location of the bubble, which can be created anywhere without the need to section the cornea. 2.1. Principle of ARFEM Elasticity measurements in the simplest terms are analogous to the well-known Hooke’s law: F = kx. (1) Hooke’s law states the amount of force, F, required to distend or compress a spring by a given distance, x, is proportional to that distance. The constant of proportionality, k, is the stiffness of the spring, or spring constant. While this relation is applicable specifically to

a linearly elastic spring, the underlying idea is the same for other elasticity measurements. Some known force is imparted on the material of interest (i.e., the cornea) and the response of the material is observed. Generally, the goal is to quantify the relationship between stress and strain in a material, otherwise known as the constitutive relation in a structural analysis. Stress, σ, in the simplest case is a force, F, applied to a material over the cross-sectional area, A, of the applied force or: σ = F/A. (2) Strain, ε, is a measure of the deformation of the material in response to the stress, and is given by: ε = ∆L/L. (3) The elastic modulus, E, is defined as the ratio between stress and strain. Strip testing, for example, is a straightforward application of the generalization above.1-3,47 A rectangular corneal strip of known dimension is put under tensile stress while the amount of stretch (strain) is measured. The elastic modulus is then directly calculated by dividing the stress by the strain. Globe inflation elasticity measurements add a level of complexity by keeping the globe intact. The tensile stress is applied by varying the intraocular pressure, while the strain is measured somewhat indirectly via surface marker displacements.4-8,29 Following this reasoning, numerous ultrasonic techniques have been used to evaluate corneal tissue response to an acoustic radiation force. A distinct advantage of using an acoustic radiation force to induce strain is the ability to remotely palpate at any arbitrary location within the tissue. Since the cornea fundamentally lacks endogenous reflectors of acoustic energy, these methods rely on the absorption of acoustic energy to generate a body force within the tissue. A body force acts throughout the volume of a body, which in this case is determined by the focusing geometry of the high-intensity transducer. If an acoustic wave is partially absorbed, there is necessarily a change in momentum of the propagating wave. By Newton’s second law, a change in momentum results in a body force acting on the absorbing volume within the medium, given by: F = dp/dt, (4)

Acoustic radiation force elastic microscopy and corneal structural correlation

Copyright © 2018. Kugler Publications. All rights reserved.

where F is force and p is momentum. The body force generates small displacements within the tissue which are tracked by low-intensity ultrasound imaging pulses or OCT. Speckle-tracking algorithms are typically used to render images of the tissue displacement within the absorbing volume as well as in the immediate vicinity. This information is used to calculate the elastic properties of the interrogated volume. However, calculation of local elasticity is hindered by the complex strain field as well as the irregular shape of the interrogated region occupying the focal volume of the transducer. ARFEM circumvents the problem of complex strain fields and irregular interrogation volumes by introducing an exogenous acoustic reflector to the cornea in the form of a femtosecond laser generated microbubble.20,48 Since the method relies on reflection of acoustic energy, the force generated is not a body force but rather a normal point force, simplifying calculations. Furthermore, reflection is a far more effective avenue for generating acoustic radiation force when compared to attenuation. 2.2. ARFEM theory During an ARFEM measurement, a force is imparted on a microbubble embedded within an elastic medium, resulting in a displacement of the bubble. The acoustic force is turned off, after which the bubble returns to its original position. Meanwhile, a low-intensity imaging ultrasound tracks the displacement of the bubble. The generation of an acoustic force needs to be considered, as well the bubble/medium response to the force. Ultrasound waves are pressure waves and carry momentum. In an elastic medium, a wave is either absorbed, reflected, or transmitted. For example, in a perfectly absorbing medium, the acoustic wave is totally absorbed, resulting in a change in momentum from a finite amount to zero. By Newton’s second law, a change in momentum results in a force. In this case, it is the acoustic radiation force. A more efficient way of generating acoustic radiation force is through reflection, as the wave is first stopped and then reversed. Thus, perfect reflection generates twice the force of perfect absorption. The cornea is not an efficient absorber, nor does it possess significant inhomogeneities to reflect/scatter acoustic energy. However, the boundary between an aqueous medium such as the cornea and a

35

gaseous bubble is nearly a perfect reflector, as given by: 2,

Z2 - Z1 ​ ​​​  ​​ (5) ​ = ​​​ ​ ​ _ R ( Z2 + Z1  )

where R is the reflection coefficient at the cornea/gas boundary, and Z1 and Z2 are the acoustic impedances of the two materials (412 and 1.50 x 106 (Pa∙s)/m for air and cornea, respectively). This results in a reflection coefficient of 0.999 for the acoustic wave reaching the bubble within the cornea. The acoustic radiation pressure can be written as: I

​P = (​ 1 + R2)​ _​ c ​.  ​ (6) where R is the reflection coefficient, I is the average acoustic intensity, and c is the speed of sound.49,50 Since the reflection coefficient is close to unity in the case of a bubble in the cornea, Equation (6) reduces to: I

​P = 2 _​ c .​  (7) The acoustic radiation pressure imparts a force normal to the cross-sectional area of the microbubble. The acoustic radiation force is given by: 2Iπa2 ​F = _ ​  c ​​, (8)  

where a is the bubble radius. The intensity of the focused ultrasound can be experimentally determined using a calibrated hydrophone, while the bubble radius can be measured directly using a microscope. Next, the movement of the bubble in response to the acoustic radiation force and the relationship between the displacement and elasticity need to be considered. The response of a viscoelastic tissue mimicking phantom to an acoustic radiation force impulse is described using the classic Voigt model.51 The Voigt model consists of an elastic element in parallel with a viscous or damping element. The model proposes that the force applied to the tissue is opposed by an elastic force proportional to displacement, and a viscous force proportional to the velocity of displacement. The differential equation is formulated as: dx

F​ = ​γ _  ​​dt ​​  + kx (9) In Equation (9), F is the applied force, x is the displace-

E. Mikula et al.

36

ment, γ is the drag coefficient, and k is the spring coefficient. Solving the differential for a force, F, applied at t = 0, gives:  τ   ) ​ ​]​​ , (10) ​x(t) = _​ k ​ [​ 1 - exp ​(-​_ t

F

where τ = γ/k and is the relaxation time constant. The bubble is rapidly displaced at first; then, the displacement tapers off at some point depending on the value of τ. Maximum displacement happens once velocity has gone to zero and there are no longer viscous forces (t >> τ), with only spring force remaining, giving: F ​​ ​xmax = _​ k . (11)

The maximum displacement of the bubble is proportional to the applied acoustic radiation force and inversely proportional to the spring constant, or Young’s modulus. Once the acoustic radiation force is turned off, the bubble should return to the original position following an exponential decay: ​ - ​_  τ   ) ​ ​​ . (12) ​x(t) = _ ​ k ​exp ( F

t

Copyright © 2018. Kugler Publications. All rights reserved.

This simple model gives a good insight into the general expected behavior of a bubble embedded in an elastic medium in response to an acoustic force. Figure 2 shows the expected path of a bubble in a viscoelastic medium in response to an acoustic radiation force . Despite the utility of the Voigt model in understand-

ing the general behavior of a viscoelastic medium in response to a force impulse, the behavior of a bubble in an acoustic field requires special consideration. The effect of radiation force on solid spheres embedded in a viscoelastic medium was studied, showing that the movement of the sphere could be used to calculate local elastic properties.52 More recently, the formation and oscillation of bubbles under acoustic fields has been investigated.53-55 The displacement of a bubble in an elastic, homogeneous, isotropic, and incompressible medium in response to an acoustic radiation force was specifically investigated in the linear approximation.56 Unlike a bubble within a liquid, a bubble in an elastic medium will only be displaced as long as the radiation force is greater than the resistive forces arising from the elastic properties of the tissue. The displacement of the bubble in polar coordinates can be written as: Fr cos ​(θ )​

(13) ​xr = ​ ______ 4πEa   ​​ Frsin ​(θ )​

​xθ = ​​  ​______ . (14) 8πEa   ​​ In ARFEM, the acoustic radiation force is applied normal to the surface of the cornea and measures the axial displacement of the bubble surface. In this respect, we are interested in the radial component of the displacement where θ = 0. Thus Equation (14) is reduced to zero while Equation (13) for displacement along the radial axis is reduced to: Fr

​ 4πEa     , (15) ​​ ​xr = _ where x is the maximum displacement of the bubble, Fr is the acoustic radiation force, E is the elastic modulus of the cornea, and a is the radius of the bubble. Substituting Equation (8) in for the acoustic radiation force Fr and rearranging to solve for E, we arrive at the elastic modulus acquired from an ARFEM measurement: Ia

​E = ​ _ ​​ 2cx     . (16) max

Fig. 2. Theoretical displacement path of a bubble in a viscoelastic medium in response to an acoustic radiation force.

The intensity, I, and bubble radius, a, are calibrated beforehand, and c is defined as the speed of sound in water (1500 m/s), while the bubble radius and maximum displacement, xmax, is measured experimentally. In this way, we can calculate the Young’s modulus of the cornea. The bubble radius can either be directly

Acoustic radiation force elastic microscopy and corneal structural correlation

measured optically or a relation between bubble radius and the amplitude of the bubble signal can be derived. Maximum bubble displacement will be in the range of 10 µm.

Copyright © 2018. Kugler Publications. All rights reserved.

2.3. ARFEM system Figure 3 illustrates the schematics of the ARFEM system. A femtosecond laser is focused into the focal volume of a dual element, confocal ultrasound transducer. A laser pulse creates a bubble at the desired location in the cornea or gelatin sample. Next, focused ultrasound from the force-generating element pushes on the bubble while the inner-tracking element monitors the axial position of the bubble with an A-scan. The sample chamber is mounted to a 3-D micro-stage enabling precise positioning of the bubble within the cornea. The laser and ultrasound foci remain fixed and aligned with each other. A commercial Ti:sapphire femtosecond laser (Coherent Inc., Santa Clara, CA, USA) is used to create microbubbles in the samples. The laser produces 130 fs pulses at 800 nm wavelength. The beam is focused through a 0.3 NA objective with a working distance of 40 mm. Pulse energy of 80 µJ is used for bubble creation. The ultrasound transducer used to probe the microbubble was custom-built by the National Institutes of Health Resource Center for Ultrasonic Transducer Technology at the University of Southern California. The transducer consists of two confocal elements. The bubble tracking element (inner) is a

Fig. 3. Experimental setup. The corneal sample and acoustic tank are placed on a 3-D positioning stage that can move independently of the laser and transducer.

37

piezoelectric, 1-3 PZT crystal with a diameter of 15 mm and has a center frequency of 17 MHz with an f-number of 2.9. The high-intensity focused ultrasound (HIFU), acoustic radiation force generating element (outer) is a PZT-4 crystal with a 30 mm diameter and has a center frequency of 1.7 MHz with an f-number of 1.4. Both have a focal length of 41 mm. The spatial peak, pulse average intensity, Isppa, of the force generating element is 125 Watts/cm2. Synchronization between the force element, imaging element, and digitizing board is necessary to ensure that the position of the bubble is measured exactly when the force is turned off. The tracking element is driven by a commercial pulser-receiver (Panametrics Model 5072PR, Waltham, MA, USA) at a pulse repetition frequency of 5 kHz, giving one A-scan every 200 µs. The pushing element is driven by an arbitrary function generator (Agilent Technologies Model 3314a, Palo Alto, CA, USA) feeding a 50 dB amplifier (ENI Model 240L, MKS Instruments, Wilmingtom, MA, USA). RF signals from the tracking element are captured by a digitizing board (Agilent Technologies, Palo Alto, CA) on a PC sampling at 100 MS/s. All components are synchronized to a 10 MHz master clock. Furthermore, the A-scan tracking pulses are synchronized with an additional tunable delay to ensure that the tracking pulse train can be moved with respect to the acoustic radiation force. A typical measurement contains three distinct portions: 1. 1 ms before the acoustic force is applied; 2. the 2 ms during the acoustic force during which the bubble is displaced; and 3. between 4 and 6 ms after the acoustic force is turned off as the bubble returns to its original position. The raw 1-D RF data is sectioned and stacked into a 2-D array, where each column represents a single A-scan. A single A-scan represents the time of flight of the ultrasound pulse from the transducer, to the surface of the bubble, and back to the transducer. The time of flight is directly related to the axial distance of the bubble surface from the transducer surface. The pulser-receiver triggers the A-scan at a 5 kHz pulse repetition frequency, resulting in a 1-D image of the cornea and bubble in every 200 µs. Thus, the resulting M-scan describes the time evolution of the bubble movement in 200 µs steps. A typical M-scan measurement is

38

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. Sample M-scan from a swollen porcine cornea showing the position (y-axis) of the bubble as a function of time (x-axis) as well as the force pulse (vertical band). The y-axis spans about 2 mm, while the x-axis spans 9 ms. The sample 1-D slice represents just one of the A-scans at 7 ms time delay taken from the 2-D image.

presented in Figure 4. An M-scan is a series of A-scan pulse echoes plotted as a function of time. This figure was derived from a porcine eye and is used here solely for visualization of the actual measurement. The porcine cornea is thicker and softer than the human cornea, allowing for easier distinction of the anterior, posterior, and bubble surfaces. The vertical checkered band is the saturated acoustic radiation force pulse as detected by the tracking element. The figure shows the position of the anterior/posterior corneal surfaces and microbubble before, during, and after the chirped force pulse. The small inset figure shows one sample A-scan taken from the 2-D image. The bubble is displaced in the direction of the acoustic force and returns to its original position once the force pulse is turned off, as indicated by the arrow in Figure 4. This 2-D image is comprised of many individual A-scans (sample A-scan shown in Fig. 4) which show the movement of the microbubble in time in response to the HIFU force. Bubble displacement is calculated from the RF data using a 1-D phase-sensitive cross-correlation method between a reference bubble A-scan and the remaining A-scans.57 The cross-correlation algorithm computes the time lag between subsequent A-scans of the bubble and compares them to the reference A-scan (original bubble position). This method is capable of subsample resolution by using phase information in the complex correlation signal. The phase zero crossing corresponds to the peak time lag between signals and is directly related to the displacement by y = tc/2, where y is displacement, t is the time lag, and c is the speed of sound in water (1500 m/s). In addition to imparting a force on the bubble, the force also induces a strain in the gelatin

E. Mikula et al.

medium containing the cornea. This is analogous to the strain induced in ARFI strain imaging. In the case of ARFEM, this strain artificially inflates the displacement of the bubble and must be accounted for. The strain of the gelatin is estimated by tracking the surface of the gelatin and subtracting its displacement from that of the bubble. Differences in time of flight of the ultrasound pulse correspond to different depths of the reflector. Ultrasound transducers with center frequencies between 7 and 20 MHz have been successfully used to detect depth differences of a single micron.58,59

3. Corneal elasticity map and relation to structure The collagen ultrastructure is known to vary throughout the cornea both radially and through its thickness along the optical axis. Likewise, it is also thought that the mechanical properties also vary as a function of changing collagen structure. Most mechanical measurements have been limited to the central cornea; a map of corneal elasticity has remained elusive. Recently, ARFEM has been used to measure ex-vivo human corneal elasticity and varying depths from the central to the peripheral cornea.21 Measurements were taken in the central (0 mm), mid (2.5 mm), and peripheral cornea (5 mm) toward the limbus. At each of these locations, measurements were performed within 150 microns of the anterior and posterior surfaces of the cornea. The elastic modulus in the direction perpendicular to the corneal surface (normal) was found to vary with location in the cornea. In the anterior cornea, the

Fig. 5. Normal elastic modulus in the anterior 150 µm of the cornea from the center to the periphery.

Acoustic radiation force elastic microscopy and corneal structural correlation

39

Fig. 7. The mean elastic moduli for six corneal samples.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 6. Normal elastic modulus in the posterior 150 µm of the cornea from the center to the periphery.

mean elastic moduli for six human corneas were 4.2 ± 1.2 kPa, 3.4 ± 0.7 kPa, and 1.9 ± 0.7 kPa in the central, mid, and peripheral regions, respectively. These results are summarized in Figure 5. In the posterior cornea, the mean elastic moduli were 2.3 ± 0.7 kPa, 1.6 ± 0.3 kPa, and 2.9 ± 1.2 kPa in the central, mid, and peripheral regions, respectively. These results are summarized in Figure 6. While the anterior cornea was roughly twice as stiff as the posterior cornea in the central and mid cornea, the trend shifted toward the periphery with the anterior elastic modulus decreasing with respect to the posterior. A direct comparison of the anterior and posterior cornea is presented in Figure 7. The ARFEM technique in the current state has the significant limitation of being unable to measure the elasticity distribution in the mechanically loaded cornea and intact globe. Given the nature of the current ARFEM device, the cornea must be excised from the globe and placed between the laser objective and ultrasound. Additionally, the cornea is laid flat against the gelatin surface in such a way that half of the cornea curves unnaturally upward. The mechanical effect of this curvature is assumed to be negligible. Previous measurements in the central cornea with the natural radius of curvature preserved showed the same 2:1 ratio in elasticity between the anterior and posterior regions.20 With these limitations, ARFEM measurements found the elasticity in the central anterior cornea to be nearly twice the elasticity in the central posterior cornea. Similar results were found using needle indentation,

which revealed the same 2:1 ratio in elastic modulus between the anterior and posterior central cornea.16 Likewise, the mid anterior cornea was found to be twice as stiff as the mid posterior cornea. Structurally, the anterior cornea possesses a highly interwoven collagen structure compared to the relative homogeneity found in the posterior cornea. Despite this apparent correlation between microstructure and elasticity in the central and mid cornea, the trend was not observed in the peripheral cornea. The peripheral anterior cornea was found to be roughly half as stiff as the central anterior cornea, while the peripheral posterior cornea was found to be roughly 30% stiffer than the central posterior cornea. It is interesting to note that interlamellar cohesive strength in the stroma is twice as strong in the periphery as it is centrally.26 Although ARFEM does not measure interlamellar cohesive strength, both results suggest a biomechanical change in the peripheral cornea. Furthermore, the peripheral anterior corneal elasticity is roughly two-thirds that of the peripheral posterior cornea. It appears that, in the periphery, the anterior and posterior corneas nearly reverse elastic moduli relative to one another. However, anterior collagen interweaving does not differ significantly between the central and peripheral cornea.17 Using NLO-HRMac, collagen fiber angle distribution relative to the corneal surface was imaged radially along the cornea. The collagen angle relative to the surface was used as a metric for collagen interweaving. No statistical difference was found in collagen angles between the central and peripheral cornea. Figure 8 shows a typical image of the human cornea using this technique. The wrinkles on the posterior surface in Figure 8A are artifacts from the mounting of

40

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 8. HRMac images of collagen structure in the cornea. (A) Half of a human cornea from the center to the limbus. While the posterior lamellae continue uninterrupted into the sclera, the anterior interwoven region seems to end abruptly at the limbus. (B) Central, (C) mid, and (D) peripheral measurement locations, respectively.

the sample. Figures 8B, C, and D show that the anterior interweaving relative to posterior collagen orientation is preserved from the center to the periphery. However, structural differences in the periphery of the cornea as suggested by x-ray scattering may be masked by the potential shifting orientation of lamellae from central to peripheral. Structurally, the cornea may be changing as it nears the limbus, with collagen fibers adopting a more tangential (circumferential) orientation in the periphery that may not be detected by SHG imaging.60 Collagen fibers in this orientation would not have been detected in the previous work by Winkler et al.,15-17 as HRMac does not image en face collagen fibers. The effect of potential tangential oriented collagen fibers on local elasticity is unknown. Additionally, as the lamellae exit the cornea they transition into the structurally unique sclera. The biomechanical effects of this transition are unknown. Furthermore, the periphery may be subject to different swelling conditions because the peripheral edge of the sample is exposed directly to the gelatin medium. The cornea is indeed thicker in the periphery, and hydration differences between the anterior and posterior could be exacerbated by the proximity of the measurements to the edge of the sample. In addition to collagen microstructure, proteoglycan (PG) distribution throughout the cornea may

E. Mikula et al.

also have an effect on local elasticity as measured by ARFEM. Specifically, it is pertinent to explore any differences in PG distribution between the anterior and posterior cornea, both centrally and peripherally. PG consists of a core protein with one or more covalently attached glycosaminoglycans (GAG). GAGs are highly polar, negatively charged, and as such, strongly bind water. The concentration of keratan sulfate, the most prominent PG in the cornea, increases from anterior to posterior in the central cornea.61 Moreover, stromal swelling is almost entirely caused by the gel pressure (swelling pressure) generated by negatively charged PGs.62 When these findings are considered along with the highly interwoven structure of the anterior cornea, it seems reasonable that the anterior cornea is resistant to edema when compared to the posterior cornea.10,27 Peripherally, ARFEM results show that the anterior corneal elasticity is roughly half that of the central anterior cornea. With studies showing that collagen interweaving does not change between the center and periphery, this result is particularly interesting. As with the central cornea, it would be interesting to know the trend in PG distribution in the peripheral cornea. It is possible that local PG concentration and the resultant swelling pressure have an effect on local elasticity as measured by ARFEM. Unfortunately, the literature does not reveal many telling details about the differences in PG concentration between the central and peripheral cornea. One study looked at total soluble protein concentration between the anterior and posterior cornea, traversing across the cornea from the limbus to the central cornea. It found that total soluble protein concentration in the peripheral anterior cornea was nearly twice that of the central anterior cornea.63 Though it may appear that this result corroborates ARFEM findings between central and peripheral elasticity, the correlation could be entirely coincidental given that the study did not specifically measure PG distribution. To truly resolve this issue, a specific measurement of the axial PG gradient in the peripheral cornea would need to be performed. Such a gradient in PG concentration could affect local hydration, thus affecting elasticity. Overall, ARFEM shows that there is a unique distribution of elasticity both axially and radially throughout the cornea. While ARFEM results in the central cornea are in reasonable agreement with other techniques, including needle indentation, Brillouin microscopy,

Acoustic radiation force elastic microscopy and corneal structural correlation

and torsional rheometry, lack of mechanical data in the peripheral cornea make comparisons difficult. It is however clear that the full picture of corneal biomechanics is quite broad, involving complex and inhomogenous collagen microstructure to varying concentration of PGs throughout the cornea. A better understanding of these variables along with elasticity measurements, especially in the peripheral cornea, would certainly help in completing the picture.

References 1. 2.

3.

4.

5. 6. 7. 8. 9. 10.

Copyright © 2018. Kugler Publications. All rights reserved.

11.

12.

13.

14.

Nyquist GW. Rheology of the cornea: experimental techniques and results. Exp Eye Res. 1968;7:183-IN182. Hoeltzel DA, Altman P, Buzard K, Choe K. Strip extensiometry for comparison of the mechanical response of bovine, rabbit, and human corneas. J Biomech Eng. 1992;114:202-215. Zeng Y, Yang J, Huang K, Lee Z, Lee X. A comparison of biomechanical properties between human and porcine cornea. J Biomech. 2001;34:533-537. Woo SL, Kobayashi AS, Schlegel WA, Lawrence C. Nonlinear material properties of intact cornea and sclera. Exp Eye Res. 1972;14:29-39. Jue B, Maurice DM. The mechanical properties of the rabbit and human cornea. J Biomech. 1986;19:847-853. Shin TJ, Vito RP, Johnson LW, McCarey BE. The distribution of strain in the human cornea. J Biomech. 1997;30:497-503. Hjortdal JO. Extensibility of the normo-hydrated human cornea. Acta Ophthalmol Scand. 1995;73:12-17. Hjortdal JØ. Regional elastic performance of the human cornea. J Biomech. 1996;29:931-942. Scarcelli G, Pineda R, Yun SH. Brillouin optical microscopy for corneal biomechanics. Invest Ophthalmol Vis Sci. 2012;53:185-190. Boote C, Dennis S, Newton RH, Puri H, Meek KM. Collagen fibrils appear more closely packed in the prepupillary cornea: Optical and biomechanical implications. Invest Ophthalmol Vis Sci. 2003;44:2941-2948. Komai Y, Ushiki T. The three-dimensional organization of collagen fibrils in the human cornea and sclera. Invest Ophthalmol Vis Sci. 1991;32:2244-2258. Bergmanson JP, Horne J, Doughty MJ, Garcia M, Gondo M. Assessment of the number of lamellae in the central region of the normal human corneal stroma at the resolution of the transmission electron microscope. Eye Contact Lens. 2005;31:281-287. Meek KM, Tuft SJ, Huang Y, et al. Changes in collagen orientation and distribution in keratoconus corneas. Invest Ophthalmol Vis Sci. 2005;46:1948-1956. Meek KM, Boote C. The use of X-ray scattering techniques to quantify the orientation and distribution of collagen in the corneal stroma. Prog Retin Eye Res.2009;28:369-392.

41

Acknowledgements This work was supported by a grant from the US National Eye Institute of the National Institutes of Health EY024600 and EY014163, an unrestricted grant from Research to Prevent Blindness, Inc. (NY, USA) and the Skirball Program in Molecular Ophthalmology.

15. Jester JV, Winkler M, Jester BE, Nien C, Chai D, Brown DJ. Evaluating corneal collagen organization using high resolution non linear optical (NLO) macroscopy. Eye Contact Lens. 2010;36:260. 16. Winkler M, Chai D, Kriling S, et al. Nonlinear optical macroscopic assessment of 3-D corneal collagen organization and axial biomechanics. Invest Ophthalmol Vis Sci. 2011;52:8818. 17. Winkler M, Shoa G, Xie Y, et al. Three-dimensional distribution of transverse collagen fibers in the anterior human corneal stroma. Invest Ophthalmol Vis Sci. 2013;54:7293-7301. 18. Mercatelli R, Ratto F, Rossi F, et al. Three-dimensional mapping of the orientation of collagen corneal lamellae in healthy and keratoconic human corneas using SHG microscopy. J Biophotonics. 2017;10:75-83. 19. Morishige N, Takagi Y, Chikama T, Takahara A, Nishida T. Three-dimensional analysis of collagen lamellae in the anterior stroma of the human cornea visualized by second harmonic generation imaging microscopy. Invest Ophthalmol Vis Sci. 2011;52:911-915. 20. Mikula E, Hollman K, Chai D, Jester JV, Juhasz T. Measurement of corneal elasticity with an acoustic radiation force elasticity microscope. Ultrasound Med Biol. 2014;40:1671-1679. 21. Mikula ER, Jester JV, Juhasz T. Measurement of an elasticity map in the human cornea. Invest Ophthalmol Vis Sci. 2016;57:3282-3286. 22. Radner W, Zehetmayer M, Aufreiter R, Mallinger R. Interlacing and cross-angle distribution of collagen lamellae in the human cornea. Cornea. 1998;17:537-543. 23. Radner W, Mallinger R. Interlacing of collagen lamellae in the midstroma of the human cornea. Cornea. 2002;21:598-601. 24. Mathew JH, Bergmanson JP, Doughty MJ. Fine structure of the interface between the anterior limiting lamina and the anterior stromal fibrils of the human cornea. Invest Ophthalmol Vis Sci. 2008;49:3914-3918. 25. Smolek M, McCarey B. Interlamellar adhesive strength in human eyebank corneas. Invest Ophthalmol Vis Sci. 1990;31:10871095. 26. Smolek MK. Interlamellar cohesive strength in the vertical meridian of human eye bank corneas. Invest Ophthalmol Vis Sci. 1993;34:2962-2969.

Copyright © 2018. Kugler Publications. All rights reserved.

42 27. Müller LJ, Pels E, Vrensen GF. The specific architecture of the anterior stroma accounts for maintenance of corneal curvature. Br J Ophthalmol. 2001;85:437-443. 28. Wang H, Prendiville PL, McDonnell PJ, Chang WV. An ultrasonic technique for the measurement of the elastic moduli of human cornea. J Biomech. 1996;29:1633-1636. 29. Elsheikh A, Wang D, Pye D. Determination of the modulus of elasticity of the human cornea. J Refract Surg. 2007;23:808-818. 30. Last JA, Thomasy SM, Croasdale CR, Russell P, Murphy CJ. Compliance profile of the human cornea as measured by atomic force microscopy. Micron. 2012;43:1293-1298. 31. Petsche SJ, Chernyak D, Martiz J, Levenston ME, Pinsky PM. Depth-dependent transverse shear properties of the human corneal stroma. Invest Ophthalmol Vis Sci. 2012;53:873-880. 32. Sarvazyan AP, Rudenko OV, Swanson SD, Fowlkes JB, Emelianov SY. Shear wave elasticity imaging: a new ultrasonic technology of medical diagnostics. Ultrasound Med Biol. 1998;24:14191435. 33. Bercoff J, Tanter M, Fink M. Supersonic shear imaging: a new technique for soft tissue elasticity mapping. IEEE Trans Ultrason Ferroelectr Freq Control. 2004;51:396-409. 34. Tanter M, Touboul D, Gennisson J-L, Bercoff J, Fink M. High-resolution quantitative imaging of cornea elasticity using supersonic shear imaging. IEEE Trans Med Imaging. 2009;28:1881-1893. 35. Dupps WJ Jr, Netto MV, Herekar S, Krueger RR. Surface wave elastometry of the cornea in porcine and human donor eyes. J Refract Surg. 2007;23:66-75. 36. Manapuram RK, Aglyamov SR, Monediado FM, et al. In vivo estimation of elastic wave parameters using phase-stabilized swept source optical coherence elastography. J Biomed Opt. 2012;17:1005011-1005013. 37. Qi W, Chen R, Chou L, et al. Phase-resolved acoustic radiation force optical coherence elastography. J Biomed Opt. 2012;17:110505. 38. Wang S, Li J, Manapuram RK, et al. Noncontact measurement of elasticity for the detection of soft-tissue tumors using phase-sensitive optical coherence tomography combined with a focused air-puff system. Opt Lett. 2012;37:5184-5186. 39. Nightingale K, Palmeri M, Bouchard R, Trahey G. Acoustic radiation force impulse imaging: a parametric analysis of factors affecting image quality. Proc IEEE Ultrason Symp: IEEE. 2003:548553. 40. Hollman KW, Emelianov SY, Neiss JH, et al. Strain imaging of corneal tissue with an ultrasound elasticity microscope. Cornea 2002;21:68-73. 41. Hollman KW, Shtein RM, Tripathy S, Kim K. Using an ultrasound elasticity microscope to map three-dimensional strain in a porcine cornea. Ultrasound Med Biol. 2013;39:1451-1459. 42. So P. Microscopy: Brillouin bioimaging. Nat Photonics. 2008;2:13-14. 43. Vaughan JM, Randall JT. Brillouin scattering, density and elastic properties of the lens and cornea of the eye. Nature. 1980;284:489-491. 44. Scarcelli G, Pineda R, Yun SH. Brillouin optical microscopy for corneal biomechanics. Invest Ophthalmol Vis Sci. 2012;53:185.

E. Mikula et al. 45. Erpelding TN, Hollman KW, O’Donnell M. Bubble-based acoustic radiation force elasticity imaging. IEEE Trans Ultrason Ferroelectr Freq Control. 2005;52:971-979. 46. van den Berg TJ, Spekreijse H. Near infrared light absorption in the human eye media. Vision Res. 1997;37:249-253. 47. Elsheikh A, Alhasso D. Mechanical anisotropy of porcine cornea and correlation with stromal microstructure. Exp Eye Res. 2009;88:1084-1091. 48. Erpelding TN, Hollman KW, O’Donnell M. Bubble-based acoustic radiation force elasticity imaging. IEEE T Ultrason Ferr. 2005;52:971-979. 49. Elrod S, Hadimioglu B, Khuri-Yakub B, et al. Nozzleless droplet formation with focused acoustic beams. J App Phys. 1989;65:3441-3447. 50. Angelsen B. Ultrasound imaging: Waves, signals, and signal processing: Emantec; 2000. 51. Walker WF, Fernandez FJ, Negron LA. A method of imaging viscoelastic parameters with acoustic radiation force. Phys Med Biol. 2000;45:1437. 52. Oestreicher HL. Field and impedance of an oscillating sphere in a viscoelastic medium with an application to biophysics. J Acoust Soc Am. 1951;23:707-714. 53. De Jong N, Bouakaz A, Frinking P. Basic acoustic properties of microbubbles. Echocardiography. 2002;19:229-240. 54. Karpiouk AB, Aglyamov SR, Bourgeois F, Ben-Yakar A, Emelianov SY. Ultrasound characterization of cavitation microbubbles produced by femtosecond laser pulses. SPIE BiOS: Biomedical Optics: International Society for Optics and Photonics; 2009:717512-717512-717517. 55. Tse C, Zohdy MJ, Ye JY, et al. Acoustic detection of controlled bubble creation by LIOB in tissue-mimicking gelatin phantoms. Ultrasonics Symposium, 2004 IEEE: IEEE; 2004:350-353. 56. Ilinskii YA, Meegan GD, Zabolotskaya EA, Emelianov SY. Gas bubble and solid sphere motion in elastic media in response to acoustic radiation force. J Acoust Soc Am. 2005;117:23382346. 57. Lubinski MA, Emelianov SY, O’Donnell M. Speckle tracking methods for ultrasonic elasticity imaging using short-time correlation. IEEE Trans Ultrason Ferroelectr Freq Control. 1999;46:82-96. 58. Erpelding TN, Hollman KW, O’Donnell M. Mapping age-related elasticity changes in porcine lenses using bubble-based acoustic radiation force. Exp Eye Res. 2007;84:332-341. 59. Roth DJ, Whalen MF, Hendricks JL, Bodis JR. Using high frequency focused water-coupled ultrasound for 3-D surface depression profiling: National Aeronautics and Space Administration, Glenn Research Center; 1999. 60. Boote C, Kamma-Lorger CS, Hayes S, et al. Quantification of collagen organization in the peripheral human cornea at micron-scale resolution. Biophys J. 2011;101:33-42. 61. Davies Y, Fullwood NJ, Marcyniuk B, Bonshek R, Tullo A, Nieduszynski IA. Keratan sulphate in the trabecular meshwork and cornea. Curr Eye Res. 1997;16:677-686. 62. Hodson SA. Corneal stromal swelling. Prog Retin Eye Res. 1997;16:99-116.

Acoustic radiation force elastic microscopy and corneal structural correlation

Copyright © 2018. Kugler Publications. All rights reserved.

63. Gong H, Johnson M, Ye WEN, Kamm RD, Freddo TF. The Non-Uniform Distribution of Albumin in Human and Bovine Cornea. Exp Eye Res. 1997;65:747-756.

43

Copyright © 2018. Kugler Publications. All rights reserved.

4. Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions W. Matthew Petroll1,2, Miguel Miron Mendoza1 Department of Ophthalmology, University of Texas Southwestern Medical Center, Dallas, TX, USA; 2Biomedical Engineering Graduate Program, University of Texas Southwestern Medical Center, Dallas, TX, USA 1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction The corneal stroma is a highly ordered structure consisting of approximately 200 collagen lamellae.1 Corneal stromal cells (keratocytes) reside between the collagen lamellae and are responsible for secreting extracellular matrix (ECM) components required to develop and maintain normal corneal structure and function.2-4 Cell-matrix mechanical interactions within the corneal stroma play a central role in fundamental biological processes such as developmental morphogenesis and wound healing. Cellular forces organize ECM into tissue-specific patterns during embryonic development, and feedback between cell and matrix mechanics is a key factor regulating this process.5-7 Following injury or surgery, wound contraction and tissue remodeling are also dependent on mechanical interactions between fibroblasts and ECM fibrils.8-10 Such interactions are also important in the field of tissue engineering, where it is necessary to either modulate cell and ECM patterning to produce specific matrix architectures or prevent cell-induced matrix disruption to maintain prefabricated 3-D structures.11,12 In adult corneal tissue, resting keratocytes are mechanically quiescent; they do not express stress fibers or generate substantial contractile forces.13,14 Following injury, surgery, or other insults, corneal keratocytes can become activated by growth factors and other cytokines present in the wound environment, and transform into a fibroblastic repair phenotype.15,16 Corneal fibroblasts proliferate, develop intracellular

stress fibers, migrate into the wound, and reorganize the ECM through the application of mechanical forces. In certain wound types, the presence of transforming growth factor beta (TGFβ) in the wound can induce transformation of corneal fibroblasts to myofibroblasts, which generate even stronger forces on the matrix and synthesize a disorganized fibrotic ECM.17,18 Together, these processes can impact visual acuity by altering corneal shape and reducing transparency due to increased light scattering by both cells and the newly synthesized ECM.19-24 In addition to growth factors and other biochemical factors that can modulate the keratocyte mechanical phenotype, feedback from the ECM itself can also impact stromal cell behavior. ECM stiffness, topography, and/or protein composition have all been shown to modulate keratocyte differentiation, contractility, and patterning. Excellent reviews on corneal structure and biomechanics at the tissue level are provided elsewhere in this book. In this chapter, we focus on the biochemical and biophysical factors regulating keratocyte micromechanical activity at the cellular and subcellular level.

2. Micromechanics of corneal keratocyte motility in 3-D collagen matrices In order to maintain structural tensegrity (tensional integrity), many of the tensile forces generated within cells are balanced by compressive elements, and do not directly act on the substrate. In this chapter we will

Correspondence: W. Matthew Petroll PhD, UT Southwestern Medical Center, 5323 Harry Hines Blvd., Dallas, TX 75390-9057, USA E-mail: [email protected] Biomechanics of the Eye, pp. 45-61 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

Copyright © 2018. Kugler Publications. All rights reserved.

46

focus on the “net” forces transmitted to the ECM, since these mediate cell spreading, migration, and matrix remodeling. These forces, generally termed “tractional forces”, are typically generated through actin-myosin II interactions within the cell that are transmitted to the ECM via focal adhesions. The pattern and amount of cellular force generation can be calculated from the deformation of a substrate with known mechanical properties.25 Dembo and Wang pioneered the use of flexible polyacrylamide sheets embedded with fluorescent microspheres as a substratum for quantifying cellular forces.26-28 This experimental model, termed “tractional force microscopy”, has become a standard assay for assessing cell mechanical behavior in a 2-D environment.29,30 However, keratocytes reside within a complex 3-D ECM in vivo, and significant differences in cell morphology, adhesion organization, and mechanical behavior have been identified in 2-D vs 3-D culture models.31-33 Furthermore, unlike rigid 2-D substrates, 3-D models also allow assessment of both cellular force generation and cell-induced matrix reorganization; biomechanical activities that are critically involved in the migratory, contractile, and remodeling phases of wound healing and development. Since the ECM of the corneal stroma and many other connective tissues is composed primarily of type I collagen fibrils, an important in-vitro model used to assess 3-D cell mechanical behavior is the fibrillar collagen matrix model.34,35 Most studies use macroscopic measurements of 3-D collagen matrix compaction as an indicator of the amount of cell-induced remodeling.36 Alternatively, force transducers can be used to measure the overall isometric tension generated by the fibroblasts inside the matrix.37,38 These global measurements have provided important insights into the regulation of cell contractility by various cytokines and signaling pathways.33,39 However, in order to assess the micromechanical activity of cells, temporal and spatial changes in subcellular mechanical behavior and local matrix patterning must be studied at higher magnification. Bard and Hay pioneered the use of differential interference contrast imaging (DIC) to visualize corneal embryonic fibroblast migration both in situ and in 3-D collagen matrices.31,40,41 This approach allows direct visualization of both changes in cell morphology and local collagen fibril organization surrounding the cells (Fig. 1). Advances in microscope optics, laser technology,

W.M. Petroll and M.M. Mendoza

Fig. 1. DIC image of a cultured rabbit corneal fibroblast inside 3-D collagen matrix. The z position shown is relative to the bottom of the collagen matrix. Individual collagen fibrils are easily discerned adjacent to the cell (arrows).42

and digital imaging allow cellular micromechanics to be studied with high temporal and spatial resolution using current microscope systems. Furthermore, live-cell labeling techniques allow direct correlation of dynamic changes in the subcellular organization of cytoskeletal, adhesive, or regulatory proteins with the pattern of cell-induced matrix deformation.42-45 As detailed below, the application of these 3-D experimental models and imaging technologies has provided important insights into the mechanics of corneal fibroblast spreading, contraction, and migration, and the resulting impact on ECM reorganization. 2.1. Visualizing the subcellular patterns of cellular force generation Roy initially performed time-lapse imaging of corneal fibroblasts plated on top of type I collagen matrices embedded with microspheres. Based on the displacement of the microspheres and the measured stiffness of the ECM, the pattern of cellular force generation was estimated using finite element modeling.46,47 These studies were the first to directly demonstrate that fibroblasts can generate tension on the matrix during both extension and retraction of pseudopodial processes. Subsequent studies combining GFP-zyxin labeling with time-lapse DIC imaging provided more detailed insights into the mechanics of tractional force generation by corneal fibroblasts.42,48 Specifically, as serum-cultured fibroblasts spread on or within 3-D matrices, new adhesions form at the front of pseudopodia while existing adhesions move backward, resulting in pulling in of the collagen fibrils in front of the cells (Fig. 2). Meanwhile, adhesions at the base of pseudopodia were shown to move toward those at the

Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions

47

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 2. Cell matrix interactions during corneal fibroblast spreading in 3-D collagen matrix. (A) and (B) show overlays of GFP-zyxin expressing cells (green) and DIC (red) at different time points. The position of corresponding adhesions are denoted by white arrows. In (B), blue arrows show the magnitude and direction of collagen displacements. (C) Collagen displacements (blue arrows) in relationship to focal adhesion displacements (green arrows). New adhesions form along collagen fibrils (arrowheads) at the front of the pseudopodia while existing adhesions move backward (compare position of white arrows in A and B). This results in pulling in of the collagen fibrils in front of the cell. Adhesions at the base of the pseudopodia move toward those at the tip, resulting in contractile-like shortening , bending of collagen fibrils (double arrowheads), and matrix compression (circled region in C).42

tip, resulting in a region of contractile-like shortening and ECM compression mechanically linking the leading edge and cell body (Fig. 2C).42,48 These data are consistent with the “frontal towing” model of cell motility first observed using 2-D tractional force microscopy,49 which divided the cell into a towing zone at the leading edge, an elastic transition zone, cargo region, and trailing end. In the towing zone, adhesions often formed in a linear pattern along individual collagen fibrils within the 3-D matrix (Fig. 2B); this is distinctly different from the groups of adjacent adhesions that form within the lamella of cells plated on planar surfaces. In addition to DIC, local collagen matrix organization can be directly visualized using confocal reflection imaging, which generates images of collagen or fibrin fibers from within 3-D matrices without the need for exogenous labeling.50 Unlike DIC, 3-D reconstructions can be generated from confocal reflection images, and the density and alignment of fibrils can be assessed quantitatively.51-53 3-D confocal reflection imaging and fluorescence labeling in fixed cells is often used to correlate changes in the matrix structure with the organization of cytoskeletal or adhesive proteins.54 This approach has been used to demonstrate that corneal fibroblasts reorganize collagen both in front of cells and at the base of pseudopodia, which is completely consistent with the pattern of force generation

observed during time-lapse DIC imaging (Fig. 3A). Interestingly, at higher cell densities, groups of collagen fibrils are compacted and aligned into straps between neighboring cells, suggesting cell-cell mechanical communication and reinforcement of ECM remodeling (Fig. 3B).55 2.2. Rho kinase regulation of keratocyte mechanical activity The Rho-family of small GTPases such as Rho, Rac, and Cdc42 play a central role in mediating the changes in cell mechanical activity in response to growth factors and other cytokines in a variety of cell types.56 Rho binds to and activates Rho kinase (ROCK), which inhibits myosin light chain (MLC) phosphatase, resulting in elevated MLC phosphorylation and increased cell contractility.57-59 In fibroblasts on rigid 2-D substrates, activated Rho stimulates the formation of stress fibers and the development of focal contacts, and these cytoskeletal changes are dependent on actomyosin contraction.60,61 Studies using corneal fibroblasts have shown that the Rho/ROCK pathway plays a central role in mediating tractional force generation. Following spreading of corneal fibroblasts in 3-D collagen matrices, inhibiting ROCK induces rapid cell body elongation, formation and extension of dendritic cell processes, and a corresponding relaxation of cell-induced tension on the

48

W.M. Petroll and M.M. Mendoza

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. FEM strain maps generated using ANSYS, showing regions of matrix tension and compression surrounding a human corneal fibroblast expressing GFP-α-actinin within a 3-D collagen matrix. (A) Cell-induced ECM deformation is observed following culture in media containing 10% fetal bovine serum (S+). Note that the ECM is under tension at the end of the cell, and under compression at the base of the pseudopodial process. (B) The magnitudes of these deformations are reduced when the cell is switched to Y-27632 (10 μM). (C) Stain on the matrix is reestablished after switching back to S+. Strain is shown relative to the “relaxed” matrix configuration determined by treating cells with Cytochalasin D and TritonX-100. Bar on right shows scale for color contour strain maps in dimensionless units ΔL/L.44 Copyright: Association for Research in Vision and Ophthalmology.

Fig. 3. (A) Color overlay of a confocal reflection image of collagen fibrils (red) and a fixed cell labeled with FITC-phalloidin (green) from a 3-D type I collagen matrix.25 (B) Color overlay of confocal reflection image of collagen fibrils (red) and a living corneal fibroblast expressing GFP-α-actinin (green) within a 3-D type I collagen matrix. Note enhancement of ECM compaction between cells (arrows). 55

matrix (Fig. 4).44 Furthermore, when ROCK is inhibited, cell-induced compaction and alignment of the ECM is significantly reduced.51 The role of ROCK in regulating corneal fibroblast migration mechanics in 3-D matrices has also been investigated using a nested matrix model that facilitates dynamic imaging of cell-matrix interactions during cell translocation. During migration, corneal fibroblasts cultured in serum-containing media generate significant tractional forces on the matrix, as indicated by inward displacement and reorganization of collagen in the front of cells.62 When ROCK is inhibited, cells become more elongated and the rate of cell migration is significantly reduced. Interestingly, these cells extended dendritic processes at random orientations, and did not exhibit the ordered mechanical sequence typical of mesenchymal cell migration (extension, contraction, and tail retraction), suggesting ROCK is also involved in mechanical coordination between the front and rear of the cell.59 ROCK has also been shown to mediate growth factor responses, such as fibroblastic transformation of keratocytes in response to basic fibroblast growth factor (FGF2) treatment and myofibroblast transformation in response to TGFβ.63,64 Specifically, treatment with Y-27632 inhibits stress fiber formation, and blocks the induction of α-SM-actin expression and the increase in cell-induced matrix remodeling normally induced by TGFβ. Inhibition of Rho/ROCK has also been shown to block the decrease in keratin sulfate proteoglycan synthesis normally associated with corneal myofibroblast transformation.63 Because of these unique properties, inhibitors of ROCK are potential candidates for reducing corneal fibrosis and scarring in vivo. Koizumi and coworkers investigated whether topical application of Y-27632 could modulate in-vivo corneal

Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions

Copyright © 2018. Kugler Publications. All rights reserved.

wound healing following lamellar keratectomy in a rabbit model.65 After 21 days of treatment with Y-27632, the expression of α-SM actin was suppressed in the center of the wound. In addition, while both treated and control corneas showed similar amounts of type I collagen matrix deposition and keratan sulfate during healing, the amount of type III collagen was reduced in the Y-27632 group. Similarly, HA1077, another ROCK inhibitor, has been shown to reduce fibrosis in the rabbit after alkali injury.66 It should be noted that epithelial resurfacing was significantly delayed in animals treated with Y-27632, thus specific targeting to the stromal keratocyte may be required for clinical application of ROCK inhibitors following surface injury to the cornea. 2.3. Rac regulation of corneal keratocyte mechanical activity In contrast to Rho, Rac generally stimulates cell spreading and migration via the creation of smaller focal complexes and actin polymerization.60,67-72 Rac can be activated by platelet-derived growth factor BB (PDGF BB), which stimulates cell spreading and migration within 3-D collagen matrices.67,73 In time-lapse studies of corneal fibroblasts in 3-D matrices, PDGF-induced cell spreading occurred via elongation, ruffling, and random branching of pseudopodial processes.43,74 In general, relaxation (decompression) of the ECM was observed along the cell body, whereas tractional forces were generated by extending cell processes, as indicated by centripetal displacement of collagen fibrils at the ends of cells. Following ROCK or myosin II inhibition, significant ECM relaxation was observed, but small displacements of collagen fibrils continued to be detected at the tips of pseudopodia. Taken together, the data suggest that during Rac-induced cell spreading within 3-D matrices, there is a shift in the distribution of forces from the center to the periphery of corneal fibroblasts. Furthermore, while ROCK mediates the generation of large myosin II-based tractional forces during cell spreading, residual forces can be generated at the tips of extending pseudopodia that may be both ROCK and myosin II-independent. For quiescent corneal keratocytes maintained in serum-free conditions (in which the level of Rho activation is low), both global and local ECM reorganization induced by PDGF BB are comparable to that produced by basal serum-free media.64 Nonetheless,

49

PDGF still stimulates cell migration through 3-D collagen matrices.75,76 During migration, PDGF induces repeated extension and retraction of dendritic cell processes which produce only small, transient matrix deformations. Furthermore, local matrix reorganization produced by migrating cells in PDGF is significantly reduced as compared to serum or TGFβ1, in which Rho predominates (Fig. 5). Following lacerating injury or incisional surgery, contractile force generation is needed to facilitate wound closure and prevent loss of the mechanical integrity of the cornea. However, following refractive surgical procedures such as photorefractive keratectomy (PRK) or laser-assisted in situ keratomileusis (LASIK), it is preferable to minimize cellular force generation and fibrosis during stromal repopulation, since these processes can alter corneal shape and transparency.22,23,77 Modulating the balance between Rho and Rac activation may shift corneal fibroblasts between these two phenotypes. Studies using human Tenon fibroblasts in 3-D collagen matrices have demonstrated that Rac1 inhibition using NSC23766 or siRNA reduces cell protrusions and inhibits serum-induced global contraction of unrestrained (floating) collagen matrices.78 In corneal keratocytes, inhibition of Rac has no significant impact on mechanical behavior in compliant collagen matrices. Within compressed collagen matrices however, the Rac inhibitor induces fibroblastic transformation of quiescent corneal keratocytes in serum-free media or PDGF. This transformation is blocked by ROCKinhibition, suggesting that fibroblastic transformation induced by Rac1 inhibition may result from a shift in the balance between Rho and Rac activation. This could be a direct result of reduced Rac activation and/or a loss of Rho inhibition by Rac1.79 As detailed in Section 3, keratocyte differentiation appears to be regulated by both the interplay between Rho and Rac signaling, and the structural and mechanical properties of the ECM. 2.4. The role of microtubules in corneal keratocyte motility Microtubules regulate numerous aspects of cell behavior including cellular transport of vesicles, control of cell shape, cell division, spindle assembly, and chromosome motion during mitosis.80 In addition, microtubules play a key role in various aspects of cell mechanical behavior. For example, microtubule

50

W.M. Petroll and M.M. Mendoza

Copyright © 2018. Kugler Publications. All rights reserved.

behavior and organization is modulated by the small GTPases Rho, Rac, and Cdc42 in order to regulate cell polarization and directed cell migration on 2-D substrates.81 Fibroblast spreading is also regulated by microtubules; however, the role of microtubules in cell spreading is highly dependent on substrate geometry and stiffness.41,82 Microtubules may also be involved in modulation of cell contractility. Kolodney et al. used an isometric force transducer to quantitatively monitor the tension exerted by a dense population of chick embryo fibroblasts within collagen matrices.83 Disrupting microtubules induced a two- to three- fold increase in force over several minutes and reached maximum at about 30 minutes. A similar pattern of increased phosphorylation of the myosin regulatory light chain was identified, suggesting that actomyosin contractile activity may underlay the increase in force. Consistent with these observations, microtubules have been shown to sequester Rho-GEF, and release of Rho-GEF following microtubule disruption induces Rho/ROCK activation and cellular ­ contraction.84-88 In corneal fibroblasts, microtubule disruption also results in Rho activation, cellular contraction, stress fiber formation and local matrix reorganization.89 Interestingly, when ROCK is inhibited, addition of nocodazole induces the formation and extension of broader “lamellipodial” processes from random locations along corneal fibroblasts, which eventually lead to a convoluted, disorganized cell shape. Thus, microtubules play an important role in the dynamic regulation of corneal fibroblast spreading mechanics, morphology, and polarity in 3-D culture.

Fig. 5. Maximum intensity projections of f-actin (green) and collagen fibrils (red) at the interface between the inner and outer matrices of nested constructs. (A) Following culture in 10% fetal bovine serum, migrating cells developed a bipolar morphology with occasional stress fibers along the cell body. Collagen fibrils were compacted and aligned parallel to the long axis of pseudopodia. (B) Following culture in TGFβ1 (10 ng/ml), cells developed a broad morphology and intracellular stress fibers were observed. Collagen fibrils were compacted both around and between the cells. (C) Migrating cells in PDGF BB (50 ng/ml) were more elongated and had branching processes. Collagen fibrils remained more randomly aligned around the cells.157 Copyright: Association for Research in Vision and Ophthalmology

3. The impact of ECM mechanical properties on corneal keratocyte behavior In addition to growth factors and other biochemical factors that can modulate the keratocyte mechanical phenotype, another key player is the structural and mechanical state of the ECM itself. As detailed in other chapters, large shifts in the global distribution of ECM tension within the cornea can be induced by lacerating injury, penetrating keratoplasty, or refractive surgery.23,24 In addition, diseases such as keratoconus can also produce changes in stromal structural and mechanical properties. Keratoconus corneas generally

Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions

Copyright © 2018. Kugler Publications. All rights reserved.

have reduced mechanical stiffness,90-93 and thinning of the central cornea in keratoconus patients induces a redistribution of tension within the stromal ECM.94,95 In contrast, treatment of keratoconus with UV crosslinking increases corneal stromal rigidity. Overall, understanding how ECM structure, stress, and elasticity modulate corneal keratocyte behavior is relevant to a range of clinical conditions.96 3.1. Modulation of keratocyte mechanical activity by ECM stiffness and anisotropy It is well established that mechanical signals from the ECM play a key role in regulating growth and function in a variety of cell types. Increasing substrate stiffness can facilitate formation of actin stress fibers and focal adhesions in contractile cells,26,97,98 and these structures tend to align along the tensile axis under anisotropic conditions.12,99-101 Studies using corneal fibroblasts have shown similar cross-talk between cell and matrix mechanics. In 3-D culture models, significant differences in cell alignment, morphology, and matrix reorganization are observed between constrained (anisotropic) and unconstrained (isotropic) rectangular matrices.102 Cells align nearly parallel to the long axis of the construct in matrices constrained at the ends, whereas cells in unconstrained matrices show no preferential orientation. Corneal fibroblasts also tend to align and compact collagen parallel to the axis of greatest effective stiffness under anisotropic conditions. Ruberti and coworkers developed a novel bioreactor in which collagen substrates seeded with corneal fibroblasts could be mechanically loaded along a single axis, and cell-matrix patterning could be assessed using time-lapse imaging.103 It was demonstrated that mechanical anisotropy induced cell and ECM alignment that was correlated over long distances, and had increased stability as compared to unbiased substrates. Cell migration and spreading can also be influenced by the mechanical stiffness of the substrate. In 3-D matrices prefabricated with directional gradients in collagen density, fibroblasts migrate towards the stiffer region,104 a phenomenon termed “durotaxis”.105 To evaluate the effect of matrix mechanical properties on corneal keratocyte migration, migration has been compared in constrained and unconstrained nested matrix constructs.75 Consistent with previous results

51

using dermal fibroblasts,71 invasion of keratocytes into the outer matrix in serum was significantly reduced in unconstrained matrices, in which effective stiffness is reduced. Interestingly, the dependency of corneal fibroblast migration on matrix constraint was eliminated when ROCK was inhibited. Migration of keratocytes cultured in PDGF BB, which have low levels of contractility, was also unaffected by changes in the effective stiffness of the ECM.75 Thus, while durotaxis appears to modulate the migration of corneal keratocytes that have transformed to a contractile fibroblastic phenotype, it does not appear to impact the motility of keratocytes that maintain a quiescent, low contractility mechanical phenotype. This is consistent with the concept whereby durotaxis only regulates contractile cells.33 It should be noted that ECM composition can also modulate the pattern of corneal fibroblast migration in 3-D culture, independent of changes in ECM stiffness. Specifically, whereas corneal fibroblasts generally move independently within 3-D collagen matrices, fibrin induces a switch to an interconnected, collective mode of cell spreading and migration which is independent of differences in ECM stiffness.106 Interestingly, corneal fibroblasts form an interconnected mesh as they migrate into the wound space following incisional surgery, and these interconnections are hypothesized to mediate force transduction during wound contraction.107,108 Furthermore, following a transcorneal freeze injury in the rabbit, repopulation of the stroma occurs through interconnected cell migration.109 Collective cell migration can influence the pattern of polarization, force generation, and tissue organization in other systems, and also plays a pivotal role in cancer invasion.110-112 3.2. Tensional homeostasis Time-dependent changes in ECM stress have also been shown to impact cell mechanical behavior. Using a tensioning culture force monitor system, Brown and coworkers demonstrated that stretching of 3-D matrices seeded with dermal fibroblasts resulted in a rapid increase in the measured force,39 which was immediately followed by a gradual cell-dependent reduction in force toward the baseline level. In contrast, reducing strain on the gel caused an initial loss of tension, followed by a cell-dependent increase back to the baseline level. Thus, in both cases cells responded to

Copyright © 2018. Kugler Publications. All rights reserved.

52

mechanical loading in a way that maintained “tensional homeostasis” (constant tension) in their surrounding matrix. Consistent with this model, fibroblast force generation in 3-D matrices often reaches a constant value that is independent of matrix stiffness.113 Tensional homeostasis may be fundamental to the regulation of tissue tension under normal conditions, during development, and also in response to injury. Dynamic changes in ECM tension have also been shown to impact corneal fibroblast behavior. The effects of cyclic stretch on the expression of matrix metalloproteinases (MMPs) and tissue inhibitors of matrix metalloproteinases (TIMPs) by corneal fibroblasts suggests that stretching magnitude determines whether the cornea undergoes matrix degradation or synthesis by changing the balance between MMPs and TIMPs secretion.114 The effect of dynamic changes in ECM tension on corneal fibroblast micromechanical behavior has also been investigated by using micropipettes to displace the collagen fibrils near a cell.74,115 In these studies, reducing effective ECM stiffness by pushing toward the front of a cell resulted in rapid cellular shortening with corresponding ECM compression along the cell body (Fig. 6A-D). This initial contraction is likely due to the release of isometric cellular contractile forces, since it is blocked by ROCK inhibition. Following contraction, pseudopodial extension (spreading) was observed at both ends of the cell. Interestingly, the ECM was pulled inward during this secondary spreading, and rapid turnover of focal adhesions was observed along extending pseudopodia. Finite element modeling (FEM) analysis demonstrated that, following the initial reduction of tension induced by the needle push, fibroblasts partially re-established baseline tension during secondary spreading, consistent with the tensional homeostasis model. In contrast to ECM compression parallel to the long axis of cells, compressing the ECM perpendicular to the long axis of corneal fibroblasts had little effect on cell morphology or mechanical activity (Fig. 6E-H). This is also consistent with the tensional homeostasis model. Specifically, since the cytoskeleton, focal adhesions, and contractile forces are all aligned parallel to the long axis of bipolar cells, reducing the effective stiffness of the ECM alongside of the cell should have little impact on cellular tension. Overall, while durotaxis has been shown to regulate cell alignment and migration within

W.M. Petroll and M.M. Mendoza

collagen matrices under static conditions,104 tensional homeostasis may modulate cell behavior in response to more transient changes in ECM tension at both the local and global level.39,115,116 During developmental morphogenesis and wound healing, such dynamic changes in local matrix tension could be produced by the mechanical activity of nearby cells and/or externally applied forces. Interestingly, when a needle is pushed toward the trailing edge of a migrating cell in 3-D, the same initial contraction and secondary spreading response identified at the leading edge is observed. This “tail plasticity” has also been observed when using 1-D substrates to simulate 3-D migration.117 Together, these data suggest that similar cytoskeletal machinery and/ or signaling networks may be present to some extent at both ends of migrating cells, facilitating remarkable plasticity and rapid responses to mechanical stimuli at either end. 3.3. Modulation of keratocyte growth factor responses by ECM stiffness Peptide growth factors present in the cornea and tear film, such as insulin growth factor (IGF), PDGF, fibroblast growth factor (FGF), interleukin-1α (IL-1α), and TGFβ,118-121 are postulated to play an important role in modulating the keratocyte phenotype during corneal wound healing. In cell culture, these growth factors differentially regulate keratocyte proliferation, cytoskeletal organization, and ECM synthesis. Importantly, the response of corneal keratocytes to growth factors can also be modulated by changes in ECM stiffness. Several studies have shown that FGF2 induces fibroblastic transformation of keratocytes on rigid 2-D substrates, as indicated by changes in cell morphology and development of stress fibers and focal adhesions.61,63,122 However, within hydrated 3-D collagen matrices (which have high compliance), FGF2 stimulates ruffling of keratocyte processes without inducing major changes in cell morphology, formation of stress fibers, or collagen matrix organization.64 When corneal keratocytes are seeded within compressed 3-D collagen matrices, fibroblastic transformation is again observed. Both glass and compressed collagen matrices are several orders of magnitude stiffer than a hydrated collagen matrix; thus, substrate mechanical properties appear to modulate the phenotypic changes induced by FGF2.

Copyright © 2018. Kugler Publications. All rights reserved.

Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions

53

Fig. 6. Fibroblast response to ECM compression using small microneedle. (A-D) Human corneal fibroblast following two days of culture in media containing 10% fetal bovine serum, inside a 3-D collagen matrix. Needle was inserted axially into the matrix above the cell (A) without inducing changes in cell behavior (B). Pushing on the ECM towards the leading edge of a cell induced rapid cellular contraction and ECM compression along the cell body (C, arrows). This initial contraction was followed by re-spreading and tractional force generation (D, red tracks; crosses mark position immediately after needle push). (E-H) Fibroblast response to ECM compression adjacent to cell body. Human corneal fibroblast one day after plating inside collagen matrix. Pushing small microneedles toward the side of the cell had no significant effect on cell morphology or tractional force generation.74

Matrix stiffness also impacts the response of ocular cells to TGFβ treatment. For example, increased matrix stiffness has been shown to enhance TGFβ-induced myofibroblast transformation of human Tenon fibroblasts.123 Consistent with these results, Murphy and coworkers recently demonstrated that corneal fibroblasts grown on compliant polyacrylamide

substrates had fewer stress fibers and expressed significantly reduced amounts of α-SMA as compared cells plated on rigid 2-D substrates.124 In hydrated 3-D collagen matrices, treatment with TGFβ1 and 2 increases cell contractility, as indicated by the formation of stress fibers and stimulation of cell-induced ECM reorganization.61,64 However, α-SM-actin labeling is negative for

54

cells plated at low cell density within these compliant matrices. In contrast, approximately 20% of cells show positive labeling for α-SM-actin localized to the stress fibers at high cell density, where mechanical cross-talk between cells increases the tension within the matrix. A similar increase in stress fiber formation and myofibroblast transformation of corneal keratocytes is observed within more rigid compressed 3-D collagen matrices, even at low cell density. Unlike FGF and TGFβ, keratocytes cultured in IGF or PDGF BB maintain a quiescent mechanical phenotype over a range of ECM environments, including rigid 2-D substrates, compliant hydrated matrices, and compressed collagen matrices.64 Thus, the effects of these growth factors do not appear to be modulated by matrix stiffness alone. IGF increases keratocyte proliferation and stimulates synthesis of ECM components resembling normal corneal stroma, and also stimulates network formation.61,125,126 Thus, it has been suggested that IGF may be involved in the maintenance of normal corneal structure and could contribute to a regenerative wound healing phenotype.61,125

Copyright © 2018. Kugler Publications. All rights reserved.

4. Modulation of corneal keratocyte differentiation and patterning by ECM topography In addition to matrix mechanical properties, nano-scale surface topography can also have a profound impact on corneal keratocyte behavior. In-vitro studies using 2-D nano-patterned substrates allow direct assessment of how changes in specific topographical parameters (i.e., height, depth, width, and spacing) can influence cell mechanical activity. Studies using fibrillar collagen provide additional insights into the feedback between cell and matrix patterning. Finally, multiphoton second harmonic generation (SHG) imaging has allowed direct correlation of cell patterning and corneal collagen organization during in-vivo wound healing. 4.1. Regulation of corneal stromal cell behavior by micro- and nano-topography in vitro Advances in material science have led to the development of in-vitro substrates with surface topographies (e.g., micropillars, grooves, ridges, and pits) modeled after in-vivo tissue matrices.127-130 Interest-

W.M. Petroll and M.M. Mendoza

ingly, small changes in topographical parameters can produce significant changes in cell morphology and migration mechanisms.127,131,132 Aligned surface grooves have been reported to inhibit the transformation of corneal fibroblasts to myofibroblasts normally observed in response to TGFβ.133 They also increase the alignment of cells and matrix within each layer of self-assembled sheets produced by corneal fibroblasts.134 On Transwell filters which have parallel, aligned grooves on the surface, human corneal fibroblasts stimulated with ascorbate analogs secrete and organize a more cornea-like ECM as compared to fibroblasts plated on planar substrates or disorganized collagen ECM.135-139 Furthermore, Connon and coworkers demonstrated that tissue equivalents produced by corneal fibroblasts plated on aligned substrates were thicker, denser, and more resistant to proteolytic degradation than those plated on unaligned substrates.11 Thus, substrate topography can modulate both the organization and differentiation of corneal fibroblasts. Importantly, Murphy and coworkers have developed methods to simultaneously modulate both the surface topography and mechanical stiffness of substrates.140 Initial studies demonstrated that corneal fibroblasts attach and align on these non-rigid substrates. This type of approach could allow novel insights into how multiple biophysical cues are integrated to determine cell differentiation and patterning. Differentiation of both embryonic and adult stem cells is also regulated by the chemical and physical characteristics or their microenvironment.7,141,142 Adult corneal stromal stem cells (CSSC), which express genes and proteins characteristic of quiescent corneal keratocytes,143,144 are influenced by substrate structure, adhesion, and topography. In 2-D culture on planar substrates, CSSC cells do not secrete an abundant ECM, but as free-floating 3-D pellets they produce an ECM containing stromal-like molecular components and regions of aligned collagen.145 Furthermore, when CSSC are cultured on an aligned nanofibrous substrata, they form a parallel lamellar ECM similar to that of adult corneal stroma.139,146-148 In contrast, on substratum of randomly oriented nanofibers, CSSC secretion and organization of a stroma-like ECM is significantly reduced.146 Therefore, overall, topographic cues from the substratum have a significant impact on the ability of CSSC to produce a cornea-like ECM.

Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions

55

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 7. In-vivo cell patterning after freeze injury in the rabbit. (A) Montage of tiled confocal images from the posterior stroma collected in situ from corneal blocks labeled with phalloidin (green) and DAPI (blue), three days after transcorneal freeze injury. W: image area closest to the center of the wound. (B) Multiphoton confocal images collected in situ showing fluorescent signal from phalloidin (green) and forward scattered SHG signal from stromal collagen lamellae (red). Graphs on right show the percent of image content aligned at each radial angle within the image for both cells and collagen. Images are from posterior stroma (20 microns above endothelium), collected seven days after freeze injury.109 Copyright: Association for Research in Vision and Ophthalmology

As with micro-patterned synthetic substrates, aligned collagen fibrils can provide contact guidance for cell spreading and migration.149-153 Corneal fibroblasts spread parallel to magnetically aligned collagen fibrils within 3-D matrices.154 In fibrillar collagen matrices in which collagen alignment is random, high-magnification DIC imaging revealed two types of collagen displacement at the leading edge during cell spreading.43 First, when a collagen fibril in front of an extending process was aligned somewhat parallel to the direction of spreading, the extending process often engaged the fibril, pulled it into alignment, then continued to spread

along it. Second, when collagen fibrils in front of an extending process were aligned more perpendicular to the direction of spreading, the extending process would often engage the first fibril, push past it to engage the second fibril, then pull the fibrils together. The first pattern of interaction tended to pull collagen fibrils at the ends of cells into an alignment parallel with the pseudopodia, whereas the second pattern resulted in compaction of the collagen fibrils in a direction perpendicular to the extending process. These interactions are consistent with the pattern of collagen organization observed following cell spreading, which includes

56

sprays of collagen aligned parallel to the long axis at the ends of cells, and fibrils aligned more perpendicular to the long axis at the base of pseudopodial processes (Fig. 3). These observations suggest that the pattern of pseudopodial extension and of cell-induced fibril displacement and realignment in 3-D matrices are significantly influenced by the initial organization of the surrounding ECM.

Copyright © 2018. Kugler Publications. All rights reserved.

4.2. Regulation of cell patterning and differentiation by matrix topography in vivo Using volume scanning electron microscopy, Quantock and coworkers demonstrated that dendritic keratocyte processes are closely associated with orthogonally arranged stromal collagen fibrils in the developing chick cornea.155 Cell and collagen alignment has also been assessed following PRK in the rabbit using multiphoton fluorescence and SHG imaging.156 Two weeks after surgery, wound healing was characterized by myofibroblast transformation of corneal keratocytes and the development of fibrotic tissue on top of the photoablated stroma. Within this fibrotic tissue, stress fibers within corneal myofibroblasts and collagen fibers were shown to be co-aligned, suggesting cell-matrix mechanical feedback. A recent study identified a unique pattern of keratocyte alignment and connectivity following transcorneal freeze injury, which was highly correlated with the structural organization of the lamellae, suggesting contact guidance of intrastromal cell migration.109 Specifically, parallel streams of aligned corneal fibroblasts were observed, particularly in the posterior cornea (Fig. 7A). Fibroblasts formed an interconnected network that extended from the wound edge to the leading edge of the migratory front, and trains of

W.M. Petroll and M.M. Mendoza

cells moving along the same path were often observed. Parallel groups of these cell chains were consistently detected, with the orientation shifting from one layer to the next. SHG imaging demonstrated that these cells were aligned parallel to the collagen lamellae (Fig. 7B). In contrast to the fibrotic layer that forms on top of the stroma following PRK, cells migrating within the stroma following freeze injury are exposed to topographic cues from the native lamellae. These cues apparently led to cell alignment via contact guidance of migration, consistent with many of the in-vitro studies cited above.

5. Conclusions The micromechanical interactions between corneal keratocytes and the stromal ECM are regulated not only by biochemical signals from growth factors and other cytokines, but also by mechanical signaling and feedback due to changes in ECM structure, stress, and elasticity. Changes in the activity of Rho GTPases appear to play a central role in modulating corneal keratocyte mechanical behavior in response to both biochemical and biomechanical cues. Together, these signals may determine the pattern and amount of cellular force generation and ECM reorganization produced following injury or refractive surgery. Feedback between biochemical and biophysical signals can also have a profound impact on keratocyte differentiation and patterning both in vitro and in vivo. Overall, mechanical interactions and cross-talk between corneal keratocytes and the ECM likely impact a range of fundamental processes in the cornea in both health and disease. 

Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions

References 1. 2. 3.

4.

5.

6.

7. 8. 9.

10. 11.

12.

13.

Copyright © 2018. Kugler Publications. All rights reserved.

14.

15.

16.

17.

Pepose JS, Ubels JL. The Cornea. In: Hart WM (ed), Adler’s Physiology of the Eye. St. Louis Mosby Year Book 1992:29-70. Hassell JR, Birk DE. The molecular basis of corneal transparency. Exp Eye Res. 2010;91:326-335. Chakravarti S, Petroll WM, Hassell J, et al. Corneal opacity in lumican-null mice: defects in collagen fibril structure and packing in the posterior stroma. Invest Ophthalmol Vis Sci. 2000;41:3365-3373. Funderburgh JL, Mann MM, Funderburgh ML. Keratocyte phenotype mediates proteoglycan structure: a role for fibroblasts in corneal fibrosis. J Biol Chem. 2003;278:45629-45637. Bard JBL, Higginson K. Fibroblast-collagen interactions in the formation of the secondary stroma of the chick cornea. J Cell Biol. 1977;74:816-827. Krieg M, Arboleda-Estudillo Y, Puech P-H, et al. Tensile forces govern germ-layer organization in zebrafish. Nat Cell Biol. 2008;10:429-436. Engler AJ, Sen S, Sweeney HL, Discher DE. Matrix elasticity directs stem cell lineage specification. Cell. 2006;126:677-689. Ehrlich HP. Wound closure: Evidence of cooperation between fibroblasts and collagen matrix. Eye. 1988;2:149-157. Gabbiani G, Hirschel BJ, Ryan GB, Statkov PR, Majno G. Granulation tissue as a contractile organ: a study of structure and function. J Exp Med. 1972;135:719-734. Martin P. Wound healing - Aiming for perfect skin regeneration. Science. 1997;276:75-81. Gouveia RM, Gonzalez-Andrades E, Cardona JC, et al. Controlling the 3D architecture of Self-Lifting Auto-generated Tissue Equivalents (SLATEs) for optimized corneal graft composition and stability. Biomaterials. 2017;121:205-219. Bourget J-M, Guillemette M, Veres T, Auger FA, Germain L. Alignment of cells and extracellular matrix within tissue-eingineered substrates. In: Pignatello R (ed), Advances in Biomaterials Science and Biomedical Applications InTech 2013. Jester JV, Barry PA, Lind GJ, Petroll WM, Garana R, Cavanagh HD. Corneal keratocytes: In situ and in vitro organization of cytoskeletal contractile proteins. Invest Ophthalmol Vis Sci. 1994;35:730-743. Lakshman N, Kim A, Petroll WM. Characterization of corneal keratocyte morphology and mechanical activity within 3-D collagen matrices. Exp Eye Res. 2010;90:350-359. Stramer BM, Zieske JD, Jung J-C, Austin JS, Fini ME. Molecular mechanisms controlling the fibrotic repair phenotype in cornea: implications for surgical outcomes. Invest Ophthalmol Vis Sci. 2003;44:4237-4246. Garana RM, Petroll WM, Chen WT, et al. Radial keratotomy II: The role of the myofibroblast in corneal wound contraction. Invest Ophthalmol Vis Sci. 1992;33:3271-3282. Jester JV, Huang J, Barry-Lane PA, Kao WW, Petroll WM, Cavanagh HD. Transforming growth factor(beta)-mediated corneal myofibroblast differentiation requires actin and fibronectin assembly. Invest Ophthalmol Vis Sci. 1999;40:19591967.

57

18. Blalock TD, Duncan MR, Varela JC, et al. Connective tissue growth factor expression and action in human corneal fibroblast cultures and rat corneas after photorefractive keratectomy. Invest Ophthalmol Vis Sci. 2003;44:1879-1887. 19. Jester JV, Brown D, Pappa A, Vasiliou V. Myofibroblast differentiation modulates keratocyte crystallin protein expression, concentration, and cellular light scattering. Invest Ophthalmol Vis Sci. 2012;53:770-778. 20. Moller-Pedersen T, Cavanagh HD, Petroll WM, Jester JV. Corneal haze development after PRK is regulated by volume of stromal tissue removal. Cornea. 1998;17:627-639. 21. Boote C, Du Y, Morgan S, et al. Quantitative assessment of ultrastructure and light scatter in mouse corneal debridement wounds. Invest Ophthalmol Vis Sci. 2012;53:2786-2795. 22. Moller-Pedersen T, Cavanagh HD, Petroll WM, Jester JV. Stromal wound healing explains refractive instability and haze development after photorefractive keratectomy: A 1-year confocal microscopic study. Ophthalmology. 2000;107:1235-1245. 23. Dupps WJ, Wilson SE. Biomechanics and wound healing in the cornea. Exp Eye Res. 2006;83:709-720. 24. Ruberti JW, Roy AS, Roberts CJ. Corneal biomechanics and biomaterials. Annu Rev Biomed Eng. 2011;13:269-295. 25. Miron-Mendoza M, Koppaka V, Zhou C, Petroll WM. Techniques for assessing 3-D cell-matrix mechanical interactions in vitro and in vivo. Exp Cell Res. 2013;319(16):2470-80. 26. Pelham RJ, Wang YL. Cell locomotion and focal adhesions are regulated by substrate flexibility. Proc Natl Acad Sci USA. 1997;94:13661-13665. 27. Wang YL, Pelham RJ, Jr. Preparation of a flexible, porous polyacrylamide substrate for mechanical studies of cultured cells. Methods Enzymol. 1998;298:489-496. 28. Pelham RJ, Wang Y. High resolution detection of mechanical forces exerted by locomoting fibroblasts on the substrate. Mol Biol Cell. 1999;10:935-945. 29. Wang JHC, Lin JS. Cell traction force and measurement methods. Biomech Model Mechan. 2007;6:361-371. 30. Legant WR, Choi CK, Miller JS, et al. Multidimensional traction force microscopy reveals out-of-plane rotational moments about focal adhesions. Proc Natl Acad Sci. 2013;110:881-886. 31. Tomasek JJ, Hay ED, Fujiwara K. Collagen modulates cell shape and cytoskeleton of embryonic corneal and fibroma fibroblasts: Distribution of actin, α-actinin and myosin. Dev Biol. 1982;92:107-122. 32. Cukierman E, Pankov R, Yamada KM. Cell interactions with three-dimensional matrices. Curr Opin Cell Biol. 2002;14:633639. 33. Grinnell F, Petroll WM. Cell motility and mechanics in three-dimensional collagen matrices. Annu Rev Cell Dev Biol. 2010;26:335-361. 34. Bell E, Ivarsson B, Merril C. Production of a tissue-like structure by contraction of collagen lattices by human fibroblasts of different proliferative potential in vivo. Proc Natl Acad Sci USA. 1979;76:1274-1278. 35. Elsdale T, Bard J. Collagen substrata for studies on cell behavior. J Cell Biol. 1972;54:626-637.

Copyright © 2018. Kugler Publications. All rights reserved.

58 36. Grinnell F, Lamke CR. Reorganization of hydrated collagen lattices by human skin fibroblasts. J Cell Sci. 1984;66:51-63. 37. Eastwood M, McGrouther DA, Brown RA. A culture force monitor for measurement of contraction forces generated in human dermal fibroblast cultures: Evidence for cell matrix mechanical signalling. Biochimica et Biophysica Acta. 1994;1201:186-192. 38. Kolodney MS, Elson EL. Correlation of myosin light chain phosphorylation with isometric contraction of fibroblasts. J Biol Chem. 1993;268:23850-23855. 39. Brown RA, Prajapati R, McGrouther DA, Yannas IV, Eastwood M. Tensional homeostasis in dermal fibroblasts: mechanical responses to mechanical loading in three-dimensional substrates. J Cell Physiol. 1998;175:323-332. 40. Bard JBL, Hay ED. The behavior of fibroblasts from the developing avian cornea: Morphology and movement in situ and in vitro. J Cell Biol. 1975;67:400-418. 41. Tomasek JJ, Hay ED. Analysis of the role of microfilaments and microtubules in acquisition of bipolarity and elongation of fibroblasts in hydrated collagen gels. J Cell Biol. 1984;99:536-549. 42. Petroll WM, Ma L. Direct, dynamic assessment of cell-matrix interactions inside fibrillar collagen lattices. Cell Motil Cytoskel. 2003;55:254-264. 43. Petroll WM, Ma L, Kim A, Ly L, Vishwanath M. Dynamic assessment of fibroblast mechanical activity during Rac-induced cell spreading in 3-D culture. J Cell Physiol. 2008;217:162-171. 44. Vishwanath M, Ma L, Jester JV, Otey CA, Petroll WM. Modulation of corneal fibroblast contractility within fibrillar collagen matrices. Invest Ophthalmol Vis Sci. 2003;44:4724-4735. 45. Packard BZ, Artym VV, Komoriya A, Yamada KM. Direct visualization of protease activity on cells migrating in three-dimensions. Matrix Biol. 2009;28:3-10. 46. Roy P, Petroll WM, Cavanagh HD, Chuong CJ, Jester JV. An in vitro force measurement assay to study the early mechanical interaction between corneal fibroblasts and collagen matrix. Exp Cell Res. 1997;232:106-117. 47. Roy P, Petroll WM, Chuong CJ, Jester JV. Effect of cell migration on the maintenance of tension on collagen matrix. Ann Biomed Eng. 1999;27:721-730. 48. Petroll WM, Ma L, Jester JV. Direct correlation of collagen matrix deformation with focal adhesion dynamics in living corneal fibroblasts. J Cell Sci. 2003;116:1481-1491. 49. Munevar S, Wang Y, Dembo M. Traction force microscopy of migrating normal and H-ras transformed 3T3 fibroblasts. Biophys J. 2001;80:1744-1757. 50. Friedl P. Dynamic imaging of cellular interactions with extracellular matrix. Histochem Cell Biol. 2004;122:183-190. 51. Kim A, Lakshman N, Petroll WM. Quantitative assessment of local collagen matrix remodeling in 3-D culture: the role of Rho kinase. Exp Cell Res. 2006;312:3683-3692. 52. Ng CP, Schwartz MA. Mechanisms of interstitual flow-induced remodeling of fibroblast-collagen cultures. Ann Biomed Eng. 2006;34:446-454. 53. Lee P-F, Yeh AT, Bayless KJ. Nonlinear optical microscopy reveals invading endothelial cells anisotropically alter three-dimensional collagen matrices. Exp Cell Res. 2009;315:396-410.

W.M. Petroll and M.M. Mendoza 54. Friedl P, Maaser K, Klein CE, Niggemann B, Krohne G, Zanker KS. Migration of highly aggressive MV3 melanoma cells in 3-dimensional collagen lattices results in local matrix reorganization and shedding of alpha2 and beta1 integrins and CD44. Cancer Res. 1997;57:2061-2070. 55. Petroll WM, Cavanagh HD, Jester JV. Dynamic three-dimensional visualization of collagen matrix remodeling and cytoskeletal organization in living corneal fibroblasts. Scanning. 2004;26:1-10. 56. Hall A. Rho GTPases and the control of cell behaviour. Biochem Soc Trans. 2005;33:891-895. 57. Parizi M, Howard EW, Tomasek JJ. Regulation of LPA-promoted myofibroblast contraction: role of Rho, myosin light chain kinase, and myosin light chain phosphatase. Exp Cell Res. 2000;254:210-220. 58. Amano M, Ito M, Kimura K, et al. Phosphorylation and activation of myosin by Rho-associated kinase (Rho-kinase). J Biol Chem. 1996;271:20246-20249. 59. Amano M, Nakayama M, Kaibuchi K. Rho-kinase/ROCK: A key regulator of the cytoskeleton and cell polarity. Cytoskeleton (Hoboken). 2010;67:545-554. 60. Rottner K, Hall A, Small JV. Interplay between Rac and Rho in the control of substrate contact dynamics. Curr Biol. 1999;9:640648. 61. Jester JV, Chang J-H. Modulation of cultured corneal keratocyte phenotype by growth factors/cytokines control in vitro contractility and extracellular matrix contraction. Exp Eye Res. 2003;77:581-592. 62. Zhou C, Petroll WM. Rho kinase regulation of fibroblast migratory mechanics in fibrillar collagen matrices. Cell Mol Bioeng. 2010;3:76-83. 63. Chen J, Guerriero E, Sado Y, SundarRaj N. Rho-mediated regulation of TGF-beta1- and FGF-2-induced activation of corneal stromal keratocytes. Invest Ophthalmol Vis Sci. 2009;50:36623670. 64. Lakshman N, Petroll WM. Growth factor regulation of corneal keratocyte mechanical phenotypes in 3-D collagen matrices. Invest Ophthalmol Vis Sci. 2012;53:1077-1086. 65. Yamamoto M, Quantock AJ, Young RD, et al. A selective inhibitor of the Rho kinase pathway, Y-27632, and its influence on wound healing in the corneal stroma. Mol Vis. 2012;18:1727-1739. 66. Fink MK, Gupta S, Ebers S, et al. ROCK inhibitor HA1077: Potenly inhibits corneal fibrosis and neovascularization. ARVO Annual Meeting 2016;Program #3481: 67. Sander EE, ten Klooster JP, van Delft S, van der Kammen RA, Collard JG. Rac downregulates Rho activity: reciprocal balance between both GTPases determines cellular morphology and migratory behavior. J Cell biol. 1999;147:1009-1021. 68. Totsukawa G, Yamakita Y, Yamashiro S, Hartshorne DJ, Sasaki Y. Distinct roles of ROCK (Rho-kinase) and MLCK in spatial regulation of MLC phosphorylation for assembly of stress fibers and focal adhesions in 3T3 fibroblasts. J Cell Biol. 2000;150:797-806. 69. Svitkina TM, Borisy GG. Arp2/3 complex and actin depolymerizing factor/cofilin in dendritic organization and treadmilling of actin filament array in lamellipodia. J Cell Biol. 1999;145:10091026.

Copyright © 2018. Kugler Publications. All rights reserved.

Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions 70. Demali KA, Burridge K. Coupling membrane protrusion and cell adhesion. J Cell Sci. 2003;116:2389-2397. 71. Grinnell F, Rocha LB, Iucu C, Rhee S, Jiang H. Nested collagen matrices: A new model to study migration of human fibroblast populations in three dimensions. Exp Cell Res. 2006;312:86-94. 72. Andresen JL, Ledet T, Ehlers N. Keratocyte migration and peptide growth factors: the effect of PDGF, bFGF, EGF, IGF-1, aFGF and TGF-beta on human keratocyte migration in a collagen gel. Curr Eye Res. 1997;16:605-613. 73. Grinnell F. Fibroblast-collagen-matrix contraction: growth-factor signalling and mechanical loading. Trends Cell Biol. 2000;10:362-365. 74. Petroll WM, Ma L. Localized application of mechanical and biochemical stimuli in 3-D culture. Dev Dyn. 2008;237:2726-2736. 75. Kim A, Zhou C, Lakshman N, Petroll WM. Corneal stromal cells use both high- and low-contractility migration mechanisms in 3-D collagen matrices. Exp Cell Res. 2012;318:741-752. 76. Zhou C, Petroll WM. MMP regulation of corneal keratocyte motility and mechanics in 3-D collagen matrices. Exp Eye Res. 2014;121:147-160. 77. Netto MV, Mohan RR, Ambrosio R Jr., Hutcheon AE, Zieske JD, Wilson SE. Wound healing in the cornea: a review of refractive surgery complications and new prospects for therapy. Cornea. 2005;24:509-522. 78. Tovell VE, Chau CY, Khaw PT, Bailly M. Rac1 inhibition prevents tissue contraction and MMP mediated matrix remodeling in the conjunctiva. Invest Ophthalmol Vis Sci. 2012;53:4682-4691. 79. Sailem H, Bousgouni V, Cooper S, Bakal C. Cross-talk between Rho and Rac GTPases drives deterministic exploration of cellular shape space and morphological heterogeneity. Open Biol. 2014;4:130132. 80. Honore S, Pasquier E, Braguer D. Understanding microtubule dynamics for improved cancer therapy. Cell Mol Life Sci. 2005;62:3039-3056. 81. Watanabe TN, J. Kaibuchi, K. Regulation of microtubules in cell migration. Trends Cell Biol. 2005;15:76-83. 82. Rhee S, Jiang H, Ho C, Grinnell F. Microtubule function in fibroblast spreading is modulated according to the tension state of cell-matrix interactions. PNAS. 2007;104:5425-5430. 83. Kolodney MS, Elson EL. Contraction due to microtubule disruption is associated with increased phosphorylation of myosin regulatory light chain. Proc Nat Acad Sci USA. 1995;92:1025210256. 84. Zhang D, Wang Z, Jin N, et al. Microtubule disruption modulates the Rho-kinase pathway in vascular smooth muscle. J Muscle Res Cell Motil. 2001;22:193-200. 85. Ren XD, Kiosses WB, Schwartz MA. Regulation of the small GTP-bounding protein Rho by cell adhesion and the cytoskeleton. EMBO J. 1999;18:578-585. 86. Liu BP C-WM, Burridge K. Microtubule depolymerization induces stress fibers, focal adhesions, and DNA synthesis via the GTP-binding protein Rho. Cell Adhes Commun. 1998;5:249-155. 87. Kwan KM, Kirschner MW. A microtubule-binding Rho-GEF controls cell morphology during convergent extension of Xenopus laevis. Development. 2005;132:4599-4610.

59

88. Krendel M, Zenke FT, Bokoch GM. Nucleotide exchange factor GEF-H1 mediates cross-talk between microtubules and the actin cytoskeleton. Nat Cell Biol. 2002;294-301. 89. Kim A, Petroll WM. Microtubule regulation of corneal fibroblast morphology and mechanical activity in 3-D culture. Exp Eye Res. 2007;85:546-556. 90. Andreassen TT, Simonsen AH, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Exp Eye Res. 1980;31:435-441. 91. Edmund C. Corneal topography and elasticity in normal and keratoconic eyes. A methodological study concerning the pathogenesis of keratoconus. Acta Ophthalmol Suppl. 1989;193:1-36. 92. Ali NQ, Patel DV, McGhee CN. Biomechanical responses of healthy and keratoconic corneas measured using a noncontact scheimpflug-based tonometer. Invest Ophthalmol Vis Sci. 2014;55:3651-3659. 93. Morishige N, Wahlert AJ, Kenney MC, et al. Second-harmonic imaging microscopy of normal human and keratoconus cornea. Invest Ophthalmol Vis Sci. 2007;48:1087-1094. 94. Ambekar R, Toussaint KC Jr., Wagoner Johnson A. The effect of keratoconus on the structural, mechanical, and optical properties of the cornea. J Mech Behav Biomed Mater. 2011;4:223236. 95. Roberts CJ, Dupps WJ Jr. Biomechanics of corneal ectasia and biomechanical treatments. J Cataract Refract Surg. 2014;40:991-998. 96. Petroll WM, Miron-Mendoza M. Mechanical interactions and crosstalk between corneal keratocytes and the extracellular matrix. 2015;133:49-57. 97. Yeung T, Georges PC, Flanagan LA, et al. Effects of substrate stiffness on cell morphology, cytoskeletal structure, and adhesion. Cell Motil Cytoskel. 2005;60:24-34. 98. Miron-Mendoza M, Seemann J, Grinnell F. The differential regulation of cell motile activity through matrix stiffness and porosity in three dimensional collagen matrices. Biomaterials. 2010;31:6425-6435. 99. Kolodney MS, Wysolmerski RB. Isometric contraction by fibroblasts and endothelial cells in tissue culture. J Cell Biol. 1992;117:73-82. 100. Takakuda K, Miyairi H. Tensile behavior of fibroblasts cultured in collagen gel. Biomaterials. 1996;17:1393-1397. 101. Wakatsuki T, Elson EL. Reciprocal interactions between cells and extracellular matrix during remodeling of tissue constructs. Biophys Chem. 2003;100:593-605. 102. Karamichos D, Lakshman N, Petroll WM. Regulation of corneal fibroblast morphology and collagen reorganization by extracellular matrix mechanical properties. Invest Ophthalmol Vis Sci. 2007;48:5030-5037. 103. Zareian R, Susilo ME, Paten JA, et al. Human corneal fibroblast pattern evolution and matrix synthesis on mechanically biased substrates. Tissue Eng Part A. 2016;22:1204-1217. 104. Hadjipanayi E, Mudera V, Brown RA. Guding cell migration in 3D: A collagen matrix with graded directional stiffness. Cell Motil Cytoskel. 2009;66:121-129.

Copyright © 2018. Kugler Publications. All rights reserved.

60 105. Lo CM, Wang HB, Dembo M, Wang YL. Cell movement is guided by the rigidity of the substrate. Biophys J. 2000;79:144-152. 106. Miron-Mendoza M, Lin X, Ma L, Ririe P, Petroll WM. Individual versus collective fibroblast spreading and migration: regulation by matrix composition in 3D culture. Exp Eye Res. 2012;99:36-44. 107. Petroll WM, Cavanagh HD, Barry P, Andrews P, Jester JV. Quantitative analysis of stress fiber orientation during corneal wound contraction. J Cell Sci. 1993;104:353-363. 108. Jester JV, Petroll WM, Barry PA, Cavanagh HD. Temporal, 3-dimensional, cellular anatomy of corneal wound tissue. J Anat. 1995;186:301-311. 109. Petroll WM, Kivanany PB, Hagenasr D, Graham EK. Corneal fibroblast migration patterns during intrastromal wound healing correlate with ECM structure and alignment. Invest Ophthalmol Vis Sci. 2015;56:7352–7361. 110. Hegerfeldt Y, Tusch M, Brocker E-B, Friedl P. Collective cell movement in primary melanoma explants: plasticity of cellcell interaction, b1-integrin function, and migration strategies. Cancer Res. 2002;62:2125-2130. 111. Ilina O, Friedl P. Mechanisms of collective cell migration at a glance. J Cell Sci. 2009;122:3203-3208. 112. Friedl P, Zallen JA. Dynamics of cell-cell and cell-matrix interactions in morphogenesis, regeneration and cancer. Curr Opin Cell Biol. 2010;22:557-559. 113. Freyman TM, Yannas IV, Yokoo R, Gibson LJ. Fibroblast contractile force is independent of the stiffness which resists the contraction. Exp Cell Res. 2002;272:153-162. 114. Liu C, Feng P, Li X, Song J, Chen W. Expression of MMP-2, MT1-MMP, and TIMP-2 by cultured rabbit corneal fibroblasts under mechanical stretch. Exp Biol Med (Maywood). 2014;239(8):907-912. 115. Petroll WM, Vishwanath M, Ma L. Corneal fibroblasts respond rapidly to changes in local mechanical stress. Invest Ophthalmol Vis Sci. 2004;45:3466-3474. 116. Mizutani T, Haga H, Kawabata K. Cellular stiffness response to external deformation: tensional homeostasis in a single fibobroblast. Cell Motil Cytoskel. 2004;59:242-248. 117. Wang YL. Exploring the basic principles of cell shape control. Frontiers in Cell Migration. Bethesda, MD 2008. 118. Kim W-J, Mohan RR, Mohan RR, Wilson SE. Effect of PDGF, IL-1α, and BMP2/4 on corneal fibroblast chemotaxis: expression of the platelet-derived growth factor system in the cornea. Invest Ophthalmol Vis Sci. 1999;40:1364-1372. 119. Musselmann K, Kane BP, Alexandrou B, Hassell JR. IGF-II is present in bovine corneal stroma and activates keratocytes to proliferate in vitro. Exp Eye Res. 2008;86:506-511. 120. Arnold DR, Moshayedi P, Schoen TJ, Jones BE, Chader GJ, Waldbillig RJ. Distribution of IGF-I and -II, IGF binding proteins (IGFBPs) and IGFBP mRNA in ocular fluids and tissues: potential sites of synthesis of IGFBPs in aqueous and vitreous. Exp Eye Res. 1993;56:555-565. 121. Tuominen IS, Tervo TM, Teppo AM, Valle TU, Gronhagen-Riska C, Vesaluoma MH. Human tear fluid PDGF-BB, TNF-alpha and TGF-beta1 vs corneal haze and regeneration of corneal epithelium and subbasal nerve plexus after PRK. Exp Eye Res. 2001;72:631-641.

W.M. Petroll and M.M. Mendoza 122. Jester JV, Huang J, Petroll WM, Cavanagh HD. TGFbeta induced myofibroblast differentiation of rabbit keratocytes requires synergistic TGFbeta, PDGF and integrin signalling. Exp Eye Res. 2002;75:645-657. 123. Meyer-ter-Vehn T, Han H, Grehn F, Schlunck G. Extracellular matrix elasticity modulates TGF-β-induced p38 activation and myofibroblast transdifferentiation in human tenon fibroblasts. Invest Ophthalmol Vis Sci. 2011;52:9149-9155. 124. Dreier B, Thomasy SM, Mendonsa R, Raghunathan VK, Russell P, Murphy CJ. Substratum compliance modulates corneal fibroblast to myofibroblast transformation. Invest Ophthalmol Vis Sci. 2013;54:5901-5907. 125. Etheredge L, Kane BP, Hassell JR. The effect of growth factor signaling on keratocytes in vitro and its relationship to the phases of stromal wound repair. Invest Ophthalmol Vis Sci. 2009;50:3128-3136. 126. Berthaut A, Mirshahi P, Benabbou N, et al. Insulin growth factor promotes human corneal fibroblast network formation in vitro. Invest Ophthalmol Vis Sci. 2011;52:7647-7653. 127. Ghibaudo M, Trichet L, Le Digabel J, Richert A, Hersen P, Ladoux B. Substrate topography induces a crossover from 2D to 3D behavior in fibroblast migration. Biophys J. 2009;97:357-368. 128. Kriparamanan R, Aswath P, Zhou A, Tang L, Nguyen KT. Nanotopography: cellular responses to nanostructured materials. J Nanosci Nanotechnol. 2006;6:1905-1919. 129. Kim DH, Provenzano PP, Smith CL, Levchenko A. Matrix nanotopography as a regulator of cell function. J Cell Biol. 2012;197:351-360. 130. Frey MT, Tsai IY, Russell TP, Hanks SK, Wang YL. Cellular responses to substrate topography: role of myosin II and focal adhesion kinase. Biophys J. 2006;90:3774-3782. 131. Teixeira AI, Nealey PF, Murphy CJ. Responses of human keratocytes to micro- and nanostructured substrates. J Biomed Mater. Res A 2004;71A:369-376. 132. Teixeira AI, Abrams GA, Bertics PJ, Murphy CJ, Nealey PF. Epithelial contact guidance on well-defined micro- and nanostructured substrates. J Cell Sci. 2003;116:1881-1892. 133. Myrna KE, Mendonsa R, Russell P, et al. Substratum topography modulates corneal fibroblast to myofibroblast transformation. Invest Ophthalmol Vis Sci. 2012;53:811-816. 134. Guillemette MD, Cui B, Roy E, et al. Surface topography induces 3D self-orientation of cells and extracellular matrix resulting in improved tissue function. Integr Biol (Camb). 2009;1:196-204. 135. Saeidi N, Guo X, Hutcheon AE, et al. Disorganized collagen scaffold interferes with fibroblast mediated deposition of organized extracellular matrix in vitro. Biotechnol Bioeng. 2012;109:2683-2698. 136. Guo XQ, Hutcheon AE, Melotti SA, Zieske JD, Trinkaus-Randall V, Ruberti JW. Morphologic characterization of organized extracellular matrix deposition by ascorbic acid-stimulated human corneal fibroblasts. Invest Ophthalmol Vis Sci. 2007;48:40564060. 137. Karamichos D, Guo XQ, Hutcheon AE, Zieske JD. Human corneal fibrosis: an in vitro model. Invest Ophthalmol Vis Sci. 2010;51:1382-1388.

Cellular micromechanics of corneal stroma: keratocyte and extracellular matrix interactions

Copyright © 2018. Kugler Publications. All rights reserved.

138. Ren R, Hutcheon AEK, Guo XQ, et al. Human primary corneal fibroblasts synthesize and deposit proteoglycans in long-term cultures. Dev Dyn. 2008;237:2705-2715. 139. Karamichos D, Funderburgh ML, Hutcheon AE, et al. A role for topographic cues in the organization of collagenous matrix by corneal fibroblasts and stem cells. PLoS One. 2014;9:e86260. 140. Garland SP, McKee CT, Chang YR, Raghunathan VK, Russell P, Murphy CJ. A cell culture substrate with biologically relevant size-scale topography and compliance of the basement membrane. Langmuir. 2014;30:2101-2108. 141. Kshitiz, Park J, Kim P, et al. Control of stem cell fate and function by engineering physical microenvironments. Integr Biol (Camb). 2012;4:1008-1018. 142. Reilly GC, Engler AJ. Intrinsic extracellular matrix properties regulate stem cell differentiation. J Biomech. 2010;43:55-62. 143. Du Y, Funderburgh ML, Mann MM, SundarRaj N, Funderburgh JL. Multipotent stem cells in human corneal stroma. Stem Cells. 2005;23:1266-1275. 144. Funderburgh JL, Funderburgh ML, Du Y. Stem Cells in the Limbal Stroma. Ocul Surf. 2016;14:113-120. 145. Du Y, SundarRaj N, Funderburgh ML, Harvey SA, Birk DE, Funderburgh JL. Secretion and organization of a cornea-like tissue in vitro by stem cells from human corneal stroma. Invest Ophthalmol Vis Sci. 2007;48:5038-5045. 146. Wu J, Du Y, Watkins SC, Funderburgh JL, Wagner WR. The engineering of organized human corneal tissue through the spatial guidance of corneal stromal stem cells. Biomaterials. 2012;33:1343-1352. 147. Wu J, Du Y, Mann MM, Yang E, Funderburgh JL, Wagner WR. Bioengineering organized, multilamellar human corneal stromal tissue by growth factor supplementation on highly aligned synthetic substrates. Tissue Eng Part A. 2013;19:2063-2075. 148. Syed-Picard FN, Du Y, Hertsenberg AJ, et al. Scaffold-free tissue engineering of functional corneal stromal tissue. J Tissue Eng Regen Med. 2016;

61

149. Doyle AD, Wang FW, Matsumoto K, Yamada KM. One-dimensional topography underlies three-dimensional fibrillar cell migration. J Cell Biol. 2009;184:481-490. 150. Provenzano PP, InMan DR, Eliceiri KW, Trier SM, Keely PJ. Contact guidance mediated three-dimensional cell migration is regulated by Rho/ROCK-dependent matrix reorganization. Biophys J. 2008;95:5374-5384. 151. Dickinson RB, Guido S, Tranquillo RT. Biased cell migration of fibroblasts exhibiting contact guidance in oreinted collagen gels. Ann Biomed Eng. 1994;22:342-356. 152. Guido S, Tranquillo RT. A methodology for the systematic and quantitative study of cell contact guidance in oriented collagen gels. Correlation of fibroblast orientation and gel birefringence. J Cell Sci. 1993;105(Pt 2):317-331. 153. Susilo ME, Paten JA, Sander EA, Nguyen TD, Ruberti JW. Correction to ‘Collagen network strengthening following cyclic tensile loading’. Interface Focus. 2016;6(3):20160020. 154. Torbet J, Malbouyres M, Builles N, et al. Orthogonal scaffold of magnetically aligned collagen lamellae for corneal stroma reconstruction. Biomaterials. 2007;28:4268-4276. 155. Young RD, Knupp C, Pinali C, et al. Three-dimensional aspects of matrix assembly by cells in the developing cornea. Proc Natl Acad Sci USA. 2014;111:687-692. 156. Farid M, Morishige N, Lam L, Wahlert A, Steinert RF, Jester JV. Detection of corneal fibrosis by imaging second harmonic-generated signals in rabbit corneas treated with mitomycin C after excimer laser surface ablation. Invest Ophthalmol Vis Sci. 2008;49:4377-4383. 157. Kim A, Lakshman N, Karamichos D, Petroll WM. Growth factor regulation of corneal keratocyte differentiation and migration in compressed collagen matrices. Invest Ophthalmol Vis Sci. 2010;51:864-875.

Copyright © 2018. Kugler Publications. All rights reserved.

5. The electrochemical basis of corneal hydration, swelling, and transparency Peter M. Pinsky, Xi Cheng

Copyright © 2018. Kugler Publications. All rights reserved.

Department of Mechanical Engineering, Stanford University, Stanford, California, USA

1. Abstract

2. Introduction

Fluid pressure, water content, and charge concentration are intimately coupled in the corneal stroma. The fluid pressure is composed of a hydrostatic pressure component associated with the intraocular pressure (IOP) and an osmotic pressure component associated with the excess concentration of ions in the stroma compared to the aqueous humor. While the value of the IOP is fixed, in the living cornea, ion pumps located in the endothelium actively modulate the osmotic pressure. The osmotic pressure in turn causes water exchange between the stroma and aqueous humor. The resulting hydration of the stroma will have a direct effect on the collagen fibril lattice, and therefore, on the transparency of the tissue. The entire system is driven by the energy of various charges, as well as the metabolic energy used in ion transport. In this chapter, we attempt to provide a comprehensive model for corneal hydration, swelling and transparency. Many parts of this system have been both experimentally investigated and modeled in previous groundbreaking studies. In this work, we describe a macroscopic model for in-vivo corneal hydration based on a novel energy approach that can be used for predicting stromal hydration under various conditions, for example, under variations in metabolic state, and for improving the description of corneal biomechanics.

The fluid pressure within the corneal stroma is composed of hydrostatic and osmotic components. The hydrostatic pressure results from the IOP of the anterior chamber, whereas the osmotic pressure results from the interplay of fixed charges and mobile ions. In fact, from an electrochemical perspective, the corneal stroma is a highly-hydrated polyelectrolyte gel consisting of an interacting mixture of fluid, solid, and ionic phases. Stromal water saturates the collagen and proteoglycan solid phase, solvates the ionic phase, and accounts for about 78% of the cornea by weight.1 A small portion of the water is cellular or bound to the stromal collagen,2,3 but most of the water is free to flow within the stroma in response to gradients in fluid pressure. The solid phase is comprised of a flexible collagen network, organized as fibrils within lamellae, and associated proteoglycans (PGs). Stromal PGs — which in adult stroma include decorin, lumican, keratocan, and mimecan — have sulfated linear sidechains of negatively charged disaccharide units called glycosaminoglycans (GAGs) that are covalently bound at one end to the PG core protein.4,5 Common stromal GAGs include keratan sulfate (KS), dermatan sulfate (DS) and chondroitin sulfate (CS). At normal pH, the stromal fixed charge is almost entirely due to GAG ionization.6 The ionic phase includes dissolved salts, primarily Na+ and Cl−, and metabolites such as ​​C​ 3​​​H​ 5​​​O​ ‒3​   ​​ (lactate ion) and HCO−3 (bicarbonate ion). Stromal mobile ions interact electrostatically with the GAG fixed charges and form cloudlike distributions,

Correspondence: Peter M. Pinsky, Department of Mechanical Engineering, Stanford University, Stanford CA 94305-4040, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 63-79 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

Copyright © 2018. Kugler Publications. All rights reserved.

64

giving rise to osmotic pressure. The aqueous humor, filling the anterior chamber, acts as an ionic bath for the stroma and provides a reservoir of water that is available for exchange with the stroma. The anterior stroma is sealed by the tight boundaries of epithelial cellular layer, making it nearly impermeable to water (although permeable to O2 and CO2).7 Water transport across the permeable endothelial layer, which partitions the stroma and aqueous humor, is driven by the osmotic pressure difference between the two phases. When ionic concentration in the stroma exceeds that in the aqueous humor, a positive osmotic pressure difference is created and water will tend to flow from the aqueous chamber into the stroma, and vice-versa when the osmotic pressure difference is negative. In the metabolically functioning (in-vivo) cornea, ion pumps, located in the endothelial layer, actively transport ions from the stroma into the aqueous humor. This lowers stromal osmotic pressure and modulates the exchange of water with the aqueous humor, and is referred to as the pump-leak mechanism of stromal hydration.8-10 The regulatory system and details of the molecular mechanisms responsible for active ion transport, which requires Na+, K+, ATPase, and carbonic anhydrase activity to transport ​​HCO​ ‒3​   ​​, Cl− and possibly Na+, are not yet fully understood.10 It may be noted that the pump-leak mechanism is not unique to the cornea. A number of tissues employ epithelial and/or endothelial layers as barriers to separate phases, and to actively mediate the exchange of solutes and solvent between those phases. Other examples include the lining of blood vessels, the kidney, organs of the gastrointestinal tract, and the choroid plexus in the brain. Charge can produce powerful forces, either directly by electrostatics or indirectly by osmotic effects, and the cornea exploits charge in a variety of remarkable ways. One of those, we believe, is the way in which charge is used for transparency. The transparency of the cornea requires individual collagen fibrils to be maintained in a quasi-regular lattice with short-range order. The origin and nature of forces that must necessarily act on fibrils to maintain the stability of the lattice have long been the subject of speculation. In this chapter, we apply the proposed thermodynamic theory of stromal osmotic pressure to describe how restoring forces can arise from GAG-based osmotic and electrostatic considerations in a manner that maintains the lattice even when strong

P.M. Pinsky and X. Cheng

random variations in GAG distributions are considered. A number of models for corneal swelling have previously been presented. Notable is the non-equilibrium model of Klyce and Russell,11 based on the phenomenological membrane transport theory of Kedem-Katchalsky,12 and the steady-state model of Bryant.13 based on the triphasic theory of Lai et al.14 These works and their extensions, for example, Ruberti et al., Liu et al., and Leung et al.,15,16,17 have modeled the stroma as one-dimensional coupled flow of solvent (water) and ionic solutes across the corneal thickness. In this chapter, a different modeling approach, based on characterizing the free energy of the stromal polyelectrolyte gel, will be introduced. The approach is intrinsically three-dimensional, provides an explicit expression for the stromal osmotic pressure, accounts for the nanoscale spatial distribution of GAG-based fixed charge, and is well-suited to implementation in finite element codes. It is shown that steady state active endothelial ion transport reduces stromal ionic concentrations, which then occur in a modified Boltzmann distribution. This leads to a modification of the osmotic pressure and stromal hydration, manifesting the macroscopic effects of the pump-leak mechanism. In Section 3, the stromal fixed charge distribution is modeled. In Section 3, the stromal free energies are identified and characterized. In Section 4, the ex-vivo cornea (no metabolic activity) is analyzed and the model is applied to stromal swelling pressure and an investigation of the stability of the collagen fibril lattice underlying transparency. In Section 5, the theory is extended to the in-vivo cornea, including active endothelial ion transport and the pump-leak mechanism of corneal hydration. In Section 6, the model is used to investigate the biomechanics of Fuch’s dystrophy, in which endothelial cells have compromised ion-pumping capacity, and to examine the effects of laser-assisted in situ keratomileusis (LASIK) on fluid pressure in the stroma.

3. GAG-based charge in the stroma 3.1. Corneal hydration measures Before characterizing the nature of charge distributions in the stroma, it is first necessary to establish a suitable definition for the level of tissue hydration. A

The electrochemical basis of corneal hydration, swelling, and transparency

65

(a) Epithelium Stroma IOP = 15 mmHg

Endothelium

K

(c)

(b)

Copyright © 2018. Kugler Publications. All rights reserved.

Fig.1. (a) The cornea is a polyelectrolyte gel loaded by the IOP. Stromal lamellae follow the corneal curvature except in the anterior region, where lamellae exhibit inclination and insert into Bowman’s layer under the epithelium. (b) An illustration of the organization of the corneal stroma showing several lamellae and a keratocyte cell. Collagen fibrils within lamellae form a lattice with short range order. (c) Cross-section of a unit cell representing the hexagonal collagen fibril lattice. The GAG-based coating region around fibrils and the interstitial GAG chains are illustrated. (d) The unit cell is a triangular prism (shown in cross-section); the coating and interstitial regions are indicated.

common definition, denoted Hw, is water weight per unit dry (collagen) weight. However, this definition is not convenient for our purpose since we will employ notions from continuum mechanics. An alternative measure is the tissue volume dilation, J, which is defined simply as the swollen volume of the tissue divided by the normo-hydrated volume. Because we will employ the dilation J throughout this work to signify hydration level, it useful to relate the two definitions. By assuming that keratocytes have the mass density of water, the hydration Hw of a sample of stromal tissue can be related to its volume dilation, J, by: (J ‒ ΦrΦcol)ρW H W(J) =  __ ΦΦ ρ     r

col col

(1)

where ρw = 1 g/cm3 and ρcol = 1.36 g/cm3 are the mass density of the water and dry collagen fibrils,18 respectively, and φcol = 0.249 is the collagen fibril volume fraction at normal hydration.3 The volume fraction of collagen molecules within the fibrils (which excludes intrafibrillar bound water) is denoted φr.6,19 We take

normal hydration to be set at Hw = 3.26 and J = 1. Using these conditions in Equation (1), we infer that φr = 0.75. Therefore, Equation (1) may be simplified to: H W(J) = 3.94J ‒ 0.74

(2)

The linearity is fully consistent with measurements.20,21 A validation of this relationship is provided by the fact that the inferred value of φr is in close agreement with the value of 0.77 reported by Goodfellow.19 In the following subsections, we aim to characterize the magnitude and nanoscale distribution of the GAG ionization charge in human stroma. This is an essential step in describing the stromal polyelectrolyte gel. 3.2. Evidence for a GAG-based fibril coating X-ray scattering studies under varying tissue hydration2 suggest that some portion of stromal PGs form a charge-rich and water-binding PG-coating surrounding each collagen fibril. The radius of the coating has been measured2 to be rc = 18.25 nm, and this radius is

66

P.M. Pinsky and X. Cheng

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 2. Disaccharide repeat units of KS, DS, CS4, and CS6.

insensitive to hydration over a wide range. The existence of such a surface ultrastructure on the collagen fibrils is corroborated by image studies from Miyagawa et al.22 and Muller et al.23 In addition, a theoretical study on transparency by Twersky24 proposed that collagen fibrils must be centered in a transparent coating and the coated fibrils occupy approximately 60% of the matrix volume, giving rc = 21.56 nm. Recent 3-D electron microscopy reconstructions of corneal collagen and GAG chains4 also suggests that some GAG chains are in close association with the fibrils, while the remaining GAG chains have a random orientation in the interfibrillar fluid. A theoretical study by Cheng and Pinsky,25 based on comparing predicted stromal swelling pressure to measurements, indicated that approximately 35% of stromal fixed charge was in the non-swelling fibril coating region, and that 65% occupied the interstitial region between coatings (Fig. 1). The study concluded that this charge arrangement was capable of producing osmotic restoring forces that maintain the stability of the fibril lattice, and that the coating region provided an effective interfibrillar electrostatic repulsion to prevent fibril clustering.

3.3. Model for GAG charge concentration The molecular structure of GAG chains is shown in Figure 2. Each sulfate group carries one negative charge per group. The KS disaccharides are sulphated at the 6− carbon position of both the Gal and GlcNAc residues. The CS disaccharides are sulfated at either the 4− or 6−carbon position of the GalNAc residue, and are designated CS4 or CS6, respectively (Fig. 2). However, a detailed fluorophore-assisted carbohydrate electrophoresis (FACE) analysis25,26 shows that, on average, only 72.6% of all available GAG monosaccharides are actually sulfated and contributing charge. If this ionization fraction is denoted fion , the stromal average charge concentration in mM is given by:  e​Ng​  ​​​L​ c​​​f​ ion​​

​​Cstroma ​  ​​ = _____ ​  Fb ​​ (3)    where e is the unit (negative) charge, Ng is the average number density (per unit volume) of GAG chains with average contour length Lc, F is the Faraday constant, and b is the length of a monosaccharide unit. The value of Cstroma has been measured indirectly,6,27 and the value used in this study, Cstroma = 38.6 mM, has been taken from Cheng and Pinsky.25 The corneal stroma is composed of parallel arrays of collagen fibrils aligned with the lamella direction and arranged with pseudo-hexagonal packing.4 Based

The electrochemical basis of corneal hydration, swelling, and transparency

on the above noted evidence, it is assumed that there exists a GAG-dense coating around each collagen fibril surface. The simplest 3-D representative unit cell within a stromal lamella is that of an equilateral triangular prism with vertices at the center of three fibrils (Fig. 1c). The unit cell is divided into three regions: fibril, fibril coating, and interstitial regions (Fig. 1d). Assuming that collagen fibrils are non-swelling and that keratocyte cells, which reside between adjacent lamellae, dilate with tissue dilation,3,25 the normalized fixed charge densities in the fibril coating and interstitial regions may be shown to be given by:25 λ 1 ‒ λ ​C​ stroma​​ ​ J​Φ​ ' ​ ​ ‒ Φ     ​ + ​_   Φ    ​ ​​ _____ (4) ​​C​ coat(​​​ J)​= ​ __ 2​C​   ​​  ​​

67

4. Basic polyelectrolyte theory for the stroma

4.1. Gibb’s free energy From the point of view of electrochemistry, the stroma is a polyelectrolyte (polymeric electrolyte) gel. It is in contact, via the endothelium, with the aqueous humor, that therefore acts as an ionic bath for the stromal electrolyte. In the living cornea, the pump-leak mechanism, alluded to in Section 2, has a strong influence on the tissue osmotic pressure. In this section, however, we develop basic theory for isolated stroma without metabolic activity, that is, for in-vitro tissue. Extension to the in-vivo case is undertaken in Section 6. ( k f 0 c ) The stroma consists of a mixture of solid, fluid, and ​C​ stroma​​ λ __ _____ ( ) ​​C​ inter​​​ J ​= ​ ​ J​Φ​ ' ​ ​ ‒ Φ     ​ ​  ​    ​​ (5) ionic phases, immersed in an ionic bath (aqueous ( k f ) 2​C​ 0​​ humor) at constant electrostatic potential, φbath, In these expressions, J is the tissue macroscopic dilation, hydrostatic pressure, Pbath , and ionic concentration, C0+ λ = 0.65 is the interstitial charge partition parameter, φk, = C0− = C0. Since no fixed charge exists in the bath, it is φf, and φc denote the volume fractions for keratocytes, reasonable to take φbath = 0. We now wish to describe collagen fibrils, and coatings, respectively, and­ the deformation of the unit cell, introduced in Section ​​Φ​ ‘k ​​  = 1 ‒ Φk ​. The normalization concentration is 2C0, 2, as the tissue undergoes a change in hydration. Let where C0 is the ionic concentration of the aqueous the reference (normo-hydrated) and current (swollen) humor. For convenience, we combine the above charge configurations of the unit cell be denoted Ω0 and Ω, respectively, with volumes v0 and v, respectively. concentrations into a single expression as follows: Using standard results from continuum mechanics, Ccoat in the coating region   (6) ​  ​ ​​ ​​C​ cell​​ = ​ ​  the motion is denoted ϕ(X): Ω0 → Ω, the deformation  Cinter in the interstitial region { gradient is F = ∂ϕ(X)/∂X, and the displacement field is u(X) = ϕ(X) −√X. The Cauchy-Green deformation tensor The expressions for coating and interstitial charge con- is defined by C = FT F and volume dilation J = detC (which centrations take into account the fact that GAG fixed is related to stromal hydration through (Eq. 2)). charge cannot occupy the fibril or keratocyte volumes. It is next assumed that the Gibbs free energy of the Thus, when the unit cell volume decreases, it does so unit cell electrolyte can be additively decomposed28 as only by reduction in interstitial fluid, which causes a follows: rapid increase in the interstitial fixed charge concentra​W(​ Φ, C)​= Welectrolyte​(Φ, J)​+ Wbath(​ J)​+ Welastic(​ C)​​ tion and osmotic pressure. This volume-exclusion effect ​=​∫Ω   ​​​​  [Шelectrolyte​(Φ, J)​ + Шbath(​ J)​ + Шelastic(​ C)​]​dΩ​ (9) built into the charge model in Equations (4) and (5) is crucial for explaining the strongly non-linear variation where Шelectrolyte, Шbath , and Шelastic denote the free energy of osmotic pressure with dilation in the cornea. For future reference, it is noted that the volumes of density (per unit reference volume) of the electrolyte, the coating and interstitial regions of the unit cell are bath solution, and the elastic fibers of the gel, respectively, and φ is the electrostatic potential. given by: A suitable form for Шelectrolyte is given by the mean-field approximation,29 and is expressed as: v​​ ​ coat​​ = Φcv0,​ (7) ' ​​v​ inter(​​​ J)​= (​ J​Φ​ k ​ ​ ‒ Φf ‒ Φc)​v0​ (8) ​Шelectrolyte​(Φ, J)​= J​[zcellFCcell(​ J)​Φ ‒ 2RTC0 where υ0 is the volume of the normo-hydrated unit cell.

|

Copyright © 2018. Kugler Publications. All rights reserved.

0

68

P.M. Pinsky and X. Cheng

| |2 ​(cosh​(_ ​ RT   ​ Φ)​‒ 1)​‒ ​ _ 2 ​​  ▽Φ ​]​​, εw

F

(10)

where zcell = −1 is the GAG-based fixed charge valence value, and R, T, F, and εw are the gas constant, temperature, Faraday constant, and dielectric permittivity of the electrolyte solvent, respectively. The first term on the right-hand side measures the free energy of the fixed charge, the second term measures the excess mean concentration of the mobile ions at any point in the electrolyte compared to the bath and, after multiplication by RT, may be interpreted as the osmotic work of introducing excess ions into the neighborhood of the fixed charges, Ccell, and the last term measures the dielectric free energy. The bath free energy density, which measures the potential of the bath hydrostatic pressure, Pbath, to do work associated with configuration volume change, by: (11) ​ bath(​ J)​= ‒Pbath(​ J ‒ 1)​.​ Ш For reasons of brevity, the elastic free energy, Шelastic, appearing in Equation (9), which corresponds to the elasticity of the collagen fibrils and their 3-D organization, is not discussed in this chapter, but full details may be found elsewhere.30 4.2. Thermodynamic equilibrium In thermodynamic equilibrium, equilibrium requires: ∂W​(Φ, C)​ ____ ​​  ∂Φ   ​ ​​|​​​ C = constant​​ = 0​

electrostatic

(12)

Copyright © 2018. Kugler Publications. All rights reserved.

and mechanical equilibrium requires: ∂W​(Φ, C)​ ____ ​​  ∂C   ​​​| ​​​ Φ = constant​​ = 0​

(13)

​▽2Φ = _ ​ εw   ( ​​ ‒Ccell(​ J)​ + 2C0sinh​(_ ​ RT   ​ Φ)​)​​

(14)

where the Gibb’s free energy, W, is given by Equation (9). Condition (Eq. (12)) implies31 that: F

F

holds over Ω. This result can also be displayed in the form of the Poisson-Boltzmann equation: F

(

 

)

​‒▽2Φ = _ ​ εw ​ ​  ‒Ccell​(J)​ + ​  ∑   ​​z​  iCi​(Φ)​ ​,​ i = +,‒

(15)

wherein the mobile ion concentrations, Ci (moles per

liter), satisfy the Boltzmann distribution given by: ​​C​ i​​​(Φ)​ = C0exp​(‒zi_ ​ RT   ​Φ)​, i = +,‒​ F

(16)

and in which the binary ion valence numbers are z+ = 1 and z− = −1. Condition (Eq. (13)) implies31 that: d ​ iv σelastic ‒ grad (​ Posmotic + Pbath)​ = 0​

(17)

holds over Ω. In this expression, σelastic is the effective Cauchy stress, Posmotic is the osmotic pressure defined by: ∂Шelectrolyte

​​P​ osmotic​​ = ‒​  ___________  ​ ,​ (18) ∂J    and Pbath is the bath (aqueous humor) hydrostatic pressure defined by: ∂Шbath

​Pbath = ‒​ _ . (19) ∂J   ​​ Finally, from Equation (17), we may identify the stromal fluid pressure Pfluid as: ​Pfluid = Posmotic + Pbath​ (20) This is a useful formulation because it provides an explicit constitutive equation for the osmotic pressure (Eq. 18). However, the Poisson-Boltzmann equation (Eq. 15) must be solved over the unit cell for the electrostatic potential φ that will be rapidly varying at the nanoscale. To address this challenge and arrive at a tractable theory, we modify the above approach by employing the concept of energy-based homogenization. 4.3. Volume-averaged free energy The idea is to employ a homogenization of the electrolyte free energy density based on its volume average over the unit cell. This is given by: 1 Ш ​​ ​ υ  ​​∫  Ω   ​​Ш ​  electrolyte​(Φ, J)​dΩ​ ​​​ ¯ electrolyte(​​​ Φ, J)​ = _ 0

0

(21)

where υ0 is the volume of the normo-hydrated (reference) unit cell Ω0. Now, the homogenized osmotic pressure is defined by: ∂​​¯ Ш​​     

​​

electrolyte ​​​ ¯​​  osmotic​​ = ‒​ ______ P     ∂J ​.​ (22)

The electrochemical basis of corneal hydration, swelling, and transparency

As noted above, the electrostatic potential φ must be solved from the Poisson-Boltzmann Equation (15). However, a good approximation for φ is given by the so-called Donnan potential, φe. The Donnan potential, φe, is defined to be that potential which satisfies the Poisson-Boltzmann Equation (15) when the fixedcharge concentration is uniform (constant). Since Ccell is piecewise constant over the coating region and interstitial region, the Donnan potential will likewise be piecewise constant over the unit cell and is given by: RT ‒1 ˜ cell(​​​ J)​= ‒ ​ _ ​​​Φ​​ F   ​ ​sinh​​  ​Ccell​ (23)

with:

˜ ​​  coat​​ in the coating region Φ​​ ˜ ​​​  cell​​ = ​ ​  Φ​​   ​ ​ ​​ {Φ​​ ˜ ​​  inter​​ in the interstitial region

|

(24)

The accuracy of this approximation has been confirmed by comparing the Donnan and true electrostatic potentials for the unit cell.30 The electrolyte free ˜ energy density is now found by replacing φ with Φ​​ ​​​  cell​​​ in Equation (10), resulting in: ˜ Ш ​​ ​ electrolyte​​​(J)​=J​[‒FCcellΦ​ ​˜ cell‒2RTC0​(cosh​(_ ​ RT   Φ​​ ​​​  cell​​)​‒ 1)​]​​ (25) F

Notice that Шelectrolyte now depends only on J since Ccell ˜ cell​​​(J)​​. This result may be introduced into (J) and ​​​Φ​​ Equation (21) to arrive at the homogenized electrolyte free energy density:

the GAGs in the coating region. It is important to note that the model has no free parameters; the osmotic pressure is expressed only in terms of experimentally determined quantities, such as collagen fibril and keratocyte volume fractions as well as stromal average charge concentration. In the next section, we explore the application of the presented theory to in-vitro swelling and the self-organization of the fibril lattice.

5. The stroma in-vitro 5.1. Swelling behavior To obtain a validation of the model, the above osmotic theory was incorporated into a finite element model of the cornea, including collagen fibrils aligned according to X-ray scattering measurements.30 The model was used to compare predicted osmotic pressure (given by (Eq. 27) with experimental measurements of swelling pressure.20,32 Stromal samples, in the form of 7 mm diameter disks, were immersed in an ionic bath of physiological concentration C0 = 150 mM, and loaded by a porous piston across their thickness (Fig. 3a). The piston load was systematically varied, and the equilibrium sample thickness recorded against piston load. The experiments were performed in confined32 and unconfined20 experimental conditions. A finite element model was created to simulate the experimental setup; the model parameters are summarized Table 1. Parameters of the electrolyte model

Copyright © 2018. Kugler Publications. All rights reserved.

1 ¯ Ш​​ ​ v0  [​​ Шcoatvcoat + Шinter vinter]​,​ (26) ​​​   electrolyte​​​(J)​ = _

where vcoat and vinter are the reference volumes of the coating and interstitial regions and given by Equations (7) and (8), respectively. The homogenized osmotic pressure may then be determined from Equation (22) which yields:

]

φf, volume fraction of the collagen fibrils (%)

24.9a

φk, volume fraction of the keratocytes (%)

11.2a

φc, volume fraction of the PG-dense coating (%)

13.3a

0.65c

Q, dimensionless parameter by the ionic pumping 0.965d ,1.0e effect P0, the hydrostatic pressure in bath solution (mmHg) 15.0d, 0e C0, bath concentration (mM)

(27)

The first term in this expression describes a Donnan-like osmotic pressure from the GAGs in the interstitial region and the second term describes the contribution from

Value

λ, the charge partition parameter

Φ

 ​(sinh‒1Ccoat ‒ sinh‒1 Cinter)​ ​​

Parameter

Cstroma, average charge density of the corneal stroma 38.6b (mM)

c   ¯ P​​   ​​ = 2​Φ​ 'k  ​R ​  TC0​ ​(​√ ​Cinter ​ 2  ​ ​+ 1  ​ ‒ 1)​ + ​ ___      ​ Cinter ​​​    osmotic J​Φ​ 'k ​ ​ ‒ Φ [ f

_

69

150

T, temperature (K) Values derived Calibrated value Value estimated25 d Values for the in-vivo corneas30 e Values for in vitro corneas a c

3,25 b

298 25

70

P.M. Pinsky and X. Cheng

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. (a) Illustration of confined and unconfined swelling pressure experiments.20,32 In both experiments, a porous piston loads the cornea in the transverse direction. (b) Comparison of predicted and experimentally measured20,32 values of swelling pressure Ps vs corneal thickness t.

5 4

t m /t 0

in Table 1. The bath hydrostatic pressure Pbath is zero in this case (and the fluid pressure in the stromal sample is purely osmotic pressure). The stroma sample was meshed with 2,500, 27-node hexahedral elements. In order to model confined and unconfined experimental conditions, edge boundary conditions were taken as zero radial displacement or free, respectively (Fig. 3a). Sample thickness vs osmotic pressure is shown in Figure 3b. The predictions show good agreement to measurements for the full range of sample hydration (Hw = 0.05-5.2). At the lowest hydration, the osmotic pressure exceeds 2,000 mmHg. Swelling pressure predictions for the confined and unconfined cases are nearly identical. This is expected because lateral expansion of the sample is restricted by the collagen fibrils, and consequently, stromal volume change in these tests is due to changes in sample thickness. 6 This study provides confirmation of the proposed model for the in-vitro case. The free swelling of the described cylindrical sample of in-vitro stroma is modeled to investigate the effect of the bath ionic concentration. Results for edge-confined free swelling of the stroma sample are shown in Figure 4, which depicts the ratio of swollen thickness to original thickness (swelling ratio) vs bath ionic concentration C0. For dilute bath solutions, the model predicts that the stroma sample will swell to approximately four times its original thickness, which may be compared to experi-

3 2 1 0 10

-3

10

-1

10

1

10

3

10

5

C0 (mM) Fig. 4. Predicted free swelling of stroma in an ionic bath ionic vs bath concentration C0; the swelling ratio is swollen thickness tm divided by original thickness t0.

mental measurements in deionized water33,34 in which human corneas were observed to swell to approximately three times their original thickness. For concentrated bath solutions, the abundance of ions results in ionic shielding of the fixed charges, reduction in osmotic pressure ,and minimal swelling. Both limiting states are captured by the swelling predictions.

Copyright © 2018. Kugler Publications. All rights reserved.

The electrochemical basis of corneal hydration, swelling, and transparency

5.2. Self-organization of the collagen lattice and transparency The stroma, which comprises about 90% of the corneal thickness, is organized into lamellae (i.e., fibers) which contain collagen types I and V in the form of 25-30 nm diameter fibrils. The collagen fibrils within a lamella appear in parallel arrays following the direction of the lamella. In a lamella cross-section, the fibrils assume a quasi-regular packing arrangement with center-to-center interfibrillar distance of 40−60 nm; this arrangement is referred to as the fibril lattice. The short-range order of this lattice produces optical interference effects that render the tissue transparent.35-38 GAGs have an important role in the maintenance of the fibril lattice. Keratan sulfate, the predominant stromal GAG component, has been shown to be involved in modulating the fibril lattice by the knockout of Chst5 in the mouse.39 Scott40 proposed that two or more GAG chains, originating at different core proteins on neighboring fibrils, may form an antiparallel duplexed association which appears as a bridge-like structure spanning the interfibrillar distance in electron microscopy after staining, and that such structures may be capable of controlling the interfibrillar spacing. The open question of how negatively charged and mutually repulsive GAG chains might form durable antiparallel associations has been discussed by Knupp et al.41 The idea of an entropic elastic interconnected fibril-GAG network was employed in the theoretical study on lattice forces and spatial order by Farrell and Hart,42 who proposed a model based on a six-fold symmetric elastic network. A six-fold symmetric structural model was also proposed by Muller et al.,23 in which GAG bridges were proposed to link next-nearest-neighboring fibrils. However, recent 3-D electron tomography imaging4,41 suggests that GAG chains do not appear to exhibit any approximation to a regular six-fold symmetric bridge network or any kind of regularity in spatial organization. Cheng and Pinsky25 modeled the GAGs as a random network of worm-like chains, and concluded that the entropic elasticity of these polymers falls far short of what is needed to maintain the lattice. All of this suggests that fibrillar bridges cannot mediate the lattice through a mechanical mechanism.4 Maurice1,38 speculated that repulsive forces must exist between adjacent fibrils to keep them separated, and that the origin of these forces was related to the

71

Fig. 5. The GAG-based osmotic restoring force mechanism acts on fibrils to stabilize the lattice. (a) Shows a set of fibrils in a regular lattice arrangement with their associated GAG chains forming fibril coatings and interstitial projections. The distribution of mobile ions is also illustrated. (b) The osmotic pressure in each subcell around the undisturbed fibril. Because the osmotic pressure is uniform, the net restoring force is zero (red dot). (c) Shows a single fibril perturbed from its lattice position. The GAG chains attached to the fibril move with the fibril and the GAG fixed charge concentration increases in advance of the fibril motion and reduces behind it. (d) The resulting osmotic pressure in each of the subcells, which is higher where GAG fixed charge concentration has increased and lower where it has reduced. The forces exerted by each of the subcells on the fibril act to restore the fibril towards its regular lattice position (red arrow). This mechanism operates regardless of the direction of the perturbation.

swelling force within the extracellular matrix. Here we propose a mechanism for collagen fibril self-organization based on osmotic pressure gradients that is robust with respect to the random organization of GAG chains.25 Consider an individual fibril in the lattice that is perturbed into to a new position in the lattice while all other fibrils maintain their positions. A restoring force must exist if the lattice is stable. The linear GAG chains are associated with each fibril and attach to that fibril at one end only via the PG core protein. It is reasonable that the attached GAG chains will displace with their supporting fibril. Because the longer chains reach into the interfibrillar fluid, a local change in position of GAG charge concentration will be created, such that the concentration will increase in advance of the displacement and reduce behind it (Fig. 5). The shorter fibril coating GAGs will not play any role in the restoring force until the coatings become close, at which point electrostatic repulsion will add an additional component.

72

P.M. Pinsky and X. Cheng

(a) 6

×10

c

2.5

λ = 0.3 λ = 0.65 λ = 1.0

5 4

f fibril (N/m)

f

r c = 21.56 nm

-3

λ = 0.3 λ = 0.65 λ = 1.0

1.5

3 2

1

0.5

1 0

×10

2

fibril

(N/m)

(b)

r = 18.25 nm

-3

0

5

10

r (nm)

15

20

0

0

5

r (nm)

10

15

Fig. 6. Electrostatic restoring force magnitude on a horizontally displaced fibril in the ideal hexagonal cell for two coating radius values: (a) rc = 18.25 nm; (b) 21.56 nm.

The external work required to move the fibril from its lattice position r0 to perturbed position r1, while fixing the position of other fibrils in the lattice, is given by: ​​W​ ext​​ = ​∫r  r​   ​​ffibril(​ r)​ · dr.​ (28) 1

0

Copyright © 2018. Kugler Publications. All rights reserved.

In thermodynamic equilibrium, the force ffibril is given by: ∂Шelectrolyte  ​​ (29) f​​ ​ fibril​​ = ‒​  ___________ ∂r    which measures the energy cost of moving the fibril through the electrolyte. In order to estimate this force, the fibril lattice is assumed to be perfectly hexagonal. The region between the central (perturbed) fibril and its six neighbors is divided into six subcells with initial volume Vk. The central fibril is then displaced from r0 to a new position r, causing a change ∆Vk in the volume of each subcell (Fig. 5). The GAG fixed charges within subcells are assumed to be conserved during fibril displacement, which is consistent with the GAG-fibril attachment. As the fibril moves into its perturbed position, the charge concentration in each of the six lattice subcells can be estimated as a function of r and the force acting on the fibril is then given by the chain rule as: k ∂​__ Ш​ electrolyte   ​​  6 ∂Jk _ k       ​ =   ​ ∑     ​​   ​ P ​   ​   ​ ​    ​ f​​ ​ fibril​​ = ‒​ ∑ ​​ ​ ​  osmotic ∂r ∂r   ​​ k = 1 k = 1

6



(30)

where the k−subcell osmotic pressure is given by: k ∂​Ш​ electrolyte   ​​ 

k   ​​ = ‒​  __    ​​P​ osmotic ∂JK  ​​ (31)

This result indicates that the local osmotic pressure variation between the subcells serves as the source of an interfibrillar restoring force. It may be easily shown that the vector ∂Jk/∂r is directed toward the center of the lattice for all subcells.25 Therefore, Equation (30) describes a set of centrally oriented restoring forces. When a fibril is perturbed away from its natural lattice position, the osmotic pressure gradient that results always produces a restoring force oriented towards the natural lattice position. When the fibril occupies that natural lattice position, the osmotic pressure is uniform, and the restoring force vanishes. A graphical interpretation of the origin of the lattice restoring force is provided in Figure 5d. Since the stromal free energy Welectrolyte has been modeled, it is possible to develop estimates for the fibril restoring force ffibril . Consider an ideal hexagonal cell with fibrils at each vertex (Fig. 5a). The stroma is assumed to be normally hydrated and GAG fixedcharge concentrations are uniform and equal in each subcell. In this case, the fibril restoring force magnitude may be computed from Equation (30); the result is depicted in Figure 6 for two assumed fibril coating radius values of 18.25 nm and 21.56 nm. The force-fibril perturbation relation exhibits two quasi-linear regimes

The electrochemical basis of corneal hydration, swelling, and transparency

2.5

Prediction Freund et al (1995)

2

g(r)

1.5 1 0.5 0 0

50

100

150

200

r (nm)

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 7. Comparison of the predicted RDF, denoted g(r), from the fibril dynamics model with the measured RDF from an electron micrograph of human cornea.43

with a transition where the coatings begin to interact. For small perturbations, the osmotic-based restoring force is dominant, but as the perturbation increases to the point where the PG-coatings begin to overlap, there is a marked increase in repulsion force between the fibrils. This provides a mechanism preventing fibril aggregation. The lattice restoring force and its role in lattice self-organization was further studied by using a transient dynamic model.25 The model included randomness in the lattice so that the fibrils are never arranged in perfect hexagonal symmetry. The goal was to investigate whether the proposed osmotic restoring forces maintained the lattice in a dynamic and random environment. The results were interpreted by computing the predicted radial distribution function (RDF) of the fibrils, which is a measure of the order of a lattice.43 RDF results from the dynamic simulation were shown to closely match measurements based on electron micrographs,43 and indicated short-range order in the lattice with correlations between any two fibrils becoming nearly random after a distance of 200 nm (Fig. 7). The average interfibrillar distance, which corresponds to the location of the first peak in the RDF, was maintained at 53 nm in all random cases studied. These results support the proposed osmotic theory for lattice self-organization.

73

6. The stroma in vivo 6.1. Active ion transport and hydration control The corneal endothelium is a 4 µm thin cellular monolayer with a very high density of mitochondria, indicating high metabolic activity, and is located on the posterior surface of the cornea. It is permeable to water, metabolic species, including glucose and lactate ion, and other salt ions. The corneal endothelium is responsible for maintaining the hydration of the cornea through a pump-leak mechanism.8 The pump function is provided by active ion transport across the endothelium9 that regulates the osmotic pressure of the stroma. The leak function refers to the passive exchange of water across the endothelium through water channels in response to the stromal osmotic pressure. In this section, we introduce a macroscopic model for the pump-leak mechanism and use the model to quantitatively illustrate how stromal hydration is modulated. The model is formulated in three steps. First, steadystate (but non-equilibrium) conditions are used to establish the jump in electrochemical potential across the endothelial layer as a function of the steady active ion fluxes. Then, thermodynamic equilibrium within the stroma is used to establish a modified Boltzmann distribution that governs ionic concentrations throughout the stroma. Finally, a modified free energy provides the stromal osmotic pressure, describing its dependence on the endothelial active ion transport. To assess the electrochemical potential jump across the endothelial layer, it is treated as an ideal membrane in which the action of the ion pumps is represented by an independently specified active steady anion flux Ja− and cation flux Ja+, transporting ions out of the stroma and into the aqueous humor.13 Because the endothelium is thin compared to the stroma, it is assumed that transport across the endothelium is 1-D. A coordinate z is introduced with z = z0 at the endothelium-aqueous humor interface and z = z* at the endothelium-stroma interface. At steady-state, net ionic fluxes resulting from both active and passive transport will vanish so that: dμ

​  dz i ​ ‒ jai = 0, i= +,‒​ ​​J​ i​​ = ‒L i_

(32)

must hold across the endothelial layer thickness z Є

74

P.M. Pinsky and X. Cheng

[z0 ,z*]. In Equation (32), Li is the membrane permeability for ionic species i, µi is the electrochemical potential, and Jai > 0 is the steady active ionic flux across the endothelium. Integrating Equation (32) across the endothelium results in the jump condition for the electrochemical potential: Jai

 L  ​​ (33)   ​​μ​ *i​ ​ ‒ μ0i = ‒h​_ i

where h = z* − z0 is the thickness of the endothelial layer, and ​​μ​ *i​ ​​ and µ0i are the ionic electrochemical potentials at z = z* and z = z0 , respectively. Since no active transport is taking place within the stroma, thermodynamic equilibrium requires µ i = ​​μ​ *i​ ​​ where µi is the electrochemical potential at any point in the stroma. Noting that: FΦ

RT

_ _ μ ​​ ​ i​​ = μ (34) ​ ​ ref i​  ​ + ​ M  ​  ln​C​ i​​ + ​z​ i​​​ M  ​,  i = +,‒​ i i where M+ and M− are the atomic weights for anions and cations, respectively, results in: RT

​C​ i​​

i

0

FΦ

__ ___ ​​μ​ i​​ ‒ ​μ​ 0i​​= ​ ___ ​M ​  ​​​  ln​ ​ C​   ​​ ​  + ​z​ i​​​  ​M​   ​​​  . ​ i

(35)

Substituting Equation (35) in Equation (33), and rearranging gives: ​​C​ i​​ = ​C​ 0​​exp​(‒​_  RT   ​____ ​  ​L​   ​​ ​)   ​ exp​(‒​z​ i​​​ _ ​  ​​. RT ) h ​M​ i​​​J​ ai​​

FΦ

i

(36)

Observing that the first expression in parenthesis on the right-hand side of Equation (36) is dimensionless, we define the membrane active transport factor Qi: ​ i ​ ​​​  J​ai  ​​ h M ​​Q​ i​​ = exp ( ​ ‒​_  RT   ​​ ____ ​Li​  ​​ ​ )​ · i = +, ‒​

(37)

Copyright © 2018. Kugler Publications. All rights reserved.

Finally, stromal ionic concentration (Eq 36) may be written as: ​​C​ i​​ = ​Q​ i​​​C​ o​​exp ( ​ ‒​z​ i​​​ _ ,​ (38) RT ​ )​ FΦ

which generalizes the Boltzmann distribution (Eq. 16). Observe that 0 ≤ Qi ≤ 1 and the value of Qi reduces with increasing active flux Jai. When no endothelial ionic pumping occurs, Jai = 0 and Qi = 1. Equation (38) expresses the idea that when active ionic pumping occurs, Qi < 1 and stromal ionic concentrations are reduced compared to when there is no pumping and Qi = 1. Reduced stromal ionic concentrations produce

reduced osmotic (swelling) pressure, and vice versa. Simply stated, active ionic pumping directly reduces the swelling tendency of the stroma. In this macroscopic description, the pump effect is embedded in the membrane active transport factor Qi. Based on Equation (38), a modified Poisson-Boltzmann equation (see Eq. 16) for the electrostatic potential in a stromal unit cell is introduced as:

(

)

​ ​ε​ w  ​​ ​ ​ ‒​C​ cell​​ + ​  ∑   ​​​z​  ​ i​​​Q​ i​​​C​ 0​​exp​(‒​z​ i_ ​​​ RT  ) ​ ​ ​,​ ​‒▽2Φ = __ F

 

FΦ

i = +,‒

(39)

The Donnan potential over the coating and interstitial regions are solved from Equation (39) by setting the right-hand side to zero, and are given as: _______

​Ccell ​  ​​ ​Ccell ​ 2  ​​  __ ​Q​  ​​ RT _ ___ ˜ cell(​​​ J)​ = ​ _ ​​​Φ​​     l ​ n​ ‒​       ​ + ​   ​  ​ + ​ ​ ​ + ​​​   ​)​ , ​ ( F Q‒  ​Q‒​ 2​ ​ Q ‒

√

(40) where the normalized fixed charge concentration Ccell is given by Equations (4-6). The electrolyte free energy density is then: ˜ ˜ ​​Ш​ cell(​​​ Φ​ ​ ,   J)​ = J​ ‒F​C​ cellΦ​​ ​​​​  cell​​ ‒ RT​C​ 0​​​ ​  ∑   ​​​​ Q​ j​​exp

(j = +,‒

[

 

F˜ ​ ‒​z​ j_ ​​​ RT   Φ​​ ​​​  cell​​)​ ‒ 2 ​ ​ ( )].​ (41)

Introducing the Donnan potentials (Eq. 40) into Equation (41), and the result into Equation (26) provides   . Now, the homogenized unit cell free energy ¯  Ш​​ ​​ electrolyte employing Equation (22) yields the modified unit cell osmotic pressure: c 2 ¯ P​​ ​  T​C​ 0​​​[​(​√ ​C​ inter   ​ ​ + Q ​  ‒ 1)​ + ​_____  J​Φ​ ' ​ ​ ‒ ​ Φ​   ​​ ​ ​C​ f2​​  ​​​   osmotic​​ = 2​Φ​ 'k  ​R

_

​Φ​  ​​

​​ sinh​​​    ​​C​ coat​​ ‒ ​​˜ sinh​​​   ​ ​C​ inter​​)​]​,​ (​ ˜

k

‒1

‒1

f

(42)

in which a modified inverse hyperbolic sine function was introduced: ˜ ​​​ sinh​​​    ​​(x)​= ln​(x + ​√ ​x​​ 2​ + Q )​  ​,​ ‒1

_

(43)

and where Q = Q+Q− is the membrane active transport parameter that describes the combined effect of both the cation and anion active transport. Equation (42) shows that the osmotic pressure is dictated by the combined membrane active transport parameter Q. Estimation of the combined membrane active transport parameter Q is challenging. Based

The electrochemical basis of corneal hydration, swelling, and transparency

(a)

700

680

680

660

660

640

640

CCT (µ m)

CCT (µ m)

700

620

620

600

600

580

580

560

560

540

540

520

75

1

1.5

2

2.5

R

3

3.5

4

4.5

L

520 0.2

0.4

0.6

RJ

0.8

1

Fig. 8. The predicted swollen CCT in Fuch’s dystrophy when (a) the endothelial ionic permeability is increased, such that 1 ≤ RL ≤ 4.5 and with normal active ionic flux RJ = 1, and (b) the active ionic flux rate is reduced, such that 0.2 ≤ RJ ≤ 1 and with normal anionic permeability RL = 1.

Copyright © 2018. Kugler Publications. All rights reserved.

on imbibition pressure measurements in the rabbit cornea, a value of Qphysio = 0.965 has been established.30. Stroma in vitro has no active ionic transport and Q = 1. In this case, the above model reduces to the in-vitro model described in Section 4. In the subsections below, we apply the in-vivo osmotic theory to examine the effects of reduced endothelial ion pumping (Fuch’s dystrophy) and the fluid pressure effects of LASIK. 6.2. Effects of reduced endothelial active ion transport Fuch’s dystrophy is usually characterized by morphological changes in endothelial cells or by an accelerated loss of endothelial cells.10,44 In this situation, the cornea will swell due to increasing endothelial ionic permeability, decreasing active ion flux, or both mechanisms simultaneously. This situation can be modeled by modifying the membrane active transport parameter using Equation (37), such that:      )lnQ physio lnQ patho = (__ R R J L

(44)

where Qpatho is the pathological transport parameter, Qphysio = 0.965, RJ is the pathological/physiological fraction of ionic flux, and RL is the pathological/physiological fraction of ionic permeability.31 A finite element model embedding the above in-vivo osmotic theory and realistic collagen organization was

created,30 and used to analyze a cornea with central corneal thickness (CCT) of 520 µm, and anterior and posterior radii of 7.87 and 6.7 mm, respectively. Figure 8a shows the predicted swollen CCT for 1 ≤ RJ ≤ 4.5 and RJ = 1, and Figure 8b shows the predicted swollen CCT for 0.2 ≤ RJ ≤ 1 and RL = 1. In both cases, the model predicts corneal swelling, with predicted maximum swollen CCT of approximately 690 µm. This lies in the range of clinical observations for Fuch’s dystrophy.45 The model also predicts that swelling is concentrated in the posterior region, a prediction that agrees with clinical observations45 that the anterior surface of the cornea is nearly normal among patients with Fuch’s dystrophy, whereas the posterior surface shows significant change. Figure 9 shows deformations due to swelling when RJ = 0.22. The results suggest the stability of the anterior surface with respect to swelling resulting from the presence of inclined lamellae. 6.3. Osmotic effects in LASIK Laser in-situ keratomileusis (LASIK) is commonly used to correct refractive errors, including myopia and hyperopia. An anterior circular hinged flap of about 150 µm thickness is first created using a femtosecond laser. The flap is then folded back to expose the stromal bed, which is reshaped by excimer laser ablation. The procedure is completed by returning the flap to conform with the ablated profile. Although laser ablation creates a new central corneal curvature with

76

P.M. Pinsky and X. Cheng

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 9. Fringe plot of vertical displacements of a cornea with simulated Fuch’s dystrophy. Ion pumping is reduced to 22% of normal (RJ = 0.22). Most swelling occurs in the posterior stroma.

the goal of achieving emmetropia, the biomechanical response of the residual (significantly thinned) stromal tissue is an important issue.46 In a study,31 normal active endothelium ionic pumping was assumed (Q = Qphysio) and the osmotic model employed to investigate the stromal fluid pressure and swelling resulting from a typical myopic correction. The ablation depth profile was determined using Munnerlyn’s theory47 for an intended correction of 5 diopters. The CCT was 520 µm, the flap thickness was 150 µm, and the maximum ablation depth was 87 µm, resulting in a residual central stromal thickness of 283 µm. The flap is returned after ablation, but it is not mechanically integrated with the stroma.46 The finite element model consisted of 7,008 27-node hexahedral elements. The solution was obtained in two steps: 1. a pre-surgical step in which the normal cornea was loaded by an IOP of 15 mmHg and the collagen prestress obtained; and 2. a post-surgical step in which the flap is separated and ablated tissue removed. Predicted curvature change, post-surgical corneal radius, and spherical equivalent agreed well with clinical measurements by Ortiz et al.48 on 85 eyes with myopia or myopic astigmatism.30 As noted in Section 6.1, the active transport parameter Qphysio was calibrated based on direct experimental measurement of imbibition pressure in in-vivo rabbit corneas.49 Those measurements imply that in the normal in-vivo (rabbit) cornea, the osmotic pressure is approximately zero and the fluid pressure is approximately IOP.30 This normal physiological condition is modeled with the active ion transport parameter Qphysio = 0.965.30 In this case, the normal pre-surgical

Fig. 10. Fringe plots of (a) the fluid pressure and (b) volume dilation J of a post-surgical cornea after LASIK designed for an intended correction of 5 diopters.

fluid pressure is approximately Pfluid = IOP throughout the stroma. Recalling that the stromal fluid pressure is given by Pfluid = Pbath +Posmotic (see Eq. 20), where Pbath = IOP, the post-surgical fluid pressure is determined from Pfluid = IOP +Posmotic , and where Posmotic could be positive or negative. The predicted fluid pressure Pfluid for the LASIK model is shown in Figure 10a. It was observed that the osmotic pressure becomes negative and the stromal fluid pressure reduces to approximately half of its normal value in the ablation region. The change in stromal fluid pressure resulting from the surgical procedure may be inferred from Figure 10a. Since the pre-surgical stromal

The electrochemical basis of corneal hydration, swelling, and transparency

77

Fig. 11. At the anterior surface, inclined lamellae insert into Bowman’s layer and act as anchors, resisting the stromal fluid pressure. In the posterior stroma, the stromal and anterior chamber fluid pressures are balanced, and the collagen does not need to be inclined. This arrangement stabilizes the refractive surface.

Copyright © 2018. Kugler Publications. All rights reserved.

fluid pressure is Pfluid = IOP, the change in stromal fluid pressure can be observed by simply subtracting IOP = 15 mmHg from the pressure scale in Figure 10a. For example, at the center of the ablation zone, the pre-surgical fluid pressure is 15 mmHg and the post-surgical fluid pressure is 4.1 mmHg, which represents a change of −10.9 mmHg. The predicted volume dilation J for the LASIK model is shown in Figure 10b. Modest swelling is indicated in Figure 10b, and is concentrated in the anterior region of the residual stroma, particularly where the ablation is deepest and lamella inclination is lost. However, if IOP increases, then the swelling increases significantly.30

7. Concluding remarks This chapter has presented an energy-based theory for stromal swelling and fluid pressure, and an application of the theory to demonstrate that GAG-based osmotic forces are capable of stabilizing the collagen lattice, which is necessary for the transparency of the cornea. The model, which has been validated against stromal swelling experiments, has no ‘free parameters’, and the

physical constants which do appear have been found through independent measurements. The precise quantification of the fluid and osmotic pressures for the in-vivo human cornea remains an open question, as direct measurements are not currently feasible. Likewise, measurement of the active transport parameter Qphysio, (see Eq. 37), which depends on the endothelial ionic permeability and active ionic flux, cannot be directly measured. We have employed experimental measurements of imbibition pressure in rabbit to assign a value to Qphysio,30 but this is not entirely satisfactory. Our investigations suggest that stromal fluid pressure is close to IOP and osmotic pressure is maintained close to zero by the endothelial ion pumps. But a final accounting requires more experimental data; the general theory presented should, however, remain relevant. The role of stromal collagen in swelling must also be considered for a full understanding of how the cornea responds to swelling forces. Although this important topic has not been included in the scope of this chapter, we remark about one interesting aspect. The anterior stroma terminates at Bowman’s layer, which supports the epithelium. In and below Bowman’s, the stromal

78

P.M. Pinsky and X. Cheng

fluid is pressurized, whereas above Bowman’s the fluid pressure is zero (atmospheric pressure can be cancelled out). How is the pressure difference equilibrated? This must be through lamella inclination, as illustrated in Figure 11. In the posterior stroma, the anterior chamber IOP and stromal fluid pressure must balance, and no lamella inclination is needed (or exists). It may be concluded that anterior lamella inclination stabilizes the refractive surface of the cornea. A detailed study of this problem has been conducted by Cheng et al.30

References 1. 2.

3. 4.

5. 6.

7. 8. 9.

Copyright © 2018. Kugler Publications. All rights reserved.

10.

11.

12.

13. 14.

Maurice DM. Clinical physiology of the cornea. Int Ophthalmol Clin. 1962;2:561-572. Fratzl P, Daxer A. 1993 Structural transformation of collagen fibrils in corneal stroma during drying. Biophys J. 1993;64:12101214. Meek KM. The cornea and sclera. In Collagen: structure and mechanics. (ed. P. Fratzl), pp. 359-396. Springer;2008. Lewis PN, Pinali C, Young RD, Meek KM, Quantock AJ, Knupp C. Structural interactions between collagen and proteoglycans are elucidated by three-dimensional electron tomography of bovine cornea. Structure. 2010;18,:239-245. Scott JE. Proteoglycan-fibrillar collagen interactions. Biochem J. 1988;252:313-323. Elliott GF, Hodson SA. Cornea, and the swelling of polyelectrolyte gels of biological interest. Rep Prog Phys. 1998;61:13251365. Maurice DM. The location of the fluid pump in the cornea. J Physiol. 1972;221:43-54. Fischbarg J, Maurice DM. An update on corneal hydration control. Exp Eye Res. 2004;78:537-541 Bonanno JA. Molecular mechanisms underlying the corneal endothelial pump. Exp Eye Res. 2012;95:2-7. Dawson DG, Ubels JL, Edelhauser HF. 2011 Cornea and Sclera. In Levin LA et al. (ed) Adler’s physiology of the eye, 11th edn. Elsevier, pp 71-130 Klyce SD, Russell SR. Numerical solution of coupled transport equations applied to corneal hydration dynamics. J Physiol. 1979;292:107-134. Kedem, O, Katchalsky, A. Thermodynamic analysis of the permeability of biological membranes to non-electrolytes. Biochim Biophys Acta. 1959;27:229-246. Bryant MR, McDonnell PJ. A triphasic analysis of corneal swelling and hydration control. Trans ASME. 1998;120:370-381. Lai WM, Hou JS, Mow VC. A triphasic theory for swelling and deformation behaviors of articular cartilage. J Biomech Eng. 1991;113:245-258.

Another aspect of the model not discussed is the convenience with which it may be implemented in finite element codes. The finite element method is an ‘energy’ method. The proposed model is also an energy method and the electrolyte free energy can be readily exploited in a finite element code. This is a significant advantage compared to all previous models, which are based on balance principles for fluxes of solvents and solutes. A detailed discussion of the finite element implementation has been given by Pinsky and Cheng.31

15. Ruberti, JW, Klyce, SD. NaCl osmotic perturbation can modulate hydration control in rabbit cornea. Exp Eye Res. 2003;76:349359. 16. Li LY, Tighe B. Numerical simulation of corneal transport processes. J R Soc Interface. 2006;3:303-310. 17. Leung BK, Bonanno JA, Radke CJ. Oxygen-deficient metabolism and corneal edema following epithelial hypoxia in the rabbit. Prog Retin Eye Res. 2011;30:471-492. 18. Meek KM, Fullwood NJ, Cooke PH, et al. Synchrotron x-ray diffraction studies of the cornea, with implications for stromal hydration. Biophys J. 1991;60:467-474. 19. Goodfellow JM, Elliot GF, Woolgar AE. X-ray diffraction studies of the corneal stroma. J Mol Biol. 1978;119:237-252. 20. Olsen T, Sperling S. The swelling pressure of the human corneal stroma as determined by a new method. Exp Eye Res. 1987;44:481-490. 21. Hedbys BO, Mishima S. The thickness-hydration relationship of cornea. Exp Eye Res. 1966;5:221-228. 22. Miyagawa A, Kobayashi M, Fujita Y, et al. Surface ultrastructure of collagen fibrils and their association with proteoglycans in human cornea and sclera by atomic force microscopy and energy-filtering transmission electron microscopy. Cornea. 2001;20:651-656. 23. Muller LJ, Pels E, Schurmans LR, Vrensen GF. A new three-dimensional model of the organization of proteoglycans and collagen fibrils in the human corneal stroma. Exp Eye Res. 2004;78:493-501. 24. Twersky V. Transparency of pair-correlated, random distributions of small scatterers, with applications to the cornea. J Opt Soc Am. 1975;65:524-530. 25. Cheng X, Pinsky PM. Mechanisms of self-organization for the collagen fibril lattice in the human cornea. J R Soc Interface. 2013;10:20130512. 26. Plaas AH, West LA, Thonar EJ, et al. Altered fine structures of corneal and skeletal keratan sulfate and chondroitin/ dermatan sulfate in macular corneal dystrophy. J Biol Chem. 2001;276:3978839796.

The electrochemical basis of corneal hydration, swelling, and transparency

Copyright © 2018. Kugler Publications. All rights reserved.

27. Hodson SA. Why the cornea swells. J Theor Biol. 1971;33:419427. 28. Katchalsky A, Michaeli I. Polyelectrolyte gels in salt solutions. J Polym Sci. 1955;15:69-86. 29. Sharp KA, Honig B. Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation. J Phys Chem. 1990;94:7684-7692. 30. Cheng X, Petsche SJ, Pinsky PM. A structural model for the in vivo human cornea including collagen-swelling interaction. J R Soc Interface. 2015;12:20150241. 31. Pinsky PM, Cheng X. A constitutive model for swelling pressure and volumetric behavior of highly-hydrated connective tissue. J Elasticity. 2017;129(1-2):145-170.doi:10.1007/s106590169616-z 32. Hedbys BO, Dohlman CH. A new method for the determination of the swelling pressure of the corneal stroma in vitro. Exp Eye Res. 1963;2:122-129. 33. Meek KM, Leonard DW, Connon CJ, Dennis S, Khan S. Transparency, swelling and scarring in the corneal stroma. Eye. 2003;17927-936. 34. Muller LJ, Pels E, Vrensen GF. The specific architecture of the anterior stroma accounts for maintenance of corneal curvature. Br J Ophthalmol. 2001;85;437-443. 35. Benedek GB. Theory of transparency of the eye. Appl Opt. 1971;10:459-473. 36. Cox JL, Farrell RA, Hart RW, Langham ME. The transparency of the mammalian cornea. J Physiol. 1970;210:601-616. 37. Kostyuk O, Nalovina O, Mubard et al. Transparency of the bovine corneal stroma at physiological hydration and its dependence on concentration of the ambient anion. J Physiol. 2002;543:633-642. 38. Maurice DM. The structure and transparency of the cornea. J Physiol. 1957;136:263286. 39. Hayashida Y, Akama TO, Beecher N, et al. Matrix morphogenesis in cornea is mediated by the modification of keratan sulfate by GlcNAc 6-O-sulfotransferase. Proc Natl Acad Sci U S A. 2006;103:13333-13338.

79

40. Scott JE. Morphometry of cupromeronic blue-stained proteoglycan molecules in animal corneas, versus that of purified proteoglycans stained in vitro, implies that tertiary structures contribute to corneal ultrastructure. J Anat. 1992;180,155-164. 41. Knupp C, Pinali C, Lewis PN, et al. The architecture of the cornea and structural basis of its transparency. Adv Protein Chem Struct Biol. 2009;78,25-49. 42. Farrell RA, Hart RW. On the theory of the spatial organization of macromolecules in connective tissue. Bull Math Biophys. 1969;31:727-760. 43. Freund DE, McCally RL, Farrell RA, Cristol SM, L’Hernault NL, Edelhauser HF. Ultrastructure in anterior and posterior stroma of perfused human and rabbit corneas. Relation to transparency Invest Ophthalmol Vis Sci. 1995;36:1508-1523. 44. Elhalis H, Azizi B, Jurkunas U. Fuchs endothelial corneal dystrophy. Ocul Sur. 2010;8:173-184. 45. Brunette I, Sherknies D, Terry MA, Chagnon M, Bourges JL, Meunier. 3-D characterization of the corneal shape in fuchs dystrophy and pseudophakic keratopathy. Invest Ophthalmol Vis Sci. 2009;52:206-214. 46. Dupps WJ, Wilson SE. Biomechanics and wound healing in the cornea. Exp Eye Res. 2009;83:709-720 47. Munnerlyn CR, Koons SJ, Marshall J. Photorefractive keratectomy: a technique for laser refractive surgery. J Cataract Refract Surg. 1988;14:46-52 48. Ortiz D, Alio JL, Pinero D. Measurement of corneal curvature change after mechanical laser in situ keratomileusis flap creation and femtosecond laser flap creation. J Cataract Refract Surg. 2008;34:238-242. 49. Hedbys BO, Mishima S, Maurice DM. The imbibition pressure of the corneal stroma. Exp. Eye Res. 1963;2:99-111.

Copyright © 2018. Kugler Publications. All rights reserved.

6. Material properties of the human cornea: anisotropy Ashkan Eliasy1, Zhou Dong1, Harald Studer2,3, Craig Boote4, Ahmed Elsheikh1,5,6 School of Engineering, University of Liverpool, Liverpool, UK; 2Swiss Eye Research Foundation, Reinach, Switzerland; 3 OCT Research Laboratory, Department of Ophthalmology, University of Basel, Switzerland; 4Structural Biophysics Group, School of Optometry and Vision Sciences, Cardiff University, Cardiff, UK; 5NIHR Biomedical Research Centre for Ophthalmology, Moorfields Eye Hospital NHS Foundation Trust, London, UK; 6Institute of Ophthalmology, University College London, London, UK

Copyright © 2018. Kugler Publications. All rights reserved.

1

1. Introduction

2. Microstructure

The cornea and sclera demonstrate complex material behavior including hyperelasticity (non-linear stressstrain relationship), viscoelasticity (dependence on strain rate of deformation), regional variation of stiffness, and dependence on age and medical history. In addition, the tissue is known to possess a high degree of anisotropy, as its mechanical behavior is dependent on the distribution of collagen fibers, the main load-carrying components of the tissue. With the collagen fibers showing significant regional variations in density and orientation, the biomechanical behavior of the tissue changes accordingly, experiencing stiffness values that vary with location and direction, and making ocular biomechanics a highly complex topic. This chapter provides an introduction into current knowledge on the mechanical anisotropy of ocular tissue, caused by the anisotropy of its microstructure. It covers most recent work by the authors and others to characterize the collagen distribution in ocular tissue and goes on to describe how this information could effectively be used in the development of representative numerical models of ocular biomechanical behavior.

Soft tissues generally consist of two main constituents: cells and extracellular matrix. According to Humphrey1, the extracellular matrix (ECM) — made of proteins, glycosaminoglycan, and water — contributes to the material properties of the eye in a number of ways; one such contribution is the provision of tissue stiffness and, as such, the ECM may be regarded as the main source of mechanical properties which affect tissue behavior. Proteins included within the ECM include the collagen fibrils (one of the most abundant proteins), elastin, and proteoglycan, which together form the unique microstructure of the tissue. A total of 28 categories of collagen types have been identified,2 among which collagen type I (fibrillar collagens) is the most common and abundant.3 In addition, types II, III, V, VI, and XI are all regarded as fibrillar collagens, differentiated by their individual self-assembly processes.4 These collagens contribute to the formation of bands of fibrils in a staggered arrangement, organized into fibers which provide mechanical support,2 and whose production has been described thoroughly in the literature (Fig. 1).2,4,5 As such, the detailed synthesis of fibrillar collagen from cell to ECM will not be given herein, although the hierarchical structure of fibrils will be briefly outlined for its important role in biomechanics.

Correspondence: Dong Zhou, School of Engineering, University of Liverpool, Brownlow Hill L69 3GH, Liverpool, UK. E-mail: [email protected] Biomechanics of the Eye, pp. 81-90 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

A. Eliasy et al.

82

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 1. Hierarchical structure of fibrils within tissue. (a) Collagen molecules are combined to form fibrils, fascicles, and tendon fibers; the interaction between fibrils and molecules is shown in (b) and (c), respectively. C-L: crosslinks between collagen molecules; PG: proteoglycan-rich matrix between fibrils. Adapted from Fratzl.3

Collagen fibrils may be treated as the fundamental building blocks in collagen-rich tissues and, as such, may be used to understand the tissues’ mechanical characteristics. The collagen molecules, which form the fibrils, can be observed via x-ray scattering to allow analysis of the tissues’ regional microstructure. On the other hand, the ground substance matrix around the fibrils is used to describe all other components,6 including but not limited to, proteoglycans, water, and elastin (Fig. 1).3 Individual collagen fibrils are crosslinked via proteoglycans and packed together, in a parallel form, in lamellae,7 which in turn are organized —layered in varying orientations — to form a composite material, providing the tissue with the general architecture shown in Figure 2. The parallel organization of fibrils within individual lamellae leads to higher stiffness in the direction of the fibrils and reduced stiffness in other directions, resulting in the tissue’s anisotropy. At a more macro scale, the cornea may be divided into five layers; namely, the epithelium, Bowman’s layer, stroma, Descemet’s membrane, and endothelium (Fig. 3). Among these layers, the stroma accounts for 90% of the cornea’s overall thickness, and therefore, has the

Fig. 2. Lamellar structure within the cornea.7

largest impact on its mechanical behavior.8-10 In the human eye, the number of lamellae within the stroma varies from approximately 300 at the center of cornea to 500 at the limbus.7 According to Meek et al.,11 two preferred meridional orientations of collagen fibrils have been found in the central human

Material properties of the human cornea: anisotropy

83

Fig. 3. Schematic structure of the cornea.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. (a) The general arrangement of fibrils in the central cornea, with preferred orientation in the vertical and horizontal directions.13 (b) The 45º sectors of the central cornea, where two thirds of collagen fibrils have been observed to have preferential orientation.

cornea by synchrotron x-ray diffraction: inferior-superior and temporal-nasal. This arrangement continues from corneal apex to 1-2 mm from the limbus, where it becomes circumferential. Indeed, Aghamohammadzadeh demonstrated maintenance of the vertical and horizontal directions of fibrils to 1 mm from the limbus, which, in contrast, has a circular disposition of fibrils (Fig. 4a).12 Among all fibrils in the central cornea, one third are orientated within 45º of the superior-inferior meridian, and a similar quantity around the temporal-nasal direction (Fig. 4b); leaving one third in the diagonal directions in between.13,14 This observation is concluded based on studies on healthy corneas and may not necessarily apply in other cases, for example, in keratoconic cases where the collagen fibrils do not seem to have clear preferred orientations.14

2. X-ray scattering method and resulting data Over the past three decades, x-ray scattering methods have evolved to allow quantitative mapping of collagen fibril orientation and distribution in the corneal stroma.15,16 This work has been facilitated, in part, by advances in synchrotron technology, whereby ultra-high intensity radiation is acquired from electrons orbiting at velocities close to the speed of light in large, circular particle accelerators.17 Contemporary instruments enable whole corneas to be mapped in the space of minutes,18 despite the tissue’s high water content and, thus, inherently weak diffracting qualities. The wide-angle x-ray scattering (WAXS) technique exploits the highly organized molecular structure of individual

84

A. Eliasy et al.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. WAXS method. (a) The ordered molecular structure of stromal collagen fibrils is used as a ‘grating’ to obtain discrete equatorial (i.e., perpendicular to the fibril axis) diffraction peaks. (b) A range of collagen fibril directions turns the diffraction peaks into arcs, whose intensity distribution can be analyzed to quantify the collagen fibril orientation distribution.

collagen fibrils in the corneal stroma. The regular 1.6 nm lateral packing of tropocollagen molecules serves as a regular ‘grating’, whose diffraction is unaffected by large variations in the diameter and packing of collagen fibrils that occur from corneal center to periphery and into the surrounding sclera,19,20 and yet can still be used to track fibrillar orientation (Fig. 5). An advantage of x-ray scattering methods is that they can be applied without the need for tissue sectioning, embedding, crystallization, or other specimen preparation steps that may perturb the native collagen organization, and thus, can provide a convenient in-situ average measure of collagen structure within the stromal volume sampled by the x-ray beam (typically 50–500 microns in cross-sectional diameter). A detailed account of the synchrotron WAXS method can be found in Meek and Boote.15 In brief, excised corneas are wrapped in polyvinylidene film (or similar), to limit dehydration, and secured in cells with x-ray-transparent windows (e.g., Mylar®). The mounted cornea is subjected to short (e.g., 1 sec) x-ray bursts along the optical axis while being translated laterally between exposures. The diffraction pattern — essentially a Fourier transform of the collagen structure — is recorded on an electronic x-ray detector (often a charge-coupled device or similar) placed typically 300–500 mm behind the specimen position. Data analysis involves careful extraction of the angular intensity distribution of the intermolecular diffraction arcs (Fig. 6). In our research, processing is carried out using bespoke MATLAB routines that involve — for each sampled point in the tissue — firstly, fitting and subtraction of a 2-D background function represent-

ing scatter from the specimen cell and all ocular tissue components (excluding fibrillar collagen) and secondly, normalization against fluctuations in incident x-ray photon flux and exposure time. The derived, collagen-specific x-ray scatter intensity (Fig. 6b) is then transposed by π/2 rad to account for equatorial scatter and extracted to π/360 rad-width azimuth angular bins.21 Figure 6c shows an example of the resulting orientation distribution plot for preferentially aligned collagen, displayed in polar coordinates. In addition to the collagen anisotropy, a number representing the relative volume of total collagen at the sampled point may be computed by integrating the angular collagen scatter profile shown in Figure 6b, given by: ​   ​​​ Icdϕ (1) ​Vc = ​​​∫0  2π where Ic is the total collagen scatter intensity at angle ϕ for a given sampled point in the tissue, and Vc is the associated collagen volume. While WAXS has proven to be a valuable tool for quantifying collagen anisotropy and content in the corneal stroma, and capable of producing data that is amenable to inclusion in numerical simulation, the technique has a few limitations. With a conventional, fixed-angle sample cell, examination of a cornea in its natural curvature leads to some artifact due to the incident x-ray beam being perpendicular to the tissue plane only at the corneal apex. As distance from the apex increases, the effective stromal thickness presented to the beam is artificially increased; this leads to a proportional increase in total x-ray scatter and apparent collagen volume, but does not affect

Material properties of the human cornea: anisotropy

85

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 6. (a) WAXS pattern from the peripheral human cornea. The two-lobed appearance of the collagen intermolecular x-ray diffraction arcs are indicative of dominant fibril alignment in the direction of the arrow. (b) Angular x-ray scatter intensity profile of pattern shown in (a), following background subtraction. The scatter may be separated into that arising from isotropically-arranged collagen fibrils (shaded region) and that arising from preferentially oriented fibrils (clear region). (c) Aligned collagen scatter displayed as a polar vector plot, whose shape reveals the collagen anisotropy. The length of a vector drawn from the center of the plot to its edge in a given direction is proportional to the relative number of fibrils preferentially aligned in that direction. (d) Second harmonic generation (SHG) multiphoton microscopy image recorded from the same specimen and region as the WAXS data. The image reveals highly aligned collagen fibril bundles whose orientation is in agreement with that indicated by the WAXS results.

the collagen anisotropy which is a 2-D projection in the stromal surface.15 When scanning the whole ocular tunic using WAXS, Pijanka et al. flattened the tissue with meridional incisions.22 However this leads to some reorientation of collagen adjacent to the cut-edges as residual stress in the tissue is released,23 an effect which can be partly restricted by fixation of the specimen in weak paraformaldehyde solution prior to incision.22 These limitations could potentially be removed by using a tilting sample cell to keep the incident x-ray perpendicular to the tissue surface at all times during scanning; such a device is currently under development by the authors. A further limitation concerns the hier-

archical structure of collagen: since WAXS relies upon a molecular signal, the helicoidal packing of the microfibrillar subunits comprising the fibrils will contribute to the angular smearing of the WAXS diffraction peaks shown in Figure 6a, leading to an underestimation in the degree of fibril anisotropy measured by WAXS. In the central cornea, the average microfibrillar tilt angle with respect to the fibril axis is estimated at ~150, but likely decreases to as little as ~50 in the periphery as corneal fibrils coalesce with the more shallowly tilted microfibrils of the sclera.24 A further point of interest is that any variation in hydration across the cornea may be expected to influence the total x-ray scatter from

A. Eliasy et al.

86

collagen; however, this effect is relatively small when using the molecular collagen signal (as compared to x-ray methods which exploit scatter at the fibrillar level) and may be further minimized by prior fixation of the tissue.

3. Extraction of microstructure data and preparation for numerical simulation Figure 7 shows an image of the anterior and posterior portions of a human eye globe after being dissected and incised to enable its flattening. The four main orientations are clearly marked on the specimens to enable the localization of individual data points during the analysis stage. The anterior and posterior portions are then scanned separately, producing maps similar to that shown in Figure 8, marking all points that have been covered by the x-ray scattering machine with a spacing of 0.5 mm in both directions. For each scanned location, 256 data points are provided representing the full collagen content in each of 256 directions covering 360º. An example plot of the 256 data points at a particular location is shown in Figure 9a, where the typical amount of data noise is clear. A noise filtration process is then used to gradually smooth the fibril content distribution until only four peaks remain in order to simplify the process of considering the microstructure data in the numerical simulation of biomechanical behavior of the eye (Fig. 9d).

Fig. 7. The anterior (right) and posterior (left) portions of a human eye being prepared for x-ray scanning. I: inferior; N: nasal; S: superior; T: temporal.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 8. The x-ray data maps for the anterior and posterior portions of the eye marking all scanned points.

Fig. 9. X-ray signal during the noise filtration process. The process continues until only four peaks remain.

Material properties of the human cornea: anisotropy

87

Implementing this process at each scanned location, six items of information are obtained: 1. total fibril content; 2. value of isotropic fibril content; 3. and 4. values of anisotropic fibril content in directions of high and low anisotropic peaks; and 5. and 6. directions of high and low anisotropic fibril content peaks. This information is made available when constructing numerical simulations of ocular behavior as explained in the following section.

Copyright © 2018. Kugler Publications. All rights reserved.

4. Numerical simulation and continuum mechanics The finite element method (FEM) is a common numerical technique for calculating approximate solutions to boundary value problems (BVPs). FEM subdivides a large problem into smaller parts — the finite elements — for each of which simple equations describing the behavior under mechanical loads can be formulated. These simple equations are subsequently assembled into a large system of equations, which is solved by applying methods of calculus of variations. FEM is implemented and made available in sophisticated engineering software tools (such as ABAQUS by Dassault Systemes, Vélizy-Villacoublay, France or ANSYS Structural by ANSYS Inc., Canonsburg, USA) and is used in various fields of application such as nuclear, aerospace, or the automotive industry. The advantages of applying computer simulations over full-scale experiments are apparent due to their much lower cost and more rapid evaluations.25 Applied to human tissue, numerical simulations can enhance our understanding of the materials’ distinct properties, reduce the need for tissue samples in laboratory experiments, and lower the risk for patient-involved clinical studies or surgical procedures. Computational FEM has seen increasing use over the last few decades to investigate biomechanical properties of the human cornea, and has been applied to the simulation of intraocular pressure measurement techniques,26 corneal transplantation or keratoplasty,27-29 surgical interventions,30 and corneal disorders.7,9,31,32 FE models of the human eye have seen rapid development, with geometries going

Fig. 10. Schematic highlighting the deformed configuration following application of a load.

from 2-D to 3-D, and material properties from isotropic to anisotropic and from homogeneous to inhomogeneous. The success of these models relies, at least in part, on the consideration of the microstructural properties of ocular tissue, such as collagen-fibril induced non-linearity, anisotropy and incompressibility. In non-linear continuum mechanics (NLCM), such material characteristics are modelled by formulating a custom strain energy function (Ψ) relating geometric body deformation (strain) to deformation energy. The NLCM employs the concept of body (or domain) configurations to describe the collection of all particles within a given continuum — when the continuum is deformed under a specific load — and the reference configuration changes to the current (or deformed) configuration (Fig. 10). In the following, bold letters are used to denote tensor quantities. Let X Є R3 denote the position of a particle in a reference configuration, then the position of the same particle in the continuum after deformation can be found and expressed as: x(X, t) = X + U(X, t)

(2)

where U is the displacement field.6 The above equation is given in material coordinates (also called Lagrangian description), with respect to material particles, X, and time, t. Hence, X acts as variables in each field function and the reference configuration coincides with current configuration, for the special case in which t is equal to zero. In such a case, deformation gradient F can be defined as:

A. Eliasy et al.

88

∂x(X) 

∂U(X) 

F =  _   = I +  _   ∂X  ∂X 

(3)

whereby F is equal to the identity tensor, I, in reference configuration. The determinant J = detF describes the change in volume and, as a consequence, also the change in density. Values J > 1.0 express volume increase; therefore, for incompressible materials with no volume changing, J = 1. The left and right Cauchy-Green deformation tensors: C = FT F and B = FFT

(4)

where the T superscript means tensor-transpose, are used to define the important strain invariants.33 It is important to note that, in contrast to F, these invariants describe pure body deformation and exclude rigid body motion. Therefore, strain energy is usually formulated in terms of the following invariants, instead of F: 1

 2  {(trC)2 - trC2}, I3 = detC = J2, I1 = trC, I2 = _ I4 = a0∙C∙a0, I6 = b0∙C∙b0

(5)

To note; while I1, I2 and I3 are isotropic, I4 and I6 are anisotropic invariants; in addition, I3 is related to volume change. As a consequence, strain energy for non-linear, anisotropic materials can be formulated as:

Copyright © 2018. Kugler Publications. All rights reserved.

Ψ = ΨISO (I1, I2, I3) + ΨANI (I4, I6, I3)

(6)

The anisotropic invariants (I4, I6) describe deformation along a preferred direction, defined by the corresponding vector (e.g., a0). They are of essential importance, as the literature clearly shows that the different directions of lamellae or fibrils within the cornea will lead to anisotropic material characteristics. Elsheikh demonstrated that the preferential orientation of fibrils throughout the thickness was strongly associated with its anisotropic behavior through the use of tensile tests of corneal tissue strips extracted from different directions.34 Greater stiffness and strength were found along superior-inferior and temporal-nasal directions, in accordance with the two preferential orientations (Fig. 11). Furthermore, due to the high water content in corneal tissue, it is usually modelled as incompressible. As such, volume change is controlled through a penalty term,

Fig. 11. Non-linear responses of three corneal strip specimens extracted in different anatomical directions.

U(J), and added to the strain energy formulation. Thus, volume change is decoupled from the deformation tensors by the isochoric split of F: 1 _ F   F = J  3  I ¯

(7)

where ¯   expresses the decoupled form of F. ConseF quently: C = J  3  I¯ C   and B = J  3  I ¯ B   2 _

2 _

(8)

As a direct result, strain energy for corneal tissue can be formulated by means of additive terms for tissue matrix, Ψm, collagen fibrils, ΨA , and incompressibility, U(J). Ψ = Ψm (¯I1, ¯ I2) + ΨA(¯I4, ¯I6) + U(J)

(9)

where ¯I  1, ¯ I2, ¯ I4, ¯ I6 are the strain invariants from Equation (9), in their decoupled form. A number of potential methods of formulating the single terms in the above strain energy function can be found in the literature.

Material properties of the human cornea: anisotropy

89

Following what has been introduced by Studer et al., in this text we have chosen to use the neo-Hookean law for tissue matrix,32 the polynomial formulation by Markert et al.35 for the anisotropic term for modeling the behavior of collagen fibrils, and a second order polynomial for the incompressibility penalty term. Noted in terms of the invariants, the penalty term is: 1

( )2 ​U(J) = ​ _ D ​ ​ J - 1 ​ ​ (10)

where D is a material constant and must be a small number (e.g., 10 -5) to make the penalty effective. The neo-Hookean law for tissue matrix is given by: ¯  ​​Ψ ​m  ​(I1, I3)​ = C10 ​(¯​ I​1   - 3)​ = C10 ​(​I3​​ ‒​  ⁄  ​​I1 ‒ 3)​​ 1 3



(11)

where C10 is a material constant and I3 is related to J. Anisotropy is modeled with two families of fibrils, in-lamella fibrils, Ψ(f,Lam), and interactions between adjacent lamellae (Ψf,Int), respectively. Both families are defined with the polynomial anisotropic strain energy formulation by Markert et al.:35 μ1 ​  ⁄  ​ ¯ ​​  f,Lam​ Ψ ​   ​​(I4, I3)​ = ​ _ ​​ ¯I​​​  ​  4​  ​ ‒ 1)​- μ1ln​​ I ¯​​  ‒​4​   ⁄  ​​ ​ μ1 ​​ ( γ1

1

2

2

μ2 ​  ⁄  ​ ¯ ​​ Ψ ​f,Int​   ​​(I6, I3)​ = ​ _ ​ ¯I​​​  ​  6​  ​ ‒ 1)​- μ2ln​​ I ¯​​  ‒​6​   ⁄  ​​​ μ2 ​​ ​ ( γ2

2

1

2



(12) (13)

where μ1, γ1 and μ2, γ2 are material constants and ln represents the natural logarithm. Both families are combined with a weighting function, Φ, defining the portion of fibrils for each direction, 0..π:

Copyright © 2018. Kugler Publications. All rights reserved.

1 ¯ Ψ​ ​ π   ​​∫0 π ​   ​​Φ(​ R,φ,θ)​​(¯ Ψ ​ ​  f,Lam   ​(I4,I3)​ + ​¯ Ψ​   f,Int   ​(I6,I3)​)​dθ​  ​​ f ​(I4,I6,I3)​ = _ (14)

Thereby, R, φ, θ are parameters of the weighting function, allowing the assignment of specific weights for each discretized fibril orientation at any point in the cornea or sclera. The values of these parameters are obtained directly from the microstructure data obtained using x-ray scattering for whole eye globes as explained in the previous section. With this technique, the microstructure is assumed to control the level of stiffness as well as the degree of mechanical anisotropy at each scanned point, and by interpolation at each integration point of each finite element used in the numerical model.

5. Current numerical models and future development steps Current models are based on collagen fibril content and anisotropy data obtained for whole eye globes using the x-ray scattering technique. Comparisons of microstructure maps obtained for different eyes reveal a high level of consistency in both the cornea and limbus and around the optic nerve head in healthy eyes. The distribution of fibrils in the sclera is less repeatable, but certain trends still remain consistent, especially in the areas around attachment to the extraocular muscles. Maps for individual eye globes are analyzed and added to a dynamic database representing the average distribution and anisotropy of collagen fibrils that could be used in the construction of numerical models for applications involving healthy eyes. The next step will be to extend the microstructure mapping to eyes with keratoconus and high myopia; the first expected to lead to variations in corneal microstructure, and the second leading to softening of the posterior sclera. Parallel work is progressing on the microstructural changes that take place in response to surgery or injury, or due to significant changes in the strain regime acting on ocular tissue. Experimental tests have shown that clear microstructural changes take place when the resulting strain regime changes beyond a certain threshold. The ability to simulate these microstructure changes may mean the ability to model ocular behavior following surgery. It is expected that numerical modeling of ocular mechanical behavior will rely increasingly on the tissue’s microstructure, and that this modeling approach will make numerical modeling of the eye, and biological tissue in general, more reliable and representative of in-vivo conditions.

A. Eliasy et al.

90

References 1.

2. 3. 4. 5.

6.

7.

8.

9.

10. 11.

12.

13.

Copyright © 2018. Kugler Publications. All rights reserved.

14.

15.

16.

17.

18.

Humphrey JD. Review paper: Continuum biomechanics of soft biological tissues. Proc Math Phys Eng Sci. 2003;459:(2029):346. Sherman, VR, Yang W, Meyers MA. The materials science of collagen. J Mech Behav Biomed Mater. 2015;52:22-50. Fratzl P. Collagen Structure and Mechanics. Peter Fratzl (ed.). [Online]. Potsdam, Springer;2008. Kadler KE, Holmes DF, TrotterJA, Chapman JA. Collagen fibril formation. J Biochem. 1996;15;316 (Pt 1):1-11. Michelacci YM. Collagens and proteoglycans of the corneal extracellular matrix. Brazilian journal of medical and biological research = Revista brasileira de pesquisas médicas e biológicas / Sociedade Brasileira de Biofísica ... [et al.]. 2003;36(8): 1037– 1046. Weiss JA, Makerc BN, Govindjeed S. Finite element implementation of incompressible, isotropic hyperelasticity transversely. 1996;135(1-2):107-128. Pinsky, PM, van der Heide D, Chernyak D. Computational modeling of mechanical anisotropy in the cornea and sclera. J Cataract Refract Surg. 2005;31(1):136–145. Nejad TM, Foster C, Gongal D. Finite element modelling of cornea mechanics: a review. Arq Bras Oftalmol. 2014;77(1):60– 65. Pandolfi A, Holzapfel G. Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations. J Biomech Eng. 2008;130(6):61006. Meek KM, Knupp C. Corneal structure and transparency. Prog Ret Eye Res. 2015; 49:1-16. Meek KM, Blamires T, Elliott GF, et al. The organisation of collagen fibrils in the human corneal stroma: a synchrotron X-ray diffraction study. Curr Eye Res. 1987;6(7):841–846. Aghamohammadzadeh H, Newton RH, Meek KM. (2004) X-ray scattering used to map the preferred collagen orientation in the human cornea and limbus. Structure. 2004;12(2):249–256. Boote C, Dennis S, Huang Y, Quantock AJ, et al. Lamellar orientation in human cornea in relation to mechanical properties. J Struct Biol. 2005;149(1):1–6. Daxer A, Fratzl P. Collagen fibril orientation in the human corneal stroma and its implication in keratoconus. Invest Ophthalmol Vis Sci. 1997;38(1):121–129. Meek KM, Boote C. The use of X-ray scattering techniques to quantify the orientation and distribution of collagen in the corneal stroma. Prog Ret Eye Res. 2009;28(5):369–392. Quantock AJ, Winkler M, Parfitt, GJ, et al. (2015) From nano to macro: Studying the hierarchical structure of the corneal extracellular matrix. Exp Eye Res.2015;133:81-99. Meek KM, Quantock AJ. The use of X-ray scattering techniques to determine corneal ultrastructure. Prog Ret Eye Res. 2001;20(1):95–137. Boote C, Dooley EP, Gardner, SJ, et al. Quantification of collagen ultrastructure after penetrating keratoplasty - Implications for corneal biomechanics. PLoS ONE. 2013;5;8(7):e68166.

19. Borcherding MS, Blacik LJ, Sittig R, et al. Proteoglycans and collagen fibre organization in human corneoscleral tissue. Exp Eye Res.1975;21(1):59–70. 20. Boote C, Dennis S, Newton RH, et al. Collagen fibrils appear more closely packed in the prepupillary cornea: optical and biomechanical implications. Invest Ophthalmol Vis Sci. 2003;44(7):2941–2948. 21. Abass A, Hayes S, White N, et al. Transverse depth-dependent changes in corneal collagen lamellar orientation and distribution. J R Soc Interface. 2015;12(104):20140717. 22. Pijanka JK, Abass A, Sorensen T, et al. (2013) A wide-angle X-ray fibre diffraction method for quantifying collagen orientation across large tissue areas: application to the human eyeball coat. J Appl Crystallogr. 2013;46(5):1481–1489. 23. Lanir Y. (2009) Mechanisms of residual stress in soft tissues. J Biomech Eng. 2009;131:(4):44506. 24. Yamamoto S, Hashizume H, Hitomi J, et al. The subfibrillar arrangement of corneal and scleral collagen fibrils as revealed by scanning electron and atomic force microscopy. Arch Histol Cytol. [Online]. 2000;63(2):127–135. 25. Belytschko T, Liu WK, Moran B. Nonlinear finite elements for continua and structures. Chichester, John Wiley;2000. 26. Elsheikh A, Wang D, Kotecha A, et al. (2006) Evaluation of Goldmann applanation tonometry using a nonlinear finite element ocular model. Ann Biomed Eng. 27. Khan SN, Shiakolas PS. Finite element analysis of Descemet’s stripping automated endothelial keratoplasty (DSAEK) surgery allograft to predict endothelial cell loss. Curr Eye Res. 2016; 42(1):32-40. 28. Djotyan GP, Soong HK, Mian S, et al. (2006) Finite-element modeling of posterior lamellar keratoplasty: Construction of theoretical nomograms for induced refractive errors. Ophthalmic Res. 2006;38(6):329–334. 29. Yang YF, Zhang J, Wang XH, et al. Simulation of corneal tissue mechanical deformation due to laser thermokeratoplasty: A finite element methods study. Australas Phys Eng Sci Med. 2009;32(4):220–225. 30. Lanchares E, Calvo B, Cristóbal JA, et al. Finite element simulation of arcuates for astigmatism correction. J Biomech. 2008;41(4):797–805. 31. Gefen A, Shalom R, Elad D, Mandel Y. (2009) Biomechanical analysis of the keratoconic cornea. J Mech Behav Biomed Mater. 2009;2(3): 224–236. 32. Studer H, Larrea X, Riedwyl H, Büchler P. Biomechanical model of human cornea based on stromal microstructure. J Biomech. 2010;43(5):836–842. 33. Spencer AJ. Continuum theory of the mechanics of fibre-reinforced composites. New York, Springer-Verlag;1984. 34. Elsheikh A, Brown M, Alhasso D, et al. Experimental assessment of corneal anisotropy. J Refract Surg. 2008;24(2):178–187. 35. Markert B, Ehlers W, Karajan N. A general polyconvex strain-energy function for fiber-reinforced materials. PAMM. 2005;5(1):245–246.

7. Inflation testing of the cornea Thao D. Nguyen1, Jun Liu2 Department of Mechanical Engineering, Johns Hopkins University, Baltimore, MD, USA; 2Department of Biomedical Engineering, The Ohio State University, Columbus, OH, USA 1

1. Introduction The mechanical behavior of the cornea is important to a number of biomedical applications, including developing tonometric methods for glaucoma screening, design of biomaterials for corneal prosthetics and wound healing, prediction of refractive surgical outcomes, study of keratoconous and corneal ectasia, and evaluation of collagen crosslinking treatments. The mechanical characterization of the cornea typically employs either uniaxial strip testing or inflation testing. Uniaxial strip tests have the advantage of directly measuring the stress-strain behavior of the tissue. Assuming that the

strip is sufficiently long and homogenous to achieve a uniform stress and strain state in a central gauge section, the strain can be calculated from the displacements of the grips and the stress from the measured force. However, preparing a corneal strip specimen to have a uniform gauge section is challenging because of the small size, large natural curvature, and large spatial variation in the thickness and collagen structure of the cornea. Uniaxial strip tests also require extensive preconditioning, a process by which the strip is cyclically loaded to achieve a repeatable reference state.1 The preconditioning process can produce large permanent

Misconception 2: Preconditioning

Copyright © 2018. Kugler Publications. All rights reserved.

Misconception 1: Uniaxial strip testing vs inflation testing Although many investigators use uniaxial strip testing as a standard methodology for biomechanical property evaluation, inflation testing uses a more physiologic loading condition. Uniaxial strip tests require long flat strips that are uniform in thickness and material properties. Strips cut from the cornea are curved, have a thickness variation of up to 60%, and variation in the collagen anisotropic structure. These variations can lead to large errors in the stress and strain measurements. Because of this, mechanical testing of the cornea has shifted from uniaxial to inflation testing, which leaves the cornea intact and in a more physiological condition.

Uniaxial and biaxial strip testing requires preconditioning to obtain a repeatable stressstrain measurement. Preconditioning subjects the specimen to cyclic loading at a given strain level (or stress level), strain rate, and rest period between each cycle. The specimen can develop large permanent strain and the stressstrain response can change significantly with preconditioning. The stress response can become stiffer or more compliant, depending on applied strain level. The stress response has to be measured at the same strain level, and if a different strain level is used, the specimen has to be preconditioned again at that strain level. The effects of preconditioning are larger for uniaxial than biaxial strip test, and is negligible for inflation test.

Correspondence: Thao D. Nguyen, Department of Mechanical Engineering, Johns Hopkins University, 3400 N. Charles St., Latrobe 223, Baltimore, MD 21210, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 91-98 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

92

T.D. Nguyen and J. Liu

deformation and alterations in the stress response.2 Inflation tests measure the deformation of the cornea to controlled pressurization. The method has been developed for both the excised cornea and whole eye globe. Compared to uniaxial strip tests, inflation tests apply a more physiological loading condition and are less sensitive to preconditioning. Tonge et al. showed that bovine corneas do not experience a systematic stiffening effect nor permanent deformation with repeated load-unload cycles.3 Elsheikh et al. showed that the stress-strain response measured by uniaxial tests is significantly stiffer than by inflation tests.4 The discrepancy may be caused by the large preconditioning effects of uniaxial strip tests. The inflation experimental setup is inexpensive and straightforward to build. Fluid injection can be provided by a water column.5-7 A programmable syringe injection system with a pressure transducer and feedback controller provides more precise pressure control and the ability to control the pressure rate.8 Tissue tests additionally require an infusion chamber with separate inlets for syringe injection and pressure measurement. The corneal specimen can be either glued or clamped in a holder and secured to the infusion chamber. For whole globe tests, fluid is directly injected into the posterior segment, e.g., by a syringe plunged into the optic nerve head9 or by a needle inserted into the anterior chamber from the limbus.6

Copyright © 2018. Kugler Publications. All rights reserved.

Misconception 3: Inflation corneal stress response

tests

and

Inflation tests do not directly measure the stress response of the cornea. The tests measure either the pressure-displacement response or the pressure-strain response of the tissue. A model for the pressure-induced stresses is needed to determine the stress state of the tissue. Unlike uniaxial strip tests, inflation tests cannot directly measure the stress response of the specimen. Rather, a model of the pressurized cornea is needed to determine the stress response from the measured deformation and ultimately determine the material properties of the tissue. A wide variety of deformation

measurement and analysis techniques have been developed for inflation testing of the cornea. These can range from simple single-point measurement systems to surface or through-thickness full-field systems. This chapter provides a review of methods measuring deformations and models for stress calculations for inflation testing of the cornea.

2. Spherical membrane model for stress and strain One approach for determining the stress response is to model the tissue as a thin shell that exhibits negligible bending under the applied pressure. The thin assumption neglects the radial stress component and through-thickness variation of the in-plane membrane stress components. Neglecting bending removes from consideration the through-thickness stress gradient caused by the bending moment and the transverse shear stress components. Furthermore, approximating the cornea as a spherical shell removes the in-plane shear stress components. The remaining stress components form an equibiaxial stress state: σ 0 0 σ = 0  σ  0  , [0 0 0]

λ 0 0 F =  0  λ  0  [0 0 λ-2]

(1)

where σθθ = σφφ = σ are the tensile membrane stress in the circumferential θ and meridional directions φ (Fig. 1). Note that the radial stress σrr = 0 because of the thin-membrane approximation. The equibiaxial stress state generates a corresponding triaxial deformation state shown in Equation (1), where λθθ = λφφ = λ are the tensile stretches in the circumferential and meridional

Fig. 1. Tensile in-plane membrane stresses in a thin spherical shell, where eθ is the circumferential direction, eφ is the meridional direction, and eR is the radial direction.

Inflation testing of the cornea

93

directions. These are equal assuming that the material properties of the tissue are isotropic. The radial strain is non-zero because of Poisson’s effect, which causes dimensions transverse to the tensile loading direction to shrink. For the cornea, which is nearly incompressible, the radial stretch λ rr = (λθθ λφφ)-1 = λ-2 is determined by the condition of zero volume change. For the thin membrane assumptions describe above, σ can be determined from the applied pressure, p, solely using equilibrium (force balance). The result is Laplace’s law: pR σ=_   2t  

(2)

(3)

The radius of curvature, R, can be calculated from either the shape of the inflating cornea or from the measured displacements. Early inflation tests used laser-sensor systems to measure the apex (apical) displacement, w,4,10 and used a spherical cap model11 to calculate the radius of curvature, R, and stretch, λ. The spherical cap model assumes that the inflating specimen deforms as a spherical cap (Fig. 2), with height h = h0 + w, where h0 is the original height of the corneal apex. The radius of curvature can be calculated from the apex height, h, and radius, a, as: a2 + h2

Copyright © 2018. Kugler Publications. All rights reserved.

   . R =  _ 2h

_ _ s = Rarcsin ( _ R ) =   2h   arcsin ( a2 + h2  )  a

a2 + h2

2ah

(5)

which gives the following for the stretch:

where R is the radius of curve at the apex and t is the thickness of the inflating specimen at the apex. The deformed thickness, t, of the cornea can be determined from the undeformed central corneal thickness, t0, using the definition for the radial stretch, λ RR = t/t0: t0 t =  _   . λ2

Fig. 2. The spherical cap model.

(4)

For a tissue inflation test, where the cornea specimen is glued to a circular holder, a refers to the holder radius. For whole globe tests, a has been approximated as the radius of the scleral-corneal junction, assuming this radius is not changed significantly by pressurization.4 Assuming that the stretch is uniform in the corneal specimen, the stretch can be determined from the definition, λ = s/s0, where s and s0 are the current and initial arc length of the corneal meridian. The arc length can be calculated from the apex height h as:

     h0(a2 +h2) arcsin ( _ a2 + h2 ) _________________ λ=     ____      2ah h(a2 + h 20)   arcsin (a  2 + h0 2  )  2ah

(6)

0

where it has been assumed that a is unchanged by pressurization. The stress and strain evaluated from the apex displacement can be applied to a non-linear constitutive model for the stress-strain behavior of the cornea to determine material properties such as the tangent modulus at each pressure. More recently, Scheimpflug imaging was used to obtain the corneal topography of the entire anterior or posterior surface during inflation,12,13 in contrast to only measuring the location of the apex. The radii of curvature at each pressure step can be calculated by fitting the elevation map to a biconic surface. Strain was defined as the change in corneal radius of curvature, i.e., the average of the horizontal and vertical radii relative to the initial radius of curvature: ε = ∆R/R. The experiments were performed in whole globes12,13 rather than clamped corneal buttons. With the thin membrane assumption, the stress can be approximated by Laplace’s law as in Equation (2). 2.1. Modification for the effect of bending Anderson et al. developed a thin spherical-shell model of the cornea,10 which can be regarded as a modification of the spherical membrane model to account for the effects of bending (see also Elsheikh and Anderson and Elsheik et al.).4,14 Although the cornea may be considered a thin shell, with a ratio of the average R/t ~,10 boundary conditions at the holder in a tissue

94

T.D. Nguyen and J. Liu

test and at the corneal-scleral interface in a whole eye test can introduce significant bending moments and transverse shear forces. The pinned boundary generates bending moments and transverse shear stresses that vary with φ from the specimen apex to the boundary, which generates a correction term to Laplace’s law for the stress resultants. The Anderson et al. model assumed a spherical shell with a pinned boundary with no horizontal displacement and no bending moment in the meridional direction at the boundary.10 They also assumed that the incremental stress-strain relationship for each pressure step, p, can be described by the linear elastic Hooke’s law: 1

​ E ​ (​ σθθ - νσφφ)​, ​εθθ = _

1

εφφ = _ ​ E ​ (​ σφφ - νσθθ)​,​

(7)

where εθθ = λθθ - 1 and εφφ = λφφ - 1 are the tensile strains, and E and ν are the Young’s modulus and Poisson’s ratio at the applied pressure, respectively. These assumptions allowed Anderson et al. to derive an expression for the apex displacement-pressure relationship:10 pR2

​​w = _ ​​    ​​(1 -ν)​​[1 - exp​(-βη)​ cos ​(βη)​]​​, 2Et

(8)

where and β = (R/t)1/2 (1- ν2)1/4 and η = arcsin (a/R). The radius of curvature, R, and thickness, t, are determined

Copyright © 2018. Kugler Publications. All rights reserved.

Misconception 4: Laplace’s law This is widely used to calculate the stress response from the pressure, radius of curvature and thickness of the tissue. However, Laplace’s law is strictly applicable only for a thin uniform shell, where the ratio of the thickness to the radius is less than t/R < 0.1, with uniform radius of curvature, thickness and material properties. The cornea has large variations thickness and material properties. The globe, in addition, exhibits a large change in curvature at the corneoscleral junction. Finite elements analysis is needed to compute the pressure-induced stresses more accurately, but it is time consuming. Laplace’s law can provide a quick estimate of the stresses.

for each pressure step from current apex height, h, using Equation (4) and Equation (3) to determine the Young’s modulus, E, for each applied pressure, p. 2.2. Limitations The spherical-shell model provides a simple method for evaluating the stress in Equation (2) and stretch in Equation (6) from the apex displacement. However, the assumptions of the model can be restrictive. The model assumes that the cornea is a thin spherical shell of uniform thickness and radius of curvature. Dubbelman et al. measured an average radius of curvature of 7.8 mm for the anterior surface and of 6.53 mm for the posterior surface15 (see also Garner et al.).16 The radius of curvature increases meridionally from apex to limbus.7 The corneal thickness also varies from 0.5 mm17 to 0.7 mm18 from the apex to the limbus. Moreover, the spherical cap model assumes that the cornea deforms homogeneously while retaining its spherical shape, which neglects the spatially varying anisotropic behavior derived from the anisotropic collagen fiber structure.19 The modeling study of Nguyen et al. suggests that the strong circumferential collagen fiber alignment in the limbus causes the peripheral cornea to become flatter under pressure.20 While the assumptions of the spherical-shell model can cause significant errors in the stress and strain calculations, the model may still be a useful method for comparative studies, e.g., to evaluate the overall effectiveness of a collagen crosslinking agent for stiffening the cornea.

3. Local strain and curvature measurements Recent inflation studies have mainly employed methods for measuring local strains and curvatures to determine the spatial variation in material properties, which is an important consideration in applications where structural changes are not uniform.21 Regional strain measurements can be achieved with a single camera imaging the relative motion of markers on the surface of the cornea. Jue et al. used two droplets of mercury placed 3-4 mm apart on the anterior corneal surface of whole globe specimens near the apex.6 The change in the separation of the two droplets caused by pressure was recorded through a keratometer. The

Inflation testing of the cornea

95

strain at each pressure can be calculated by dividing the change in the separation by the original separation. In experiments on human corneas, Hjortdal et al. placed eleven mercury droplets on the anterior surface and nine droplets on the posterior surface.7 The droplets were positioned from apex to the limbus. The motion of the particles was observed under a microscope and captured by a video camera. The polar coordinates (r,θ) of each droplet were determined at each pressure, allowing the meridional separation, lφ and circumferential separation, lθ between two adjacent droplets to be calculated, assuming axisymmetry, at each pressure. Each specimen was inflation-tested twice. In the first test, the specimen was imaged top-down to calculate regional strains from the (r,θ) positions as: Iθ - Iθ0

​  I    ​, ​εθθ = _ θ0

Iφ - Iφ0

εφφ =_ ​  I    ,​​ φ0

(9)

where lφ0 and lθ0 are separations between droplets at the baseline pressure. In the second inflation test, the specimen was imaged in profile and an automatic tracing algorithm was used to extract points (x, z) along the profile edge, which were then used to calculate the regional meridional and circumferential radius of curvature, Rφ and Rθ, assuming axisymmetry as: ​​[1 + ​​(​z​​ l​)​​​ 2​]​​​ 3/2​ ​z ​

x

R ​ φ = ​ ________    ​​,  ( ll)

Rθ = _ ​​ cos α      ​​,

(10)

where α is the angle between the surface normal and the horizontal x-axis. For a non-spherical axisymmetric thin shell, the circumferential and meridional stresses are not equal. The membrane stresses for an axisymmetric thin shell can be calculated directly from equilibrium as: ​ 2t θ ​, σφφ =_ ​ 2t θ​​  2 -  ​ _  ​ ​,​ (11) ​σθθ =_ ( Rφ ) for a spherical cap, Rφ = Rθ, and Equation (11) reduces to Laplace’s Law for a spherical shell in Equation (2). Shin et al. scattered 30 μm silicon carbide particles randomly on the anterior surface.22 Six markers were identified along a meridian and the strains were calculated as the change in the arc length between two adjacent particles. Woo et al. designed a laser-sensor system to measure the relative deformation of two markers placed on either side of the specimen apex.5 An inverse finite element analysis (IFEA) was used to determine

Copyright © 2018. Kugler Publications. All rights reserved.

pR

pR

Rθ

the non-linear stress-strain response of the tissues that reproduced the displacements of the markers. 3.1. Limitations Measuring the relative displacement of multiple markers allows calculation of regional surface strains, curvatures, and stresses to determine regional variations in material properties. The ability to measure local curvatures also removes the restrictive spherical cap and homogeneous tissue assumptions from the stress and material properties analysis. However, for methods imaging the deformation of the markers in a single meridional plane, the analysis requires an axisymmetric model of the cornea and corneal deformations. The thin-shell model for calculating stresses also has limitations due to the assumptions explained in Section 2.2.

4. Full-field deformation measurement A number of recent inflation tests have applied speckle-tracking methods for detailed, high-spatial resolution measurement of displacement and strain fields. Boyce et al. used 3-D digital image correlation (DIC), to map the surface deformation field of the bovine cornea.8 A comprehensive description of the theory and implementation of digital image correlation methods is provided by Sutton.23 Graphite powder was dispersed on the surface of the cornea to create a speckle pattern of dark and light contrasting pattern that moves with the underlying material. The deforming specimen was imaged top-down by two cameras arranged in stereo. DIC provides the original configuration of the specimen surface (at baseline pressure), as well as the displacement field of the surface as a function of pressure (Fig. 3). The DIC method compares the distribution of gray values of pixel subsets from the reference image (at the reference pressure) to those of subsequent deformed images by optimizing the parameters of a correlation function to track the motion of material points over time. The method has the potential for high accuracy. The resolution and error in the displacement correlation and strain calculations depends on many factors, including the contrast of the speckling pattern, lighting, and the stereo angle.24 Displacement uncertainties of < 10μm25 and spatial resolution of 1%

96

T.D. Nguyen and J. Liu

Fig. 4. Through-thickness compressive strains at inflation from 5 to 15 mmHg in a canine cornea before (c) and after (d) UVA-riboflavin induced collagen crosslinking, measured by high-frequency ultrasound speckle tracking.28

ultrasound signal. The RF signal is created by coherent scattering of the sub-resolution microstructures of the tissue and provides a natural speckle pattern for motion tracking. Tang and Liu applied a cross-correlation algorithm to calculate the displacement field from RF signals obtained at two consecutive pressures.29 Using RF signals instead of images, along with spline interpolation of the correlation coefficients, the method was capable of sub-pixel displacement accuracies (e.g., sub-micron in the axial direction) and accurate strain measurements in the range of 1-5% and potentially lower strains. Using the ultrasound speckle tracking method, Palko et al. reported a significant increase in tangential (i.e., in-plane stretch) strains from the anterior to the posterior cornea during inflation, while the radial compressive strains remained unchanged through the depth of the stroma.28 This method was also able to detect significant strain reduction in corneas after UVA-riboflavin collagen crosslinking treatment (Fig. 4).

Copyright © 2018. Kugler Publications. All rights reserved.

5. Outlook

Fig. 3. Typical displacement components U, V, and W at a pressure of 8 kPa (60 mmHg) measured by DIC in bovine corneas.8

of the field of view can be realized.26 Ultrasound elastography methods have been developed to map the strain fields in cross-sections of the cornea27–28 in inflation tests. A high-frequency ultrasound system is used to scan the cross-section of the cornea and acquire the radio frequency (RF)

Collagen fibers have a spatially heterogeneous organizational pattern in the cornea.19 The simplified thin-shell model and fixed boundary conditions are likely inadequate for capturing clinically significant features of corneal mechanical behavior that is essential for visual acuity. Advances in imaging techniques and data analysis will allow for more comprehensive full-field characterization of the whole cornea, including the limbal region, during pressurization of the whole eye under physiological boundary conditions. Cruz Perez et al. has reported a 3-D ultrasound speckle-tracking method that can be applied to scan the full volume of the cornea from limbus to limbus, and compute the

Inflation testing of the cornea

full-field displacements in 3-D and the full strain tensor, including both in-plane and out-of-plane normal strains and shear strains.30 In addition, the high-frequency ultrasound imaging used for speckle tracking also simultaneously provides anatomic delineations of the deforming cornea at high spatial resolution, allowing analyses of the shape change. Digital volume correlation (DVC) is another method that can be potentially applied to analyze volume images obtained from, e.g., optical coherence tomography scans and laser scanning microscopy to map the 3-D strain field in the cornea.31 The displacement field is determined

References

Copyright © 2018. Kugler Publications. All rights reserved.

1.

Fung YC. Biomechanics: mechanical properties of living tissues. Springer-Verlag, New York, NY, 1993. 2. Boyce BL, Jones RE, Grazier JM, Nguyen TD, Grazier JM. Stress-controlled viscoelastic tensile response of bovine cornea. J. Biomech. 2007;40(11):2367–2376. 3. Tonge TK, Murienne BJ, Coudrillier B, Rothkopf SAW, Nguyen TD. Minimal preconditioning effects observed for inflation tests of planar tissues. J Biomech Eng. 2013;135(11):1–14. 4. Elsheikh A, Anderson K. Comparative study of corneal strip extensometry and inflation tests. J R Soc Interface. 2005;2(3):177– 185. 5. Woo SL-Y, Kobayashi AS, Schlegel WA, Lawrence C. Nonlinear material properties of intact cornea and sclera. Exp Eye Res. 1972;14(1):29–39. 6. Jue W, Maurice DM. The mechanical properties of the rabbit and human cornea. J Biomech. 1991;24:907–922. 7. Hjortdal JO. Regional elastic performance of the human cornea. J Biomech. 1996;29:931–942. 8. Boyce BL, Grazier JM, Jones RE, Nguyen TD. Full-field Deformation of bovine cornea under constrained inflation conditions. Biomaterials. 2007;40:2367-2376. 9. Bisplinghoff JA, McNally C, Manoogian SJ, Duma SM. Dynamic material properties of the human sclera. J Biomech. 2009;42(10):1493–1497. 10. Anderson K, El-Sheikh A, Newson T. Application of structural analysis to the mechanical behaviour of the cornea. J R Soc Interface. 2004;1(1):3–15. 11. Small MK, Nix WD. Analysis of the accuracy of the bulge test in deter-mining the mechanical properties of thin films. J Mater Res. 1992;7(6):1553–1563. 12. Kling S, Remon L, Pérez-Escudero A, Merayo-Lloves J, Marcos S. Corneal biomechanical changes after collagen cross-linking from porcine eye inflation experiments. Invest Ophthalmol Vis Sci. 2010;51(8):3961-3968.

97

in DVC by correlating the image intensity distribution between a reference image and a deformed one. The method has been applied successfully to map the deformation response of 3-D cell cultures and biological materials, including the sclera and lamina cribrosa.32,33 These new methods will generate useful geometrical and deformation data. Combined with finite element models, these data can help us better understand the spatially varying biomechanical properties of the cornea, and how these properties, along with corneal shape, may be altered by different clinical procedures.34,35

13. Lombardo G, Serrao S, Rosati M, Lombardo M. Analysis of the viscoelastic properties of the human cornea using Scheimpflug imaging in inflation experiment of eye globes. PLoS One. 2014;9(11):e112169. 14. Elsheikh A, Wang D, Brown M, Rama P, Campan-elli M, Pye D. Assessment of corneal biomechanical properties and their variation with age. Curr Eye Res. 2007;32(1):11–19. 15. Dubbelman M, Weeber HA, Van der Heijde RGL, Völker-Dieben HJ. Radius and asphericity of the posterior corneal surface de-termined by corrected Scheimpflug photography. Acta Ophthalmol Scand. 2002;80(4):379– 383. 16. Garner LF, Owens H, Yap MK, Frith MJ, Kinnear RF. Radius of curvature of the posterior surface of the cornea. Optom Vis Sci. 1997;74(7):496–498. 17. Martola EL, Baum JL. Central and peripheral corneal thickness. A clinical study. Arch Ophthalmol. 1968;79(1):28–30. 18. Feng Y, Simpson TL. Comparison of human central cornea and limbus in vivo using optical coherence tomography. Optom Vis Sci. 2005;82:416–419. 19. Boote C, Dennis S, Meek K. Spatial mapping of collagen fibril organisation in primate cornea-an X-ray diffraction investigation. J Struct Biol. 2004;146(3):359–367. 20. Nguyen TD, Boyce BL. An inverse finite element method for determining the anisotropic properties of the cornea. Biomech. Model. Mechanobiol. 2011;10(3):323–337. 21. Meek KM, Tuft SJ, Huang Y, et al. Changes in collagen orientation and distribution in keratoconus corneas. Invest Ophthalmol Vis Sci. 2005;46(6):1948–1956. 22. Shin TJ, Vito RP, Johnson LW, Mccarey BE. The distribution of strain in the human cornea. J Biomech. 1997;30(5):497-503. 23. Schreier H, Orteu J-J, Sutton MA. Image correlation for shape, motion and deformation measurements. Number Vdic. US, Boston, MA: Springer; 2009.

98

Copyright © 2018. Kugler Publications. All rights reserved.

24. Ke X-D, Schreier HW, Sutton MA, Wang YQ. Error assessment in stereo-based deformation measurements Part II: Experimental validation of uncertainty and bias estimates. Exp Mech. 2011;51:423–441. 25. Coudrillier B, Tian J, Alexander S, Myers KM, Quigley HA, Nguyen TD. Biomechanics of the human posterior sclera: age- and glaucoma-related changes measured using inflation testing. Invest Ophthalmol Vis Sci. 2012;53(4):1714-28. 26. Sutton MA, Ke X, Lessner SM, et al. Strain field measurements on mouse carotid arteries using micro-scopic three-dimensional digital image correlation. J Biomed Mater Res. 2007; 84A(1):178–190. 27. Hollman KW, Emelianov SY, Neiss JH, et al. Strain imaging of corneal tissue with an ultrasound elasticity microscope. Cornea. 2002;21(1):68-73. 28. Palko JR, Tang J, Cruz perez B, Pan X, Liu J. Spatially heterogeneous corneal mechanical responses before and after riboflavin-ultraviolet-A crosslinking. J Cataract Refract Surg. 2014;40(6):1021-31. 29. Tang J, Liu J. Ultrasonic measurement of scleral cross-sectional strains during elevations of intraocular pressure: method validation and initial results in posterior porcine sclera. J Biomech Eng. 2012;134(9):091007.

T.D. Nguyen and J. Liu 30. Cruz PB, Pavlatos E, Morris HJ, et al. Mapping 3D Strains with Ultrasound Speckle Tracking: Method Validation and Initial Results in Porcine Scleral Inflation. Ann Biomed Eng. 2016;44(7):2302-12. 31. Bay BK, Smith TS, Fyhrie DP, Saad M. Digital volume correlation: Three-dimensional strain mapping using x-ray tomography, Exp Mech. 1999;39:217–226. 32. Nguyen C, Midgett D, Kimball EC, et al. Measuring Deformation in the Mouse Optic Nerve Head and Peripapillary Sclera. Invest Ophthalmol Vis Sci. 2017;58(2):721-733. 33. Midgett DE, Pease ME, Jefferys JL, et al. The pressure-induced deformation response of the human lamina cribrosa: Analysis of regional variations. Acta Biomater. 2017;53:123-139. 34. Pandolfi A, Fotia G, Manganiello F. Finite element simulations of laser refractive corneal surgery. Eng Comput. 2009;25(1): 15-24. 35. Sinha roy A, Rocha KM, Randleman JB, Stulting RD, Dupps WJ. Corrigendum to “Inverse computational analysis of in vivo corneal elastic modulus change after collagen crosslinking for keratoconus” [Exp. Eye Res. 113C (2013) 92-104]. Exp Eye Res. 2016;145:472.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

NON-DESTRUCTIVE CORNEAL BIOMECHANICAL MEASUREMENT

Copyright © 2018. Kugler Publications. All rights reserved.

8. Optical coherence tomography principles and elastography Matthew R. Ford1, Vinicius De Stefano1,2, William J. Dupps Jr.1,3 Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA; 2Ophthalmology and Visual Sciences, Federal University of São Paulo, São Paulo, SP, Brazil; 3Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA 1

1. Elastography

Copyright © 2018. Kugler Publications. All rights reserved.

Elastography is a technique that provides a spatial map of tissue mechanical properties with many potential applications in both the medical and non-medical fields. For the purposes of this book, the mechanical properties of the cornea have important implications for corneal shape and function as well as responses to interventions. In this chapter, we will endeavor to provide some basic background on elastography in general, as well as its application to optical coherence tomography (OCT). Elastography is a relatively new field of medical imaging that involves inferring mechanical information about the imaged tissue by application of some form

of physical perturbation. The tissue response to the perturbation is then monitored by any of a variety of methods. The most common method is the application of cross-correlation methods to locate identical regions across subsequent images or repeated local scans. Other methods typically involve advanced signal processing on the incoming data, and may or may not involve more complicated scan types. As time goes on, more methods are being developed, but certain fundamental principles are important for understanding the advantages and limitations of the various approaches to elastography. Ophir first demonstrated modern elastography using ultrasound as the imaging modality by compressing the tissue using the ultrasound probe itself.1 By application

Fig. 1. A flow chart of the elastography process. Elastographic imaging is contained almost entirely in the upper left box. The majority of quantitative data needs to be analyzed using FEM (upper right box) to create maps of tissue mechanical properties. Some techniques bypass the modeling step utilizing relative stiffness indicators instead of a quantitative estimate. Correspondence: William J. Dupps Jr., Cleveland Clinic Main Campus, Mail Code i32, 9500 Euclid Avenue, Cleveland, OH 44195, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 103-115 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

104

Copyright © 2018. Kugler Publications. All rights reserved.

of a cross-correlation technique, he was able to track the displacement of the tissue by the change in the position and/or phase of the ultrasound signal. In this early technique, the stiffness of the tissue was assumed to be inversely proportional to the displacement of the tissue. Later work in the field would show that the instantaneous strain (in 1-D) could be computed as the derivative of the axial displacement.2 Elastography has gone on to be applied to other forms of medical imaging using many different types of contrast or signal for tracking. Conversion of measured data into biomechanical properties is typically not a straightforward process. This has been addressed in some applications by the use of finite element modeling (FEM) in an inversely posed problem to derive material properties from measured displacement behaviors. A diagram of this process is shown in Figure 1. 1.1. Perturbation types Many combinations of imaging methods and perturbations can be and have been leveraged for elastography. However, perturbation methods can be categorized into three main subgroups: external or bulk perturbation, internal or local perturbation, and endogenous sources of elastographic information. External or bulk perturbation is the most common and most easily understood tissue perturbation type used in elastography. This perturbation involves applying a bulk force or disturbance to the tissue being imaged. In ultrasound elastography, this frequently means manually applying pressure with the imaging probe in contact with the tissue.1 In OCT-based elastography, this has been accomplished with a variety of transparent windows and/or adjacent perturbation devices.3–6 The application of shear waves, ultrasound waves, thermal gradients, or pressure changes have all been used to perturb the tissue and measure tissue biomechanical properties.7,8 Internal or local perturbation techniques involve applying force or other perturbation techniques locally using either an introduced agent or some form of locally intense radiation force like focused ultrasound. These perturbation techniques can produce highly localized information and may require less intense perturbation sources. Additionally, the methods used can be useful in ensuring that the imaging technique and the perturbation source do not conflict with each other. Some of

M. Ford, V. De Stefano and W.J. Dupps

the methods used include applying a magnetic field to local magnetic particles,9 using focused ultrasound to produce a local compression,10 and using a laser to excite a local shockwave.11 Endogenous sources of elastographic information are rarer than the other two types. However, they show promise for investigating the mechanical properties of tissue. In the field of magnetic resonance imaging (MRI), diffusion tensor scans are used to monitor the flow (motion) over time within an imaging volume. The rate of flow has been used to measure anisotropy in tissue behavior.12 Intravascular elastography can utilize the blood pressure cycle as a perturbation source.13

2. OCT OCT is a non-invasive, high-resolution imaging technique that provides cross-sectional images of tissue microstructure from video rate to several orders of magnitude faster.14,15 The non-invasive, non-contact optical nature of OCT confers important advantages in a number of clinical fields including cardiology, gastroenterology, gynecology, urology, ophthalmology, and dermatology.16 Due to the anatomic scales involved and the easy accessibility of the eye to optical imaging, these advantages extend to elastography of the eye and warrant a strong foundation in the principles of optical coherence imaging. 2.1. OCT: basic concepts OCT is a medical imaging technique in which a coherent light source illuminates a tissue surface and a reference arm, and cross-sectional images are developed from the interference patterns generated by the combination of the two reflections. The majority of OCT systems operate upon the principle of low-coherence interferometry as developed for use in axial or a-line prioritized imaging. In this technique, the low-coherence source allows for the different depths present within the scan beam to be differentiated from one another. This is shown diagramatically in Figure 2. The broader the bandwidth of the low-coherence source, the shorter the axial separation, thus resulting in better imaging resolution. The relationship between light source and axial imaging resolution is a function of the coherence length given by:

Optical coherence tomography principles and elastography

Fig. 2. A simple diagram of a basic Michelson interferometer signal demonstrating the concept of low-coherence interferometry and signal falloff with distance. 2 2ln2 ​λ​ 0​​ 

Copyright © 2018. Kugler Publications. All rights reserved.

​lc = _ ​  π ​​   _   ​​ (1) λΔ where lc is the coherence length, λ0 is the central wavelength, and Δλ is the bandwidth of the light source. Since the coherence length determines the axial distance over which a reflector can be observed, it can and is frequently used as the measure of axial resolution, as seen in Equation (1) and shown in figure 3. Typical systems have a resolution of around 5-15 µm (axial) and as much as 3 mm imaging depth in tissue. Since the axial resolution is a function of the light source, the lateral resolution is inherently decoupled from the axial resolution and is instead a function of the optics of the sample arm. Imaging depth is a function of the range from which singly scattered light can be distinguished from noise. As such, it tends to be a function of the scattering properties of the tissue. With modern electronics and a shot noise limited system, imaging depth is typically in the range of 0.5 mm (cardiac or muscle) to 3 mm depth in tissue (posterior eye, fatty tissue).16 The lateral resolution is a function of the scanning optics and not a function of the coherence length of the source. Thus, the lateral resolution is a function of the focusing optics and is determined by the spot size of the focused beam in the tissue. In terms of conventional optics, OCT optical designs are forced to deal with the tradeoff between depth of focus and spot size. Low numerical aperture lenses (lens systems) are typically used to maintain a long depth of focus and an intermediate spot size.

105

Fig. 3. An example of OCT system signal generated by three partial reflectors in the sample arm. The upper graph indicates the position of the reflectors, the middle graph shows the raw time domain OCT signal, and the bottom graph shows the demodulated OCT signal.

Δx 2

b ​ = π_ ​  2λ  ​​ (2) _​  ​​ (3) ​Δ x = ​ _ π ​  ​(​ d ) 4λ

f

Equation (2) shows the tradeoff between the lateral resolution, Δx, and the depth of focus, b, as a function of the wavelength, λ. Equation (3) shows the spot size as a function of the focal length, f, and the beam diameter, d. There are three main sources of noise in any given OCT system.17 These consist of receiver noise, shot noise, and excess photon noise. In most OCT systems, the operating regime is chosen such that the system is operating between the minimum optical power defined by the receiver noise and the maximum power defined by excess photon noise. In this region, a properly designed system will approach the shot noise limit as closely as possible. The signal-to-noise ratio (SNR) in a shot noise limited OCT system is given by: ρPsPR

​SNR = _  ​ 2eβ   ​​ (4) where ρ is the detector responsivity, Ps is the power returning from the sample arm, PR is the power returning from the reference arm, e is the electronic charge, and β is the detection bandwidth.

106

M. Ford, V. De Stefano and W.J. Dupps

2.2. Time domain OCT The OCT systems data acquisition discussed up to this point have all been described in the time domain. In this version of OCT, the low-coherence light source emits a broad spectrum of light continuously and the reference arm is moved to generate the OCT signal. This setup allows for a theoretically limitless imaging depth, but is restricted to imaging rates determined by the speed at which the reference arm (mirror or retro-reflector) can be moved. This limits the a-line imaging rate of time domain OCT to levels in the hundreds of Hz. This in turn sets an upper limit on the frame rate of one or two frames per second. While sufficient for ex-vivo samples, the desire for in-vivo imaging drove the development of new techniques to better deal with problems like patient motion. 2.3. Fourier domain OCT The next major development in improving the speed of OCT was the change to Fourier domain OCT (FDOCT). Compared to time domain OCT, FDOCT (also known as spectral domain OCT) utilizes a spectral interference pattern18,19 instead of the usual temporal interference pattern. In addition, due to the additional integration time at each a-line, FDOCT enjoys an SNR advantage and improves the sensitivity of FDOCT by about 20 dB over time domain OCT without the penalty due to increasing imaging speed.20,21 The FDOCT SNR is given by: ρPsPR Δt _    2e ​​

Copyright © 2018. Kugler Publications. All rights reserved.

​ NR =  ​ S (5)

where the first three terms are the same as for TDOCT mentioned above, and Δt is the integration time of the spectrometer or the sweep time of the light source. The FDOCT SNR advantage is clear from this equation, as it linearly decreases in SNR with speed, whereas TDOCT SNR decreases with increasing bandwidth. Since the bandwidth increases greatly as speed increases, the resultant SNR penalty for TDOCT systems is far greater than an equivalent speed increase for FDOCT systems. The increased imaging speed led to an explosion of development in various methods of improving image acquisition techniques. Two separate basic versions of FDOCT were developed. The first, generally referred to as FDOCT, utilizes a spectrometer in lieu of the single

detector used in time domain OCT. The camera and spectrometer optics become the limiting factors in terms of speed and falloff in the OCT imaging.22 The camera also plays a role in sensitivity and noise, but other components of the system may dominate these aspects of the imaging system. The second major type of FDOCT system is commonly referred to as swept source OCT (SSOCT). In SSOCT, the broadband source is replaced with a narrowband source capable of sweeping a bandwidth over a period of time.23 The detector setup remains similar to TDOCT, though with greatly increased bandwidth. 2.3. Swept source OCT The development of SSOCT lead to some unexpected changes in OCT imaging. If we consider the Fourier domain pairs used in imaging, the sampling in wavenumber (or k-space) is a function of the sampling optical system. For this discussion, the wavelength to wavenumber conversion will be ignored as it raises the complexity unnecessarily. Take, for instance, the standard spectrometer setup consisting of a focusing optical system which spreads the light by wavenumber on a-line scan camera. In wavenumber, the sampling function becomes the number of pixels on the camera containing the wavenumber spectrum. However, the sampling function becomes the convolution of the pixel shape with the spectrum itself. This results in the sampled, transformed OCT signal being convolved with a sinc-squared function. This results in the signal becoming smaller with depth regardless of the sample arm optics. This phenomenon is referred to as “falloff” and occurs in all camera-based spectrometers. However, the larger the number of pixels, the smaller the width of the pixel and the more extended the falloff depth. As line scan cameras for use with OCT have improved with greater number of pixels, the falloff problem has become less of an issue, but has not disappeared altogether. The push for speed in swept source systems has led to some truly unique light sources. Many of the new light sources are capable of imaging beyond the 100kHz a-line rate,24,25 and some are even capable of greater than MHz line rates.26 The development pathway started with short cavity lasers capable of imaging in the low to mid kilohertz range.23,25 These lasers were ultimately limited in speed by the length of the cavity.

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence tomography principles and elastography

As the repetition rate went up, the power in the cavity decreased because the number of passes through the gain medium was reduced. This also resulted in a loss of mode locking, resulting in a broader linewidth. A unique solution was found by Huber et al.24 whereby a very long cavity was constructed and the sweep rate of the laser was tuned to match the time it took for the light to pass through the cavity. This creates a high-speed, high-power laser in which mode locking determines the linewidth of the system, resulting in very narrow instantaneous linewidths. The micro electromechanical (MEM)s community went the opposite direction and developed vertical cavity surface emitting lasers (VCSEL).27 By constructing semi-conductor layered cavities on a wafer, and placing a small tunable MEMS filter on top, a cavity of only a fraction of a millimeter can be constructed. Since the cavity is so small, the light will pass through the gain medium many times at almost any practical sweep rate before exiting through the filter. This effectively limits the scan rate to the rate at which the MEMS filter can be swept. The unexpected consequence of these developments is the aforementioned convolution that occurs when sampling the spectrum. In the case of SSOCT signals, the convolution is between the instantaneous linewidth of the laser source and the sampling rate of the analog-to-digital (A/D) acquisition hardware. Since the linewidth of the laser sources is typically extremely small, the sampling rate of the A/D dominates this transform. With A/D boards acquisition rates improving into the high hundreds of megahertz and even gigahertz sampling rates, the falloff range of the system becomes tens of millimeters. With proper sample arm design, this nicely solves the problems associated with in-vivo imaging when the distance between the sample arm and the tissue cannot be easily controlled, such as with endoscopic or catheter-based imaging. It is also useful in tissues with high transparency, such as the anterior chamber of the human eye.

3. Anterior segment imaging with OCT The most common medical application of OCT is imaging the posterior region of the human eye, primarily the retina. The ability to image the layers of the retina in

107

real time in a non-contact manner cannot be matched by any other medical imaging technique currently on the market. Imaging of the anterior segment with OCT is not only more convenient than other techniques — such as ultrasound biomicroscopy which requires a coupling fluid — but also a useful tool for cross-sectional visualization of ophthalmic surgeries like lamellar corneal transplantation.28 3.1. Image development and speckle in OCT imaging The use of any coherent imaging (OCT, ultrasound, radar, etc.) creates an image pattern/noise commonly referred to as speckle. Speckle is a phenomenon that results from the interaction of the imaging radiation with objects that are smaller than the resolution of the system. The interaction of these multiple reflectors within the resolvable volume results in an erroneous detector signal that is some mixing function of the overlapping signals. This mixed signal creates what appears on the image to be a pattern within what should be a relatively smooth region, as shown in Figure 4. For instance, in moderate resolution raw OCT images, the corneal stroma looks like a gravel road in grayscale. In contrast,

Fig. 4. (Top) An example image of corneal stroma as taken with OCT. Note the dot-like pattern caused by image speckle that is in contrast to the relatively featureless repeating layered nature of the stroma. (Bottom) A blowup of a small portion of the corneal stroma seen on the top taken from the red outline on the corneal image.

108

we know from histological imaging that the stroma should be a relatively smooth tissue with a few cells mixed in between the collagen layers. While in most instances speckle is regarded as noise or an error and is something to be filtered or removed, it has been utilized to produce information. Barton et al. noted that OCT speckle decorrelation was related to flow within the imaging volume.29 The importance of this observation is that the speckle pattern is stable over short periods of time provided flow is limited. In the avascular cornea, where fluid movement is also restricted by an anionic hydrophilic matrix and collagen lamellae, this means the speckle pattern is relatively stable (on the order of tens of seconds) and can therefore be used to track a portion of the cornea even when there are no suitable structural features for tracking.3 This is beneficial in relatively uniform structures like the anterior segment of the eye.

4. Optical coherence elastography

Copyright © 2018. Kugler Publications. All rights reserved.

Fundamentally, the elastography process consists of perturbing a tissue while monitoring the subsequent behavior of the tissue in response. In the various types of elastography, there are two basic types of perturbation. The first is a perturbation applied at the surface using either the device itself or a second object.1 The second type of perturbation involves using a mechanism — techniques such as focused ultrasound or magnetically susceptible moving particles — to induce a mechanical shift inside the tissue at a specific location.30,31 In either case, the tissue is perturbed

M. Ford, V. De Stefano and W.J. Dupps

while imaging is occurring, and a method is applied to measure the subsequent displacement of the tissue. Figure 5 shows the basic principle of elastography as performed with an ultrasound transducer. Ultrasound elastography was developed by Ophir et 1 al. for use with ultrasound signal tracking to estimate biological tissue stiffness. It was first applied in the cornea approximately a decade later when Hollman et al.32 utilized a water bath and through-focusing to image the full-thickness cornea. OCT-based elastography was first described by Schmitt, which greatly improved the resolution of elastography and removed the constraint of a coupling fluid.33 The technique used embedded tissue markers and dermal tissue features as correlation targets. Spectral domain OCT elastography has been extensively studied with cardiovascular catheterization procedures to identify vulnerable plaques.34,35 Torre-Ibarra et al. described the use of phase-contrast spectral OCT to estimate 1-D (axial) corneal displacements.36 In addition, studying the effects of other perturbation types with OCT and holography have been used to approximate elastographic measurements.37,38 4.1. Cross-correlation analysis or digital image correlation While a number of different tissue-tracking methods have been proposed and demonstrated with OCT-based elastography, cross-correlation methods (sometimes called digital image correlation) are one of the more common and most investigated techniques. OCT elastography correlation has been done in multiple dimensions and with multiple methods.

Fig. 5. A simple representation of the elastographic process utilizing an ultrasound probe. An image is acquired with the ultrasound probe in the first frame, the tissue is then compressed and imaged again as in the second frame, and then image processing is applied to determine where each portion of the image moved during the compression cycle.

Optical coherence tomography principles and elastography

109

Fig. 7. A time sequence of corneal displacement taken over approximately 20 mmHg and less than 1 minute of time. The cornea was excised and placed on an artificial anterior chamber. Pressure was controlled using a saline drip and gravity pump.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 6. An example diagram of the cross-correlation displacement tracking procedure. The two frames are compared to generate a displacement map which is then represented with various colors to indicate magnitude and direction of displacement.

Image correlation is achieved by tracking some component of the image that is consistent throughout the applied perturbation and the underlying tissue structure. Both endogenous and exogenous (externally applied) image features have been used for cross-correlation tracking. The basic principles of cross-correlation analysis are straightforward, although there are many variations. In its simplest form, a function measuring how similar two regions of an image are to each other is defined. These regions can be arbitrary or specific to a certain type of feature. For each region of interest in the image(s), the equation is used to compare them. The region which returns the highest likelihood of a match is then assumed to be the actual displacement the region underwent. Additional filtering can be used to reduce false positives dependent upon the method used. A color representation of this method can be seen in Figure 6. 4.2. Tissue perturbation history with elastography Early work in corneal elastography focused on excised corneas and artificial anterior chamber mounts or destructive testing.39 Intraocular pressure (IOP) was

Fig. 8. Measured displacements of the cornea when it remains attached to the whole globe. (A) OCT magnitude image of the cornea. (B) Measured displacement of the cornea. (C) Strain map generated from (B), showing the lack of measureable strain in the presence of large bulk deformations in the ex vivo eye mount.

particularly attractive, as it is a natural stressor of the cornea and can be altered both physically and with drugs. Figure 7 shows some of our own early work. The tissue-perturbation method consisted of altering IOP by varying the pressure behind the cornea using the artificial anterior chamber. The experiments successfully monitored displacements in the tissue related to both location and corneal properties. Further work in corneal elastography focused on moving towards a more clinically relevant regime.

110

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 9. A patient being scanned with a custom OCT elastography device. The patient's head is stabilized with a bite plate.

M. Ford, V. De Stefano and W.J. Dupps

As the research community shifted towards a more complete ex-vivo model utilizing the whole globe rather than just the cornea, IOP became a much less attractive perturbation. Early work shown in Figure 8 indicates that when the cornea remains attached to the whole globe of the eye, the change in IOP results in a bulk displacement of the tissue. Very little elastographic information can be gained from bulk tissue displacement, highlighting the need to find alternative methods of tissue perturbation. It is important to note that, while this technique did not distinguish anything in these experiments, others using longer perturbation times or different tissue types (e.g., rabbit, porcine, canine) were able to measure tissue strain.8,40,41 The push for more clinically relevant optical coherence elastography (OCE) resulted in additional techniques being designed and tested. A detailed discussion of many of these techniques is contained

Fig. 10. Three-dimensional representation of the gonioscopy lens and whole globe in the OCT sample arm path with mechanically translating mobile arm attached.4

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence tomography principles and elastography

in the next chapter. For the purposes of continuing the introduction to OCE, we will discuss the most traditional form of compression elastography. By utilizing an optically clear compression device, as shown in our laboratory’s clinical elastography prototype (Fig. 9), the cornea can be compressed without significantly compromising OCT imaging quality. Other investigators have used ring-shaped or immediately adjacent compression devices to compress the tissue without interfering with the imaging process.5 As the corneal stroma is a relatively thin tissue (~400-600 µm) with a liquid interface at the posterior surface, it presents a wholly unique tissue for elastographic measurements. Most elastographic measurements compress the tissue against a relatively stiff underlying feature like bone or muscle, whereas the cornea is largely unconstrained in the sagittal plane. This makes it difficult to create a measurable strain at physiologically safe compressions. Some researchers have overcome this limitation with more extreme resolution techniques like phase sensitivity or phase contrast.36 The authors’ work has included a focus on measurements of the lateral motion induced during an axial compression, which captures mechanical behavior in the direction of collagen fiber action in the cornea. The following experiment example covers a basic OCE process. OCT imaging was performed using a technique previously described by the author’s group,3 and consisted of scanning a 4 mm x 40 µm region with lateral oversampling of approximately ten times the spot size (20 µm) to ensure accurate capture of the speckle pattern. Imaging was performed at a line rate of 47000 A-scans/sec with no averaging. The system consisted of a custom-built k-space linear FDOCT system with 12 µm axial resolution in air and a spot size of approximately 20 µm in air with a scanning range of 15 mm x 15 mm laterally. The system was driven by a custom C++ software suite. A standard clinical gonioscopy lens with a 4 mm central aperture (Volk, Mentor, OH, USA) was used to perturb the tissue. The OCT sample arm beam was passed through the central unobstructed view of the gonioscopy lens as shown in Figures 9 and 10. This enabled an imaging window of approximately 4 mm in width. The imaging window was oriented along one of the two principal meridia chosen at random.

111

Fig. 11. (A) Examples of axial and lateral displacement maps for a single eye in the post-deturgessence state. Lateral displacements (top frame) and axial displacements (bottom frame) are presented in µm for a 20 µm axial compression as described in the Methods. The axial displacement data shows a measured group displacement of approximately 20 µm. (B) Cumulative regional corneal displacements for the nasal-temporal meridian of the same eye in (A). Lateral-to-axial displacement ratios for the (A) edematous state, (B) deturgessed state, and (C) post-crosslinking state are plotted for serial compressions. Each line corresponds to one of the six defined regions of interest within the same 2-D section of the cornea.4

The gonioscopy lens was physically mounted to a computer-controlled translation stage which was used to control the displacement of the gonioscopy lens on the cornea. The gonioscopy lens was displaced in 20 µm increments along the scan direction (axially) through a total range of 220 µm. Images were acquired before and after each displacement increment. Displacement tracking was performed using the method described previously.3 This type of experiment produces results as shown in Figure 11. This particular experiment covers the behavior of an ex-vivo human whole globe under three different physiologic states: edematous, normal, and crosslinked. In this experiment, the slope of the cumulative displacement curves is inversely proportional to the stiffness of the cornea. The stiffer the cornea, the flatter the curve. This type of experiment represents one of the most straightforward methods of OCE as a standard compression and displacement measurement. After a few adaptations, this technique was tested in vivo for the first time. Corneal compression is achieved using a flat

Copyright © 2018. Kugler Publications. All rights reserved.

112

M. Ford, V. De Stefano and W.J. Dupps

Fig. 12. OCT and optical coherence elastography images of rabbit corneas three months post-crosslinking with various crosslinking methods employed. Color maps show lateral corneal displacement magnitudes as a function of corneal depth during an axial push with a curved lens. Blue represents less displacement (stiffer) and red represents more displacement (less stiff). Standard: An epithelium off crosslinking following the most common clinical protocol. Femtosecond: Crosslinking with a femtosecond laser flap rather than traditional epithelium removal. BKC: A novel crosslinking procedure utilizing a novel chemical cocktail to allow crosslinking without removing the epithelium. Tetracaine: Epithelium-on crosslinking procedure with tetracaine adjuvant. Uncrosslinked: This control group underwent no crosslinking treatment.43

Optical coherence tomography principles and elastography

113

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 13. Statistical curves taken from the experiment in Torricelli et al. These curves show how the various crosslinking procedures affected the elastographic data in the five different experimental protocols.43

lens (instead of a gonioscopy lens) attached to a linear actuator and rapid sampling rate force transducers. A 2-D cross-correlation algorithm is applied to track frame-by-frame intrastromal speckle displacement, creating an elastogram based on the displacement amplitude. The heterogeneous elastic properties of the cornea were revealed from the variations in the axial and lateral displacements. Further application of this technique has been applied to the investigation of various chemical and clinical methods of crosslinking.42,43 The technique was able to distinguish the varying impact of the methods on rabbit corneas three months after the crosslinking treatment was applied (Fig. 12). Figure 13 demonstrates the resultant mechanical measures on the distribution of mechanical values measured in each cornea. The measured value and variance of the properties was used to infer the effects of the various crosslinking methods on the rabbit corneas. The translation of elastography to live human eyes is ongoing. The compression method described above3,4 has been adapted and modified to suit in-vivo applications. Some of the preliminary work done on live subjects involves creating elastograms similar to those in Figure 8. Figure 14 illustrates the recorded displacements in a healthy cornea. It is possible to observe the distinct behavior of the anterior and posterior corneal stroma: even though the compression apparatus is applied to the anterior portion, the posterior stroma has a higher cumulative displacement vector. This corresponds to known depth-dependent gradients from ex-vivo human corneal measurements summarized in earlier chapters and reflects the higher corneal stromal elastic strength in the anterior cornea near Bowman membrane.

Fig. 14. (First panel) Raw OCT image of a patient's cornea. (Second panel) The same cornea compressed with a flat glass lens with the anterior and posterior regions used in the graph below highlighted in their matching color. (Third panel) Graph showing the force vs displacement relationship in the cornea shown. (Fourth panel) The overlay of the resulting slope values with the compressed cornea. The colormap represents the slope values for every pixel within the cornea. Note: warmer colors indicate a higher displacement magnitude in the posterior stroma when compared to the anterior stroma.

114

M. Ford, V. De Stefano and W.J. Dupps

In closing, the development of elastography and its adaptation to a readily available clinical imaging modality, OCT, has significant implications for the measurement and understanding of corneal biomechanics. Even though preliminary results already point toward a feasible and non-invasive method to infer corneal biomechanics, this technology is not yet commercially available. Studies are ongoing to validate the method in clinical settings, including change analyses in refractive surgery patients and corneal crosslinking subjects. Inverse FEM is also being used to estimate local intracorneal differences in Young’s modulus to convert displacement data to traditional material property formulations that can be used for clinical diagnostics, prognosis of corneal ectasia risk, and computational prediction of surgical outcomes. 

Acknowledgements This work has been supported by the US National Institutes of Health (NIH) Bioengineering Research Grant R01 EY023381; Ohio Third Frontier Innovation Platform Award TECH 13-059; an Unrestricted Grant from Research to Prevent Blindness Inc. (NY; USA) to the Department of Ophthalmology of the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University; NIH-National Eye Institute P30 Core Grant (IP30EY025585-01A1); Unrestricted Grant from Research to Prevent Blindness, Inc., awarded to the Cole Eye Institute; and CAPES Grant PDSE - 99999.007333/201503. Also supported by the Sara J. Cheheyl Fund for Ocular Biomechanics Research at the Cole Eye Institute and the Pender Ophthalmology Research Fund. The authors wish to state the following financial disclosures: Vinicius De Stefano: none; Matthew R. Ford: Patent; and William J. Dupps, Jr.: Patent.

References 1.

2.

3.

4.

5.

Copyright © 2018. Kugler Publications. All rights reserved.

6.

7.

8.

9.

Ophir J, Cespedes I, Ponnekanti H, Yazdi Y. Elastography: a quantitative method for imaging the elasticity of biological tissues. Ultrason Imaging. 1991;134:111–134. Luo J, Bai J, He P, Ying K. Axial strain calculation using a low-pass digital differentiator in ultrasound elastography. IEEE Trans Ultrason Ferroelectr Freq Control. 2004;51(9):1119–1127. Ford MR, Dupps WJ, Rollins AM, Roy AS, Hu Z. Method for optical coherence elastography of the cornea. J Biomed Opt. 2011;16(1):16005. Ford MR, Roy AS, Rollins AM, Dupps WJ. Serial biomechanical comparison of edematous, normal, and collagen crosslinked human donor corneas using optical coherence elastography. J Cataract Refract Surg. 2014;40(6):1041–1047. Kennedy BF, Liang X, Adie SG, et al. In vivo three-dimensional optical coherence elastography. Optics. 2011;19(7):6623–6634. Kirkpatrick SJ, Wang RK, Duncan DD. OCT-based elastography for large and small deformations. Opt Express. 2006;14(24):11585–97. Manapuram RK, Aglyamov SR, Monediado FM, et al. In vivo estimation of elastic wave parameters using phase-stabilized swept source optical coherence elastography. JBO Lett. 2012;17(10):15–18. Wong FF, Lar DR, Schultz DS, Stewart JM. Whole Globe Inflation Testing of Exogenously Crosslinked Sclera Using Genipin and Mthylglyoxal. Exp Eye Res. 2012;103:17–21. Oldenburg A, Toublan F, Suslick K, Wei A, Boppart S. Magnetomotive contrast for in vivo optical coherence tomography. Opt Express. 2005;13(17):6597–614.

10. Tanter M, Touboul D, Gennisson JL, Bercoff J, Fink M. High-resolution quantitative imaging of cornea elasticity using supersonic shear imaging. IEEE Trans Med Imaging. 2009;28(12):1881–1893. 11. Li C, Guan G, Zhang F, Nabi G, Wang RK. Laser induced surface acoustic wave combined with phase sensitive optical coherence tomography for superficial tissue characterization : a solution for practical application. Biomed Opt Express. 2014;5(5):1403–1418. 12. Anderson AT, Van Houten EEW, McGarry MDJ, et al. Observation of direction-dependent mechanical properties in the human brain with multi-excitation MR elastography. J Mech Behav Biomed Mater. 2016;59:538–546. 13. de Korte CL, van der Steen AF, Céspedes EI, Pasterkamp G. Intravascular ultrasound elastography in human arteries: initial experience in vitro. Ultrasound Med Biol. 1998;24(3):401–8. 14. Huang D, Swanson EA, Lin CP, et al. Optical coherence tomography. Science. 1991;254(5035):1178–1181. 15. Eigenwillig CM, Biedermann BR, Palte G, Huber R. K-space linear Fourier domain mode locked laser and applications for optical coherence tomography. Opt Express. 2008;16(12):8916–8937. 16. Bouma BE, Tearney GJ. Handbook of Optical Coherence Tomography. Boca Raton: CRC Press 2001, 1st ed. 17. Rollins AM, Izatt JA. Optimal interferometer designs for optical coherence tomography. Opt Lett 1999;24(21):1484– 1486.

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence tomography principles and elastography 18. Wojtkowski M, Leitgeb R, Kowalczyk A, Bajraszewski T, Fercher AF. In vivo human retinal imaging by Fourier domain optical coherence tomography. J Biomed Opt. 2002;7(3):457–463. 19. Fercher AF, Hitzenberger CK, Kamp G, El-Zaiat SY. Measurement of intraocular distances by backscattering spectral interferometry. Opt Commun. 1995;117(1–2):43–48. 20. Choma M, Sarunic M, Yang C, Izatt J. Sensitivity advantage of swept source and Fourier domain optical coherence tomography. Opt Express. 2003;11(18):2183–2189. 21. Leitgeb R, Hitzenberger C, Fercher A. Performance of fourier domain vs. time domain optical coherence tomography. Opt Express. 2003;11(8):889–894. 22. Hu Z, Rollins AM. Fourier domain optical coherence tomography with a linear-in-wavenumber spectrometer. Opt Lett. 2007;32(24):3525–3527. 23. Golubovic B, Bouma BE, Tearney GJ, Fujimoto JG. Optical frequency-domain reflectometry using rapid wavelength tuning of a Cr4+:forsterite laser. Opt Lett. 1997;22(22):1704–1706. 24. Huber R, Wojtkowski M, Fujimoto JG. Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography. Opt Express. 2006;14(8):3225–3237. 25. Lim H, de Boer JF, Park BH, Lee EC, Yelin R, Yun SH. Optical frequency domain imaging with a rapidly swept laser in the 815-870 nm range. Opt Express. 2006;14(13):5937–5944. 26. Wieser W, Biedermann BR, Klein T, Eigenwillig CM, Huber R. Multi-megahertz OCT: High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second. Opt Express. 2010;18(14):14685–14704. 27. Jayaraman V, Jiang J, Li H, et al. OCT imaging up to 760 kHz axial scan rate using single-mode 1310nm MEMS-tunable VCSELs with 100nm tuning range. CLEO 2011 - Laser Sci to Photonic Appl. 2011;11(9):1–2. 28. Ehlers JP, Dupps WJ, Kaiser PK et al. The Prospective Intraoperative and Perioperative Ophthalmic Imaging with Optical Coherence Tomography (PIONEER) Study: 2-year Results. Am J Ophthalmol. 2014;158(5):999-1007. 29. Barton JK, Stromski S. Flow measurement without phase information in optical coherence tomography images. Opt Express 2005;13(14):5234. 30. Liang X, Orescanin M, Toohey KS, Insana MF, Boppart SA. Acoustomotive optical coherence elastography for measuring material mechanical properties. Opt Lett. 2009;34(19):2894– 2896. 31. Fromageau J, Gennisson JL, Schmitt C, Maurice RL, Mongrain R, Cloutier G. Estimation of polyvinyl alcohol cryogel mechanical properties with four ultrasound elastography methods and comparison with gold standard testings. IEEE Trans Ultrason Ferroelectr Freq Control. 2007;54(3):498–508.

115 32. Hollman KW, Emelianov SY, Neiss JH, et al. Strain imaging of corneal tissue with an ultrasound elasticity microscope. Cornea. 2002;21(1):68–73. 33. Schmitt J. OCT elastography: imaging microscopic deformation and strain of tissue. Opt Express. 1998;3(6):199–211. 34. Rogowska J, Patel NA, Fujimoto JG, Brezinski ME. Optical coherence tomographic elastography technique for measuring deformation and strain of atherosclerotic tissues. Heart. 2004;90(5):556–562. 35. Rogowska J, Patel N, Plummer S, Brezinski ME. Quantitative optical coherence tomographic elastography: method for assessing arterial mechanical properties. Br J Radiol. 2006;79(945):707–711. 36. De la Torre-Ibarra MH, Ruiz PD, Huntley JM. Double-shot depth-resolved displacement field measurement using phase-contrast spectral optical coherence tomography. Opt Express. 2006;14(21):9643–56. 37. Dupps W, Netto M, Herekar S, Krueger R. Surface wave elastometry of the cornea in porcine and human donor eyes. J Refract. 2007;23(1):66–75. 38. Luce DA. Determining in vivo biomechanical properties of the cornea with an ocular response analyzer. J Cataract Refract Surg. 2005;31(1):156–162. 39. Andreassen T, Simonsen AH, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Exp Eye Res. 1980;31:435–441. 40. Liu J, Roberts CJ. Influence of corneal biomechanical properties on intraocular pressure measurement: Quantitative analysis. J Cataract Refract Surg. 2005;31(1):146–155. 41. Tang J, Liu J. Ultrasonic measurement of scleral cross-sectional strains during elevations of intraocular pressure: method validation and initial results in posterior porcine sclera. J Biomech Eng. 2012;134(9):91007. 42. Torricelli AAM, Ford MR, Singh V, Santhiago MR, Dupps WJ, Wilson SE. BAC-EDTA transepithelial riboflavin-UVA crosslinking has greater biomechanical stiffening effect than standard epithelium-off in rabbit corneas. Exp Eye Res. 2014;125:114– 117. 43. Armstrong BK, Lin MP, Ford MR, et al. Biological and biomechanical responses to traditional epithelium-off and transepithelial riboflavin-UVA CXL techniques in rabbits. J Refract Surg. 2013;29(5):332–341. 44. Girard MJ, Dupps WJ, Baskaran M, et al. Translating ocular biomechanics into clinical practice: current state and future prospects. Curr Eye Res. 2015;40(1):1-18.

Copyright © 2018. Kugler Publications. All rights reserved.

9. Optical coherence elastography for ocular biomechanics Manmohan Singh1, Michael D. Twa2, Kirill V. Larin1,3 Department of Biomedical Engineering, University of Houston, Houston, TX, USA; 2School of Optometry, University of Alabama at Birmingham, Birmingham, AL, USA; 3Department of Molecular Physiology and Biophysics, Baylor College of Medicine, Houston, TX , USA 1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction The biomechanical properties of ocular tissues are intrinsically tied to ocular health and visual performance. Diseases such as keratoconus1 and iatrogenic ectasia,2 and treatments such as laser-assisted in situ keratomileusis (LASIK) surgery3 and UV-induced collagen crosslinking4 (CXL) can alter the biomechanical properties of the cornea, and consequently, affect vision quality. Because the physical structure of the cornea is so closely tied to visual acuity (the cornea accounts for approximately 2/3 of the total refractive power of the eye),5 it has motivated numerous clinical treatments designed to modify the structure of this tissue and alter or improve vision, e.g., radial keratotomy and LASIK. Nevertheless, corneal biomechanical properties have proven particularly challenging to understand due to its structure and ultrastructural organization. The cornea is a dense regular connective tissue bounded by stratified surface epithelium externally and a simple squamous endothelium on the inner (aqueous) surface.6 The main tissue mass (the stroma) is comprised of collagen fibrils, precisely separated by an osmotically active extracellular matrix to preserve optical transparency.7,8 In the human cornea, these fibrils are organized into approximately 270 lamellar sheets that are approximately 2 µm thick and highly interwoven in the anterior 30-50%, but are wider and run more parallel to the surface in the deeper cornea.9 X-ray diffraction studies have shown that the collagen fibrils are preferentially

oriented superior to inferior and nasal to temporal in the central cornea, but become more circumferential in the tissue periphery.10,11 Consequently, corneal tissue is anisotropic and inhomogeneous, which makes quantitative measurements of corneal biomechanical properties challenging and often requires simplifying assumptions. A non-invasive method which can rapidly and quantitatively characterize the biomechanical properties of the cornea with micrometer-scale spatial resolution would provide valuable insight into the mechanical changes of the cornea caused by diseases and therapeutic procedures. As mentioned earlier, techniques such as x-ray scattering12 and electron microscopy13 have helped us gain a deep understanding about the ultrastructure of the cornea. However, elucidating quantitative biomechanical properties from these measurements is still a challenge. Understanding the alterations to the corneal mechanical properties objectively would provide useful information for selecting the most effective treatment and its timing. Several techniques based on global corneal deformation have been the basis for recent studies of corneal biomechanical properties. Commercially available devices such as the ORA (Reichert, Inc., Depew, NY, USA) and Corvis (Oculus Optikgeräte GmbH, Wetzlar, Germany) provide information about the mechanical response of the cornea and other ocular structures to an air puff, and can be used for indirect measurements of tissue properties. The description of these methods is discussed in Chapters 12 and 13.

Correspondence:Dr. Kirill V. Larin, Department of Biomedical Engineering, University of Houston, 3517 Cullen Blvd, SERC Room 2027, Houston, TX 77204, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 117-145 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

Copyright © 2018. Kugler Publications. All rights reserved.

118

Brillouin microscopy is a fundamentally different optical approach to quantify material properties that can be truly non-invasive. It is based upon non-linear properties of light that occur when light interacts with solid materials. In principle, when objects are interrogated with monochromatic light, photons will experience a slight frequency (Doppler) shift that can be related to the material properties of the object and its density. This non-invasive optical technique based on analyzing the Brillouin frequency shift is capable of generating depth-resolved elasticity distribution maps of the cornea with micrometer scale spatial resolution.14,15 Brillouin microscopy has been used to investigate the depth-resolved Brillouin shift in human corneal buttons with and without keratoconus16 in ex-vivo porcine corneas before and after CXL,17 and in human eyes in vivo.18 The applications and quantitative biomechanical parameters obtained from the Brillouin shift are discussed in Chapter 11. Elastography imaging is a technique that evolved from ultrasound imaging for the purpose of quantifying tissue stiffness,19 e.g., breast tumor detection. In principle, elastography imaging has several essential elements that include: high-resolution imaging, the application of a mechanical force to cause tissue distortion, re-imaging of the resulting tissue deformation response, and mathematical modeling and analysis to link the observed tissue response to the biomechanical properties of the tissue, e.g., Young’s modulus. Optical coherence tomography (OCT) is a well-established, low-coherence interferometric imaging technique that is analogous to ultrasound imaging.20,21 Because OCT is based on the principle of light interferometry, it provides greater resolution than ultrasound: micrometer-scale spatial resolution in lateral and axial dimensions, completely non-invasively. While OCT has limited depth penetration of a few millimeters in scattering media such as the skin or retina, imaging depth is not an issue for the majority of ophthalmological applications due to the transparency of the cornea and lens. Thus, OCT is well established in ophthalmology for structural imaging due to its depth-resolved micrometer-scale spatial resolution, high-imaging speed, and non-invasive nature.21-23 OCT-based elastography, also termed as optical coherence elastography (OCE), was introduced by

M. Singh, M.D. Twa and K.V. Larin

Fig. 1. The position of OCE among various non-destructive elasticity imaging and measurement techniques in terms of detection scale. AFM: atomic force microscopy; OT: optical tweezers; MPM: multiphoton microscopy; CBM: confocal Brillouin microscopy; LSI: laser speckle imaging; UE: ultrasound elastography; HI: holographic imaging; MRE: magnetic resonance elastography.26

Schmitt in 1998,24 and was first used to assess tissue biomechanics through measurement of localized deformations inside the sample. OCE generally relies on an external or internal stimulation approach to load the tissue and an OCT-based detection method to measure the corresponding tissue response.25-28 Early development of OCE featured static mechanical contact loading and cross-correlation-based speckle tracking to quantify point-wise positional strain to an unknown force.29-32 The emergence of phase-resolved OCT detection, which utilizes the interferometric phase information from the complex OCT signal, enabled nanoscale and sub-nanoscale sensitivity to dynamic tissue displacement,33-35 allowing OCE techniques to assess different parameters of the tissue deformation with high precision and accuracy to reconstruct tissue biomechanical properties.36-40 The development of OCE for other applications resulted in various methods to apply mechanical loads to tissues.37,38,41-47 Reinforced by the high spatial resolution of OCT, the imaging or measurement resolution of OCE ranges from several microns to hundreds of microns depending on the method used to reconstruct biomechanical properties.48-52 OCE maintains the same or even larger field of view as OCT.53 Figure 1 indicates the position of OCE among various non-destructive elasticity imaging and measurement techniques with respect to the spatial scale of

Optical coherence elastography for ocular biomechanics

119

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 2. (a) Corneal compression technique using a clinical gonioscopy lens with integration of OCT optics. (b) Structural image of cornea with regions of interest (ROI). (c) Displacement vector field obtained by 2-D cross-correlation of the red ROI in (b). (d) Mean lateral vs axial displacement for each of the ROIs in (b).65

mechanical assessment.26 In terms of spatial resolution and field of view, OCE fills the gap among traditional elastographic methods and thus has the potential to greatly influence the mechanical characterization of ocular and other tissues of similar dimensions. Based on the parameters that are used to obtain the qualitative or quantitative tissue mechanical properties, current OCE loading techniques can be divided into two major categories: static and dynamic excitation. Static elastographic techniques rely on applying a uniform stress and measuring the subsequent displacement.19 As an analogue to uniaxial mechanical compression testing,54 OCE methods that employ static/quasi-static loading and measure the displacement amplitude or strain30,31,48,55-58 generally rely on the definition of Young’s modulus under one-dimensional Hooke’s law.59 This approach presumes that the strain or the amplitude of deformation is inversely proportional to the Young’s modulus of the tissue, and assumes that the stress applied to the sample is uniform over the area of interest. This further relies on the assumption that the tissue is isotropic and homogenous.49 Furthermore, the viscous properties of the sample are frequently assumed to be negligible from the tissue response to mechanical loading. Because the stress is unknown throughout the sample, the majority of current OCE techniques employing this type of mechanical loading generally remain qualitative. However, these methods can provide spatial resolution that is equal or close to the resolution of OCT structural imaging. Recent development of a stress sensor has enabled quantitative mapping of Young’s modulus with micrometer-scale resolution.60,61 In contrast to static loading, dynamic elastographic techniques primarily rely on imaging the

propagation of mechanically induced elastic waves.62-64 The quantification of tissue biomechanical properties using dynamic loading is not significantly affected by pre-loading conditions, uniform stress application, and other factors. The choice of mechanical loading is determined by the specific applications and requirements and tissue type.

2. Structural image-based OCE The first OCE investigations of corneal biomechanical properties utilized structural imaging to quantify displacements in the cornea before and after static compression. Ford and colleagues used a standard clinical gonioscopy lens to load the cornea and 2-D cross-correlation was used to create an elastogram based on the displacement amplitude (Fig. 2).65 The heterogeneous elastic properties of the cornea were revealed from the variations in the axial and lateral displacements. However, the uneven stress distribution in the cornea (due to the non-uniform contact between the gonioscopy lens and anterior surface of the cornea) resulted in artifacts in the elasticity estimates, and no quantitative biomechanical parameters were obtained. This technique was also used to study the changes in normal, edematous, and CXL human corneas in the whole eye globe configuration at an artificially controlled intraocular pressure (IOP).66 The hydration and CXL treatment showed spatially varying results in the ratio of the axial to lateral displacements. Furthermore, the displacement ratio had a greater degree of variance between the treatment conditions when measurements were made in the superior/

120

M. Singh, M.D. Twa and K.V. Larin

Fig. 3. (a-c) The temporal displacement of the cornea at the apex for (a) virgin, (b) riboflavin-hydrated, and (c) CXL porcine cornea in vitro after air-puff loading. (d-f) The spatial displacement (red) before and (green) after air-puff stimulation for (d) virgin, (e) riboflavin-hydrated, and (f) CXL porcine cornea in vitro.44

Copyright © 2018. Kugler Publications. All rights reserved.

inferior axis as compared to the nasal/temporal axis, revealing the mechanical anisotropy of the cornea. This technique has also been used to investigate the efficacy of various CXL techniques in the rabbit cornea.67 While contact-based methods can provide valuable information about the mechanical properties of the cornea, non-contact loading methods may offer advantages for patient comfort in clinical applications. Consequently, OCE has been combined with non-contact air-puff excitation similar to the ORA and Corvis. Alonso-Caneiro and colleagues investigated the temporal deformation profile at different transverse locations and regions of the anterior human eye in vivo after excitation by the air puff.42 The displacements calculated from the spatio-temporal profiles obtained from the OCT structural images were used to estimate the variations in elasticity of the layers and different lateral positions of the cornea. The displacement

amplitudes were then correlated with corneal thickness and IOP to demonstrate the effects of the geometry and IOP on the air-puff induced displacement amplitude. Dorronsoro and colleagues further developed this technique to investigate the effects of CXL on porcine corneas with an artificially controlled IOP on parameters such as inwards velocity, amplitude, and outwards velocity (Fig. 3).44 In addition to the apical temporal displacement profiles, the spatial displacement distribution was obtained by scanning a transverse meridian across the apex. However, measurements of large amplitude displacements can be compounded by the motion of the whole eye and the boundary between the target and surrounding tissue, and the large displacements induce non-linear mechanical responses in the tissue which require complex modeling to quantitatively obtain the biomechanical properties of the cornea.68 Moreover, due to the large displacement amplitude,

Fig. 4. (a) Phase-sensitive OCE system, murine sample, and OCT image showing (blue) excitation and (red) OCE measurement positions on the cornea. (b) Damping of the elastic wave demonstrated by the amplitude. (c) Elastic wave velocity as a function of age.70

Optical coherence elastography for ocular biomechanics

121

4. Non-contact phase-sensitive corneal OCE However, non-contact excitation techniques may be preferable for the cornea. Li and colleagues utilized a 532 nm pulsed laser to photothermally induce a mechanical wave in primate corneas which was imaged by a PhS-OCE system (Fig. 5).71 This non-contact all-optical system was used to investigate the elastic hysteresis of primate corneas while cycling IOP. The Young’s modulus, E, was calculated from the surface wave velocity, cg, by the surface wave equation: 2ρ​​(1 + ν)​​​ 3​

​​c​ g2 ​​ , (1) ​ ​E = ​ _______ (​​ 0.87 + 1.12v )​​​ 2​    Fig. 5. (a) All-optical PhS-OCE assessment of corneal elasticity. A pulsed 532 nm laser induced a surface wave at the indicated position and temporal displacement profiles were obtained from the locations marked by red arrows. (b) The vertical temporal displacement profiles obtained at an IOP of 15 mmHg at the positions indicated by the red arrows in (a). (c) The elastic hysteresis of the cornea while cycling IOP as quantified by Equation (1).71

these methods can only provide mechanical contrast at the macro scale.

Copyright © 2018. Kugler Publications. All rights reserved.

3. Phase-sensitive corneal OCE The localized biomechanical properties of the cornea can be obtained by reducing the deformation amplitude, which minimizes the influence of surrounding regions on the measured displacement. Analyzing the phase of the complex OCT signal has led to displacement sensitivity at the nanometer scale,69 which has enabled ultra-sensitive OCE measurements.32 With the ability to detect sub-micrometer displacements with sufficient signalto-noise ratio (SNR), various contact and non-contact methods of loading the cornea have been proposed to induce low-amplitude displacements, which were detected by phase-sensitive OCE (PhS-OCE) systems. Manapuram and colleagues utilized a wire tip with a rounded edge and contact area of ~0.6mm2 to induce micrometer-scale amplitude elastic waves in mouse corneas in vivo (Fig. 4).70 The elastic wave was imaged by a PhS-OCE system with a displacement sensitivity of 1.9 nm, and the wave velocity was quantified as a function of age. The results demonstrated that corneal stiffness increases with age, as expected.

where ρ was the material density, and ν was the Poisson’s ratio. To overcome the repeated laser excitations and subsequent tissue damage, Song and colleagues utilized an ultra-fast OCE technique to image laser-induced elastic waves in the cornea.72 The basis of technique will be discussed later in this chapter. This ultra-fast OCE technique shows promise for evaluating quantitative corneal biomechanical properties because of the broad bandwidth of the laser-induced elastic wave. However, issues with laser safety exposure limits need to be overcome before this excitation technique can be clinically viable. Other non-contact excitation techniques have also been investigated, such as acoustic vibrography.73,74 Akca and colleagues first reported the observation of sound-induced vibrational modes in ex-vivo bovine corneas.74 The corneas were vibrated at relatively low power and low frequencies with a speaker. The excitation frequency was then swept, and the resonant modes were detected with a PhS-OCE system and mapped. Their results showed a clear reliance of the resonant modes of the corneas based on the age and mass of the samples. Validation with finite element modeling (FEM) showed good agreement with the numerical simulations and OCE-measured resonant modes. To further elaborate on this technique, Kling and colleagues investigated the effects of CXL on the resonant frequencies of porcine and bovine ex-vivo corneas.73 Again, the OCE measurements were combined with FEM simulations, and the results, shown in Figure 6, demonstrate the shift in the resonant frequencies and stiffening of the corneal tissues after the CXL treatment.

122

M. Singh, M.D. Twa and K.V. Larin

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 6. (a) FEM simulation results of a cornea showing the vibration modes at the indicated frequencies. (b) Theoretical and (c) OCE-measured vibration modes of (blue) virgin and (red) CXL porcine corneas.73

Fig. 7. (a) Micro air-pulse excitation system setup. (b) OCE measurement of the air pulse-induced elastic wave. (c) Vertical temporal displacement profiles of the two measurement positions in (b) illustrating the elastic wave propagation. (d) Comparison of the Young’s modulus of gelatin phantoms of various concentrations as obtained by (blue) OCE and (red) uniaxial mechanical testing.47

Optical coherence elastography for ocular biomechanics

Copyright © 2018. Kugler Publications. All rights reserved.

5. Air-pulse corneal OCE Another method of non-contact excitation that is specifically suited for non-invasive and safe excitation of the cornea is micro air-pulse stimulation.47,64 Unlike the ORA, Corvis, and previous OCE investigations which utilized a relatively long-duration and large-amplitude air puff, a short duration (≤ 1ms) highly-localized micro air-pulse was used to induce displacements at the micrometer scale (Fig. 7a). The air-pulse induced a low-amplitude (micrometer scale) displacement in the sample, which then propagated as an elastic wave. To validate the air-pulse-induced elastic wave method, the stiffness of tissue-mimicking gelatin phantoms was evaluated (Fig. 7b-d).47 The group velocity of the elastic wave was translated to Young’s modulus by Equation (1) and compared to the elasticity as measured by uniaxial mechanical testing (Fig. 7d). The OCE and mechanical testing results were in good agreement, showing promise for this non-contact OCE method. After validation on the phantoms, the air-pulse OCE technique was used to investigate the elasticity of the murine cornea in vivo.75 A 2-D grid of M-mode images was captured on the cornea and the elastic wave propagation delays at the corneal surface were mapped (Fig. 8). Utilizing this method, the spatial elasticity distribution of in-situ rabbit corneas before and after CXL was assessed.76 Similar to Figure 8, a 2-D grid of M-mode images was acquired, and the elastic wave amplitude and propagation delay at the corneal surface were mapped (Fig. 9). The results showed that the elastic wave amplitude and propagation delays were smaller after the CXL treatment as compared to the untreated rabbit corneas, indicating stiffening of the corneal tissue due to the CXL treatment. Mechanical testing was also conducted on excised corneal strips, and the results also showed a large increase in elasticity after the CXL treatment. An automated method of imaging the depth-resolved elastic wave propagation in the cornea was developed by synchronizing M-mode images acquired at successive locations in a line (M-B mode imaging) with the air-pulse.64 This technique was used to demonstrate that the elastic wave velocity was faster in mature rabbit corneas as compared to young rabbit corneas, indicating that the rabbit cornea becomes stiffer with age (Fig. 10), which has been shown by various other

123

techniques such as mechanical testing.77,78 In addition to the elastic wave velocity, analysis of the relaxation process of the air-pulse induced displacement has also been proposed as a method to characterize the biomechanical properties of the cornea.79 This method has the benefit of requiring only a single excitation for an elasticity assessment by fitting the OCE-measured relaxation process at the excitation position to a standard exponential function of d(t) = ae-bt, where b was the relaxation rate to be determined (Fig. 11). Gelatin phantoms of various concentrations were utilized for validation experiments to demonstrate how the relaxation process changes as a function of stiffness. After the phantom experiments, the measurements were repeated on mouse corneas of varying ages in vivo to elucidate the stiffening effects of aging on murine corneas by the air-pulse induced relaxation process. While no quantitative biomechanical parameters were obtained from this early investigation, the OCE measurements could be combined with analytical models to reconstruct the viscoelasticity of ocular tissues.80 A more quantitative approach of analyzing the micro air-pulse induced localized deformation was utilized by Singh and colleagues to evaluate custom CXL treatments.81 A 2-D grid of OCE measurements, where the OCT probe beam and air-pulse excitation were co-focused, were taken to measure spatial heterogeneity of the cornea. After validation with homogeneous and heterogeneous tissue-mimicking agar phantoms, rabbit corneas were partially CXL by masking a 2 mm diameter region at the apex to block UV irradiation and subsequent crosslinking. Rather than utilizing the relaxation rate of the displacement, a simple kinematic model was used to obtain the damped natural frequency (DNF) of the air-pulse induced deformation.82 It has been shown that the DNF is very well correlated to the square root of Young’s modulus,38 thus providing a more quantitative measurement of stiffness as compared to the relaxation rate. Maps of the DNF in a rabbit cornea before traditional CXL, after traditional CXL, and after partial CXL are depicted in Figures 12a, b, and c, respectively. This technique shows promise, particularly for customized CXL techniques,83 but the long acquisition times of tens of minutes will need to be significantly reduced before in-vivo use of this technique becomes feasible. Since CXL is generally used to treat

Copyright © 2018. Kugler Publications. All rights reserved.

124

M. Singh, M.D. Twa and K.V. Larin

Fig. 8. (a) Schematic of PhS-OCE system during in-vivo murine cornea experiments. (b) Excitation and OCE measurement positions on murine cornea. (c) Elastic wave propagation delays obtained from a murine cornea in vivo.75

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence elastography for ocular biomechanics

125

Fig. 9. Elastic wave propagation delay in (a) untreated and (b) CXL-treated rabbit cornea in situ. (c) Elastic wave velocity in the untreated and CXL rabbit corneas. (d) Young’s modulus of untreated and CXL rabbit corneal strips measured by mechanical testing.76

126

M. Singh, M.D. Twa and K.V. Larin

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 10. Automated method for imaging the air-pulse induced elastic wave by OCE. (a) OCE system schematic. (b) Triggering and acquisition synchronization. (c) M-B mode scanning. (d) Data processing for M-B mode OCE imaging. The M-mode structural images from each OCE measurement position were combined to form the structural image of the cornea during the OCE scan. The resulting structural image was used to mask the corresponding phase data to remove data from pixels with an insufficient signal. The phase data was then unwrapped and converted to real displacement and corrected for the surface motion and refractive index mismatch between air and the cornea. (e) Elastic wave propagation in a (top) young and (bottom) mature rabbit cornea at 1.92 ms after the air-pulse excitation. (f) Elastic wave velocity for the young and mature eyes.64

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence elastography for ocular biomechanics

127

Fig. 11 (a) OCE-measured relaxation process of a micro air-pulse induced deformation in gelatin phantoms of various concentrations. The relaxation process was fitted to the exponential function d(t) = ae -bt, where b was the relaxation rate to be determined. (b) The relaxation rates of the gelatin phantoms of various concentrations. (c) Typical vertical temporal displacement profile from the apex of a mouse cornea in vivo. Similar to (a), the relaxation process was fitted to the exponential function. (d) Relaxation rates for murine corneas of various ages.79

128

M. Singh, M.D. Twa and K.V. Larin

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 12. Damped natural frequency (DNF) maps of the air-pulse induced deformation in a rabbit cornea (a) before and (b) after traditional CXL. (c) DNF map in a partially CXL rabbit cornea where the blue region was masked during UV irradiation to prevent crosslinking.81

keratoconus, the structural changes in the cornea can be evaluated by traditional OCT imaging,84-86 and this co-focused air-pulse OCE technique could be used to evaluate selected regions of the corneal tissue before and after CXL treatment. It is well understood that CXL increases the stiffness of the cornea.87 However, IOP elevation can also increase the apparent stiffness of the cornea,88,89 and decoupling the effects of these two parameters on the measured elasticity of the cornea remains a challenge. For instance, a normal cornea at an elevated IOP and a CXL-treated cornea at a physiological IOP may exhibit the same measured stiffness. Recently, Li and colleagues were able to demonstrate that the amplitude attenuation of the air-pulse induced elastic wave is different in materials with the same elasticity, but different viscosity (Fig. 13)90 with the automated OCE wave-imaging method.64 After this technique was validated on agar and gelatin phantoms with similar Young’s moduli measured by mechanical testing, the elastic wave velocity in porcine corneas in situ before and after CXL and at various artificially controlled IOPs was measured. The velocity in an untreated cornea at 30 mmHg IOP and a CXL-treated cornea at 20 mmHg IOP was very similar. However, the amplitude attenuation was slower in the CXL-treated cornea, indicating that CXL treatment decreased corneal viscosity. This method could form the basis for differentiating IOP from the measured mechanical properties of ocular tissues. While useful, these aforementioned wave-based OCE techniques did not provide depth-resolved imaging of corneal biomechanical properties. To overcome this limitation, Wang and Larin demonstrated high-resolution, depth-wise elasticity mapping in rabbit

corneas.91 By utilizing spectral analysis to obtain the phase velocities at frequencies within the bandwidth of the air-pulse induced elastic wave, the micro-scale depth-resolved elasticity distribution in the cornea revealed the major layers of the rabbit cornea, as shown in Figure 14, and that the stiffness of the cornea decreases from the anterior region to the posterior region. Briefly describing the method, a fast Fourier transform (FFT) was performed on the vertical temporal displacement profile at each OCE measurement position for each imaged in-depth layer (sample profiles shown in Fig. 14a and corresponding power spectra shown in Fig. 14b) to obtain the phase shift, Δφf, at each FFT bin frequency. The phase shifts at each frequency were linearly fitted to the OCE measurement position distances. The phase velocity, c(f), for each imaged in-depth layer and for each frequency was calculated by c(f) = 2πfΔd/Δφf, where f was an FFT frequency bin, Δd was the propagation distance, and Δφf was the phase shift at f. In Figure 14c, the plot of phase velocity over depth shows how the depth-wise distribution of the corneal stiffness correlates to the structural features of the cornea illustrated in Figure 14d, including the epithelium, the anterior and posterior stroma, and the innermost region. Moroever, the dispersion of the elastic wave was calculated by this method, and the dispersion plots for each of the corneal layers is plotted in Figure 14e. The automated OCE technique developed by Wang and Larin for cornea64 was extrapolated into 3-D by Singh and colleagues to study the effects of CXL on the porcine cornea.92 Rather than a line measurement, a 2-D grid of OCE measurements was taken, and the elastic wave propagation was visualized in 3-D. Figure 15 shows

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence elastography for ocular biomechanics

129

Fig. 13. Differentiating samples of the same measured stiffness by OCE. (a) Young’s modulus of gelatin and agar phantoms as assessed by OCE and mechanical testing showing similar elasticities. (b) The attenuation of the elastic wave amplitude in the agar and gelatin phantoms in (a). (c) The elastic wave velocity in untreated (UT) and CXL porcine cornea at various IOPs, with the red text indicating the same elastic wave velocity in the corneas under different tissue conditions. (d) Amplitude attenuation of the elastic wave in the porcine cornea at the two conditions in red text in (c). An exponential fit to y(x) = ae-bx was applied where b was to be determined.90

130

M. Singh, M.D. Twa and K.V. Larin

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 14. Depth-resolved micro-scale elasticity distribution in the cornea assessed by non-contact air-pulse PhS-OCE. (a) Selected vertical temporal displacement profiles of the air-pulse induced elastic wave at 0.5, 1.0, 1.5, 2.0, and 2.5 mm from the excitation. (b) Amplitude spectra of the displacement profiles in (a) illustrating the dispersion of the wave. (c) Depth-wise phase velocities of the air-pulse induced elastic wave at ~391 Hz. (d) OCT structural image with the same regions as marked in (c). (e) Dispersion curve of the four main regions indicated in (c) and (d) over the predominant spectral range of the elastic wave.91

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence elastography for ocular biomechanics

131

Fig. 15. (a,d) 3-D and (b,d) en-face views of the air-pulse induced elastic wave propagation in a porcine cornea (a,b) before and (d,e) after CXL. The velocity of wave in all directions (c) before and (f) after CXL.92

132

M. Singh, M.D. Twa and K.V. Larin

Fig. 16. Group velocity of the air-pulse induced elastic wave in a typical porcine cornea at (a) 15, (b) 20, (c) 25, (d) 30 mmHg IOP. (e) Overall group velocity of the elastic wave of all meridional angles in seven porcine samples. The mechanical anisotropy was quantified by (f) the normalized fractional anisotropy (NFA) and (g) the standard deviation of the modified planar anisotropy coefficient (MPAC).93

Copyright © 2018. Kugler Publications. All rights reserved.

the propagation of the air-pulse induced elastic wave in a porcine cornea at 15 mmHg IOP (left column) before and (right column) after CXL. A 3-D view (Figs. 15a and d) and en-face image (Figs. 15b and e) of the air-pulse induced elastic wave at 2.5 ms after excitation are depicted. Clearly, the elastic wave propagated further in the cornea after CXL as the same time, which means a faster velocity and a stiffer material. After quantifying the velocity in each direction as plotted in Figures 15c and f, the results showed that the velocity increased by ~1.7 X after CXL, showing a distinct increase in stiffness. Moreover, a small degree of mechanical anisotropy became evident after CXL, but further analysis of the elastic anisotropic properties was not performed.

6. Evaluating corneal elastic anisotropy with OCE Singh and colleagues imaged the propagation of the air-pulse induced elastic wave at different meridional angles to study the elastic anisotropy of the porcine cornea as a function of IOP (Fig. 16).93 The IOP was controlled by the closed-loop artificial IOP control system developed by Twa and colleagues.76 The elastic wave was imaged along one meridian,64 the sample

was rotated by 20°, and the OCE measurements were repeated along the new meridian. This technique ensured that the excitation was at the corneal apex, and that the air-pulse inertia did not influence the wave velocity. Polar plots of group velocity of the elastic wave in a typical sample at 15 (Fig. 16a), 20 (Fig. 16b), 25 (Fig. 16c), and 30 mmHg (Fig. 16d) IOP showed that the overall elastic wave velocity and mechanical anisotropy increased as a function of IOP. This trend was seen in all seven imaged samples, where the overall group velocity increased as a function of IOP (Fig. 16e), and the mechanical anisotropy, as quantified by the normalized fractional anisotropy (NFA)94 (Fig. 16f), and the standard deviation of the modified planar anisotropy coefficient (MPAC)95 (Fig. 16g), also increased as a function of IOP. In addition to the effects of IOP on the mechanical anisotropy of the porcine cornea, Singh et al. also evaluated the effects of CXL on the elastic anisotropy and hysteresis while cycling IOP.96 Here, a sliding window algorithm was used to map the spatial elastic wave velocity in the corneas, which was then translated to Young’s modulus by Equation (1). The results showed that there is indeed contralateral elastic symmetry in the porcine cornea, and that CXL does not change the orientation of the elastic anisotropy (Fig. 17).

Optical coherence elastography for ocular biomechanics

133

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 17. Polar maps of Young’s modulus of a pair of fellow in situ porcine corneas where (1) was untreated and (2) was CXL-treated while increasing IOP at (a) 15, (b) 20, (c) 25, and (d) 30 mmHg, and while decreasing IOP at (e) 25, (d) 20, and (f) 15 mmHg.96

134

M. Singh, M.D. Twa and K.V. Larin

Fig. 18. (a) Comparison of the (red) OCE-measured phase velocities from a 2% tissue-mimicking agar phantom to the (blue) analytical solution of the RLFE equation with E = 160 kPa. (b) Comparison of the Young’s modulus as obtained by OCE + RLFE to the stiffness as measured by mechanical testing of the phantom in (a). (c) Comparison of the (red) OCE-measured phase velocities and (blue) modified RLFE for the cornea with E = 60 kPa and η = 0.33 Pa•s for a porcine cornea at 20 mmHg IOP.98

However, CXL does increase the degree of mechanical anisotropy, which indicates that there may be an angular dependence to the corneal stiffening due to CXL. Moreover, there was a noticeable hysteresis while cycling IOP in not only the corneal stiffness, as demonstrated with OCE previously by Li et al.,71 but also the elastic anisotropy.

Copyright © 2018. Kugler Publications. All rights reserved.

7. Analytical wave models for corneal OCE As mentioned previously, Li and colleagues demonstrated that the amplitude attenuation can elucidate the differences in viscosity in corneas of the same measured elasticity.90 The elasticity estimates were obtained by translating the elastic wave group velocity to Young’s modulus by Equation (1), which was derived under many assumptions. Han and colleagues investigated the accuracy of Equation (1), the shear wave equation, and Rayleigh-Lamb Frequency Equation (RLFE) as compared to mechanical testing on tissue-mimicking agar phantoms of various concentrations.97 The phase velocities, as calculated by the algorithm presented by Wang and Larin,91 were utilized to quantify Young’s modulus with the RFLE. The results showed that the RLFE provided a more accurate elasticity estimate as compared to the shear wave equation and surface wave Equation (1). Although Equation (1) has been used in number of corneal OCE studies,71,75,90,92,96 it assumes the sample

is a homogeneous isotropic thin plate in half-space, which is not strictly satisfied. Furthermore, the effects of thickness, curvature, and the solid-fluid boundary at the posterior surface of the cornea are not integrated into Equation (1). Therefore, Han and colleagues developed a more robust mechanical wave model for the cornea based on the RLFE.98,99 Briefly, the standard RLFE describes the frequency-dependent velocity of a Rayleigh-Lamb wave in a thin plate of known thickness with free boundary conditions.100 The standard RLFE was modified to account for the solid-fluid effect between the corneal posterior surface and aqueous humor, and Han et al. have provided a detailed derivation of the modified RLFE (mRLFE) for the cornea, as well as validation with FEM.99 A preliminary investigation showed that the Young’s modulus of an in-situ porcine cornea at 20 mmHg IOP was 60 kPa with a shear viscosity of 0.33 Pa·s (Fig. 18).98 A more detailed study showed that the Young’s modulus and shear viscosity increase as a function of IOP, which is more pronounced after CXL.99 Moreover, the viscosity of the cornea is dramatically reduced by the CXL treatment, which was evident in earlier work that showed that the elastic wave attenuates more quickly in untreated corneas as compared to CXL-treated corneas.90 However, the thin-plate geometry assumption was still present in the mRLFE, but mechanical testing showed that the standard RLFE combined with the phase velocities from OCE measurements can provide an accurate assessment of elasticity as compared to mechanical testing.97

Optical coherence elastography for ocular biomechanics

135

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 19. (a) Changes in the CCT of rabbit corneas before and after UV-CXL and RGX. (b) The Young’s modulus and (c) shear viscosity of the corneas as obtained by fitting the phase velocities of the air-pulse induced elastic wave to the modified RLFE.99,100 (e) The depth-wise phase velocities of the elastic wave and turning point used to determine how much of the corresponding virgin cornea was affected by either crosslinking technique (AR%). (f) The AR% of the corneas by both crosslinking techniques. N = 4 for both cross-linking techniques. The asterisk indicates P < 0.05 by a one-tailed paired t-test.101

Utilizing the automated air-pulse induced elastic wave imaging technique,64 the depth-resolved micro-scale elasticity technique pioneered by Wang and Larin,91 and the modified RLFE developed by Han and colleagues,98,99 Singh and colleagues compared two CXL techniques on in situ rabbit corneas: riboflavin/UV-A (labeled as UV-CXL in this work to avoid ambiguity) and rose-bengal/green light (RGX).101 RGX has been proposed as a safer alternative to UV-CXL with fewer side-effects, such as keratocyte and endothelial cell toxicity, due to the use of green light in lieu of UV irradiation.102 The central cornea thickness (CCT) significantly decreased after UV-CXL, but only slightly decreased after RGX, as plotted in Figure 19a. Figure 19b shows UV-CXL significantly increased the Young’s modulus of the rabbit corneas, while RGX did not significantly affect the stiffness. The shear viscosity of the corneas was unaffected by crosslinking by either technique, as depicted in Figure19c. Figure19d plots the depth-wise phase velocities of a cornea after RGX, which shows the turning point that was used to determine what percentage of the virgin corneal thickness was

stiffened by either crosslinking technique (AR%). The results, as depicted in Figure19e, showed that UV-CXL stiffens the anterior ~1/3 of the cornea while RGX only stiffens the anterior ~1/7 of the entire corneal thickness.

8. FEM and OCE Equation (1) is based on a half-infinite depth assumption,100 yet has been used in corneal OCE investigations. To understand the influence of this assumption on the accuracy of subsequent elastographic quantification, Han and colleagues investigated the effects of curvature and thickness on an air-pulse induced elastic wave in tissue-mimicking agar phantoms and contact lenses by OCE and FEM (Fig. 20).103 The thickness and curvature were individually altered in otherwise identical materials to isolate the effects of the respective parameters. The OCE measurements and FEM simulations demonstrated that the elastic wave group velocity decreases as the radius of curvature increases, and the velocity increases with

136

M. Singh, M.D. Twa and K.V. Larin

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 20. (a) 2-D cross-section views of FE models of various geometries. (b) 3-D FE model showing the excitation position, boundary conditions, and temporal displacement profile prescribed as the external excitation at the apex. The excitation was fitted to an OCE-measured displacement profile at the stimulation position. (c-e) The effect of the radius of curvature on the elastic wave group velocity when all other parameters were fixed. (c) FEM simulations of the elastic wave in a spherical shell with varying radius of curvature. OCE-measured and FEM-calculated elastic wave group velocity in (d) contact lenses and (e) tissue-mimicking agar phantoms of varying curvatures. (f, g) OCE-measured and FEM-calculated elastic wave group velocity while the thickness was varied and all other parameters were fixed. (f) FEM-simulated group velocity as a function of thickness of a normal human cornea-like structure as depicted in (a). (g) OCE-measured and FEM-calculated velocity in agar phantoms of various thicknesses.103

Fig. 21. (a) FEM model with the FSI at the posterior surface. (b) OCE-measured and FEM-simulated group velocity of an air-pulse induced elastic wave in a contact lens with and without fluid in its posterior gap. (c) OCE-measured and FEM-simulated group velocity of rabbit corneas (untreated) before and (RGX) after rose-bengal/green light corneal collagen crosslinking (n = 3). FEM simulations were conducted (FEM¬fsi) with and (FEM) without a fluid-structure interface at the posterior surface.104

Optical coherence elastography for ocular biomechanics

137

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 22. (a) Full-field OCE setup based on a white light Linnik interferometer. (b) Sample stage used to mechanically compress and translate the sample. (c) (Top) Full-field OCT image of ex-vivo porcine cornea and (bottom) elastic strain overlayed on the OCT image.48

thickness. Therefore, the effects of curvature and thickness should be considered when determining the biomechanical properties of the cornea. In addition to studying the effects of sample geometry, Han and colleagues also investigated the effects of the fluid-structure interface (FSI) at the posterior surface of the cornea on the propagation of the air-pulse induced elastic wave by combining OCE and FEM.104 First, OCE measurements were performed on soft contact lenses with and without fluid in the posterior gap to simulate the presence and absence of the FSI, and corresponding FE simulations were conducted based on the OCE results. Then, an FE model of the rabbit cornea was constructed with and without the FSI, as

shown in Figure 21a. The OCE measurements and FEM simulations were in good agreement and showed that the velocity of the air-pulse induced elastic wave was dramatically reduced when fluid was present in the posterior gap, as plotted in Figure 21b. To investigate the effect of the FSI on the cornea, OCE measurements were made on fresh in-situ rabbit corneas in the whole eye globe configuration before and after RGX. The OCE measurements were utilized in FEM simulations and showed that integrating the FSI at the corneal posterior surface dramatically reduced the elastic wave propagation speed just as with the contact lenses, and that RGX stiffens the cornea but only slightly (Fig. 21c). These results demonstrated that the FSI at the corneal

138

M. Singh, M.D. Twa and K.V. Larin

Fig. 23. (a) PhS-OCE system with an A-scan rate of ~1.5 MHz. (b) Depth-wise elastic wave group velocity in tissue-mimicking agar phantoms of various concentrations. (c) Comparison of Young’s modulus as obtained by OCE and mechanical testing. (d) Elasticity of in-situ porcine cornea in the whole eye globe configuration at various IOPs as quantified by Equation (1).107

posterior surface must be considered to accurately reconstruct corneal biomechanical properties.

Copyright © 2018. Kugler Publications. All rights reserved.

9. Ultra-fast corneal OCE While all of the previously mentioned OCE techniques have provided valuable insight into the dynamics of corneal biomechanical properties, they have predominantly relied on acquiring multiple M-mode images (M-B mode) in a line along the elastic wave propagation path. This requires an excitation for each OCE measurement position and proper synchronization between the OCT system and the excitation source. However, other techniques have been proposed which do not utilize M-B mode imaging such as full-field OCE (FF-OCE)48 or line-field low-coherence holography (LF-LCH).105 Nahas et al. demonstrated an FF-OCE system that utilized a white light Linnik interferometer to obtain 2D en-face images of the sample, and the phase of each en-face image was obtained by a standard four-step phase shifting algorithm.48 After static compression, the phase difference in an ex-vivo porcine cornea was translated to elastic strain and demonstrated that the epithelium is significantly softer than the rest of the cornea (Fig. 22). This technique was expanded to image the propagation of an elastic wave with the benefit of requiring only a single excitation to capture the wave.106

However, depth-resolved imaging requires translating the sample vertically, and thus, requires multiple stimulations to obtain depth-resolved elasticity assessments. Similarly, Liu et al. used a line beam and a Hilbert-based spatial phase shifting algorithm to image the propagation of an air-pulse induced elastic wave with a single excitation in a porcine cornea at various IOPs.105 The results showed that the cornea stiffened as IOP was increased, and they were able to achieve an ultra-fast line rate of 100 kHz while imaging the cornea. However, no depth-resolved measurements were made due to the limited scattering and corneal curvature. As with M-B mode OCE measurements, FF-OCE elasticity assessments require multiple stimulations to obtain a depth-resolved elastogram. Singh and colleagues have recently demonstrated a non-contact phase-sensitive OCE system which utilized a 4X buffered Fourier domain mode-locked (FDML) swept source laser with an A-scan rate of ~1.5 MHz and a micro air-pulse to characterize the elasticity of in situ porcine corneas at various IOPs using a single excitation (Fig. 23).107 Because of the much faster source, multiple B-scans were acquired (B-M mode) over time, and the elastic wave was directly imaged. B-M mode imaging enables the use of only a single excitation and the total imaging acquisition time was ~30 ms. However, there is an intrinsic trade-off between spatial resolution and frame-rate with B-M mode imaging. Nevertheless,

Optical coherence elastography for ocular biomechanics

139

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 24. Assessment of the age-related biomechanical properties of the rabbit lens by a co-focused ultrasound and PhS-OCE system. The data for the young and mature lenses are plotted in red and blue, respectively. (a) Schematic of the experimental setup. (b) OCT structural imaging of the anterior part of a rabbit eye, with the OCE measurement position marked by the red dot. (c) Amplitude of the vertical displacement as measured by the PhS-OCE system. (b) Undamped natural frequency of the displacement. Comparison of the (e) OCE-measured and (f) model-based vertical temporal displacement profiles. From the model-based method, the (g) Young’s modulus of the young and mature rabbit lens was determined to be 2.5 and 7.4 kPa, respectively. (h) The shear viscosity was estimated as 0.37 and 0.57 Pa·s for the young and mature lenses, respectively. (i) Stress-strain curve of the lens as measured by uniaxial mechanical testing. (j) Young’s modulus of the rabbit lenses at strain = 0.1 as measured by mechanical testing.82

the rapid acquisition speed enabled this technique to adhere to maximum permissible exposure (MPE) limitations for laser exposure to the cornea. B-M mode scanning has since been utilized by Song and colleagues with photothermal excitation72 and Ambrozinski et al. with air-coupled ultrasonic stimulation.109 As mentioned earlier, the IOP and corneal biomechanical properties are tightly linked, and separating these two parameters is nontrivial. Utilizing the ultra-fast B-M mode imaging enabled by FDML swept sources, Singh et al. developed a non-contact applanation-based tonometer using OCT. A large air-puff deformed in situ porcine corneas at various controlled IOPs. The dynamic response of the corneas was imaged at a frame-rate of several kilohertz to fully capture the inwards and outwards processes and is shown in Figure 24a. The times when the cornea was flat, i.e., applanated, were correlated with the measured air puff pressure profile to quantify the IOP. Additionally, micro air-pulse OCE measurements were taken with the same system (Fig. 24b), demonstrating that a single OCT instrument is capable of measuring corneal geometry, eye-globe IOP, and corneal biomechanical properties. When coupled with spectral analysis.91 robust mechanical models,98,99 and GPU accelerated OCE,110 this technique may be able to provide near real-time depth-resolved elasticity estimates of the cornea,

micrometer-scale measurements of corneal geometry, and accurate IOP assessment of the eye-globe. These three parameters would provide for a much more encompassing assessment of visual health than a single parameter. Furthermore, parallel scanning and acquisition techniques111 may be able to provide 3-D OCE measurements with only a single excitation. Rapid non-invasive imaging, GPU-accelerated processing, and single excitation measurements show great promise for translating corneal OCE techniques to the clinic where patient comfort, assessment time, and laser exposure limits are critical criteria. An alternative approach is passive elastography, which requires no external excitation and can be performed at low frame rates.112-114 Nguyen and colleagues have recently demonstrated passive OCE on an anesthetized rat in vivo.115 However, only a wavelength map was demonstrated and no biomechanical parameters were quantified. As mentioned earlier, waves in the cornea are most likely Lamb waves, which are highly dispersive, particularly at low frequencies, in the cornea. Nevertheless, the field of passive elastography has a solid foundation to build upon, including Lamb wave propagation,116,117 and shows promise for quantifying corneal biomechanical parameters without the need for any external excitation.

140

Copyright © 2018. Kugler Publications. All rights reserved.

10. Crystalline lens OCE While the cornea has been the subject of the majority of investigations due to its accessibility and importance in visual acuity, the crystalline lens is also a critical component of vision. Understanding the biomechanical changes in the lens would help understand the etiology and progression of diseases such as lenticular ­cataract118-120 and presbyopia.121-125 Acoustic-based techniques,126-128 Brillouin microscopy,129 and mechanical testing130 have revealed that the lens stiffens with age, which may be a primary cause of presbyopia. While these techniques have provided valuable information, their previously mentioned limitations are applicable to the lens as well as the cornea. OCE techniques may be able to overcome the limitations of invasiveness, large amplitude displacements, and quantitative biomechanical characterization as with the previously mentioned techniques. Manupuram and colleagues investigated the feasibility of using OCE to detect mechanical waves in a dissected murine crystalline lens.131 Similar to Manapuram et al.,70 a stiff wire was used to mechanically stimulate the lens, and the PhS-OCE system imaged the displacements at the top and bottom surfaces of the lens. The preliminary experiments showed that OCE could be used to characterize the biomechanical properties of the lens due to its high spatial and temporal resolutions. Wu and colleagues further replaced the wire with acoustic radiation force loading to induce low-amplitude displacements at the apex of young and mature rabbit lenses in the whole eye-globe configuration, which were imaged by a PhS-OCE system.82 In addition to the deformation amplitude and damping characteristics, a model-based elasticity reconstruction method was utilized to quantify the viscoelasticity of the lenses based on the temporal vertical displacement profiles.80 The biomechanical parameters reconstructed from the OCE measurements, combined with the model-based method, were compared with the measurements by uniaxial mechanical testing. The results showed that the crystalline lenses in mature rabbits were significantly stiffer than the young lenses (Fig. 24). Since the crystalline lens is primarily transparent to OCT imaging, evaluating the spatial variation in lenticular biomechanical properties is a challenge. Hsieh and colleagues have proposed a technique for imaging

M. Singh, M.D. Twa and K.V. Larin

elastic wave propagation in the crystalline lens that moves the excitation source and images a position on the lens with strong scattering, which is generally near the periphery of the lens.132 This technique was able to spatially resolve the biomechanical properties of clear phantoms and shows promise for characterizing the spatial variations in lenticular biomechanical properties.

11. Summary and conclusions Due to its non-invasive nature, rapid imaging speed, micrometer spatial resolution, and sub-micron displacement sensitivity, OCE is a promising technique for assessing the biomechanical properties of ocular tissues. While other elastographic techniques, such as ultrasound elastography and magnetic resonance elastography, have proven their effectiveness in the clinic, their spatial and temporal resolutions limit their use for small and thin samples, such as the cornea and crystalline lens. Since OCT is already a proven tool in ophthalmology,21-23 OCE can be easily implemented with commercially available systems. Early OCE investigations utilized a clinical gonioscopy lens to mechanically load the cornea, and 2-D cross-correlation provided an elastogram where the axial and lateral displacements were used to characterize the biomechanical properties of the cornea.65 This technique was then used to investigate the effects of edema and various crosslinking techniques on the elasticity of the cornea.66 To eliminate the need for contact, air -puff loading similar to the ORA and Corvis has been proposed.42,44 Here, a large amplitude (mm scale) deformation was induced in the cornea and spatio-temporal analysis was used to study the changes in the stiffness of the cornea as function of IOP42 and CXL.44 However, the large amplitude deformations induced in the cornea reduced the spatial resolution of the biomechanical assessment and induced non-linear responses, making accurate quantification of biomechanical parameters such as Young’s modulus difficult. The development of PhS-OCE techniques provided a method to overcome the large amplitude displacement limitations by increasing the deformation sensitivity to the sub-micrometer scale. Again, ocular PhS-OCE investigations primarily began with contact-based stimulation techniques such as a

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence elastography for ocular biomechanics

wire tip70,131 or mechanical compression.48,65-67 However, the development of non-contact PhS-OCE techniques such as photothermal excitation,71,72 acoustic vibrography,73,74 and particularly micro air-pulse stimulation64,75,76,79,81,90-93,96-99,101,103-105,107,108 and recently, most recently, air-coupled ultrasonic excitation109 show promise for translating ocular OCE to the clinic. In order to accurately quantify biomechanical parameters such as Young’s modulus, selection of a proper mechanical model is crucial. A common method of reconstructing the stiffness of the cornea is by utilizing various parameters, such as velocity and spectral analysis, of an externally induced elastic wave.64,7072,75,76,90-93,96-99,101,103-105,107-109,131,132 The majority of these investigations have utilized the group velocity of the elastic wave, which was translated to Young’s modulus by the surface wave Equation (1). While this can provide a rapid first order assessment of the elasticity, there are more robust mechanical models which can provide more accurate assessments of corneal stiffness and can incorporate crucial geometrical parameters such as thickness and proper boundary conditions.98,99,103,104 Furthermore, the elastic wave group velocity cannot provide micro-scale spatial resolution, but spectral analysis revealed the depth-resolved micro-scale elasticity distribution in the rabbit cornea.91,101 The majority of mechanical models utilized in corneal OCE investigations assume that the sample has a thin-plate geometry, which is not strictly satisfied by the cornea. Han and colleagues demonstrated that the curvature and thickness have a measurable effect on the elastic wave velocity.103 Hence, accurately quantifying the biomechanical properties of the cornea requires incorporating the true corneal geometry and selecting appropriate mechanical models that can consider these parameters. Another concern to be overcome before before OCE can be clinically relevant is the MPE laser exposure limits for the cornea. Because of the rapid propagation speed of the elastic wave in the cornea, direct imaging of the wave was not previously possible. Multiple M-mode images were acquired in various locations along the wave propagation path (M-B mode), and temporal analysis was used to calculate the wave velocity. However, this requires multiple exposures and

141

excitations, which increased the acquisition times to clinically unacceptable durations, and consequently, the laser exposure limits were exceeded. Techniques such as full-field OCE can image the propagation of the elastic wave with only a single excitation, but acquiring depth-resolved assessments requires translating the sample in the z-axis and repeating the measurement.48,106 Singh and colleagues utilized an ultra-fast Fourier Domain Mode-Locked swept source laser to directly image the elastic wave in a porcine cornea in situ,107 which has since been utilized by others.72,109 Although the spatial and temporal resolution were significantly decreased as compared to traditional M-B mode imaging, only a single excitation is required, reducing the acquisition time to milliseconds and ensuring that the laser exposure was within acceptable limits. In addition to the cornea, the crystalline lens is a critical component of vision. Diseases such as presbyopia and cataract can significantly degrade visual acuity, and understanding the biomechanical changes in the lens associated with these diseases will provide valuable insight into understanding their etiology and developing effective treatments. OCE investigations into the biomechanical properties of the crystalline lens have been limited due to its location inside the eye globe and optical transparency. Nevertheless, OCE can still provide valuable information about the biomechanical properties of the crystalline lens. Manapuram and colleagues demonstrated the feasibility of PhS-OCE for detecting mechanical wave in the lens.131 Wu and colleagues quantitatively demonstrated that the rabbit lens stiffens with age with the use of acoustic radiation force loading PhS-OCE detection,82 and Hsieh and colleagues have proposed a moving excitation source technique to overcome the limited scattering of the lens.132 With the development of ultra-fast OCT laser sources,111,133,134 GPU-accelerated OCE,110 and parallel scanning and acquisition techniques111 there is still significant headroom for OCE to evolve and begin its transition from the laboratory to the clinic. Moreover, techniques such as passive elastography are ­promising,115 which may enable elastographic evaluation of ocular tissues without any external excitation.

142

M. Singh, M.D. Twa and K.V. Larin

References 1.

2.

3.

4.

5. 6. 7.

8.

9.

10.

11.

12.

13.

Copyright © 2018. Kugler Publications. All rights reserved.

14.

15.

16.

17.

Andreassen TT, Simonsen AH, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Exp Eye Res. 1980;31(4):435-441. Moshirfar M, Edmonds JN, Behunin NL, Christiansen SM. Corneal biomechanics in iatrogenic ectasia and keratoconus: A review of the literature. Oman J Ophthalmol. 2013;6(1):12-17. Pepose JS, Feigenbaum SK, Qazi MA, Sanderson JP, Roberts CJ. Changes in corneal biomechanics and intraocular pressure following LASIK using static, dynamic, and noncontact tonometry. Am J Ophthalmol. 2007;143(1):39-47. Wollensak G, Spoerl E, Seiler T. Riboflavin/ultraviolet-a-induced collagen crosslinking for the treatment of keratoconus. Am J Ophthalmol. 2003;135(5):620-627. Ruberti JW, Roy AS, Roberts CJ. Corneal biomechanics and biomaterials. Annu Rev Biomed Eng. 2011;13:269-295. Bron AJ. The architecture of the corneal stroma. Br J Ophthalmol. 2001;85(4):379-381. Muller LJ, Pels E, Schurmans LR, Vrensen GF. A new three-dimensional model of the organization of proteoglycans and collagen fibrils in the human corneal stroma. Exp Eye Res. 2004;78(3):493-501. Muller LJ, Pels E, Vrensen GF. The specific architecture of the anterior stroma accounts for maintenance of corneal curvature. Br J Ophthalmol. 2001;85(4):437-443. Jester JV, Winkler M, Jester BE, Nien C, Chai D, Brown DJ. Evaluating corneal collagen organization using high-resolution nonlinear optical macroscopy. Eye Contact Lens. 2010;36(5):260264. Aghamohammadzadeh H, Newton RH, Meek KM. X-ray scattering used to map the preferred collagen orientation in the human cornea and limbus. Structure. 2004;12(2):249-256. Boote C, Dennis S, Meek K. Spatial mapping of collagen fibril organisation in primate cornea-an X-ray diffraction investigation. J Struct Biol. 2004;146(3):359-367. Meek KM, Blamires T, Elliott GF, Gyi TJ, Nave C. The organisation of collagen fibrils in the human corneal stroma: a synchrotron X-ray diffraction study. Curr Eye Res. 1987;6(7):841-846. Komai Y, Ushiki T. The three-dimensional organization of collagen fibrils in the human cornea and sclera. Invest Ophthalmol Vis Sci. 1991;32(8):2244-2258. Vaughan JM, Randall JT. Brillouin scattering, density and elastic properties of the lens and cornea of the eye. Nature. 1980;284(5755):489-491. Scarcelli G, Pineda R, Yun SH. Brillouin optical microscopy for corneal biomechanics. Invest Ophthalmol Vis Sci. 2012;53(1):185-190. Scarcelli G, Besner S, Pineda R, Yun SH. Biomechanical characterization of keratoconus corneas ex vivo with Brillouin microscopy. Invest Ophthalmol Vis Sci. 2014;55(7):4490-4495. Scarcelli G, Kling S, Quijano E, Pineda R, Marcos S, Yun SH. Brillouin microscopy of collagen crosslinking: noncontact depth-dependent analysis of corneal elastic modulus. Invest Ophthalmol Vis Sci. 2013;54(2):1418-1425.

18. Scarcelli G, Yun SH. In vivo Brillouin optical microscopy of the human eye. Opt Express. 2012;20(8):9197-9202. 19. Ophir J, Cespedes I, Ponnekanti H, Yazdi Y, Li X. Elastography: a quantitative method for imaging the elasticity of biological tissues. Ultrason Imaging. 1991;13(2):111-134. 20. Huang D, Swanson EA, Lin CP, et al. Optical coherence tomography. Science. 1991;254(5035):1178-1181. 21. Drexler W, Fujimoto JG. Optical Coherence Tomography: Technology and Applications. Springer International Publishing; 2015. 22. Fujimoto J, Swanson E. The Development, Commercialization, and Impact of Optical Coherence Tomography. Invest Ophthalmol Vis Sci. 2016;57(9):OCT1-OCT13. 23. Adhi M, Duker JS. Optical coherence tomography--current and future applications. Curr Opin Ophthalmol. 2013;24(3):213-221. 24. Schmitt J. OCT elastography: imaging microscopic deformation and strain of tissue. Opt Express. 1998;3(6):199-211. 25. Kennedy BF, Kennedy KM, Sampson DD. A Review of Optical Coherence Elastography: Fundamentals, Techniques and Prospects. IEEE J Sel Top Quant. 2014;20(2):272-288. 26. Wang S, Larin KV. Optical coherence elastography for tissue characterization: a review. J Biophotonics. 2015;8(4):279-302. 27. Mulligan JA, Untracht GR, Chandrasekaran SN, Brown CN, Adie SG. Emerging Approaches for High-Resolution Imaging of Tissue Biomechanics With Optical Coherence Elastography. IEEE J Sel Top Quant. 2016;22(3):1-20. 28. Larin KV, Sampson DD. Optical coherence elastography - OCT at work in tissue biomechanics [Invited]. Biomed Opt Express. 2017;8(2):1172-1202. 29. Rogowska J, Patel NA, Fujimoto JG, Brezinski ME. Optical coherence tomographic elastography technique for measuring deformation and strain of atherosclerotic tissues. Heart. 2004;90(5):556-562. 30. Chan R, Chau A, Karl W, et al. OCT-based arterial elastography: robust estimation exploiting tissue biomechanics. Opt Express. 2004;12(19):4558-4572. 31. Chau AH, Chan RC, Shishkov M, et al. Mechanical analysis of atherosclerotic plaques based on optical coherence tomography. Ann Biomed Eng. 2004;32(11):1494-1503. 32. Khalil AS, Chan RC, Chau AH, Bouma BE, Mofrad MR. Tissue elasticity estimation with optical coherence elastography: toward mechanical characterization of in vivo soft tissue. Ann Biomed Eng. 2005;33(11):1631-1639. 33. Zhao Y, Chen Z, Saxer C, Xiang S, de Boer JF, Nelson JS. Phase-resolved optical coherence tomography and optical Doppler tomography for imaging blood flow in human skin with fast scanning speed and high velocity sensitivity. Opt Lett. 2000;25(2):114-116. 34. Kirkpatrick SJ, Wang RK, Duncan DD. OCT-based elastography for large and small deformations. Opt Express. 2006;14(24):11585-11597. 35. Wang RK, Nuttall AL. Phase-sensitive optical coherence tomography imaging of the tissue motion within the organ of Corti at a subnanometer scale: a preliminary study. J Biomed Opt. 2010;15(5):056005.

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence elastography for ocular biomechanics 36. Wang RKK, Ma ZH, Kirkpatrick SJ. Tissue Doppler optical coherence elastography for real time strain rate and strain mapping of soft tissue. Appl Phys Lett. 2006;89(14):144103. 37. Liang X, Orescanin M, Toohey KS, Insana MF, Boppart SA. Acoustomotive optical coherence elastography for measuring material mechanical properties. Opt Lett. 2009;34(19):2894-2896. 38. Crecea V, Oldenburg AL, Liang X, Ralston TS, Boppart SA. Magnetomotive nanoparticle transducers for optical rheology of viscoelastic materials. Opt Express. 2009;17(25):23114-23122. 39. Li C, Huang Z, Wang RK. Elastic properties of soft tissue-mimicking phantoms assessed by combined use of laser ultrasonics and low coherence interferometry. Opt Express. 2011;19(11):10153-10163. 40. Razani M, Mariampillai A, Sun C, Luk TW, Yang VX, Kolios MC. Feasibility of optical coherence elastography measurements of shear wave propagation in homogeneous tissue equivalent phantoms. Biomed Opt Express. 2012;3(5):972-980. 41. Ahmad A, Kim J, Sobh NA, Shemonski ND, Boppart SA. Magnetomotive optical coherence elastography using magnetic particles to induce mechanical waves. Biomed Opt Express. 2014;5(7):2349-2361. 42. Alonso-Caneiro D, Karnowski K, Kaluzny BJ, Kowalczyk A, Wojtkowski M. Assessment of corneal dynamics with high-speed swept source optical coherence tomography combined with an air puff system. Opt Express. 2011;19(15):14188-14199. 43. Crecea V, Ahmad A, Boppart SA. Magnetomotive optical coherence elastography for microrheology of biological tissues. J Biomed Opt. 2013;18(12):121504. 44. Dorronsoro C, Pascual D, Perez-Merino P, Kling S, Marcos S. Dynamic OCT measurement of corneal deformation by an air puff in normal and cross-linked corneas. Biomed Opt Express. 2012;3(3):473-487. 45. Qi W, Li R, Ma T, Kirk Shung K, Zhou Q, Chen Z. Confocal acoustic radiation force optical coherence elastography using a ring ultrasonic transducer. Appl Phys Lett. 2014;104(12):123702. 46. Wang S, Aglyamov S, Karpiouk A, et al. Assessing the mechanical properties of tissue-mimicking phantoms at different depths as an approach to measure biomechanical gradient of crystalline lens. Biomed Opt Express. 2013;4(12):2769-2780. 47. Wang S, Larin KV, Li JS, et al. A focused air-pulse system for optical-coherence-tomography-based measurements of tissue elasticity. Laser Phys Lett. 2013;10(7):075605. 48. Nahas A, Bauer M, Roux S, Boccara AC. 3D static elastography at the micrometer scale using Full Field OCT. Biomed Opt Express. 2013;4(10):2138-2149. 49. Kennedy KM, Ford C, Kennedy BF, Bush MB, Sampson DD. Analysis of mechanical contrast in optical coherence elastography. J Biomed Opt. 2013;18(12):121508. 50. Li C, Guan G, Cheng X, Huang Z, Wang RK. Quantitative elastography provided by surface acoustic waves measured by phase-sensitive optical coherence tomography. Opt Lett. 2012;37(4):722-724. 51. Adie SG, Liang X, Kennedy BF, John R, Sampson DD, Boppart SA. Spectroscopic optical coherence elastography. Opt Express. 2010;18(25):25519-25534.

143 52. Song S, Huang Z, Nguyen TM, et al. Shear modulus imaging by direct visualization of propagating shear waves with phase-sensitive optical coherence tomography. J Biomed Opt. 2013;18(12):121509. 53. Allen WM, Chin L, Wijesinghe P, et al. Wide-field optical coherence micro-elastography for intraoperative assessment of human breast cancer margins. Biomed Opt Express. 2016;7(10):4139-4153. 54. Fung YC. Biomechanics: Mechanical Properties of Living Tissues. New York: Springer; 2013. 55. Ko HJ, Tan W, Stack R, Boppart SA. Optical coherence elastography of engineered and developing tissue. Tissue Eng. 2006;12(1):63-73. 56. Kennedy BF, McLaughlin RA, Kennedy KM, et al. Optical coherence micro-elastography: mechanical-contrast imaging of tissue microstructure. Biomed Opt Express. 2014;5(7):21132124. 57. Kennedy BF, Malheiro FG, Chin L, Sampson DD. Three-dimensional optical coherence elastography by phase-sensitive comparison of C-scans. J Biomed Opt. 2014;19(7):076006. 58. Chin L, Kennedy BF, Kennedy KM, et al. Three-dimensional optical coherence micro-elastography of skeletal muscle tissue. Biomed Opt Express. 2014;5(9):3090-3102. 59. DeWolf J, Mazurek D, Beer F, Jr. Johnston ER. Mechanics of Materials. Columbus: McGraw-Hill Education; 2014. 60. Kennedy KM, Es’haghian S, Chin L, McLaughlin RA, Sampson DD, Kennedy BF. Optical palpation: optical coherence tomography-based tactile imaging using a compliant sensor. Opt Lett. 2014;39(10):3014-3017. 61. Kennedy KM, Chin L, McLaughlin RA, et al. Quantitative micro-elastography: imaging of tissue elasticity using compression optical coherence elastography. Sci Rep. 2015;5:15538. 62. Bercoff J, Tanter M, Fink M. Supersonic shear imaging: a new technique for soft tissue elasticity mapping. IEEE Trans Ultrason Ferroelectr Freq Control. 2004;51(4):396-409. 63. Muthupillai R, Lomas DJ, Rossman PJ, Greenleaf JF, Manduca A, Ehman RL. Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science. 1995;269(5232):1854-1857. 64. Wang S, Larin KV. Shear wave imaging optical coherence tomography (SWI-OCT) for ocular tissue biomechanics. Opt Lett. 2014;39(1):41-44. 65. Ford MR, Dupps WJ, Jr., Rollins AM, Roy AS, Hu Z. Method for optical coherence elastography of the cornea. J Biomed Opt. 2011;16(1):016005. 66. Ford MR, Sinha Roy A, Rollins AM, Dupps WJ, Jr. Serial biomechanical comparison of edematous, normal, and collagen crosslinked human donor corneas using optical coherence elastography. J Cataract Refract Surg. 2014;40(6):1041-1047. 67. Armstrong BK, Lin MP, Ford MR, et al. Biological and biomechanical responses to traditional epithelium-off and transepithelial riboflavin-UVA CXL techniques in rabbits. J Refract Surg. 2013;29(5):332-341. 68. Sinha Roy A, Kurian M, Matalia H, Shetty R. Air-puff associated quantification of non-linear biomechanical properties

144

69.

70.

71.

72.

73.

74.

75.

76.

77.

78.

79.

Copyright © 2018. Kugler Publications. All rights reserved.

80.

81.

82.

83.

84.

M. Singh, M.D. Twa and K.V. Larin of the human cornea in vivo. J Mech Behav Biomed Mater. 2015;48:173-182. Sticker M, Hitzenberger CK, Leitgeb R, Fercher AF. Quantitative differential phase measurement and imaging in transparent and turbid media by optical coherence tomography. Opt Lett. 2001;26(8):518-520. Manapuram RK, Aglyamov SR, Monediado FM, et al. In vivo estimation of elastic wave parameters using phase-stabilized swept source optical coherence elastography. J Biomed Opt. 2012;17(10):100501. Li C, Guan G, Huang Z, Johnstone M, Wang RK. Noncontact all-optical measurement of corneal elasticity. Opt Lett. 2012;37(10):1625-1627. Song S, Wei W, Hsieh BY, et al. Strategies to improve phase-stability of ultrafast swept source optical coherence tomography for single shot imaging of transient mechanical waves at 16 kHz frame rate. Appl Phys Lett. 2016;108(19):191104. Kling S, Akca IB, Chang EW, et al. Numerical model of optical coherence tomographic vibrography imaging to estimate corneal biomechanical properties. J R Soc Interface. 2014;11(101):20140920. Akca BI, Chang EW, Kling S, et al. Observation of sound-induced corneal vibrational modes by optical coherence tomography. Biomed Opt Express. 2015;6(9):3313-3319. Li J, Wang S, Manapuram RK, et al. Dynamic optical coherence tomography measurements of elastic wave propagation in tissue-mimicking phantoms and mouse cornea in vivo. J Biomed Opt. 2013;18(12):121503. Twa MD, Li J, Vantipalli S, et al. Spatial characterization of corneal biomechanical properties with optical coherence elastography after UV cross-linking. Biomed Opt Express. 2014;5(5):1419-1427. Elsheikh A, Wang D, Brown M, Rama P, Campanelli M, Pye D. Assessment of corneal biomechanical properties and their variation with age. Curr Eye Res. 2007;32(1):11-19. Elsheikh A, Geraghty B, Rama P, Campanelli M, Meek KM. Characterization of age-related variation in corneal biomechanical properties. J R Soc Interface. 2010;7(51):1475-1485. Li J, Wang S, Singh M, et al. Air-pulse OCE for assessment of age-related changes in mouse cornea in vivo. Laser Phys Lett. 2014;11(6):065601. Aglyamov SR, Wang S, Karpiouk AB, et al. The dynamic deformation of a layered viscoelastic medium under surface excitation. Phys Med Biol. 2015;60(11):4295-4312. Singh M, Li J, Vantipalli S, Han Z, Larin KV, Twa MD. Optical coherence elastography for evaluating customized riboflavin/UV-A corneal collagen crosslinking. J Biomed Opt. 2017;22(9):91504. Wu C, Han Z, Wang S, et al. Assessing age-related changes in the biomechanical properties of rabbit lens using a coaligned ultrasound and optical coherence elastography system. Invest Ophthalmol Vis Sci. 2015;56(2):1292-1300. Seiler TG, Fischinger I, Koller T, Zapp D, Frueh BE, Seiler T. Customized Corneal Cross-linking: One-Year Results. Am J Ophthalmol. 2016;166:14-21. Prospero Ponce CM, Rocha KM, Smith SD, Krueger RR. Central and peripheral corneal thickness measured with optical coher-

85.

86.

87.

88.

89.

90.

91.

92.

93.

94.

95.

96.

97.

98.

99.

ence tomography, Scheimpflug imaging, and ultrasound pachymetry in normal, keratoconus-suspect, and post-laser in situ keratomileusis eyes. J Cataract Refract Surg. 2009;35(6):10551062. Fukuda S, Yamanari M, Lim Y, et al. Keratoconus diagnosis using anterior segment polarization-sensitive optical coherence tomography. Invest Ophthalmol Vis Sci. 2013;54(2):1384-1391. Fujimoto H, Maeda N, Shintani A, et al. Quantitative Evaluation of the Natural Progression of Keratoconus Using Three-Dimensional Optical Coherence Tomography. Invest Ophthalmol Vis Sci. 2016;57(9):OCT169-175. Wollensak G, Spoerl E, Seiler T. Stress-strain measurements of human and porcine corneas after riboflavin-ultraviolet-A-induced cross-linking. J Cataract Refract Surg. 2003;29(9):17801785. Liu J, He X. Corneal stiffness affects IOP elevation during rapid volume change in the eye. Invest Ophthalmol Vis Sci. 2009;50(5):2224-2229. Orssengo GJ, Pye DC. Determination of the true intraocular pressure and modulus of elasticity of the human cornea in vivo. Bull Math Biol. 1999;61(3):551-572. Li J, Han Z, Singh M, Twa MD, Larin KV. Differentiating untreated and cross-linked porcine corneas of the same measured stiffness with optical coherence elastography. J Biomed Opt. 2014;19(11):110502. Wang S, Larin KV. Noncontact depth-resolved micro-scale optical coherence elastography of the cornea. Biomed Opt Express. 2014;5(11):3807-3821. Singh M, Li J, Vantipalli S, et al. Noncontact Elastic Wave Imaging Optical Coherence Elastography for Evaluating Changes in Corneal Elasticity Due to Crosslinking. IEEE J Sel Top Quantum Electron. 2016;22(3). Singh M, Li J, Han Z, et al. Investigating Elastic Anisotropy of the Porcine Cornea as a Function of Intraocular Pressure With Optical Coherence Elastography. J Refract Surg. 2016;32(8):562-567. Couade M, Pernot M, Messas E, et al. In vivo quantitative mapping of myocardial stiffening and transmural anisotropy during the cardiac cycle. IEEE Trans Med Imaging. 2011;30(2):295-305. Lankford WT, Snyder SC, Bauscher JA. New Criteria for Predicting the Press Performance of Deep Drawing Sheets. T Am Soc Metal. 1950;42:1197-1232. Singh M, Li J, Han Z, et al. Assessing the effects of riboflavin/ UV-A crosslinking on porcine corneal mechanical anisotropy with optical coherence elastography. Biomed Opt Express. 2017;8(1):349-366. Han Z, Li J, Singh M, et al. Quantitative methods for reconstructing tissue biomechanical properties in optical coherence elastography: a comparison study. Phys Med Biol. 2015;60(9):35313547. Han Z, Aglyamov SR, Li J, et al. Quantitative assessment of corneal viscoelasticity using optical coherence elastography and a modified Rayleigh-Lamb equation. J Biomed Opt. 2015;20(2):20501. Han Z, Li J, Singh M, et al. Optical coherence elastography assessment of corneal viscoelasticity with a modified RayleighLamb wave model. J Mech Behav Biomed Mater. 2017;66:87-94.

Copyright © 2018. Kugler Publications. All rights reserved.

Optical coherence elastography for ocular biomechanics 100. Graff KF. Wave Motion in Elastic Solids. New York: Dover Publications; 2012. 101. Singh M, Li J, Han Z, et al. Evaluating the Effects of Riboflavin/ UV-A and Rose-Bengal/Green Light Cross-Linking of the Rabbit Cornea by Noncontact Optical Coherence Elastography. Invest Ophthalmol Vis Sci. 2016;57(9):OCT112-120. 102. Cherfan D, Verter EE, Melki S, et al. Collagen cross-linking using rose bengal and green light to increase corneal stiffness. Invest Ophthalmol Vis Sci. 2013;54(5):3426-3433. 103. Han Z, Li J, Singh M, et al. Analysis of the effects of curvature and thickness on elastic wave velocity in cornea-like structures by finite element modeling and optical coherence elastography. Appl Phys Lett. 2015;106(23):233702. 104. Han Z, Li J, Singh M, et al. Analysis of the effect of the fluid-structure interface on elastic wave velocity in cornea-like structures by OCE and FEM. Laser Phys Lett. 2016;13(3):035602. 105. Liu CH, Schill A, Raghunathan R, et al. Ultra-fast line-field low coherence holographic elastography using spatial phase shifting. Biomed Opt Express. 2017;8(2):993. 106. Nahas A, Tanter M, Nguyen TM, Chassot JM, Fink M, Claude Boccara A. From supersonic shear wave imaging to full-field optical coherence shear wave elastography. J Biomed Opt. 2013;18(12):121514. 107. Singh M, Wu C, Liu CH, et al. Phase-sensitive optical coherence elastography at 1.5 million A-Lines per second. Opt Lett. 2015;40(11):2588-2591. 108. Singh M, Han Z, Nair A, Schill A, Twa MD, Larin KV. Applanation optical coherence elastography: noncontact measurement of intraocular pressure, corneal biomechanical properties, and corneal geometry with a single instrument. J Biomed Opt. 2017;22(2):020502-020502. 109. Ambrozinski L, Song S, Yoon SJ, et al. Acoustic micro-tapping for non-contact 4D imaging of tissue elasticity. Sci Rep. 2016;6:38967. 110. Kirk RW, Kennedy BF, Sampson DD, McLaughlin RA. Near Video-Rate Optical Coherence Elastography by Acceleration With a Graphics Processing Unit. J Lightwave Technol. 2015;33(16):3481-3485. 111. Drexler W, Liu M, Kumar A, Kamali T, Unterhuber A, Leitgeb RA. Optical coherence tomography today: speed, contrast, and multimodality. J Biomed Opt. 2014;19(7):071412. 112. Catheline S, Benech N, Brum J, Negreira C. Time reversal of elastic waves in soft solids. Phys Rev Lett. 2008;100(6):064301. 113. Brum J, Catheline S, Benech N, Negreira C. Shear elasticity estimation from surface wave: the time reversal approach. J Acoust Soc Am. 2008;124(6):3377-3380. 114. Ammari H, Bustos LG, Kang H, Lee H. Transient elasticity imaging and time reversal. P Roy Soc Edinb A. 2011;141(06):1121-1140. 115. Nguyen TM, Zorgani A, Lescanne M, Boccara C, Fink M, Catheline S. Diffuse shear wave imaging: toward passive elastography using low-frame rate spectral-domain optical coherence tomography. J Biomed Opt. 2016;21(12):126013. 116. Park HW, Kim SB, Sohn H. Understanding a time reversal process in Lamb wave propagation. Wave Motion. 2009;46(7):451-467.

145 117. Watkins R, Jha R. A modified time reversal method for Lamb wave based diagnostics of composite structures. Mechanical Systems and Signal Processing. 2012;31:345-354. 118. Dolin PJ. Ultraviolet radiation and cataract: a review of the epidemiological evidence. Br J Ophthalmol. 1994;78(6):478-482. 119. Behndig A, Montan P, Stenevi U, Kugelberg M, Lundstrom M. One million cataract surgeries: Swedish National Cataract Register 1992-2009. J Cataract Refract Surg. 2011;37(8):15391545. 120. Livingston PM, Carson CA, Taylor HR. The epidemiology of cataract: a review of the literature. Ophthalmic Epidemiol. 1995;2(3):151-164. 121. Heys KR, Cram SL, Truscott RJ. Massive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia? Mol Vis. 2004;10(114):956-963. 122. Glasser A, Croft MA, Kaufman PL. Aging of the human crystalline lens and presbyopia. Int Ophthalmol Clin. 2001;41(2):1-15. 123. Glasser A, Campbell MC. Presbyopia and the optical changes in the human crystalline lens with age. Vision Res. 1998;38(2):209-229. 124. Koretz JF, Cook CA, Kaufman PL. Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus. Invest Ophthalmol Vis Sci. 1997;38(3):569-578. 125. Charman WN. The eye in focus: accommodation and presbyopia. Clin Exp Optom. 2008;91(3):207-225. 126. Erpelding TN, Hollman KW, O’Donnell M. Mapping age-related elasticity changes in porcine lenses using bubble-based acoustic radiation force. Exp Eye Res. 2007;84(2):332-341. 127. Hollman KW, O’Donnell M, Erpelding TN. Mapping elasticity in human lenses using bubble-based acoustic radiation force. Exp Eye Res. 2007;85(6):890-893. 128. Yoon S, Aglyamov S, Karpiouk A, Emelianov S. The mechanical properties of ex vivo bovine and porcine crystalline lenses: age-related changes and location-dependent variations. Ultrasound Med Biol. 2013;39(6):1120-1127. 129. Scarcelli G, Kim P, Yun SH. In vivo measurement of age-related stiffening in the crystalline lens by Brillouin optical microscopy. Biophys J. 2011;101(6):1539-1545. 130. Reilly M, Ravi N. Microindentation of the young porcine ocular lens. J Biomech Eng. 2009;131(4):044502. 131. Manapuram RK, Baranov SA, Manne VGR, et al. Assessment of wave propagation on surfaces of crystalline lens with phase sensitive optical coherence tomography. Laser Phys Lett. 2011;8(2):164-168. 132. Hsieh BY, Song S, Nguyen TM, et al. Moving-source elastic wave reconstruction for high-resolution optical coherence elastography. J Biomed Opt. 2016;21(11):116006. 133. Huber R, Adler DC, Fujimoto JG. Buffered Fourier domain mode locking: unidirectional swept laser sources for optical coherence tomography imaging at 370,000 lines/s. Opt Lett. 2006;31(20):2975-2977. 134. Huber R, Wojtkowski M, Fujimoto JG. Fourier Domain Mode Locking (FDML): A new laser operating regime and applications for optical coherence tomography. Opt Express. 2006;14(8):3225-3237.

Copyright © 2018. Kugler Publications. All rights reserved.

10. Electronic speckle pattern interferometry and lateral shearing interferometry Abby Wilson1, John Marshall2 Wolfson School of Mechanical, Manufacturing and Electrical Engineering, Loughborough, UK; 2Institute of Ophthalmology, University College London, London, UK

1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction Determination of the biomechanics of the cornea is currently an area where there is a great deal of interest. Several diseases have a direct association with changes in corneal biomechanics, and invasive surgeries such as corneal transplants, cataract surgery, and refractive surgery can directly affect corneal biomechanics. With respect to refractive surgery alone, over 50 million procedures have been carried out worldwide to-date, and the demand for better visual outcomes, lower surgical risk, and better long term results has led to interest in the development of less invasive or non-invasive techniques such as small incision lenticule extraction (SMILE) and corneal collagen crosslinking. Since the biomechanics of the cornea have a direct association with corneal shape and visual acuity, there is a need for measurement techniques that can establish what the normal biomechanics of the cornea are and how they change with intervention or disease, as this may enable earlier diagnosis of disease, provide a screening tool for people at risk of potential complications after refractive surgery, such as post laser-assisted in situ keratomileusis (LASIK) ectasia, enable better surgical outcomes, and optimize current corrective techniques, along with assisting in the development of new techniques. There remains a lack of understanding and agreement as to what the normal biomechanics of the cornea are. A large range of parameters have been evaluated across

different studies, with Young’s modulus being the most common. A wide range of values for the Young’s modulus of the cornea has been quoted, ranging from 0.1 to 57 MPa.1 As the cornea is a viscoelastic biological material, the measured Young’s modulus can be dependent on several factors including loading rate, load magnitude, hydration, and temperature. In addition to this, the cornea is anisotropic, and therefore the Young’s modulus will vary with direction and depth. Due to the simplicity of the technique, a lot of the current biomechanical data on the cornea has been established using strip extensiometry. This method has many drawbacks as the structure of the cornea is damaged prior to testing and the applied loads are not representative of those experienced in vivo in either magnitude or direction. Inflation testing, in the form of either whole globe inflation testing, or inflation testing of corneoscleral buttons in an artificial anterior chamber, is generally considered a better option for ex-vivo investigation as the structure of the cornea is maintained and the hydrostatic loading method simulates the forces to which the cornea is exposed to in vivo under intraocular pressure (IOP). The problem with many of the current methods used to measure the response of the cornea to inflation testing are that they measure the response at only a single point, or have a limited resolution, and/or the sensitivity of the techniques requires the pressure increases to fall beyond the physiological range. Ideally, a reliable method to determine the biomechanics of the cornea in vivo would exist, thus enabling

Correspondence: Abby Wilson, 113 Cleveland Terrace, Darlington, County Durham, DL3 8HX, UK. Email: [email protected] Biomechanics of the Eye, pp. 147-157 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

Copyright © 2018. Kugler Publications. All rights reserved.

148

individual assessment. Current in-vivo biomechanical assessment involves measuring the deformation response of the cornea to an air puff directed at the apex via high-speed Scheimpflug imaging. Several parameters including maximum deformation amplitude, corneal velocity, and corneal radius of curvature at highest concavity, are used to predict whether the biomechanics of the cornea are normal or abnormal. The limitations of this method are that several factors, such as IOP and corneal thickness, can affect the response; the response is only measured at the central cross-section and the air puff loading method forces the cornea outside its normal range of motion. Electronic speckle pattern interferometry (ESPI) and lateral shearing interferometry (LSI) are highly sensitive techniques that are used to measure the full-field displacement or the rate of change of displacement of surfaces by detecting changes to the phase of light scattered from the surface of an object that occur in response to a specific disturbance such as an applied load, vibration, or temperature change. Quantitative measurement across a large surface area can be achieved in milliseconds and results can be viewed live. In addition to this, since the ESPI and LSI techniques are non-destructive, non-contact, and highly sensitive they can be used to test a large range of materials under a large range of different loading conditions. For these reasons they have been used in a wide range of applications from evaluating the quality of parts used in the manufacturing of space shuttles2 and lifeboats to evaluating the stress distribution in the femur before and after hip replacement.3 The high sensitivity of ESPI means the technique is confined to being used in laboratory conditions, where the environment can be tightly controlled and disturbances can be minimized. LSI, on the other hand, can be used for a much wider range of applications as it has greater stability due to the fact the object is used as its own reference, making it much less sensitive to environmental disturbances. Another advantage to LSI and other types of shearing interferometry is that there is a large range of possible configurations, so an instrument can be designed to have a sensitivity to suit a specific application; the range of sensitivity can also be extended and optimized due to the ability to control the sensitivity through varying the amount of shear.

A. Wilson and J. Marshall

Both ESPI and shearing interferometry have previously been used to evaluate the cornea, with the effects of different incisions made during refractive surgery on the response of the cornea to changes in IOP evaluated with ESPI,4,5 and the effects of age6 and corneal collagen crosslinking7 on corneal stiffness evaluated by radial shearing interferometry (RSI). Rather than LSI, RSI was used in the previous studies, due to the fact the cornea deforms in several directions in response to a pressure change, and it was desired to evaluate the radial expansion. There are several limitations to the use of RSI that make LSI a better option for corneal evaluation. Firstly, RSI has no sensitivity at the center of the measurement area, meaning no data at the apex is obtained during measurement. Since this area is highly critical to vision, measurement here is important. Secondly, RSI has non-uniform sensitivity across the whole surface, going from zero at the center to a maximum at the outside; this variation in sensitivity means it is difficult to generate high-quality data across the whole surface, as it likely the data will decorrelate at the outside before sufficient data can be established close to the center. In contrast to RSI, LSI has uniform sensitivity across the measurement area, and by using LSI with both horizontal and vertical shear, the response of the corneal surface can be evaluated with respect to all directions. Interpretation of the LSI data is also simplified due to the uniform sensitivity making visual interpretation of the interferograms easier. Overall, several features of the ESPI and LSI techniques make them a useful tool for corneal biomechanical assessment. The high sensitivity and full-field nature means it is possible to map the dynamic response of the full surface of the cornea to physiological pressure changes over a single measurement. The high resolution means very small details can be picked out that would otherwise be missed with other techniques, and the non-contact and non-destructive nature means corneas can be measured before and after intervention. In addition, the greater stability of the LSI technique and the ability to generate data using laser powers within the maximum permissible exposure limits means there is potential that, in the future, LSI could be further developed as a tool for in-vivo assessment.

Electronic speckle pattern interferometry and lateral shearing interferometry

149

2. Working principles of ESPI and LSI Both ESPI and LSI depend on the formation of speckle. Speckle is formed when coherent light is used to illuminate an object. The formation of speckle depends on the surface of the object generating adequate backscatter and being optically rough, which means having surface height variations greater than the wavelength of the illumination source. The term speckle comes from the fact the light scattered from the object’s surface has a random phase. These scattered light waves interfere with each other, giving rise to constructive and destructive interference which, when viewed, appears as bright and dark ‘speckles’ on the surface of the illuminated object. To extract phase information from the speckle, the light scattered from the object must be captured by an imaging system and compared with light scattered from a reference. In this case, each speckle can be considered as a unique data point with a specific intensity relating to the height of the object’s surface at a specific point at the time of measurement. If the object deforms in some way, changes to the phase of the scattered light occur, resulting in the formation of a new speckle pattern. Tracking the changes in speckle patterns which occur due to microscopic changes to an object’s surface in response to a specific stimulus is the basis for speckle interferometry measurement techniques

Copyright © 2018. Kugler Publications. All rights reserved.

3. ESPI

Fig. 1. Interference pattern formed from interference of the object beam and reference beam before deformation (left); interference pattern formed from the interference of the object beam and reference beam after deformation (middle); and interference pattern formed after subtraction of the interference patterns shown in the middle and left panels (right).

and can be represented in the same way. The two intensity distributions are then subtracted from one another, and this subtraction gives rise to a third interference pattern containing a series of dark and bright fringes, with an example shown in Figure 1. These fringes are areas of equal phase change. In ESPI, the phase change is a function of the wavelength of the illumination source, λ, the illumination angle with respect to the image plane, θ, and the magnitude of the in-plane, u,v, and out-of-plane, w, components of displacement. It describes the change in the optical path length at each speckle as a function of the wavelength of the illumination source.9 The in-plane and out-of-plane directions are defined with respect to the imaging system and not the surface of the object (unless the object has a flat surface and is positioned perpendicular to the imaging system). The phase change for each speckle can be represented mathematically as:9 2π

In ESPI, the back scattered light from an object is captured by the imaging system and combined with light from a reference beam. This gives rise to a speckle interference pattern with a specific intensity, I, describing the object in its current state; this can be represented by the following equation8 and calculated for each pixel in the image: _

​I = Ir + I0 + 2​√ IrI0 ​ cosΔϕ​

(1)

where Ir and Io are the intensities of the object wavefront and the reference wavefront, respectively, and cos ∆ϕ is the phase difference between the two wavefronts. This intensity distribution is then stored; if the object is then deformed, a new interference pattern is formed

​∆ϕdef = ​ _  ​ ​[u sinθxz + w​(1 + cosθxz)]​ ​​ λ 

(2)

with illumination in the xz plane and u representing in-plane displacement with respect to the x axis, and as: 2π

​∆ϕdef = ​ _  ​ ​ v sinθyz + w​(1 + cosθyz)​]​​ λ  [

(3)

with illumination in the yz plane and v representing in-plane displacement with respect to the y axis. The out-of-plane component relates to movement in the direction normal to the surface, and is therefore usually associated with surface elevation or bending/ curvature changes to the surface, whereas the in-plane component relates to movement of the surface in a plane perpendicular to the viewing direction, and is usually associated with stretching or compression of a

150

A. Wilson and J. Marshall

surface or bulk displacement along the x or y axes. Usually, unless the loading is tightly controlled and only applied in a single plane, the measured phase change of a speckle will have both out-of-plane and in-plane components. To determine the magnitude of deformation in each of these planes, the displacement components must be separated, which can be achieved via manipulation of the optical set-up. If the illumination is normal to the object’s surface (θ=0°), then there is no sensitivity to in-plane deformation as sin(0°)= 0. In this case, the phase change is a function of λ and w only, as shown by the following equation: 4π

​  λ   ​w​ (4) ​∆ϕdef = _ To determine the in-plane component, pure in-plane stress can be applied in a specific axis while the object is illuminated at an angle, or the optical configuration can be designed so the components of in-plane displacement can be isolated. This can be achieved in a number of ways, but commonly the object is illuminated from equal and opposite angles simultaneously.9 In this case, the change in the optical path length is a function of both the illumination beams, and the phase change equation becomes: 2π

 ​ ​[u sinθ + w​(1 + cosθ)​ - u sin-θ +w​(1 + cos-θ)]​ ​​ ∆ ​ ϕdef = ​ _ λ  (5) Due to the fact that illumination is from equal and opposite angles, the out-of-plane components cancel each other out and the equation can be reduced to: 4π

​∆ϕdef = _ ​  λ    ​u sinθxz​ (6)

quantitative data and determine the magnitude and direction (positive or negative) of deformation, phase stepping must be implemented. Phase stepping can be in the spatial or temporal domain. The majority of interferometers described in the literature use temporal phase stepping. This is because, for most situations, temporal phase stepping has advantages over spatial phase stepping. Temporal phase stepping has better spatial resolution as the speckle size can be smaller.10 Since the speckle size is governed by the numerical aperture of the imaging system, this in turn leads to another advantage, as it is possible to achieve adequate image intensity under conditions of lower laser power or low levels of backscatter since the aperture can be opened to a greater extent than in the spatial phase shifting case. Conventionally, temporal phase stepping involves taking three or more interferograms at each object state with a known phase step between them so the three unknowns in the intensity equation, I1, I2, ∆ϕ, can be resolved. The specific phase shift can be achieved via several different methods; commonly a mirror attached to a piezo electric translation stage is used to shift the reference beam by a known amount. Once the specific phase at each pixel has been evaluated, a wrapped phase map is produced. In this wrapped phase map, the specific phase between 0 and 2​π​at each pixel is plotted at a specific greyscale level resulting in an appearance like the example in Figure 2, where the fringes develop gradually from white to black. Phase unwrapping is then used to remove the discontinuities that occur due to the asymptotic nature of the arctangent function,8 resulting in a continuous phase map containing the absolute value of the phase change

Copyright © 2018. Kugler Publications. All rights reserved.

4π

​∆ϕdef = _ ​  λ    ​v sinθyz​ (7) for Illumination in the xz and yz planes, respectively.

4. Phase stepping The distribution and quantity of interference fringes in the images gives visual information as to how the object has deformed, with a high fringe concentration indicating greater displacement. However, to gather

Fig. 2. Diagram demonstrating the process of phase unwrapping.

Electronic speckle pattern interferometry and lateral shearing interferometry

at each pixel. An example of an unwrapped phase map is also given in Figure 2.

5. LSI In LSI, instead of combining the object wave with a reference wave in the image space, the object wave is split into two, and one or both parts of the wavefronts are shifted either vertically or horizontally, dependent upon the desired sensitivity direction. The wavefronts are then recombined to create an interference pattern in the same way the object beam and the reference beam are combined in ESPI. Due to the interference of the object wave with a transformed copy of itself, the subtraction of two interferograms gives the 1st derivative of displacement, i.e., the rate of change of displacement between two interfered points, before and after deformation. For horizontal and vertical shear, the phase change due to deformation can be represented mathematically as:11 ​ ϕdef = -​ _ ∆  ​​  ​ _ ​δx sinθxz + ​_  δx  ​ δx​(1 + cos θxz)​]​​ λ  [ δx  (Horizontal shear) (8) 2π δu

δw

​ ϕdef = -​ _ ∆  ​​  ​ _ ​ δy sinθxz + ​ _  ​ δy​ 1 + cos θxz)​]​​ δy ( λ  [ δy (Vertical shear) (9) 2π δu

δw

with illumination in the xz plane. And: ∆ ​ ϕdef = -​ _  ​​  _ ​   ​δx sinθyz + ​ _  ​ δx​ 1 + cos θyz)​]​​ λ  [ δx δx  ( (Horizontal shear) (10) 2π δv

δw

​∆ϕdef = -​ _  ​​  _ ​   ​ δy sinθyz + ​ _  ​ δy​ 1 + cos θyz)​]​​ δy ( λ  [ δy (Vertical shear) (11)

Copyright © 2018. Kugler Publications. All rights reserved.

2π δv

δw

with illumination in the yz plane, where ∂u/∂x and ∂v/∂x are the in-plane displacement derivatives with respect to the x axis; ∂u/∂y and ∂v/∂y are the in-plane displacement derivatives with respect to the vertical axis; ∂w/∂x and ∂w/∂y are the horizontal and vertical out-ofplane displacement derivatives, respectively; δx is the magnitude of horizontal shear; δy is the magnitude of vertical shear; and θxz and θyz are the illumination angles with respect to the xz plane and yz plane, respectively. The evaluation of these components gives us information as to how the object has deformed at a

151

given point. For an initially flat surface imaged normal to the surface: ∂w/∂x and ∂w/∂y relate to surface slope changes with respect to the x and y directions, and ∂u/∂x and ∂v/∂y relate to the rate of change of displacement (strain components ε xx and εyy) in the x and y directions, respectively. Finally, ∂v/∂x and ∂u/∂y relate to rotational aspects of deformation, and addition of these components gives the in-plane shear strain γxy at a given point. To quantify each of these components, their individual contributions to the overall phase change must be determined. As with ESPI, pure out-of-plane sensitivity can be achieved via normal illumination, so ∆ϕdef becomes: 4π ∂w 

(12)

4π ∂w 

(13)

​∆ϕdef = -​_   λ  ​ ​ _  ​ δx ​(Horizontal shear) ∂x  ​∆ϕdef = -​_   λ  ​ ​ _ ∂y ​ δy ​(Vertical shear)

Equal and opposite illumination angles can be used to isolate the in-plane information via subtraction of the phase change data recorded from the two illumination conditions individually; in this case ∆ϕdef becomes: 4π ∂u 

(14)

4π ∂u 

(15)

4π ∂v 

(16)

4π ∂v 

(17)

​∆ϕdef = -​_   λ  ​ ​ _ ∂x  ​δx sin θxz ​(Horizontal shear) ​∆ϕdef = -​_   λ  ​ ​ _ ∂y ​ δy sin θxz ​(Vertical shear) ​∆ϕdef = -​_   λ  ​ ​ _   x sin θyz ​(Horizontal shear) ∂x ​δ ​∆ϕdef = -​_   λ  ​ ​ _ ∂y ​δy sin θyz ​(Vertical shear)

By using this two beam set-up for shearing interferometry, it is also possible to obtain the out-of-plane component via addition of the recorded phase change from each of the illumination angles. The equal and opposite in-plane sensitivity directions achieved at each of the illumination angles means that the in-plane component is cancelled out via addition. Establishing the rate-of-change of displacement with respect to a specific sensitivity direction can be important when trying to identify defects or areas of weakness in objects, and these areas can often be better highlighted by LSI interferograms over the ESPI interferograms. An example is given in Figure 3 for a flat piece of rubber with a superficial diagonal cut

152

Fig. 3. Wrapped and unwrapped phase maps obtained via ESPI and LSI for an initially flat rubber sample with a superficial diagonal cut from top right to bottom left, clamped in an artificial anterior chamber, responding to an increase in hydrostatic pressure of 0.15 mmHg.

Copyright © 2018. Kugler Publications. All rights reserved.

extending top right to bottom left. When this object deforms under an increase in hydrostatic pressure, the position of the defect is more obvious when viewing the LSI data. However, interpretation of the LSI data is less intuitive than interpretation of the displacement data provided by the ESPI technique, especially for someone who is not experienced with the technique or the principles of strain measurement. Therefore, it is often useful to present the results in terms of displacement. Displacement data can be obtained from the LSI technique alone through integration of each of the components describing the rate of change of displacement in a specific direction. This is useful as it means displacement data can be obtained outside of laboratory environments.

6. Specific challenges associated with the application of ESPI and LSI to the cornea There are several challenges when considering the application of ESPI and LSI for the measurement of corneal biomechanics, including: 1. generating an adequate signal to noise ratio;

A. Wilson and J. Marshall

2. establishing adequate stability of the cornea during measurement; 3. uniformity of illumination; and 4. accounting for corneal curvature. Since the surface of the cornea is very smooth and designed to transmit light in the 400-1400 nm range, a surface coating in required to obtain adequate surface roughness and to ensure that the light is scattered from the surface of the cornea. Any coating applied to the surface of the cornea must have negligible stiffness and move with the surface of the cornea while not influencing its movement; this presents less of a challenge ex vivo, as non-soluble powder based coatings can be used. However, with regards to in-vivo measurement, this remains an area for which a solution does not yet exist and significant further development is required ESPI and LSI both require the object to be sufficiently stable while measurement is being taken. This can present a challenge, especially if considering in-vivo application as movement of the head, movement of the eye, and break-up of the tear film could all present problems. Ex-vivo problems can still be encountered due to the hydration changes that can occur during testing time. However, since the measurement time is very short and the powder coating helps to increase the stability of the surface, the quality of measurement is not affected. The curvature of the cornea introduces several challenges. Much of the work reported in the literature to date where ESPI and LSI have been used to establish quantitative data on the mechanical properties of objects has been done on simple, flat objects, under uniaxial loading conditions. As the cornea is curved, when illuminating from an angle, the brightness of illumination varies across the surface of the cornea, and this makes it difficult to establish a single exposure level for which high quality data can be collected across the whole surface while optimizing the sensitivity to in-plane and out-of-plane deformation. Because of this, the commonly used dual-beam angled illumination technique used to separate the in-plane and outof-plane components of phase change is not effective. The corneal curvature also means interpretation of the results has added complexity. As the out-of-plane and in-plane deformation is measured with respect to the imaging system and not the surface of the cornea.

Electronic speckle pattern interferometry and lateral shearing interferometry

153

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. Diagram demonstrating what the measured out-of-plane displacement represents across different positions on the surface of a curved object.

At the center of the cornea the measured out-of-plane deformation represents the total movement of this point on the cornea, whereas in the peripheral areas the measured out-of-plane deformation is a component of the total deformation and the in-plane component must also be determined. A diagrammatic representation of this is shown in Figure 4. This can cause the phase maps that show out-of-plane and in-plane deformation to be difficult to interpret directly. This particular curvature issue can present a problem specifically with regards to LSI since even if the gradient of the surface does not change in response to a pressure increase, a change in the rate-of-displacement may be observed due to the differing angle of deformation at interfered points. As a result, the outof-plane component contributes a different amount to the total movement. This factor means that the rate of change in out-of-plane displacement obtained via the LSI technique does not represent surface gradient change, unless it can be assumed that interfered points deform at similar angles. In addition, the curvature of the cornea results in non-uniformity with regards to the magnitude of applied shear. Because the 3-D profile of the cornea is not accounted for in the image plane, the sheared distance between points at the edges will be greater than at the center. Hence, if the mechanical properties are equal across the entire surface, the curved areas at the edges will appear weaker than the center as the movement between interfered points will be greater,

despite being equal per unit distance. This factor can be easily corrected for during post-processing if information regarding the shape of the test surface is known. So far, due to a combination of the factors discussed, direct measurement of the in-plane component of deformation using either the ESPI or LSI techniques has not been achieved on the cornea. However, out-ofplane evaluation using normal illumination with both the ESPI and LSI techniques has been successful. The results obtained via these techniques have been used alongside surface profile information and video analysis of the central cross-section of the cornea deforming under increased hydrostatic pressure to make estimations for the in-plane components. Examples of results obtained via ESPI and LSI on corneas before and after cross-inking in specific topographical locations are shown in the following section.

7. ESPI and LSI to determine corneal biomechanics and to detect changes to biomechanics introduced by collagen crosslinking To demonstrate the ability of the technique to detect biomechanical changes in corneas, a study was conducted where human and porcine corneas were investigated before and after applying crosslinking to specific topographic locations. The human corneas

154

used in this study were provided by Moorfields Biobank and supported by NIHR funding. Research ethical approval was obtained from The Moorfields Biobank Internal Ethics Committee. In this study, the corneoscleral buttons were clamped into a custom-designed artificial anterior chamber and set under a baseline pressure of 16.5 mmHg. Data were captured before and after a pressure increase

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. Wrapped ESPI fringes corresponding to out-of-plane displacement of the cornea in response to a hydrostatic pressure increase of 0.5 mmHg (left); corresponding horizontal LSI fringes (right).

A. Wilson and J. Marshall

of 0.5 mmHg, which was achieved by linear vertical motion of a tank attached to the chamber. A set of measurements were taken prior to crosslinking. The cornea was then soaked in riboflavin (VibeX-Xtra, Avedro Inc., MA, USA) for ten minutes and crosslinked via exposure to a UVA source (KXL, Avedro Inc.) at a power of 15 mW/ cm2 for a time of eight minutes delivering a total energy of 7.2 J/cm2. Due to the full-field nature of the ESPI and LSI techniques, it was possible to evaluate the response of the corneas across the full surface. It was observed that that the response of the cornea was highly nonuniform, with the rate of displacement significantly greater in the peripheral areas compared with the central regions. This was evident from the ESPI and LSI data, as the ESPI fringes were more concentrated in the outside regions and there was an absence of fringes across the center in the LSI plots. An example of these fringe distributions for one of the human corneas tested is shown in Figure 5.

Fig. 6. (Left) Plots showing the out-of-plane displacement measured for a cornea responding to a hydrostatic pressure increase of 0.5 mmHg before (left) and after (right) crosslinking down a 3 mm vertical strip (section enclosed by dotted red lines).

Electronic speckle pattern interferometry and lateral shearing interferometry

155

Fig. 8. Surface plot of the out-of-plane displacement component obtained via ESPI in response to a pressure increase of 0.5 mmHg (left); corresponding wrapped horizontal LSI data.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 7. Vector plots representing the profile of deformation predicted for the measured out-of-plane data for a cornea before and after crosslinking along a central vertical 3 mm strip. The length and size of the arrow head is proportional to the relative displacement.

Figure 6 shows plots of the out-of-plane displacement component measured via ESPI for the same cornea, before and after crosslinking, down a 3 mm vertical strip along the superior-inferior axis. Significant changes to both the magnitude and distribution of the out-of-plane displacement component were observed in response to the same pressure change before and after crosslinking. These changes were successfully detected via ESPI as well as in the LSI data. The out-of-plane data shown in Figure 5 were used in combination with measurement of the surface profile, while assuming deformation normal to the surface to produce scaled-up vector plots, to demonstrate how the profile of deformation would be expected to change along the central nasal-temporal axis before and after crosslinking. These plots are shown in Figure 7. Previous to this study, the specific changes introduced by crosslinking on the dynamic response of the cornea to a pressure change had not been shown across the full surface of the cornea. In addition to demonstrating the full-field effect of crosslinking, the ESPI and LSI techniques were also effective for identifying potentially weak areas or areas of damage in corneas. An example of this is shown in Figure 8 for a cornea where there was a small hole present at the limbus on the left side. The ESPI surface

plot is shown in Figure 8, alongside the LSI fringe distribution in which the fringes are concentrated around the area of damage. After testing approximately sixty porcine corneas using the two techniques, it was also possible to identify areas on specific corneas that were deforming abnormally when compared to the majority of corneas tested through evaluation of the fringe distributions. These specific areas could then be crosslinked selectively in an attempt to normalize the response. An example of this is shown for a porcine cornea where the right side appeared to be significantly weaker than the left during intial examination, causing it to displace by a greater amount in response to a pressure change. After crosslinking the right side of the cornea only, the response became more equal across the surface of the cornea.

8. Conclusions As demonstrated by the results included in this chapter, there are many advantages to using ESPI and LSI as measurement tools to evaluate the biomechanics of the cornea. The high sensitivity of the techniques means biomechanical changes, such as those introduced by crosslinking or damage, can be detected and evaluated across the whole surface of the cornea in response to a small pressure change well within the physiological range. The results obtained via these techniques highlighted the non-uniform response of the cornea, with less resistance to deformation observed in the peripheral regions. The highly anisotropic response of the cornea demonstrates the need for full-field evaluation when investigating its biomechanics. In addition, the

156

A. Wilson and J. Marshall

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 9. Plots showing the out-of-plane displacement measured via ESPI for a porcine cornea deforming to a 0.5 mmHg increase in hydrostatic pressure before (top left) and after (top right) crosslinking the right side. Line plot comparing the out-of-plane displacement measured along the horizontal centerline before and after crosslinking.

evaluation of a single Young’s modulus value, as has been common in previous studies, does not provide sufficient information. With high-resolution full-field information, such as that provided via ESPI and LSI, it is possible to identify specific areas of abnormality, which is important for diagnosing diseases such as keratoconus or ectasia, where the biomechanics can be affected in a specific region. Also, an understanding of the biomechanics across different regions of the cornea could assist in improving current surgical techniques, as the position of incisions could be modified to avoid specific areas that are thought to be most critical to maintaining the structural integrity of the cornea. It could also assist in the development and optimization of targeted crosslinking that could be used in the treatment of keratoconus or for refractive correction.

However, there are still several challenges associated with using the techniques described to measure corneal biomechanics. Due to the way the fringes form when using the LSI technique and the limitations of the instrument, it has been found during initial testing that the data are quick to decorrelate. A second issue, to-date, is that integration of the LSI data to obtain displacement does not yet give consistently accurate quantitative data that match the displacement data measured using the ESPI device, although the profile of the data is similar; hence, this is an area where futher research is required. If in-vivo measurement were desired, significant further development of the LSI technique would be required to address these current issues.

Electronic speckle pattern interferometry and lateral shearing interferometry

Acknowledgements The authors wish to acknowledge Professor John Tyrer for his contribution to this work. Testing was conducted at both Loughborough University, Leicestershire, UK, and Laser Optical Engineering Ltd., Leicestershire, UK.

References 1.

2.

3.

Copyright © 2018. Kugler Publications. All rights reserved.

4.

Garcia-Porta N, Fernandes P, Queiros A, Salgado-Borges J, Parafita-Mato M, González-Méijome JM. Corneal biomechanical properties in different ocular conditions and new measurement techniques. ISRN Ophthalmol. 2014;724546. Ibrahim JS, Petzing JN, Tyrer JR. Deformation analysis of aircraft wheels using a speckle shearing interferometer. Proc Inst Mech Eng Part G J Aerosp Eng. 2004;218: 287–295. Tyrer JR, Heras-Palou C, Slater T. Three-dimensional human femoral strain analysis using ESPI. Opt Lasers Eng. 1995;23:291– 303. Jaycock PD, Lobo L, Ibrahim J, Tyrer J, Marshall J. Interferometric Technique to measure biomechanical changes in the cornea induced by refractive surgery. J Cataract Refract Surg. 2005;31:175–184.

5.

157

Knox Cartwright NE, Tyrer JR, Jaycock PD, Marshall, J. Effects of variation in depth and side cut angulations in LASIK and thinflap LASIK using a femtosecond laser: A biomechanical study. J Refract Surg. 2012;8:419–425. 6. Knox Cartwright NE, Tyrer JR, Marshall J. Age-related differences in the elasticity of the human cornea. Invest Ophthalmol Vis Sci. 2011;52:4324–4329. 7. Knox Cartwright N, Tyrer J, Marshall J. In vitro quantification of the stiffening effect of corneal cross-linking in the human cornea using radial shearing speckle pattern interferometry. J Refract Surg. 2012;28:503–508. 8. Moore A J, Tyrer JR. Two-dimensional strain measurement with ESPI. Opt Lasers Eng. 1996;24:381–402. 9. Petzing JN, Tyrer JR. Recent developments and applications in electronic speckle pattern interferometry. J Strain Anal Eng Des. 1998;33:153–169. 10. Burke J, Helmers H. Spatial versus temporal phase shifting in electronic speckle-pattern interferometry: noise comparison in phase maps. Appl Opt. 2000; 39(25): 4598-4606. 11. Tyrer JR, Petzing, JN. In-plane electronic speckle pattern shearing interferometry. Opt Lasers Eng. 1997;26:395–406.

Copyright © 2018. Kugler Publications. All rights reserved.

11. Brillouin microscopy Giuliano Scarcelli1, Seok Hyun Yun2,3 Fischell Department of Bioengineering, University of Maryland, College Park, MD, USA; 2Wellman Center for Photomedicine, Massachusetts General Hospital, Cambridge, MA, USA; 3Department of Dermatology, Harvard Medical School, Boston, MA, USA 1

1. Introduction Brillouin microscopy is an optical technology developed for the biomechanical characterization of tissue at high 3-D resolution. This chapter describes the physics of Brillouin light scattering, and the link between Brillouin spectroscopic signatures and the biomechanical properties of the cornea. A brief summary of the technology that enabled Brillouin imaging of the cornea is given. Finally, current and future perspectives of Brillouin microscopy for clinical applications are discussed.

Copyright © 2018. Kugler Publications. All rights reserved.

2. Brillouin scattering Light scattering generally refers to a series of phenomena in which optical radiation is incident upon a medium and is reemitted after interaction within the medium. Analyzing the scattered light, important information regarding the material of interest can be accessed in purely optical fashion without contact and typically with high spatial resolution. Light scattering at low optical intensity is non-invasive and does not alter the material properties. This is particularly important for applications in biological research and clinical medicine. Light scattering phenomena are generally divided into elastic and inelastic processes. In elastic scattering, no exchange of energy occurs during the light-matter interaction so that the scattered light has the same frequency (or wavelength) of the

incident light. In inelastic scattering, the light-matter interaction induces a change in frequency between incident and scattered light. Brillouin scattering is an inelastic scattering phenomenon in which the change in energy occurs due to acoustic vibrations or “acoustic phonons” present in the material. Brillouin scattering is analogous to Raman scattering, which is based on molecular vibrations and therefore used to characterize the chemical properties of a sample. Brillouin scattering involves the propagation of the collective motion of molecules, or acoustic wave, which is directly governed by the mechanical properties of the material. The acoustic waves that give rise to spontaneous Brillouin scattering originate from thermodynamic fluctuations that are naturally present in the tissue. In any medium, local density and pressure intrinsically fluctuate due to fundamental thermal energy. Such density and pressure fluctuations generate periodic and traveling refractive index variation that can be thought of as microscopic sound waves, hence acoustic vibrations or phonons. At a microscopic level, then the medium is equivalent to a traveling diffraction grating that propagates in the medium at the velocity of sound. As a result, when light enters the material it can be diffracted in a different direction in a similar fashion to Bragg-diffraction occurring in crystals and with different frequency due to an exchange of energy similar to the frequency shift occurring due to Doppler interactions. Figure 1 illustrates this interaction. Monochromatic pump light with a frequency Vp = ωP/2π or wavelength λ P = C/VP is incident on a medium. At room temperature,

Correspondence:Giuliano Scarcelli, Kim Engineering Building 2218, Fischell Department of Bioengineering, University of Maryland, College Park MD 20742, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 159-168 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

160

G. Scarcelli and S.H. Yun

√

_

α M’ ​ π ​ ​  _ ​ ρ ​ ​​  , Δ ​ VB = _

(4) where α is the attenuation coefficient of the sound wave inside the sample, related to the viscosity of the material. The magnitude of the scattered radiation provides additional information related to the coupling of acoustic and optical energy inside the sample, and is determined by the scattering cross-section RB:1,2 ​RB = _ ​ V  ​ ​ _     ​ ≈ ____ ​  2​λ​ 4 ​ ​ ​ ​ _ ​​ ρ ​ _ ​ ​​​  ​​ ρV 2 ​  ( ∂ρ ) dΩ 1 dσ

INT

π2kT 1

∂ε

2

P

(5)

where VINT is the interaction volume inside the sample, k is Boltzmann constant, T is the temperature, ρ is the density of the material, and ​​​(ρ​∂ε ⁄ ∂ρ​)​​​ 2​​is known as the electrostriction coefficient of the material. Fig. 1. Illustration of the Brillouin scattering principle.

Copyright © 2018. Kugler Publications. All rights reserved.

the scattered light presents a doublet with Stokes and anti-Stokes components depending on whether the scattered light acquired or lost energy due to Brillouin interaction. For the scattering phenomenon to occur, phase-matching conditions involving the energy and momentum of incident light, scattering light, and the acoustic wave are given by:

3. Brillouin spectroscopy and its potential for mechanical characterization

Brillouin spectroscopy is the technique that measures the spectrum of the Brillouin scattered light with respect to the pump waves, thereby probing the characteristics of acoustic phonons in a medium. In principle, at least three independent parameters can be extracted ​ωB = ωp - ωs​ (1) by each collected spectrum and can serve as contrast ¯ ​​  B  = ¯ k​ k​ ​  p  -​¯  k​   s ​ (2) mechanism for imaging: 1. Brillouin frequency shift from Equation (3); where ω and k are angular frequency and wave number, 2. Brillouin linewidth from Equation (4); and respectively, and the subscripts B, p, and s represent the 3. Brillouin intensity from Equation (5). Brillouin acoustic phonons, and pump and scattering From a mechanical standpoint, Brillouin scattering (or signal) photons, respectively. The frequency of the monitors the stress response of a sample to a 1-D phase-matched phonons, i.e., the difference between sinusoidal strain of high frequency (GHz). Therefore, all the pump and scattering photons, is given by: Brillouin spectral quantities are peculiar signatures of the sampled material that could serve as a mechanical θ 2n _ _ _ M’ ρ √ ​VB = ± ​ λ  ​​    ​ ⁄  ​  cos​(​ 2 ​)​​ (3) fingerprint of the medium. In the case of viscoelastic P materials, the stress of the sample will be determined where n is the refractive index of the sampled material, by the complex longitudinal modulus, ­​M = M’ + iM”,​ M’ is the real part of the longitudinal elastic modulus of whose real part expresses the elastic response and the material (on which we will focus the next section), ρ whose imaginary part expresses the viscous response, is the density of the material and θ is the angle between i.e., the loss of acoustic energy in the sample. The specincident _ and scattered optical radiation; importantly,​ troscopic signatures parameters directly measured are M’⁄ ρ  ​  ​​is the hypersonic sound velocity inside the related to the longitudinal modulus by the following V = √ ​  ​ medium. In this scenario, the linewidth of Brillouin relationships:3 2 2 radiation is due to the lifetime of the acoustic phonon λP λ ρ ______ ρ P _ _ ______ ​M’ = ​ n2 ( ​​​   ​ 2cos ​( θ​  ⁄ 2)​  ​ ) ​ ​​​  ​VB2; M’’ =  ​n2 ( ​​​   ​ 2cos​( θ​  ⁄ 2)​  ​ ) ​ ​​​  ​VB2ΔVB2​. within the material, i.e., by: (6)

Brillouin microscopy

161

Fig. 2. Various types of sample deformation in response to the stress field, F, which defines different mechanical moduli. (a) Young’s modulus. (b) Bulk modulus. (c) Shear modulus. (d) Longitudinal modulus. The Brillouin frequency shift is related to the local longitudinal modulus of medium.

Therefore, other than the constants in parenthesis, which are determined by the experimental settings, we can achieve a non-invasive direct measurement of the local longitudinal elastic modulus of material, if we can measure or estimate the index and density of the material under consideration. However, in theory, both index of refraction and density of material are not constant from sample to sample nor uniform within samples; for the case of corneal tissues, though, the factor ​​ρ ⁄n  ​​ can be approximated to a constant. In fact, both density and index are dependent on the amount of collagen and interstitial medium in the cornea relative to its water content so that their variations tend to compensate each other for the purpose of Brillouin modulus measurements. Human corneas in normo-hydrated conditions (~3.5 mg H2O/mgdrytissue) have a refractive index of 1.376 and a density of 1.07 g/ml; in highly swollen conditions (~7.5 mg H2O/mgdrytissue), corneas have a refractive index of 1.362 and a density of 1.04 g/ml.4,5 Hence, even among extreme opposite conditions of hydration, the range of variation for ρ​​  ⁄n  ​​is between 0.565 g/ml and 0.560 g/ml, which accounts for less than 1% variation in Brillouin shift; in standard physiological conditions, this effect is expected to be much smaller. However, even after the index/density are estimated and the longitudinal elastic modulus of material is retrieved, a fundamental problem remains open, i.e., the relationship between the longitudinal modulus and the conventional elastic moduli obtained with standard mechanical tests has never been worked out and is not straightforward for soft biological tissues.2,8,11 For this discussion, in the rest of the section we will focus on 2

Copyright © 2018. Kugler Publications. All rights reserved.

2

the real part of the complex elastic modulus, i.e., on the elastic response of the material. We shall begin with a brief overview of the types of elastic moduli and measurement methods. Consider an isotropic material. Young’s modulus, E, is defined as the ratio between an applied axial or longitudinal stress (force over area, F/A) and resulting axial strain (relative elongation/compression over initial length ­­Δz/ z0) (Fig. 2a). To a good approximation, this quantity can be measured by compressive or tensile stress-strain tests, and many commercial instruments exist for this task (e.g., Instron). The Poisson’s ratio, σ, is commonly used to describe the ratio between transverse (shear) strain and axial strain under axial loading. The bulk modulus, K, is a useful parameter to describe liquids, as it refers to the situation where the material is uniformly loaded and all the strains normal to the stress direction are equal (Fig. 2b). It is defined as the ratio of applied stress, or pressure, to volume change, ΔV/V, and can be expressed in terms of Young’s modulus and Poisson’s ratio as K = E/3(1-2σ). The shear modulus describes a situation where all the strains perpendicular to the stress direction are zero (Fig. 2c), i.e., alterations in material shape are induced without involving a volume change. To a good approximation, this situation is reproduced in commercial dynamic mechanical analyzers and rheometers, or alternatively, in acoustic measurements using shear waves. The shear modulus, G, is defined as the ratio between shear stress and shear strain, Δx/z0 and is related to Young’s modulus as follows: G = E/2(1+σ). The longitudinal modulus, M, in a similar fashion to Young’s modulus, is defined as the

162

G. Scarcelli and S.H. Yun

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. (a) A representative cross-sectional Brillouin image of a normal porcine cornea. The horizontal and vertical span is 0.05 mm (x) by 0.8 mm (z). (b) Brillouin depth profiles of a porcine cornea (N = 3).

ratio of axial stress to axial strain. The difference is that the material perturbation occurs in a strictly uniaxial strain state and no shear strain is produced (Fig. 2d). This happens in response to longitudinal acoustic waves, as in the case Brillouin microscopy, where rapidly oscillating and purely longitudinal stresses are induced. The longitudinal modulus is related to the bulk and shear moduli as follows: M = K+4/3G. The high water content of biological tissues causes the tissues to have low compressibility, i.e., σ = ~0.5 and high bulk modulus. As a result, the longitudinal modulus, M, is much higher than the conventional Young’s or shear modulus. In addition, most biological materials, including the cornea, exhibit viscoelastic properties characterized by frequency-dependent moduli.6 In response to fast mechanical or acoustic modulation, such as GHz acoustic phonons, slower relaxation processes have no time to respond and thus contribute little to the softness of the material. As a consequence, the modulus tends to increase with frequency. Finally, standard mechanical measurements are performed with relatively slow time scales and with a sample in contact with large plates. These plates effectively work as a heat sink, so that the modulus is evaluated in an isothermal condition. On the other hand, in Brillouin microscopy the time

scale is too short for heat transfer between a sampled region and surrounding material to occur. Therefore, Brillouin microscopy can be considered an adiabatic measurement of the elastic modulus. Adiabatic methods yield slightly higher values for longitudinal elastic moduli with respect to isothermal methods, because the heat generated due to acoustic oscillations induces local expansion or compression against the acoustic pressure. The relationship between adiabatic and isothermal moduli can be calculated from thermodynamic arguments.7

4. Brillouin mechanical characterization for corneal tissue As explained in the previous section, for soft biological tissue, no straightforward theoretical link has been worked out between the Brillouin-measured longitudinal elastic modulus and more familiar mechanical properties such as the Young’s modulus or the shear modulus of materials. However, a strong correlation between these two entities is expected to exist as they are both analogously governed by two fundamental energy components of entropic and kinetic nature.

Copyright © 2018. Kugler Publications. All rights reserved.

Brillouin microscopy

In a simplified picture of the microscopic origin of material elasticity, the entropic component is related to microscopic arrangement and conformation. Therefore, in tissue, it will mainly depend on the amount of crosslinking within a sample; the internal energy component is instead derived by the intermolecular distances, and therefore, in tissue, it will strongly depend on the dry-mass to water ratio within a sample. Following this consideration, we set out to investigate, empirically, the relation between Brillouin-measured longitudinal modulus and standard shear modulus in corneal tissue. Let us begin by showing a representative image of corneal tissue taken with Brillouin microscopy.8 Figure 3a shows the cross-sectional image of the anterior segment of a normal porcine eyeball in x-z plane. To acquire a Brillouin image, the scattering spectrum is analyzed at each location to determine the local Brillouin frequency shift; by moving the sample with a motorized x-y-z stage, the Brillouin shift at each location is measured and an image is obtained by plotting the measured frequency shifts with color encoding. The Brillouin image reveals the remarkable spatial variation of Brillouin frequency shift throughout the depth of the cornea. Figure 3b shows typical axial profiles obtained from three different porcine samples by averaging the cross-sectional image over the transverse axis. It is clear that the Brillouin frequency shift is the highest in the anterior region, and it decreases gradually toward the inner layers. This result is very interesting if compared with the microstructural organization of corneal stroma. The anterior part of the stroma shows a markedly interwoven and intertwined organization of collagen fibers, whereas in the posterior region of the cornea, collagen fibers mostly run parallel to the corneal surface. This microstructural organization has important mechanical consequences: Kohlhaas et al. reported that the anterior part of the stroma has nearly three times higher elastic moduli than the posterior part of the stroma in human eyes.9 Muller et al. showed that the collagen fiber network in the anterior stroma is mainly responsible for the structural integrity of the cornea in human eyes.10 The observation of decreasing Brillouin frequency shift through depth therefore seems to match the expectations from a micromechanical standpoint, although the existence of a microstructural organization similar to the human cornea has not been

163

Fig. 4. Comparison of Brillouin-related longitudinal modulus and quasi-static shear modulus of thin flaps (100-300 microns) cut from anterior (N = 4), central (N = 6), and posterior (N = 12) corneal tissue. Circles: experimental data; error bars: s.e.m.; solid line: log-log linear fit.

confirmed in porcine corneas. Recently, Randleman et al. performed tensile stress-strain tests on shaved-off corneal layers and found an interestingly similar trend of decreasing elastic modulus through the corneal depth.11 The variation of mechanical properties through corneal depth is very suitable to build an empirical correlation between Brillouin modulus and standard shear modulus, as shown in Figure 4. To do so, Brillouin depth profiles were acquired on intact porcine corneas and longitudinal modulus values were computed using fixed index/density data taken from the literature. For shear rheometry, corneal tissue samples were cut with a biopsy punch in order to retrieve thin flaps from anterior, central, and posterior portions of the cornea. The shear modulus of the thin flaps was measured at 0.5 Hz frequency with 0.1% strain amplitude with a stress-controlled rheometer (AR-G2, TA Instruments, New Castle, DE, USA). For each flap, thickness was accurately measured in order to calculate the corresponding average longitudinal modulus from the Brillouin depth profile. Figure 4 shows a logarithmic plot of Brillouin-related longitudinal modulus vs quasi-static shear modulus, showing a strong correlation between the two quantities and a log-log linear trend (R > 0.99). The log-log correlation between gold-standard mechanical measurements and Brillouin-measured moduli is consistent with what we previously found for crystalline tissue and other polymeric materials.12 This provides the potential of having a quantitative char-

164

G. Scarcelli and S.H. Yun

acterization of corneal mechanical properties after proper calibration. In particular, if for a given material we can write: ​log​(M’ )​ = a log​(E’ )​ + b or log(M’) = a log(G’) + b.​ (7) This correlation seems to suggest a power-law relationship ​M’≈ Mo ​​(ω​  ⁄ Φ ​)​​​ β​​, where M0, Φ0, and β are constant for a given material. Power-law frequency scaling was previously found in tissue, polymer, and cytoskeleton up to kHz13-16 and in MHz regime.17,18 The above equations represent the quantitative nature of the Brillouin measurements with respect to conventional rheological properties. The coefficients a-b are intrinsic properties of the material that have a fundamental basis on atomic and molecular interactions, and can be empirically determined. From the log-log linear relationship, we can also obtain: 0

ΔM’

ΔE’

ΔM’

ΔG’

Copyright © 2018. Kugler Publications. All rights reserved.

_ _ _  ​​_ M’   ​ = a ​  E’   ​ or ​  M’   ​ = a​  G’   ​​ ,

(8)

where ΔM′, ΔE′, and ΔG′ are respective derivatives or variations. The coefficient a, therefore, relates the sensitivity of the spectral measurements (or of the longitudinal modulus) to the sensitivity of the instrument to actual variations in Young’s or shear modulus. For example, current instruments can reach very high frequency sensitivity of ±1 MHz/√Hz. This value corresponds to a very small relative error in longitudinal moduli, ΔM′/M′ ≈ +/-0.3% for an integration time of 0.1 s. However, using a = 0.03 measured with porcine corneal tissues, we determine that the Brillouin measurement can detect a difference in Young’s or shear moduli, ΔE′/E′ of about 9% at an integration time of 0.1 s. The log-log correlation is particularly useful to quantify the mechanical outcome of crosslinking protocols. In fact, we can interpret the change of elastic modulus induced by a corneal collagen crosslinking (CXL) protocol as given by the relationship in Equation (8): ​​ΔM’⁄ M’​ = a​ΔE’⁄ E’​​. Therefore, the comparison of the mechanical changes induced by two different procedures should yield the same ratio in both Brillouin and Young’s case, i.e.: Δ​M​ ‘1 ​​  ​ΔE​ ‘1 ​​  ___  ​​ (9)  ​​ ​ΔM​ ‘ ​ ​ ​ = ​ ___ ​ΔE​ ‘2 ​​  2

where the subscripts 1 and 2 indicate the two CXL procedures. Since the traditional Dresden protocol is considered as the gold-standard of CXL procedures, we can introduce a corneal stiffening index (CSI), defined as a universal quantitative measure of the mechanical outcome of a specific CXL procedure (denoted by a subscript X) compared to the traditional Dresden protocol: ​ΔM​ ‘X ​​ 

​ΔE​ ‘X ​​ 

 ​​ΔM​ ‘  ​    ​  ​​ = 100 *  ​​___     ​​ ​CSIx Ξ 100 * ____ ​ΔE​ ‘  ​​  Dresden

Dresden

(10)

The mechanical interpretation of the CSI is straightforward: a procedure with a CSI of 50 would produce approximately 50% of the modulus increase of the Dresden protocol. Using the CSI concept, we have been able to characterize the mechanical outcome of several CXL procedures, including the variation of light dose, soaking time, and epithelium debridement.19 Interestingly, CSI allows using non-contact, non-invasive Brillouin microscopy to assess the same mechanical properties of CXL procedures that gold-standard stressstrain tests and shear rheometry provide, without any calibration measurement. Moreover, it is conceivable that the concept of CSI can be extended to abnormal conditions of the cornea, such as keratoconus or ectasia, where a negative index would indicate the pathologic loss of strength of the tissue.

5. Brillouin microscopy technology Brillouin scattering was first described by Leon Brillouin in 1922.20 Since the 1970s, using the spectrometer developed by JR Sandercock, Brillouin scattering spectroscopy has been widely used for material characterization21 and environmental sensing.22 In the biological realm, in the 1980s, Brillouin scattering was observed in collagen fibers,23,24 cornea, and crystalline lens25 ex vivo. However, Brillouin spectroscopy has not been exploited in biological research or for in-vivo applications because Brillouin spectra typically took minutes to hours to be acquired. The main technological challenge in Brillouin spectroscopy is that Brillouin light spectral components are extremely close in frequency (or wavelength) to the input light or the elastically scattered light. Elastic scattered light or residual components of the input light

Copyright © 2018. Kugler Publications. All rights reserved.

Brillouin microscopy

typically are orders of magnitude stronger than Brillouin scattered light in most biological tissues and optical configurations. Ordinary spectrometers lack spectral resolution, i.e., the ability to resolve Brillouin signal in the order of GHz (0.1–0.5 cm-1), and lack spectral extinction, i.e., the ability to detect Brillouin scattered light in the presence of strong radiation components of similar frequency. For high spectral resolution and extinction, traditionally, Brillouin spectroscopy has relied on multiple-pass scanning Fabry-Perot (FP) interferometers.26,27 Spectral scanning is achieved by changing the spacing between the two mirrors forming a FP cavity. However, in scanning instruments, only a particular narrowband spectral component is measured at a time, resulting in a limited throughput and a long scanning time. An alternative, non-scanning approach is using a combination of dispersed beam and a FP etalon, where all of the transmitted spectral components can be detected simultaneously with charge-coupled devices (CCD).28,29 However, even though the scanning is removed, only a particular narrowband spectral component is transmitted per angle, while the remaining components of the spectrum are reflected and lost. Also, the higher the resolution required from the FP spectrometer, the lower the throughput of the spectrometer. This fundamental throughput limit was overcome by a parallel-detection spectroscopic approach developed in 200830 using a diffractive tilted etalon, called virtually-imaged phased array (VIPA),31,32 in combination with a CCD camera. The VIPA spectrometer has fundamentally superior performance to achieve high spectral resolution with high temporal resolution. As in angle-dispersive FP spectrometers, the spectral selection is given by the interference of multiple reflections at two optical flats yielding equivalent performances to FP interferometers in terms of resolution. Unlike FP etalons, though, the first surface is totally reflective but is cut (or coated) to allow all the light to enter the interferometer. In addition to minimizing losses, this design avoids useful light being wasted in a reflected interference pattern. As a consequence, with respect to an equivalent FP spectrometer, the signal strength is improved by about two orders of magnitude. This has been the crucial progress that enabled to transform the Brillouin method from a point-sample spectroscopy technique to an imaging technology. Imaging

165

Fig. 5. Schematic representation of a Brillouin microscope composed by a laser-scanning confocal microscope connected to a Brillouin spectrometer via a single-mode optical fiber.

Brillouin instruments are usually the combination of a laser-scanning confocal microscope with a VIPA-based spectrometer, as shown in Figure 5. Recent years have seen a rapid development of VIPA-based Brillouin spectroscopy to dramatically improve the spectral extinction and efficiency of the setup.33,34 The development of a clinically viable Brillouin microscope and the first Brillouin measurement of the human eye in vivo were reported in 2012. For clinical use, the instrument employs low-power laser light at 780 nm, which is scanned across each location of the eye for about 100 ms, and a Brillouin spectrometer optimized for the infrared wavelength.35

6. Brillouin microscopy of keratoconic corneas One of the most promising applications of Brillouin microscopy is within the field of keratoconus and corneal ectasia. Keratoconus is the most common corneal degeneration in the US36 and the leading cause for corneal transplantation.37 Undetected keratoconus is also responsible for most cases of corneal ectasia after refractive surgery.38,39 The clinical presentation of keratoconus is corneal thinning and steepening. However, this morphological manifestation is probably the last stage of the progression of a degenerative disorder, which probably starts with a genetic predisposition40 and is driven by a mechanical imbalance in

Copyright © 2018. Kugler Publications. All rights reserved.

166

the anterior segment of the eye.41 In fact, in healthy corneas, normal shape is maintained as the mechanical strength of stromal collagen fibers resists to the outward intraocular pressure. In contrast, keratoconic corneas have been shown to have altered collagen organization42,43 and reduced number of crosslinks,44 which hint at a reduced structural stability of keratoconic corneas.45 Brillouin optical microscopy is uniquely capable of testing whether keratoconic corneas present a loss of mechanical strength. Recent results for the analysis of keratoconus are particularly encouraging in this respect.46,47 Brillouin imaging was performed on advanced keratoconic corneas vs healthy samples both ex vivo and in vivo. Tissue samples from normal donor corneas used in Descemet’s stripping endothelial keratoplasty (DSEK) and advanced keratoconic corneas from patients undergoing deep anterior lamellar keratoplasty (DALK) were used for ex-vivo analysis. For in-vivo analysis, patients with advanced keratoconus were recruited and measured just before undergoing DALK surgery. The results of ex-vivo and in-vivo investigations are remarkably consistent. Keratoconus corneas presented overall lower Brillouin shift, indicating reduced mechanical stability. Most importantly, the spatial distribution of elastic modulus across the cornea reveals stark differences. The Brillouin shift of the normal cornea is relatively uniform laterally across the central region. By contrast, the keratoconic corneas present a strong spatial variation. Within the cone, the anterior Brillouin shift is substantially lower than that of normal corneas by about 100 MHz, which corresponds to a 2-3% reduction in longitudinal modulus, and to approximately a 70% reduction in Young’s modulus based on the empirical conversion factor measured with the porcine cornea tissue samples. Away from the cone, the elastic modulus and its depth dependence are very different from the cone region, and apparently, comparable to the normal cornea. Hence, Brillouin microscopy has provided the first experimental proof that a spatial asymmetry in the distribution of elastic modulus exists in keratoconic corneas, whereas it is not present in normal corneas. This is particularly important because, from a mechanical standpoint, a localized loss of mechanical strength could be a crucial driver of the progression

G. Scarcelli and S.H. Yun

of keratoconus.48 In this scenario, the spatial variation of Brillouin mechanical signatures seems a promising metric to detect the early onset and progression of keratoconus. Establishing the relationship between this mechanical instability and the morphological changes will be crucial to evaluate the diagnostic and prognostic potential of this novel technique for keratoconus patients and, potentially, for screening of at-risk subjects for post laser-assisted in situ keratomileusis (LASIK) ectasia.

7. Future directions Brillouin microscopy has the potential of providing high-resolution maps of corneal elasticity, thus filling this need. In the long term, biomechanical measurement of corneal elasticity is expected to reduce the errors in the tonometric measurement of true intraocular pressure.49,50 In the short term, the first application of Brillouin technology, as we have seen, is related to keratoconus and corneal ectasia. Early diagnosis of ectasia and keratoconus could allow patients to receive interventions such as corneal crosslinking (CXL), which increases the elastic modulus of the cornea51 to halt disease progression. Identification of early keratoconus and assessment of its progression status, as well as monitoring CXL mechanical outcomes are immediate application targets for Brillouin microscopy. A clinical device that could measure relevant biomechanical properties of the cornea through Brillouin microscopy could find widespread application in both ophthalmic research and clinical practice. While the current standard of care is structural analysis by pachymetry and topography, the biomechanical properties of the cornea are also known to be an important indicator of corneal health, but have proven heretofore difficult to measure. Currently available Brillouin microscopes have reached the level of performance required to enable clinical testing. Clinical studies to test the potential of Brillouin microscopy to characterize keratoconus and ectasia patients as well as CXL procedures have begun. However, a major component of the future of Brillouin microscopy remains linked to its technology development. The difference between an advanced case of keratoconus and a healthy cornea is very

Brillouin microscopy

notable. However, earlier stages of the disease are expected to show much smaller mechanical differences. Given the current level of mechanical sensitivities of in-vivo instruments, Brillouin technology offers about ten separable categories for the stratification of patients into different disease stages. A strong focus is therefore placed towards technological improvements that could enhance the sensitivity of the mechanical measurements. These efforts can go into two directions: on one hand, the best of Brillouin spectrometers still introduces ~10dB losses, therefore, novel spectral analysis solutions at high throughput are needed; on the other hand, the sensitivity achieved by in-vivo instruments is currently limited by spectral drifts and jitters due to environmental factors such

167

as temperature variations or laser instabilities; as a result, if, for example, locking mechanisms or absolute frequency standards were to be used for calibration, higher sensitivities could be achieved. Importantly, all the experiments so far reported have used much smaller illumination levels than those routinely used in other ophthalmic instruments; therefore, improved speed and sensitivity could be expected by increasing the light power used for Brillouin measurements. From a translational perspective, it is hoped that engineering efforts in the near future will make Brillouin microscopy portable, easy to operate by non-experts, and economical by lowering the cost of the instrument. It is foreseeable that such technological development will crucially advance the widespread use of the technology.

References

Copyright © 2018. Kugler Publications. All rights reserved.

1.

Cummins HZ, Gammon RW. Rayleigh and Brillouin scattering in liquids: the Landau-Placzek ratio. J Chem Phys. 1966;44(7):2785-1796 2. Nguyenvo NM, Pfeifer SJ. A model of spontaneous Brillouin-scattering as the noise source for stimulated scattering. IEEE J Quantum Electron. 1993;29:508-524. 3. Faris GW, Jusinski LE, Hickman AP. High-resolution stimulated Brillouin gain spectroscopy in glasses and crystals. J Opt Soc Am B. 1993;10:587-599. 4. Meek KM, Leonard DW, Connon CJ, Dennis S, Khan S. Transparency, swelling and scarring in the corneal stroma. Eye. 2003;17:927-936. 5. Patel S, Alio JL, Perez-Santonja JJ. Refractive index change in bovine and human corneal stroma before and after LASIK: A study of untreated and re-treated corneas implicating stromal hydration. Invest Ophthalmol Vis Sci. 2004;45:3523-3530. 6. Mofrad MRK, Kamm RD, Cytoskeletal Mechanics. New York: Cambridge University Press; 2006. 7. Schreiber E, Anderson OL, Soga N. Elastic constants and their measurement. McGraw-Hill; 1973. 8. Scarcelli G, Pineda R, Yun S. Brillouin optical microscopy for corneal biomechanics. Invest Ophthalmol Vis Sci. 2014;55(7):4490-4495. 9. Kohlhaas M, Spoerl E, Schilde T, Unger G, Wittig C, Pillunat LE. Biomechanical evidence of the distribution of cross-links in corneas treated with riboflavin and ultraviolet A light. J Cataract Refract Surg. 2006;32:279-283. 10. Muller LJ, Pels E, Vrensen G. The specific architecture of the anterior stroma accounts for maintenance of corneal curvature. Br J Ophthalmol. 2001;85:437-443. 11. Randleman JB, Dawson DG, Grossniklaus HE, B. E. McCarey BE, Edelhauser HE, Depth-dependent cohesive tensile strength in

12.

13. 14.

15. 16.

17. 18.

19.

20.

21. 22.

human donor corneas: Implications for refractive surgery. J Refract Surg. 2008;24:85-89. Scarcelli G, Kim P, Yun S. In vivo measurement of age-related stiffening in the crystalline lens by Brillouin optical microscopy. Biophys J. 2011;101:1539-1584. Deng LH, Trepat X, Butler JP, et al. Fast and slow dynamics of the cytoskeleton. Nat Mater. 2006;5:636-640. Fabry B, Maksym GN, Butler JP, Glogauer M, Navajas D, Fredberg JJ. Scaling the microrheology of living cells. Phys Rev Lett. 2001;87:1481021-1481024. Gittes F, MacKintosh FC. Dynamic shear modulus of a semiflexible polymer network. Phys Rev E. 1998;58:R1241-R1244. Jonas M, Huang HD, Kamm RD, So PTC, Fast fluorescence laser tracking microrheometry, II: Quantitative studies of cytoskeletal mechanotransduction. Biophys J. 2008;95:895-909. Duck FA. Physical Properties of Tissue. London: Academic; 1990. Holm S, Sinkus R. A unifying fractional wave equation for compressional and shear waves. J Acoust Soc Am. 2010;127:542548. Scarcelli G, Kling S, Quijano E, Pineda R, Marcos S, Yun SH. Brillouin microscopy of collagen crosslinking: noncontact depth-dependent analysis of corneal elastic modulus. Invest Ophthalmol Vis Sci. 2013;54:1418-1425, Feb 2013. Brillouin L. Diffusion de la lumiere et des rayonnes X par un corps transparent homogene; influence del’agitation thermique. Ann Phys. (Paris). 1922;9(17):88-122. Dil JG. Brillouin-scattering in condensed matter. Rep Prog Phys. 1982;45:285-334.. Eloranta EW. High Spectral Resolution Lidar in Lidar: Range-Resolved Optical Remote Sensing of the Atmosphere. In: Springer Series in Optical Sciences. K. Weitkamp, Ed. New York: Springer-Verlag; 2005.

168

Copyright © 2018. Kugler Publications. All rights reserved.

23. Harley R, James D, Miller A, White JW. Phonons and elastic-moduli of collagen and muscle. Nature. 1977;267:285-287. 24. Randall J, Vaughan JM. Brillouin-scattering in systems of biological significance. Phil Trans R Soc Lond A. 1979;293:133-140. 25. Vaughan JM, Randall JT. Brillouin-scattering, density and elastic properties of the lens and cornea of the eye. Nature. 1980;284:489-491. 26. Sandercock JR. Some recent developments in Brillouin-scattering. RCA Rev. 1975;36:89-107. 27. Sandercock JR. Light-scattering from surface acoustic phonons in metals and semiconductors. Solid State Commun. 1978;26:547-551. 28. Itoh S. Very rapid nonscanning Brillouin spectroscopy using fixed etalons and multichannel detectors. Jpn J Appl Phys Pt 1. 1998;37:3134-3135. 29. Koski KJ, Yarger JL. Brillouin imaging. App Phys Lett. 2005; 87(6):061903. 30. Scarcelli G, Yun SH. Brillouin confocal microscopy for three-dimensional mechanical imaging. Nat Photonics. 2008;2:39-43. 31. Shirasaki M. Large angular dispersion by a virtually imaged phased array and its alication to a wavelength demultiplexer. Opt Lett. 1996;21: 366-368. 32. Xiao SJ, Weiner AM, Lin C. Experimental and theoretical study of hyperfine WDM demultiplexer performance using the virtually imaged phased-array (VIPA). J Lightwave Technol. 2005;23:1456-1467. 33. Scarcelli G, Kim P, Yun SH. Cross-axis cascading of spectral dispersion. Opt Lett. 2008;33:2979-2981. 34. 34.Scarcelli G, Yun SH. Multistage VIPA etalons for high-extinction parallel Brillouin spectroscopy. Opt Express. 2011;19:10913-10922. 35. Scarcelli G, Yun SH. In vivo Brillouin optical microscopy of the human eye. Opt Express. 2012;20:9197. 36. Krachmer JH, Feder RS, Belin MW. Keratoconus and related noninflammatory corneal thinning disorders. Surv Ophthalmol. 1984;28: 293-322. 37. Jun AS, Cope L, Speck C, et al. Subnormal cytokine profile in the tear fluid of keratoconus patients. Plos One. 2011; Jun AS, Cope L, Speck C, et al. Subnormal cytokine profile in the tear fluid of keratoconus patients. Plos One. 2011; 6(1):e164376. 38. Rabinowitz Y. Ectasia after laser in situ keratomileusis, Curr Opin Ophthalmol. 2006;17:421-427.

G. Scarcelli and S.H. Yun 39. Binder PS, Lindstrom RL, Stulting RD, et al. Keratoconus and corneal ectasia after LASIK, J Refract Surg. 2005;21:749-752. 40. Lu Y, Vitart V, Burdon KP, et al. Genome-wide association analyses identify multiple loci associated with central corneal thickness and keratoconus. Nature Genet. 2013;45:155-163. 41. Roy AS, Dus WJ Jr. Patient-specific computational modeling of keratoconus progression and differential responses to collagen cross-linking. Invest Ophthalmol Vis Sci. 2012;52:9174-9187. 42. Meek K, Tuft S, Y. Huang Y, et al. Changes in collagen orientation and distribution in keratoconus corneas. Invest Ophthalmol Vis Sci. 2005;46,:1948-2004. 43. Morishige N, Wahlert AJ, Kenney MC, et al. Second-harmonic imaging microscopy of normal human and keratoconus cornea. Invest Ophthalmol Vis Sci. 2007;48(3):1087-1094. 44. Zimmermann DR, Fischer RW, Winterhalter KH, Witmer R, Vaughan L. Comparative studies of collagens in normal and keratoconus corneas. Exp Eye Res. 1998;46:431-442. 45. Petsche SJ, Pinsky PM. The role of 3-D collagen organization in stromal elasticity: a model based on X-ray diffraction data and second harmonic-generated images. Biomech Model Mechanobiol. 2014;12:1101-1113. 46. Scarcelli G, Besner S, Pineda R, Yun SH. Biomechanical characterization of keratoconus corneas ex vivo with Brillouin microscopy. Invest Ophthalmol Vis Sci. 2014;55:4490-4495. 47. Scarcelli G, Besner S, Pineda R, Kalout P, Yun SH. In vivo biomechanical imaging of normal and keratoconus corneas. JAMA Ophthalmol. 2015;133(4):480-482. 48. Roberts CJ, Dus WJ Jr. Biomechanics of corneal ectasia and biomechanical treatments. J Cataract Refract Surg. 2014;40:991998. 49. Liu J, Roberts CJ. Influence of corneal biomechanical properties on intraocular pressure measurement - Quantitative analysis. J Cataract Refract Surg. 2005;31:146-155. 50. Pepose JS, Feigenbaum SK, Qazi MA, Sanderson JP, Roberts CJ. Changes in corneal biomechanics and intraocular pressure following LASIK using static, dynamic, and noncontact tonometry. Am J Ophthalmol. 2007;143:39-47. 51. Wollensak G. Crosslinking treatment of progressive keratoconus: new hope. Curr Opin Ophthalmol. 2006;17:356-360.

12. Deformation response to an air puff: clinical methods Katie Hallahan1, William J. Dupps Jr.1,2, Cynthia J. Roberts3 Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA; 2Department of Biomedical Engineering, Case Western Reserve University, Cleveland, OH, USA; 3Department of Ophthalmology & Visual Science, Department of Biomedical Engineering, The Ohio State University, OH, USA 1

1. Introduction

Copyright © 2018. Kugler Publications. All rights reserved.

Current clinical tools that measure in-vivo corneal biomechanics include non-contact methods that employ an air puff perturbation. The Ocular Response Analyzer (ORA, Reichert Inc., Depew, NY, USA) and Corneal Visualization Scheimpflug Technology (Corvis ST, Oculus Optikgeräte GmbH, Wetzlar, Germany) are commercially available devices (Fig. 1) that characterize the cornea’s deformation response to an air puff. They have been used to investigate biomechanics in the setting of keratoconus and various systemic diseases, as well as to quantify the changes associated with interventions such as refractive surgery and corneal crosslinking.

Fig. 1a. Ocular Response Analyzer.100

Fig. 1b. Corvis ST.100

Correspondence: Cynthia J. Roberts PhD, Department of Ophthalmology & Visual Science, The Ohio State University, 915 Olentangy River Road, 5th Floor, Columbus, OH 43212, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 169-186 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

170

2. Air puff based biomechanical assessment devices

Copyright © 2018. Kugler Publications. All rights reserved.

2.1. ORA The ORA is a modified non-contact tonometer that indirectly measures aspects of the corneal biomechanical deformation response during application of a high-speed air puff. Applanation events during corneal deformation and recovery of form are indicated by two peak intensities of reflected infrared (IR) light while pressure from an air puff of approximately 25-30 ms duration is applied. The air puff pressure profile is varied with each measurement according to the real-time deformation response, and is thus variable in both length and maximum amplitude. Eyes with lower intraocular pressure (IOP) receive a lower maximum air pressure, and eyes with a higher IOP receive a higher maximum air pressure.1 The ORA initially reported two biomechanical parameters — Corneal Hysteresis (CH) and Corneal Resistance Factor (CRF) — which describe the viscoelastic damping capabilities of the cornea and associated structures.2 CH is calculated as the difference between the pressures recorded at the inward and outgoing applanation events, where a higher CH reflects a greater capacity for the absorption of kinetic energy (Fig. 2). CRF is calculated as the pressure at the first applanation time point minus the pressure at corneal applanation during recovery of form, weighted by an empirical adjustment to account for central corneal thickness. This formula biases CRF towards the pressure associated with the ingoing applanation event and thus, the initial elastic resistance of the cornea. Additionally,

Fig. 2. Signal diagram from the ORA.2

K. Hallahan, W.J. Dupps, Jr and C.J. Roberts

the ORA reports a Goldmann-correlated IOP (IOPg) and a cornea-compensated IOP (IOPcc), the latter designed to be less sensitive to corneal properties compared to traditional applanation tonometry.3 The exact relationship of ORA parameters, such as CH and CRF, to classical biomechanical properties, such as elastic modulus, is poorly defined. Hysteresis in classical mechanics is calculated as the area within the loading and unloading stress-strain loop of a viscoelastic material, and represents the energy dissipated by the material (Fig. 3).4,5 Glass et al. developed a model to show how viscosity and elasticity affect CH, which represents a difference in surface shape vs air pressure between loading and unloading. They demonstrated that low CH could be associated with high or low elasticity depending on the viscosity; thus, no direct relationship between CH and corneal elastic modulus was established.6 CH and CRF have shown variability and overlap between normal corneas and corneas in different disease states, to be described later in this chapter. Moreover, a range of values for CH and CRF have been described for normal corneas, as researchers report these values for their healthy controls in a variety of studies. These mean values have ranged from 9.3 ± 1.4 mmHg7 to 11.4 ± 1.4 mmHg8 for CH, and 9.2 ± 1.4 mmHg9 to 11.9 ± 1.5 mmHg10 for CRF. However, CH and CRF can be influenced by IOP and age, which may explain the spread in these parameters for normal corneas. The relationship between ORA parameters and patient age has also been investigated. Some studies found that increased age correlates with decreased CH and CRF,11,12 whereas others found no correlation.13

Fig. 3. Example of stress-strain curve for a viscoelastic material.

Deformation response to an air puff: clinical methods

171

Copyright © 2018. Kugler Publications. All rights reserved.

Table 1. Second generation Ocular Response Analyzer parameters Name (derived from upper 75% of applanation peak)

Name (derived from upper 50% of applanation peak)

aindex

 

Degree of non-monotonicity of rising and falling edges of peak 1, normalized by area

bindex

 

Degree of non-monotonicity of rising and falling edges of peak 2, normalized by area

p1area

p1area1

Area of peak1

p2area

p2area2

Area of peak2

aspect1

aspect11

Aspect ratio of peak1 (height/width)

aspect2

aspect21

Aspect ratio of peak2 (height/width)

uslope1

uslope11

Upslope of peak1

uslope2

uslope21

Upslope of peak2

dslope1

dslope11

Downslope of peak1

dslope2

dslope21

Downslope of peak2

w1

w11

Width of peak1 at base of peak1

w2

w21

Width of peak2 at base of peak2

h1

h11

Height of peak1

h2

h21

Height of peak2

dive1

 

Absolute value of monotonic decrease on downslope part of peak1 starting at the peak value

dive2

 

Absolute value of monotonic decrease on downslope part of peak2 starting at the peak value

path1

path11

Absolute value of path length around peak1

path2

path21

Absolute value of path length around peak2

mslew1

 

Maximum single-step increase in rise of peak1

mslew2

 

Maximum single-step increase in rise of peak2

slew1

 

Aspect ratio of dive1 (value of dive divided by width of dive region)

slew2

 

Aspect ratio of dive2 (value of dive divided by width of dive region)

aplhf

 

High frequency noise in region between peaks

Description

While some evidence exists that the cornea becomes significantly stiffer with age, possibly secondary to non-enzymatic crosslinking affecting stromal collagen fibrils,14,15 this effect on CH and CRF has not been well-defined and is most likely non-linear. Second generation ORA parameters were introduced with the release of ORA software version 4.01. An additional 37 parameters were derived from mathematical analyses of the ORA output infrared (IR) and pressure signals (Table 1 and Fig. 4). These parameters examine features of the applanation peaks such as area, slope, width, and height. Given that the derivation of the new parameters was done with a stochastic approach, their relationship to specific biomechanical properties remains unclear. Research groups have also independently derived custom parameters from the ORA signals. The

Fig. 4. Example of select ORA second generation parameters.100

172

K. Hallahan, W.J. Dupps, Jr and C.J. Roberts

Table 2. Ocular Response Analyzer custom parameters19

Operational Definition

Related to

1: Applanation A1 Signal Intensity

Peak intensity of 1st applanation event

Maximum surface area achieving planarity during inward deformation

 

A2

Peak intensity of 2nd applanation event

 

ApplanationPeakDiff

A2 – A1

Maximum surface area achieving planarity during recovery Difference in maximum planarity between inward and recovery phases

Group

Variable

 

ConcavityMin

 

ConcavityMean

Depth and irregularity (non-planarity) of deformation Depth and irregularity of deformation, averaged

Difference in applanation pressures, weighted toward pressure required to produce the first 2: Pressure P1 - 0.7P2 applanation, maximizes correlation to central corneal thickness Difference in pressures between the two Corneal Hysteresis   applanation events (a single cross-section of P2 - P1 (CH), mmHg the pressure-deformation relationship) Average of the pressures at the two applanation   P1P2Avg (P1+P2)/2 events Peak value of Force and time required to reach first   Pmax pressure signal applanation event 3: Response Time lapse between Temporal delay of deformation recovery ConcavityDuration Time (msec) A1 and A2 between applanation events Time lapse Temporal delay of deformation recovery ConcavityDuration_   between A1 and A2, between applanation events, normalized by IOPcc normalized by IOPcc IOPcc Time from onset of Time required to achieve maximum   ConcavityTime applied pressure to deformation from onset of impulse ConcavityMin Time between Pmax Delay between peak applied pressure and   LagTime and ConcavityMin maximal deformation Time from onset of Time required to achieve first applanation from ApplanationOnsetTime   applied pressure onset of impulse (AOT) to A1 Corneal Resistance Factor (CRF), mmHg

Copyright © 2018. Kugler Publications. All rights reserved.

Minimum applanation intensity between A1 and A2 Mean applanation intensity between A1 and A2

Deformation response to an air puff: clinical methods

Group

Variable

4: Applanation Intensity and SlopeUp Response Time (msec-1)  

SlopeDown

Copyright © 2018. Kugler Publications. All rights reserved.

5: Pressure and Hysteresis Loop Area Applanation (HLA) Intensity

 

Hysteresis Loop Area Closed Form (HLAc)

6: Pressure and Time

Impulse

 

P_rate

173

Operational Definition

Related to

Positive slope of the first applanation peak, from Rate of achieving peak planarity inflection point to peak Negative slope of the first applanation peak, from peak to inflection point Area enclosed by pressure vs applanation function (Figure 1B) HLA plus interpolated region between applanation events (Figure 1C) Area under pressure vs time curve Slope of pressure vs. time from onset to peak pressure

amplitudes of the IR peaks have been related qualitatively to stiffness, with higher peak amplitude associated with greater stiffness.16-18 Using a comprehensive mechanical perspective, Hallahan et al. approached describing the material behavior of the cornea in terms of time and magnitude of the air puff perturbation with the corneal response throughout the loading and unloading cycle. A panel of custom parameters was derived from the applanation signal intensity, applied pressure, and temporal aspects of the infrared signal (Table 2).19 Touboul et al. suggested a parameter, CH-CRF, as a possible signature of corneal weakness that might be attractive in forme fruste keratoconus screening.20 Avetisov et al. developed an elasticity coefficient from the ORA applanation curve that describes velocity change occurring at the end of applanation.21 The value of exploring other features of the ORA signal has been recognized, and active efforts

Rate of loss of peak planarity

Hysteresis aggregated over entire deformation cycle except concavity

Hysteresis of complete corneal deformation cycle (including concavity)

Air pressure intensity Rate of pressure rise leading to first applanation event (A1)

to derive more information at the signal analysis level are underway. 2.2. Corvis ST Dynamic cross-sectional imaging is another non-contact technique for studying corneal biomechanics. This technology, commercially available as the Corvis ST system, combines cross-sectional imaging and high-speed photography via a Scheimpflug camera (4330 frames/sec) to record the central 8 mm horizontal meridian of the cornea’s multi-phased response to an air puff perturbation.22 The first phase, or ingoing convex phase, captures the cornea passing from its original configuration through applanation, where it enters the ingoing concave phase to a point of highest concavity (HC) deformation. Next, the oscillation phase occurs until the maximum applied pressure is reached, and finally, the cornea undergoes both the outgoing

174

K. Hallahan, W.J. Dupps, Jr and C.J. Roberts

Fig. 5. Phases of Deformation for the Corvis ST. The blue line represents total apex deformation; the green line represents whole eye motion; and the red line is the difference between the two, which represents pure corneal deflection.23

concave phase through second applanation, where it enters the outgoing convex phase and returns to its natural state (Fig. 5).23 The Corvis ST user interface includes graphs that show the corneal deformation amplitude, applanation length, corneal velocity, and other parameters over time. It also reports the parameters of time, length, and velocity at ingoing (A1) and outgoing applanation (A2) events, as well as the time, peak distance, radius based on a best parabolic fit, and deformation amplitude when the cornea is at its highest concavity during the air pressure loading cycle

described (Table 3). Intraocular pressure, a validated biomechanically corrected IOP (bIOP), and corneal pachymetry are also measured by the Corvis ST. Many custom parameters have been extrapolated from the Corvis ST output data, as well. A parameter named Inverse Concave Radius is calculated by plotting the inverse concave radius of the cornea over time of the air pulse and finding the integrated sum between the first and second applanation events. Central-peripheral Deformation Amplitude Ratio describes the ratio between the deformation amplitude at the apex

Copyright © 2018. Kugler Publications. All rights reserved.

Table 3. A subset of Corvis ST parameters Parameter Name

Description

Intraocular Pressure

 

bIOP

Cornea-compensated intraocular pressure estimate derived by finite element modeling

Central Corneal Thickness

 

A1-Time

Time from initiation of air puff to first applanation

A2-Time

Time from initiation of air puff to second applanation

A1-Length

Length of the flattened cornea at first applanation

A2-Length

Length of the flattened cornea at second applanation

Vin

Corneal velocity during the first applanation

Vout

Corneal velocity during the second applanation

Highest Concavity Time

Time from initiation of air puff until the highest concavity of the cornea is reached

Highest Concavity Curvature

Central curvature radius at the highest concavity

Peak Distance

Distance between the two surrounding corneal peaks at highest concavity

Deflection Amplitude

Corneal apex displacement in reference to its initial state

Deformation Amplitude

Maximum deformation amplitude at the corneal apex from initiation of air puff to highest concavity (includes whole eye movement and pure corneal deflection)

Deformation response to an air puff: clinical methods

175

and the average deformation amplitude in a nasal and temporal zone 1 mm from the central cornea. Central-peripheral Deflection Amplitude Ratio is calculated similarly, only it uses the Deflection Amplitude and a peripheral zone of 2 mm. These ratio-based parameters are thought to increase in corneas that are less resistant to deformation; ectatic corneas would have higher values, for example. Delta Arc Length reflects the change of the arc length during the highest concavity moment from the cornea’s resting state in a defined 7 mm zone.24 Steinberg et al. introduced new parameters named Applanation Length Level and Deflection Length Level. The Applanation Length Level was calculated by finding the median applanation length within pre-defined frames between the first and second applanation events. Deflection Length Level was calculated by finding the median deflection length within twelve frames of the maximum deflection length.25 Other independently derived biomechanical parameters for the Corvis ST continue to be developed. The correlation between Corvis ST parameters and other ocular characteristics in normal eyes has been studied with multiple findings. In one study, no parameters were associated with sex.26 In another, Peak Distance correlated positively with sex.27 With

regards to age, correlations have been variable. Valbon showed no association between age and Corvis ST biomechanical parameters, with the exception of Highest Concavity Time.28 Using linear modeling, Asoaka found A1-Length, A2-Time, Vout, and maximum Deformation Amplitude to all be dependent on age to some extent.27 A separate study showed that, primarily, whole eye movement followed by Deformation Amplitude Ratio and Inverse Concave Radius were most influenced by age.24 Several Corvis ST biomechanical metrics have been shown to be influenced by central corneal thickness (CCT) to variable extent. Again, using linear modeling, Asoaka’s group demonstrated that A2-Length and Vout were dependent on central pachymetry.27 CCT also correlated with Highest Concavity Curvature, Deformation Amplitude Ratio, and Deflection Amplitude Ratio.24 In a separate large study of 1262 eyes, A1-time and Highest Concavity Curvature trended strongly with CCT.29 Finally, IOP has been shown to be not only the strongest predictor of Deformation Amplitude with the Corvis ST, but also to influence other parameters.30,31 A biomechanically corrected estimate of IOP (bIOP), which included finite element modeling in its

Pachymetry Group (μm)

Normality

Peak Distance

Highest Concavity Curvature

Inverse Concave Radius

Vin

Vout

Deformation Amplitude

HC Deflection Amplitude

Whole Eye Movement

HC Deflection Area

Highest Concavity Delta Arc Length

Deformation Amplitude Ratio

Deflection Amplitude Ratio

Copyright © 2018. Kugler Publications. All rights reserved.

Table 4. Minimum and maximum pachymetry normative values for selected Corvis ST parameters24

< 520

Min

4.513

5.737

0.111

0.13

-0.546

0.892

0.709

0.131

2.228

-0.182

1.49

4.107

 

Max

5.608

8.198

0.161

0.197

-0.256

1.279

1.115

0.413

4.471

-0.082

1.727

6.12

520 to 546

Min

4.523

5.811

0.106

0.128

-0.559

0.879

0.707

0.126

2.303

-0.186

1.498

4.11

 

Max

5.536

8.619

0.16

0.199

-0.237

1.263

1.094

0.408

4.322

-0.091

1.724

6.031

547 to 573

Min

4.371

5.897

0.103

0.116

-0.513

0.826

0.662

0.142

2.112

-0.189

1.451

3.783

 

Max

5.553

8.895

0.152

0.195

-0.228

1.263

1.078

0.405

4.274

-0.09

1.697

5.909

> 573

Min

4.238

5.813

0.095

0.109

-0.468

0.814

0.63

0.145

2.017

-0.179

1.452

3.817

 

Max

5.44

9.564

0.15

0.195

-0.204

1.196

1.008

0.429

3.915

-0.093

1.641

5.553

176

K. Hallahan, W.J. Dupps, Jr and C.J. Roberts

development,32 was found to influence all parameters with the exception of Deflection Amplitude (DA) Ratio, Highest Concavity (HC) Radius of Curvature, and Inverse Concave Radius.24 A1-Time, A2-Time, Vin, Vout, and maximum Deformation Amplitude positively correlated with IOP by Goldmann applanation.27 Furthermore, A1-Time, A2-Time, and Deformation Amplitude showed significant differences by IOP when data were stratified by CCT.29 The non-linear properties of the cornea are the source of this relationship, such that as load (IOP) increases, the cornea becomes stiffer. Thus, IOP must be taken into account in any clinical evaluation of biomechanical properties. As mentioned, the three parameters that are the least affected by IOP are DA Ratio, HC radius of curvature, and Inverse Concave Radius. Therefore, these should be the focus of biomechanical comparisons when IOP is not matched between groups. The range of Corvis ST parameter values in normal corneas has been investigated and continues to be defined amongst different populations. In a study of healthy Brazilian patients with an age of 35.80 ± 12.83 years, the following mean values were found: mean Deformation Amplitude: 1.05 ± 0.08 mm; Highest Concavity Time: 18.83 ± 0.93 ms; A1-Time: 8.32 ± 0.33 ms; A2-Time: 23.80 ± 0.44 ms; A1-Length: 2.07 ± 0.38 mm; A2-Length: 2.37 ± 0.47 mm; Highest Concavity Curvature: 11.09 ± 2.06 mm; Vin: 0.21 ± 0.05 m/s; and Vout: 0.33 ± 0.07 m/s.26 However, given the influence

of other ocular characteristics on biomechanical parameters, as discussed above, it has been suggested that parameters be corrected for these associations, or at least interpreted in light of differences in IOP. This was done after an analysis of Corvis ST data from a cohort of 705 healthy patients in a multicenter study, where Vinciguerra et al. provided normative biomechanical parameter values, corrected for CCT, age, and bIOP (Tables 4, 5, and 6), to be discussed in Chapter 13.24

3. Measuring corneal biomechanical characteristics in disease states 3.1. Keratoconus Keratoconus (KC) is an ectatic disease that often requires specialty contact lens wear or corneal transplantation for visual rehabilitation. Its diagnosis is confirmed based on characteristic corneal topographic signs and slit lamp microscopy criteria.33 However, the diagnosis of forme fruste kerataconus (FFKC) is an area of ongoing research, as it is difficult to predict based on topography alone and in the absence of clinical findings.34-36 In this context, the characterization of biomechanical properties in normal and pathologic corneas may provide insight into the mechanism of ectatic disease and aid diagnosis. Using the ORA, low CH and CRF have been associated with ectatic disease.37-39 For example, a study by Shah

Deflection Amplitude Ratio

Deformation Amplitude Ratio

Highest Concavity Delta Arc Length

HC Deflection Area

Whole Eye Movement

HC Deflection Amplitude

Deformation Amplitude

Vout

Vin

Inverse Concave Radius

Highest Concavity Curvature

Peak Distance

Normality

bIOP Group (mm Hg)

Copyright © 2018. Kugler Publications. All rights reserved.

Table 5. Minimum and maximum bIOP normative values for selected Corvis ST parameters24

< 13.2

Min

4.65

5.844

0.107

0.13

-0.615

0.964

0.735

0.156

2.458

-0.19

1.465

3.698

 

Max

5.648

8.453

0.154

0.198

-0.229

1.305

1.153

0.438

4.627

-0.101

1.739

6.127

13.2 to 14.9

Min

4.651

5.946

0.105

0.132

-0.529

0.924

0.739

0.163

2.475

-0.188

1.459

3.773

 

Max

5.535

8.577

0.157

0.196

-0.261

1.259

1.092

0.407

4.339

-0.097

1.733

6.184

14.9 to 16.5

Min

4.474

6.056

0.101

0.126

-0.489

0.876

0.699

0.13

2.276

-0.182

1.471

3.859

 

Max

5.427

10.089

0.16

0.194

-0.253

1.188

1.037

0.38

4.039

-0.087

1.704

6.086

> 16.6

Min

4.324

5.69

0.099

0.107

-0.478

0.827

0.651

0.114

2.098

-0.084

1.466

4.008

 

Max

5.227

9.685

0.16

0.195

-0.207

1.114

0.963

0.379

3.612

-0.167

1.686

5.922

Deformation response to an air puff: clinical methods

177

Deflection Amplitude Ratio

Deformation Amplitude Ratio

Highest Concavity Delta Arc Length

Whole Eye Movement

HC Deflection Area

HC Deflection Amplitude

5.556

0.104

0.124

-0.552

0.837

0.679

0.123

2.173

-0.188

1.481

3.897

 

Max

5.535

8.81

0.161

0.195

-0.235

1.25

1.096

0.359

4.339

-0.087

1.729

6.191

32 to 45

Min

4.441

5.814

0.102

0.125

-0.54

0.851

0.686

0.15

2.228

-0.178

1.487

3.943

 

Max

5.55

8.651

0.161

0.204

-0.219

1.26

1.079

0.383

4.232

-0.091

1.708

6.054

Vout

4.442

Vin

Min

Normality

< 32

Age Group (y)

Deformation Amplitude

Inverse Concave Radius

Highest Concavity Curvature

Peak Distance

Table 6. Minimum and maximum age normative values for selected Corvis ST parameters24

45 to 58

Min

4.387

5.932

0.105

0.121

-0.52

0.885

0.664

0.177

2.107

-0.181

1.451

3.776

 

Max

5.589

8.678

0.151

0.195

-0.226

1.272

1.099

0.441

4.362

-0.094

1.696

5.872

> 58

Min

4.476

6.042

0.104

0.118

-0.532

0.866

0.678

0.197

2.232

-0.189

1.421

3.655

 

Max

5.602

8.964

0.148

0.191

-0.208

1.296

1.091

0.446

4.337

-0.088

1.679

5.91

Copyright © 2018. Kugler Publications. All rights reserved.

.

et al. suggested that keratoconic eyes are less rigid and more compliant than normal corneas. After comparing CH and mean CCT between 207 normal and 93 keratoconic eyes, CH and CCT were found to be significantly lower in KC eyes.37 Others have also demonstrated inverse relationships between CH or CRF and Kmax in KC eyes.20,40 The general trends described above suggested that ORA parameters may be useful in assessing KC progression and severity stages.37 However, when using CH and CRF to distinguish early KC from normal corneas or to define cut-off values within differing KC severity grades, the utility of the ORA was less clear. Schweitzer et al. demonstrated significantly lower values of CH and CRF in forme fruste KC compared to normal eyes.41 However, when Kirwan et al. compared FFKC, KC, and normal eyes, they found no difference in CH and CRF between normal and FFKC eyes. Significant differences were demonstrated only when KC was compared against the combination of FFKC and normals.36 Fontes et al. also failed to show that CH and CRF differed significantly when comparing low-grade KC from the normal state.39 In all published studies, CH and CRF had a high degree of overlap between groups that limited the ORA’s diagnostic utility for keratoconus.36,37,39,41 Moreover, measurements of CH and CRF in KC detection studies were often confounded by CCT41,42 or did not account for differences in IOP, which may alter corneal behavior.36,37,39,41

The ORA did, however, provide a Keratoconus Match Index (KMI) and Keratoconus Match Probability (KMP) which are calculated from a neural network developed from seven ORA parameters. The KMI is a composite value where the average value for the normal population is 1, and for a possible KC patient at any stage, the average value is 0. The KMP shows which population the KMI best matches and to what percentage — normal, KC suspect, KC mild, moderate, or severe. Cut-off values that correspond to KC severity have been suggested for KMI (Healthy: 0.77; KC stage 1: 0.32; KC stage 2: -0.08; KC stage 3: -0.3), but these thresholds have not been validated.43 And while some studies have shown the KMI to have a KC predictive accuracy of 94% 44 to almost 98%,45 Reichert is clear to point out that the ORA does not diagnose disease, and these indices only represent the similarity of a patient’s ORA waveform output to data from reference populations. In addition, these parameters are no longer available on ORA devices, although they are still available in older software versions. The second generation and independently derived ORA parameters have shown promise in their sensitivity to early ectatic disease and stage severity. Mikielewicz et al. found 14 parameters that significantly correlated with KC severity; CRF and p2area were the best performers.46 In another study, P1, dslope1, P2, and dslope2 were significantly different between normal and KC eyes, while CRF, the downslope of P2

Copyright © 2018. Kugler Publications. All rights reserved.

178

derived from the upper 50% of the applanation peak, dslope1, and the upslope of P1 were able to distinguish normal eyes from FFKC.47 When comparing healthy eyes with subclinical KC, significant differences were found in the values of the following parameters: CH, CRF, ccCH, ccCRF, CH-CRF, timein, timeout, deltatime, bindex, p1area, aindex, p2area, aspect1, aspect2, uslope1, uslope2, dslope1, dslope2, w2, h1, h2, dive1, dive2, path1, mslew1, mslew2, slew1, slew2, p1area1, p2area1, aspect21, uslope11, uslope21, dslope21, w21, h11, and h21, but there was significant overlap between normal and ectatic eyes. Even when these factors were placed in a multivariate model to detect subclinical KC, its performance was underwhelming (specificity: 83.9%; sensitivity: 74.0%; area under the curve (AUC): 0.85).42 The custom ORA parameters of Hallahan et al. found that parameters that were related to the depth of corneal deformation performed best when differentiating normal eyes from KC. ConcavityMin (area under the receiver operating characteristic curve (AUROC): 0.985 ± 0.002) and Hysteresis Loop Area (AUROC: 0.967 ± 0.002) outperformed CH and CRF. These parameters also positively trended with KC staging, but a larger sample size would be needed to determine if these variables are useful for disease staging.19 Touboul’s custom parameter, CH-CRF, was greater in KC eyes, and rare in normal and glaucoma study groups.20 Despite further signal analysis using the ORA, no precise model based on ORA biomechanical parameters can easily distinguish eyes at risk for developing KC. Corneal biomechanical properties in KC as measured by the Corvis ST have been investigated as well. In multiple studies, a higher Deformation Amplitude was associated with KC even after controlling for CCT and IOP, but no diagnostic cut-off was identified.48-50 A small study found significant differences between healthy and KC eyes for Deformation Amplitude (normal eyes: 1.08 ± 0.03; KC eyes: 1.26 ± 0.03) and the Highest Corneal Curvature (normal eyes: 7.70 ± 0.26; KC eyes: 5.61 ± 0.26) after adjusting for age, CCT, and IOP.48 In a separate study comparing healthy eyes to eyes with subclinical KC, the Corvis ST parameters that were found to be significantly different between groups after correcting for CCT and IOP included the following: A1-Time (normal eyes: 5.78 ± 0.28 ms; KC eyes: 5.65 ± 0.21 ms), A2-Length (normal eyes: 1.39 ± 0.08; KC eyes: 2.84 ± 0.07), Vout (normal eyes: -0.34 ± 0.07; KC eyes: -0.43 ± 0.07), and

K. Hallahan, W.J. Dupps, Jr and C.J. Roberts

maximum Deformation Amplitude, which was the best isolated discriminate parameter but did not perform strongly (specificity: 79.3%; sensitivity: 53.6%; AUROC: 0.775). When Deformation Amplitude, CCT, and A1-Time were placed in a model, the function performed much better with an AUROC of 0.893, 85,7%, and 82.1%, respectively.49 The custom parameters Applanation Length Level and Deflection Length Level did not outperform the single frame-derived parameters when trying to improve KC screening.25 Finally, in a separate study, Vin was the best predictive parameter of KC with an AUROC of 0.79.51 When examining the ability of Corvis ST parameters to distinguish between KC stages, results have been variable. In a study that divided patients into normal, subclinical KC, KC suspect, manifest KC, and advanced KC groups based on the KISA% index, some parameters changed between groups, but no single parameter consistently differed between stages. For example, A1-Length, A2-Length, Highest Concavity Curvature, and the deflection length at the highest concavity revealed statistically significant differences between normal eyes and KC suspects. Applanation Length Level and Deflection Length Level were significantly different when comparing normal to advanced KC. A2 length showed the highest discriminative power between normal and KC suspect eyes, but generally did not perform well (sensitivity: 67%; specificity: 67%). No parameters differed between normal and subclinical KC.25 In a recent study which matched bIOP between normal and keratoconic subjects, all investigated parameters showed a significant difference between groups. In addition, a novel stiffness parameter was introduced that takes into account the load on the cornea.23 Finally, combining multiple aspects of the cornea including dynamic corneal response parameters and corneal thickness measurements has provided promising discriminatory power in the diagnosis of KC. A combined biomechanical index called the Corvis Biomechanical Index (CBI) was recently developed accounting for several derivatives of Corvis parameters: Deformation Amplitude ratio at 1 and 2 mm, Vin, standard deviation of Deformation Amplitude at highest concavity, Ambrosio’s Relational Thickness to the horizontal profile, and a novel stiffness parameter. The CBI performed well with an AUROC of 0.983, and

Deformation response to an air puff: clinical methods

Copyright © 2018. Kugler Publications. All rights reserved.

the index was validated by an external dataset.52 The CBI and the development of other models that combine biomechanical parameters with biometric markers hold promise in helping to diagnose early KC.

179

3.2. Pellucid marginal degeneration Investigations into the correlation between biomechanical parameters and pellucid marginal degeneration (PMD) have also been conducted. PMD, like KC, is an ectatic disease. It is characterized by inferior peripheral thinning, corneal protrusion superior to maximal thinning, against the rule astigmatism, and characteristic topographic findings.53 Labiris found that KMI had a predictive accuracy of 94% when comparing PMD eyes to normal eyes, but the KMP index identified a significant percentage of topographically-defined PMD eyes as normal.44,54 Likewise, in a separate study, KMI was found to be significantly lower in the PMD group, whereas CH and CRF, even when adjusted for IOP and CCT, did not differ from controls.55 The Corvis ST parameters Deformation Amplitude and A2-Time were significantly different in PMD eyes compared to normal eyes.55 These trends could be helpful for confirming diagnosis or monitoring the progression of PMD. However, it has not been shown whether biomechanical parameters can aid in detecting early disease, and no disease threshold values have been defined.

as detected by spectral-domain optical coherence tomography.57 Another prospective study over four years found that eyes with lower CH had faster rates of visual field loss, with each 1 mmHg lower CH being associated with a 0.25%/year faster rate of visual field index decline. Moreover, the effect of IOP on rates of progression depended on CH.58 The association of lower CH and rapid visual field progression has also been found in normal tension glaucoma patients.59 On the other hand, in cases of primary angle closure glaucoma, no association was found between ORA parameters and glaucoma severity, but this study did not look at progression or compare patients to their baseline value.60 The use of Corvis ST parameters in glaucoma has been investigated to a lesser extent. One study showed that higher A1-Time and lower Deformation Amplitude and A2-Time were significantly different in primary open angle glaucoma patients compared to normal eyes, but the parameters were not used to mark progression or predict glaucoma severity.61 Future studies should examine whether Corvis ST dynamic corneal response parameters are independent risk factors for glaucoma progression. Currently, ORA’s CH likely has some clinical utility in identifying open angle glaucoma patients who are at higher risk for visual field loss and and may therefore need more aggressive treatment.

3.3. Glaucoma Both the ORA and Corvis ST have IOP measuring capabilities, but beyond this function in monitoring glaucoma, investigators have looked at biomechanical parameters as independent markers for progression of glaucomatous disease. The ORA’s CH in particular has emerged as an independent risk factor for visual field loss. As early as 2006, an association between lower CH and higher risk of visual field loss progression was discovered in a cross-sectional study of primary open angle glaucoma patients. In this study, however, CH was not a significant risk factor when axial length was included in a multivariate linear regression model.56 Regardless, several other study groups have identified similar findings. In a prospective observational cohort study over four years, Zhang et al. found that CH had a significant effect on rates of retinal nerve fiber layer loss, where each 1 mmHg lower CH was associated with a 0.13 um/year faster rate of nerve fiber layer decline

3.4. Systemic diseases Some interest has been expressed in investigating the ocular biomechanics in systemic diseases that can affect the eye, such as connective tissue and autoimmune diseases. For example, in conjunction with geometric variables from corneal tomography and optical biometry, Beene et al. investigated the ability of ORA parameters to predict Marfan syndrome, an autosomal dominant connective tissue disorder caused by mutations in FBN1.62 Current diagnosis of Marfan syndrome depends on the Ghent criteria,63 but the ability to diagnose the disease early or in atypical cases continues to be of importance given the possible life-threatening sequelae of vascular-related pathology. Because FBN1 can be found throughout the human eye, examination of Marfan syndrome effects on ocular biomechanics was conducted. ConcavityMin was the best performing single ORA variable (47.5 ± 20.0; AUROC: 0.80) with values being lower in the

Copyright © 2018. Kugler Publications. All rights reserved.

180

study group. Other parameter trends in Marfan corneas included lower ConcavityMean, P1, P2, P1P2Avg, and decreased Hysteresis Loop Area, indicating that the cornea in Marfan syndrome has decreased resistance to bending and a decreased ability to dissipate externally applied energy.64 In comparison to previously published positive likelihood ratios (LR+) for other systemic and ophthalmic manifestations of Marfan syndrome,65 ConcavityMin met the criterion for high diagnostic power (LR+ >10) with an LR+ of 12.9, suggesting that a simple, non-invasive ocular biomechanical measurement may have a role in the clinical diagnosis of Marfan syndrome.64 Associations between biomechanical parameters and the ocular effects of autoimmune disease have also been studied in systemic lupus erythematosus (SLE) and thyroid eye disease (TED). SLE, a chronic inflammatory disease, can cause dry eye, retinal vascular changes, and rarely affect the cornea.66 In a small prospective study, mean CH and CRF were found to be significantly lower in SLE eyes compared to age-matched controls.10 TED, which is often associated with Graves’ disease, can cause extraocular muscle enlargement and lead to orbital congestion and decreased orbital ­compliance.67-69 Using the ORA, CH was found to be significantly lower in TED patients compared to healthy eyes.70 With the Corvis ST, multiple parameters (Deformation Amplitude, Peak Distance, Vout, Highest Concavity Curvature, Highest Concavity Time, A2-Length, A1-Time, A2-Time, and custom parameter Maximum Orbital Deformation) were significantly different between TED and normal eyes, even after adjusting for patient age, gender, IOP, CCT, and maximum keratometry.71 Although the direct utility of this information remains unclear, the authors suggest these biomechanical characteristics should be taken into consideration when measuring IOP or considering refractive surgery in eyes with connective tissue or autoimmune disease.

4. Measurements of corneal biomechanics in response to interventions 4.1. Refractive surgery Characterization of corneal biomechanics has become important in identifying eyes at risk for complications

K. Hallahan, W.J. Dupps, Jr and C.J. Roberts

associated with refractive surgery. For instance, early detection of KC is necessary as the disease is a contraindication for laser in situ keratomileusis (LASIK). Additionally, the identification of patients at risk for post-LASIK ectasia, while rare, represents a matter of significance considering that refractive surgeries are elective.72 Current tools such as topography and central corneal thickness are limited in their ability to screen for ectasia susceptibility.72-74 A renewed interest in better understanding post-refractive surgery corneal biomechanics has emerged in light of reports of post-LASIK keratoectasia with no identifiable preoperative risk factors.75 Studies have used the ORA to investigate these features and identify parameters that could be markers of post-refractive surgery ectasia risk. For instance, Luce suggested that low CH values might be predictors of a “pre-ectatic” state and refractive surgery outcomes.2 CH and CRF have been shown to decrease after refractive surgery, especially after LASIK.2,20,76 In a study by Ortiz et al. comparing ORA measurements between normal, keratoconus, and post-LASIK patients, the keratoconus group presented with significantly lower values of CH and CRF compared to normal eyes and post-LASIK eyes, and a significant decrease in these parameters was observed in the LASIK group one month after surgery.12 When comparing manifest KC to post-femtosecond LASIK eyes using ORA second generation software, multiple parameters differed significantly between groups. After controlling for CCT and age, CH, p1area, upslope1, dslope1, w2, aindix, and aphlf were statistically significant. A multivariate logistic regression model with these parameters performed well when distinguishing pathologic KC eyes from iatrogenic changes associated with femtosecond LASIK (AUROC: 0.932).77 Custom ORA parameters and their response to LASIK and photorefractive keratectomy (PRK) have also been investigated. A retrospective study of 156 eyes of 156 consecutive normal refractive surgery candidates compared corneal biomechanical properties before and after femtosecond-LASIK and PRK with similar myopic ablation. Customized ORA parameters (Table 2), CH, CRF, central corneal thickness, residual stromal bed, and percentage of tissue depth altered (PTA) were measured or calculated preoperatively and postoperatively at month one and three. Investigators noted that

Copyright © 2018. Kugler Publications. All rights reserved.

Deformation response to an air puff: clinical methods

myopic keratorefractive surgery resulted in parameter changes that reflected an increased depth of corneal deformation, lower applanation pressures, more rapid onset of maximum deformation, slower recovery of deformation, and reductions in the comprehensive analog of hysteresis (Hysteresis Loop Area). These changes did not significantly differ between postoperative month one and three. There were no statistically significant differences in surgically induced changes in the biomechanical parameters between LASIK and PRK, possibly due to the fact that much of the biomechanical strength of the cornea resides in the anterior third, and that the flap thickness and amount of myopic treatment in this study preserved sufficient amounts of anterior stroma in both groups. Notably, when correlating ORA parameters to other tissue geometry-related variables in this study, the investigators found that ablation depth and residual stromal bed thickness were incomplete predictors of the biomechanical impact of corneal refractive surgery. However, taken together, preoperative ORA variables and PTA were much stronger predictors of LASIK-induced biomechanical changes.78 In fact, PTA has subsequently been determined to be an important risk metric for ectasia.79,80 Changes in biomechanical parameters per the Corvis ST have also been noted after refractive surgery. A small study by Frings et al. found that A1-Length, A2-Length, mean first and second deflection lengths, mean first and second deflection amplitudes, and Peak Distance all showed statistically significant changes. However, in this study, a microkeratome was used to create the LASIK flap, which could potentially affect post-LASIK corneal biomechanics to a higher proportion than thinner flaps created with a more precise femtosecond laser.81 A separate study attempted to evaluate the biomechanical changes induced by femtosecond laser flap creation alone by comparing Corvis ST parameters before and after flap creation, but before mechanical flap lifting. A significant increase in A1-Length and Vin was noted.82 Interestingly, in an investigation with longer follow-up, early postoperative Corvis ST parameter changes were not sustained. At postoperative month one, no significant differences in a small set of biomechanical parameters for PRK or post-LASIK corneas were found compared to pre-operative measurements.83 However, none of the new, more sensitive

181

deformation parameters were used in this study. While biomechanical parameter trends associated with post-refractive surgery have emerged, a clinically useful ectasia risk nomogram that takes these changes into account has yet to be developed. Attempts to explain the incidence of keratoectasia after LASIK include the suggestion that LASIK might induce a higher risk of viscoelastic failure compared to PRK since it is performed in the deeper layers of the corneal stroma with material properties that are different from anterior stroma.84 Gatinel et al. suggested that flap creation played a role in the reduction of CH values, so that the decrease of biomechanical parameters after LASIK could be attributed to the combination of flap creation and corneal stromal thinning.85 Studies have not clearly supported these theories, however. For example, when comparing CH between LASIK and laser-assisted subepithelial keratectomy (LASEK), Kirwan and O’Keefe found similar reductions in CH following both procedures, indicating that a thin LASIK flap (120 um) did not induce any additional biomechanical compromise as measured by the ORA.86 Similar findings were presented by Slade when assessing the biomechanical effects of PRK and sub-Bowman keratomileusis (SBK), suggesting that PRK offered no biomechanical advantage over SBK.87 With the emergence of small incision lenticule extraction (SMILE) refractive surgery, one might similarly hypothesize SMILE procedures to be more biomechanically stable compared to LASIK. Osman et al. found that CH and CRF decreased significantly after SMILE and LASIK, with the greater percent change being found in LASIK eyes. Using Corvis ST, Deformation Amplitude and Highest Concavity peak distances increased significantly in both the SMILE and LASIK groups. Again, the mean percentage of change was significantly greater in the LASIK group.88 Likewise, in a separate study examining 40 SMILE eyes and 40 femtosecond-LASIK eyes, CH and CRF decreased significantly postoperatively. At three and six months post-procedure, values were significantly lower in the femtosecond LASIK group.89 When comparing eyes treated for more than 6.00 diopters of myopia, CH, CRF, p1area, and p2area decreased after SMILE and, to a significantly greater extent, after LASIK.90 However, not all studies have consistently reproduced these findings. Some have found that while CH and CRF decreased sig-

182

Copyright © 2018. Kugler Publications. All rights reserved.

nificantly after SMILE and femtosecond-LASIK, there were no significant differences in postoperative CH or CRF values between groups.91,92 It is important to note that any negative findings comparing different refractive surgery modalities does not necessarily prove a lack of biomechanical effect of these modalities. The sensitivity of CH and CRF to detect clinically significant alterations in properties remains poorly defined. For example, Kertautret et al. have published a case of unilateral corneal ectasia after bilateral LASIK. The study was designed to evaluate biomechanical differences between normal corneas after LASIK and corneas that developed ectasia. They found analogous results of CH and CRF between both eyes. Nevertheless, the ORA signal shape showed multiple oscillations and diminished spikes in the ectatic eye, advocating that details of the waveform could provide more information to differentiate between an ectatic and a stable cornea postoperatively.16 4.2. Corneal crosslinking Corneal collagen crosslinking (CXL) is an accepted treatment for early stage KC and post-LASIK ectasia. By combining riboflavin and ultraviolet-A photoactivation, CXL has been shown to halt disease progression, likely by increasing corneal biomechanical strength.93 The effects on corneal biomechanics, namely, increased stress measurements94,95 and increased Young modulus,96 have been demonstrated with in-vitro studies. While one would expect a similar reflection in increased corneal strength in vivo, the exact effects continue to be defined through clinical modalities like those that employ an air puff perturbation. In a prospective observational study comparing 50 normal, 100 KC, and 25 post-CXL eyes, significant negative correlations were observed between CH, CRF, and Kmax in KC eyes, whereas no association was found in the normal or crosslinked eyes. The relationship of corneal curvature to ORA biomechanical parameters was similar between normal and crosslinked eyes.40 Other groups, however, have not been able to conclusively correlate biomechanical parameters with changes post-CXL. Greenstein et al. found that, despite an increase in CRF at one month, neither CH nor CRF measurements were significantly different from pre-treatment measurements at one year after CXL.97 Additional

K. Hallahan, W.J. Dupps, Jr and C.J. Roberts

studies similarly found no change in CH or CRF at least three months post-CXL.98,99 Although a small subset of custom derived ORA parameters (ApplanationOnsetTime, P1P2avg, Impulse, and Pmax) increased by a small but statistically significant amount after CXL in a subset of post-refractive surgery ectasia eyes, the magnitude of changes was low and did not commensurate with the degree of clinical improvement following CXL treatment.98 Despite finding no significant difference in CH one year after CXL treatment in another study, significant differences were found in the amplitude of both applanation peaks in the IR signal of the ORA, highlighting the importance of signal analysis.18 Further studies should examine additional characteristics of the ORA waveform and Corvis ST data in order to capture clinical biomechanical changes associated with CXL treatment.

5. Conclusion Air puff based methods for biomechanical assessment have helped drive increased awareness of the importance of corneal and ocular biomechanical behaviors in clinical ophthalmology. The contribution of IOP in the clinical assessment of corneal biomechanical properties is critically important, since higher IOP leads to stiffer corneal behavior. This is especially important when the air puff in a non-contact tonometer is used as the applied load to assess biomechanical deformation response. Since their development, the usefulness of non-contact tonometers has been to provide an estimate of IOP without the need for a topical anesthetic. It should not be surprising that IOP influences the measured response, whether it is by indirect assessment with the ORA or direct visualization with the Corvis ST. The challenge of these current methods lies in interpreting the provided data in a clinically meaningful manner. Not all confounding variables, including IOP, have been controlled in many of the studies presented, and may therefore be the source for some of the inconsistent results. Normative data for the Corvis ST are also presented, accounting for IOP, CCT, and age, which may be clinically useful. As we understand more about interpreting corneal biomechanics, these new parameters can be incorporated into clinical practice.

Deformation response to an air puff: clinical methods

References 1. 2.

3. 4.

5. 6.

7.

8.

9.

10.

11.

12.

13.

Copyright © 2018. Kugler Publications. All rights reserved.

14.

15.

16.

17.

Roberts CJ. Concepts and Misconceptions in Corneal Biomechanics. J Cataract Refract Surg 2014;40(6):862-869. Luce D. Determining in vivo biomechanical properties of the cornea with an ocular response analyzer. J Cataract Refract Surg. 2005;31:156-62. Luce DA. IOVS 2006;47:ARVO E-Abstract 2266. Boyce B, Jones R, Nguyen T, Grazier J. Stress-controlled viscoelastic tensile response of bovine cornea. J Biomech. 2007;40:2367-2376. Kotecha A. What biomechanical properties of the cornea are relevant for the clinician? Surv Ophthalmol. 2007;52:S109-S14 6.Glass DH, Roberts CJ, Litsky AS, Weber PA. A viscoelastic biomechanical model of the cornea describing the effect of viscosity and elasticity on hysteresis. Invest Ophthalmol Vis Sci. 2008;49:3919-3926. Goldich Y, Burkina Y, Gerber Y, et al. Effect of diabetes mellitus on biomechanical parameters of the cornea. J Cataract Refract Surg. 2009; 35(4):715-719. Yeneral NM, Kucumen RB, Gorgun E. Changes in corneal biomechanics in patients with keratoconus after penetrating keratoplasty. Cornea. 2010; 29(11):1247-1251. Emre S, Kayikcioglu O, Ates H, et al. Corneal hysteresis, corneal resistance factor, and intraocular pressure measurement in patients with scleroderma using the reichert ocular response analyzer. Cornea. 2010; 29(6):628-631. Yazici AT, Kara N, Yüksel K, et al. The biomechanical properties of the cornea in patients with systemic lupus erythematosus. Eye. 2011;25:1005-1009. Kamiya K, Shimizu K, Ohmoto F. Effect of aging on corneal biomechanics parameters using the ocular response analyzer. J Refract Surg. 2009;25(10):888-893. Ortiz D, Piñero D, Shabayek MH, Arnalich-Montiel F, Alio JL. Corneal biomechanical properties in normal, post-laser in situ keratomileusis, and keratoconic eyes. J Cataract Refract Surg 2007;33:1371-1375. Kirwan C, O’Keefe M, Lanigan B. Corneal hysteresis and intraocular pressure measurement in children using the Reichert Ocular Response Analyzer. Am J Ophthalmol. 2006;142:990992. Elsheikh A, Wang D, Brown M .Rama P, Campanella M, Pye D. Assessment of corneal biomechanics properties and their variation with age. Curr Eye Res. 2007;32(1):11-19. Sherrard ES, Novakovic P, Speedwell L. Age-related changes of the corneal endothelium and stroma as seen in vivo by specular microscopy. Eye (Lond). 1987;1(Pt 2):197-203. Kerautret J, Colin J, Touboul D, Roberts C. Biomechanical characteristics of the ectatic cornea. J Cataract Refract Surg. 2008;34:510-513. Qazi MA, Sanderson JP, Mahmoud AM, Yoon EY, Roberts, CJ, Pepose, JS. Postoperative changes in intraocular pressure and corneal biomechanical metrics: Laser in situ keratomileusis versus laser-assisted subepithelial keratectomy. J Cataract Refract Surg. 2009;35(10):1774-1788.

183 18. Vinciguerra P, Albè E, Mahmoud AM, Trazza S, Hafezi F, Roberts CJ. Intra- and postoperative variation in ocular response analyzer parameters in keratoconic eyes after corneal cross-linking. J Refract Surg 2010;26(9):669-676. 19. Hallahan KM, Sinha Roy A, Ambrosia R Jr, Salomao M, Dupps WJ Jr. Discriminant value of custom ocular response analyzer waveform derivatives in keratoconus. Ophthalmology. 2014; 121(2):459-468. 20. Touboul D, Roberts C, Kérautret J, et al. Correlations between corneal hysteresis, intraocular pressure, and corneal central pachymetry. J Cataract Refract Surg. 2008; 34:616-622. 21. Avetisov SE, Novikov IA, Bubnova IA, Antonov AA, Siplivyi VI. Determination of corneal elasticity coefficient using the ORA database. J Refract Surg. 2010;26:520-524. 22. Bonatti JA, Bechara SJ, Carricondo PC, Kara-José N. Proposal for a new approach to corneal biomechanics: dynamic corneal topography. Arq Bras Oftalmol. 2009;72:264-267. 23. Roberts CJ, Mahmoud AM, Bons JP, et al. Introduction of two novel stiffness parameters and interpretation of air puff induced biomechanical deformation parameters with a dynamic Scheimpflug analyzer. J Refract Surg. 2017;33(4):266273 24. Vinciguerra R, Elsheikh A, Roberts CJ, et al. Influence of pachymetry and intraocular pressure on dynamic corneal response parameters in healthy patients. J Refract Surg. 2016;32(8):550561. 25. Steinberg J, Katz T, Lucke K, Frings A, Druchkiv V, Linke SL. Screening for keratoconus with new dynamic biomechanical in vivo Scheimpflug analyses. Cornea. 2015;34:1404-1412. 26. Valbon BF, Ambrósio R, Fontes BM, Luz A, Roberts CJ, Alves MR. Ocular biomechanics metrics by Corvis ST in healthy Brazilian patients. J Refract Surg. 2014;30(70):468-473. 27. Asaoka R, Nakakura S, Tabuchi H, et al. The relationship between Corvis ST tonometry measured corneal parameters and intraocular pressure, corneal thickness and corneal curvature. PLoS ONE. 2015;10(10):e0140385. 28. Valbon BF, Ambrosia R Jr, Fontes BM, Alves MR. Effects of age on corneal deformation by non-contact tonometry integrated with an ultra-high-speed (UHS) Scheimpflug camera. Arc Bras Oftalmol. 2013;76(4):229-232. 29. Huseynova T, Waring GO 4th, Roberts C, Krueger RR, Tomita M. Corneal biomechanics as a fun action of intraocular pressure and pachymetry by dynamic infrared signal and Scheimpflug imaging analysis in normal eyes. Am J Ophthalmal .2014;157(4):885-893. 30. Kling S, Marcos S. Contributing factors to corneal deformation in air puff measurements. Invest Ophthalmol Vis Sci. 2013; 54:5078–5085. 31. Roberts CJ, Mahmoud AM, Ramos I, Caldas D, Siqueira da Silva R, Ambrosio R Jr. Factors influencing corneal deformation and estimation of intraocular pressure. IOVS 2011;52:ARVO EAbstract 4384. 32. Joda AA, Shervin MMS, Kook D, Elsheikh A. Development and validation of a correction equation for Corvis tonometry. Comput Methods Biomech Biomed Engin. 2015;1-11.

Copyright © 2018. Kugler Publications. All rights reserved.

184 33. Holladay J. Keratoconus detection using corneal topography. J Refract Surg. 2009;25:S958-S62. 34. Rabinowitz Y. Keratoconus. Surv Ophthalmol. 1998;42:297-319. 35. Goldich Y, Barkana Y, Morad Y, Hartstein M, Avni I, Zadok D. Can we measure corneal biomechanical changes after collagen cross-linking in eyes with keratoconus?--A pilot study. Cornea. 2009;28:498-502. 36. Kirwan C, O’Malley D, O’Keefe M. Corneal hysteresis and corneal resistance factor in keratoectasia: findings using the Reichert Ocular Response Analyzer. Ophthalmologica. 2008;222:334337. 37. Shah S, Laiquizzaman M, Bhojwani R, Mantry S, Cunliffe I. Assessment of the biomechanical properties of the cornea with the Ocular Response Analyzer in normal and keratoconic eyes. Invest Ophthalmol Vis Sci. 2007;48:3026-3031. 38. Fontes BM, Ambrósio R, Salomão M, Velarde GC, Nosé W. Biomechanical and tomographic analysis of unilateral keratoconus. J Refract Surg. 2010;26:677-681. 39. Fontes BM, Ambrósio R, Jardim D, Velarde GC, Nosé W. Corneal biomechanical metrics and anterior segment parameters in mild keratoconus. Ophthalmology. 2010;117:673-679. 40. Viswanathan D, Kumar NL, Males JJ, Graham SL. Relationship of structural characteristics to biomechanical profile in normal, keratoconic, and crosslinked eyes. Cornea. 2015;34:791-796. 41. Schweitzer C, Roberts CJ, Mahmoud AM, Colin J, Maurice-Tison S, Kerautret. Screening of forme fruste keratoconus with the Ocular Response Analyzer. Invest Ophthalmol Vis Sci. 2010;51:2403-2410. 42. Galetti JD, Ruisenor Vazquez PR, Bonthox FF, Pfortner T, Galletti JG. Multivariate analysis of the Ocular Response Analyzer’s corneal deformation response curve for early keratoconus detection. J Ophthalmol. 2015;2015:496382. 43. Goebels S, Eppig T, Wagenpfeil S, Cayless A, Seitz B, Langenbucher A. Staging of keracotonus indices regarding tomography, topography, and biomechanical measurements. Am J Ophthalmol. 2015;159(4):733-738. 44. Labiris G, Giarmoukakis A, Gatzioufas Z, Sideroudi H, Kozobolis V, Seitz B. Diagnostic capacity of the keratoconus match index and keratoconus match probability in subclinical keratoconus. J Cataract Refract Surg. 2014;40(6):999-1005. 45. Labiris G, Gatzioufas Z, Sideroudi H, Giarmoukakis A, Kozobolis V, Seitz B. Biomechanical diagnosis of keratoconus: evaluation of the keratoconus match index and the keratoconus match probability. Acta Ophthalmol. 2013;91:e258-e262. 46. Mikielewicz M, Kotliar K, Barraquer RI, Michael R. Air-pulse corneal applanation signal curve parameters for the characterisation of keratoconus. Br J Ophthalmol. 2011;95:793-798. 47. Zhang L, Danesh J, Tannan A, Phan V, Yu F, Hamilton DR. Second-generation corneal deformation signal waveform analysis in normal, from frusta keratconic, and manifest keratoconic corneas after statistical correction for potentially confounding founders. J Cataract Refract Surg. 2015;41(10):2196-2204. 48. Ye C, Yu M, Lai G, Jhanji V. Variability of corneal deformation response in normal and keratoconic eyes. Optom Vis Sci. 2015;92(7):e149-e153.

K. Hallahan, W.J. Dupps, Jr and C.J. Roberts 49. Pena-Garcia P, Peris-Martinez C, Abbouda A, Ruiz-Moreno JM. Detection of subclinical keratoconus through non-contact tonometry and the use of discriminant biomechanical functions. J Biomech. 2016;49:353-363. 50. Ali NQ, Patel DV, McGhee CNJ. Biomechanical responses of healthy and keratoconic corneas measured using a noncontact Scheimpflug-based tonometer. Invest Ophthalmol Vis Sci. 2014;55:3651-3659. 51. Tian L, Huang YF, Wang LQ, Bai H, Wang Q, Jiang JJ, Wu Y, Gao M. Corneal biomechanics assessment using cornea visualization Scheimpflug technology in keratoconic and normal eyes. J Ophthalmol. 2014;2014:147516. 52. Vinciguerra R, Ambrosio R, Elsheikh A, et al. Detection of keratoconus with a new biomechanics index. J Refract Surg. 2016;32(12):803-810. 53. Krachmer JH, Feder RS, Belin MW. Keratoconus and related non-inflammatory corneal thinning disorders. Surv Ophthalmol. 1984;28:293-322. 54. Labiris G, Giarmoukakis A, Sideroudi H, Song X, Kozobolis V, Seitz B. Diagnostic capacity of biomechanical indices from a dynamic bidirectional applanation device in pellucid marginal degeneration. J Cataract Refract Surg. 2014;40(6):1006-1012. 55. Lenk J, Haustein M, Terai N, Spoerl E, Raiskup F. Characterization of ocular biomechanics in pellucid marginal degeneration. Cornea. 2016;35:506-509. 56. Congdon NG, Broman AT, Bandeen-Roche K, et al. Central corneal thickness and corneal hysteresis associated with glaucoma damage. Am J Ophthalmol. 2006;141(5):868–875. 57. Zhang C, Tatham AJ, Abe RY, et al. Corneal hysteresis and progressive retinal nerve fiber layer loss in glaucoma. Am J Ophthalmology. 2016;166:29-36. 58. Medeiros FA, Meira-Freitas D, Lisboa R, Kuang TM, Zangwill LM, Weinreb RN. Corneal hysteresis as a risk factor for glaucoma progression: a prospective longitudinal study. Ophthalmology. 2013;120:1533-1540. 59. Hong Y, Shoji N, Morita T. Comparison of corneal biomechanical properties in normal tension glaucoma patients with different visual field progression speed. Int J Ophthalmol. 2016;9(7):973978. 60. Nongpiur ME, Png O, Chiew JW, et al. Lack of association between corneal hysteresis and corneal resistance factor with glaucoma severity in primary angle closure glaucoma. Invest Ophthalmol Vis Sci. 2015;56:6879-6885. 61. Wang W, Du S, Zhang X. Corneal deformation response in patients with primary open-angle glaucoma and in healthy subjects analyzed by Corvis ST. Invest Ophthalmol Vis Sci. 2015;56:5557-5565. 62. Dietz HC, Cutting GR, Pyeritz RE, et al. Marfan syndrome caused by a recurrent de novo missense mutation in the fibrillin gene. Nature. 1991;352(6333):337-339. 63. Loeys BL, Dietz HC, Braverman AC, et al. The revised Ghent nosology for the Marfan syndrome. J Med Genet. 2010;47(7):476-485. 64. Beene LC, Traboulsi EI, Seven I, et al. Corneal deformation response and ocular geometry: a noninvasive diagnostic strategy in Marfan syndrome. Am J Ophthalmol. 2016;161:56-64.

Copyright © 2018. Kugler Publications. All rights reserved.

Deformation response to an air puff: clinical methods 65. Rybczynski M, Bernhard AM, Rehder U, et al. The spectrum of syndromes and manifestations in individuals screened for suspected Marfan syndrome. Am J Med Genet A. 2008;146A(24):3157-3166. 66. Davies JB, Rao PK. Ocular manifestations of systemic lupus erythematosus. Curr Opin Ophthalmol. 2008;19:512-518. 67. Perros P, Neoh C, Dickenson J. Thyroid eye disease. BMJ. 2009;338-560. 68. Enzmann D, Marshall Jr WH, Rosenthal AR, Kriss JP. Computed tomography in Graves’ ophthalmopathy. Radiology. 1976;118:615-620. 69. Frueh BR. Graves’ eye disease: orbital compliance and other physical measurements. Trans Am Ophthalmol Soc. 1984;82:492-598. 70. Moghimi S, Safizadeh M, Mazioumi M, Hosseini H, Vahedian, Rajabi MT. Evaluation of corneal biomechancal properties in patients with thyroid eye disease using ocular response analyzer. J Glaucoma. 2016;25(3):269-273. 71. Vellara HR, Hart R, Gokul A. In vivo ocular biomechanical compliance in thyroid eye disease. Br J Ophthalmol. 2017;101(8):10761079 72. Pallikaris IG, Kymionis GD, Astyrakakis NI. Corneal ectasia induced by laser in situ keratomileusis. J Cataract Refract Surg 2001;27:1796-1802. 73. Condon, PI, O’Keefe M, Binder PS. Long-term results of laser in situ keratomileusis for high myopia: risk for ectasia. J Cataract Refract Surg. 2007;33:583-590. 74. Binder PS. Analysis of ectasia after laser in situ keratomileusis: risk factors. J Cataract Refract Surg. 2007;33:1530-1538. 75. Seiler T, Koufala K, Richter G. Iatrogenic keratoectasia after laser in situ keratomileusis. J Refract Surg. 1998;14:312-317. 76. Pepose JS, Feigenbaum SK, Qazi MA, Sanderson JP, Roberts CJ. Changes in corneal biomechanics and intraocular pressure following LASIK using static, dynamic, and noncontact tonometry. Am J Ophthalmol. 2007;143(1):39–47. 77. Zarei-Ghanavati S, Ramirez-Miranda A, Yu F, Hamilton DR. Corneal deformation signal waveform analysis in keratoconic versus post-femtosecond laser in situ keratomileusis eyes after statistical correction for potentially confounding factors. J Cataract Refract Surg. 2012;38:607-614. 78. Santhiago MR, Wilson SE, Hallahan KM, et al. Changes in custom biomechanical variables after femtosecond laser in situ keratomileusis and photo refractive keratectomy for myopia. J Cataract Refract Surg. 2014;40:918-928. 79. Santhiago MR, Smadja D, Gomes BF, et al. Association between the percent tissue altered and post-laser in situ keratomileusis ectasia in eyes with normal preoperative topography. Am J Ophthalmol. 2014;158(1):87-95. 80. Santhiago MR, Smadja D, Wilson SE, Krueger RR, Montero ML, Randleman JB. Role of percent tissue altered on ectasia after LASIK in eyes with suspicious topography. J Refract Surg. 2015;31(4):258-65. 81. Frings A, Linke SJ, Bauer EL, Druchkiv V, Katz T, Steinberg J. Effects of laser in situ keratomileusis (LASIK) on corneal biomechaimcal measurements with the Corvis ST tonometer. Clin Ophthalmol. 2015; 9:305-311.

185 82. Leccisotti A, Fields SV, Moore J, Shah S, Moore TC. Changes in ocular biomechanics after femtosecond laser creation of a laser in situ keratomileusis flap. J Cataract Refract Surg. 2016;42:127131. 83. Hassan Z, Modis LJr, Szalai E. Examination of ocular biomechanics with a new Scheimpflug technology after corneal refractive surgery. Cont Lens Anterior Eye. 2014;37:337-341. 84. Dupps WJ Jr, Wilson Se. Biomechanics and wound healing in the cornea. Exp Eye Res. 2006; 83(4):709-720. 85. Gatinel D, Chaabouni S, Adam PA, Munck J, Puech M, Hoang-Xuan T. Corneal hysteresis, resistance factor, topography, and pachymetry after corneal lamellar flap. J Refract Surg. 2007;23:7684. 86. Kirwan C, O’Keefe M. Corneal hysteresis using the Reichert Ocular Response Analyzer: findings pre- and post-LASIK and LASEK. Acta Opthalmol. 2008;86:216-218. 87. Slade SG. Thin-flap laser-assisted in situ keratomileusis. Curr Opin Ophthalmol. 2008; 86:215-218. 88. Osman IM, Helaly HA, Abdalla M, Shousha MA. Corneal biomechanical changes in eyes with small incision lenticule extraction and laser assisted I situ keratomileusis. BMC Ophthalmol. 2016;16:123. 89. Wu D, Wang Y, Zhang L, Wei S, Tang X. Corneal biomechanical effects: small-incision lenticule extraction versus femtosecond laser-assisted laser in situ keratomileusis. J Cataract Refract Surg. 2014;40:954-962. 90. Wang D, Liu M, Chen Y, Zhang X, Xu Y, Wang J, ho To C, Liu Q. Differences in the cornea biomechanical changes after SMILE and LASIK. J Refract Surg. 2014;30(10):702-707. 91. Agca A, Ozgurhan EB, Demirok A, et al. Comparison of corneal hysteresis and corneal resistance factor after small incision lenticule extraction and femtosecond laser-assisted LASIK: A prospective fellow eye study. Cont Lens Anterior Eye. 2014;37(2):77-80. 92. Zhang J, Zheng L, Zhao X. Corneal biomechanics after small-incision lenticule extraction versus Q-value-guided femtosecond laser-assisted in situ keratomileusis. J Curr Ophthalmol. 2016;28:181-187. 93. Wollensak G, Spoerl E, Seiler T. Riboflavin/ultraviolet-A-induced collagen crosslinking for the treatment of keratoconus. Am J Ophthalmol. 2003;135(5):620-627. 94. Wollensak G, Spoerl E, Seiler T. Stress-strain measurements of human and porcine corneas after riboflavin-ultraviolet-A-induced cross-linking. J Cataract Refract Surg. 2003; 29:17801785. 95. Wollensak G, Iomdina E. Long-term biomechanical properties of rabbit cornea after photodynamic collagen crosslinking. Acta Ophthalmol. 2009;87:48-51. 96. Ahearne M, Yang Y, Then KY, Liu KK. Non-destructive mechanical characterization of UVA/riboflavin crosslinked collagen hydrogels. Br J Ophthalmol. 2008;92:268-271. 97. Greenstein SA, Fry KL, Hersh PS. In vivo biomechanical changes after corneal collagen cross-linking for keratoconus and corneal ectasia: 1-year analysis of a randomized, controlled, clinical trial. Cornea. 2012;31:21-25.

186

Copyright © 2018. Kugler Publications. All rights reserved.

98. Hallahan KM, Rocha K, Roy AS, Randleman JB, Stulting RD, Dupps Jr WJ. Effects of corneal cross-linking on ocular response analyzer waveform-derived variables in keratoconus and postrefractive surgery ectasia. Eye Contact Lens. 2014;40(6):339344. 99. Sedaghat M, Naderi M, Zarei-Ghanavati M. Biomechanical parameters of the cornea after collagen crosslinking measured by waveform analysis. J Cataract Refract Surg 2010;36:1728-1731.

K. Hallahan, W.J. Dupps, Jr and C.J. Roberts 100. Pinero DP, Alcon N. In vivo characterization of corneal biomechanics. J Cataract Refract Surg. 2014;40:870-887.

13. Factors contributing to air-puff derived corneal responses Riccardo Vinciguerra1, Renato Ambrósio Jr.2-3, Simone Donati1, Claudio Azzolini4, Paolo Vinciguerra5-6 St. Paul’s Eye Unit, Royal Liverpool University Hospital, Liverpool, United Kingdom; 2Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro, Brazil; 3Department of Ophthalmology, Federal University of São Paulo, São Paulo, Brazil; 4Department of Medicine and Surgery, University of Insubria, Varese, Italy; 5Humanitas University, Department of Biomedical Sciences, Milan, Italy; 6Humanitas Clinical and Research, Rozzano, Italy.

1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction As early as 1619, Scheiner postulated the first precise description of the corneal shape using glass balls of known curvatures.1 From that first report, many other diagnostic instruments have been developed to describe corneal shape, from keratometry to corneal topography (front surface curvature maps)2 and, subsequently, 3-D corneal tomography systems.3 However, these instruments cannot measure biomechanical instability, which is thought to be the initiating event in diseases such as keratoconus, even before notable changes in corneal morphology take place.4,5 For this reason, there has been increasing interest in developing instruments to measure the in-vivo biomechanical properties of the cornea to aid the diagnosis of ectasia at a “biomechanical” stage, when topography and tomography are normal. In addition, there are many other clinical applications for the measurement of in-vivo biomechanical corneal response. A theory has been proposed that the initiating event in keratoconus could be a focal reduction in biomechanical properties, resulting in thinning as the weaker area strains more than the surrounding stronger areas.6 The cause may be an underlying pathology, or perhaps a genetic predisposition with an external insult as a trigger, such as eye rubbing in a focal region. The consequence is that the focal reduction in elastic modulus generates greater deformation for the same load. This is followed

by bulging with increased curvature, which redistributes the stress, thus continuing the cycle. For this reason, it is the disparity in corneal properties which drives continued progression.6 Until recently, the evaluation of corneal biomechanical properties had been restricted to ex-vivo laboratory studies,7,8 and to mathematical corneal models.6,9,10 However, this changed with the introduction of the first instrument able to evaluate corneal biomechanical response parameters in vivo: the Ocular Response Analyzer (ORA, Reichert Inc., Depew, NY).11 The ORA is a modified non-contact tonometer (NCT) designed to provide a more accurate measurement of intraocular pressure (IOP) through compensation for corneal biomechanics. It analyzes corneal behavior during a bi-directional applanation process induced by an air jet, and produces estimates of corneal hysteresis and corneal resistance factor, along with a set of 36 waveform-derived parameters.12-14 The Corvis ST (OCULUS Optikgeräte GmbH, Wetzlar, Germany) was later introduced as a non-contact tonometer (NCT) which monitors the response of the cornea to an air pressure pulse using an ultra-high speed (UHS) Scheimpflug camera, and uses the captured image sequence to produce estimates of IOP and a large number of deformation response parameters.15 Newer non-commercially available research methods for direct clinical biomechanical measurements of the cornea have been recently introduced, particularly Brillouin microscopy.

Correspondence: Dr. Paolo Vinciguerra, Humanitas Clinical and Research Center, Via Manzoni 56, 20089 Rozzano, Milan, Italy. E-mail: [email protected] Biomechanics of the Eye, pp. 187-195 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

188

2. General concepts in in-vivo biomechanical measurements The in-vivo measurement and interpretation of corneal biomechanics is extremely difficult due to the complexity of the viscoelastic biomechanical behavior.12,16 A material with linear elastic properties could be described with a single number, the elastic modulus, defined by the slope of the stress-strain curve. In an elastic material, the loading and unloading phases follow the same path. The cornea, however, is a viscoelastic material, a property which adds complexity to its measurement. Behavior is different during loading and unloading, and its response to an applied force has a time-dependent component. The consequence is that experimental conditions affect resulting measurements; a faster strain rate produces a stiffer corneal response. Additionally, the stress-strain relationship is non-linear during both the loading and unloading phases, with a non-constant elastic modulus.17 Another confounding factor is IOP: according to Laplace’s law, the wall tension is a function of internal pressure. This implies that, as IOP increases, the wall tension will increase; due to the non-linear properties, a soft cornea with higher IOP may exhibit stiffer behavior than a fundamentally stiffer cornea with a lower IOP. The same complexity affects IOP measurements, as they are influenced by corneal stiffness, which is not only dependent on the thickness, as widely accepted, but also on the tissue elastic modulus, which changes with age and medical history, and additionally increases with greater values of IOP.

Copyright © 2018. Kugler Publications. All rights reserved.

3. ORA The ORA is a device aimed at characterizing corneal biomechanical response as a function of an applied air puff. It was presented as a device with the capability of obtaining a measurement of IOP, called corneal compensated IOP (IOPcc), which is less dependent on corneal thickness in comparison with applanation tonometers. However, it differs from a non-contact tonometer in that it also acquires information concerning corneal biomechanics. The ORA comprises an infrared emitter and detector that are aligned with the cornea, such that the light from the emitter is reflected

R. Vinciguerra et al.

by the cornea onto the detector. At the beginning of the measurement, the cornea is in its natural convex state, and the light is reflected in many directions, producing only a small signal on the detector. As the cornea flattens under the applied air pressure, acting like a mirror, the reflected light becomes fully aligned with the detector, which produces a signal spike. Due to the dynamic nature of the measurement, the cornea continues to deform to a state of concavity as the air pressure reaches a maximum. As the air pressure decreases and the cornea recovers its original shape, it passes through applanation a second time, creating a second spike on the infrared detector. Additionally, the ORA has an ultrasound probe to obtain a pachymetry measurement. However, since the probe is manually operated, it can be difficult to find the thinnest point. In an ectatic cornea, the corneal apex and the reflex may not be properly aligned. The direct consequence is that the peak infrared signal of the ORA (reflex) is reduced as the cornea is deformed. In very advanced keratoconus, the ratio between signal and noise is very low, making any measurement and calculation more difficult and imprecise. The first version of the ORA offered two biomechanical parameters, namely, corneal hysteresis (CH) and corneal resistance factor (CRF).16 The difference in the pressure between the first inward applanation event and second outward applanation event is termed Corneal Hysteresis, and represents the viscoelastic nature of the cornea. A sample signal from a patient with keratoconus is given in Figure 1. The CRF is derived from the formula (P1-kP2), where k is a constant. The constant k has a value determined from an empirical analysis of the relationship between

Fig. 1. Example of signals from the ORA exam, showing raw infrared light signal (red), corresponding fitted line (blue), and air pressure signal (green).

Factors contributing to air-puff derived corneal responses

189

Fig. 2. User interface for the Corvis ST.

both P1 and P2 and central corneal thickness (CCT), such that the correlation between CRF and CCT is maximized. According to a previous simulation done with a viscoelastic model aimed to analyze the impact of viscosity and elasticity on CH, CH could be associated with high or low elasticity depending on the viscosity.18 As a consequence, there is not a direct relationship between CH and the elastic modulus.18

Copyright © 2018. Kugler Publications. All rights reserved.

4. Corvis ST The Corvis ST (Oculus, Wetzlar, Germany), introduced during the 2010 American Academy of Ophthalmology meeting, is a novel NCT system that is able to evaluate corneal deformation using an UHS Scheimpflug camera with UV-free 455 nm blue light, covering 8.5 mm horizontally of a single slit.15,16,19 The camera is able to capture 4300 frames per second, which offers true visualization and details of the deformation response of the cornea. A major difference with the ORA is that the air puff deforms the cornea with a constant maximal pressure

and pressure profile.12,16,19 The air puff is applied concentrically on the corneal apex (first Purkinje reflex) with automatic release. The consistent air puff profile of the Corvis ST, in combination with imaging of the entire deformation process, allows direct analysis of the factors that influence air puff driven deformation. Therefore, the remainder of this chapter will focus on data and analysis derived from this device. The Corvis ST has other features that differentiate it from the ORA. First, the precision of the measurement is not affected by either corneal deformation or magnitude of pre-existing ectasia. If a cornea is misaligned, the Scheimpflug image can still be analyzed and parameters measured, even in very advanced keratoconus. This feature permits the calculation of complex parameters such as the Deformation Amplitude (DA) Ratio and Delta Arc-Length (described in the following paragraphs). Finally, as previously mentioned, the Corvis measures the pachymetry directly in the entire horizontal meridian, while conversely, the ORA measures only one point with the ultrasound probe.

190

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. (Top) Illustration of first applanation (A1) length. (Middle) Illustration of the concave radius of curvature at highest convavity (HC). (Bottom) Illustration of the second applanation (A2) length.

The air puff forces the cornea inwards (ingoing phase) through first applanation (inward or first applanation) into a concavity phase until it achieves the highest concavity (HC). There is an oscillation period before the outgoing or returning phase. The cornea undergoes a second applanation (outward or second applanation) before returning to its natural convex shape. The timing and corresponding pressure of the air puff are monitored during the complete measurement to identify the correlation between corneal state and air pressure.15 The Corvis ST provides a set of corneal deformation parameters based on the dynamic inspection of the corneal response during the NCT process (Fig. 2).12,16,19 The camera starts capturing images, marking the zero value for the time a few milliseconds before the initiation of an air pulse from the pump. From the images taken prior to corneal motion, thickness and curvature data are obtained. Corneal thickness is measured through the horizontal Scheimpflug image. This allows for the calculation of the rate of increase of corneal thickness from the apex towards the nasal and temporal sides. The characterization of the thickness profile enables the calculation of the Ambrósio Relational Thickness through the horizontal meridian (ARTh),20 which is a relative simplification of the tomographic relational thickness calculations available on the Pentacam.21

R. Vinciguerra et al.

Fig. 4. Total corneal apex displacement through the time course of a single air puff is defined by Deformation Amplitude (red line), which is the sum of both pure corneal motion in the Deflection Amplitude (blue line) and whole eye motion (green line).

As previously mentioned, the cornea deforms inwards due to the influence of the air pulse. The applanation of the cornea is defined by the transition from a convex to a concave shape in a zone 0.5 mm in diameter around the corneal apex.22 The time of first applanation can be determined with high accuracy by the interpolation between single frames, with the resolution of applanation time reported to 0.001 ms. This interpolated time is correlated to the pressure value of the air pulse that is measured within the nozzle. A calibration factor is used to calculate the IOP value based on the applanation pressure that best matches standard Goldmann applantion tonometry.15 A finite element method was applied and clinically-validated for the biomechanical correction of IOP (bIOP) based on data beyond central corneal thickness (CCT) and age,23 including corneal deformation response.24-26 The applanation length is the line that describes the applanated part of the cornea, defined as having a constant slope (Fig. 3). The same measurement parameters are extracted for the second corneal applanation moment that occurs during the outgoing phase. Corneal velocity is registered at the corneal apex through the applanation measurement and recorded at both applanation times.15 The Corvis ST provides a set of corneal deformation

Factors contributing to air-puff derived corneal responses

191

Fig. 6. The peak distance describes the distance between the two highest points of the cornea’s temporal-nasal cross-section (marked with X) at the moment of highest concavity.

Fig. 7. Illustration of Deformation Amplitude Ratio 1 mm (DA Ratio 1 mm), which is the ratio of the corneal apex displacement (red arrow) divided by the average displacement 1 mm on either side (green arrows).

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. (Top) Illustration of the concave radius of curvature at highest concavity. (Bottom) The inverse concave radius is plotted between first applanation (A1) and second applanation (A2).

parameters, including analysis of those that occur at the highest concavity moment.12,15 The deformation amplitude refers to the movement of the corneal apex in the anterior-posterior direction, and is determined as the highest displacement of the apex at the highest concavity moment (Fig. 4).12,15,22 During the measurement, there is a slight but significant movement of the whole eye. As the cornea deforms and approaches maximum displacement, the whole eye displays a slow linear motion in the anterior-posterior direction. Typically, when the cornea reaches maximum displacement, the backward whole eye motion becomes more pronounced and non-linear in nature, as the air puff pressure continues to increase to a consistent maximum. The deformation amplitude is indeed the sum of actual corneal deflection amplitude and whole eye movement (Fig. 4). The nasal and temporal edge points that are 4 mm away from the central corneal apex are used to track the whole eye movement, which can be seen in the video of corneal deformation, especially near the end of the air puff when corneal deflection has already recovered. In addition, the radius of curvature at highest concavity and thus, the inverse concave radius, is

Fig. 8. (Top) Illustration of Delta Arc-Length, which is determined as the difference of the length of the blue line at highest concavity and the arc-length prior to initiation of deformation. (Bottom) Plot of the arc-length over the time course of the air puff, showing that it decreases as the cornea deforms.

calculated based on a parabolic fit that is also plotted versus time (Figs. 2 and 5).12,15 The peak distance describes the distance between the two highest points of the cornea’s temporal-nasal cross-section at highest concavity (Fig. 6); this is not the same as the deflection length.12 The DA Ratio parameter is calculated as the ratio between the deformation of the apex and the average

192

R. Vinciguerra et al.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 9. Example of the Vinciguerra Screening Report, which compares the current patient exam (red lines in each of the four plots) to the normative values at the patient’s specific bIOP (gray lines). The Corvis Biomechanical Index (CBI) is shown in the lower left corner with this specific patient in the normal green range.

deformation amplitude 2 mm on either side of the apex (DA Ratio 2 mm).22 In addition, DA Ratio 1 mm is a similar parameter that calculates the ratio between the central deformation and the average 1 mm on either side of center (Fig. 7). Both DA Ratios are expected to have weak correlations with IOP.22 The Delta Arc-Length parameter describes the change of the arc-length during the highest concavity moment from the initial state, in a defined 7 mm zone. This parameter is calculated 3.5 mm from the apex to both sides in the horizontal direction (Fig. 8). The temporal changes in the Delta Arc-Length are also calculated. As previously, mentioned, it has been demonstrated that IOP and pachymetry have important influences on most corneal biomechanical metrics provided by both the Corvis ST and ORA.24,27,28 To evaluate in-vivo corneal biomechanics, it is therefore relevant to investigate the

distribution and normal limits for the data represented by the dynamic corneal response parameters (DCRs) derived from the direct imaging provided by the Corvis ST, and determine if these metrics have correlations with IOP and corneal thickness. A recently published multicenter study by Vinciguerra et al. evaluated this particular topic. The publication investigated in detail the influence of pachymetry and IOP on response parameters. The second section of the paper introduced normative values for all DCRs provided by the Corvis ST in healthy patients.22 Seven hundred-five healthy patients comprised the dataset for evaluation in the multicenter retrospective study. In order to analyze the IOP, CCT, and age dependency of Corvis ST dynamic corneal response parameters obtained, the authors divided the entire dataset for repeat analysis three different times with respect to IOP, CCT, and age, each time into four

Copyright © 2018. Kugler Publications. All rights reserved.

Factors contributing to air-puff derived corneal responses

different subgroups. In other words, there was one analysis with four subgroups of IOP, a second analysis with four subgroups of CCT, and a third analysis with four subgroups of age. The biomechanical response data were then examined to achieve normative values with their dependence on corrected and clinically-validated IOP estimates developed using the finite element method (bIOP), central corneal thickness (CCT) and age, as well as to evaluate the influence of bIOP, CCT, and age. The results showed that all DCRs were correlated with bIOP, except Deflection Amplitude (Defla) Ratio, Highest Concavity (HC) radius, and Inverse Concave Radius. This conclusion provided evidence that Deflection Amplitude Ratio, HC Radius, and Inverse Concave Radius are suitable parameters to properly evaluate in-vivo corneal biomechanics due to their relative independence from IOP. Furthermore, the paper confirmed that many parameters used in earlier publications, e.g., deformation amplitude, are deeply influenced by IOP24,27 and that, if IOP is not matched or compensated statistically, comparisons between groups would not be valid. The analysis of the influence of corneal thickness showed that the CCT subgroups did not show significant differences for bIOP and age, but were significantly dissimilar for uncorrected IOP. This important result confirmed that the bIOP correction algorithm is able to compensate for these confounding factors. This outcome has a significant impact on the assessment of in-vivo corneal biomechanics. The creation of an IOP-corrected algorithm with significantly reduced influence by CCT and age, which contribute to stiffness, is important in evaluating corneal biomechanics. Due to Laplace’s law, interpreting the biomechanical characteristics of the cornea is almost impossible without correcting IOP for these factors. Finally, the results of analysis of the age subgroups revealed that Whole Eye Movement (WEM), followed by DA Ratio and Inverse Concave Radius, were the three parameters most influenced by age. The authors suggested that the correlation between WEM and age, but not with CCT, may be attributed to the change in the retrobulbar fat composition with regards to age.29 Conversely, the manuscript concludes that the correlation of DA Ratio and Inverse Concave Radius with age, together with their correlation with pachymetry,

193

probably indicates the capability of these DCRs to quantify changes in corneal biomechanics. Indeed, it is known that the elastic modulus increases with age.30 The creation of the normative values, included in the most recent release of Corvis ST software (September 2016), allows the user to compare the selected exam to the corresponding normative value ranges with dependence on bIOP, age, and pachymetry. The normative values are displayed in the Vinciguerra Screening Report (Fig. 9), which includes in one single interface the comparison of normative values to imported exams, as well as an index to separate normal from keratoconic patients, the Corvis Biomechanical Index (CBI). The CBI parameter was developed to separate normal from keratoconic patients. The paper that introduced this index included 662 patients enrolled in two different continents.31 Logistic regression was used to define the optimal combination of best predictors from the individual indices to create the CBI for the accurate separation between normal and keratoconic eyes, using one dataset as training and the other as the validation dataset to exclude over-fitting. The results of this study showed that, with a cut-off of 0.5, CBI was able to correctly classify 98.2 % of the cases with 100% specificity and 94.1% sensitivity in the training dataset. In the validation dataset, the same cut-off point correctly classified 98.8% of the cases with 98.4% specificity and 100% sensitivity.31

5. Conclusion Direct evaluation of in-vivo corneal biomechanics promises to increase understanding of corneal behavior, making detection of ectatic diseases and characterization of ectasia susceptibility possible.32,33 Featuring the absence of relevant signs in topography and tomography scans, an initial pre-clinical phase of an ectatic disorder might be first detected by biomechanical measurement, in theory. The evaluation of the influence of pachymetry, age, and IOP on air puff deformation using the Corvis ST DCRs led to the creation of normative values as a function of these confounding parameters, providing the possibility to interpret corneal biomechanical response in the context of normative values and

R. Vinciguerra et al.

194

suspect pathology in clinical practice in an individual patient exam. Finally, the introduction of the Corvis Biomechanical Index, which was shown to be highly sensitive and specific to separate healthy from ectatic eyes,

References 1. 2.

3. 4.

5.

6. 7.

8.

9.

10.

11.

Copyright © 2018. Kugler Publications. All rights reserved.

12. 13.

14.

15.

Daxecker F. Christoph Scheiner’s eye studies. Doc Ophthalmol. 1992;81:27-35. Wilson SE, Ambrosio R Jr. Computerized corneal topography and its importance to wavefront technology. Cornea. 2001;20:441-454. Ambrosio R Jr, Belin MW. Imaging of the cornea: topography vs tomography. J Refract Surg. 2010;26:847-849. Roberts CJ. Biomechanics in Keratoconus. In: Barbara A, ed. Textbook of Keratoconus: New Insights 1ed. New Delhi: Jaypee Brothers Medical Publishers; 2012:29-32. Scarcelli G, Besner S, Pineda R, Yun SH. Biomechanical characterization of keratoconus corneas ex vivo with Brillouin microscopy. Invest Ophthalmol Vis Sci. 2014;55:4490-4495. Dupps WJ Jr. Biomechanical modeling of corneal ectasia. J Refract Surg. 2005;21:186-190. Andreassen TT, Simonsen AH, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Exp Eye Res. 1980;31:435-441. Elsheikh A, Geraghty B, Rama P, Campanelli M, Meek KM. Characterization of age-related variation in corneal biomechanical properties. J R Soc Interface. 2010;7:1475-1485. Liu J, Roberts CJ. Influence of corneal biomechanical properties on intraocular pressure measurement: quantitative analysis. J Cataract Refract Surg. 2005;31:146-155. Carvalho LA, Prado M, Cunha RH, et al. Keratoconus prediction using a finite element model of the cornea with local biomechanical properties. Arq Bras Oftalmol. 2009;72:139-145. Luce DA. Determining in vivo biomechanical properties of the cornea with an ocular response analyzer. J Cataract Refract. Surg 2005;31:156-162. Roberts CJ. Concepts and misconceptions in corneal biomechanics. J Cataract Refract Surg. 2014;40:862-869. Mikielewicz M, Kotliar K, Barraquer RI, Michael R. Air-pulse corneal applanation signal curve parameters for the characterisation of keratoconus. Br J Ophthalmol. 2011;95:793-798. Hallahan KM, Sinha Roy A, Ambrosio R Jr, Salomao M, Dupps WJ Jr. Discriminant value of custom ocular response analyzer waveform derivatives in keratoconus. Ophthalmology. 2014;121:459-468. Ambrósio R Jr, Ramos I, Luz A, et al. Dynamic ultra-high speed Scheimpflug imaging for assessing corneal biomechanical properties. Revista Brasileira de Oftalmologia. 2013;72:99-102.

gives new hope for the early detection of ectasia in a pre-topographic-tomographic “biomechanical stage”. Further validation of this index in different populations is warranted.

16. Pinero DP, Alcon N. In vivo characterization of corneal biomechanics. J Cataract Refract Surg. 2014;40:870-887. 17. Elsheikh A, Wang D, Pye D. Determination of the modulus of elasticity of the human cornea. J Refract Surg. 2007;23:808-818. 18. Glass DH, Roberts CJ, Litsky AS, Weber PA. A viscoelastic biomechanical model of the cornea describing the effect of viscosity and elasticity on hysteresis. Invest Ophthalmol Vis Sci. 2008;49:3919-3926. 19. Ambrosio R Jr, Ramos I, Luz A, et al. Dynamic Ultra-High Speed Scheimpflug Imaging for assessing corneal biomechanical properties. Rev Bras Oftalmol. 2013;72. 20. Lopes BT, Ramos IdC, Salomão MQ, Canedo ALC, Ambrósio R Jr. Perfil paquimétrico horizontal para a detecção do ceratocone. Revista Brasileira de Oftalmologia. 2015;74:382-385. 21. Ambrosio R Jr, Caiado AL, Guerra FP, et al. Novel pachymetric parameters based on corneal tomography for diagnosing keratoconus. J Refract Surg. 2011;27:753-8. 22. Vinciguerra R, Elsheikh A, Roberts CJ, et al. Influence of Pachymetry and Intraocular Pressure on Dynamic Corneal Response Parameters in Healthy Patients. J Refract Surg. 2016;32(8):550-561. 23. Joda AA, Shervin MM, Kook D, Elsheikh A. Development and validation of a correction equation for Corvis tonometry. Comput Methods Biomech Biomed Engin. 2016;19(9):943-53. 24. Bao F, Deng M, Wang Q, et al. Evaluation of the relationship of corneal biomechanical metrics with physical intraocular pressure and central corneal thickness in ex vivo rabbit eye globes. Exp Eye Res. 2015;137:11-17. 25. Bao F, Huang Z, Huang J, et al. Clinical evaluation of methods to correct intraocular pressure measurements by the Goldmann applanation tonometer, ocular response analyzer, and Corvis ST tonometer for the effects of corneal stiffness parameters. J Glaucoma. 2016;25(6):510-9. 26. Joda AA, Shervin MM, Kook D, Elsheikh A. Development and validation of a correction equation for Corvis tonometry. Comput Methods Biomech Biomed Engin. 2016;19:943-53. 27. Huseynova T, Waring GOt, Roberts C, Krueger RR, Tomita M. Corneal biomechanics as a function of intraocular pressure and pachymetry by dynamic infrared signal and Scheimpflug imaging analysis in normal eyes. Am J Ophthalmol. 2014;157:885-893. 28. Kling S, Marcos S. Contributing factors to corneal deformation in air puff measurements. Invest Ophthalmol Vis Sci. 2013;54:5078-5085.

Factors contributing to air-puff derived corneal responses

Copyright © 2018. Kugler Publications. All rights reserved.

29. Regensburg NI, Wiersinga WM, van Velthoven ME, et al. Age and gender-specific reference values of orbital fat and muscle volumes in Caucasians. Br J Ophthalmol. 2011;95:1660-1663. 30. Knox Cartwright NE, Tyrer JR, Marshall J. Age-related differences in the elasticity of the human cornea. Invest Ophthalmol Vis Sci. 2011;52:4324-4329. 31. Vinciguerra R, Elsheikh A, Roberts CJ, et al. Detection of Keratoconus with a new Corvis ST Biomechanical Index. J Refract Surg. 2016;32(12):803-810.

195 32. Dupps WJ Jr, Roberts CJ. Corneal biomechanics: a decade later. J Cataract Refract Surg. 2014;40:857. 33. Dupps WJ Jr, Wilson SE. Biomechanics and wound healing in the cornea. Exp Eye Res. 2006;83:709-720.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

BIOMECHANICS OF CORNEAL DISEASE AND THERAPEUTICS

Copyright © 2018. Kugler Publications. All rights reserved.

14. Biomechanics in ectasia detection: ORA and Corvis ST Renato Ambrósio Jr.1,2,3, Fernando Faria Correia2,4,5,6, Bernardo T. Lopes1,2,3, Rui Carneiro Freitas2,4, Isaac Ramos2,7, Marcella Q. Salomão1,2,3, Allan Luz1,2,8 Department for Ophthalmology of the Federal University of The State of Rio de Janeiro (UniRIO) and Federal University of São Paulo (UNIFESP), Brazil; 2Rio de Janeiro Corneal Tomography and Biomechanics Study Group, Rio de Janeiro, Brazil; 3Instituto de Olhos Renato Ambrósio and VisareRIO, Rio de Janeiro, Brazil; 4Cornea and Refractive Department, Hospital de Braga, Braga, Portugal; 5Cornea and Refractive Department, Instituto CUF, Porto, Porto, Portugal; 6School of Health Sciences, University of Minho, Braga, Portugal; 7Hospital de Olhos Santa Luzia, Maceió, Brazil; 8Hospital de Olhos de Sergipe, Aracaju, Brazil 1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction Keratoconus (KC) and ectatic corneal diseases (ECD) have been recognized for over 150 years.1,2 However, over the last three decades, the advent of refractive surgery had enabled significant improvements in the understanding and management of these conditions.2-5 The detection of mild forms of the disease has gained substantial relevance because these cases are at very high risk for iatrogenic progressive ectasia (keratectasia) after corneal refractive procedures.6,7 In addition, the advent of collagen crosslinking for the treatment of ECD has determined the need to increase sensitivity both for detecting the early stages of the disease and monitoring its progression.8,9 The advent of corneal topography10,11 and corneal tomography12 has increased our ability to identify corneal ectasia at much earlier stages, prior to the patient developing symptoms and loss of acuity (DCVA).13-16 However, despite the evolution of corneal shape analysis, there is a consensus that the pathophysiology of corneal ectatic diseases is related to biomechanical decompensation.5 The two-hit hypothesis proposes an underlying genetic predisposition coupled with external environmental factors, including eye rubbing and atopy.2 Thereby, curvature, elevation,

and pachymetric changes occur as secondary events that lead to ocular aberrations,17 while the primary abnormality is related to biomechanical properties and architectural stability.18,19 Interestingly, the hypothesis of altered biomechanical properties as the cause for ectasia progression after laser-assisted in situ keratomileusis (LASIK) has been considered since the first report of ectasia.6 In fact, the enhanced screening approach for ectasia risk should not be limited to the detection of mild KC, and should consider data beyond classic topography and central thickness,20 into 3-D shape analysis and corneal biomechanics.21 In this chapter, we describe the clinical applications for biomechanical assessments provided by two commercially available devices available for the diagnosis and management of KC.

2. The Ocular Response Analyzer (ORA) The ORA (Reichert Ophthalmic Instruments, Buffalo, NY, USA) was introduced during the 2005 ESCRS meeting (Lisbon, Portugal) as the first commercial device to evaluate in-vivo corneal biomechanical response.22 This is a non-contact tonometer (NCT) designed to provide a more accurate measurement of intraocular pressure

Correspondence: Renato Ambrósio Jr, MD, PhD, Rua Conde de Bonfim 211, Rio de Janeiro, RJ, Brazil. E-mail: [email protected] Biomechanics of the Eye, pp. 199-215 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

Copyright © 2018. Kugler Publications. All rights reserved.

200

(IOP) through the understanding and compensation for corneal properties. The ORA analyzes corneal response during the bidirectional applanation process induced by an air jet pressurizing the cornea. In this system, the maximal pressure of the air puff varies accordingly to the first applanation event. The measurement takes approximately 25 milliseconds. Corneal deformation is monitored by an advanced electro-optical system that captures the infrared reflex of the corneal apex (approximately 3 mm zone) through a pinhole device.22-24 Since the maximum air puff pressure of the ORA is customized to each exam, eyes with earlier first applanation, typically with lower IOP, receive a lower maximum pressure while eyes with higher IOP receive a greater maximum pressure.23,24 After auto-alignment to the corneal apex, the air puff starts. As previously stated, the pump is controlled accordingly to the first applanation signal, when there is an internal command on the instrument for the air pump to shut down. The air pressure forces the cornea to deform (inward phase), passing first applanation when the pressure (P1) is registered. The cornea goes into a slight concavity configuration until the air pressure decreases, making the cornea gradually recover its normal configuration, passing through a second applanation (P2) state. Both applanation events are registered by a peak on the corneal reflex signal, which corresponds to two independent pressure values. These pressure measurements (P1 and P2) are the basis for the first-generation variables reported by the original ORA software. The difference between the two pressures is called corneal hysteresis (CH), a concept derived from Greek which means ‘‘lagging behind’’.22-24 The corneal resistance factor (CRF) is based on the formula P1 – kP2, where k is a constant developed through empirical evaluation of the relationship between P1, P2, and central corneal thickness (CCT), so that CRF is more strongly associated with CCT than CH. The concept behind CRF was to develop a parameter that reflects corneal resistance.22 Previous studies described a statistically significant positive correlation between CH, CRF, and CCT (CH, r = 0.4655; CRF, r = 0.5760).25 Shah was the first to report that hysteresis had statistically significant lower values in keratoconic eyes compared to normal eyes.26 In this seminal study, 207 normal eyes were compared to 93 keratoconic eyes

R. Ambrósio Jr. et al.

based on hysteresis and ultrasonic CCT. Eyes were diagnosed as keratoconic based on clinical examination including corneal topography. Mean CH was 10.7 ± 2.0 (SD) mm Hg (range: 6.1-17.6) in normal eyes, which was statistically significantly lower (p 1 year) stability and normal tomography. The hypothesis on this study was that the N and Stable-KCS groups would have different deformation responses than ectatic corneas (FFKC and KC groups). The first and second applanation times and lengths were recorded, along with other metrics that were computed in the first-generation software of the

Biomechanics in ectasia detection: ORA and Corvis ST

205

Fig. 6. Box plot showing the Corvis-Factor 1 distribution in normal, FFKC, KC, and KC-suspect (ABT/KCS) groups.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. ROC curve (graphical plot of the sensitivity vs 100–specificity) for the Corvis-Factor 1. The cutoff was 0.2527 mmHg, with 87.3% sensitivity and 89.3% specificity.

instrument (Table 1). Considering the N and KC groups, statistically significant distributions were found for all studied parameters (Mann-Whitney, p < 0.05). However, there was a significant overlap and the best parameter was the radius of curvature at highest concavity, with an area under the ROC curve of 0.852. The Brazilian Study Group of Artificial Intelligence and Corneal Analysis (BrAIN) group calculated a linear regression model for the combination of parameters in order to maximize the separation between the N and KC groups, finding the Corvis-Factor 1, which had an AUC of 0.945 (Fig. 5). The distribution of the Corvis-Factor 1 among the groups is presented in Figure 6. Figures 7, 8, 9, and 10 include examples from eyes in each group. Interestingly, there were no significant differences among the groups (Kruskall-Wallis Test, p < 0.001). The post hoc Dunn’s test found no differences in Corvis-Factor 1 for the FFKC and KC groups and for the N and KCS groups (Table 2), but there were significant differences for N

vs FFKC, N vs KC, stable-KCS vs FFKC, and stable-KCS vs KC. The mean and standard deviations for the Corvis-Factor 1 are presented in Table 3. While this study was performed with the Corvis ST prototype, it demonstrated that the data derived from such an instrument has the potential to effectively distinguish normal from ectatic corneas, as well as to enhance specificity in cases with mild topographic abnormalities.58 Ali and coworkers reported that KC was associated with a greater deformation amplitude compared to healthy eyes.56 Despite not having a good discriminative ability, the deformation amplitude variable was considered potentially useful for KC diagnosis and monitoring.56 A comparative study enrolled 52 keratoconic eyes and 52 normal eyes to compare the corneal deformation response parameters between the groups.59 In this study, the majority of the biomechanical variables (deformation amplitude, maximum corneal inward velocity, maximum corneal outward velocity, maximum deformation area) were significantly between the groups. In the ROC curve analysis, the maximum corneal inward velocity was the best predictive parameter, with an AUC of 0.79.59 Another study described that the deformation amplitude parameter was the best predictive parameter (AUC of 0.882), but there was a significant overlap between keratoconic and normal corneas.60 Another research study was purposed to improve ectasia screening

R. Ambrósio Jr. et al.

206

Table 1. Corneal deformation parameters provided by the Corvis ST.

CORVIS ST – PARAMETERS 1st applanation

Moment at the first applanation of the cornea during air puff (in milliseconds). In parethesis is the length of the applanation at this moment (in millimeters).

Highest concavity

Moment that the cornea assumes its maximum concavity during the air puff (in milliseconds). In parenthesis is the length of the distance between the two peaks of the cornea at this moment (in milliseconds).

2nd applanation

Moment at the first applanation of the cornea during air puff (in milliseconds). In parethesis is the length of the applanation at this moment (in millimeters).

Maximum deformation

Measurement (in millimeters) of the maximum corneal deformation during the air puff.

Wing distance

Length of the distance between the two peaks of the cornea at this moment (in millimeters).

Maximum velocity (in)

Maximum velocity during the ingoing phase (in meters per second [m/s]).

Maximum velocity (out)

Maximum velocity during the outgoing phase (in meters per second [m/s]).

Curvature radius normal Radius of curvature of the cornea in its natural state (in millimeters). Curvature radius HC

Corneal curvature radius at the time of maximum concavity during the air puff (in millimeters).

Corneal thickness

Measurement of the corneal thickness (in micrometers).

IOP

Measurement of the intraocular pressure (in millimeters of mercury [mmHg]).

Table 2. Corvis–Factor 1 parameter comparisons between normal, FFKC and KC groups (Kruskall-Wallis test; post hoc Dunn’s test).

Copyright © 2018. Kugler Publications. All rights reserved.

Normal KC FFKC

KC < 0.05

FFKC < 0.05 NS

ABT/IS NS < 0.05 < 0.05

Table 3. Mean and standard deviations for the Corvis-Factor 1 parameter in normal, FFKC, KC and KC suspect (ABT/KCS) groups.

Ave SD n

N -0,00801 0,218348 177

FFKC 0,345529 0,196043 20

KC 0,506829 0,26691 79

ABT 0,133745 0,181624 16

Copyright © 2018. Kugler Publications. All rights reserved.

Biomechanics in ectasia detection: ORA and Corvis ST

207

Fig. 7. Curvature, tomographic, and biomechanical analysis of a normal cornea. The collected data showed unremarkable findings in this clinical case.

Copyright © 2018. Kugler Publications. All rights reserved.

208

R. Ambrósio Jr. et al.

Fig. 8. Curvature, tomographic, and biomechanical analysis of a KC cornea. The axial curvature map showed an inferior steeping. The BAD-D demonstrated abnormal elevation maps and pachymetric progression. The D value was 7.89. The Corvis–Factor 1 value was also abnormal (0.55).

Copyright © 2018. Kugler Publications. All rights reserved.

Biomechanics in ectasia detection: ORA and Corvis ST

209

Fig. 9. Curvature, tomographic, and biomechanical analysis of a FFKC. The axial curvature map was relatively normal. The BAD-D demonstrated abnormal posterior elevation maps and pachymetric progression. The final D value was 2.84. The Corvis-Factor 1 value was abnormal (0.46).

Copyright © 2018. Kugler Publications. All rights reserved.

210

R. Ambrósio Jr. et al.

Fig. 10. Curvature, tomographic, and biomechanical analysis of a KC suspect. Despite the axial curvature map displaying an asymmetric bowtie, the BAD-D demonstrated unremarkable findings in the elevation maps and in the pachymetric progression graphs. The D value was 0.31. The CorVis-Factor 1 value was normal (0.02). This stable KCS case demonstrates enhanced specificity, as it would be considered as a false positive on topography (front surface data). In fact, the tomographic and biomechanical data confirms this is not an ectatic cornea.

Copyright © 2018. Kugler Publications. All rights reserved.

Biomechanics in ectasia detection: ORA and Corvis ST

methodology with the introduction of new in-vivo biomechanical Scheimpflug analyses.61 The new “applanation length level” and “deflection length level” variables demonstrated consistently increasing differences with increasing statistical significance between normal eyes and those with advancing KC stages. However, when comparing normal and subclinical KC eyes, none of the analyzed parameters showed statistically significant differences.61 Vinciguerra and coworkers introduced the Corvis Biomechanical Index (CBI), which showed an optimized accuracy for detecting KC.62 This parameter was derived from the CCT profile and deformation parameters provided by the Corvis ST. The study enrolled 658 patients from two clinics located on different continents, and were used to create and validate the CBI parameter by using two distinct databases. The ROC curve analysis of the training dataset showed an area under the curve of 0.983. With a cutoff value of 0.5, 98.2% of the cases were correctly classified with 100% specificity and 94.1% sensitivity. In the validation dataset, the same cutoff point correctly classified 98.8% of the cases with 98.4% specificity and 100% sensitivity.62 A recent multicenter study introduced the Tomographic/Biomechanical Index (TBI), a novel index for enhanced ectasia detection.63 This parameter was developed using the random forest method with leaveone-out cross-validation (RF/LOOCV) in combination with parameters from Scheimpflug-based corneal tomography and biomechanical assessments. This research study demonstrated that TBI is more sensitive than previous methods for detecting sub-clinical ectasia among eyes with normal topography in very asymmetric patients. For this study, one eye was randomly selected from 480 patients with normal corneas and 204 KC patients, which comprised groups I and II, respectively. Group III enrolled 72 non-operated ectatic eyes from 94 patients with very asymmetric ectasia, whose fellow eyes (group IV) presented with normal topography. The TBI AUROC for detecting ectasia (groups II, III and IV) of TBI was 0.996, being statistically greater (DeLong, p < 0.001) than BAD-D (0.956) and CBI (0.936). With a cutoff value of 0.79, the TBI provided 100% sensitivity for detecting clinical ectasia (groups II and III) with 100% specificity. Considering group IV, AUROC for TBI, BAD-D and CBI were 0.985, 0.839, and 0.822, respectively, with the TBI accuracy statistically greater than

211

other parameters (DeLong, p < 0.001). An optimized TBI cutoff value of 0.29 provided 90.4% sensitivity in group IV, with 96% specificity.63 In practice, the TBI enhances sensitivity in cases with normal topography as well as normal tomography findings from very asymmetric patients with clinical ectasia detected in the fellow eye. Figure 11 refers to a 35-year-old male patient who presented with advanced ectasia in the left eye and a relatively normal right eye. The display combines corneal tomography and biomechanical evaluations from Oculus Corvis ST and Pentacam HR. In this case, advanced ectasia in the left eye was straightforwardly detected on biomicroscopy, while the right eye presented with 20/20 leave only DCVA and a normal slit lamp exam. Corneal topometric findings from Placido-disk reflection (Keratograph 5M, Oculus) and rotating Scheimpflug (Pentacam HR) were similar in the right eye, with a normal pattern including maximal keratometry less than 42 D, inferior-superior (IS) asymmetry less than 1 D and no abnormal pattern detected on the TKC (Topometric KC Classification). Interestingly, the BADD was 1.18, which is less than the threshold for turning yellow (1.6) on BAD-D and also lower than the optimal cutoff values in studies involving very asymmetric ectasia patients and the preoperative data from patients that developed ectasia after LASIK.16,64 While this case would be a good example of a false negative tomographic evaluation, the relatively higher value of BAD-D would arguably have identified some level of abnormality which is consistent with some level of susceptibility.64 However, the integration of tomographic and biomechanical data does augment the ability to detect abnormality with the predisposition for ectasia progression. While CBI62 is low, it is notable that stiffness parameter (SP-A1) and integrated radius are abnormal in this case. However, the integration of data is fundamental to augment accuracy. The TBI of 0.34 is lower than the threshold for frank ectasia (0.79), but is higher than the optimized cutoff for the cases in group IV (0.29) in the original TBI study, which provided 90.4% sensitivity with 96% specificity.63

4. Conclusions Evaluation of in-vivo corneal biomechanics promises to provide an ultimate analysis for the understanding

Copyright © 2018. Kugler Publications. All rights reserved.

212

R. Ambrósio Jr. et al.

Fig. 11. The ARV (Ambrósio, Roberts & Vinciguerra Display) corneal tomographic and biomechanical assessment of a patient with very asymmetric ectasia. In this clinical case, the left eye presents clinical KC, which is confirmed by the topographic and tomographic data. The contralateral eye shows no sign of corneal ectasia in the curvature map and the tomographic data also show unremarkable findings (BAD-D: 1.18). The CBI provided by the Corvis ST is within the normal range (0.00). The combined tomographic and biomechanical evaluation demonstrates signs of ectasia susceptibility in the left eye (TBI: 0.34).

Biomechanics in ectasia detection: ORA and Corvis ST

of corneal behavior, enabling the detection of ectatic diseases and characterization of ectasia susceptibility. In addition to safety, such evaluation may also allow for the customization of treatments for refractive and therapeutic procedures. Although different studies have attempted to evaluate biomechanical response, primarily using the dynamic bidirectional applanation device, it is difficult to obtain precise conclusions. The interpretation of biomechanical parameters is challenging due to the complexity of the corneal viscoelastic behavior and the impact of intraocular pressure. However, this is a very active research area where fast developments are to be anticipated. Different

References

Copyright © 2018. Kugler Publications. All rights reserved.

1.

Krachmer JH, Feder RS, Belin MW. Keratoconus and related noninflammatory corneal thinning disorders. Surv Ophthalmol. 1984;28:293-322. 2. McGhee CN, Kim BZ, Wilson PJ. Contemporary treatment paradigms in keratoconus. Cornea. 2015;34 (Supp. 10)S16-23. 3. Ambrósio RJ. Keratoconus and ectatic corneal diseases: Are we facing a new subspeciality? Int J of Kerat and Ectatic Dis. 2012;1:vii. 4. Gomes JA, Tan D, Rapuano CJ, et al. Global consensus on keratoconus and ectatic diseases. Cornea. 2015;34:359-369. 5. Gomes JA, Tan D, Rapuano CJ, et al. Global consensus on keratoconus and ectatic diseases. Cornea. 2015;34:359-369. 6. Seiler T, Quurke AW. Iatrogenic keratectasia after LASIK in a case of forme fruste keratoconus. J Cataract Refract Surg. 1998;24:1007-1009. 7. Binder PS. Ectasia after laser in situ keratomileusis. J Cataract Refract Surg. 2003;29:2419-2249. 8. Wollensak G, Spoerl E, Seiler T. Riboflavin/ultraviolet-a-induced collagen crosslinking for the treatment of keratoconus. Am J Ophthalmol. 2003;135:620-627. 9. da Paz AC, Bersanetti PA, Salomao MQ, Ambrosio R, Schor P. Theoretical basis, laboratory evidence, and clinical research of chemical surgery of the cornea: cross-linking. J Ophthalmol. 2014;2014:890823. 10. Wilson SE, Ambrosio R. Computerized corneal topography and its importance to wavefront technology. Cornea. 2001;20:441454. 11. Maeda N, Klyce SD, Tano Y. Detection and classification of mild irregular astigmatism in patients with good visual acuity. Surv Ophthalmol. 1998;43:53-58. 12. Ambrosio R Jr, Belin MW. Imaging of the cornea: topography vs tomography. J Refract Surg. 2010;26:847-849.

213

approaches for interpretation of the data from these devices may prove their clinical usefulness. In addition, other technologies for biomechanical assessment are also under development, such as Brillouin microscopy.65-67

Acknowledgements Conflicts of Interest: Renato Ambrósio MD, PhD is a consult of OCULUS Optikgeräte GmbH. For the remaining authors, none were declared.

13. Smadja D, Touboul D, Cohen A, et al. Detection of subclinical keratoconus using an automated decision tree classification. Am J Ophthalmol. 2013;156:237-46 e1. 14. Saad A, Gatinel D. Topographic and tomographic properties of forme fruste keratoconus corneas. Invest Ophthalmol Vis Sci. 2010;51:5546-5555. 15. Belin MW, Villavicencio OF, Ambrosio RR Jr. Tomographic parameters for the detection of keratoconus: suggestions for screening and treatment parameters. Eye Contact Lens. 2014;40:326-330. 16. Ambrosio R Jr, Valbon BF, Faria-Correia F, Ramos I, Luz A. Scheimpflug imaging for laser refractive surgery. Curr Opin Ophthalmol. 2013;24:310-320. 17. Schoneveld P, Pesudovs K, Coster DJ. Predicting visual performance from optical quality metrics in keratoconus. Clin Exp Optom. 2009;92:289-296. 18. Dupps WJ Jr, Roberts CJ. Corneal biomechanics: a decade later. J Cataract Refract Surg. 2014;40:857. 19. Roberts CJ, Dupps WJ Jr. Biomechanics of corneal ectasia and biomechanical treatments. J Cataract Refract Surg. 2014;40:991-998. 20. Ambrosio R Jr, Klyce SD, Wilson SE. Corneal topographic and pachymetric screening of keratorefractive patients. J Refract Surg. 2003;19:24-29. 21. Ambrosio R Jr, Nogueira LP, Caldas DL, et al. Evaluation of corneal shape and biomechanics before LASIK. Int Ophthalmol Clin. 2011;51:11-38. 22. Luce DA. Determining in vivo biomechanical properties of the cornea with an ocular response analyzer. J Cataract Refract Surg. 2005;31:156-162. 23. Roberts CJ. Concepts and misconceptions in corneal biomechanics. J Cataract Refract Surg. 2014;40:862-869. 24. Pinero DP, Alcon N. In vivo characterization of corneal biomechanics. J Cataract Refract Surg. 2014;40:870-87.

Copyright © 2018. Kugler Publications. All rights reserved.

214 25. Fontes BM, Ambrosio R Jr, Alonso RS, Jardim D, Velarde GC, Nose W. Corneal biomechanical metrics in eyes with refraction of -19.00 to +9.00 D in healthy Brazilian patients. J Refract Surg. 2008;24:941-945. 26. Shah S, Laiquzzaman M, Bhojwani R, Mantry S, Cunliffe I. Assessment of the biomechanical properties of the cornea with the ocular response analyzer in normal and keratoconic eyes. Invest Ophthalmol Vis Sci. 2007;48:3026-3031. 27. Fontes BM, Ambrosio R Jr, Velarde GC, Nose W. Corneal biomechanical evaluation in healthy thin corneas compared with matched keratoconus cases. Arq Bras Oftalmol. 2011;74:13-16. 28. Fontes BM, Ambrosio Junior R, Jardim D, Velarde GC, Nose W. Ability of corneal biomechanical metrics and anterior segment data in the differentiation of keratoconus and healthy corneas. Arq Bras Oftalmol. 2010;73:333-337. 29. Fontes BM, Ambrosio R Jr, Velarde GC, Nose W. Ocular response analyzer measurements in keratoconus with normal central corneal thickness compared with matched normal control eyes. J Refract Surg. 2011;27:209-215. 30. Fontes BM, Ambrosio R Jr, Jardim D, Velarde GC, Nose W. Corneal biomechanical metrics and anterior segment parameters in mild keratoconus. Ophthalmology. 2010;117:673-679. 31. Wolffsohn JS, Safeen S, Shah S, Laiquzzaman M. Changes of corneal biomechanics with keratoconus. Cornea. 2012;31:849-854. 32. Shah S, Laiquzzaman M. Comparison of corneal biomechanics in pre and post-refractive surgery and keratoconic eyes by Ocular Response Analyser. Cont Lens Anterior Eye. 2009;32:129132; quiz 51. 33. Lopes B, Ramos ICdO, Ribeiro G, et al. Bioestatísticas: conceitos fundamentais e aplicações práticas. Revista Brasileira de Oftalmologia. 2014;73:16-22. 34. Kerautret J, Colin J, Touboul D, Roberts C. Biomechanical characteristics of the ectatic cornea. J Cataract Refract Surg. 2008;34:510-513. 35. Galletti JD, Ruisenor Vazquez PR, Fuentes Bonthoux F, Pfortner T, Galletti JG. Multivariate analysis of the ocular response analyzer’s corneal deformation response curve for early keratoconus detection. J Ophthalmol. 2015;2015:496382. 36. Hallahan KM, Sinha Roy A, Ambrosio R Jr, Salomao M, Dupps WJ Jr. Discriminant value of custom ocular response analyzer waveform derivatives in keratoconus. Ophthalmology. 2014;121:459-468. 37. Ventura BV, Machado AP, Ambrosio R Jr, et al. Analysis of waveform-derived ORA parameters in early forms of keratoconus and normal corneas. J Refract Surg. 2013;29:637-643. 38. Luz A, Fontes BM, Lopes B, Ramos I, Schor P, Ambrosio R Jr. ORA waveform-derived biomechanical parameters to distinguish normal from keratoconic eyes. Arq Bras Oftalmol. 2013;76:111117. 39. Mikielewicz M, Kotliar K, Barraquer RI, Michael R. Air-pulse corneal applanation signal curve parameters for the characterisation of keratoconus. Br J Ophthalmol. 2011;95:793-798. 40. Luz A, Fontes B, Ramos I, et al. Evaluation of ocular biomechanical indices to distinguish normal from keratoconus eyes. Int J Ker Cor Ect Dis. 2012;1:145-150.

R. Ambrósio Jr. et al. 41. Qazi MA, Sanderson JP, Mahmoud AM, Yoon EY, Roberts CJ, Pepose JS. Postoperative changes in intraocular pressure and corneal biomechanical metrics Laser in situ keratomileusis versus laser-assisted subepithelial keratectomy. J Cataract Refract Surg. 2009;35:1774-1788. 42. Ambrosio R Jr, Caiado AL, Guerra FP, et al. Novel pachymetric parameters based on corneal tomography for diagnosing keratoconus. J Refract Surg. 2011;27:753-758. 43. Ambrosio R Jr. Percentage thickness increase and absolute difference from thinnest to describe thickness profile. J Refract Surg. 2010;26:84-6; author reply 6-7. 44. Ambrosio R Jr, Alonso RS, Luz A, Coca Velarde LG. Corneal-thickness spatial profile and corneal-volume distribution: tomographic indices to detect keratoconus. J Cataract Refract Surg. 2006;32:1851-1859. 45. Goebels S, Eppig T, Wagenpfeil S, Cayless A, Seitz B, Langenbucher A. Staging of keratoconus indices regarding tomography, topography, and biomechanical measurements. Am J Ophthalmol. 2015;159:733-738. 46. Labiris G, Giarmoukakis A, Gatzioufas Z, Sideroudi H, Kozobolis V, Seitz B. Diagnostic capacity of the keratoconus match index and keratoconus match probability in subclinical keratoconus. J Cataract Refract Surg. 2014;40:999-1005. 47. Labiris G, Gatzioufas Z, Sideroudi H, Giarmoukakis A, Kozobolis V, Seitz B. Biomechanical diagnosis of keratoconus: evaluation of the keratoconus match index and the keratoconus match probability. Acta Ophthalmol. 2013;91:e258-62. 48. Rabinowitz YS, Li X, Canedo AL, Ambrosio R Jr, Bykhovskaya Y. Optical coherence tomography combined with videokeratography to differentiate mild keratoconus subtypes. J Refract Surg. 2014;30:80-87. 49. Smadja D, Santhiago MR, Mello GR, Krueger RR, Colin J, Touboul D. Influence of the reference surface shape for discriminating between normal corneas, subclinical keratoconus, and keratoconus. J Refract Surg. 2013;29:274-281. 50. Johnson RD, Nguyen MT, Lee N, Hamilton DR. Corneal biomechanical properties in normal, forme fruste keratoconus, and manifest keratoconus after statistical correction for potentially confounding factors. Cornea 2011;30:516-523. 51. Wagner H, Barr JT, Zadnik K. Collaborative Longitudinal Evaluation of Keratoconus (CLEK) Study: methods and findings to date. Cont Lens Anterior Eye. 2007;30:223-232. 52. Ambrosio R Jr, Ramos I, Luz A, et al. Dynamic Ultra-High Speed Scheimpflug Imaging for assessing corneal biomechanical properties. Rev Bras Oftalmol. 2013;72. 53. Ye C, Yu M, Lai G, Jhanji V. Variability of corneal deformation response in normal and keratoconic eyes. Optom Vis Sci. 2015;92:e149-53. 54. Koprowski R. Open source software for the analysis of corneal deformation parameters on the images from the Corvis tonometer. Biomed Eng Online. 2015;14:31. 55. Bak-Nielsen S, Pedersen IB, Ivarsen A, Hjortdal J. Repeatability, reproducibility, and age dependency of dynamic Scheimpflug-based pneumotonometer and its correlation with a dynamic bidirectional pneumotonometry device. Cornea. 2015;34:71-7.

Biomechanics in ectasia detection: ORA and Corvis ST

Copyright © 2018. Kugler Publications. All rights reserved.

56. Ali NQ, Patel DV, McGhee CN. Biomechanical responses of healthy and keratoconic corneas measured using a noncontact scheimpflug-based tonometer. Invest Ophthalmol Vis Sci. 2014;55:3651-3659. 57. Nemeth G, Hassan Z, Csutak A, Szalai E, Berta A, Modis L Jr. Repeatability of ocular biomechanical data measurements with a Scheimpflug-based noncontact device on normal corneas. J Refract Surg. 2013;29:558-563. 58. Salomao MQ, Faria-Correia F, Ramos I, Luz A, Ambrósio RJ. Integration of Scheimpflug-based Corneal Tomography and Biomechanical Assessments for Enhancing Ectasia Detection. Int J Ker Cor Ect Dis. 2016;5:1-5. 59. Tian L, Ko MW, Wang LK, et al. Assessment of ocular biomechanics using dynamic ultra high-speed Scheimpflug imaging in keratoconic and normal eyes. J Refract Surg. 2014;30:785791. 60. Tian L, Huang YF, Wang LQ, et al. Corneal biomechanical assessment using corneal visualization scheimpflug technology in keratoconic and normal eyes. J Ophthalmol. 2014;2014:147516. 61. Steinberg J, Katz T, Lucke K, Frings A, Druchkiv V, Linke SJ. Screening for keratoconus with new dynamic biomechanical in vivo Scheimpflug analyses. Cornea. 2015;34(11):1404-1412

215 62. Vinciguerra R, Ambrosio R Jr, Elsheikh A, et al. Detection of keratoconus with a new biomechanical index. J Refract Surg. 2016;32:803-810. 63. Ambrósio RJ, Lopes BT, Faria-Correia F, et al. Integration of Scheimpflug-based corneal tomography and biomechanical assessments for enhancing ectasia detection. J Refract Surg. 2017;33(7):434-443 64. Ambrósio R Jr, Ramos I, Lopes B, et al. Assessing ectasia susceptibility prior to LASIK: the role of age and residual stromal bed (RSB) in conjunction to Belin-Ambrósio deviation index (BAD-D). Rev Bras Oftalmol. 2014;73:75-80. 65. Scarcelli G, Besner S, Pineda R, Yun SH. Biomechanical characterization of keratoconus corneas ex vivo with Brillouin microscopy. Invest Ophthalmol Vis Sci. 2014;55:4490-4495. 66. Girard MJ, Dupps WJ, Baskaran M, et al. Translating ocular biomechanics into clinical practice: current state and future prospects. Curr Eye Res. 2015;40:1-18. 67. Scarcelli G, Kling S, Quijano E, Pineda R, Marcos S, Yun SH. Brillouin microscopy of collagen crosslinking: noncontact depth-dependent analysis of corneal elastic modulus. Invest Ophthalmol Vis Sci. 2013;54:1418-1425.

Copyright © 2018. Kugler Publications. All rights reserved.

15. Mechanisms of collagen crosslinking and implications on biomechanics Eberhard Spoerl1, David C. Paik2 Carl Gustav Carus University Hospital, Department of Ophthalmology, Dresden, Germany; 2Paik Laboratory for Tissue Cross-linking, Columbia University Medical Center, New York, NY, USA

1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction The biomechanical behavior of collagen-containing tissues like the cornea or sclera depends on the arrangement of collagen molecules into fibrils of various diameters, and their higher order organization into sheets, i.e., lamellae and fibers, i.e., bundles, as well as the proteoglycan matrix that interconnects them. The collagen lamellae and bundles can be interwoven or more orthogonal, and a main process regarding their stabilization is the crosslinking of the collagen, be it through a precisely controlled enzymatic or more non-specific, random, adventitious non-enzymatic process. Crosslinkages within and along the surface of the fibril help to stabilize the mechanical properties of the higher-ordered fibrillar collagen structures, which are the main load-bearing elements present in the extracellular matrix (ECM). Such tensile properties prevent collagen fibril slippage, which has been suggested to occur during keratoconus (KC) development, leading ultimately to a dilated, increasingly curved surface (i.e., “the cone”). The mechanisms maintaining such a physiologic mechanical tissue state are controlled by a well-regulated, enzymatic crosslinking system, and its alterations provide an attractive hypothesis for KC pathogenesis. In addition, it should be pointed out that it is not only important to consider the overall macroscopic biomechanical behavior of the cornea when considering the effects of intentionally altering tissue mechanical properties for therapy,

but also, the stiffness of the corneal ECM, i.e., tensional homeostasis, has been shown to be a potent regulator of cellular behavior.1 Tissue mechanical properties can be modified by several substances artificially or in pathological processes (Fig. 1). Weakening can be induced by non-mammalian collagenases,2 matrix metalloproteinases,3 hormones (e.g., estrogen, cortisol),4-6 etc. For instance, collagenase can be used to produce corneal ectasia7 or weaken the peripapillary sclera at the optic nerve head.2 On the other hand, an increase of tissue stiffness can be achieved by several crosslinking methods (Fig. 1). In the biological sciences, the term crosslinking is used to express the formation of covalent chemical bridges following reactions between proteins or other molecules. In the case of collagens, crosslinks can change the physical properties of the crosslinked tissue or material. During the natural ageing process, both enzymatic and non-enzymatic crosslinking reactions occur to collagenous proteins. This occurs throughout the body and in various parts of eye tissue as well. The most common use of induced corneal crosslinking (CXL) is in the management of ectatic corneal disorders, which can halt the progression of disease. In the case of KC, visual acuity becomes worse due to an increasing irregularity in the corneal surface causing deterioration in optical imaging properties. Although in the case of KC the total collagen content of the cornea likely does not differ significantly from that of

Correspondence:Eberhard Spoerl, PhD, Associate Professor, Department of Ophthalmology, Carl Gustav Carus University Hospital, Fetscherstraße 74, D-01307, Dresden, Germany E-mail: [email protected] Biomechanics of the Eye, pp. 217-231 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

218

E. Spoerl and D.C. Paik

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 1. The two main kinds of biomechanical modification of collagen tissues.

the normal cornea, its stiffness is decreased by a factor of approximately 0.7.8 This factor suggests that crosslinking disruption within and/or between the collagen molecules could be present. Although a reduction of crosslinking has, among other things, already been suggested as a cause of KC9 it has not been confirmed (see discussion below). A similar reduction of the stiffness of the cornea also occurs after laser-assisted in situ keratomileusis (LASIK), where in very rare cases, owing to complex causes (e.g., preexisting KC, excessive tissue ablation, connective tissue diseases, etc.), keratectasia can develop. A refractive surgery procedure such as LASIK biomechanically weakens the cornea, since the effective corneal thickness becomes reduced to a degree determined by the thickness of the flap plus the depth of the ablation. If the remaining corneal stroma can no longer entirely compensate for the higher mechanical tension incurred (force per cross-sectional area), the cornea will bulge, resulting in a deterioration of optical imaging properties.10 The goal

of collagen crosslinking treatment with riboflavin/UVA light is to artificially increase the degree of crosslinks in the corneal stroma and, in this way, re-establish tissue mechanical stability.

2. Principles of crosslinking 2.1. Enzymatic crosslinking Under physiological conditions, collagen molecules assemble into fibrils that can then undergo an enzymatic post-translational modification in the extracellular space that results in fibril stabilization, i.e., maturation. This occurs through the action of the enzyme lysyl oxidase, i.e., protein-6-oxidase or LOX, and its related LOX-like enzymes (LOXL-1 to 4).11,12,13 In this way, the collagen fibrils attain their natural firmness and stability, as well as their tissue-specific elastic properties. LOX transforms the epsilon amino groups of certain lysines and hydroxylysines into aldehyde groups

Copyright © 2018. Kugler Publications. All rights reserved.

Mechanisms of collagen crosslinking and implications on biomechanics

through an oxidative deamination. These newly formed aldehydes can then spontaneously react with a second ε-amino group of lysine/hydroxylysine, in proximity, to create a Schiff base as an aldimine or keto-imine. Thus, difunctional lysine- (lys) and hydroxylysine- (OH-lys) derived crosslinks are the initial compounds formed enzymatically. The degree of hydroxylation (by lysyl hydroxylases) can also vary and will determine, to some extent, which di- and tri-functional crosslinks ­result.14-16 The subsequent development of the trifunctional histidine crosslink histidinohydroxylysinonorleucine (HHL) occurs spontaneously across such a Schiff base. From a chemical crosslink perspective, the cornea is unique from most other collagenous tissues in that trifunctional histidine collagen crosslinks are formed,17 similar to skin.18 Many other collagenous tissues are known to contain varying levels of the tri-functional lysine/hydroxylysine-derived pyridinolines rather than HHL, as in the cornea and skin. Traditional methods of difunctional crosslink analysis used tritiated NaB3H4 and other pre- or post-column derivatization methods that involve addition of a reaction chamber to enhance detector sensivity or selectivity. The trifunctional crosslink HHL has been measured using post-column derivatization methods, and the trifunctional pyridinolines (295ex/395em) and advanced glycation end-product (AGE) crosslink pentosidine (335ex/385em) by native fluorescence.14-16 Newer methods that employ liquid chromatography with mass spectrometry (LC/MS) are currently being used,19,20 as well as site-specificity analysis using matrix-assisted laser desorption ionization with timeof-flight mass spectrometry (MALDI-TOF).21 There are several conditions that have been associated with an alteration in LOX or LOXL activity. For example, in the case of Ehlers-Danlos syndrome there is a lysyl oxidase deficiency; in the case of keloids and scars, the activity activity of this enzyme is heightened.22 In the case of KC, recent genetic23 and immunohistochemistry24,25 studies have implicated LOX in the pathogenesis of KC. In addition, the activity of lysyl oxidase could be interfered with by a heightened pH-level in tear fluid, which has been observed in KC.26 Pathologically, the keratoconic cornea displays features that may be attributable to collagen crosslink alterations, including changes in the variation of distribution of collagen fibril diameters. In other words, as

219

the disease progresses, there is a greater proportion of fibril structures that are both very small or very large in diameter, which become particularly conspicuous in all corneal layers with severe disease.27 This may also be the reason for changed corneal densitometry in KC.28 Similar changes can be induced in animals through the use of lysyl oxidase inhibitors such a beta-aminopropionitrile (BAPN),29,30 a well-known agent for inducing lathyrism in animals and humans. Breaks (fractures) in Bowman’s layer have also been described as one of the earliest findings by scanning electron microscopy31 along with other abnormalities of the KC extracellular matrix (ECM).32,33 The initial attempt to measure difunctional enzymatic crosslinks in KC was reported in 1978,9 at which time the investigators found that KC corneas contained higher levels of lysinonorleucine (LNL). However, contrary findings were then reported in follow-up studies carried out in 198534 and 1988.35 HHL, a major non-reducible tri-functional crosslink, was not included in any of these studies as the methods for detection were not available at the time. A recent report using LC/MS techniques supports the finding that LNL is decreased in KC corneas, with no differences in HHL seen. This raises the possibility of an elastic or microfibril defect in KC pathogenesis.36 Future studies will be needed in order to clearly delineate alterations in enzymatic crosslinks that may underlie the disease. 2.2. Non-enzymatic crosslinking Although tissue crosslinking has been carried out for a number of purposes over many decades (and even centuries), the application of crosslinking methods to living tissues for therapeutic benefit is relatively new and began with the work of Seiler, Spoerl, and Wollensak.37 In other words, changing the mechanical properties of “living tissue” for therapeutic intent is quite different than cross-inking tissues for re-implantation or for building tissue engineered scaffolds, for example. This “paradigm shift” in our view toward tissue crosslinking has opened the door to the exploration of chemical crosslinking agents that could be used for crosslinking in vivo using a topical or injectable preparation. There are hundreds of crosslinking agents that have been used for a variety of purposes, including both industrial as well as biomedical applications. The areas of application are vast and there is significant overlap. For example, formaldehyde38 and glutaraldehyde,39 two

Copyright © 2018. Kugler Publications. All rights reserved.

220

of the most widely used crosslinking agents, are used in the production of resins for manufacturing plywood, textiles, etc., as well as for leather-making and rubber-hardening for tires. They have also been used in important biomedical applications such as fixation of bioprostheses (i.e., heart valves, skin grafting materials, etc.), biological scaffolds, hydrogels, and tissue fixation for histology/pathology. Some of the many commercially used crosslinking agents include other aldehyde agents such as glyceraldehyde,40 methylglyoxal,41 the group of carbodiimides,42 genipin,43 imidoesters such as dimethyl adipimidate and dimethyl suberimidate, Denacol-epoxys, derivatives of ethylene glycol dimethacrylate, derivatives of methylenebisacrylamide, and divinyl benzene. The lists are seemingly endless. Although many of these compounds are excellent crosslinking agents for in-vitro crosslinking applications, the list of available agents is much more limited when considering their possible use as in-vivo tissue cross-inking agents. Several aspects that are less relevant when considering in-vitro use become critical when considering their use in living organisms. Considerations for the cornea include: efficacy under physiological pH and temperature, permeability, coloration and effects on light transmission, and toxicity. The latter includes cytotoxicity, organismal toxicity, and genotoxicity, i.e., mutagenicity/carcinogenicity. Even in the absence of intentional crosslinking, with age alone the number of crosslinks, and therewith also the mechanical stiffness of various structures, increases.44,45 This has been observed in cornea, skin,46 the ocular lens,47 blood vessels,48 lungs,49 and joint cartilage. Oxidation and glycosylation as natural non-enzymatic tissue crosslinking mechanisms have been studied over the years. The oxidation of proteins is the basis for the free radical theory of aging. According to this theory, free oxygen radical species such as superoxide and hydroxyl radicals damage tissue proteins. The accumulation of these reaction products of oxidation are thought to contribute to age-related illness and the clinical manifestations of old age through crosslinking and other mechanisms.50 The non-enzymatic glycosylation (NEG) of proteins has also been implicated as a non-enzymatic collagen crosslinking mechanism relevant to diabetes and the aging process, i.e., sugar aldehydes forming advanced

E. Spoerl and D.C. Paik

glycation endproducts (AGEs).51 Glucose modification of proteins such as hemoglobin, alpha-crystallin in the eye, and collagens occurs via an Amadori rearrangement resulting in the formation of such compounds that include adducts, i.e., carboxymethyl-lysine and crosslinks, i.e., pentosidine. Abnormally rapid formation of such products of NEG, as would occur in diabetic individuals, is thought to contribute significantly to the alteration of tissue proteins which result in the clinical manifestations of diabetes. Although particularly relevant to longstanding diabetes, the NEG mechanism has also been shown to play a role in the non-diabetic aging process. Such AGEs-linkages can lead to undesirable biomechanical changes in the eye. A well-known example is the stiffer lens observed in diabetics as a result of modification of lens crystallins.52 However, diabetes can also produce a higher stiffness in the cornea which could, in turn, have a protective effect on the development of KC, i.e., prevent or limit the severity of disease.53,54 AGEs can also increase the stiffness of the sclera which, in turn, may also prevent the development of axial elongation seen in myopia, given that axial length has been shown to be shorter in diabetics.55 2.2.1. Other chemical crosslinking agents There are a number of chemical crosslinking agents that could be used for crosslinking corneal or scleral tissue and include glutaraldehyde, formaldehyde, diphenylphosphoryl, genipin,56,57 nitroalcohols,58-61 and other formaldehyde-releasing substances.62 The preferred use of these agents is for the modification of the properties of tissues containing collagen in the process of tissue engineering. That being said, recent studies suggest that the class of aliphatic β-nitroalcohols and other formaldehyde releasers (FARs) may be suitable. These compounds serve as formaldehyde delivery systems to induce biomechanical change under conditions of physiological pH and temperature. Although they deliver formaldehyde, they are less toxic than formaldehyde and test negative in genotoxicity testing.62 Interestingly, FARs are a group of compounds commonly used as preservatives in cosmetics and personal care products, and as fabric crosslinkers in the textile industry (i.e., for making wrinkle-free clothing), and include bronopol (BP), a well-known

Mechanisms of collagen crosslinking and implications on biomechanics

221

Fig. 2. Excitation of riboflavin and the two possible reaction mechanisms.

Copyright © 2018. Kugler Publications. All rights reserved.

compound.63 They are known to release formaldehyde in a pH- and concentration-dependent manner as determined by 13C nuclear magnetic resonance (NMR) equilibrium studies. FARs in commercial use include O- and N-formal compounds. There are two types of N-formal compounds: amide-based and amine-based. The type of group attached to the N-formal group confers different formaldehyde release properties. Slower release occurs with the amide-based N-formals — such as diazolidinyl urea (DAU), imidazolidinyl urea (IMU), DMDM hydantoin (DMDM) — which can act as formaldehyde reservoirs, whereas amine based N-formals, like sodium hydroxymethylglycinate (SMG), have been reported to decompose completely under alkaline conditions at 0.5%, the maximum allowed SMG concentration in cosmetics products as determined by European cosmetics standards.64 Efforts continue toward developing topical chemical crosslinking agents appropriate for treatment of living tissue. 2.2.2. Photo-oxidative cross-linking (UV, ionizing radiation) The most well-known photo-oxidative crosslinking reactions of the eye relate to the development of lens cortical cataract. However, the vitreous and scleral collagen can also become crosslinked. Photosensitizers such as rose bengal or riboflavin can potentiate this effect if they are used for treatment.

3. Photo-oxidative crosslinking with riboflavin (photo-oxidative CXL) The photo-oxidative crosslinking method with riboflavin and UVA light was chosen for stiffening of the cornea because it has a localized effect, a short period of therapy is sufficient, and it leaves the transparency of the cornea unaltered. Riboflavin is a vitamin (vitamin B2) also used as a coloring agent in food processing (e.g., in vanilla pudding) which is both non-toxic and available as medication. 3.1. Biochemical mechanism of photo-oxidative CXL The photochemical basis of crosslinking lies in the photodynamic type I-II reactions induced by the interaction between riboflavin and UVA-light, releasing reactive oxygen species that mediate crosslink formation between and within collagen fibers and proteoglycans. In this photochemical reaction, radicals are created by UV light. To increase the effectiveness of this process in the presence of UV radiation, a special photosensitizer (transfer molecule) of riboflavin is used. If riboflavin absorbs energy from UV light, it excites (excited singlet riboflavin1RF*; lifetime: 10 -8 s). In an exchange mechanism, the excited singlet riboflavin is transformed into triplet-excited riboflavin (3RF*; lifetime :10 -2 s).65 Type I and type II reactions can be differentiated (Fig. 2). For a type II reaction, oxygen is necessary to form singlet oxygen. Singlet oxygen is the physically excited form of the oxygen molecule,66 in which the

222

E. Spoerl and D.C. Paik

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. Location of the crosslinks.75

number of electrons remains constant but the spin, that is, the direction in which an electron is turning, changes. Through interaction with triplet oxygen (3O2), very reactive singlet oxygen (1O2) — an oxygen radical which continues to interact with the carbonyl group of collagens — is created. However, if the necessary oxygen is depleted by UV then type I reaction dominates.67 In CXL both reactions take place. It should be kept in mind that photoproducts from riboflavin photochemical reactions have been described, including lumichrome and lumiflavin. Thus, it is not unreasonable to suggest that these photoproducts and others could themselves be involved in the crosslinking reactions.68 In this photochemical process, active locations along the molecule chain that react with each other intermolecularly or intramolecularly creating covalent bonds between the amino acids (especially histidines, lysines, hydroxylysines, and tyrosine), the so-called crosslinkages, are created. The formation of dityrosine from tyrosine, due to which the intermolecular and intramolecular linkages of the collagen molecules can be created, has also been observed.69-71 The amine groups do not play a major role in riboflavin UV crosslinking.72 However, this CXL is carbonyl-dependent and involves the formation of advanced glycation endproduct crosslinks,73 like in age-related crosslinking. Recent work indicates that CXL generates crosslinks not only between collagen molecules, but also between proteoglycan core proteins (Fig. 3).74,75 Thus, interfibrillar bonds seem to also be possible, whereas the CXL does not increase interlamellar crosslinks.76 The prerequisite for the initiation of a chemical reaction by light is the absorption of this light by the reactive system. The photochemical crosslinking effect (photopolymerization) occurs only where riboflavin is activated by UV light.

3.2. Possibilities of enrichment of riboflavin in the stroma A sufficient concentration of riboflavin and oxygen is the prerequisite for a strong biomechanical crosslinking effect in the stroma. There are various methods by which this concentration in the stroma may be achieved: 1. diffusion in the de-epithelialized stroma (standard method); and 2. diffusion through the epithelium into the stroma (transepithelial method); 3. direct introduction of riboflavin into the stroma (pocket technique, ring technique, needle technique). 3.2.1. Standard method or “epithelium-off” method The intact epithelium constitutes a diffusion barrier for riboflavin (molecular weight 376 g/mol) and must therefore be mechanically removed prior to the application of the riboflavin drops.77,78 A certain amount of time is required for the diffusion of riboflavin into the deeper levels of the stroma in accordance with the law of diffusion.79,80 For this reason, it is very important to drip riboflavin solution onto the de-epithelialized cornea approximately 15 minutes prior to radiation in order to achieve a high total concentration and a high total absorption, thus guaranteeing the protection of the corneal endothelium, lens and, retina. In the anterior stroma, the concentration is of course highest; 15 minutes after riboflavin application, a dynamic equilibrium has been established and the concentration will show a linear decrease deeper in the stroma, as calculations and measurements have proven.79,81-84 3.2.2. Transepithelial method or “epithelium-on” method There are several methods by which the penetration of riboflavin through the epithelium can be increased:

Mechanisms of collagen crosslinking and implications on biomechanics

1. increased contact time (viscous solution, ring application); 2. changing the permeability of the epithelium (benzalkonium choride (BAC), ethylendiaminatetetraacetic acid (EDTA), channel-forming peptides, mechanical changes); and 3. altering the physicochemical properties of the riboflavin solution (osmolarity, iontophoresis, concentration). BAC increases epithelial permeability by loosening the tight junctions. This pharmacological modification of corneal epithelial permeability represents a novel method to avoid epithelial debridement in CXL.85,86 Therefore, some surgeons modify the standard protocol and perform the treatment without removing the epithelium by using benzalkonium chloride (BAC), tetracaine, or pilocarpine containing BAC and EDTA. For this reason, a transepithelial riboflavin solution in transepithelial CXL procedures should not contain dextran, but 0.01% BAC or EDTA and 0.44% NaCl to increase permeability of the epithelium, allowing riboflavin to reach a high concentration in the corneal stroma.87

Copyright © 2018. Kugler Publications. All rights reserved.

3.2.3. Direct application The direct application of riboflavin into the stroma was proposed by Daxer.88 He produces a pocket in the stroma and fills riboflavin in this pocket. Seiler created channels with fs-laser.89 The same technique is used if intracorneal rings are implanted. Then the riboflavin is filled in the canal and the cornea is crosslinked.90-92 3.2.4. Iontophoresis Iontophoresis is a non-invasive technique in which a weak electric current is used to enhance the penetration of electrically charged molecules into tissue. Riboflavin is negatively charged and suitable for iontophoresis. In five minutes of iontophoresis, a sufficient riboflavin concentration is reached in the stroma for crosslinking. Thus, this technique does not only leave the epithelium intact, but also shortens pre-treatment time.92 3.3. Absorption of UV radiation in the cornea In order to limit the crosslinking effect only to the corneal stroma, the greatest part of the UV light must be absorbed there since radiation only has an effect where it is absorbed, thus transferring energy to the

223

tissue according to the First Law of Photochemistry. The riboflavin concentration of 0.1% was chosen for the treatment of a stroma of a thickness of approximately 400 µm (this value corresponds approximately to the average in cases of KC)94 for two reasons. Since the biomechanical effect in a large area of concentration (0.015 to 0.5%) is independent of the concentration,95 the concentration was chosen in consideration of the UV protective effect.77 This concentration of 0.1% produces a large absorption coefficient,96,97 so that 90% of the UV radiation is absorbed in the stroma while the endothelium, ocular lens, and retina remain largely protected from the UV light. Due to the high absorption coefficient (µ = 50 cm-1),98 the irradiation intensity of the UV light is lessened so much on its way through the cornea that, with a radiation dose of 5.4 J/ cm², the destruction threshold for the endothelium is not reached.79 Increasing corneal thickness to 400 µm can be achieved in the case of a thin cornea by swelling using a hypo-osmolar riboflavin solution without reaching the toxicity threshold for the endothelium.99 The absorption coefficient and thus the concentration must, however, not be too high either, so that as thick a layer of the stroma as possible is cross-linking strength at a particular stromal depth using the concentration of riboflavin and the UV dosage as input.80 3.4. UV irradiation Riboflavin has two absorption maxima, at 365 nm and 430 nm; radiation with 365 nm achieves a greater crosslinking effect (W= h · c/λ) owing to the higher energy content (λ = wavelength, c = velocity of light, h = Planck’s constant).100 Due to the absorption maximum of riboflavin at 365 nm, this wavelength was specially chosen for UV light treatment. This achieves an absorption of 90% of UV light in a de-epithelialized cornea 400 µm thick without endangering the lens or the cornea. The irradiation procedure is independent of the nature of the riboflavin application. Today, various irradiation systems which work with UV light emission diodes and supply a homogeneous irradiation dosage of 5.4 J/cm² on a circular area 8-11 mm in diameter on the cornea are available as sources of UV radiation. Some devices make it possible to choose the size of the area to be irradiated. The choice of an 8 to 9 mm diameter irradiation area minimizes the risk of UV exposure of the limbus and sclera. The oxygen in the tissue is critical in

224

E. Spoerl and D.C. Paik

Fig. 4. Treatment parameters for riboflavin/UV CXL.

the crosslinking process.101,102 In the beginning of the procedure, oxygen is still present in sufficient quantity to enable the formation of crosslinkages. However, if it is depleted, this may interfere with crosslinking.67 All parameters — irradiation intensity, irradiation time, and riboflavin concentration (Fig. 4) — have been tested in experiments,99 including animal experiments,76 and have proven themselves in clinical studies.103

Copyright © 2018. Kugler Publications. All rights reserved.

4. Effects and proof of ex-vivo crosslinking Currently, the photochemically induced crosslinks in the cornea cannot be directly visualized using either spectrophotometric labeling methods or other microscopic techniques. That being said, CXL causes changes to numerous physicochemical properties of corneal tissue, from which one can conclude that covalent crosslinking has taken place. Some changes are detailed below (Fig. 5). 4.1. An increase in stiffness and Young’s modulus Evidence of biomechanical property changes have been shown following CXL using stress-strain measurements (uniaxial, biaxial, and inflation testing), indention measurements, scanning acoustic microscopy, ultrasound

shear waves, Brillouin microscopy, autofluorescence, second harmonic generated signal detection, and other techniques. Stress-strain measurements with uniaxial strip-extensometry techniques revealed that corneas that have been crosslinked with riboflavin/UVA are stiffer than the untreated cornea by a factor of approximately 1.7, which is why using this technique as a treatment for KC makes sense.100,104-106 The CXL-induced stiffening effect appears to be higher in cases in which there is a higher collagen content and in older corneas.104,107 A significant increase in corneal stiffness was shown in treated corneas of enucleated human and porcine eyes, as indicated by a rise in stress. An increase in Young’s modulus was also determined both in porcine and human corneas (by factors of 1.7).104,106 Investigations in rabbit corneas showed a 1.7x higher breaking strength (failure-tension) of crosslinked corneas.72 Further investigations of biomechanical properties using tangential sectioning techniques indicate that an increased stiffening effect occurs in the anterior (approximately 200 µm) over the posterior stroma, both in enucleated porcine and enucleated human corneas.105 This “anterior stromal effect” seen using CXL has been further supported by simultaneous evaluation of the posterior corneal stroma, which, by comparison with the anterior stroma, shows a lesser increase in fiber diameter,108 greater sus-

Mechanisms of collagen crosslinking and implications on biomechanics

225

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. Changes in properties after crosslinking.

ceptibility to enzymatic degradation,109,110 and lower thermal shrinkage temperature.111 Long-lasting improvements in the biomechanical properties of corneal tissue have been confirmed in rabbit studies for 12 weeks77 and up to 8 months following CXL.112 Using inflation testing experiments for stress-strain measurements of the whole eye, Kling et al. found Young’s modulus was 1.6 times higher for the crosslinked porcine cornea in comparison to the untreated cornea.113 Similar results were also found using an indentation technique known as atomic force microscopy (or AFM). In these studies, Young’s modulus in the anterior cornea was 1.9 times higher in the crosslinked cornea in comparison to the untreated cornea. In the posterior cornea, there was no difference between treated and untreated corneas, similar to the results described earlier using the aforementioned techniques.114 Other new biomechanical testing techniques confirm the mechanical property changes induced by CXL. Scanning acoustic microscopy has been reported to detect changes in corneal stiffness after application of CXL.115 In an in-vivo study using porcine eyes, supersonic shear wave imaging has shown a 56% higher shear wave velocity (an indicator for increased stiffness) in CXL-treated corneas.116 Brillouin microscopy

has also shown analogous findings which indicate that the cornea is stiffer after crosslinking.116 These types of biomechanical changes have also been shown in scleral tissue using different crosslinking techniques.2,117-120 4.2. A raising of the shrinkage temperature The reported shift in thermal shrinkage (or denaturation) temperature of the cornea following CXL varies from +1.7 to 2.5ºC. This also provides laboratory evidence that crosslinking has been induced, since shrinkage temperature positively correlates with the degree of crosslinking.59,109 Given that the cornea is so predominately comprised of collagen lamellae, the major thermal denaturation that occurs reflects the unwinding of the fibril-containing collagen molecules. 4.3. A decrease in the swelling facility Cross-linked collagen also shows a lessened tendency to swell.121 This property could be exploited for the treatment of bullous keratopathy and/or decompensated Fuchs´ endothelial dystrophy. 4.4. An increase in the thickness of collagen fibrils Morphologically, the effect of CXL has been demonstrated by measuring collagen fibril diameter in treated

226

rabbit corneas. Transmission electron microscopy revealed a statistically significant increase in collagen fibril diameter in both anterior and posterior stroma, although this effect was more pronounced in the anterior stroma.108 4.5. An increase in the resistance to enzymatic degradation processes In KC, higher levels of collagen-degrading enzymes have been measured in tear fluid, which can contribute to collagen degradation and eventual thinning of the corneal stroma.122,123 A CXL-treated cornea will become relatively resistant to enzymatic digestion which could, in part, explain how and why the treatment works. This property of resistance to enzymatic digestion will also tend to lengthen the turnover time of corneal collagen by preventing its enzymatic digestion by endogenous matrix metalloproteinases. In theory, this will prolong the therapeutic effect.109

Copyright © 2018. Kugler Publications. All rights reserved.

4.6. The creation of molecular aggregates with a higher molecular weight124 The creation of molecular aggregates with a higher molecular weight124 has been shown using sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and is a common method for evaluating increases in covalent crosslinking, particularly for soluble proteins, but also for fibrillary collagens. 4.7. A decrease in permeability41,125 A decrease in permeability41,125 has also been shown and could be relevant for clinical issues. The degree of non-enzymatic crosslinking increases with age, where it is cumulatively increased, particularly in long-lived proteins such as collagens. The available evidence using a variety of physicochemical techniques indicate that the CXL method induces covalent crosslinking particularly focused on the anterior stroma.

5. The influence of CXL on intraocular pressure (IOP) measurement In applanation tonometry, corneal thickness and stiffness influence the measurement of IOP. Because of this, it is to be expected that after crosslinking and stiffening of the cornea, the IOP measurement could

E. Spoerl and D.C. Paik

be artifactually high. A dramatic non-clinical demonstration of this potential artifact was produced after glutaraldehyde CXL of ex-vivo human globes resulted in corneal IOP artifacts over twice as high as intravitreal IOP measurements.126 In an in-vitro model of human corneas, an overestimation of the IOP by Goldmann applanation tonometry after CXL was in the range of 1.3-3.1 mmHg.127 However, since the cornea becomes firmer only by a factor of 1.7, that is, the Young’s modulus increases by a factor of 1.7, the IOP is measured as at most 1.6 mmHg too high, according to a calculation by Liu.128 In a study involving a large number of cases (55 eyes), this effect — a too-high IOP value of 1.5 mmHg after CXL — was demonstrated with statistical significance.129 However, the influence of CXL on IOP measurement in individual cases is difficult to predict due to variations in IOP.

6. Safety of CXL If possible, eye exposure to UV light should be avoided. Health and safety regulations allow a daily UVA irradiation intensity of 1 mW/cm² without a photosensitizer for the unprotected eye.130 Of this, approximately 35% is absorbed by the cornea, and it may be assumed that the endothelium is exposed to 0.65 mW/ cm². In animal experiments the damage threshold of the endothelial cells in the case of a 30-minute UVA irradiation without a photosensitizer was found to be 4 mW/cm².131 In the case of collagen crosslinking with riboflavin and UVA light, an irradiation of 3 mW/cm² following the application of riboflavin is used. In a layer of stroma approximately 400 µm thick, 90% of the UV radiation is absorbed in the riboflavin-treated cornea, so that the endothelium is exposed to only 0.18 mW/ cm².79 This value is below the damage threshold of 0.35 mW/cm² established in animal experiments for the endothelium,131 and also below the health and safety regulations value of 0.65 mW/cm². Further safety for the retina can be achieved via the choice of irradiation equipment. Due to the short distance from the source of irradiation to the eye and the divergent irradiation (Koehler irradiation principle), the UV radiation is not focused on the retina. Thus, only very shallow irradiation densities, which lie well under the damage threshold, are reached on the lens

Mechanisms of collagen crosslinking and implications on biomechanics

or retina. Grewal132 and also Vinciguerra133 found no significant difference in crystalline lens density before and 12 months after CXL using Scheimpflug imaging. No retinal morphology changes after CXL were observed.

7. Conclusion The crosslinking procedure performed by means of riboflavin and UVA light showed a significant increase in biomechanical rigidity in porcine and human corneas. From other experiments on the diameter of corneal collagen fibers, resistance to enzymatic digestion, and keratocyte loss after the CXL procedure, we see that the crosslinking effect and cytotoxic effect are significantly higher in the anterior portion of the corneal stroma. This is caused by the significant increase in UVA absorption by riboflavin, leading to a rapid reduction of UVA irradiance and collagen CXL across the cornea. The anterior localization of the main CXL effect has the

References 1.

2.

3.

Copyright © 2018. Kugler Publications. All rights reserved.

4.

5.

6.

7.

Petroll WM, Miron-Mendoza M. Mechanical interactions and crosstalk between corneal keratocytes and the extracellular matrix. Exp Eye Res. 2015;133:49-57. Spoerl E, Boehm AG, Pillunat LE. The influence of various substances on the biomechanical behavior of lamina cribrosa and peripapillary sclera. Invest Ophthalmol Vis Sci. 2005;46(4):12861290. Amar S, Smith L, Fields GB. Matrix metalloproteinase collagenolysis in health and disease. Biochim Biophys Acta. 2017;1864(11):1940-1951. Spoerl E, Zubaty V, Raiskup-Wolf F, Pillunat LE. Oestrogen-induced changes in biomechanics in the cornea as a possible reason for keratectasia. Br J Ophthalmol. 2007;91(11):15471550. Spoerl E, Zubaty V, Terai N, Pillunat LE, Raiskup F. Influence of high-dose cortisol on the biomechanics of incubated porcine corneal strips. J Refract Surg. 2009;25(9):S794-798. Lenk J, Spoerl E, Stalder T, et al. Increased hair cortisol concentrations in patients with progressive keratoconus. J Refract Surg. 2017;33(6):383-388. Hong CW, Sinha-Roy A, Schoenfield L, McMahon JT, Dupps WJ, Jr. Collagenase-mediated tissue modeling of corneal ectasia and collagen cross-linking treatments. Invest Ophthalmol Vis Sci. 2012;53(4):2321-2327.

227

advantage of allowing us to achieve a relatively high increase in corneal rigidity in human eyes due to the relatively small thickness of the human cornea while sparing the endothelium, lens, and retina from cytotoxic damage. Other CXL methods that have been proposed and also tested in vitro have a biomechanical effect on the cornea comparable to riboflavin-UVA treatment, but cannot be used clinically because of the development of corneal haze and scarring.104 In summary, safe clinical application of CXL must respect the following criteria: to facilitate diffusion of riboflavin throughout the corneal stroma, the epithelium should be removed or a sufficient permeability of the epithelium must be guaranteed, 0.1% riboflavin solution should be applied for at least 10 minutes before the UV exposure (during UV exposure, the riboflavin serves as both a photosensitizer and a UV blocker), the UV dosage of 5.4 J/ cm2 with wavelength of 370nm must be homogenous and the cornea to be cross-linked must have a minimal thickness of 400μm to protect endothelium.79

8.

9. 10.

11. 12.

13. 14. 15. 16.

17.

Andreassen TT, Simonsen AH, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Exp Eye Res. 1980;31(4):435-441. Cannon DJ, Foster CS. Collagen crosslinking in keratoconus. Invest Ophthalmol Vis Sci. 1978;17(1):63-65. Randleman JB. Post-laser in-situ keratomileusis ectasia: current understanding and future directions. Curr Opin Ophthalmol. 2006;17(4):406-412. Kagan HM, Trackman PC. Properties and function of lysyl oxidase. Am J Respir Cell Mol Biol. 1991;5(3):206-210. Trackman PC. Diverse biological functions of extracellular collagen processing enzymes. J Cell Biochem. 2005;96(5):927937. Yamauchi M, Sricholpech M. Lysine post-translational modifications of collagen. Essays Biochem. 2012;52:113-133. Avery NC, Sims TJ, Bailey AJ. quantitative determination of collagen cross-links. Methods Mol Biol. 2009;522:103-121. Eyre DR, Weis MA, Wu JJ. Advances in collagen cross-link analysis. Methods. 2008;45(1):65-74. Robins SP. Biochemistry and functional significance of collagen cross-linking. Biochem Soc Trans. 2007;35(5):849852. Yamauchi M, Chandler GS, Tanzawa H, Katz EP. Cross-linking and the molecular packing of corneal collagen. Biochem Biophys Res Commun. 1996;219(2):311-315.

Copyright © 2018. Kugler Publications. All rights reserved.

228 18. Yamauchi M, London RE, Guenat C, Hashimoto F, Mechanic GL. Structure and formation of a stable histidine-based trifunctional cross-link in skin collagen. J Biol Chem. 1987;262(24):1142811434. 19. Gineyts E, Borel O, Chapurlat R, Garnero P. Quantification of immature and mature collagen crosslinks by liquid chromatography-electrospray ionization mass spectrometry in connective tissues. J Chromatogr B Analyt Technol Biomed Life Sci. 2010;878(19):1449-1454. 20. Yoshida K, Jiang H, Kim M, et al. Quantitative evaluation of collagen crosslinks and corresponding tensile mechanical properties in mouse cervical tissue during normal pregnancy. PloS One. 2014;9(11):e112391. 21. Henkel W, Dreisewerd K. Cyanogen bromide peptides of the fibrillar collagens I, III, and V and their mass spectrometric characterization: detection of linear peptides, peptide glycosylation, and cross-linking peptides involved in formation of homoand heterotypic fibrils. J Proteome Res. 2007;6(11):4269-4289. 22. Uzawa K, Marshall MK, Katz EP, Tanzawa H, Yeowell HN, Yamauchi M. Altered posttranslational modifications of collagen in keloid. Biochem Biophys Res Commun. 1998;249(3):652-655. 23. Bykhovskaya Y, Li X, Epifantseva I, et al. Variation in the lysyl oxidase (LOX) gene is associated with keratoconus in family-based and case-control studies. Invest Ophthalmol Vis Sci. 2012;53(7):4152-4157. 24. Dudakova L, Liskova P, Trojek T, Palos M, Kalasova S, Jirsova K. Changes in lysyl oxidase (LOX) distribution and its decreased activity in keratoconus corneas. Exp Eye Res. 2012;104:74-81. 25. Pahuja N, Kumar NR, Shroff R, et al. Differential molecular expression of extracellular matrix and inflammatory genes at the corneal cone apex drives focal weakening in keratoconus. Invest Ophthalmol Visl Sci. 2016;57(13):5372-5382. 26. Avetisov S, Mamikonian V, Novikov I. The role of tear acidity and Cu-cofactor of lysyl oxidase activity in the pathogenesis of keratoconus. Vestn Oftalmol. 2011;127(2):3-8. 27. Akhtar S, Bron AJ, Salvi SM, Hawksworth NR, Tuft SJ, Meek KM. Ultrastructural analysis of collagen fibrils and proteoglycans in keratoconus. Acta Ophthalmol. 2008;86(7):764-772. 28. Lopes B, Ramos I, Ambrosio R Jr. Corneal densitometry in keratoconus. Cornea. 2014;33(12):1282-1286. 29. Shore RC, Moxham BJ, Berkovitz BK. Changes in collagen fibril diameters in a lathyritic connective tissue. Connect Tissue Res. 1984;12(3-4):249-255. 30. McBrien NA, Norton TT. Prevention of collagen crosslinking increases form-deprivation myopia in tree shrew. Exp Eye Res. 1994;59(4):475-486. 31. Sawaguchi S, Fukuchi T, Abe H, Kaiya T, Sugar J, Yue BY. Three-dimensional scanning electron microscopic study of keratoconus corneas. Arch Ophthalmol. 1998;116(1):62-68. 32. Kenney MC, Nesburn AB, Burgeson RE, Butkowski RJ, Ljubimov AV. Abnormalities of the extracellular matrix in keratoconus corneas. Cornea. 1997;16(3):345-351. 33. Pouliquen Y, Faure JP, Limon S, Bisson J. Extracellular deposits of corneal stroma in keratoconus. Electron microscopic study. Arch Ophtalmol Rev Gen Ophtalmol. 1968;28(3):283-294.

E. Spoerl and D.C. Paik 34. Oxlund H, Simonsen AH. Biochemical studies of normal and keratoconus corneas. Acta Ophthalmol (Copenh). 1985;63(6):666-669. 35. Critchfield JW, Calandra AJ, Nesburn AB, Kenney MC. Keratoconus: I. Biochemical studies. Exp Eye Res. 1988;46(6):953-963. 36. Takaoka A, Babar N, Hogan J, et al. An evaluation of lysyl oxidase-derived crossl linking in keratoconus by liquid chromatography/mass spectrometry. Invest Ophthalmol Vis Sci. 2016;57(1):126-136. 37. Wollensak G, Spoerl E, Seiler T. Riboflavin/ultraviolet –a-induced collagen crosslinking for the treatment of keratoconus. Am J Ophthalmol. 2003;135(5):620-627. 38. Heck HD, Casanova M, Starr TB. Formaldehyde toxicity--new understanding. Crit Rev Toxicol. 1990;20(6):397-426. 39. Nimni ME. Glutaraldehyde fixation revisited. J Long Term Eff Med Implants. 2001;11(3-4):151-161. 40. Wollensak G. Thermomechanical stability of sclera after glyceraldehyde crosslinking. Graefes Arch Clin Exp Ophthalmol. 2011;249(3):399-406. 41. Stewart JM, Schultz DS, Lee OT, Trinidad ML. Exogenous collagen cross-linking reduces scleral permeability: modeling the effects of age-related cross-link accumulation. Invest Ophthalmol Vis Sci. 2009;50(1):352-357. 42. Liu Y, Gan L, Carlsson DJ, et al. A simple, cross-linked collagen tissue substitute for corneal implantation. Invest Ophthalmol Vis Sci. 2006;47(5):1869-1875. 43. Tsai CC, Huang RN, Sung HW, Liang HC. In vitro evaluation of the genotoxicity of a naturally occurring crosslinking agent (genipin) for biologic tissue fixation. J Biomed Mater Res. 2000;52(1):58-65. 44. Elsheikh A, Wang D, Brown M, Rama P, Campanelli M, Pye D. Assessment of corneal biomechanical properties and their variation with age. Curr Eye Res. 2007;32(1):11-19. 45. Knox Cartwright NE, Tyrer JR, Marshall J. Age-related differences in the elasticity of the human cornea. Invest Ophthalmol Vis Sci. 2010;52(7):4324-4329. 46. Lavker RM, Zheng PS, Dong G. Aged skin: a study by light, transmission electron, and scanning electron microscopy. J Invest Dermatol. 1987;88(3Suppl):44s-51s. 47. Bron AJ, Vrensen GF, Koretz J, Maraini G, Harding JJ. The ageing lens. Ophthalmologica. 2000;214(1):86-104. 48. Bilato C, Crow MT. Atherosclerosis and the vascular biology of aging. Aging (Milano). 1996;8(4):221-234. 49. Rossi A, Ganassini A, Tantucci C, Grassi V. Aging and the respiratory system. Aging (Milano). 1996;8(3)143-161. 50. Harman D. Free radical theory of aging. Mutat Res. 1992;275(36):257-266. 51. Dunn JA, McCance DR, Thorpe SR, Lyons TJ, Baynes JW. Age-dependent accumulation of N epsilon-(carboxymethyl)lysine and N epsilon-(carboxymethyl)hydroxylysine in human skin collagen. Biochemistry. 1991;30(5):1205-1210. 52. Lee AT, Cerami A. Role of glycation in aging. Ann N Y Acad Sci. 1992;663:63-70. 53. Kuo IC, Broman A, Pirouzmanesh A, Melia M. Is there an association between diabetes and keratoconus? Ophthalmology. 2006;113(2):184-190.

Copyright © 2018. Kugler Publications. All rights reserved.

Mechanisms of collagen crosslinking and implications on biomechanics 54. Seiler T, Huhle S, Spoerl E, Kunath H. Manifest diabetes and keratoconus: a retrospective case-control study. Graefes Arch Clin Exp Ophthalmol. 2000;238(10):822-825. 55. Pierro L, Brancato R, Robino X, Lattanzio R, Jansen A, Calori G. Axial length in patients with diabetes. Retina. 1999;19(5):401-404. 56. Avila MY, Gerena VA, Navia JL. Corneal crosslinking with genipin, comparison with UV-Riboflavin in ex-vivo model. Mol Vis. 2012;18:1068-1073. 57. Avila MY, Navia JL. Effect of genipin collagen crosslinking on porcine corneas. J Cataract Refract Surg. 2010;36(4):659-664. 58. Paik DC, Wen Q, Airiani S, Braunstein RE, Trokel SL. Aliphatic beta-nitro alcohols for non-enzymatic collagen cross-linking of scleral tissue. Exp Eye Res. 2008;87(3):279-285. 59. Paik DC, Wen Q, Braunstein RE, Airiani S, Trokel SL. Initial studies using aliphatic beta-nitro alcohols for therapeutic corneal cross-linking. Invest Ophthalmol Vis Sci. 2009;50(3):1098-1105. 60. Paik DC, Solomon MR, Wen Q, Turro NJ, Trokel SL. Aliphatic beta-nitroalcohols for therapeutic corneoscleral cross-linking: chemical mechanisms and higher order nitroalcohols. Invest Ophthalmol Vis Sci. 2010;51(2):836-843. 61. Wen Q, Trokel SL, Kim M, Paik DC. Aliphatic beta-nitroalcohols for therapeutic corneoscleral cross-linking: corneal permeability considerations. Cornea. 2013;32(2):179-184. 62. Babar N, Kim M, Cao K, et al. Cosmetic preservatives as therapeutic corneal and scleral tissue cross-linking agents. Invest Ophthalmol Vis Sci. 2015;56(2):1274-1282. 63. de Groot AC, Flyvholm MA, Lensen G, Menne T, Coenraads PJ. Formaldehyde-releasers: relationship to formaldehyde contact allergy. Contact allergy to formaldehyde and inventory of formaldehyde-releasers. Contact Dermatitis. 2009;61(2):63-85. 64. Emeis D, Anker W, Wittern KP. Quantitative 13C NMR spectroscopic studies on the equilibrium of formaldehyde with its releasing cosmetic preservatives. Anal Chem. 2007;79(5):20962100. 65. Huang R, Choe E, DB M. Kinetics for singlet oxygen formation by riboflavin photosensitization and the reaction between riboflavin and singlet oxygen. J Food Sci. 2004;69:726-732. 66. Elstner E F. Der Sauerstoff Biochemie, Biologie, Medizin. Mannhaim-Leipzig-Wien-Zürich, 1990:288. 67. Kamaev P, Friedman MD, Sherr E, Muller D. Photochemical kinetics of corneal cross-linking with riboflavin. Invest Ophthalmol Vis Sci. 2012;53(4):2360-2367. 68. Sheraz MA, Kazi SH, Ahmed S, Qadeer K, Khan MF, Iqbal A. Multicomponent spectrometric analysis of riboflavin and photoproducts and their kinetic applications. Cent Eur J Chem. 2014;12(6):635-642. 69. Balasubramanian D, Kanwar R. Molecular pathology of dityrosine cross-links in proteins: structural and functional analysis of four proteins. Mol Cell Biochem. 2002;234-235(1-2):27-38. 70. Kato Y, Uchida K, Kawakishi S. Aggregation of collagen exposed to UVA in the presence of riboflavin: a plausible role of tyrosine modification. Photochem Photobiol. 1994;59(3):343-349. 71. Marcovich AL. Brandis A, Daphna O, et al. Stiffening of rabbit corneas by the bacteriochlorphyll derivate WST11 using near infrared light. Invest Ophthalmol Vis Sci. 2012;53(10):6378-88.

229

72. McCall AS, Kraft S, Edelhauser HF, et al. Mechanisms of corneal tissue cross-linking in response to treatment with topical riboflavin and long-wavelength ultraviolet radiation (UVA). Invest Ophthalmol Vis Sci. 2010;51(1):129-138. 73. Brummer G, Littlechild S, McCall S, Zhang Y, Conrad GW. The Role of Non-Enzymatic Glycation and Carbonyls in Collagen Cross-Linking for the Treatment of Keratoconus. Invest Ophthalmol Vis Sci. 2011;52(9):6363-9. 74. Zhang Y, Conrad AH, Conrad GW. Effects of ultraviolet-A and riboflavin on the interaction of collagen and proteoglycans during corneal cross-linking. J Biol Chem. 2011;286(15):1301113022. 75. Hayes S, Kamma-Lorger CS, Boote C, et al. The effect of riboflavin/UVA collagen cross-linking therapy on the structure and hydrodynamic behaviour of the ungulate and rabbit corneal stroma. PloS One. 2013;8(1):e52860. 76. Wollensak G, Sporl E, Mazzotta C, Kalinski T, Sel S. Interlamellar cohesion after corneal crosslinking using riboflavin and ultraviolet A light. Br J Ophthalmol. 2011;95(6):876-880. 77. Sporl E, Schreiber J, Hellmund K, Seiler T, Knuschke P. Studies on the stabilization of the cornea in rabbits. Ophthalmologe. 2000;97(3):203-206. 78. Hayes S, O’Brart DP, Lamdin LS, et al. Effect of complete epithelial debridement before riboflavin-ultraviolet-A corneal collagen crosslinking therapy. J Cataract Refract Surg. 2008;34(4):657661. 79. Spoerl E, Mrochen M, Sliney D, Trokel S, Seiler T. Safety of UVA-riboflavin cross-linking of the cornea. Cornea. 2007;26(4):385389. 80. Schumacher S, Mrochen M, Wernli J, Bueeler M, Seiler T. Optimization model for UV-riboflavin corneal cross-linking. Invest Ophthalmol Vis Sci. 2012;53(2):762-769. 81. Cui L, Huxlin KR, Xu L, MacRae S, Knox WH. High-resolution, noninvasive, two-photon fluorescence measurement of molecular concentrations in corneal tissue. Invest Ophthalmol Vis Sci. 2011;52(5):2556-2564. 82. Kampik D, Ralla B, Keller S, Hirschberg M, Friedl P, Geerling G. Influence of corneal collagen crosslinking with riboflavin and ultraviolet-a irradiation on excimer laser surgery. Invest Ophthalmol Vis Sci. 2010;51(8):3929-3934. 83. Spoerl E, Raiskup F, Kampik D, Geerling G. Correlation between UV absorption and riboflavin concentration in different depths of the cornea in CXL. Curr Eye Res. 2010;35(11):1040-1041; author reply 1042-1043. 84. Friedman MD, Pertaub R, Usher D, Sherr E, Kamaev P, Muller D. Advanced corneal cross-linking system with fluorescence dosimetry. J Ophthalmol. 2012;2012. 85. Boxer Wachler BS. Corneal collagen crosslinking with riboflavin. Cataract & Refract Surg Today. 2005;1:73-74. 86. Pinelli R. Corneal cross-linking with riboflavin: Entering a new era in ophthalmology. Ophthalmology Times Europe. 2006;2:36-38. 87. Raiskup F, Pinelli R, Spoerl E. Riboflavin osmolar modification for transepithelial corneal cross-linking. Curr Eye Res. 2012;37(3):234-238.

Copyright © 2018. Kugler Publications. All rights reserved.

230 88. Daxer A, Mahmoud HA, Venkateswaran RS. Corneal crosslinking and visual rehabilitation in keratoconus in one session without epithelial debridement: new technique. Cornea. 2010;29(10):1176-1179. 89. Seiler TG, Fischinger I, Senfft T, Schmidinger G, Seiler T. Intrastromal application of riboflavin for corneal crosslinking. Invest Ophthalmol Vis Sci. 2014;55(7):4261-4265. 90. Coskunseven E, Jankov MR, 2nd, Hafezi F, Atun S, Arslan E, Kymionis GD. Effect of treatment sequence in combined intrastromal corneal rings and corneal collagen crosslinking for keratoconus. J Cataract Refract Surg. 2009;35(12):2084-2091. 91. Ertan A, Karacal H, Kamburoglu G. Refractive and topographic results of transepithelial cross-linking treatment in eyes with intacs. Cornea. 2009;28(7):719-723. 92. Kamburoglu G, Ertan A. Intacs implantation with sequential collagen cross-linking treatment in postoperative LASIK ectasia. J Refract Surg. 2008;24(7):S726-729. 93. Vinciguerra P, Romano V, Rosetta P, et al. Transepithelial Iontophoresis Versus Standard Corneal Collagen Cross-linking: 1-Year Results of a Prospective Clinical Study. J Refract Surg. 2016;32(10):672-678. 94. Pflugfelder SC, Liu Z, Feuer W, Verm A. Corneal thickness indices discriminate between keratoconus and contact lens-induced corneal thinning. Ophthalmology. 2002;109(12):2336-2341. 95. Schreiber J. Verfestigung der Hornhaut durch UVA 365 nm und Riboflavin oder durch Glutaraldehyd. Thesis, TU Dresden 2003. 96. Wollensak G, Aurich H, Wirbelauer C, Sel S. Significance of the riboflavin film in corneal collagen crosslinking. J Cataract Refract Surg. 2010;36(1):114-120. 97. Iseli HP, Popp M, Seiler T, Spoerl E, Mrochen M. Laboratory measurement of the absorption coefficient of riboflavin for ultraviolet light (365 nm). J Refract Surg. 2011;27(3):195-201. 98. Schumacher S, Mrochen M, Spoerl E. Absorption of UV-light by riboflavin solutions with different concentration. J Refract Surg. 2012;28(2):91-92. 99. Hafezi F, Mrochen M, Iseli HP, Seiler T. Collagen crosslinking with ultraviolet-A and hypoosmolar riboflavin solution in thin corneas. J Cataract Refract Surg. 2009;35(4):621-624. 100. Spoerl E, Huhle M, Seiler T. Induction of cross-links in corneal tissue. Exp Eye Res. 1998;66(1):97-103. 101. Richoz O, Hammer A, Tabibian D, Gatzioufas Z, Hafezi F. The biomechanical effect of corneal collagen cross-linking (CXL) with riboflavin and UV-A is oxygen dependent. Transl Vis Sci Technol. 2013;2(7):6. 102. Kling S, Hafezi F. An algorithm to predict the biomechanical stiffening effect in corneal cross-linking. J Refract Surg. 2017;33(2):128-136. 103. Raiskup F, Theuring A, Pillunat LE, Spoerl E. Corneal collagen crosslinking with riboflavin and ultraviolet-A light in progressive keratoconus: ten-year results. J Cataract Refract Surg. 2015;41(1):41-46. 104. Wollensak G, Spoerl E, Seiler T. Stress-strain measurements of human and porcine corneas after riboflavin-ultraviolet-A-induced cross-linking. J Cataract Refract Surg. 2003;29(9):17801785.

E. Spoerl and D.C. Paik 105. Kohlhaas M, Spoerl E, Schilde T, Unger G, Wittig C, Pillunat LE. Biomechanical evidence of the distribution of cross-links in corneas treated with riboflavin and ultraviolet A light. J Cataract Refract Surg. 2006;32(2):279-283. 106. Lanchares E, del Buey MA, Cristobal JA, Lavilla L, Calvo B. Biomechanical property analysis after corneal collagen cross-linking in relation to ultraviolet A irradiation time. Graefes Arch Clin Exp Ophthalmol. 2011;249(8):1223-1227. 107. Ahearne M, Yang Y, Then KY, Liu KK. Non-destructive mechanical characterisation of UVA/riboflavin crosslinked collagen hydrogels. Br J Ophthalmol. 2008;92(2):268-271. 108. Wollensak G, Wilsch M, Spoerl E, Seiler T. Collagen fiber diameter in the rabbit cornea after collagen crosslinking by riboflavin/UVA. Cornea. 2004;23(5):503-507. 109. Spoerl E, Wollensak G, Seiler T. Increased resistance of crosslinked cornea against enzymatic digestion. Curr Eye Res. 2004;29(1):35-40. 110. Schilde T, Kohlhaas M, Spoerl E, Pillunat LE. Enzymatic evidence of the depth dependence of stiffening on riboflavin/UVA treated corneas. Ophthalmologe. 2008;105(2):165-169. 111. Spoerl E, Wollensak G, Dittert DD, Seiler T. Thermomechanical behavior of collagen-cross-linked porcine cornea. Ophthalmologica. 2004;218(2):136-140. 112. Wollensak G, Iomdina E. Long-term biomechanical properties of rabbit cornea after photodynamic collagen crosslinking. Acta Ophthalmol. 2009;87(1):48-51. 113. Kling S, Remon L, Perez-Escudero A, Merayo-Lloves J, Marcos S. Corneal biomechanical changes after collagen cross-linking from porcine eye inflation experiments. Invest Ophthalmol Visl Sci. 2010;51(8):3961-3968. 114. Dias JM, Ziebarth NM. Anterior and posterior corneal stroma elasticity assessed using nanoindentation. Exp Eye Res. 2013;115:41-46. 115. Beshtawi IM, Akhtar R, Hillarby MC, et al. Biomechanical properties of human corneas following low- and high-intensity collagen cross-linking determined with scanning acoustic microscopy. Invest Ophthalmol Vis Sci. 2013;54(8):5273-5280. 116. Nguyen TM, Aubry JF, Touboul D, et al. Monitoring of cornea elastic properties changes during UV-A/riboflavin-induced corneal collagen cross-linking using supersonic shear wave imaging: a pilot study. Invest Ophthalmol Vis Sci. 2012;53(9):5948-5954. 117. Scarcelli G, Kling S, Quijano E, Pineda R, Marcos S, Yun SH. Brillouin microscopy of collagen crosslinking: noncontact depth-dependent analysis of corneal elastic modulus. Invest Ophthalmol Vis Sci. 2013;54(2):1418-1425. 118. Wollensak G, Spoerl E. Collagen crosslinking of human and porcine sclera. J Cataract Refract Surg. 2004;30(3):689-695. 119. Liu TX, Wang Z. Collagen crosslinking of porcine sclera using genipin. Acta Ophthalmol. 2013;91(4):e253-257. 120. Schuldt C, Karl A, Korber N, et al. Dose-dependent collagen cross-linking of rabbit scleral tissue by blue light and riboflavin treatment probed by dynamic shear rheology. Acta Ophthalmol. 2015;93(5):e328-36.

Mechanisms of collagen crosslinking and implications on biomechanics

Copyright © 2018. Kugler Publications. All rights reserved.

121. Wollensak G, Aurich H, Pham DT, Wirbelauer C. Hydration behavior of porcine cornea crosslinked with riboflavin and ultraviolet A. J Cataract Refract Surg. 2007;33(3):516-521. 122. Mackiewicz Z, Maatta M, Stenman M, Konttinen L, Tervo T, Konttinen YT. Collagenolytic proteinases in keratoconus. Cornea. 2006;25(5):603-610. 123. Seppala HP, Maatta M, Rautia M, et al. EMMPRIN and MMP-1 in keratoconus. Cornea. 2006;25(3):325-330. 124. Wollensak G, Redl B. Gel electrophoretic analysis of corneal collagen after photodynamic cross-linking treatment. Cornea. 2008;27(3):353-356. 125. Stewart JM, Schultz DS, Lee OT, Trinidad ML. Collagen crosslinks reduce corneal permeability. Invest Ophthalmol Vis Sci. 2009;50(4):1606-1612. 126. Dupps WJ Jr, Netto MV, Herekar S, Krueger RR. Surface wave elastometry of the cornea in porcine and human donor eyes. J Refract Surg. 2007;23(1):66-75. 127. Romppainen T, Bachmann LM, Kaufmann C, Kniestedt C, Mrochen M, Thiel MA. Effect of riboflavin-UVA-induced collagen cross-linking on intraocular pressure measurement. Invest Ophthalmol Vis Sci. 2007;48(12):5494-5498. 128. Liu J, Roberts CJ. Influence of corneal biomechanical properties on intraocular pressure measurement: quantitative analysis. J Cataract Refract Surg. 2005;31(1):146-155.

231

129. Kymionis GD, Grentzelos MA, Kounis GA, et al. Intraocular pressure measurements after corneal collagen crosslinking with riboflavin and ultraviolet A in eyes with keratoconus. J Cataract Refract Surg. 2010;36(10):1724-1727. 130. Sliney D, Aron-Rosa D, DeLori F, et al. Adjustment of guidelines for exposure of the eye to optical radiation from ocular instruments: statement from a task group of the International Commission on Non-Ionizing Radiation Protection (ICNIRP). Appl Opt. 2005;44(11):2162-2176. 131. Wollensak G, Spoerl E, Wilsch M, Seiler T. Endothelial cell damage after riboflavin-ultraviolet-A treatment in the rabbit. J Cataract Refract Surg. 2003;29(9):1786-1790. 132. Grewal DS, Brar GS, Jain R, Sood V, Singla M, Grewal SP. Corneal collagen crosslinking using riboflavin and ultraviolet-A light for keratoconus: one-year analysis using Scheimpflug imaging. J Cataract Refract Surg. 2009;35(3):425-432. 133. Vinciguerra P, Camesasca FI, Romano MR. Corneal crosslinking and lens opacity. Ophthalmology. 2011;118(12):2519 e25112512.

Copyright © 2018. Kugler Publications. All rights reserved.

16. Crosslinking kinetics and alternative techniques Michael Mrochen1,5, Rebecca McQuaid2, Nicole Lemanski3, Bojan Pajic4,5 IROC Science AG, Zürich, Switzerland; 2University College of Dublin, Dublin, Ireland; 3Mabel Cheng MD PLLC, Albany, USA; 4Orasis AG, Reinach, Switzerland; 5Swiss Eye Research Foundation, Reinach AG, Switzerland

1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction Collagen corneal crosslinking (CXL) has become an established surgical procedure since the first publication of clinical results in 2003.1 Designed to increase the biochemical strength of the cornea, CXL is an established treatment for keratoconus (KC) and post-laser-assisted in situ keratomileusis (LASIK) ectasia, with numerous clinical studies showing that it is helps to slow disease progression, regularize the cornea, and improve visual acuity in patients with these disorders.1-6 Other indications include pellucid marginal degeneration, iatrogenic keratectasia after other forms of refractive laser surgery, and corneal melting that does not respond to conventional therapy. More recently, CXL has also been investigated as a treatment for refractive errors including myopia, hyperopia, and astigmatism,7 as well as for infectious keratitis.8 The standard CXL treatment protocol that has gained wide acceptance consists of exposure to UVA light at an intensity 3 mW/cm2 for 30 minutes, and is termed the Dresden protocol due to its origin in the University Eye Hospital in Dresden, Germany. It uses a 0.1–0.15% aqueous solution of riboflavin-5-phosphate (vitamin B2) that provides high absorption, and therefore, a good shielding-effect at a wavelength of 360 to 370 nm. The typically used radiant exposure at an energy dose of 5.4 J/cm² allows for biomechanical stiffening of the cornea following treatment. Using such light intensities, radiant exposures at ultraviolet-A (UVA) wavelength range ensures exposure of ultra-violet

light on the cornea is below harmful levels, i.e., under the cytotoxic threshold for the endothelium and other internal structures of the eye.9-11 CXL was first evaluated pre-clinically as a conservative treatment for keratectasia in 1998 by Spoerl and colleagues.12 Enucleated porcine eyes were treated with different crosslinking methods: 1. sunlight and light with wavelengths of 254 nm, 365nm, and 436 nm, in combination with 0.5% riboflavin solution; 2. chemical agents such as glutaraldehyde (1% and 0.1% for 10 min). Untreated corneas were used as a control. They found that compared to untreated corneas, treatment with riboflavin and UV-irradiation, as well as weak glutaraldehyde or Karnovsky’s solutions significantly increased corneal stiffness.12 This early in-vitro study paved the way for the prospective, non-randomized clinical pilot study by Wollensak et al. in 23 eyes with moderate or advanced progressive KC. Data from this study showed that treatment with riboflavin UVA irradiation (370 nm, 3mW/cm2 for 30 minutes) halted KC progression in all eyes and caused topographic disease regression in 16 eyes (70%).1 The initial clinical results have been confirmed and reproduced during the past 15 years in multiple clinical studies, and have led to regulatory approvals around the world, including FDA approval of the Dresden protocol in 2016.

Correspondence:Michael Mrochen, IROC Science AG, Technoparkstrasse 1, 8005 Zürich, Switzerland. E-mail: [email protected] Biomechanics of the Eye, pp. 233-244 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

234

2. The kinetics of CXL

Copyright © 2018. Kugler Publications. All rights reserved.

The kinetic processes involved in CXL are somewhat complex; however, it is important to have, at the very least, a rudimentary understanding of the photochemical processes behind the technology in order to be able to optimize and tailor treatment according to the patient’s individual needs. CXL is a photochemical reaction that involves four important factors: 1. energy dose of the applied UV light; 2. concentration or formulation of riboflavin; 3. oxygen concentration within the tissue; and 4. timing of riboflavin diffusion, oxygen diffusion, and light exposure. Riboflavin acts as a photosensitizer that is activated by the absorbed UV light to create reactive oxygen species (ROS), such as oxygen radicals or hydrogen peroxide, which help produce bonds between molecules in the stroma, thus increasing the biomechanical strength of the cornea. Thus, it is important to not only consider the distribution of the riboflavin concentration within the cornea during illumination as well as the resulting light distribution (which is responsible for the photoactivation of riboflavin within the tissue), but also that activated riboflavin needs oxygen to create ROS. Consequently, the diffusion of riboflavin, the absorbed number of photons (energy dose) of UV light, the oxygen concentration, and the timing of the interplay between these factors are important in optimizing the crosslinking effect. Without the combination of riboflavin, oxygen, and UV light there can be no biomechanical stiffening effect on the cornea. 2.1. Photochemistry of CXL It is known that upon photochemical activation, oxygen species are released from each of the carboxylic groups present in riboflavin, leading to the generation of light-activated riboflavin and single reactive oxygens in solution (O2-). As there are two by-products of the photochemical activation, there are two mechanisms available to interact with the collagen structure. In the direct mechanism (Type I), the light-activated riboflavin interacts directly with the collagen molecule by hydrogen abstraction of amines to stabilize its own carbon double bonds, therefore enabling intermolec-

M. Mrochen et al.

ular covalent crosslinks to form in the collagen. In the indirect mechanism (Type II), single reactive oxygens form hydrogen peroxide (H2O2) and free radicals (e.g., superoxide anion O2-), which in turn oxidize the collagen molecule and therefore enable the formation of indirect covalent crosslinks. Most crosslinking occurs through Type I photochemical reactions.13-15 It seems to be of relevance that when an anaerobic solution of riboflavin is exposed to blue or ultraviolet light in the presence of an electron donor, the yellow color of the solution is reduced in intensity. The spectrum of the resulting solution is identical to that of chemically reduced riboflavin. The aeration of the reduced riboflavin solution results in a complete return of the color equal to the spectrum of the color such that the spectrum of the original and aerated solutions. The photoreaction of riboflavin in the presence of an electron donor would appear to be a photoreduction. In aqueous media, photoreduction in the presence of an electron donor is considered to be more efficient than photobleaching.16-18 As a result of Type I and Type II reactions, two reaction mechanisms are competing for oxygen in the cornea: excited riboflavin and reduced-state riboflavin. Consequently, oxygen is rapidly consumed in the cornea. Unfortunately, reduced-state riboflavin is not reactive and does not act as a photosensitizer. Only new oxygen molecules that diffuse into the cornea from the atmosphere can lead to further crosslinking activities. The depletion of oxygen during CXL suggests a combined Type I and Type II mechanism after several minutes as oxygen begins to replenish itself. It should be noted that Herekar19 reported on the depletion of oxygen during CXL and found a significant reduction of oxygen available for Type II reactions within the first three to five minutes at an intensity of 3 mW/cm2. At an intensity of 16 mW/cm2, the depletion occurred in less than one minute. Thus, during CXL, both anaerobic and aerobic conditions are created in the cornea. Anaerobic conditions occur where reduced-state riboflavin is formed and all oxygen is consumed. Aerobic conditions occur when oxygen from the air diffuses into the cornea. It is reasonable to conclude, then, that oxygen diffusion time might be a primary driver for the depth and effectiveness of CXL. Specifically, reducing the diffusion time will create a thinner aerobic layer, producing a

Crosslinking kinetics and alternative techniques

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 1. The photochemical relationship between oxygen, riboflavin, and UVA light.

CXL effect only at the anterior part of cornea. Higher diffusion of oxygen will cause deeper CXL effects and, hence, result in higher efficacy (Fig. 1). Kamaev and colleagues20 developed a theoretical model to describe the CXL photochemical kinetics of riboflavin. After instillation with drops of riboflavin solution in distilled water, de-epithelialized porcine corneas were exposed to 365 nm UVA light under varying irradiance and temperature. Oxygen concentration in the cornea at a known depth was monitored during UVA illumination with a dissolved oxygen fiberoptic microsensor. On the basis of the known chemical reactions and diffusion rates of riboflavin and oxygen into the cornea, the authors developed a theoretical model consistent with experimental results of corneal oxygen consumption during UVA irradiation under different conditions. Specifically, they suggested that oxygen concentration in the cornea is modulated by UVA irradiance and temperature, and quickly decreases at the beginning of UVA exposure. The model also suggests that the main photochemical kinetics mechanism is the direct interaction between riboflavin triplets and reactive groups of corneal proteins, which leads to the crosslinking of the proteins mainly through radical reactions. The authors added that oxygen measurements in the cornea monitored in this study support a predominant Type I photosensitizing mechanism for CXL with riboflavin after a very short initial Type II photochemical mechanism at the start of the illumination. More than halfway through the period of illumination, the oxygen concentration in the cornea slowly increases to a concentration at which a Type II mechanism may begin to play an additional role.

235

2.2 Predicting biomechanical stiffening In 2017, Kling and Hafezi21 published details of an algorithm that predicts the stiffening effect of CXL and verified its accuracy with results obtained from experimental measurements. The algorithm considered several factors. These included the reaction kinetics of riboflavin diffusion and riboflavin photodegradation to determine the effective riboflavin concentration in different stromal layers, as well as the oxygen diffusion and UV absorption to determine the amount of reactive oxygen species as a function of time and stromal depth. Enucleated porcine (n = 66) and rabbit (n = 2) eyes were de-epithelialized, followed by riboflavin instillation for 30 minutes and UV irradiation. Different pulsed and continuous-light conditions were analyzed with irradiances ranging from 3 to 100 mW/cm2  and irradiation times from 8 to 30 minutes. Stress-relaxation measurements were performed directly after treatment using a load of 0.6 MPa. The authors observed a linear relationship between the concentration of newly induced crosslinks and the experimentally observed stiffening factor (R2  = 0.9432). Furthermore, an additional 1 mol/m3  of crosslinks increased the mechanical stress resistance of the cornea by 50.4%. They also found that the efficacy of standard CXL was inversely related to corneal thickness.  Kling and Hafezi concluded that the biomechanical efficacy of CXL may be increased by prolonged UV irradiation at reduced irradiances or by a higher oxygen pressure in the environment.

3. Beyond the Dresden Protocol: treatment optimization A desire for faster treatment times, improved outcomes, and increased patient comfort have led researchers to investigate alternative CXL protocols including accelerated CXL, pulsed CXL, Epi-ON CXL, and use of chemical enhancers. 3.1. Accelerated CXL Reduced treatment time could help improve practice efficiency and throughput volumes, increase patient comfort, and reduce the risk of corneal dehydration. A number of researchers have investigated whether increasing the irradiation intensity of CXL may allow treatment time to be halved, but with similar or

236

Copyright © 2018. Kugler Publications. All rights reserved.

improved biomechanical effects as the standard Dresden protocol. 3.1.1. Experimental studies In a study by Schumacher and colleagues,22 72 porcine eyes were cut into three strips, and each strip randomly exposed to a different treatment:  rapid  (10 mW/cm2, 9 minutes),  standard  (3 mW/cm2, 30 minutes), or no (control, 0 mW/cm 2) irradiation. Findings showed that rapid  UV  crosslinking  treatment was equivalent to the standard procedure in terms of increased corneal stiffness. In another study by Wernil et al.,23 100 porcine eyes received riboflavin and UV treatment with a constant irradiation dose of 5.4 J/cm2 but at different intensities (ranging from 3 to 90 mW/cm2) and illumination times (30 minutes to 1 minute). A control group (80 eyes) was not irradiated, but underwent the same treatment. Findings showed that there was a statistically significant difference (compared to controls) in corneal stiffness in the groups which received 3 to 45 mW/cm2 UVA, but not in those that received more than 45 mW/cm2. Hammer et al.24 also investigated the biomechanical properties of four groups of porcine corneas which were exposed to riboflavin 0.1 % and UVA irradiation of equal total energy (3 mW/cm2 for 30 minutes, 9 mW/cm2 for 10 minutes, and 18 mW/cm2 for 5 minutes). Controls were exposed to riboflavin 0.1% without irradiation. Data showed a decreased stiffening effect with high irradiance/short irradiation time settings. Specifically, there were significant differences between 3 mW/cm2 and 9 mW/cm2, 3 mW/cm2 and 18 mW/cm2, 3 mW/cm2 and the control group, and 9 mW/cm2 and the control group. There was no difference between 18 mW/cm2 and the control group, nor between 9 mW/cm2 and 18 mW/cm2. In contrast, data from a study by Krueger and Spoerl25 showed that while CXL induced a 1.3 to 1.5-fold increase in corneal stiffness compared to controls (p < 0.05), there was no significant difference between UVA intensities (i.e., 2 mW/cm2, 45 minutes; 3 mW/ cm2, 30 minutes; 10 mW/cm2, 9 minutes; and, 15 mW/ cm2, 6 minutes). Chai et al.26 used collagen autofluorescence intensity to compare corneal stiffness after UVA exposure (3 mW/15 minutes after 3 mW/30 minutes) vs controls in rabbit eyes. Corneal stiffness was significantly and dose-dependently increased after UVA. Autofluorescence was detected only within the anterior

M. Mrochen et al.

stroma of the UVA-treated groups, with no significant difference in the depth of autofluorescence between different UVA exposure levels. Collectively, these findings suggest there is a fine balance between treatment time and UVA irradiation intensity in optimizing the biochemical stiffness of the cornea, and that CXL does not necessarily follow a linear intensity relationship. 3.1.2. Clinical findings: efficacy and safety To date, most of the studies evaluating accelerated CXL have been undertaken in porcine or donor human corneal eyes. However, several centers have begun to evaluate accelerated high-intensity protocols in patients with corneal ectasia. Cummings et al.,27 for example, evaluated patients with progressive KC who received either standard-intensity CXL (UVA 365 nm light for 30 minutes at an irradiance of 3.0 mW/cm2) or high-intensity CXL (UVA 365 nm light for 10 minutes at 9.0 mW/cm2); in both cases, the total UVA dose was 5.4 J/cm2. Findings showed that there was no significant difference between groups in uncorrected visual acuity (UCVA), best spectacle-corrected visual acuity (BSCVA), and refractive astigmatism. However, the high-intensity protocol appeared to have a greater corneal flattening effect. In a study by Choi and colleagues,28 15 eyes with primary KC received CXL under the standard Dresden protocol (3 mW/cm for 30 minutes, dose 5.4 J/cm2) and 13 eyes were treated with an accelerated protocol (30 mW/cm for 3 minutes 40 s, dose 6.6 J/cm2). Interestingly, they found accelerated  CXL with higher UV intensity and reduced irradiation time showed a smaller topographic flattening effect than the conventional Dresden protocol. Sadoughi and coworkers29 have also compared the Dresden protocol with accelerated CXL (9  mW/cm2  for 10 minutes) in patients with progressive KC. In a similar fashion to the study by Cummings et al., they found that accelerated CXL had similar refractive, visual, keratometric, and aberrometric results, and less adverse effects on the  corneal  thickness and endothelial cells as compared with the conventional method after 12 months follow-up. Bozkurt et al.30 evaluated visual, refractive, and corneal topography as well as wavefront aberration results following  accelerated  CXL over a 24-month

Copyright © 2018. Kugler Publications. All rights reserved.

Crosslinking kinetics and alternative techniques

period. All eyes received 30 mW/cm2  for 4 minutes, giving a total UVA dose of 7.2 J/cm2, which is greater than the standard Dresden protocol. Mean uncorrected distance visual acuity (UDVA) and corrected distance visual acuity (CDVA) were significantly improved at one and two years after treatment, while keratography values from corneal topography for steepest meridian Ksteep, flattest meridian Kflat, averaged central cornea Kmean and at the corneal apex Kapex were significantly lower than baseline at 12 and 24 months postoperative. Total higher order aberrations and coma decreased significantly at both the 12 and 24 month visits. In another study,31 patients with progressive KC received UVA radiation for 3 minutes at an irradiance of 30 mW/cm2. After 12 months, there was a significant decrease in Kmax (maximal dioptric value of anterior corneal topography), average keratometry, and thinnest corneal thickness, and a significant improvement in BCVA. The authors reported that pain or foreign-body sensation following CXL appeared in the first two days, but lasted no more than one week in all cases. Safety is a key consideration when employing accelerated CXL. Kanellopoulos and colleagues,32 who investigated the safety of 7 mW/cm2 with an illumination time of 15 minutes, found that no adverse events or negative biomechanical effects, i.e., ectasia or epithelial ingrowth as a result of higher-intensity UVA irradiation. However, in a study of 40 eyes with progressive KC or post-LASIK ectasia, Badawi33 reported that CXL using UVA 10 mW/cm2  for 9 minutes had a transient negative impact on endothelial cell density and/or endothelial morphology. The authors suggest that perhaps a key limitation of accelerated CXL could be its impact on the corneal endothelium. Although published studies suggest that accelerated CXL may improve visual outcomes in patients with ectasia, the optimal treatment protocol is unclear and requires further investigation. Clinicians should also consider the effect of accelerated protocols on treatment depth. For example, Kymionis et al.34 reported on the depth of the stromal demarcation line after using CXL with 10 minutes of irradiation time and 9 mW/cm2 or 30 minutes with 3 mW/cm2. Findings show that the corneal  stroma demarcation line was significantly deeper after a 30-minute CXL treatment than after a 10-minute CXL procedure with high-intensity UVA irradiation, suggesting greater therapeutic effect

237

Fig. 2. Correlation between treatment time and stromal demarcation.20

with the Dresden protocol. Figure 2 shows an analysis of published data describes the correlation between the demarcation line and treatment. This chart clearly shows that the depth of demarcation line is time-dependent and should be considered when designing a treatment plan. From the available experimental and clinical information, it could be concluded that one of the primary limitations of reducing the treatment time is the relevance of oxygen diffusion in creating an aerobic environment in the anterior part of the stroma. As the total illumination time reduces, it leads to a reduced time for oxygen diffusion, and therefore, photochemical reactions (Type I and Type II) in a shallower anterior part of the stroma, which in turn lead to increased stiffening of the tissue. 3.2. Pulsed accelerated CXL Kamaev et al.20 previously developed a theoretical model to describe the photochemical kinetics of riboflavin-CXL. They noted UVA illumination caused a rapid depletion of oxygen in de-epithelialized riboflavin-soaked corneas, but that turning the UVA light off led to restoration of the original oxygen level within three to four minutes. As noted earlier, aerobic conditions are dominant during the first 10 to 15 seconds of UVA exposure. During this time, photo oxidation of the substrate (cornea) occurs due to its reaction with ROS, consistent with what is a predominantly Type II photochemical mechanism. After the first 10 to 15 seconds of UVA

M. Mrochen et al.

238

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. Oxygen dynamics during pulsed UV light corneal crosslinking (PL-CXL).20

exposure, oxygen is depleted. At this stage, a Type I photochemical mechanism, in which riboflavin is reduced, is dominant. Since it has been shown that switching off the UVA light restores oxygen to the original levels, pulsing the UV light during crosslinking treatment will theoretically restart a Type II reaction, allowing the release of singlet oxygen for crosslinking of collagen molecules (Fig. 3). However, pulsing the UVA light increases the treatment time, and since one of the aims of developing optimized treatment protocols is to shorten the treatment time vs the standard Dresden protocol, this may be considered a disadvantage. Nevertheless, clinical findings are promising. Mazzotta et al.35 conducted a clinical study of continuous (CL-ACXL) and pulsed light (PL-ACXL) accelerated corneal collagen crosslinking in a series of 20 patients with progressive KC. Patients in the PL-AXCL group received 8 minutes (1 second on/1 second off) of UVA exposure at 30 mW/cm2  with an energy dose of 7.2 J/cm2, while patients in the CL-ACXL group received 4 minutes of continuous UVA light exposure (30 mW/cm2), with an energy dose of 7.2 J/cm2. Pulsed light treatment showed a slightly better functional outcome both in UDVA, and in CDVA, even though there was no statistically significant difference between the two treatment modalities.

Mazzotta and colleagues also performed in-vivo confocal microscopy and corneal optical coherence tomography (OCT) to allow a precise qualitative analysis of the cornea following PL-ACXL and CL-ACXL.36 The authors reported that PL-ACXL had an apoptotic effect at 200 μm of stromal depth (range 190–240 μm), whereas CL-ACXL revealed a penetration of 160 μm on average (range 150–200 μm), both at confocal and corneal OCT analysis, that appeared inferior (approximately −40 μm) to pulsed light.  Moramorca et al.37 also evaluated corneal stroma demarcation following pulsed CXL in patients with progressive KC. In this study, patients received either accelerated CXL using continuous UVA light exposure at 30 mW/cm2 for 4 minutes or accelerated CXL using pulsed UVA light with 8 minutes (1 second on/1 second off) of UVA exposure at 30 mW/cm2 for a total energy dose of 7.2 J/cm2. Corneal stromal demarcation line depth was measured one month after surgery using anterior segment optical coherence tomography (AS-OCT). The authors reported that the mean depth of stromal demarcation line was 149.32 ± 36.03 μm in the continuous UVA group and 213 ± 47.38 μm in the pulsed UVA group. The difference in stromal demarcation line depth between groups was statistically significant. These findings suggest that pulsed light treatment

Crosslinking kinetics and alternative techniques

Copyright © 2018. Kugler Publications. All rights reserved.

may penetrate deeper in the corneal stroma as compared with continuous light treatment through a combination of prolonging treatment time (vs continuous accelerated CXL) and inducing intraoperative oxygen reuptake. As a consequence, pulsing might slightly increase efficacy, but essentially does not reduce treatment time substantially as oxygen diffusion is still needed during the pulsed illumination regime. 3.3. Trans-epithelial (Epi-ON) CXL The Dresden Protocol requires removal of the corneal epithelium in order to allow sufficient penetration of the riboflavin molecules. Thus, the Dresden Protocol employs what is known as an “epi-OFF” procedure. The reason for this approach is that riboflavin would not diffuse sufficiently into the corneal stroma without epithelial removal; a longer riboflavin loading time may be required to reach the desired endpoint with Epi-ON. In an in-vivo confocal microscopy study of eyes with progressive KC, the CXL procedure was performed with standard technique and transepithelial technique after prolonged riboflavin drop application (two hours). Acar et al.38 reported that transepithelial CXL with prolonged preoperative  riboflavin  application  can achieve similar depth of  effect  in the stroma with less pronounced  confocal  microscopic changes as compared with the standard CXL with complete epithelial debridement. Clearly, undergoing a two-hour application of riboflavin is not ideal for either patient or surgeon. However, since Epi-ON reduces patient discomfort during and after the procedure by avoiding epithelial removal, and is preferable for patients with thin corneas and low to moderate grade KC, researchers are investigating ways to deliver riboflavin so as to avoid epithelium removal. One approach is the use of 0.01% benzalkonium chloride (BAC) 0.01%,39,40 which helps to loosen the tight junctions between epithelial cells, thus allowing the riboflavin molecule to pass into the corneal stroma. BAC may be used alone or in combination with ethylenedinaminetetraacetic acid (EDTA), which also acts a permeability enhancer. An alternative approach is iontophoresis-assisted CXL, in which application of an electric current enables a similar distribution of riboflavin and biomechanical stiffening after exposure to the UVA light, as seen in standard CXL. Although this method looks promising,

239

longer in-vivo studies are required to determine the efficacy of this technique. The filtration of riboflavin through femtosecond or mechanically created channels has also been investigated.39,41 To date, none of the Epi-ON techniques have demonstrated efficacy equivalent to the standard Epi-OFF techniques. In addition to riboflavin diffusion, another factor to consider when leaving the epithelial layer in place is oxygen diffusion. Since the availability of oxygen is a key factor in the creation of crosslinks, this may also have an impact on the efficacy of Epi-ON procedures. Further studies are required to determine the efficacy of transepithelial CXL vs traditional CXL, and whether use of enhancements (e.g., BAC, EDTA, and iontophoresis) can override the limitations inherent in an Epi-ON approach.

4. Combining CXL with refractive procedures Another important element in the development of CXL is the modification of the established Dresden protocol, which was designed for KC and keratectasia using an Epi-OFF procedure, for combined or new applications. 4.1. Photorefractive intrastromal corneal crosslinking: CXL for refractive treatment Photorefractive intrastromal corneal crosslinking (PiXL) is a form of CXL which uses riboflavin and a UVA 365 nm wavelength light source with customizable illumination pattern. The technique causes differential corneal stiffening to reshape the cornea, enabling refractive change. Thus far, studies have focused on the use of PiXL as a treatment for low myopia. Feasibility study findings published in 2014 42 showed that transepithelial application of 12 J/cm2 in a predetermined pattern led to an average improvement of 2.3 diopters (D) one week postoperative. Six-month outcomes from a 12-month study undertaken in 39 eyes by Elling et al.43 showed significant improvements in UCVA and no loss of BCVA. In a nine-month study of eight patients, a mean myopia reduction of 0.75 D with no loss of BCVA was noted.44 4.2. Photorefractive keratectomy with CXL: Athens Protocol CXL has also been used in combination with partial

240

Copyright © 2018. Kugler Publications. All rights reserved.

topography-guided photorefractive keratectomy (PRK) for the treatment of KC. A  6.5 mm phototherapeutic keratectomy is first performed to remove 50 μm of epithelium followed by the topography-guided partial PRK. Mitomycin C (0.02% for 20 seconds) is applied, and then CXL is undertaken.  In a three-year study of 231 patients with KC, the Athens Protocol was shown to arrest keratectasia progression and improve corneal regularity.45 In the Athens Protocol, PRK and CXL are performed in the same session (simultaneous). Some surgeons use CXL followed by PRK up to one year later (sequential). However, A. John Kanellopoulos, who developed the Athens Protocol, reports that simultaneous treatment offers the advantages of less PRK-associated scarring and better penetration of riboflavin and UVA to achieve a wider and deeper CXL effect with greater corneal flattening.46 4.3. Intrastromal corneal ring segments and CXL The use of intrastromal corneal ring segments (ICRS) combined with CXL as a treatment for corneal ectatic disorders has been widely reported in the literature. Findings suggest that CXL may have an additive effect on spherical equivalent refractions and keratometry.4749 However, it is unclear what effects ICRS may have on the CXL procedure, and whether it may be necessary to inject riboflavin into the ICRS channels to aid diffusion. The effect that combining ICRS with CXL has on oxygen levels also remains unclear. Another consideration is that ICRS channels may be created either manually or using a femtosecond laser. In femtosecond laser cases, El-Raggal and colleagues suggest that channel creation and ICRS insertion should be performed before or with CXL, since an ICRS-induced flattening of the cornea may be affected by CXL-induced corneal stiffness if CXL is undertaken first. Furthermore, the authors note that creating the channel after CXL is challenging. Specifically, using the 1.5 microJ default femtosecond power setting may require mechanical dissection to complete the channel.50 4.4. Small incision lenticule extraction and CXL The small incision lenticule extraction (SMILE) procedure has been shown to be a safe and effective treatment for myopia. Treatment involves cutting a small lenticule in the corneal stroma with a femtosecond laser, which is subsequently removed through a small incision. SMILE

M. Mrochen et al.

may also be combined with CXL (known as SMILE Xtra). In SMILE XTRA, riboflavin is inserted into the channel, followed by CXL treatment. SMILE Xtra may help strengthen the cornea, which may be particularly beneficial for patients with forme fruste KC or early KC, as it may help stop the progression of the ectatic disease while improving visual outcomes. In one study, 15 eyes with forme fruste KC and/ or irregular corneas with a CDVA of 20/40 or better and residual corneal thickness greater than 400 μm underwent SMILE followed by intrastromal injection of riboflavin inside the pocket. UVA light with a wavelength of 370 nm to 3 mW/cm2  was applied for 30 minutes (Dresden Protocol). Findings showed that there were significant improvements in UDVA and spherical equivalent; however, best-CDVA did not improve significantly as compared with preoperative.51 SMILE has also been used in combination with accelerated CXL. For example, Ganesh et al.52 reported on 12-month outcomes following SMILE with accelerated CXL in patients with thin corneas and borderline topography. Immediately after removal of the lenticule, 0.1 mL 0.25% riboflavin in saline was injected into the interface and allowed to diffuse for 60 seconds followed by washing with saline. Accelerated CXL with UVA radiation was performed at 365 μm wavelength, with energy of 45 mW/cm2  delivered in continuous mode for 75 seconds for a total energy of 3.4 J/cm2. Mean UCVA was 20/25 or better in all eyes. No eyes lost lines of CDVA and there were no complications like haze, keratitis, ectasia, or regression. Reductions in mean spherical equivalent (SE) central corneal thickness and keratometry were also noted. While these findings are encouraging, further research is needed to determine the optimal riboflavin soaking time. The effect of the lenticule on UVA light distribution and oxygen diffusion is also unclear. 4.5. Photoactivated chromophore for infectious keratitis-CXL CXL is also being investigated as a treatment of infectious keratitis. Known in this context as photoactivated chromophore for infectious keratitis (PACK)-CXL, the procedure may provide an alternative to standard antibiotic therapy in treating infectious corneal disorders.53 The antimicrobial effect occurs due to the effect of UV light interacting with riboflavin.

Crosslinking kinetics and alternative techniques

The resulting ROS damage the pathogen cell walls; riboflavin may also interact with the nucleic acids of the pathogen, thus preventing replication. Of note, Said and colleagues54 compared PACK-CXL with standard anti-microbial therapy in 40 eyes of 40 patients with advanced infectious keratitis and coexisting corneal melting. Twenty-one patients underwent PACK-CXL and antimicrobial therapy while 19 patients received antimicrobial therapy only. Although PACK-CXL did not shorten the time to corneal healing, the complication rate was 21% in the antimicrobial group, whereas there was no incidence of corneal perforation or infection recurrence in the PACK-CXL group. PACK-CXL typically uses the Dresden Protocol; however, accelerated protocols have been used. Richoz used accelerated CXL and noted that the killing rates for Staphylococcus aureus were 92.5% ± 5.5% (5 minutes at 18 mW/cm²) and 94.4% ± 2.9% (2.5 minutes at 36 m ­ W/ cm²). For Pseudomonas aeruginosa, the killing rates were 93.2% ± 8.3% (5 minutes at 18 mW/cm²) and 92.9% ± 5.0% (2.5 minutes at 36 mW/cm²).55 PACK-CXL may prove particularly beneficial both for patients with antibiotic resistance and those in developing countries due to the cost of traditional antimicrobial therapy.

Copyright © 2018. Kugler Publications. All rights reserved.

5. Scleral CXL Scleral CXL (SXL) has also been proposed as a treatment for progressive myopia. Designed to slow down the axial elongation process, SXL uses riboflavin and blue light, and has been investigated in animal eyes. In a study by Iseli et al.,56 the sclera of three-week-old rabbits (39 pigmented and 15 albino rabbits) were treated with different blue light intensities (450 ± 50  nm) and riboflavin. According to the authors, light microscopic examinations demonstrated degenerative changes in ocular tissue after irradiation with blue light intensities above 400 mW/cm2. However, a significant reduction in eye growth could be detected by SXL treatment with the minimal efficient blue light intensity of 15 mW/cm2, which remained stable for 24 weeks. Another study by Iseli’s team57 found that constant riboflavin application combined with different blue light intensities from 12 mW/cm2 to 100 mW/cm2 increased the relative elastic

241

modulus of scleral tissue by factors up to 1.8, but that increasing the light intensity further caused a decline of the relative elastic modulus. These data suggest that riboflavin/blue light application increases the biomechanical stiffness of the sclera in a dose-dependent manner up to certain light intensities; however, studies are ongoing to determine the optimal treatment protocol.

6. Alternative approaches The success of riboflavin photochemical  crosslinking as well as its associated challenges has led researchers to investigate alternative approaches to biomechanical strengthening of the cornea. 6.1. Non-enzymatic CXL The use of chemical CXL agents including glutaraldehyde, formaldehyde, diphenylphosphoryl, and genipin has been investigated. In a 2008 study, Paik et al. evaluated short chain  aliphatic  beta-nitro  alcohol s. They noted that 2-nitroethanol, 2-nitro-1-propanol, and 3-nitro-2-pentanol are particularly effective crosslinking agents at pH 7.4, showing both time- and concentration-dependent effects.58 6.2. Therapeutic tissue crosslinking (TXL) Therapeutic tissue crosslinking of the sclera using 40–400 mM sodium hydroxymethyglycinate (SMG) is currently under investigation for the treatment of high myopia. TXL consists of a single sub-Tenon’s injection of SMG with a soak time of 3.5 hours to allow the solution to react. Findings from a 2016 study by Kim and colleagues59 undertaken in cadaveric rabbit heads showed that SMG exerted a concentration-dependent crosslinking effect with effects equal or superior to standard CXL, i.e., the Dresden protocol. Although this approach has been applied to the cornea, TXL is particularly useful for treating the posterior sclera, a region that is difficult for UVA light to access. 6.3. Collagen crosslinking with rose bengal-green light and UVA (RBX) A new technique has been introduced using rose bengal (RB) as a substitute for riboflavin. Rose bengal is a photosensitizer with common clinical applications

M. Mrochen et al.

242

such as wound healing, and has recently been used for intraocular lens (IOL) implants in order to attach capsular bag tissue to polymers.60 Recent studies using animal models have shown a crosslinking effect at a depth of 100 µm in the corneal stroma (without keratocyte damage), which could be beneficial to ultrathin corneas.61 As in traditional CXL using UVA light and riboflavin, RBX appears to initiate crosslinking by an oxygen-dependent mechanism.62 In a study that compared RBX with traditional CXL in 12 enucleated rabbit eyes, RBX increased corneal stiffness by a factor of 11 and traditional CXL by a factor of 6.25.63 Rose bengal staining takes one to two minutes, followed by an irradiation for 200 seconds (wavelength of green light 532 nm, irradiance 0.25 W/cm²). Although RBX is an evolving treatment, this form of crosslinking may eventually prove to be a safe, rapid (12-15-minute total treatment time), and effective treatment for KC and other ectatic disorders.

References 1.

2.

3.

Copyright © 2018. Kugler Publications. All rights reserved.

4.

5.

6.

7.

Wollensak G, Spoerl E, Seiler T. Riboflavin/ultraviolet-a-induced collagen crosslinking for the treatment of keratoconus. Am J Ophthalmol. 2003;135(5):620-627. Toprak I Yildirim C. Effects of corneal collagen crosslinking on corneal topographic indices in patients with keratoconus. Eye Contact Lens. 2013;39(6):385-387. Ghanem RC, Santhiago MR, Berti T, Netto MV, Ghanem VC. Topographic, corneal wavefront, and refractive outcomes 2 years after collagen crosslinking for progressive keratoconus. Cornea. 2014;33(1):43-48. Sloot F, Soeters N, van der Valk R, Tahzib NG. Effective corneal collagen crosslinking in advanced cases of progressive keratoconus. J Cataract Refract Surg. 2013; 39(8):1141-1145. Guber I, Guber J, Kaufmann C, Bachmann LM, Thiel MA. Visual recovery after corneal crosslinking for keratoconus: a 1-year follow-up study. Graefes Arch Clin Exp Ophthalmol. 2013;251(3):803-807. Caporossi A, Mazzotta C, Baiocchi S, Caporossi T. Long-term results of riboflavin ultraviolet a corneal collagen cross-linking for keratoconus in Italy: the Siena eye cross study. Am J Ophthalmol. 2010;149(4):585-593. Kanellopoulos AJ. Novel myopic refractive correction with transepithelial very high-fluence collagen cross-linking applied in a customized pattern: early clinical results of a feasibility study. Clin Ophthalmol. (Auckland, NZ). 2014;8:697-702.

7. Conclusion CXL plays a key role in the management of corneal ectatic disorders and may also have applications in the treatment of myopia and infectious keratitis. While CXL offers tremendous potential in ophthalmology, an understanding of the photochemical processes involved in this technology is vital in terms of protocol optimization and planning better treatment outcomes. For example, reducing treatment time without diminishing safety and efficacy is an important consideration for both surgeon and patient, and requires further research to determine the risks and benefits of optimized CXL. Optimizing CXL should focus on identifying the best combination between temporal and spatial distribution of riboflavin and UV light as well as oxygen availability within the corneal stroma for a specific application. Clinicians should also consider investigating the effect of lateral changes in light intensity, which might open the door for new applications in CXL by selective treatment of specific regions of the cornea.

8.

9.

10.

11.

12. 13. 14.

15.

16.

Jiang L-Z, Qiu S-Y, Li Z-W, Zhang X, Tao X-C, Mu G-Y. Therapeutic and inducing effect of corneal crosslinking on infectious keratitis. Int J Ophthalmol. 2016;9(12):1820-1823. Wollensak G, Spoerl E, Wilsch M, Seiler T. Keratocytes aptosis after corneal collagen cross-linking using riboflavin/UVA treatment. Cornea. 2004;23:43-49. Wollensak G, Spoerl E, Wilsch M, Seiler T. Endothelial cell damage after riboflavin/ultraviolet: A treatment in the rabbit. J Cataract Refract Surg. 2003;29:1786-1790. Schumacher S, Mrochen M, Wernli J, Bueeler M, Seiler T. Optimization model for UV-riboflavin corneal cross-linking. Cornea. 2012;53:762-769 Spoerl E, Huhle M, Seiler T. Induction of cross-links in corneal tissue. Exp Eye Res. 1998;66(1):97-103. Lichtman JW, Conchello JA. Fluorescence microscopy: review. Nat Methods. 2005;2:910-919. 14, Rich H, Odlyha M, Cheema U, Mudera V, Bozec L. Effects of photochemical riboflavin-mediated crosslinks on the physical properties of collagen constructs and fibrils. J Mater Sci Mater Med. 2014;25(1):11-21. Balasubramanian D, Du X, Zigler JS. The reaction of singlet oxygen with proteins, with special reference to crystallins. Photochem Photobiol. 1990;52:761-768. Carr DO. Mechanism of riboflavin-catalyzed oxidations. Iowa State University;1960. Available from: http://lib.dr.iastate.edu/ rtd/2813/

Copyright © 2018. Kugler Publications. All rights reserved.

Crosslinking kinetics and alternative techniques 17. Cairns WL. Products of riboflavin photodegradation; William Louis, Iowa State University;1970. Available from: http://lib. dr.iastate.edu/rtd/4214/ 18. Smith EC. The photochemical degradation of riboflavin; Eddie Carol Smith, Iowa State University;1963. Available from: http:// lib.dr.iastate.edu/rtd/2947/ 19. Herekar S. Fractionated Cross-linking: preliminary lab investigation. 3rd International congress on corneal cross linking. 8th December 2007, Zurich, Switzerland. 20. Kamaev P, Friedman P, Sherr E, Muller D. Photochemical kinetics of corneal cross-linking with riboflavin. Invest Ophthalmol Vis Sci. 2012;53(4):2360–2367. 21. Kling S, Hafezi F. An algorithm to predict the biomechanical stiffening effect in corneal cross-linking. J Refract Surg. 2017;33(2):128-136. 22. Schumacher S, Oeftiger L, Mrochen M. Equivalence of biomechanical changes induced by rapid and standard corneal cross-linking, using riboflavin and ultraviolet radiation. Invest Ophthalmol Vis Sci. 2011;52:9048–52. 23. Wernli J, Schumacher S, Spoerl E, Mrochen M. The efficacy of corneal-crosslinking shows a very sudden decrease with very high intensity UV light and short treatment time. Invest Ophthalmol Vis Sci. 2013;54(2):1176-80. 24. Hammer A, Richoz O, Arba Mosquera S, Tabibian D, Hoogewoud F, Hafezi F. Corneal biomechanical properties at different corneal cross-linking (CXL) irradiances. Invest Ophthalmol Vis Sci. 2014 May 2;55(5):2881-4. 25. Krueger R and Spoerl E. Paper presented at the IV International Congress of CXL, 2008. 26. Chai D, Gaster RN, Roizenblatt R, Juhasz T, Brown DJ, Jester JV. Quantitative assessment of UVA-Riboflavin corneal cross-linking using nonlinear optical microscopy. Invest Ophthalmol Vis Sci. 2011;52(7):4231-4238. 27. Cummings AB, McQuaid R, Naughton S, Brennan E, Mrochen M. Optimizing corneal cross-linking in the treatment of keratoconus: A comparison of outcomes after standard- and high-intensity protocols. Cornea. 2016;35(6):814-22. 28. Choi M, Kim J, Kim EK, Seo KY, Kim TI. Comparison of the conventional dresden protocol and accelerated protocol with higher ultraviolet intensity in corneal collagen cross-linking for keratoconus. Cornea. 2017;36(5):523-529. 29. Sadoughi MM, Einollahi B, Baradaran-Rafii A, Roshandel D, Hasani H, Nazeri M. Accelerated versus conventional corneal collagen cross-linking in patients with keratoconus: an intrapatient comparative study. Int Ophthalmol. 2016; Dec 29. doi:10.1007/s10792-016-0423-0. 30. Bozkurt E, Ozgurhan EB, Akcay BIS, et al. Refractive, topographic, and aberrometric results at 2-year follow-up for accelerated corneal cross-link for progressive keratoconus. J Ophthalmol. 2017;2017:5714372. 31. Aixinjueluo W, Usui T, Miyai T, Toyono T, Sakisaka T, Yamagami S. Accelerated transepithelial corneal cross-linking for progressive keratoconus: a prospective study of 12 months. Br J Ophthalmol. 2017;101(9):1244-1249. 32. Kannellopoulos AJ. Collagen cross-linking in early keratoconus

243

33.

34.

35.

36.

37.

38.

39.

40.

41. 42.

43.

44. 45.

46.

47.

with riboflavin in a femtosecond laser-created pocket: Initial clinical results. J Refract Surg. 2009;25:1034-1037. Badawi AE. Corneal endothelial changes after accelerated corneal collagen cross-linking in keratoconus and post LASIK ectasia. Clin Ophthalmol. (Auckland, NZ). 2016;10:1891-1898. Kymionis GD, Tsoulnaras KI, Grentzelos MA. Corneal stroma demarcation line after standard and high-intensity collagen crosslinking determined with anterior segment optical coherence tomography. J Cataract Refract Surg. 2014;40:736-740. Mazzotta C, Traversi C, Paradiso AL, Latronico ME, Rechichi M. Pulsed light accelerated crosslinking versus continuous light accelerated crosslinking: one-year results. J Ophthalmol. 2014; 2014:604731. Mazzotta C, Traversi C, Caragiuli S, Rechichi M. Pulsed vs continuous light accelerated corneal collagen crosslinking: in vivo qualitative investigation by confocal microscopy and corneal OCT. Eye. 2014;28(10):1179-1183. Moramarco A, Lovieno A, Sartori A, Fontana L. Corneal stromal demarcation line after accelerated crosslinking using continuous and pulsed light. J Cataract Refract Surg. 2015;41(11):25462551. Acar BT Utine CA, Ozturk V, Acar S, Ciftci F. Can the effect of transepithelial corneal collagen crosslinking be improved by increasing the duration of topical riboflavin application? An in vivo confocal microscopy study. Eye Contact Lens. 2014;40(4):207-212. Mencucci R, Ambrosini S, Paladini I, et al. early effects of corneal collagen cross-linking by iontophoresis in ex vivo human corneas. Graefes Arch Clin Exp Ophthalmol. 2015; 253:277-286. Seiler TG, Fischinger I, Senfft T, Schmidinger G, Seiler T. Intrastromal application of riboflavin for corneal crosslinking. Invest Ophthalmol Vis Sci. 2014;55:4261-4265. Kannellopoulos A.J, Asimellis G. Presbyopic PiXL Cross-Linking. Curr Ophthalmol Rep. 2015;3:1-8. Kanellopoulos AJ. Novel myopic refractive correction with transepithelial very high-fluence collagen cross-linking applied in a customized pattern: early clinical results of a feasibility study. Clin Ophthalmol. (Auckland, NZ). 2014;8:697-702. Elling M, Kersten-Gomez I, Dick HB. Photorefractive intrastromal corneal crosslinking for the treatment of myopic refractive errors: Six-month interim findings. J Cataract Refract Surg. 2017;43(6):789-795. Studies show promising results for PiXL procedure in low myopia. Primary Care Optometry News;January 2017. Kanellopoulos AJ, Asimellis G. Keratoconus management: Long-term stability of topography-guided normalization combined with high-fluence CXL stabilization (The Athens Protocol). J Refract Surg. 2014;30(2):88-92. Kanellopoulos AJ. Comparison of sequential vs same-day simultaneous collagen cross-linking and topographyguided PRK for treatment of keratoconus. J Refract Surg. 2009;25(9):S812S818. Alió JL, Artola A, Hassanein A, Haroun H, Galal A. One or 2 Intacs segments for the correction of keratoconus. J Cataract Refract Surg. 2005;31(5):943-953.

244

Copyright © 2018. Kugler Publications. All rights reserved.

48. El-Raggal TM. Sequential versus concurrent KERARINGS insertion and corneal collagen cross-linking for keratoconus. Br J Ophthalmol. 2011;95(1):37-41. 49. El Awady H, Shawky M, Ghanem AA. Evaluation of collagen cross-linking in keratoconus eyes with Kera intracorneal ring implantation. Eur J Ophthalmol. 2012;22(Suppl 7):S62-S68. 50. El-Raggal TM. Effect of corneal collagen crosslinking on femtosecond laser channel creation for intrastromal corneal ring segment implantation in keratoconus. J Cataract Refract Surg. 2011;37(4):701–705. 51. Graue-Hernandez EO, Pagano GL, Garcia-De la Rosa G, et al. Combined small-incision lenticule extraction and intrastromal corneal collagen crosslinking to treat mild keratoconus: Longterm follow-up. J Cataract Refract Surg. 2015;41(11):2524-2532. 52. Ganesh S, Brar S. Clinical outcomes of small incision lenticule extraction with accelerated cross-linking (ReLExSMILE Xtra) in patients with thin corneas and borderline topography. J Ophthalmol. 2015;2015:263412. 53. Tabibian D, Richoz O, Hafezi F. PACK-CXL: Corneal cross-linking for treatment of infectious keratitis. J Ophthalmic Vis Res. 2015;10(1):77-80. 54. Said DG, Elalfy MS, Gatzioufas Z, et al. Collagen cross-linking with photoactivated riboflavin (PACK-CXL) for the treatment of advanced infectious keratitis with corneal melting. Ophthalmology. 2014;121(7):1377-1382. 55. Richoz O, Kling S, Hoogewoud F, Hammer A, Tabibian D, Francois P, et al. Antibacterial efficacy of accelerated photoactivated chromophore for keratitis-corneal collagen cross-linking (PACK-CXL). J Refract Surg. 2014;30:850–854.

M. Mrochen et al. 56. Iseli HP, Körber N, Koch C, et al. Scleral cross-linking by riboflavin and blue light application in young rabbits: damage threshold and eye growth inhibition. Graefes Arch Clin Exp Ophthalmol. 2016;254(1):109-22. 57. Schuldt C, Karl A, Körber N, et al. Dose-dependent collagen cross-linking of rabbit scleral tissue by blue light and riboflavin treatment probed by dynamic shear rheology. Acta Ophthalmol. 2015;93(5):e328-36. 58. Paik DC, Wen Q, Airiani S, et al. Aliphatic beta-nitro alcohols for non-enzymatic collagen cross-linking of scleral tissue. Exp Eye Res. 2008;87:279-285. 59. Kim SY, Babar N,, Munteanu EL, et al. Evaluating the toxicity/ fixation balance for corneal cross-linking with sodium hydroxymethylglycinate (SMG) and riboflavin-UVA (CXL) in an ex vivo rabbit model using confocal laser scanning fluorescence microscopy. Cornea. 2016;35: 550-556. 60. Bradford S, Mikula E, Chai D, et al. Corneal cross-linking and mechanical stiffening using Non Linear Magic. ARVO Proceedings 1361;2016. 61. Zhu H, Alt C, Webb RH, Melki S, Kochevar IE. Corneal crosslinking with rose bengal and green light: efficacy and safety evaluation. Cornea. 2016;35(9):1234-41. 62. Cherfan D, Verter EE, Melki S, et al. Collagen cross-linking using rose bengal and green light to increase corneal stiffness. Invest Ophthalmol Vis Sci. 2013;54(5):3426-3433. 63. Bekesi N, Kochevar IE, Marcos S. Corneal biomechanical response following collagen crosslinking with rose bengal-green light and riboflavin-UVA. Invest Ophthalmol Vis Sci. 2016;57(3):992-1001.

17. Computational modeling of corneal refractive surgery, ectasia, and corneal crosslinking Ibrahim Seven1, Vinicius Silbiger De Stefano1, William J. Dupps Jr.1,2,3 Ocular Biomechanics & Imaging Lab, Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA; 2Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA; 3Department of Ophthalmology, Cleveland Clinic Lerner College of Medicine, Case Western Reserve University, Cleveland, OH, USA 1

1. Introduction

Copyright © 2018. Kugler Publications. All rights reserved.

The goal of predicting the cornea’s structural behavior incorporates many of the themes addressed in the preceding chapters. Independently, aspects of corneal microstructure, tomographic shape, biomechanical properties, loading conditions, and surgical specifications provide some predictive insight into the cornea’s likely response to refractive surgery or its propensity for ectatic disease. However, a predictive solution that aspires to be comprehensive, patient-specific, and more deterministic than stochastic is feasible only through computational approaches that account for the major drivers of response, including detailed 3-D geometry, complex loading scenarios, and mechanical constitutive equations describing the relationships between stress and strain (Fig. 1).

Finite element analysis (FEA) is a powerful tool for approaching such complex problems at the microstructural and macrostructural scales. FEA has been widely used for decades in the aviation, civil engineering, and the automotive industries. The National Science Foundation1 and the US Food and Drug Administration2 have recognized the increasingly important role of computational simulation in health and medicine. Specifically, the clinical domains of corneal disease and keratorefractive surgery offer rich subjects for translational investigation and proof-of-concept for the broader field of simulation-based medicine. The cornea’s shape is linked explicitly to visual function through direct optical relationships; small changes in corneal geometry greatly impact refractive error, higher order aberrations, and visual quality. This structure-function relationship strongly supports the

Fig. 1. Schematic illustration of the inputs and outputs of the finite element modeling (FEM) approach to structural simulation of disease states or putative surgical interventions. Correspondence: William J. Dupps, Jr., MD, PhD, 9500 Euclid Ave/i-32, Cleveland OH 44195, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 245-260 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

246

I. Seven, V.S. De Stefano and W.J. Dupps Jr

qualitative, engineering-based approach to predicting optical outcomes in corneal surgery that is the subject of this chapter. Our goal is not to present an exhaustive review of the subject, but rather to introduce the reader to the topic through an application-oriented approach and encourage further reading and research.

Copyright © 2018. Kugler Publications. All rights reserved.

2. Computational modeling of keratorefractive surgery Historically, the field of keratorefractive surgery arose when incisional procedures such as radial keratotomy (RK) and astigmatic keratotomy (AK) were used to directly leverage the biomechanical relationship between corneal structure and shape. Surgical algorithms for these procedures attempt to relate refractive responses to incision location, depth, and length as well as patient age (a surrogate for corneal stiffness). As corneal refractive surgery shifted toward photoablative modes of treatment such as photorefractive keratectomy (PRK) and laser in-situ keratomileusis (LASIK), Munnerlyn et al.3 developed a mathematical algorithm for calculating the requisite pattern of tissue removal which temporarily shifted thinking away from biomechanical responses toward an understanding of photoablation as “shape subtraction” that treats the cornea as biomechanically and biologically inert.4,5 While advances in the precision of laser delivery systems, eye tracking, and registration technologies have supported excellent refractive outcomes in many cases, treatment paradigms that do not explicitly account for biomechanics ultimately fail to account for important clinical phenomena such as refractive over- and under-correction, induction of higher order aberrations, and corneal ectasia.4,6-8 One of the main goals of computational mechanics in corneal surgery is to leverage existing diagnostic technology to address this “precision gap” and bring richer data sets to bear on the problem of preoperative prediction of individual patient outcomes. 2.1. Incisional keratotomy Computational efforts in corneal refractive surgery began with simpler geometrical and material assumptions, evolving in complexity as understanding of corneal microscopic and macroscopic structural

Fig. 2. Refractive change in the model in response to varying numbers of incisions at 3 mm diameter. Incision depth: 99%; incision length: 4 mm; IOP: 15 mmHg; D: diopters.12

characteristics increased9-11 and computational capabilities improved. The earliest studies reflected the clinical interests of the time and investigated incisional procedures such as RK and AK. RK simulations investigated the impact of variations in parameters such as number of incisions, incision depth, incision width, and intraocular pressure (IOP) on corneal curvature and optomechanical outcomes.12-14 In these simulations and related sensitivity analyses, stresses in the non-incised deep cornea increased after surgery in proportion to the number of incisions. Central flattening increased significantly when the number of incisions increased from four to eight, but demonstrated diminishing increases beyond eight incisions (Fig. 2).12 Greater central flattening was observed in simulations with higher IOP for a given number of incisions (Fig. 2), and longer and deeper incisions produced higher corrections (Fig. 3).12 In an early attempt at optimizing incisional parameters for a specific degree of preoperative refractive error, Velinsky and Bryant employed a linear transversely isotropic model and used ray tracing to balance the optical effect of RK parameters and their surgical invasiveness (defined as incision length x depth).15 They outlined a general approach to the use of FEA for optimizing incisional surgery (summarized in Fig. 4) and argued the need for ongoing research into the use of computational aids for surgical guidance.15 Similar findings regarding the relationship between incision length and depth were observed in AK models.13,16,17 Studies of AK have replicated the clinical observation that arcuate incisions performed perpen-

Computational modeling of corneal refractive surgery, ectasia, and corneal crosslinking

247

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. (Left) The refractive change in the model as a function of incision percentage depth. (Right) The refractive change in the model in response to the change in elastic modulus. D: diopters; kPa: kilopascals.12

dicular to the steep meridian reduced the curvature in that meridian while slightly steepening the flat meridian (a phenomenon known clinically as “coupling”). Longer incisions closer to the corneal optical zone produced higher astigmatic correction. Most RK and AK studies have not demonstrated a significant relationship between preoperative corneal curvature and the magnitude of simulated correction. However, these models employed simpler geometries without features such as irregular astigmatism or corneal thickness (except a one-eye study),18 and more recent work on astigmatic surgical simulations in a clinical sample of ten eyes suggests that eye-to-eye variance in high resolution curvature and thickness features does in fact impact the quality and quantity of astigmatic effect.19 The choice of constitutive models has been shown to strongly impact AK outcome predictions.20 Alastrué demonstrated that isotropic and linear assumptions tended to overestimate the amount of correction, whereas a fiber-dependent anisotropic material model produced more realistic outcomes.17 A subsequent study by Lanchares et al. also suggested that an anisotropic model produced post-AK outcomes that more closely replicated those of a clinical nomogram.21 Fig. 4. Workflow optimization including corneal imaging, mesh generation, and optical evaluation of the model outcomes using ray tracing. OZ: optical zone.15

2.2. Computational modeling of photoablative surgery: PRK and LASIK In one of the earliest attempts to simulate the structural effects of PRK, Manganiello et al. used a generic biconic corneal geometry with a constant thickness and fiber-dependent material model representing the preferred orientations of the collagen fibers, which were expounded upon in Chapter 2.22 A myopic treatment

248

Copyright © 2018. Kugler Publications. All rights reserved.

and a myopic astigmatism treatment were simulated using the Munnerlyn equation to approximate the ablation pattern.3 The corneal elastic properties were assumed to remain constant after surgery. Higher corneal stresses were observed in post-PRK models than in pre-PRK models were subjected to the same IOP. Additionally, the displacements in the post-PRK corneal model were more sensitive to IOP increases. Predicted dioptric power changes as a function of IOP were dependent on the limbal boundary condition assumptions, which were modeled in three ways: fixed in all directions, elastic support with springs, and free rotations (Fig. 5). These results underlined the importance of model assumptions at the corneoscleral junction, and suggested that non-physiological constraints on the cornea at the limbus should be avoided or at least considered as a source of error in models that adopt such assumptions. Subsequent studies from the same group advanced the computational model by adding a probability distribution function to the material model that represents not only the direction, but also the density of the collagen fibers in the cornea.23 Simulation results using this model were compared to experimental tensile and inflational testing data,24,25 and PRK was simulated with patient-specific geometries and customized material constants. These studies explored the impact of the more detailed fiber component through a sensitivity analysis, and examined the relationship between

Fig. 5. Refractive power of a post-PRK corneal model in response to varying IOP for different limbal boundary condition assumptions. Fixed: The nodes at the limbus are confined in all directions, Elastic support: The nodes at the limbus are fixed using springs, Free rotations: The nodes at the limbus cannot move in principal directions, but can rotate freely.22

I. Seven, V.S. De Stefano and W.J. Dupps Jr

collagen fibril stiffness and corneal stress maps.24,25 Unlike PRK and related surface ablation procedures, LASIK incorporates a corneal flap under which the photoablative portion of the procedure is performed. By preserving the corneal epithelium, LASIK affords a faster and more comfortable recovery than PRK, and rapidly became the most frequently performed refractive surgery by the early 2000s. The addition of a flap introduces important structural implications:5 a deeper surgical insult, a different biomechanical steady state after surgery than PRK that influences refractive outcomes, and a higher demonstrated risk of ectasia.26 Clinically, creation of a LASIK flap — even without delivery of any excimer laser photoablation under the flap to reshape the stromal bed — induces some hyperopic shift,27,28 a phenomenon that is related biomechanically to the flattening effect seen with phototherapeutic keratectomy (PTK).29 Therefore, studying the biomechanics of LASIK and the LASIK flap is fundamental in terms of the accuracy and predictably of clinical outcomes. In a computational study of LASIK flap creation alone, Deenadayalu et al. incorporated patient-specific geometry from a corneal topographer into a 3-D linearly elastic orthotropic corneoscleral model,30 to investigate the impact of several model variables on the magnitude of flap-induced flattening. The study modeled the flap as a 3000 incision with no reduction in the flap material properties within the flap. As shown in Figure 6, flap-induced hyperopic shift increased as: 1. corneal elastic modulus decreased; 2. flap thickness increased; and 3. IOP increased. Flap diameter had minimal effect on induced flattening. The sensitivity of computational modeling outcomes to patient-specific variations in corneal elastic modulus in a full myopic LASIK procedure (flap and photoablation) was investigated by Sinha Roy and Dupps in a whole-eye, 2-D, hyperelastic, isotropic model.32 The model incorporated a dedicated flap interface wound layer that modeled a reduction in cohesive strength based on the experimental literature, and no corneal elastic modulus change was applied within the flap. Figure 7 demonstrates the predicted change in corneal apical power as a function of IOP for 2 D, 4 D, and 6 Dspherical myopic treatments using weak and stiff

Computational modeling of corneal refractive surgery, ectasia, and corneal crosslinking

249

Fig. 7. Achieved myopic correction as a function of IOP, expressed as the change in apical refractive power from the pre- to the postoperative condition. Solid lines: change in the lower corneal stiffness (W) model; dotted lines: change in the stiffer corneal (H) model; D: diopters.32

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 6. The average treatment-induced change in refractive power in response to flap thickness (FT), IOP, and flap diameter (FD). 31

corneal material property assumptions extracted from published human eye studies performed under similar control conditions. In simulations where geometry was held constant and only the level of correction and material properties were modified, weaker corneas tended toward under-correction (residual myopia) relative to stronger corneas. With higher attempted corrections incorporating more tissue ablation, the degree of residual steepness was even greater. A sub-analysis of anterior chamber depth (ACD) confirmed that relative under-correction was attributable to an increase in posterior corneal elevation with LASIK, indicative of structural bowing, in weaker corneas. The study also included simulations (Fig. 8) that constrained the cornea at the limbus and excluded the extra-corneal structures from the model, demonstrated a significant impact on the displacement behavior (spatial pattern and magnitudes) and corneal curvature change in LASIK simulations. A key conclusion of the study was, that with all other variables held constant, increasing corneal stiffness favored corneal flattening. This provided an explanation for the clinical phenomenon of corneal flattening in corneal crosslinking (CXL) and led to additional work, described in the next section, aimed at further exploring this effect. A subsequent inverse FE study explored the question of the magnitude of effective elastic modulus reduction in clinical LASIK cases. In this study, patient-specif-

Fig. 8. Change in ACD in response to IOP. (Left) Lower corneal stiffness model before and after 6.00 D LASIK. (Right) Higher corneal stiffness model before and after 6.00 D LASIK. D: diopters. 32

ic pre-LASIK and post-LASIK tomographies from both eyes of a bilateral LASIK patient were modeled, and an inverse FE optimization was performed to determine the amount of LASIK-induced weakening of the residual stromal bed (RSB).33 The study simulated patient-specific LASIK treatments using spatially dependent hyperelastic material properties, and simulations were repeated with no weakening, uniform weakening, and radially non-uniform (peak at center) weakening within a 6 mm optical zone. The differences between simulated and clinical geometries were smaller when a radially non-uniform weakening was implemented with a 65% peak weakening at the center of the treatment zone diameter, and eye-specific variability in this approximation of weakening was noted. This was the first computational study to estimate surgically induced elastic weakening in LASIK from clinical topographic data, and it demonstrated that significant elastic weakening was required to replicate clinical LASIK outcomes in a two-eye pilot study.

250

I. Seven, V.S. De Stefano and W.J. Dupps Jr

Fig. 10. Scatterplot and linear regression comparing case-specific predictions of mean central corneal curvature (Kmean) change to actual change in vertex-corrected SE manifest refraction.36

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 9. (A) En-face and cross-sectional view of the finite element mesh for the LASIK and SMILE models. The schematic shows the LASIK flap or SMILE cap (brown), RSB, (dark green), anterior stroma adjacent to flap/cap (light green), and the healed wound layer along the interface between the flap/cap and RSB (dark line). Section A and Section B represent the cross-section view of the cornea along the vertical meridian, respectively. 34

While not a photoablative procedure, femtosecond laser assisted small-incision intrastromal lenticule extraction (SMILE) has significant structural analogy to LASIK but eliminates most of the circumferential flap incision by preserving a corneal cap and removing an intrastromal lenticule through a smaller incision. This topic, including related computational modeling studies, is dealt with in more detail in Chapter 18. In a computational modeling study that incorporated a more advanced depth-dependent, anisotropic material model adapted from previous literature23 that included collagen fiber density and preferred orientation as a separate entity, the structural effect of a flap was compared directly to analogous procedures with no flap (SMILE).34 The study included disruption of collagen fibers within the optical zone due to flap and wound layers, which more realistically represents the flap’s structural effects (Fig. 9). It was found that the disruption of the fibers during creation of a flap generated higher stresses in the residual stromal bed, since this layer became the only load-bearing region within the cornea. Figure 9 illustrates von-Mises stresses in the RSB before and after flap, and indicates

Misconception 1: Finite element analysis predictions of corneal interventions are equally accurate across all post-operative time points Biological factors in the post-treatment healing process such as inflammation, collagen reparative processes and edema are not explicitly simulated in most finite element models. Most of these effects are maximal in the early postoperative period and plateau at postoperative timepoints that vary by procedure and individual. Computational models that are developed for clinical predictive purposes are best validated for clinically established surgical stability endpoints when acute responses have generally ceased. Inverse modeling has been used to indirectly account for the post-acute effects of these variables on material properties, but individual differences in these responses will contribute to some variability in predicted outcomes. an increase as flap thickness and myopic spherical correction increased. Since surface deformations can be calculated, and this calculation can be transformed into axial and tangential curvature values and then related directly to refractive change, computational modeling has the potential to provide clinicians with a surgical guidance tool for demonstrating likely surgical outcomes and

Computational modeling of corneal refractive surgery, ectasia, and corneal crosslinking

Fig. 11. Scatterplot and linear regression of the case-specific prediction error in mean central corneal curvature (D) as a function of preoperative CH (mmHg), indicating a trend toward overestimation of myopic correction in subjects with lower CH.36

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 12. Percentage of cases with less than or equal to 0.25, 0.50, 0.75, and 1.00 D of error in the actual vs predicted anterior tangential curvature of the central 3 mm (Kmean, D). Green: prediction error; blue: CH-adjusted prediction error.36

measures of structural impact. Some studies demonstrated this potential by calculating absolute curvature values22,32 or computing the curvature change between pre- and post-treatment models.34,35 However, validation of any computational model is ultimately required to assess its suitability for clinical prediction. A recent study36 attempted to address this important gap in the literature by assessing the predictive accuracy of simulation-based LASIK outcomes using a fiber-dependent, anisotropic material model on 20 eyes of 12 patients. In this study, simulated keratometry (SimK) values and the mean tangential curvature of the central 3 mm (Kmean) were obtained from the anterior surfaces of the clinical tomographies; case-specific computational models were then compared to three-month clinical outcomes. The mean difference for Kmean between simulated and actual post-LASIK cases was not statistically significant (-0.13 ± 0.36 D, P = 0.1). The mean difference between the surgically induced clinical change in Kmean and the model predicted change was -0.11 ± 0.34 D (P = 0.2). The surgically induced Kmean

251

changes in the model were also a strong predictor of the change in manifest refraction, accounting for 97% of the variance (p < 0.00001) in actual spherical equivalent refractive change (Fig. 10). Another key finding of this study was demonstrating, for the first time, that clinical measurements from the Ocular Response Analyzer (in this case, corneal hysteresis (CH)) were a useful correlate to model prediction error (r = 0.63, P = 0.041) (Fig. 11). This correlation was then used as a statistical adjuster to improve the outcome prediction (Fig. 12). In summary, this study demonstrated that a clinically feasible approach to computational simulation predicted corneal curvature and manifest refraction outcomes with an acceptable level of accuracy in clinical LASIK cases. Efforts to automate the computational tools presented in this chapter are underway. An automated workflow for the steps described in these studies is in place to allow software-driven tomography file transfer and treatment data entry, cloud-based FEA simulation, and electronic delivery of results in under three minutes with the goal of providing a useful tool for clinical guidance in de-novo refractive cases.

3. Computational modeling of corneal ectatic disease Keratoconus (KC) is characterized clinically by a region of abnormally high curvature, reduced corneal thickness, and progressive corneal topographic irregularity that reduces quality of life and often requires corneal transplantation in its most advanced forms.5,37 Tensile testing of corneal strips cut from KC keratoplasty buttons has demonstrated 50% to 60% reductions in the strain-dependent corneal elastic modulus relative to normal cadaveric tissue.38,39 These findings, along with clinical signs of KC such as corneal stress lines (Vogt striae) and rupture of Descemet`s membrane (potentially leading to corneal hydrops), support the concept of biomechanical failure as a central pathologic feature of the disease.23,40 The factors that precipitate this biomechanical failure are still under investigation, and probably include interactions of genetic, biochemical, and ultrastructural abnormalities. Computational studies have attempted to shed light on the relationship between biomechanical properties and the phenomena of KC onset and progression.41-44

252

I. Seven, V.S. De Stefano and W.J. Dupps Jr

Fig. 16. Clinical tangential curvature maps of the anterior corneal surface of (A) the less affected right eye and (B) the more affected left eye of a patient with asymmetric KC before simulation of progression in the right eye.44

Fig. 13. Models of (a) normal cornea, (b) keratoconic cornea with a single thinned region, and (c) keratoconic cornea with two thinned regions. All dimensions are in mm.42

Fig. 17. (A,B) Whole-eye FEM model showing the cornea and sclera. (C) A schematic representation of the model showing the weaker KC zone and the CXL zone in a standard 9 mm diameter simulated treatment.44

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 14. Corneal apex displacement (mm) as a function of IOP (mmHg). Comparison between healthy (red line) and KC (blue line) corneas.41

Fig. 15. En-face map of maximum Cauchy stress (MPa) at 15 mmHg IOP for (left) a healthy cornea (max 0.11 MPa) and (right) a keratoconic cornea (max 0.20 MPa).22

Gefen et al. investigated the biomechanical factors that may produce topographic features of KC using a generic 3-D geometry and a linear orthotropic FE model.42 The study looked at three potential manifestations of biomechanical failure: localized thinning, reduction in tissue meridian elastic modulus (principal), and reduction in shear modulus. Figure 13 demonstrates how the thinning was simulated by geometric manipulation of the model. While localized thinning had the greatest impact on the topographic steepening over the range of parameter values studied for the three variables, the investigators reduced corneal thickness to 200 μ, an extreme degree of disease severity that could bias the sensitivity analysis toward thickness as a driver. Additional uncertainty arises from the lack of quantitative data

Computational modeling of corneal refractive surgery, ectasia, and corneal crosslinking

253

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 18. (A-C) Incremental topographic steepening in the tangential curvature maps of the anterior corneal surface (A, right eye) with focal 10%, 30%, and 45% reductions in the elastic modulus. (D-F) Corresponding difference in tangential curvature between the weakened cornea and the pre-weakening in-vivo state (Fig. 18 A).44

on actual decrements of elastic or shear moduli in keratoconic progression, but such sensitivity analyses are still very useful for investigating the interplay of potential disease drivers. Pandolfi and Manganiello performed a study that proposed a fiber-dependent constitutive model for the cornea, simulating KC by reducing collagen fibril stiffness and the cohesive force between these fibers and their surrounding ground matrix.41 Much greater increases in apical displacement were observed in the keratoconic model than in the healthy cornea model for the same IOP (Fig. 14),41 and higher stresses were observed in keratoconic models (Fig. 15).22 Carvalho et al. explored the contribution of reductions in local elastic properties to surface topography in a 3-D cornea-scleral shell model with generic geometry,45 and observed higher von Mises stresses and deformations within the cone region, where the material properties were reduced. Sinha Roy and Dupps applied a 3-D corneoscleral FE model to the question of KC progression by incorporating patient-specific models of a highly asymmetric bilateral keratoconus case (Fig. 16).44 A circular zone of reduced elastic modulus was implemented in the model of the less clinically affected eye (Fig. 17) with the goal of incrementally weakening the cornea to simulate progression as a

Fig. 19. Maximum anterior surface curvature (Kmax) as a function of the decrease in hyperelastic modulus in a simulation of KC progression in an eye with subclinical KC (right eye).44

function of elastic modulus degradation. Decreases in elastic modulus in the weak zone were modeled as an exponential decay from the edge to the center of the circular zone, where the center was placed at the steepest point of the cornea. The diameter of the weak zone was estimated to be 7 mm by extrapolating from experimental x-ray diffraction evidence of similar diameters of collagen fibril disorganization.9 With further weakening of the cornea, the tangential curvature increased, producing a steep cone surrounded by an annular zone of progressive flattening (decreased

254

I. Seven, V.S. De Stefano and W.J. Dupps Jr

Misconception 2: A material model needs to represent all microstructural components of the tissue to the highest degree possible While rich microstructural representation of a tissue is desirable for many reasons, the objective of the model is also an important consideration in determining the level of complexity required. Model complexity absolutely impacts computational time and is a less certain driver of predictive performance depending on the application, thus an optimal balance of model fidelity and performance in its specific context of use should be sought. Hyper-specification of models with details that are derived from generic tissue specimens do not necessarily improve model performance at the macroscopic geometry level, and a variety of material formulations may be capable of appropriately representing the stress strain behavior under typical loading-unloading scenarios.

Copyright © 2018. Kugler Publications. All rights reserved.

tangential curvature). With a 45% reduction in elastic modulus, the maximum tangential curvature on the anterior surface (Kmax) increased by 12.23 D in the right eye. Kmax in the more clinically affected left eye (Fig. 18B) was 47.1 D. If similar pre-disease geometries and elastic moduli are assumed, a 32% reduction (Fig. 19) in elastic modulus would be required to produce the degree of steepening observed in the more affected eye. Figure 19 illustrates the important finding that corneal curvature increases exponentially, not linearly, as a function of decreasing elastic modulus, and this suggests a potential prognostic role for elastic modulus measurements in predicting progression risk, progression rates, and optimal treatment timing with CXL procedures.

4. Computational modeling of CXL effects CXL is a treatment for KC and corneal ectasia that augments corneal material strength with the primary goal of stabilizing progressive disease.46 Treatment generally first involves corneal exposure to a photosensitizing chemical agent such as riboflavin47 or

Fig. 20. Tangential curvature maps of the anterior corneal surface of (left) a central cone (region of maximum curvature) in a second patient and (right) a more eccentric cone in a third patient before simulation of CXL effects.44

rose-bengal48 followed by photoactivation, where the interaction of chemical agent, light, oxygen, and collagenous tissue leads to increased corneal tensile strength.49 Many experimental techniques, including but not limited to strip extensiometry, 50 inflation testing,51 contact,52 and non-contact53 tissue imaging methods have been used to quantify the strengthening effect of crosslinking. Computational modeling studies have been important in the development of our understanding of crosslinking effects in the traditional context of use, but have also enabled in-silico investigation of concepts for enhancing optical results of crosslinking and applying crosslinking methods to the correction of refractive error. Sinha Roy and Dupps investigated alternative crosslinking patterns in computational models to enhance the normalizing effect of crosslinking treatment in KC.44 The study simulated CXL procedures that incorporated the physical effects of radial variation and axial attenuation of the intensity of typical clinical UVA sources. The study also explored the performance of putative CXL protocols with smoother peripheral spatial intensity transitions, different CXL-induced stiffening depths, and cone-centered treatment approaches. To investigate the influence of topographic cone location on post-CXL outcomes, two morphologically different KC eyes — one with a central cone and another with a more eccentric cone — were used to construct whole-eye, 3-D models (Fig. 20). The induced corneal stiffening in response to crosslinking was modeled as an increase in corneal elastic modulus extending either 200 μm or 300 μm into the anterior corneal stroma. Broad-beam 9 mm treatments (the current clinical standard), variable-intensity broad-beam treatment, and cone-localized, small-area, variable-intensity treatments were simulated using the two different pre-treatment corneal geometries. The

Computational modeling of corneal refractive surgery, ectasia, and corneal crosslinking

255

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 21. Tangential curvature maps of a cornea with a central cone after simulated CXL to a maximum depth of 300 μm in (A) a standard broad-beam stiffening protocol, (B) variable intensity broad-beam protocol, and (C) a cone-localized, variable-intensity protocol. (D-F) Corresponding tangential curvature difference maps.44

Fig. 22. Tangential curvature maps of a cornea with a more eccentric cone after simulated CXL to a maximum depth of 200 μm in (A) a standard broad-beam stiffening protocol, (B) a variable-intensity broad-beam protocol, and (C) a cone-localized, variable-intensity protocol. (D-F) Corresponding tangential curvature difference maps.44

Copyright © 2018. Kugler Publications. All rights reserved.

256

study demonstrated flattening effects of the standard broad-beam treatment that were comparable in magnitude and spatial pattern to published clinical results. Simulation of a deeper CXL effect resulted in enhanced flattening of the cone in all cases. Greater flattening of the cone was achieved with a reduction in the treatment diameter (allowing more compensatory steepening in the flatter areas of the cornea distal to the cone), more gradual intensity transition zones, and centration of treatment on the center of the cone (Fig. 21). CXL-induced topographic change was sensitive to cone location; the eccentric cone centralized slightly with the standard CXL simulation, decentered slightly with a smaller treatment zone, and remained in its original location with the cone-centered, variable-intensity treatment (Fig. 22). This was the first proof-of-concept that localized stiffening in crosslinking could be leveraged to produce more regularization of the keratoconic cornea, as well as the first controlled demonstration of how other CXL parameters might interact with various corneal geometries to produce very different outcomes from case to case. It should be noted that the CXL treatment was centered on the point of minimum corneal elastic modulus in these simulations: centering clinical treatments on more readily available clinical measures of cone location such as tangential curvature, elevation features, or axial curvature, which are now being explored clinically, are likely to produce slightly different results. It is proposed that treatment centration targeting the weakest zone will produce optimal results, but such an approach will depend on the clinical availability of spatially resolved biomechanical measurement techniques. The goals of shape optimization will also need to be balanced with the goals of disease stabilization, where the latter objective may require some treatment of the areas of the cornea away from the epicenter of weakness to protect against disease progression in the peripheral cornea. While this study established important mechanistic links between corneal stiffening and topographic improvement of the disease, clinical measurements of actual material property changes after crosslinking are elusive.54,55 In-vivo measurement of the material property changes associated with various permutations of CXL is of significant basic interest for understanding the biomechanical foundations of crosslink-

I. Seven, V.S. De Stefano and W.J. Dupps Jr

Fig. 23. Four candidate patterns for treating corneal astigmatism with crosslinking-mediated stromal stiffening investigated in a virtual trial approach.19

ing treatment and its many variables. Quantitative assessment of material property changes in living tissue is critical to the long-term goal of applying patient-specific models to the prediction and optimization of the treatment outcomes. Sinha Roy et al. attempted to estimate the magnitude of CXL-induced stiffening by comparing pre- and post-CXL corneal models using the inverse FE modeling method.33 Models were built using patient-specific tomographies and IOP measurements, and the simulated CXL procedures were designed to approximate the treatment parameters used in the clinical series from which the modeled patients were derived. To estimate the change in modulus, the material properties of the anterior stroma were perturbed and optimized to minimize the difference between the computed FE and measured in-vivo anterior surface curvature of the cornea. The study revealed that corneal elastic modulus did indeed increase following CXL to an extent that agrees well with experimental data. Furthermore, the magnitude of stiffening increased as postoperative time progressed, a change that could be related to either modulus-driven changes in the stroma over time or simultaneous changes in epithelial geometry. The impact of the assumed scleral-to-corneal elastic modulus ratio (S/C) on the modulus change estimates

Copyright © 2018. Kugler Publications. All rights reserved.

Computational modeling of corneal refractive surgery, ectasia, and corneal crosslinking

from the inverse analysis was also explored. Three different S/C ratios (3, 4, and 5) were simulated in the whole-eye model and impacted the range of the estimated modulus increase from a factor of 2.11 ± 1.48 to a factor of 1.96 ± 1.23 (a difference of 7%). The large standard deviations in estimated modulus change illustrate that the effects of CXL on elastic modulus may vary significantly from patient to patient. While the clinical application of CXL is primarily directed at stabilization of corneal ectatic disease, there is an increased interest in using CXL to produce non-ablative changes in corneal shape to treat refractive disorders. Since UV-riboflavin crosslinking begins with non-specific, full-thickness, pan-corneal saturation of the stroma with riboflavin49 and UVA irradiance is required to activate stiffening, the latter can be spatially directed to create specific patterns of stiffening. The studies described earlier in this section provided proofof-concept for this approach. If local shape changes can be controlled to reduce the refractive errors associated with KC, it could potentially be applied to more common refractive errors. To expand the theoretical foundations for such an approach, four candidate patterns (Fig. 23) were generated for potential astigmatic corrections using CXL and tested in 3-D, patient-specific, isotropic models of ten eyes of astigmatic patients in a computational virtual trial.19 As an initial assessment of the effect of pattern orientation on astigmatic outcome, two simulations of the linear bowtie pattern were compared on a patient model from the study population, one simulation with the major axis oriented on the steep axis of astigmatism, and the other with the major axis perpendicular to the steep axis. Treatment on the flat axis of astigmatism reduced preoperative astigmatism from 2.20 D to 0.88 D, whereas treatment on the steep axis increased astigmatism to 2.60 D. Next, all four candidate patterns were simulated on all ten model eyes using orientation perpendicular to each eye’s steep axis of astigmatism. Statistically significant mean reductions in corneal astigmatism were achieved with each of the four patterns using 100% stiffness increase (2x stiffening), with the linear bowtie pattern producing the largest and most consistent magnitudes of correction of the investigated patterns. The astigmatic effect resulted from statistically significant increases in curvature

257

Fig. 24. An example of a validation comparison to assess predictive fidelity in a FE simulation of crosslinking for myopic correction. Axial corneal curvature maps of the actual post-treatment patient (left) and the simulation result (right). Quantitative prediction error in central corneal curvature was less than 0.25 D. (Seven and Dupps, unpublished)

along the flat (treated) meridian coupled, with statistically significant decreases in curvature along the steep (untreated) meridian. To explore the dependence of simulation results on the model material formulation, the linear bowtie pattern was also modeled in all ten eyes with fiber-dependence and depth-dependent properties. The mean astigmatic reduction was nominally decreased in the fiber-dependent model from -1.08 ± 0.13 to -1.03 ± 0.1 (p = 0.6), suggesting insignificant levels of dependence on a fiber-based model for this application. Simulated CXL-based treatments also appeared to reduce astigmatism without inducing the 4- to 6-fold increases in higher-order aberrations that have been associated with relaxing incisions.56 In the simulations of CXL-medicated astigmatic treatment, no consistent increases in spherical aberration, coma, or trefoil were noted. In practice, AK and CXL-mediated astigmatic treatments could easily be combined because the treatments Misconception 3: The predictive performance of a corneal finite element model can be assumed to be comparable for different imaging input techniques Patient-specific corneal finite element models are constructed from corneal tomographic images. There is significant inter-device variation in curvature, thickness and elevation measurements obtained with different commercially available devices. These differences are propagated through computational models beginning with geometry meshing and are important sources of prediction variability.

258

involve orthogonal axes. In a separate single-patient computational modeling study, our group found that a combination of AK in the steep meridian and linear bowtie pattern CXL in the flat meridian corrected higher levels of astigmatism than could be corrected with either modality alone.18 With the guidance of these previous simulations, the linear bowtie pattern was applied clinically to treat corneal astigmatism in a patient using a dedicated system for custom UV pattern delivery,57 and produced similar reductions in corneal astigmatism. Unpublished studies by our group in collaboration with Avedro have also explored selective crosslinking patterns for myopia (Fig. 24) and hyperopia using central small diameter treatments and annular treatment zones, respectively, and clinical trials are underway.58

5. Future impact of computational modeling in corneal and refractive surgery

Copyright © 2018. Kugler Publications. All rights reserved.

In this chapter, we have surveyed FEM and its application to clinical questions in corneal disease and refractive surgery. Clinical translation of computational modeling principles is a major focus of our research group, and one goal is to introduce tools that can shift the current paradigms of surgical planning from retrospective, population-based, probabilistic approaches to more structurally informed, individualized, simulation-based approaches that appeal to common biomechanical principles influencing all varieties of corneal

I. Seven, V.S. De Stefano and W.J. Dupps Jr

surgery. Potential applications are not limited to those discussed in the previous sections, but include a host of others, including intracorneal implants, 59, 60 corneal tissue inlays,61 and corneal ectasia risk assessment.62,63 As methods for biomechanical measurement become more readily available and models can begin to incorporate patient-specific corneal property profiles, the predictive value of computational simulations and their clinical utility will only increase.

Acknowledgements Financial disclosure: William J. Dupps, Jr. is on the medical advisory board of Avedro (Waltham, MA, USA) and is an inventor of patents involving computational modeling that are held by Cleveland Clinic Innovations and licensed to OptoQuest Inc. (Cleveland, OH, USA). Dr. Dupps has received research funding for this work from the US National Institutes of Health Bioengineering Research Grant (R01 EY022381), an Ohio Third Frontier Commission Innovation Platform Award (TECH 13-059, OH, USA), the National Keratoconus Foundation (USA), an Unrestricted Grant from Research to Prevent Blindness (NY, USA) to the Department of Ophthalmology of the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University, the Pender Ophthalmology Research Fund (USA), and the Sara J. Cheheyl Fund for Ocular Biomechanics Research (USA) at the Cole Eye Institute. William J. Dupps, Jr. is a recipient of a Research to Prevent Blindness Career Development Award.

Computational modeling of corneal refractive surgery, ectasia, and corneal crosslinking

References 1.

2.

3.

4. 5. 6.

7.

8.

9.

10.

11.

12.

Copyright © 2018. Kugler Publications. All rights reserved.

13.

14. 15. 16.

17.

National Science Foundation (NSF). Revolutionizing Engineering Science through Simulation. A Report of the National Science Foundation Blue Ribbon Panel on Simulation-Based Engineering Science. National Science Foundation; 2006. Morrison TM. Reporting of computational modeling studies in medical device submissions. FDA, Division of Applied Mechanics 2016. https://www.fda.gov/downloads/MedicalDevices/DeviceRegulationandGuidance/GuidanceDocuments/ UCM381813.pdf accessed on October 13, 2017 Munnerlyn CR, Koons SJ, Marshall J. Photorefractive keratectomy: a technique for laser refractive surgery. J Cataract Refract Surg. 1988;14(1):46-52. Roberts C. The Cornea is not a piece of plastic. J Refract Surg. 200;16:407-13. Dupps WJ, Jr., Wilson SE. Biomechanics and wound healing in the cornea. Exp Eye Res. 2006;83(4):709-20. Marcos S, Cano D, Barbero S. Increase in corneal asphericity after standard laser in situ Keratomileusis for myopia is not inherent to the Munnerlyn Algorithm. J Refract Surg. 2003;19:s592-6. Moreno-Barriuso E, Lloves JM, Marcos S, et al. Ocular aberrations before and after myopic corneal refractive surgery: LASIK-induced changes measured with laser ray tracing Invest Ophthalmol Vis Sci. 2001;42(6):1396-403. Cano D, Barbero S, Marcos S. Comparison of real and computer-simulated outcomes of LASIK refractive surgery. J Opt Soc Am A Opt Image Sci Vis. 2004;21(6):926-936. Meek KM, Tuft SJ, Huang Y, et al. Changes in collagen orientation and distribution in keratoconus corneas. Invest Ophthalmol Vis Sci. 2005;46(6):1948-1956. Winkler M, Chai D, Kriling S, et al. Nonlinear optical macroscopic assessment of 3-D corneal collagen organization and axial biomechanics. Invest Ophthalmol Vis Sci. 2011;52(12):88188827. Winkler M, Shoa G, Xie Y, et al. Three-dimensional distribution of transverse collagen fibers in the anterior human corneal stroma. Invest Ophthalmol Vis Sci. 2013;54(12):7293-7301. Hanna KD, Jouve L, Waring G. Preliminary computer simulation of the effects of radial keratotomy. Arch Ophthalmol. 1989;107:911-918. Hanna KD, Jouve L, Waring G. Computer simulation of arcuate and radial incisions involving the corneoscleral limbus. Eye. 1989;3:227-229. Pinsky PM, Datye DV. Numerical modeling of radial, astigmatic, and hexagonal keratotomy. Refract Corneal Surg. 1992;8(2):164-172. Velinsky S, Bryant MR. On the computer-aided and optimal design keratorefractive surgery. Corneal Surg. 1992;8:173-82. Hanna KD, Jouve FE, Waring GO, Ciarlet PG. Computer simulation of arcuate keratotomy for astigmatism. Refract Corneal Surg. 1992;8(2):152-163. Pinsky PM, van der Heide D, Chernyak D. Computational modeling of mechanical anisotropy in the cornea and sclera. J Cataract Refract Surg. 2005;31(1):136-45.

259

18. Seven I, Dupps WJ. Patient-specific finite element simulations of standard incisional astigmatism surgery and a novel patterned collagen crosslinking approach to astigmatism treatment. J Med Device. 2013;7(4):0409131-409132. 19. Seven I, Sinha Roy A, Dupps WJ, Jr. Patterned corneal collagen crosslinking for astigmatism: computational modeling study. J Cataract Refract Surg. 2014;40(6):943-953. 20. Alastrué V. Biomechanical modeling of refractive corneal surgery. J Biomech Eng. 2005;128(1):150. 21. Lanchares E, Calvo B, Cristobal JA, Doblare M. Finite element simulation of arcuates for astigmatism correction. J Biomech. 2008;41(4):797-805. 22. Manganiello F, Pandolfi A, Fotia G. Numerical prediction of laser refractive corneal surgery. 2006. 23. Pandolfi A, Holzapfel GA. Three-dimensional modeling and computational analysis of the human cornea considering distributed collagen fibril orientations. J Biomech Eng. 2008;130(6):061006. 24. Sanchez P, Moutsouris K, Pandolfi A. Biomechanical and optical behavior of human corneas before and after photorefractive keratectomy. J Cataract Refract Surg. 2014;40(6):905-917. 25. Simonini I, Pandolfi A. Customized finite element modelling of the human cornea. PLoS One. 2015;10(6):e0130426. 26. Pallikaris IG, Kymionis GD, Astyrakakis NI. Corneal ectasia induced by laser in situ keratomileusis. J Cataract Refract Surg. 2001;27(11):1796-1802. 27. Potgieter FJ, Roberts C, Cox IG, et al. Prediction of flap response. J Cataract Refract Surg. 2005;31(1):106-114. 28. Krueger RR, Dupps WJ, Jr. Biomechanical effects of femtosecond and microkeratome-based flap creation: prospective contralateral examination of two patients. J Refract Surg. 2007;23(8):800-807. 29. Dupps WJ Jr., Roberts C. Effect of acute biomechanical changes on corneal curvature after photokeratectomy. J Refract Surg. 2001;17(6):658-669. 30. Deenadayalu C, Mobasher B, Rajan SD, Hall GW. Refractive change induced by the LASIK flap in a biomechanical finite element model. J Refract Surg. 2006;22(3):286-292. 31. Deenadayalu C, Mobasher B, Rajan DS, Hall GW. Refractive change induced by the LASIK flap in a biomechnaical finite element model. J Refract Surg. 2006;22:286-292. 32. Roy AS, Dupps WJ, Jr. Effects of altered corneal stiffness on native and postoperative LASIK corneal biomechanical behavior: A whole-eye finite element analysis. J Refract Surg. 2009;25(10):875-887. 33. Sinha Roy A, Rocha KM, Randleman JB, et al. Inverse computational analysis of in vivo corneal elastic modulus change after collagen crosslinking for keratoconus. Exp Eye Res. 2013;113:92-104. 34. Sinha Roy A, Dupps WJ Jr., Roberts CJ. Comparison of biomechanical effects of small-incision lenticule extraction and laser in situ keratomileusis: finite-element analysis. J Cataract Refract Surg. 2014;40(6):971-980. 35. Roy AS, Dupps WJ Jr. Patient-specific modeling of corneal refractive surgery outcomes and inverse estimation of elastic property changes. J Biomech Eng. 2011;133(1):011002.

Copyright © 2018. Kugler Publications. All rights reserved.

260 36. Seven I, Vahdati A, De Stefano VS, et al. Comparison of patient-specific computational modeling predictions and clinical outcomes of LASIK for myopia. Invest Ophthalmol Vis Sci. 2016;57(14):6287-6297. 37. Rabinowitz Y. Keratoconus. Surv Ophthalmol. 1998;42:297-319. 38. Andreassen TT, Simonsen AH, Oxlund H. Biomechanical properties of keratoconus and normal corneas. Exp Eye Res. 1980;31(4):435-441. 39. Nash IS, Greene PR, Foster CS. Comparison of mechanical properties of keratoconus and normal corneas. Exp Eye Res. 1982;35(5):413-424. 40. Dupps Jr WJ. Biomechanical modeling of corneal ectasia. J Cataract Refract Surg. 2005;21(2):186-90. 41. Pandolfi A, Manganiello F. A model for the human cornea: constitutive formulation and numerical analysis. Biomech Model Mechanobiol. 2006;5(4):237-246. 42. Gefen A, Shalom R, Elad D, Mandel Y. Biomechanical analysis of the keratoconic cornea. J Mech Behav Biomed Mater. 2009;2(3):224-236. 43. Carvalho LA, Prado M, Cunha RH, et al. Keratoconus prediction using a finite element model of the cornea with local biomechanical properties. Arq Bras Oftalmol. 2009;72(2):139-145. 44. Roy AS, Dupps WJ, Jr. Patient-specific computational modeling of keratoconus progression and differential responses to collagen cross-linking. Invest Ophthalmol Vis Sci. 2011;52(12):9174-9187. 45. Carvalho LA, Prado M, Cunha RH, et al. Keratoconus prediction using a finite element model of the cornea with local biomechanical properties. Arq Bras Oftalmol. 2009;72(2):139-45. 46. Wollensak G, Spoerl E, Seiler T. Riboflavin/ultraviolet-a– induced collagen crosslinking for the treatment of keratoconus. Am J Ophthalmol 2003;135(5):620-627. 47. Wollensak G, Spoerl E, Seiler T. Riboflavin/ultraviolet-a-induced collagen crosslinking for the treatment of keratoconus. Am J Ophthalmol. 2003;135(5):620-762. 48. Cherfan D, Verter EE, Melki S, et al. Collagen cross-linking using rose bengal and green light to increase corneal stiffness. Invest Ophthalmol Vis Sci. 2013;54(5):3426-3433. 49. Spoerl E, Huhle M, Seiler T. Induction of cross-links in corneal tissue. Exp Eye Res. 1998;66(1):97-103. 50. Wollensak G, Spoerl E, Seiler T. Stress-strain measurements of human and porcine corneas after riboflavin-ultraviolet-A-induced cross-linking. J Cataract Refract Surg. 2003;29(9):17801785. 51. Kling S, Remon L, Perez-Escudero A, et al. Corneal biomechanical changes after collagen cross-linking from porcine eye inflation experiments. Invest Ophthalmol Vis Sci. 2010;51(8):39613968.

I. Seven, V.S. De Stefano and W.J. Dupps Jr 52. Ford MR, Sinha Roy A, Rollins AM, Dupps WJ Jr. Serial biomechanical comparison of edematous, normal, and collagen crosslinked human donor corneas using optical coherence elastography. J Cataract Refract Surg. 2014;40(6):1041-1047. 53. Scarcelli G, Kling S, Quijano E, et al. Brillouin microscopy of collagen crosslinking: noncontact depth-dependent analysis of corneal elastic modulus. Invest Ophthalmol Vis Sci. 2013;54(2):1418-1425. 54. Sedaghat M, Naderi M, Zarei-Ghanavati M. Biomechanical parameters of the cornea after collagen crosslinking measured by waveform analysis. J Cataract Refract Surg. 2010;36(10):17281731. 55. Spoerl E, Terai N, Scholz F, et al. Detection of biomechanical changes after corneal cross-linking using Ocular Response Analyzer software. J Refract Surg. 2011;27(6):452-457. 56. Montes-Mico R, Munoz G, Albarran-Diego C, et al. Corneal aberrations after astigmatic keratotomy combined with laser in situ keratomileusis. J Cataract Refract Surg. 2004;30(7):1418-1424. 57. Kanellopoulos AJ, Dupps WJ, Seven I, Asimellis G. Toric topographically customized transepithelial, pulsed, very high-fluence, higher energy and higher riboflavin concentration collagen cross-linking in keratoconus. Case Rep Ophthalmol. 2014;5(2):172-180. 58. Elling M, Kersten-Gomez I, Dick HB. Photorefractive intrastromal corneal crosslinking for the treatment of myopic refractive errors: Six-month interim findings. J Cataract Refract Surg. 2017;43(6):789-795. 59. Lago MA, Rupérez MJ, Monserrat C, et al. Patient-specific simulation of the intrastromal ring segment implantation in corneas with keratoconus. J Mech Behav Biomed Mater. 2015;51:260268. 60. Kling S, Marcos S. Finite-element modeling of intrastromal ring segment implantation into a hyperelastic cornea. Invest Ophthalmol Vis Sci. 2013;54(1):881-889. 61. Studer HP, Pradhan KR, Reinstein DZ, et al. Biomechanical modeling of femtosecond laser keyhole endokeratophakia surgery. J Refract Surg. 2015;31(7):480-486. 62. Vahdati A, Seven I, Mysore N, Randleman JB, Dupps WJ. Computational biomechanical analysis of asymmetric ectasia risk in unilateral post-LASIK ectasia. J Refract Surg. 2016;32(12):811820. 63. Dupps WJ, Seven I. A large-scale computational analysis of corneal structural response and ectasia risk in myopic laser refractive surgery. Trans Am Ophthalmol Soc. 2016;114:T1.

18. Comparative biomechanics of intrastromal lenticule extraction and LASIK Dan Z. Reinstein1,2,3,4, Timothy J. Archer1, Ibrahim Seven5, Cynthia Roberts6, William J. Dupps Jr.5,7 London Vision Clinic, London, UK; 2Department of Ophthalmology, Columbia University Medical Center, New York, NY, USA; 3Centre Hospitalier National d’Ophtalmologie, Paris, France; 4Biomedical Science Research Institute, University of Ulster, Coleraine, Northern Ireland; 5Ocular Biomechanics & Imaging Lab, Cole Eye Institute, Cleveland Clinic, Cleveland, OH, USA; 6Department of Ophthalmology & Visual Science, and Biomedical Engineering; The Ohio State University, Columbus, OH, USA; 7Department of Biomedical Engineering, Lerner Research Institute, Cleveland Clinic, Cleveland, OH, USA 1

Copyright © 2018. Kugler Publications. All rights reserved.

1. History of intrastromal refractive surgery Ever since femtosecond lasers were first introduced into refractive surgery, the ultimate goal has been to create an intrastromal lenticule that can then be removed manually in one piece, thereby circumventing the need for incremental photoablation by an excimer laser. A precursor to modern refractive lenticule extraction (ReLEx) was first described in 1996 using a picosecond laser to generate an intrastromal lenticule that was removed manually after lifting the flap;1,2 however significant manual dissection was required, leading to an irregular surface. The switch to femtosecond improved the precision,3 and studies were performed in rabbit eyes in 19984 and in partially sighted eyes in 2003,5 however, these initial studies were not followed up with further clinical trials. Following the introduction of the VisuMax femtosecond laser (Carl Zeiss Meditec, Jena, Germany),6 the intrastromal lenticule method was reintroduced in a procedure called femtosecond lenticule extraction (FLEx). The six-month results of the first ten fully seeing eyes treated were first presented in 2006 and published in 2008,7 and results of a larger population have since been reported.8,9 The refractive results were similar to those observed in laser-assisted in situ keratomileusis

Fig. 1. Incision geometry of the SMILE procedure. The lenticule cut (1) is performed (the underside of the lenticule), followed by the lenticule sidecuts (2). Next, the cap interface (3) is created (the upper side of the lenticule), and finally a 2-3 mm small incision (4) is created super-temporally. The lenticule interfaces are dissected using a flap separator and the lenticule is extracted manually, all via the small incision.

Correspondence:Dan Z. Reinstein, MD, London Vision Clinic, 138 Harley Street, London W1G 7LA, UK. E-mail: [email protected] Biomechanics of the Eye, pp. 261-276 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

262

(LASIK), but visual recovery time was longer due to the lack of optimization in energy parameters and scan modes; further refinements have led to much improved visual recovery times.10 Following the successful implementation of FLEx, a new procedure called small incision lenticule extraction (SMILE) was developed. This procedure involves passing a dissector through a small 2-3 mm incision to separate the lenticular interfaces and allow the lenticule to be removed, as shown in Figure 1, thus eliminating the need to create a flap. The SMILE procedure is now gaining popularity following the results of the first prospective trials,11-13 and a growing number of other related studies are now being published.14-26

2. Potential biomechanical advantages of SMILE

Copyright © 2018. Kugler Publications. All rights reserved.

One of the potential benefits of the SMILE procedure is increased biomechanical stability compared to LASIK due to the absence of a flap. There are two main reasons for this: 1. vertical cuts (e.g., flap sidecut) have more biomechanical impact than horizontal cuts; and 2. anterior stromal lamellae are stronger than posterior stromal lamellae. 2.1. Vertical cuts have more biomechanical impact than horizontal cuts In 2000, we published a paper showing that the peripheral stroma actually thickens after LASIK, as shown in Figure 2.27 This biomechanical change seems to be an important cause for the majority of spherical aberration induction (probably about 85%) rather than the more commonly discussed reasons of laser fluence projection and reflection errors in the periphery due to the curvature of the cornea. In a study presented at ARVO in 2000, biomechanical and epithelial thickness changes were found to explain the majority of the refractive inaccuracy of LASIK.28 This is consistent with the later results of a contralateral eye study using a different laser used to perform LASIK in each eye, with matched optical zone sizes. Results showed a significant difference only in the induction of spherical aberration between eyes, with the larger transition zone, and thus, larger ablation zone, associated with lower

D.Z. Reinstein et al.

Fig. 2. Artemis very high-frequency digital ultrasound (ArcScan Inc.) stromal thickness maps before (left) and three months after (middle) LASIK for -9.00 D myopia using the MEL80 excimer laser with a 6 mm optical zone. The color scales are thickness in μm and a Cartesian grid is superimposed at 1 mm intervals for the 10 mm diameter. Scans were centered on the corneal vertex. The difference map (right) shows the change in stromal thickness (red/orange: stromal thinning; blue/green: stromal thickening) demonstrating the tissue removed by the ablation centrally with less tissue removal radially as expected for a myopic ablation. However, outside the 6 mm optical zone, the stroma was actually thicker after LASIK.

spherical aberration induction.29 The larger ablation zone reduced the size of the unablated periphery and resulted in less spherical aberration. The early findings also agreed with the results reported by Dupps and Roberts30 of peripheral stromal thickening outside the treatment zone after phototherapeutic keratectomy (PTK) in ex-vivo human donor globes, which correlated with induced central flattening. At the same time, Roberts also proposed a model to further explain the relationship between peripheral thickening and biomechanical central flattening.31 Briefly, the cornea is made of layers of collagen lamellae running from limbus to limbus oriented at precise angles with respect to adjacent lamellae, contributing to corneal transparency and strength. Stromal collagen lamellae are surrounded by several proteoglycans responsible for proper spacing of collagen and stromal hydration. The creation of a flap and stromal tissue ablation severs the anterior corneal lamellae, which means that the peripheral anterior lamellae are no longer under tension and therefore relax, resulting in redistribution of water content with stromal thickening and increased water content in the periphery. The consequence of this expansion of peripheral anterior lamellae is to exert a pulling force on the posterior lamellae, which causes central flattening. However, the posterior lamellae also have to contend with an unchanged intraocular pressure (IOP), which can result in shape changes over time due to the redistribution of forces. Recently, Knox Cartwright et al.32 performed a study

Comparative biomechanics of intrastromal lenticule extraction and LASIK

263

Table 1. Percentage increase in central corneal strain (to an IOP change from 15 mmHg to 15.5 mmHg) after the creation of a LASIK flap, a sidecut, or delamination at both 90 μm and 160 μm.32

90 μm

160 μm

LASIK flap

9%

32%

Sidecut only

9%

33%

Delamination only

5%

5%

Copyright © 2018. Kugler Publications. All rights reserved.

on human cadaver eyes that compared the corneal strain produced by a LASIK flap, a sidecut only, and a delamination cut only, with each incision type performed at both 90 μm and 160 μm. Table 1 summarizes the results, which found that the increase in strain was equivalent between a LASIK flap and a sidecut alone at both depths, with a significantly greater increase for the 160 μm depth. In contrast, the increase in strain after only a delamination cut was significantly lower than after only a LASIK flap or sidecut. Also, the strain did not increase when only a delamination cut was performed at the greater 160 μm depth. A similar result has also been found in a study by Medeiros et al.,33 who showed in pig eyes that there were significantly greater biomechanical changes following the creation of a thick flap of 300 μm compared to a thin flap of 100 μm. Applying this finding to SMILE, since only a small anterior corneal sidecut is created, it is predicted that there will be slightly less increase in corneal strain in SMILE compared to thin-flap LASIK, and a significant difference in corneal strain compared to LASIK with a thicker flap because these procedures involve vertical sidecuts of a much larger area and/or depth. 2.2. Anterior stromal lamellae are stronger than posterior stromal lamellae Randleman et al.34 demonstrated that the cohesive tensile strength (i.e., how strongly the stromal lamellae are held together) of the stroma decreases from anterior to posterior within the central corneal region (Fig. 3). In an experiment in which the cohesive tensile strength was measured for strips of stromal lamellae cut from different depths within donor corneoscleral buttons, a strong negative correlation was found between stromal depth and cohesive tensile strength. The anterior 40% of the central corneal stroma was found to be the strongest region of the cornea, whereas the posterior 60% of the stroma was at least 50% weaker. A number

Fig. 3. Scatter plot of the percentage of maximum cohesive tensile strength against the percentage of residual stromal depth using data from the study by Randleman et al.34 Regression analysis found that a fourth order polynomial provided the closest fit to the data and the R2 of 0.93 demonstrated the high correlation achieved. 51

of other authors have reached similar conclusions by other indirect means.35-40 In addition to cohesive tensile strength, tangential tensile strength (i.e., stiffness along the stromal lamellae) and shear strength (i.e., resistance to torsional forces) have both been found to vary with depth in the stroma. Kohlhaas et al.41 and Scarcelli et al.42 found that the tangential tensile strength and Brillouin-derived elasticity, respectively, were greater for anterior stroma than posterior stroma, each using different methodologies. Petsche et al.43 found a similar result for decreasing transverse shear strength with stromal depth. An interesting finding of these studies is the non-linear nature of the change in tensile strength through the stroma. The cohesive tensile strength appears to decrease rapidly for the anterior-most 30%.34 There is then a region between 70% and 20% depth where the cohesive tensile strength decreases slowly, but then drops off sharply again for the posterior-most 20%. This non-linearity may be associated with the known different collagen organizational layers within the stroma, in which there is greater interconnectivity of stromal collagen in the anterior ­stroma.37,44-46 Of note is the remarkable similarity of this curve to that reported by Scarcelli et al.42 (Fig. 4), which demonstrates the strong correlation between corneal biomechanical

264

D.Z. Reinstein et al.

strength rather than simply in terms of residual stromal thickness. For example, a rough adjustment would be to say that anterior stroma is approximately 50% stronger than posterior stroma, so a further 50% of the untouched anterior stromal thickness in SMILE can be added to get an adjusted total uncut stromal thickness value that can be compared to a LASIK residual stromal bed thickness. In reality, we can go further than this by basing the calculation on the real stromal tensile strength data.

Fig. 4. Tangential tensile strength (longitudinal modulus of elasticity) measured by Brillouin microscopy at different depths in a (bovine) cornea including the epithelium (I), anterior stroma (II), posterior stroma (III), and the innermost region near the endothelium (IV).42

Copyright © 2018. Kugler Publications. All rights reserved.

properties and stromal depth. This finding also agrees with studies that have found other depth-dependent properties of the corneal stroma such as decreasing refractive index,47 greater UVB absorption in the anterior stroma,48 and varying excimer laser ablation rates.49,50 2.3. Paradigm shift in residual stromal thickness calculation Surgeons are accustomed to calculating the residual stromal thickness in LASIK as the amount of stromal tissue left under the flap, so the first instinct is to apply this rule to SMILE. However, the actual residual stromal thickness in SMILE should be calculated as the stromal thickness below the posterior lenticule interface plus the stromal thickness between the anterior lenticule interface and Bowman’s layer, since the anterior stromal lamellae integrity is effectively maintained. Therefore, the first change to be considered is the total uncut stromal thickness in SMILE as opposed to the LASIK residual stromal bed thickness. However, given that SMILE effectively leaves anterior corneal stroma intact while the keratomileusis takes place in the deeper and therefore weaker portion of the cornea (as described above), it is reasonable to assume that, for any given refractive correction, SMILE will leave the cornea with greater tensile strength than either LASIK or PRK. To take this into account, it is important to start thinking more in terms of tensile

2.4. Biomechanics model: comparing SMILE to PRK and LASIK A mathematical model was recently developed, based directly on the Randleman34 depth-dependent tensile strength data to calculate the postoperative tensile strength, allowing for comparison between between PRK, LASIK and SMILE.51 Given the similarity between different studies measuring the different types of tensile strength as described above, the assumption was made that cohesive tensile strength is representative of the overall corneal biomechanics. It is suggested that this total tensile strength (TTS) value should replace residual stromal thickness as the limiting factor for corneal refractive surgery. To derive the model, a non-linear regression analysis was first performed on the Randleman34 data, and it was determined that a fourth order curve maximized the fit to the data with R2 = 0.930, demonstrating the very high correlation achieved by a non-linear fit. The TTS of the untreated cornea was then calculated as the area under the regression line by integration (Fig. 5). The TTS of the cornea after LASIK was derived by calculating the area under the regression line for all depths below the residual stromal bed thickness (assuming the flap does not contribute to the tensile strength of the postoperative cornea).52 This value was divided by the TTS of the untreated cornea to represent the relative postoperative total tensile strength (PTTS) as a percentage. Similarly, the TTS of the cornea after PRK was derived by calculating the area under the regression line for all depths below the stromal thickness after ablation. Finally, the TTS of the cornea after SMILE was calculated as the area under the regression line for all depths below the lower lenticule interface added to the area under the regression line for all depths above the upper lenticule interface or within the stromal cap. This

Comparative biomechanics of intrastromal lenticule extraction and LASIK

265

Copyright © 2018. Kugler Publications. All rights reserved.

assumes that the keyhole incision made in SMILE does not reduce the tensile strength of the anterior region within the stromal cap. This is a reasonable assumption since the sidecut is small in length and the many intact lamellae surrounding this incision effectively maintain the integrity of the anterior cornea. The model was then applied to a variety of different scenarios and a number of conclusions could be drawn from the analyses: 1. The PTTS was greater after SMILE than after PRK: In SMILE, the refractive stromal tissue removal takes place in deeper and relatively weaker stroma, leaving the stronger anterior stroma effectively intact, meaning that for any given refractive correction, SMILE will leave the cornea with greater tensile strength than PRK. 2. The PTTS was greater after SMILE than after LASIK: Given that the anterior stroma is left effectively intact, SMILE will — by definition — leave the cornea with greater tensile strength than LASIK for any given refractive correction. 3. The PTTS increased for SMILE with increasing cap thickness (Fig. 6): If SMILE is performed deeper in the cornea, more of the stronger anterior stroma will remain, and hence, the PTTS will be greater;

Fig. 5. The fourth order polynomial regression equation was integrated to calculate the area under the curve for the relevant stromal depths after PRK, LASIK, and SMILE, as demonstrated by the green shaded regions. The red areas represent the tissue removed (excimer laser ablation/lenticule extraction) and the purple area in LASIK represents the LASIK flap. 51

Fig. 6. Scatter plot of the relative TTS after LASIK (purple) and SMILE (green) plotted against a range of flap/cap thicknesses for a fixed central corneal thickness of 550 μm and ablation depth/ lenticule thickness of 100 μm (approximately -7.75 D). In LASIK, the postoperative relative TTS decreased for greater flap thickness by 0.22%/μm. In SMILE, the postoperative relative TTS increased for greater cap thickness by 0.08%/μm. 51

266

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 7. Scatter plot comparing TTS for a fixed ablation with varying corneal thicknesses after LASIK (purple), PRK (blue), and SMILE (green) against a range of central corneal thickness for a fixed ablation depth/lenticule thickness of 100 μm (approximately -7.75 D), a LASIK flap thickness of 110 μm, and a SMILE cap thickness of 130 μm. The relative PTTS was greatest after SMILE, followed by PRK, and was lowest after LASIK. 51

this is in contrast to LASIK, where a thicker flap results in lower PTTS given the minimal contribution of the flap to corneal biomechanics after healing. 4. The PTTS decreased for thinner corneas, but the difference between procedures also increased for thinner corneas (Fig. 7): For example, in LASIK, flap stroma plus ablation within the stronger anterior stroma would comprise a greater percentage loss of TTS than lenticular removal from relatively weaker stromal tissue deeper within the stroma while leaving stronger anterior stroma uncut. These results can be quantified in the example scenario represented in Figure 8, which shows the relative PTTS after LASIK (purple), photorefractive keratectomy (PRK) (blue), and SMILE (green) plotted against a range of ablation depths for a fixed central corneal thickness of 550 μm, a LASIK flap thickness of 110 μm, and a SMILE cap thickness of 130 μm. The orange lines indicate that the relative PTTS reached 60% for an ablation depth of 73 μm in LASIK (approximately -5.75 diopters (D)), 132 μm in PRK (approximately -10.00 D), and 175 μm in SMILE (approximately -13.50 D), translating to a 7.75 D difference between LASIK and SMILE for a cornea of

D.Z. Reinstein et al.

Fig. 8. This graph shows the relative TTS after LASIK (purple), PRK (blue), and SMILE (green) plotted against a range of ablation depths for a fixed central corneal thickness of 550 μm, a LASIK flap thickness of 110 μm, and a SMILE cap thickness of 130 μm. The orange lines indicate that the relative PTTS reached 60% for an ablation depth of 73 μm in LASIK (approximately -5.75 D), 132 μm in PRK (approximately -10.00 D), and 175 μm in SMILE (approximately -13.50 D), translating to a 7.75 D difference between LASIK and SMILE for a cornea of the same relative PTTS. The red lines indicate that the relative PTTS after a 100 μm tissue removal would be 54% in LASIK, 68% in PRK, and 75% in SMILE. 51

the same relative PTTS. The red lines indicate that the relative PTTS after a 100 μm tissue removal would be 54% in LASIK, 68% in PRK, and 75% in SMILE. The conclusion that deeper is better in SMILE also brings an associated advantage of potentially further reducing the impact on dry eye as even more of the anterior corneal anatomy is preserved, hence further reducing the disruption of the anterior stromal nerve plexus. A number of studies have demonstrated the reduction in dry eye after SMILE according to a significantly smaller reduction and faster recovery of corneal sensation.16-22 In this model, there are some factors that have not been considered. Firstly, this model only considers the central point on the cornea. A full model of the cornea, e.g., by finite element analysis, that can take into account the stromal thickness progression and the volume of the ablation profile would be a significant improvement, but is likely to provide the same data qualitatively, albeit perhaps more accurately in terms of absolute tensile strength changes. In the analytic model, the assumption was made that

Copyright © 2018. Kugler Publications. All rights reserved.

Comparative biomechanics of intrastromal lenticule extraction and LASIK

the stromal lamellae in the LASIK flap do not contribute to the TTS of the cornea at all, an assumption that is supported by published studies demonstrating negligible contribution. Schmack et al.52 found that the mean tensile strength of the central and paracentral LASIK wounds was only 2.4% than that measured in control eyes. As described earlier, Knox Cartwright et al.32 experimentally demonstrated a LASIK flap depth-dependent increase in corneal strain, reporting an increase in strain of 9% for a 110 μm flap and 33% for a 160 μm flap. This result is predicted by the analytic model that showed the remaining relative TTS would be less for thicker flaps, as would be expected. Another factor not considered is that Bowman’s layer remains intact after SMILE, which is not true in either LASIK or PRK. Bowman’s layer has been shown to have very different biomechanical properties to stromal tissue as demonstrated by Seiler et al.,53 who showed that removing Bowman’s layer with an excimer laser reduced the Young’s modulus by 4.75%. Leaving Bowman’s layer intact may further increase the corneal biomechanical stability after SMILE compared with LASIK and PRK. Finally, the present model in addition does not consider the effect of the tunnel-incision on tensile strength changes which, although small, will not be zero. It is important to point out that while SMILE has a benefit associated with corneal biomechanics, the procedure does still reduce the overall tensile strength of the cornea; the advantage is that this reduction is less than in LASIK and PRK. Following the publication of cases of ectasia54-57 after SMILE in eyes with forme fruste keratoconus (FFKC), it has become apparent that this distinction needs to be stressed; keratoconus (KC) is and always has been a relative contraindication to tissue subtractive procedures which should be only carried out in certain special circumstances with concomitant crosslinking and proper informed consent. The distribution of properties with depth in KC has been shown to be abnormal, and therefore, the tensile strength analysis no longer applies.58 In summary, considering the safety of subtractive corneal refractive surgical procedures in terms of tensile strength represents a paradigm shift away from classical residual stromal thickness limits. The residual thickness based safety of corneal laser refractive surgery should be thought of at least in terms of total

267

residual uncut stroma. Ideally, a parameter such as TTS, which takes the non-linearity of the strength of the stroma into account, may be more appropriate. For example, the residual stromal bed thickness under the interface in SMILE could easily be less than 250 μm due to the additional strength provided by the untouched stromal lamellae in the cap, as long as the total remaining corneal tensile strength is comparable to that of the post-LASIK 250 μm residual stromal bed thickness standard. In this new case of using remaining TTS, the minimum would evidently be defined as the TTS remaining after LASIK with a residual stromal bed thickness of 250 μm. 2.5. Computational modeling studies Computational models that are representative of physiologic material behaviors can be helpful in understanding surgical corneal biomechanical responses. Finite element analysis (FEA) has been used to investigate the claimed biomechanical advantage of SMILE over LASIK using patient-specific parameters. An initial study on this topic employed a 3-D corneoscleral model59 to compare several permutations of LASIK and SMILE surgeries in one eye. The small incision in SMILE was modelled with a 25° arc width, producing a proportionate reduction of the fibril stiffness within the cap and compared to the wider arc width of an analogous LASIK flap. Three and 9 D spherical myopic SMILE and LASIK corrections were performed in silico, and each procedure was simulated using both 100 µm and 300 µm cap/flap thickness for each magnitude of myopic correction. A reference model with the same postoperative geometry but unaltered material properties was used as a reference for comparing model-derived mechanical stresses (von-Mises stress) after each simulation. All myopic treatments increased residual stromal bed (RSB) stresses, and these stresses increased more with higher attempted corrections and thicker caps/flaps. In comparison to SMILE, LASIK induced higher stresses, and this difference also increased as the degree of myopic correction and the flap/cap thickness increased. SMILE simulations produced much closer stresses to the reference model that assumed no material weakening (Fig. 9). By leveraging a comprehensive 3-D structural modeling approach and expressing biomechanical impact in terms of traditional engineering stresses, this study

268

D.Z. Reinstein et al.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 9. Comparison of von-Mises stresses (in Pascals) from computational models in the corneal flap/cap region and residual stromal bed simulating a 9 D myopic correction and 100-mm flap/cap for LASIK, SMILE, and a reference postoperative geometry with no material weakening. Stress remained concentrated in the anterior corneal regions after SMILE and RSB stresses increased less with SMILE than with LASIK. The stress distribution after SMILE most closely resembled the stresses in the reference (materially unaltered) model. 59

provided an important quantitative demonstration of the potential biomechanical advantages of SMILE over comparable LASIK procedures. Following this study, a clinical modeling study involving ten eyes of five patients that received contralateral flap-based FLEx (mechanically analogous to LASIK) and flap-less SMILE were investigated using an inverse FEA approach.60 Inverse FEA begins with a similar microstructurally motivated finite element model, taking the preoperative and postoperative geometries as well as the surgical parameters as inputs, and iteratively computes the material property change required to produce the transition from preoperative to postoperative geometry. This approach yields an indirect but empirically driven measurement of the mechanical impact of the simulated procedure. The biomechanical assumptions for SMILE remained the same as the earlier study. The procedures were simulated using the eye-specific corneal geometry from clinical tomography and case-specific treatment parameters. For each patient, preoperative material constants were obtained through inverse FE analyses, and the surgically induced change in fiber stiffness

within each flap or cap was determined by minimization of the error between the simulated and actual six-month topographic outcomes. The mean pairwise reduction in effective stromal collagen fiber stiffness was 49% greater (range 2-87%) for flap-based FLEx than for SMILE. While this study demonstrated the same findings of lower RSB stresses and deformations in SMILE cases than in flap-based cases, it also highlighted important eye-to-eye variations in the magnitude of this differential impact. Displacements and stresses were also more affected by a simulated increase in IOP from 15 mmHg to 30 mmHg in FLEx than SMILE eyes. This provocative IOP inflation demonstrating a greater mechanical sensitivity to higher load scenarios after flap-based surgeries is a potentially important factor in ectasia risk, particularly in the context of the much higher IOP elevations associated with eye rubbing.61 Although the modeling studies described heretofore support the argument for a biomechanical advantage with SMILE over LASIK, these studies have not gone so far as to directly predict ectasia risk. The potential utility of model-derived mechanical strain as a predictor of ectasia was first put forth in a modeling report investi-

Copyright © 2018. Kugler Publications. All rights reserved.

Comparative biomechanics of intrastromal lenticule extraction and LASIK

269

Fig. 10. Structural risk score based on computational model-derived maximum principal strain across the anterior stroma at pre-op, post-SMILE simulation (left panel), and post-LASIK simulation (right panel) for a previously reported post-SMILE ectasia case. Note the high intrinsic preoperative risk indicated on the lower color scale, which is referenced to a library of strain data from eyes spanning the continuum of ectasia risk. Surgically induced strain is an incremental increase from the preoperative loading state expressed as a percent change, which was higher for a hypothetical LASIK procedure than for SMILE. Color strain maps illustrate strain profiles, and the ‘x’ indicates the location of maximum strain.

270

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 11. Ex-vivo data from Brillouin microscopy of normal and keratoconic corneal tissue demonstrating a preferential reduction in anterior stromal elastic properties in KC. 58

gating strain differences in the eyes of a bilateral LASIK patient who developed ectasia in only one eye, notably, in the absence of other discernibly asymmetric risk factors.62 The eye that developed ectasia demonstrated higher maximum principal strains and von Mises stresses, both pre-LASIK and post-LASIK, in tomography-driven case-specific FEA simulations. This study was followed by a large-scale computational analysis63 of 40 eyes with different degrees of clinical ectasia risk, listed in order from low risk negative controls to high risk positive controls: normal pre-LASIK subjects; eyes with atypical but non-keratoconic topography; subjects disqualified for LASIK but not diagnosed with KC; and manifest KC eyes. The study compared several candidate susceptibility metrics and resolved those that had the strongest predictive value for clinical risk category. The highest performing metrics included the regionally averaged maximum principal strain across the anterior RSB and the local strain maximum. These strain metrics were significantly higher in eyes with confirmed ectatic predisposition in pre-operative models and after simulations of PRK and LASIK in all eyes. This study generated a preliminary reference database for retrospective and prospective risk assessment studies using model-based strain, and the Cleveland Clinic authors have incorporated this into a computational risk analysis tool that is being developed for commercial translation (SpecifEye™, OptoQuest Inc., Cleveland OH, USA). We have had an opportunity to model some previously reported post-SMILE ectasia

D.Z. Reinstein et al.

Fig. 12. Scatter plot showing the change in spherical aberration (OSA notation) plotted against the spherical equivalent refraction treated by SMILE in a 6, 6.5, and 7 mm optical zone.

cases, including a bilateral case of a patient with manifest KC who was refused LASIK by one surgeon and was subsequently treated with SMILE by another.54 The clinically programmed SMILE procedure and a hypothetical LASIK procedure with same flap and refractive correction were simulated, and while simulated SMILE induced a 14% increase in strain, LASIK induced a 17% increase (Fig. 10). However, based on the susceptibility grade generated by referencing the database from previous large-scale analysis,63 the intrinsic ectasia susceptibility of the eye was already high (Fig. 10). This case makes the important point that ectasia is possible without any surgery at all, for example, in KC. Some degree of risk is intrinsic to the cornea, and surgery merely adds incrementally to this risk. The incremental biomechanical benefit of SMILE over LASIK illustrated in Figure 10 was not enough to overcome the cornea’s high baseline risk for ectasia. A critically important factor related to ectasia in the setting of SMILE is the peculiar depth-dependence of corneal biomechanical properties in predisposed or pre-keratoconic eyes. Some microstructural abnormalities such as loss of transverse bridging fibers in KC are concentrated at the level of Bowman’s layer, where absence of normal fibrillar interweaving44,64,65 is likely to produce localized weakness that preferentially reduces anterior stromal biomechanical integrity. Ex-vivo data from Brillouin microscopy of normal and keratoconic corneal tissue confirms a preferential reduction in anterior stromal elastic properties in

Comparative biomechanics of intrastromal lenticule extraction and LASIK

Fig. 13. PTTS (as calculated by a previously published model)51 plotted against maximum myopic meridian treated for a routine clinical population of SMILE cases and a population of LASIK cases matched for sphere, cylinder, and pachymetry. Despite a larger optical zone used in the SMILE group, the PTTS was still 16% greater on average than in the LASIK group.

Copyright © 2018. Kugler Publications. All rights reserved.

KC (Fig. 11).58 While SMILE has potential advantages in normal eyes where the anterior stroma is notably stronger than the more posterior stroma, if preferential anterior weakness exists that has not yet manifested in clinically discernible topographic changes, this relative advantage would be reduced while structural dependence on the stroma posterior to Bowman’s layer would increase. In cases involving corneas with significantly compromised anterior stromal properties, PRK could indeed have certain advantages over both SMILE and LASIK by ablating primarily the anterior zone of relative weakness. In view of these considerations, the capability for depth-dependent corneal property assessment in individual eyes is a critically important area of research in support of the goal of more personalized risk assessment. Until then, it is important to treat at-risk corneas as high-risk even in the setting of SMILE.

3. Evidence for biomechanical advantages of SMILE As described earlier, spherical aberration induction is largely due to peripheral stromal expansion outside the ablation zone. Peripheral stromal expansion is caused by relaxation of severed stromal collagen lamellae, so it would be expected to find less stromal expansion after SMILE as fewer lamellae are cut, and hence it would be

271

Fig. 14. Change in spherical aberration (OSA notation) plotted against maximum myopic meridian treated for a routine clinical population of SMILE cases and a population of LASIK cases matched for sphere, cylinder, and pachymetry. The greater PTTS after SMILE enabled the use of a larger optical zone in the SMILE group, and consequently, a lower induction of spherical aberration and therefore better optical quality than in the LASIK group.

expected for less spherical aberration to be induced. In a recent study,66 the induction of spherical aberration between SMILE, where the refractive lenticule is only minimally aspheric, was compared to LASIK using the MEL80 with the Laser Blended Vision (LBV) module,67 which uses a non-linear aspherically optimized ablation profile. The LASIK group was matched by refraction to within ±0.25 D and all eyes were treated with a 6 mm optical zone in both groups. Corneal spherical aberration (Atlas) was analyzed across the 3-7 mm diameter, and no difference was found between the two groups. Therefore, though minimally aspheric, SMILE produced similar spherical aberration induction to the highly aspherically optimized myopic LBV profile. This indicates that the femtosecond flapless procedure leads to less induction of spherical aberration than expected for a non-aspheric conventional excimer myopic profile. Following this study, the induction of spherical aberration after SMILE for optical zones of 6, 6.5, and 7 mm was investigated. The induced spherical aberration decreased as expected for larger SMILE optical zones; the regression line slope was 0.081 for 6 mm, 0.059 for 6.5 mm, and 0.030 for 7 mm (Fig. 12). Another factor to be considered is the ablation depth. Due to the aspheric optimization of the LBV ablation profiles, the ablation depth is greater than the SMILE lenticule thickness for the same optical zone; a

Copyright © 2018. Kugler Publications. All rights reserved.

272

6 mm LBV ablation is equivalent to a 6.25 mm SMILE lenticule in terms of stromal tissue removal. Therefore, since we know that spherical aberration induction decreases for larger optical zones, spherical aberration induction after SMILE is significantly less than LASIK for an equivalent stromal tissue removal. Finally, it is important to also consider the biomechanical difference between the two procedures, as described earlier. According to the model, the difference in tensile strength is enough that the cornea is still significantly stronger after SMILE than LASIK, even when a much larger optical zone is used in SMILE (i.e., greater tissue removal). Further increasing the optical zone enables less spherical aberration induction, and therefore, better optical quality can be achieved while still leaving the cornea stronger than in LASIK. To demonstrate this, the model was retrospectively applied to a SMILE case series (n = 96) and the PTTS was compared to a control group of LASIK eyes matched for refraction (±0.25 D) and pachymetry (±20 μm).68 Optical zone was not part of the matching criteria, so that the populations represented routine clinical use of the two procedures. Mean optical zone was 6.70 ± 0.39 mm (range: 5.90 to 7.00 mm) for the SMILE group and 6.08 ± 0.22 mm (range: 5.75 to 7.00 mm) for the LASIK group. Mean lenticule thickness was 107 ± 19 μm (range: 72 to 149 μm) for the SMILE group, and mean ablation depth was 87 ± 25 μm (range: 25 to 134 μm) for the LASIK group. Mean SMILE cap thickness was 130 μm (range: 120 to 140 μm). Mean LASIK flap thickness was 96 μm (range: 80 to 120 μm). Mean spherical equivalent refraction was -4.83 ± 1.59 D (range: up to -8.00 D) for both groups. Mean central corneal pachymetry was 539 ± 30 μm (range: 468 to 591 μm) for the SMILE group and 545 ± 36 μm (range: 469 to 626 μm) for the LASIK group. Figure 13 shows the PTTS calculated for all eyes using our model. Mean PTTS was 73% (range: 65 to 82%) for the SMILE group and 57% (range: 45 to 72%) for the LASIK group. Figure 14 shows the corneal spherical aberration induction (Atlas) for a 6 mm analysis zone for both groups. Mean change in spherical aberration (OSA notation) was 0.11 ± 0.16 μm (range: -0.19 to 0.51 μm) for the SMILE group and 0.31 ± 0.12 μm (range: -0.11 to 0.66 μm) for the LASIK group.

D.Z. Reinstein et al.

4. Evidence for other biomechanical changes after SMILE Using the Artemis very high-frequency (VHF) digital digital ultrasound scanner (ArcScan Inc., Morrison, CO, USA), the accuracy of cap thickness and lenticule thickness achieved in SMILE have been measured. In a study including 70 eyes of 37 patients,14 the mean central cap thickness accuracy was found to be -0.7 μm (range: -11 to +14 μm) for intended cap thicknesses over the range of 80 to 140 μm (i.e., the cap was on average 0.7 μm thinner than the intended cap thickness). The reproducibility of central cap thickness was found to be 4.4 μm.14 In a second study in the same population,15 the readout central lenticule depth was 8.2 μm thicker on average than the Artemis measured stromal thickness change. The systematic difference of 8 μm could be due to one of three reasons, or a combination of these: 1. an error in the VisuMax cutting accuracy for one of the two layers; 2. error with the stromal change measurement by Artemis VHF digital ultrasound; or 3. evidence for a biomechanical change in the stroma. For there to be an error in the lenticule thickness due to VisuMax cutting accuracy, there would have to be an error only in one of the interfaces. However, as described earlier, the cap thickness was accurate with a central accuracy of -0.7 μm.14 Therefore, if the lenticule thickness difference was due to the VisuMax cutting accuracy, the error must have been in the lower interface of the lenticule. However, the accuracy of cap thickness was found to be similar for cap thicknesses between 80 and 140 μm,14 which provides evidence that the accuracy of the VisuMax does not vary with depth (although this needs to be confirmed for depths at which the lower interface of the lenticule is created). As with any measurement, there are always associated measurement errors. In this study, Artemis VHF digital ultrasound measurements of stromal thickness were made before and at least three months after surgery. This method eliminates the error induced by epithelial thickness changes that would be included with any full corneal thickness change method.14,69 The Artemis also has a very high repeatability for corneal (1.68 μm) and stromal (1.78 μm) thickness measure-

Copyright © 2018. Kugler Publications. All rights reserved.

Comparative biomechanics of intrastromal lenticule extraction and LASIK

ments, so this source of error was minimized.70 In any event, errors such as these would be randomly distributed and would be likely to average out rather than result in a systematic error. Another source of error is the alignment between the two scans. In contrast to the other sources of measurement error, alignment error could be expected to be more likely to occur in one direction. As the corneal pachymetry is thinnest centrally and radially thicker toward the periphery, the lenticule is centered close to the thinnest point on the cornea in most cases unless the pachymetry is significantly decentered from the corneal vertex. Therefore, any misalignment in the postoperative scan will mean that the thinnest point of the postoperative scan will not be aligned with the thinnest point of the preoperative scan. This means that, in the majority of cases, an alignment error will tend to underestimate the change in stromal thickness, as was observed in this population. However, it is unlikely that these alignment errors could explain a systematic difference of 8 μm because the pachymetric progression of the central stroma is relatively gradual.71 Therefore, the present study seems to provide evidence for some central stromal expansion caused by biomechanical changes occurring after SMILE. One possible mechanism could be that the lamellae severed by the lenticule in between the residual bed and the cap might be recoiling and causing expansion of the stroma as they are no longer under tension, similar to the known peripheral stromal expansion after LASIK.27,31 This expansion might be keeping the bottom lamellae of the cap slightly apart from the top lamellae of the residual bed. It seems unlikely that there would be any reason for the stroma in the residual bed or the cap to be expanding, as they are still under tension. For example, the high accuracy of cap thickness that we have previously reported14 provides evidence for biomechanical stability within the cap. It is almost inevitable that there will be biomechanical changes after any corneal surgical procedure, so it is not surprising that there was a difference between the theoretical and achieved lenticule thickness. The fact that the difference was only 8 μm, a proportion of which can be explained by measurement error, implies that there is actually very little biomechanical change after SMILE compared to LASIK, as might be expected given that the strongest anterior stroma34 and Bowman’s

273

layer53 remain intact. This was also borne out in the results of the study, as there was a lower degree of scatter in the SMILE data compared with a similar LASIK population,69 indicating that there may have been a less variable biomechanical response after SMILE.

5. Summary The evolution of SMILE, a flapless intrastromal keyhole keratomileusis procedure, has introduced a new method for corneal refractive surgery that minimizes the change in corneal biomechanics, compared to PRK and LASIK, by leaving the stronger anterior stroma intact. Despite SMILE lenticule profiles being essentially spherical, induction of spherical aberration in SMILE was lower than aspheric LASIK for equivalent or greater tissue removal. In preserving stronger anterior stromal lamellae, SMILE optical zones can be safely increased to improve spherical aberration control while still leaving postoperative relative corneal tensile strength higher than for an equivalent modern aspheric LASIK procedure.

Acknowledgements Financial disclosure: Dr. Reinstein is a consultant for Carl Zeiss Meditec, has a proprietary interest in the Artemis technology (ArcScan Inc., Morrison, Colorado), and is an author of patents related to VHF digital ultrasound administered by the Cornell Center for Technology Enterprise and Commercialization (CCTEC), Ithaca, New York. Dr. Dupps has authored patents on computational modeling that are held by Cleveland Clinic Innovations and licensed to OptoQuest Inc, Cleveland, Ohio. Dr. Dupps has also received research funding from Zeiss, NIH (R01 EY022381), and an Ohio Third Frontier Commission Innovation Platform Award (TECH-013). Dr. Roberts is a consultant for Oculus Optikgeräte GmbH, Ziemer Ophthalmic Systems AG, and Opitimeyes. She has also received research funding from Carl Zeiss Meditec. The remaining authors have no proprietary or financial interest in the materials presented herein.

D.Z. Reinstein et al.

274

References 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Copyright © 2018. Kugler Publications. All rights reserved.

11.

12.

13.

14.

Ito M, Quantock AJ, Malhan S, Schanzlin DJ, Krueger RR. Picosecond laser in situ keratomileusis with a 1053-nm Nd:YLF laser. J Refract Surg. 1996;12:721-728. Krueger RR, Juhasz T, Gualano A, Marchi V. The picosecond laser for nonmechanical laser in situ keratomileusis. J Refract Surg. 1998;14:467-469. Kurtz RM, Horvath C, Liu HH, Krueger RR, Juhasz T. Lamellar refractive surgery with scanned intrastromal picosecond and femtosecond laser pulses in animal eyes. J Refract Surg. 1998;14:541-548. Heisterkamp A, Mamom T, Kermani O, et al. Intrastromal refractive surgery with ultrashort laser pulses: in vivo study on the rabbit eye. Graefes Arch Clin Exp Ophthalmol. 2003;241:511517. Ratkay-Traub I, Ferincz IE, Juhasz T, Kurtz RM, Krueger RR. First clinical results with the femtosecond neodynium-glass laser in refractive surgery. J Refract Surg. 2003;19:94-103. Reinstein DZ, Archer TJ, Gobbe M, Johnson N. Accuracy and reproducibility of artemis central flap thickness and visual outcomes of LASIK with the Carl Zeiss Meditec VisuMax Femtosecond Laser and MEL 80 Excimer Laser Platforms. J Refract Surg. 2010;26:107-119. Sekundo W, Kunert K, Russmann C, Gille A, Bissmann W, Stobrawa G, Sticker M, Bischoff M, Blum M. First efficacy and safety study of femtosecond lenticule extraction for the correction of myopia: six-month results. J Cataract Refract Surg. 2008;34:1513-1520. Blum M, Kunert KS, Engelbrecht C, Dawczynski J, Sekundo W. [Femtosecond lenticule extraction (FLEx) - Results after 12 months in myopic astigmatism]. Klin Monbl Augenheilkd. 2010;227:961-965. Vestergaard A, Ivarsen A, Asp S, Hjortdal JO. Femtosecond (FS) laser vision correction procedure for moderate to high myopia: a prospective study of ReLEx(®) flex and comparison with a retrospective study of FS-laser in situ keratomileusis. Acta Ophthalmol. 2012. Shah R, Shah S. Effect of scanning patterns on the results of femtosecond laser lenticule extraction refractive surgery. J Cataract Refract Surg. 2011;37:1636-1647. Sekundo W, Kunert KS, Blum M. Small incision corneal refractive surgery using the Small Incision Lenticule Extraction (SMILE) procedure for the correction of myopia and myopic astigmatism: results of a 6 month prospective study. Br J Ophthalmol. 2011;95:335-339. Shah R, Shah S, Sengupta S. Results of small incision lenticule extraction: All-in-one femtosecond laser refractive surgery. J Cataract Refract Surg. 2011;37:127-137. Hjortdal JO, Vestergaard AH, Ivarsen A, Ragunathan S, Asp S. Predictors for the outcome of small-incision lenticule extraction for Myopia. J Refract Surg. 2012;28:865-871. Reinstein DZ, Archer TJ, Gobbe M. Accuracy and reproducibility of cap thickness in small incision lenticule extraction. J Refract Surg. 2013;29:810-815.

15. Reinstein DZ, Archer TJ, Gobbe M. Lenticule thickness readout for small incision lenticule extraction compared to Artemis three-dimensional very high-frequency digital ultrasound stromal measurements. J Refract Surg. 2014;30:304-309. 16. Li M, Zhao J, Shen Y, Li T, He L, Xu H, Yu Y, Zhou X. Comparison of dry eye and corneal sensitivity between small incision lenticule extraction and femtosecond LASIK for myopia. PLoS One. 2013;8:e77797. 17. Vestergaard AH, Gronbech KT, Grauslund J, Ivarsen AR, Hjortdal JO. Subbasal nerve morphology, corneal sensation, and tear film evaluation after refractive femtosecond laser lenticule extraction. Graefes Arch Clin Exp Ophthalmol. 2013;251:2591-2600. 18. Demirok A, Ozgurhan EB, Agca A, Kara N, Bozkurt E, Cankaya KI, Yilmaz OF. Corneal sensation after corneal refractive surgery with small incision lenticule extraction. Optom Vis Sci. 2013;90:1040-1047. 19. Wei S, Wang Y. Comparison of corneal sensitivity between FS-LASIK and femtosecond lenticule extraction (ReLEx flex) or small-incision lenticule extraction (ReLEx smile) for myopic eyes. Graefes Arch Clin Exp Ophthalmol. 2013;251:1645-1654. 20. Wei SS, Wang Y, Geng WL, et al. Early outcomes of corneal sensitivity changes after small incision lenticule extraction and femtosecond lenticule extraction. Zhonghua Yan Ke Za Zhi. 2013;49:299-304. 21. Li M, Niu L, Qin B, et al. Confocal Comparison of Corneal Reinnervation after Small Incision Lenticule Extraction (SMILE) and Femtosecond Laser In Situ Keratomileusis (FS-LASIK). PLoS One. 2013;8:e81435. 22. Reinstein DZ, Archer TJ, Gobbe M, Bartoli E. Corneal sensitivity after small-incision lenticule extraction and laser in situ keratomileusis. J Cataract Refract Surg. 2015;41:1580-1587. 23. Sekundo W, Gertnere J, Bertelmann T, Solomatin I. One-year refractive results, contrast sensitivity, high-order aberrations and complications after myopic Small-Incision Lenticule Extraction (ReLEx SMILE). Graefes Arch Clin Exp Ophthalmol. 2014;252(5):837-43. 24. Kamiya K, Shimizu K, Igarashi A, Kobashi H. Visual and refractive outcomes of femtosecond lenticule extraction and small-incision lenticule extraction for myopia. Am J Ophthalmol. 2014;157:128-134 e122. 25. Ivarsen A, Asp S, Hjortdal J. Safety and complications of more than 1500 small-incision lenticule extraction procedures. Ophthalmology. 2014;121:822-828. 26. Pradhan KR, Reinstein DZ, Carp GI, Archer TJ, Gobbe M, Dhungana P. Quality control outcomes analysis of small-incision lenticule extraction for myopia by a novice surgeon at the first refractive surgery unit in Nepal during the first 2 years of operation. J Cataract Refract Surg. 2016;42:267-274. 27. Reinstein DZ, Silverman RH, Raevsky T, et al. Arc-scanning very high-frequency digital ultrasound for 3D pachymetric mapping of the corneal epithelium and stroma in laser in situ keratomileusis. J Refract Surg. 2000;16:414-430. 28. Reinstein DZ, Srivannaboon S, Silverman RH, Coleman DJ. The accuracy of routine LASIK; isolation of biomechanical and epithelial factors. Invest Ophthalmol Vis Sci. 2000;41(Suppl):S318.

Copyright © 2018. Kugler Publications. All rights reserved.

Comparative biomechanics of intrastromal lenticule extraction and LASIK 29. Twa MD, Lembach RG, Bullimore MA, Roberts C. A prospective randomized clinical trial of laser in situ keratomileusis with two different lasers. Am J Ophthalmol. 2005;140:173-183. 30. Dupps WJ Jr, Roberts C. Effect of acute biomechanical changes on corneal curvature after photokeratectomy. J Refract Surg. 2001;17:658-669. 31. Roberts C. The cornea is not a piece of plastic. J Refract Surg. 2000;16:407-413. 32. Knox Cartwright NE, Tyrer JR, Jaycock PD, Marshall J. Effects of variation in depth and side cut angulations in LASIK and thinflap LASIK using a femtosecond laser: A biomechanical study. J Refract Surg. 2012;28:419-425. 33. Medeiros FW, Sinha-Roy A, Alves MR, Dupps WJ Jr. Biomechanical corneal changes induced by different flap thickness created by femtosecond laser. Clinics (Sao Paulo). 2011;66:1067-1071. 34. Randleman JB, Dawson DG, Grossniklaus HE, McCarey BE, Edelhauser HF. Depth-dependent cohesive tensile strength in human donor corneas: implications for refractive surgery. J Refract Surg. 2008;24:S85-89. 35. MacRae S, Rich L, Phillips D, Bedrossian R. Diurnal variation in vision after radial keratotomy. Am J Ophthalmol. 1989;107:262267. 36. Maloney RK. Effect of corneal hydration and intraocular pressure on keratometric power after experimental radial keratotomy. Ophthalmology. 1990;97:927-933. 37. Muller LJ, Pels E, Vrensen GF. The specific architecture of the anterior stroma accounts for maintenance of corneal curvature. Br J Ophthalmol. 2001;85:437-443. 38. Ousley PJ, Terry MA. Hydration effects on corneal topography. Arch Ophthalmol. 1996;114:181-185. 39. Simon G, Ren Q. Biomechanical behavior of the cornea and its response to radial keratotomy. J Refract Corneal Surg. 1994;10:343-351; discussion 351-346. 40. Simon G, Small RH, Ren Q, Parel JM. Effect of corneal hydration on Goldmann applanation tonometry and corneal topography. Refract Corneal Surg. 1993;9:110-117. 41. Kohlhaas M, Spoerl E, Schilde T, Unger G, Wittig C, Pillunat LE. Biomechanical evidence of the distribution of cross-links in corneas treated with riboflavin and ultraviolet A light. J Cataract Refract Surg. 2006;32:279-283. 42. Scarcelli G, Pineda R, Yun SH. Brillouin optical microscopy for corneal biomechanics. Invest Ophthalmol Vis Sci. 2012;53:185190. 43. Petsche SJ, Chernyak D, Martiz J, Levenston ME, Pinsky PM. Depth-dependent transverse shear properties of the human corneal stroma. Invest Ophthalmol Vis Sci. 2012;53:873-880. 44. Winkler M, Shoa G, Xie Y, et al. Three-dimensional distribution of transverse collagen fibers in the anterior human corneal stroma. Invest Ophthalmol Vis Sci. 2013;54:7293-7301. 45. Dawson DG, Grossniklaus HE, McCarey BE, Edelhauser HF. Biomechanical and wound healing characteristics of corneas after excimer laser keratorefractive surgery: is there a difference between advanced surface ablation and sub-Bowman’s keratomileusis? J Refract Surg. 2008;24:S90-96.

275

46. Roy AS, Dupps WJ Jr. Patient-specific computational modeling of keratoconus progression and differential responses to collagen cross-linking. Invest Ophthalmol Vis Sci. 2011;52:9174-9187. 47. Patel S. Refractive index of the mammalian cornea and its influence during pachometry. Ophthalmic Physiol Opt. 1987;7:503506. 48. Kolozsvari L, Nogradi A, Hopp B, Bor Z. UV absorbance of the human cornea in the 240- to 400-nm range. Invest Ophthalmol Vis Sci. 2002;43:2165-2168. 49. Seiler T, Kriegerowski M, Schnoy N, Bende T. Ablation rate of human corneal epithelium and Bowman’s layer with the excimer laser (193 nm). Refract Corneal Surg. 1990;6:99-102. 50. Huebscher HJ, Genth U, Seiler T. Determination of excimer laser ablation rate of the human cornea using in vivo Scheimpflug videography. Invest Ophthalmol Vis Sci. 1996;37:42-46. 51. Reinstein DZ, Archer TJ, Randleman JB. Mathematical model to compare the relative tensile strength of the cornea after PRK, LASIK, and small incision lenticule extraction. J Refract Surg. 2013;29:454-460. 52. Schmack I, Dawson DG, McCarey BE, Waring GO, 3rd, Grossniklaus HE, Edelhauser HF. Cohesive tensile strength of human LASIK wounds with histologic, ultrastructural, and clinical correlations. J Refract Surg. 2005;21:433-445. 53. Seiler T, Matallana M, Sendler S, Bende T. Does Bowman’s layer determine the biomechanical properties of the cornea? Refract Corneal Surg. 1992;8:139-142. 54. El-Naggar MT. Bilateral ectasia after femtosecond laser-assisted small-incision lenticule extraction. J Cataract Refract Surg. 2015;41:884-888. 55. Mattila JS, Holopainen JM. Bilateral ectasia after femtosecond laser-assisted Small Incision Lenticule Extraction (SMILE). J Refract Surg. 2016;32:497-500. 56. Wang Y, Cui C, Li Z, Tao X, Zhang C, Zhang X, Mu G. Corneal ectasia 6.5 months after small-incision lenticule extraction. J Cataract Refract Surg. 2015;41:1100-1106. 57. Sachdev G, Sachdev MS, Sachdev R, Gupta H. Unilateral corneal ectasia following small-incision lenticule extraction. J Cataract Refract Surg. 2015;41:2014-2018. 58. Scarcelli G, Besner S, Pineda R, Yun SH. Biomechanical characterization of keratoconus corneas ex vivo with Brillouin microscopy. Invest Ophthalmol Vis Sci. 2014;55:4490-4495. 59. Sinha Roy A, Dupps WJ Jr, Roberts CJ. Comparison of biomechanical effects of small-incision lenticule extraction and laser in situ keratomileusis: finite-element analysis. J Cataract Refract Surg. 2014;40:971-980. 60. Seven I, Vahdati A, Roberts CJ, Pedersen IB, Hjortdal J, Dupps WJ. Biomechanical comparison of contralateral flap-based and no-flap femtosecond lenticule extraction procedures using inverse finite element analysis. ARVO. Denver, 2015. 61. Downs JC. IOP telemetry in the nonhuman primate. Exp Eye Res. 2015;141:91-98. 62. Vahdati A, Seven I, Mysore N, Randleman JB, Dupps WJ. Computational Biomechanical Analysis of Asymmetric Ectasia Risk in Unilateral Post-LASIK Ectasia. J Refract Surg. 2016;32(12):811820.

276

Copyright © 2018. Kugler Publications. All rights reserved.

63. Dupps WJ Jr, Seven I. A large-scale computational analysis of corneal structural response and ectasia risk in myopic laser refractive surgery. Trans Am Ophthalmol Soc. 2016;114:T11-T116. 64. Morishige N, Wahlert AJ, Kenney MC, et al. Second-harmonic imaging microscopy of normal human and keratoconus cornea. Invest Ophthalmol Vis Sci. 2007;48:1087-1094. 65. Morishige N, Takagi Y, Chikama T, Takahara A, Nishida T. Three-dimensional analysis of collagen lamellae in the anterior stroma of the human cornea visualized by second harmonic generation imaging microscopy. Invest Ophthalmol Vis Sci. 2011;52:911-915. 66. Reinstein DZ, Archer TJ, Gobbe M. Spherical Aberration change as a function of pupil size: a comparison between Small Incision Lenticule Extraction [SMILE] and non-linear aspheric LASIK in moderate to high myopia. ARVO. Fort Lauderdale, USA, 2012. 67. Reinstein DZ, Archer TJ, Gobbe M. LASIK for Myopic astigmatism and presbyopia using non-linear aspheric micro-monovision with the Carl Zeiss Meditec MEL 80 platform. J Refract Surg. 2011;27:23-37.

D.Z. Reinstein et al. 68. Reinstein DZ, Archer TJ, Gobbe M. ReLEx SMILE induces significantly less spherical aberration than Wavefront Optimised sub-bowman’s LASIK for any given residual postoperative relative tensile strength. ARVO 2014. Orlando, FL, USA, 2014. 69. Reinstein DZ, Archer TJ, Gobbe M. Corneal Ablation Depth Readout of the MEL80 Excimer Laser Compared to Artemis Three-dimensional Very High-frequency Digital Ultrasound Stromal Measurements. J Refract Surg. 2010;26:949-959. 70. Reinstein DZ, Archer TJ, Gobbe M, Silverman RH, Coleman DJ. Repeatability of Layered Corneal Pachymetry with the Artemis Very High-frequency Digital Ultrasound Arc-Scanner. J Refract Surg. 2010;26:646-659. 71. Reinstein DZ, Archer TJ, Gobbe M, Silverman R, Coleman DJ. Stromal thickness in the normal cornea: three-dimensional display with Artemis very high-frequency digital ultrasound. J Refract Surg. 2009;25:776-786.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

TRABECULAR MESHWORK BIOMECHANICS

Copyright © 2018. Kugler Publications. All rights reserved.

19. Iris biomechanics Anup Dev Pant, Rouzbeh Amini Department of Biomedical Engineering, The University of Akron, Akron, OH, USA

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction The iris extends antero-medially from the ciliary body of the eye and is located anterior to the lens and posterior to the cornea (Fig. 1). The distal ends of the iris form the pupil, which is responsible for the amount of light reaching the retina in response to changes in ambient light. The iris divides the anterior segment of the eye into the anterior chamber and the posterior chamber (Fig. 1). Its thickness varies from 372 ± 58 μm at the iris root to 645 ± 103 μm at its thickest point within the pupillary margin.1 The iris is comprised of two smooth muscles: the sphincter iridis and the dilator pupillae (Fig. 2). The sphincter and dilator muscle fibers are aligned in the

circumferential and radial directions, respectively. The contraction and relaxation of the iris muscles controls the pupil diameter from 1 mm at complete pupil constriction to 9 mm at complete pupil dilation. Both muscles are enervated via the autonomic nervous system.2 The iris stroma occupies the space between the anterior border layer and the anterior surface of the dilator muscle. It contains loose connective tissue, which contains pigmented cells and capillaries.3 The collagen network present in the stroma supports the structure of the iris. The stroma also contains blood vessels, nerves, and various other cells. In normal eyes, the stroma is freely permeable to the aqueous humor as well as particles measuring between 40 and 200 μm in diameter.

Fig. 1. Anatomy of the ocular anterior segment and the flow of aqueous humor. Image courtesy: NEI, NIH, Bethesda, MD, USA

Fig. 2. Histological cross-section of the porcine iris showing its three comprising segments: active smooth muscles-the Sphincter Iridis and the Dilator Pupillae , along with the passive iris stroma. Histology image: Julie E. Whitcomb

Correspondence:Rouzbeh Amini, Department of Biomedical Engineering, The University of Akron, Room 301F, Olson Research Center, 260 S. Forge St., Akron, OH 44325, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 281-290 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

282

The biomechanics of the iris plays an important role in understanding the normal physiology of the eye and the pathophysiology of ocular disease, particularly glaucoma. In this chapter, an overview of iris biomechanics in relation to glaucoma is presented. In addition, a section is dedicated to experimental methods used to quantify the mechanical properties of the iris. Finally, since iris biomechanics is closely related to intraoperative floppy iris syndrome, a section is dedicated to this complication.

Copyright © 2018. Kugler Publications. All rights reserved.

2. Iris biomechanics and glaucoma 2.1. Iris configuration Iris configuration plays an important role both in open-angle glaucoma and in angle-closure glaucoma. For example, in pigmentary glaucoma, a curious form of open-angle glaucoma, the iris is abnormally bowed towards the posterior. Although not known with an absolute level of certainty, the cause of the posterior bowing of the iris is attributed to “reverse pupillary block”,4,5 a transient elevation of pressure in the anterior chamber. It is widely accepted4,6,7 that in pigmentary glaucoma, pieces of the iris pigment separate from the iris surface and enter the aqueous humor flow when the iris posterior pigment epithelium is mechanically rubbed against opposing tissues, i.e., zonular fibers. The pigment granules are carried by the aqueous humor flow and are deposited in the outflow pathway, i.e., the trabecular meshwork. It could be postulated that continuous deposition of the pigment particles decreases the permeability of the trabecular meshwork, and consequently, decreases the outflow. Decreased outflow, if not accompanied with decreased inflow, would increase the intraocular pressure. It has been experimentally proven,8 however, that the increase in the intraocular pressure is not caused by an excessive amount of particle deposition in the trabecular meshwork. The exact cause for pigmentary glaucoma remains unknown, but the abnormal posteriorly bowed iris configuration is a characteristic of pigmentary glaucoma. In angle-closure glaucoma, the iris is abnormally positioned more towards the anterior and the periphery of the iris, mechanically blocking the outflow pathway of the aqueous humor. In fact, angle closure derives its

A.D. Pant and R. Amini

name from the closed or narrowed anterior chamber angle caused by the anterior bowing of the iris. This abnormal iris configuration is again an important characteristic of angle-closure glaucoma. Considering its important role in the pathophysiology of glaucoma, the iris configuration and factors affecting it have been studied extensively. For example, certain dynamic physiological phenomena such as pupil constriction,9,10 pupil dilation,11,12 blinking,13 and accommodation14-16 can affect the iris profile and possibly change the anterior chamber angle. In general, the iris configuration is determined by two main forces: 1. external forces generated by the flow of aqueous humor; and 2. internal forces generated by the passive response of the iris and the active contraction of its constituent muscles. Each of these two forces are discussed in more detail below. 2.2. External forces affecting iris configuration The external forces acting on the iris to change its configuration are generated from its interaction with the flow of aqueous humor. The ciliary body secretes aqueous humor into the posterior chamber behind the iris. The aqueous humor then flows into the anterior chamber through a narrow gap between the lens and the iris tip (Fig. 1). In some cases, there is a significant resistance for the flow as a result of the close proximity of the iris tip to the anterior surface of the lens. The resistance results in an increase in the pressure of the posterior chamber and leads to a phenomenon known as pupillary block.17 In pupillary block, the higher pressure in the posterior chamber generates a net force that pushes the iris periphery towards the anterior, leading to a significant narrowing or complete closure of the anterior chamber angle and consequently creating blockage of the outflow pathway.18-20 The pupillary block has a number of potential causes, such as posterior annular synechia, anterior shifting of the lens, or adhesion of the iris to the vitreous humor or to the posterior capsule following extracapsular cataract extraction. Laser peripheral iridotomy is a common surgical method to treat pupillary block and angle closure.21-23 In this method, a surgical hole is made on the periphery of the iris to equalize the pressure between the

Iris biomechanics

283

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. Ex-vivo and in-silico models of porcine iris contraction before (left) and after dilation (right). In the realistic model (b), the iris curvature was similar to that of the experiment (a). Anteriorly positioning (c) or thickening of the dilator muscle (d) in the artificial models led to a predicted curvature inconsistent with the experimental data.12

anterior and posterior chambers. Once the pressure is equalized in the two chambers, the net force pushing the iris forward decreases, the iris moves toward the posterior, the anterior chamber angle opens, and the outflow pathway blockage is removed. Laser peripheral iridotomy is also a useful treatment option for reverse pupillary block associated with pigmentary glaucoma.24 The same mechanism of equalizing the pressure between the anterior and posterior chambers moves the iris forward and removes the reverse pupillary block. 2.3. Iris internal forces The passive and active internal forces influencing the iris profile are determined by the mechanical structure of the iris and the activity of its constituent muscles. For example, anterior bowing of the iris could also be caused by activation of the dilator muscle. We have previously hypothesized that the iris bows anteriorly

during dilation even in the absence of aqueous humor– induced pupillary block.12 We tested this hypothesis in in-vivo, ex-vivo, and in-silico models. In the in-vivo studies, dilation was induced (using dark and light conditions) in patients who had undergone laser peripheral iridotomy. In this group of patients, because a surgical hole existed on the iris, the resistance to the aqueous humor flow from the posterior chamber to the anterior chamber was minimized and the pupillary block was eliminated. It was observed, however, that the curvature-to-chord length ratio, a measure of iris concavity,25 increased significantly during dilation. We also induced dilation using pharmacological agents on freshly excised porcine irides. Similar to the in-vivo cases, it was observed that the ex-vivo irides bow forward during dilation. Since the irides were dissected from the rest of the eye and were pinned in a petri dish, any chance of pupillary block was eliminated in the ex-vivo experiments, as well. Finally, we developed a computer model of the iris dilation. In

284

A.D. Pant and R. Amini

the in-silico model, we were able to artificially increase the thickness of the dilator muscle or move its location anteriorly without changing any other parameter of the model (Fig. 3). Interestingly, we observed that iris anterior bowing was not as pronounced in those cases. Our study showed that pupillary block is a dynamic phenomenon and that increased posterior chamber pressure, i.e., a static phenomenon, cannot provide an explanation for all cases of anterior bowing of the iris.

Copyright © 2018. Kugler Publications. All rights reserved.

2.4. Synergistic role of the external and internal iris forces on the iris configuration In 1968, Mapstone used a simple vector analysis and showed that contraction of the sphincter muscle during miosis and the material forces generated due to iris stiffness could lead to a net force that narrows the gap between the iris tip and the lens, and thus, induces pupillary block (Fig. 4).9 While one cannot draw any quantitative conclusion about the aqueous humor flow based on Mapstone’s study, his simple approach showed how a narrow iris–lens gap and subsequent resistance to the aqueous humor flow could occur following active iris contraction. Such a resistance, in return, would amplify the aqueous humor pressure and increase the amount of external forces applied on the posterior surface of the iris. In recent years, a better understanding of the synergistic role of the external and internal iris forces has been obtained via more sophisticated biophysical models of the anterior

Fig. 4. Mapstone’s force vector analysis. The force generated by the activity of the sphincter muscle or the active sphincter force (FAS) acts perpendicular to the corneal axis. The material stiffness force (FMS) acts towards the iris root. The sum of these two forces, in part, generates a pupil blocking force (FPB) that acts perpendicular to the lenticular surface.

Fig. 5. Finite element simulation of iris (light gray) deformation when pupil diameter is changed from 3.0 mm to 5.4 mm. The anterior chamber angle is noticeably less narrow in the compressible iris (top) when compared to the incompressible one (bottom). The difference in the angle is easier to detect in the magnified insets.11

segment.5,10,11,13,15,16,26 For example, using computational models of the iris and aqueous humor interaction, Huang and Barocas have quantitatively confirmed that miosis leads to pupillary block.10 Biomechanical studies have also shown that iris mechanical stiffness and iris compressibility could affect the aqueous humor flow and iris configuration.11,26 Stiffer irides require more external and internal forces to deform.26 In addition, similar to the cases of isolated iris,12 study of iris–aqueous humor interaction in the anterior eye has shown that incompressible irides lead to a more significant decrease in the anterior chamber angle when compared to a compressible iris.11 The iris incompressibility causes bulging at the iris root as the dilator muscle contracts radially, which then pushes the iris stroma into the angle (Fig. 5). The increased iris curvature is attributed to pupillary block, whereas the narrowing of the anterior chamber angle is due to its incompressibility. Because of the importance of iris mechanical stiffness and compressibility in determining the overall iris configuration in normal and glaucomatous eyes, we have provided more detailed explanations in the following sections. 2.5. Iris incompressibility and the dynamic nature of the iris biomechanics in angle closure glaucoma To detect angle closure glaucoma at its earlier stages, anatomical risk factors are mainly used in clinical practice. Anatomical risk factors for angle closure

Copyright © 2018. Kugler Publications. All rights reserved.

Iris biomechanics

glaucoma include: 1. shorter anterior chamber depth; 2. shorter axial length; 3. greater lens thickness; 4. a more anterior relative lens position;27-32 5. smaller anterior chamber diameter and volume;33 6. smaller corneal diameter;30,32 and 7. steeper curvature of the anterior lens surface.34 These risk factors are all static anatomical factors but, as stated above, the dynamic behavior of the eye during physiological phenomena such as dilation can affect the iris profile and could be more relevant to the mechanistic role of the iris biomechanics in the pathophysiology of glaucoma. Therefore, in addition to static anatomical risk factors, it is important to investigate parameters affecting the dynamic behavior of the anterior eye. Recently, it has been shown that in individuals at risk for or suffering from angle closure glaucoma, iris cross-sectional area does not change significantly during dilation under light and/or pharmacological stimulation.35 In open angle glaucoma suspects, however, the cross-sectional area significantly reduced during dilation. Such an interesting response was independent of the subjects’ age, the side of the eye affected, past acute angle closure attack, and various anterior segment biometrics such as corneal curvature and thickness.35 It was observed that in angle-closure-suspects, the iris thickened during dilation and bulged in the proximity of the iris root, leading to a narrowed anterior chamber angle. Such an observation is consistent with the outcomes of computational models of incompressible irides.11 Unlike angle-closure glaucoma suspects, after dilation, the irides in open-angle glaucoma patients became thinner and maintained an open anterior chamber angle. In these individuals, it was postulated that during dilation, the iris quickly released extracellular fluid into the anterior chamber and thus reduced its volume.35 Similar observations have been made in normal individuals. In particular, it has been shown that normal irides would reduce their volume in dark conditions or after pharmacological stimulation for pupil dilation.36 The disparity between the volume loss in healthy and angle-closure glaucomatous eyes during dilation has been attributed to the compressible (spongy, porous) nature of the iris independent of iris color or iris thickness.36 Normal irides also lose volume during pupil

285

dilation by a loss of extracellular fluid from the stroma into the anterior chamber aqueous humor. In contrast, the angle-closure glaucoma irides that presumably contain compact or water-retentive stroma would retain more fluid and respond in a more incompressible manner. Although the issue of iris incompressibility and angle-closure glaucoma is still a topic of active research, iris material properties such as stiffness and compressibility that are involved in dynamic phenomena in the anterior eye could be used as new risk factors for angle-closure glaucoma in the future. In our previous studies, we have mechanically deformed the stromal region of the porcine iris via indentation.37 Although the indentation deformation was not identical to dilation, the porous nature of the stroma was speculated in our study as we observed a time-dependent response of the iris during indentation. In particular, demonstrating a classic viscoelastic response, the iris was found to be stiffer when it was indented more rapidly. One could postulate that, due to the porous nature of the iris, when the iris is indented more slowly, the fluid can leave the stroma, and thus, the iris is less resistant to the external force. During rapid indentation, however, the extracellular fluid does not have an opportunity to leave the iris stroma and thus more force is needed to deform the iris.

3. Iris mechanical properties As discussed previously, the displacement of the iris from its normal morphology plays an important role in certain types of glaucoma.17,38 In most cases, clinical evidence suggests that deleterious changes in the iris configuration are caused by pressure differences between the anterior and posterior chambers.39,40 As the mechanical properties of the iris are essential in studying the response of the tissue to such pressure difference between the anterior and posterior chambers, a few investigators have conducted experimental tests to quantify the mechanical properties of the iris (see Table 1 for a summary of such studies). These experiments generally involve measurements of iris deformation under a controlled mechanical loading environment, e.g., uniaxial extension. This section presents a summary of studies conducted to quantify mechanical properties of the iris.

286

A.D. Pant and R. Amini

Table 1. Comparison of the experimental values measured for the mechanical properties of the iris Investigators

Tissue tested

Methods

Results

Bovine iris in the circumferential direction

Azimuthal (loop) extension was conducted using hook attachments allowing the iris to be stretched by its inner radius. The Young’s modulus was calculated from the forcelength curve.

Average circumferential Young’s modulus of the sphincter region was 340 kPa both for intact and for excised tissues. Average circumferential Young’s modulus of the dilator region was 890 kPa for the excised iris sectors and 760 kPa for the intact samples.

Bovine iris in the radial direction

In the excised tissues, radial extension was conducted: first, a slice with uniform width (5 mm) was cut out of the iris. The ends of this tissue were then attached with cyanoacrylate glue onto the grips of the materials tester. In the case of the intact tissue, the portions of the inner and outer edge of the iris were glued to the tester grips. Radial extension tests were then performed.

The elastic moduli in the radial direction for the dilator region were estimated to be 27 kPa and 9.6 kPa for the intact and excised irides, respectively.

Porcine iris

Indentation experiments were conducted using a 1-mm cylindrical indenter tip on both anterior and posterior surfaces. Effective instantaneous and equilibrium moduli for both surfaces of the tissue were calculated from the load displacement curve.

The effective instantaneous moduli were calculated to be 6.0 ± 0.6 kPa and 4.0 ± 0.5 kPa from indentation on the posterior and anterior surfaces of the irides, respectively. The equilibrium effective moduli were calculated to be 4.4 ± 0.9 kPa and 2.3 ± 0.3 kPa for the posterior and anterior cases, respectively.

Porcine iris

Radial and circumferential elastic moduli of irides were calculated for passive tissues and active tissues (following administration of pharmacological agents to stimulate miosis or mydriasis). Samples were stretched up to 40% strain. The radial modulus was calculated from the linear portion of the stress–strain curve. The circumferential modulus was calculated by fitting the stress–strain data to an analytical model while treating the iris as a collection of circular elastic bands.41

Heys and Barocas 41

Whitcomb et al.37

Copyright © 2018. Kugler Publications. All rights reserved.

Whitcomb et al.42

Heys and Barocas were among the first investigators to characterize the iris mechanical properties. Their work involved conducting uniaxial extension tests on bovine irides. Heys and Barocas found the iris to be anisotropic (i.e., it responded differently in the radial and circumferential directions), elastic, and nearly incompressible.41 They determined the passive mechanical behavior of the iris and its two constituent muscles, the sphincter and dilator muscles, via radial and circumferential extension. They also measured the response of the entire intact iris to uniaxial extension as compared to that of an excised sector of the tissue.

In the radial direction, the passive iris modulus was 4.0 ± 0.9 kPa. The activate iris moduli were 7.7 ± 2.0 kPa, 6.9 ± 2.2 kPa, and 8.4 ± 1.7 when pilocarpine, phenylephrine, and tropicamide were used, respectively. For the case of circumferential extension, the passive iris modulus was 2.97 ±1.3 kPa and the active iris modulus was 5.34 ± 2.1 kPa (induced by pilocarpine).

The average circumferential Young’s modulus of the sphincter region was found to be 340 kPa for both intact and excised tissues. The average circumferential Young’s modulus of the dilator region was 890 kPa for the excised iris sectors and 760 kPa for intact samples. The modulus in the radial direction for the dilator region was estimated to be 27 kPa for intact and 9.6 kPa for dissected samples. Whitcomb et al. measured the iris mechanical response using an indentation testing protocol.37 Recognizing the potential differences between the stiffer muscular layer on the posterior of the iris and the

Copyright © 2018. Kugler Publications. All rights reserved.

Iris biomechanics

more fibrous and softer stromal layer on the anterior, they designed an experiment to indent the iris both anteriorly and posteriorly. Using a viscoelastic material model, Whitcomb et al. reported an instantaneous modulus and an equilibrium modulus for excised porcine irides. The instantaneous modulus represents the mechanical response of the tissue to a rapid change in the loading or deformation, and is generally larger in value from the equilibrium modulus. In the study conducted by Whitcomb et al., the instantaneous modulus, when the posterior surface was indented, was 6.0 ± 0.6 kPa (mean ± 95% confidence interval), 50% larger than that of the anterior surface indentation (4.0 ± 0.5 kPa). Similarly, the equilibrium modulus of posterior indentation was 4.4 ± 0.9 kPa, approximately twice as large as the equilibrium modulus of the anterior indentation (2.3 ± 0.3 kPa).37 Whitcomb et al. concluded that the posterior components — the dilator, pigment epithelium, and sphincter — are stiffer than the iris stroma on the anterior. In another interesting study, Whitcomb et al. investigated the effects of commonly used ocular medications on the stiffness of the porcine irides. The elastic modulus of the iris was calculated before and after the application of three drugs: pilocarpine, phenylephrine, and tropicamide. Unlike their other study, where they had divided the study of the iris into dilator and sphincter, in this work they studied the iris as a whole. For the excised irides, the passive iris modulus was reported to be 4.0 ± 0.9 kPa (mean ± standard deviation), whereas the active iris modulus was significantly different with the application of any of the pharmacological agents (7.7 ± 2.0 kPa, 6.9 ± 2.2 kPa, and 8.4 ± 1.7 kPa in response to pilocarpine, phenylephrine, and tropicamide, respectively) in the radial direction.42 Whitcomb et al. found a similar trend in the intact irides, with approximately 25% higher values, and found a significant increase in the radial modulus after the addition of all three drugs (Fig. 6). However, they did not find any significant differences in the modulus between the intact and excised tissue nor between the three drugs applied. The average passive iris modulus in the circumferential direction was 2.97 ± 1.3 kPa, and the active iris modulus was 5.34 ± 2.1 kPa (in response to pilocarpine). Their results showed that the circumferential modulus values were significantly smaller than the radial modulus values, a result inconsistent with

287

Fig. 6. Force-displacement response in a typical intact porcine iris shows that active iris is much stiffer than the passive one.42

the study of Heys and Barocas in bovine irides.42 Collectively, the experimental tests on the bovine and porcine irides have suggested that the tissue stiffness is different in the muscular segment of the iris (dilator and sphincter) when compared to the stromal region. Since the structural components of the human iris, i.e., the smooth muscles in the dilator and sphincter regions and the fibrous tissue in the stroma are similar to those of the porcine and bovine irides, one may postulate that human irides will respond to mechanical loading in a similar manner. Therefore, the assumption of anisotropic and elastic (or viscoelastic, depending on the time scale of the deformation) is reasonable for human irides as well. However, the exact values of these properties in the human iris are not currently available and should be obtained using donor eyes. Another limitation of the mechanical tests on the isolated irides is that the tissue may not fully mimic the in-vivo responses. For example, because blood flows in the living iris, it should be stiffer under compressional loading. Fortunately, with the advent of imaging modalities such as anterior segment optical coherence tomography, the in-vivo deformation of the iris can be quantified precisely. Using such accurate measures of iris deformation and potentially more advanced theoretical and computational models, such as inverse finite element modeling, in-vivo mechanical properties of the human iris could be estimated in the future. Since tissue properties such as compressibility and stiffness could be possible risk factors for angle-closure glaucoma,36,40 the quantification of iris mechanical

288

properties in vivo could provide a better understanding of glaucoma pathophysiology. Further, comparison between the healthy and glaucomatous irides could potentially lead to the development of alternative and/ or additional methods for prediction and management of the disease.

4. Intraoperative floppy iris syndrome

Copyright © 2018. Kugler Publications. All rights reserved.

Another complication in which the iris plays a major role is the intraoperative floppy iris syndrome (IFIS). During cataract surgery, surgeons prefer to have unimpeded access to the anterior surface of the lens. In certain patients, however, such access is hindered by undesirable symptoms such as: 1. pupil constriction and lack of response to medications that induce dilation; 2. a flaccid and floppy iris stroma that billows in response to intraocular flow; and 3. the tendency of the floppy iris to prolapse toward the cataract extraction area. Such complications during cataract surgery are collectively known as IFIS. Recent studies have identified tamsulosin (Flomax), a selective α blocker widely used for treating benign prostatic hypertrophy, to be associated with this complication.43 Chang and Campbell proposed the loss of the tone of the dilator muscle, which likely contributes to the structural rigidity of the iris, as the cause for IFIS. They found that even people who had been off tamsulosin for more than a year had also developed IFIS, further strengthening the hypothesis that dilator atrophy (perhaps due to lack of stimulation) was the cause of flaccid and floppy irides.43 In another study, Santaella et al. found significant differences between the thickness of the dilator muscle

A.D. Pant and R. Amini

in patients who had received tamsulosin and a control group.44 Using donor eyes, they found that patients with a history of tamsulosin use had much thinner iris dilator muscles.44 Prata et al. also found that patients using systemic alpha-1 adrenoceptor antagonists had significantly lower values for dilator muscle region thickness and lower ratios of dilator muscle region thickness to sphincter muscle region thickness when compared to the normal population.45 As shown by Whitcomb et al.37,46 both active and passive mechanical properties of the dilator muscle are important in identifying the overall response of the iris. As such, one could postulate that dilator muscle atrophy due to the use of tamsulosin could change the iris mechanical properties and negatively affect the response of the tissue. Some investigators, however, have proposed iris vascular dysfunction as the reason for IFIS in contrast to the idea of iris dilator atrophy.48 Their immunohistochemical staining results have shown strong immunoreactivity detected around the iris vasculature of normal tissue, in comparison to those of the IFIS eyes. They found that the alpha-1 adrenoceptors to be localized both on the iris arteriolar muscularis and on the dilator muscle. One can presume that the iris vasculature plays an important role in supporting the iris structure apart from delivering nutrients. It was thus speculated that the iris vessel would form a web, which has a tremendous ability to coil and uncoil to allow for iris dilation. Such coiling and uncoiling ability is presumably lost in IFIS cases, and the flaccid irides exhibit poor dilation responses.47 Clearly, it is not trivial to conclude whether the cause of IFIS is the result of dilator atrophy, vascular dysfunction, or a combination of both factors. In the future, quantification of mechanical properties of irides in normal eyes and in irides that have been exposed to tamsulosin could provide better understanding of the mechanism of IFIS.

Iris biomechanics

References 1.

2. 3. 4.

5.

6. 7. 8.

9. 10.

11.

12.

13.

14.

Copyright © 2018. Kugler Publications. All rights reserved.

15.

16. 17. 18.

19.

Pavlin C, Harasiewicz K, Foster F. Ultrasound biomicroscopy analysis of the anterior segment in normal and glaucomatous eyes. Am J Ophthalmol. 1992;113:381-389. Kaufman PL, Adler FH, Levin LA, Alm A. Adler’s Physiology of the Eye. Elsevier Health Sciences; 2011. Hossler F. Ultrastructure Atlas of Human Tissues. Wiley; 2014. Karickhoff JR. Reverse pupillary block in pigmentary glaucoma: Follow up and new developments. Ophthalmic Surg. 1993;24(8):562-563. Amini R, Barocas VH. Reverse pupillary block slows iris contour recovery from corneoscleral indentation. J Biomech Eng. 2010;132:071010. Farrar SM, Shields MB. Current concepts in pigmentary glaucoma. Surv Ophthalmol. 1993;37(4):233-252. Sugar HS. Pigmentary glaucoma. A 25-year review. Am J Ophthalmol. 1966;62(3):499-507. Murphy CG, Johnson M, Alvarado JA. Juxtacanalicular tissue in pigmentary and primary open angle glaucoma. The hydrodynamic role of pigment and other constituents. Arch Ophthalmol. 1992;110(12):1779-1785. Mapstone R. Mechanics of pupil block. Br J Ophthalmol. 1968;52(1):19-25. Huang EC, Barocas VH. Active iris mechanics and pupillary block: Steady-state analysis and comparison with anatomical risk factors. Ann Biomed Eng. 2004;32(9):1276-1285. Jouzdani S, Amini R, Barocas VH. Contribution of different anatomical and physiologic factors to iris contour and anterior chamber angle changes during pupil dilation: Theoretical analysis. Invest Ophthalmol Vis Sci. 2013;54(4):2977-2984. Amini R, Whitcomb JE, Al-Qaisi MK, et al. The posterior location of the dilator muscle induces anterior iris bowing during dilation, even in the absence of pupillary block. Invest Ophthalmol Vis Sci. 2012;53(3):1188-1194. Amini R, Jouzdani S, Barocas VH. Increased iris–lens contact following spontaneous blinking: Mathematical modeling. J Biomech Eng. 2012;45(13):2293-2296. Dorairaj S, Oliveira C, Fose AK, et al. Accommodation-induced changes in iris curvature. Exp Eye Res. 2008;86(2):220-225. Heys JJ, Barocas VH. Computational evaluation of the role of accommodation in pigmentary glaucoma. Invest Ophthalmol Vis Sci. 2002;43(3):700-708. Huang EC, Barocas VH. Accommodative microfluctuations and iris contour. J Vis. 2006;6(5):653-660. Kahook MY, Schuman JS, Epstein DL, editors. Chandler and Grant’s Glaucoma. Slack Incorporated; 2013. Tello C, Tran HV, Liebmann J, Ritch R. Angle closure: Classification, concepts, and the role of ultrasound biomicroscopy in diagnosis and treatment. Semin Ophthalmol. 2002;17(2):69-78. Congdon NG, Friedman DS. Angle-closure glaucoma: Impact, etiology, diagnosis, and treatment. Curr Opin Ophthalmol. 2003;14(2):70-73.

289 20. Quigley HA, Friedman DS, Congdon NG. Possible mechanisms of primary angle-closure and malignant glaucoma. J Glaucoma. 2003;12(2):167-180. 21. Liebmann JM, Ritch R. Laser iridotomy. Ophthalmic Surg Lasers. 1996;27(3):209-227. 22. Caronia RM, Liebmann JM, Stegman Z, Sokol J, Ritch R. Increase in iris-lens contact after laser iridotomy for pupillary block angle closure. Am J Ophthalmol. 1996;122(1):53-57. 23. Liebmann JM, Ritch R. Laser surgery for angle closure glaucoma. Semin Ophthalmol. 2002;17(2):84-91. 24. Breingan PJ, Esaki K, Ishikawa H, Liebmann JM, Greenfield DS, Ritch R. Iridolenticular contact decreases following laser iridotomy for pigment dispersion syndrome. Arch Ophthalmol. 1999;117(3):325-328. 25. Amini R, Whitcomb JE, Prata TS, et al. Quantification of iris concavity. Journal of Ophthalmic & Vision Research. 2010;5(3):211. 26. Heys JJ, Barocas VH, Taravella MJ. Modeling passive mechanical interaction between aqueous humor and iris. J Biomech Eng. 2001;123(6):540-547. 27. Lowe RF. Aetiology of the anatomical basis for primary angle-closure glaucoma. Biometrical comparisons between normal eyes and eyes with primary angle-closure glaucoma. Br J Ophthalmol. 1970;54(3):161-169. 28. Marchini G, Pagliarusco A, Toscano A, Tosi R, Brunelli C, Bonomi L. Ultrasound biomicroscopic and conventional ultrasonographic study of ocular dimensions in primary angle-closure glaucoma. Ophthalmology. 1998;105(11):2091-2098. 29. Sihota R, Ghate D, Mohan S, Gupta V, Pandey RM, Dada T. Study of biometric parameters in family members of primary angle closure glaucoma patients. Eye (Lond). 2008;22(4):521-527. 30. Sihota R, Lakshmaiah NC, Agarwal HC, Pandey RM, Titiyal JS. Ocular parameters in the subgroups of angle closure glaucoma. Clin Experiment Ophthalmol. 2000;28(4):253-258. 31. Sihota R, Dada T, Gupta R, Lakshminarayan P, Pandey RM. Ultrasound biomicroscopy in the subtypes of primary angle closure glaucoma. J Glaucoma. 2005;14(5):387-391. 32. Tomlinson A, Leighton DA. Ocular dimensions and the heredity of open-angle glaucoma. Br J Ophthalmol. 1974;58(1):68-74. 33. Lee DA, Brubaker RF, Ilstrup DM. Anterior chamber dimensions in patients with narrow angles and angle-closure glaucoma. Arch Ophthalmol. 1984;102(1):46-50. 34. Lowe RF. Anterior lens curvature. comparisons between normal eyes and those with primary angle-closure glaucoma. Br J Ophthalmol. 1972;56(5):409-413. 35. Quigley HA, Silver DM, Friedman DS, et al. Iris cross-sectional area decreases with pupil dilation and its dynamic behavior is a risk factor in angle closure. J Glaucoma. 2009;18(3):173-179. 36. Quigley HA. The iris is a sponge: A cause of angle closure. Ophthalmology. 2010;117(1):1-2. 37. Whitcomb JE, Amini R, Simha NK, Barocas VH. Anterior–posterior asymmetry in iris mechanics measured by indentation. Exp Eye Res. 2011;93(4):475-481.

290

Copyright © 2018. Kugler Publications. All rights reserved.

38. Epstein DL, Hashimoto JM, Anderson PJ, Grant WM. Experimental perfusions through the anterior and vitreous chambers with possible relationships to malignant glaucoma. Am J Ophthalmol. 1979;88(6):1078-1086. 39. Tiedeman JS. A physical analysis of the factors that determine the contour of the iris. Am J Ophthalmol. 1991;111(3):338-343. 40. Narayanaswamy A, Hoon N, Lim C, Aung T. Young’s modulus determination of normal and glaucomatous human irides. Invest Ophthalmol Vis Sci. 2015:6139. 41. Heys J, Barocas VH. Mechanical characterization of the bovine iris. J Biomech. 1999;32(9):999-1003. 42. Whitcomb JE, Barnett VA, Olsen TW, Barocas VH. Ex vivo porcine iris stiffening due to drug stimulation. Exp Eye Res. 2009;89(4):456-461. 43. Chang DF, Campbell JR. Intraoperative floppy iris syndrome associated with tamsulosin. J Cataract Refract Surg. 2005;31(4):664-673.

A.D. Pant and R. Amini 44. Santaella RM, Destafeno JJ, Stinnett SS, Proia AD, Chang DF, Kim T. The effect of α 1-adrenergic receptor antagonist tamsulosin (flomax) on iris dilator smooth muscle anatomy. Ophthalmology. 2010;117(9):1743-1749. 45. Prata TS, Palmiero P, Angelilli A, et al. Iris morphologic changes related to α 1-adrenergic receptor antagonists: Implications for intraoperative floppy iris syndrome. Ophthalmology. 2009;116(5):877-881. 46. Whitcomb JE, Amini R, Simha N, Barocas VH. Assessment of the mechanical properties of the iris dilator and stroma using nanoindentation. Invest Ophthalmol Vis Sci. 2009;50(5):4907. 47. Panagis L, Basile M, Friedman AH, Danias J. Intraoperative floppy iris syndrome: Report of a case and histopathologic analysis. Arch Ophthalmol. 2010;128(11):1437-1441.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

ACCOMMODATION, PRESBYOPIA, AND LENS BIOMECHANICS

Copyright © 2018. Kugler Publications. All rights reserved.

20. Accommodation and presbyopia Matthew A. Reilly Department of Biomedical Engineering, Department of Ophthalmology & Visual Science, The Ohio State University, Columbus, OH, USA

1. Introduction

Copyright © 2018. Kugler Publications. All rights reserved.

Accommodation is the ability of the eye to dynamically increase its optical power to allow near vision.1-3 Presbyopia is the progressive loss of accommodation amplitude with age.4 The pathogenesis of presbyopia is generally thought to be related to age-related changes in the lens5-9 but is sometimes ascribed to other tissues.10 Reilly recently demonstrated that the loss of accommodation is due solely to changes in the lens, specifically the balance of forces between the lens and its capsule, and changes in optical properties.11 Thus, while the role of the surrounding tissues, such as the vitreous,12 zonules,13,14 and choroid15 remains critical for the success of any method which might restore or prolong the eye’s natural ability to both accommodate and disaccommodate, this chapter will focus on the mechanics of the lens and its capsule.

Fig. 1. Schematic of normal lens substitution following phacoemulsification with a traditional intraocular lens (above) and lens refilling (below).

Presbyopia clinically manifests in the fifth decade of life and affects every human.4 The loss of productivity and optical correction costs over $20 billion annually in the United States.16 This amount will undoubtedly increase as the population continues to age and more advanced optical devices become available. The traditional treatment of reading glasses or bifocals offer clear vision at only two distances and requires spectacles. Numerous surgical procedures and implants,17 such as intraocular lenses18 and corneal inlays,19 are gaining in popularity while offering marginal visual improvement. An alternative approach called lens refilling would restore the natural mechanism of accommodation (Fig. 1).3,20-25 However, many questions remain regarding the mechanism of accommodation, the driving force(s) behind presbyopia, and the properties of the natural lens and capsule. The significant interest in restoring accommodation has led to considerable recent progress in these areas. These are reviewed below. 1.1. Anatomy Figure 2 shows the anatomy of the anterior half of the eye with emphasis on tissues relevant to accommodation. Light enters the eye through the cornea, which is generally regarded as having a fixed optical power. The lens (Fig. 3) is the pivotal tissue in accommodation. It is suspended by many small fibers, called zonules, which connect the choroid (via the ciliary processes) to the lens capsule near its equator. The capsule is a basement membrane comprised primarily of collagen IV and laminins.26

Correspondence: Matthew A. Reilly, Department of Biomedical Engineering, The Ohio State University, 296 Bevis Hall, 1080 Carmack Rd, Columbus, OH 43210, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 295-306 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

296

M.A. Reilly

anterior and posterior surfaces are offset, thereby minimizing the resulting optical disruption.33 As the fiber cells approach this terminal differentiation step, they discard their organelles to maintain lens transparency.34-36 These mature fiber cells then enter a quasi-senescent state with virtually no metabolic activity and are unable to produce or maintain proteins or lipids.37,38 The lens is unable to discard old cells or transport denatured proteins in mature fiber cells due to the loss of organelles — a prerequisite for transparency within the optical zone.34-36,39 Thus, all constituents of fiber cells at the center of the lens have been present since the embryonic stage of development.40 Additional cells are constantly added on like the layers of an onion, with the innermost layers called the nucleus and the outer layers the cortex.41 Fig. 2. Ocular anatomy of tissues involved in accommodation.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. Schematic of lens anatomy and morphology.

The lens itself contains only two cell types: epithelial and fiber cells. The fiber cells themselves do not proliferate.27 A monolayer of cuboidal epithelial cells covers the interior, anterior surface of the capsule.28 Epithelial cells near the equator differentiate into elongated fiber cells29 during which time their length increases by up to 1000-fold.30 The tips of these fiber cells attach to the posterior capsule and the apical surface of the epithelium, gradually marching towards the optical axis. Upon arrival at its destination, the fiber tip meets a corresponding tip from an opposing cell, forming a suture line.31,32 The suture lines at the

1.2. Accommodation mechanics In humans, accommodation is accomplished via contraction of the ciliary muscle, which minimizes tension in the zonular fibers2 while maximizing tension in the choroid (Fig. 4).15,42 Tension in the lens capsule is in turn minimized,1 and the lens/capsule complex is in a residually loaded state.11 This means its geometry is dictated solely by the mechanical interactions of the lens fiber cells and the capsule since there are no applied external forces. In the young eye, the lens “rounds up” taking on a thicker, more curved shape with increased optical power.43 Disaccommodation is then the dynamic decrease in the eye’s optical power to allow distance vision. Disaccommodation is caused by the relaxation of the ciliary muscle. This minimizes the tension in the choroid while maximizing tension in the zonules and lens capsule. The tension in the capsule is distributed over the surface of the lens to compress the fiber cells, resulting in a thinner, flatter lens with lower optical power.44 This zonular tension is balanced by tension arising in the choroid (Fig. 4).15 1.3. Effects of aging It is now well known that the lens volume45,46 and stiffness8,47-51 increase throughout life. In particular, the elastic modulus of the nucleus increases by several orders of magnitude with age.49,51,52 These studies assume that the lens is an isotropic, elastic solid to simplify the analysis of experimental data. However, it

Accommodation and presbyopia

297

Fig. 4. Simplified biomechanical model of the accommodative tissues. Adapted from Beers and van der Heijde.42

1.4. Mechanisms of aging The lens grows continuously throughout life,45 resulting in increased volume and surface area.46 Continuous growth would necessarily introduce residual stresses in the capsule unless it is actively remodeled; as yet, it is unknown whether the capsule remodels or grows after birth. The surface area-to-volume ratio decreases with age while the distance from the surface to the center of the lens increases, thereby increasing relative resistance to small molecule transport to the lens nucleus even in the absence of internal changes to the lens. The gap junctions are also modified in the nucleus of aged lenses.62 Gap junctions containing connexin 46 are known to be essential to transport glutathione within the lens.63 Some combination of these factors results in the absence of antioxidant capacity in the nucleus of aged lenses. The surface area-to-volume ratio nL ‒ nA _ nL ‒ nV  _ ​ P =   ​      ​ +   ​      ​ ​(nL ‒ n R AV)​  RP decreases with age while the distance from the surface t  _ ​(nL ‒ nA)​  ______ ______ ​    R  ​​     R  ​ ‒  ​    nL ​​  to the center of the lens increases.64 Some combination A P of these factors contributes to oxidative stress in the where nA is the refractive index of the aqueous humor nucleus, possibly contributing to the binding of proteins and nV is the refractive index of the vitreous humor. to membranes, and presumably, lens stiffening. Thus, all geometric changes in lens shape, as well as Neither the proteins65-68 nor lipids37,69-72 can be the diminishing refractive index of the lens, result in replenished within the organelle-free zone in the center decreased power in the fully accommodated state with of the lens. Both undergo extensive changes throughout life, resulting in a significant increase in the fraction of age. Combined, these findings indicate that the lens proteins which are insoluble73 and binding of proteins eventually changes from a flexible, curved, optically to the cell membranes.68 These changes are correlated dense tissue capable of both accommodation and with lens stiffening, 73 though a mechanistic model by disaccommodation to a stiffer, flatter tissue with a lower which precipitation and stiffening are related has not refractive index which is incapable of “rounding up” for yet been developed. Reilly et al. demonstrated that the porcine lens is near vision.

Copyright © 2018. Kugler Publications. All rights reserved.

is known that the lens is viscoelastic25,50,53-56 and that its cytoplasm is highly viscous.57 Still less is known regarding the mechanics of the lens capsule, with data indicating that the elastic modulus may increase58 or decrease59 with age. The relative importance of lens volume, lens stiffness, and capsule stiffness in determining the accommodated shape of the lens is unknown. No studies have yet reported the residual stresses in the lens fiber cells and capsule, nor is it known to what extent, if any, the lens capsule may remodel with age. The lens’ fully accommodated axial thickness, t,60 anterior, RA, and posterior, RP, radii of curvature increase significantly with age while the equivalent refractive index, nL, decreases.7 Each of these factors contributes to the optical power, P, of the lens according to the lensmaker’s equation:61

298

a useful model for the presbyopic human lens.25,56,74 The pig lens’ optical power is largely independent of its equatorial diameter.25,74 It has an elastic modulus gradient with a maximum value at the center of the lens and a minimum value at the surface.75 Refilling the porcine lens capsule with a soft polymeric material can also increase the accommodation amplitude in a volume-dependent manner.25 The dependence of optical power changes on refill material volume in the absence of mechanical property differences may indicate the importance of lens growth, as opposed to only lens stiffness, as a driving force for presbyopia. Recent spinning tests found that the stiffness of the lens nucleus does not increase rapidly until around age 36, 51 long after most accommodation has already been lost.4 Volume changes have been observed in the lens during accommodation.76-78 This may imply that the lens acts as a poroelastic sponge being squeezed by the capsule during disaccommodation, thereby driving the flow of nutrients in and waste out of the lens. Once accommodative changes decrease due to lens growth, this convective transport mechanism would be diminished. This decrease would occur in parallel with increased resistance to diffusive transport. Together, these changes could compromise maintenance of nuclear proteins leading to the aforementioned precipitation-driven stiffening. This hypothesis remains to be tested but, if found to be true, would indicate that presbyopia causes lens stiffening rather than lens stiffening causing presbyopia. Resolving this chickenor-egg question may open the door to new treatments to reverse or even prevent presbyopia.

Copyright © 2018. Kugler Publications. All rights reserved.

2. Mechanical properties 2.1. Lens fiber cells Lens spinning is the oldest mechanical test for measuring the lens’ intrinsic mechanical properties 47 and remains useful for extracting the mechanical properties of larger mammalian lenses, but is not useful for mouse lenses due to their small size. Spinning does not require destructive sectioning of the lens fiber cells as does indentation. However, as with the other tests mentioned above, interpretation of the data can lead to erroneous conclusions.79 Burd et al. developed

M.A. Reilly

an inverse finite element analysis-based technique for characterizing the mechanical property distribution in whole lenses80 which was subsequently applied to a large number of human lenses.51 This method requires the specification of a mathematical formula describing how the shear modulus varies within the lens. This test has not yet been successfully applied to encapsulated lenses, and is therefore not useful for evaluating the optomechanical response of candidate lens refilling materials except in a qualitative way. Inclusion of the capsule in an inverse finite element model is possible, but again, would require detailed knowledge of local thickness and mechanical properties of the capsule, as well as knowledge of the boundary condition, e.g., adhesion, friction, or slip, between the capsule and material. Reilly et al. found a shear modulus of 608 Pa at the center and 68 Pa at the surface of the young porcine lens.81 Wilde et al. reported an age-related increase in shear modulus at the center of the human lens from 10 Pa at age 10 to 20 kPa at age 60, while the shear modulus at the surface remained relatively constant at about 500 Pa.51 Indentation can be used to measure intrinsic local mechanical properties of the lens. It has been used on porcine56 and human49 lenses indicating the presence of mechanical property gradients. One limitation of this approach is the need to destructively section the lens fiber cells. This may alter the mechanical properties of the remaining sample. The method by which mechanical properties are obtained via indentation assumes the sample is very large relative to the indentation probe and depth of indentation, and that the sample is mechanically homogeneous and isotropic.82 Additional solutions have been developed for more complex scenarios which would allow testing of the encapsulated lens,83,84 but these have not yet been applied. Applying the standard solution to nanoindentation of an encapsulated lens85 is therefore not an appropriate way to measure lens elasticity, since this solution assumes that the material being tested is mechanically homogeneous, though interpretation of nanoindentation data may yield useful insights when analyzed appropriately. Reilly and Ravi measured the elastic modulus distribution of the young porcine lens to be about 2 kPa at the center and 750 Pa at the surface,56 very similar to what was determined using a spinning test on lenses of the same age.81 Weeber et al.

Copyright © 2018. Kugler Publications. All rights reserved.

Accommodation and presbyopia

found that the shear modulus at the center of the lens increased three orders of magnitude, from 25 Pa at age 20 to 25 kPa at age 58, while the modulus at the surface (determined by extrapolation from more central measurements) increased from 25 Pa to 2 kPa over the same period.49 These findings are broadly consistent with the aforementioned spinning results.51 Compression testing has been used to qualitatively compare lenses from mouse,86-89 pig,90 and human8 lenses. Interpretation of compression tests has thus far been limited to qualitative stiffness measurements. Since stiffness is an extrinsic metric, it is not generally possible to objectively compare lenses of different sizes or shapes. The presence of the lens capsule further confounds these measurements. While commercial compression testing software may output an elastic modulus value (an intrinsic measurement of the material stiffness), it is unreliable because the assumptions which are used by the software are inappropriate for lens compression: these software packages assume a uniform cross-section of the sample and uniform mechanical properties throughout the sample. Extraction of an elastic modulus from such tests will require the development of an inverse finite element analysis approach. This is particularly complicated in the case of encapsulated lenses, as the local mechanical properties and thickness variations in the capsule must be included in the model. Brillouin light scattering has been used to characterize the bulk modulus (that is, the resistance to volumetric changes under applied loading) in porcine91 and human lenses.92 This technique allows non-invasive, local measurements,93 and has been used to characterize age-related changes in the lens,94 including protein aggregation.95 To date, it is the only technique used to mechanically characterize the lens in vivo.94,96 Measurements rely on naturally-occurring phonon-induced deformations arising within the lens, yielding excitations in the gigahertz regime and therefore representing strain rates far higher (or time scales far shorter) than those involved in physiological loading. Bubble-based acoustic radiation force has been used to determine spatial variations in the stiffness of porcine lenses97 and elastic modulus for human lenses.98 This method showed an increase in the elastic modulus at the center of the lens from 5.5 kPa in middle age to 10.5 kPa in old age, while the modulus at 4 mm away from

299

the center was relatively constant at about 1 kPa. Optoacoustic imaging has also been brought to bear on the lens,99 and has thus far been used to demonstrate the presence of age-related mechanical property gradients in rabbit,100 bovine, and porcine lenses.101 This technique yielded slightly higher elastic modulus values for the young porcine lens than Reilly and Ravi reported using microindentation56 and spinning.81 2.2. Lens capsule Krag and Andreassen used an excimer laser to dissect rings of the capsule which were then subjected to uniaxial tensile testing. This technique was used to characterize porcine102 and human capsules.103 The capsule’s stress-strain behavior was non-linear, with a concave upward shape common to most biological tissues. They estimated the elastic modulus at 10% strain and reported an increase in the capsule’s elastic modulus up to age 30, after which it remained constant at about 1.5 MPa.58 Inflation testing has been used to examine the mechanical properties of the lens capsule.59 Inflation results in biaxial loading of the capsule yielding stresses similar to what might be expected in vivo104 and has been used to study mouse,105 pig,26,106-108 and human59,109 lens capsules. Of these studies, only Fisher reported age-related changes in human lens capsules with the result that the elastic modulus decreased linearly with age from 8 MPa at birth to 1.5 MPa at age 80.59 Recent theoretical work has made significant strides in reconciling these two datasets using a network-based structural constitutive model.104 This model predicted that a network with structural features similar to those of the lens capsule should stiffen under uniaxial extension while behaving more linearly under biaxial loading, e.g., inflation, just as experiments had shown previously. This model has since been used to show that regional variations are not required to explain inflation data from the human capsule.110

3. Mechanical modeling O’Neill and Doyle proposed the first numerical model of accommodation, modeling the lens capsule as a membrane surrounding an incompressible fluid.111 Burd et al. later developed a finite element model

Copyright © 2018. Kugler Publications. All rights reserved.

300

of disaccommodation — essentially similar to a lens stretching experiment — and noted that the input data required to build the model were of insufficient quantity and quality to give reliable predictions.112 This finding was a major driving force behind renewed interest in the study of accommodation and presbyopia. Hermans et al. used more recent geometric measurements of the lens in developing a finite element model of disaccommodation,113 leading to the finding that the force exerted on the lens by the zonules appears to be independent of age.114 Weeber et al.115 refined this model using recent data describing the age-related mechanical property gradient found within the human lens.49 This resulted in an age-related decrease in the change in optical power arising during disaccommodation which slightly underpredicted the clinically-observed accommodation amplitude. Ljubimova et al. developed a finite element model of disaccommodation which included the vitreous humor and a more sophisticated representation of zonular loading.116,117 This model relied on older measurements of lens geometry and mechanical properties, again achieving qualitative rather than quantitative agreement with clinical measurements of accommodation and disaccommodation. Chien et al. simulated accommodation using a membrane model encompassing an incompressible fluid subject to a step displacement at the equator.118 However, this model predicted optical changes contrary to all available data, possibly owing to a singularity arising at the equator; the presence of this singularity may have altered the equilibrium solution of the strain energy variational formulation. Furthermore, this model appears to be limited in its ability to achieve the higher levels of accommodation known to occur in the young human eye.4,11 To overcome this limitation, Reilly and Ravi showed that biconvex shells enclosing an incompressible fluid and subject to physical constraints on the deformation arising during disaccommodation, such as continuous curvature at the equator, tend to deform in accordance with the Helmholtz theory of accommodation.119 The simplicity of this model meant it could never yield quantitative agreement with clinical measurements of lens shape changes arising during accommodation. Reilly11 therefore implemented a geometric

M.A. Reilly

mechanics model of accommodation with an age-related disaccommodated geometry subject to the same constraints as the Reilly and Ravi model.119 Despite its simplicity, this model was able to quantitatively predict changes arising in the young lens during accommodation as well as all changes between ages 25-55. Reilly also showed that allowing localized deformations at the equator could give rise to optical changes similar to those predicted by Chien’s model,118 but that this mechanism of accommodation is inherently less efficient than the Helmholtz theory. This was the first model to simulate accommodation rather than disaccommodation, and led to the important clarification that the residual stresses between the lens and the capsule govern the ability of the lens to accommodate. Recently, Wilkes and Reilly developed an improved finite element model of accommodation including the lens, capsule, and zonules.120 This was the first model to attempt to incorporate the residual stresses essential to disaccommodation. This was accomplished by using thermal strain and temperature as a pseudo-variable to pre-tension the zonules and capsule. A centripetal displacement was then applied to the distal ends of the zonules, thereby relaxing the zonular tension and inducing accommodation. The stiffness of the lens fiber cells was increased in a homogeneous manner to simulate aging while all other parameters were held constant. This resulted in a significant decline in accommodation amplitude with stiffness, although this deficit was less than that reported clinically,4 leading to the conclusion that stiffening could explain most, but not all, of the age-related accommodation deficits occurring in clinical presbyopia. Wilkes and Reilly have incorporated this model into a model of the whole human eye suitable for the study of accommodation.121 This model includes a novel constitutive model for smooth muscle activation and contraction enabling the mathematical simulation of ciliary muscle contraction. Inclusion of the whole eye will catalyze the understanding of the complex interactions of ocular tissues during accommodation. Once validated, it may also be used to evaluate surgical procedures or devices which seek to restore accommodation.

Accommodation and presbyopia

Copyright © 2018. Kugler Publications. All rights reserved.

4. Restoring accommodation 4.1. The role of animal models Numerous studies have utilized non-human primate models to study various facets of accommodation.9 Primates generally have the same mechanism of accommodation as humans,122 whereas other animals either do not accommodate25 or do so by a different mechanism, such as axial translation of the lens.123 While non-human primates are the best animal model with which accommodation might be studied, it is important to note that some features of presbyopia may be different between primates and humans. For example, the human lens exhibits different growth patterns,45 and shows some differences at the molecular level38 as well as gross anatomical differences in the lens and adjacent structures.124 Mice are an unlikely model for the study of presbyopia, as they are not believed to accommodate. However, the ability to insert, delete, modify, or alter the regulation of lens-specific proteins in mice allows some insights into the molecular mechanisms governing age-related changes in the optical and mechanical properties of the lens. Most work on mouse lens models has been focused on cataractogenesis rather than presbyopia. Still, several recent studies have used mice to give significant insights into the biomolecular driving forces of lens stiffening.87-89 Koopmans et al. performed lens refilling in vivo in nine adolescent rhesus monkeys using a proprietary silicone-based material.22 While some useful accommodation was measured using autorefractometry, the accommodation amplitude was far lower than the control eye in all cases. Furthermore, the refilled capsular bags experienced posterior capsular opacification despite an experimental treatment to prevent it. Still, this is a groundbreaking experiment, as any candidate lens refilling material would necessarily need to be successfully evaluated in primates before implantation in humans. 4.2. Lens stretching Ex-vivo lens stretching is a useful tool for evaluating the functional optomechanical relationship between equatorial diameter, stretching force, and optical changes in the lens. Lens stretching has been a very popular method for evaluating the role of mechanical

301

forces in altering the optical power of the lens. Feline,125 porcine,24,25,74,126 primate,22,126 and human23,127-132 (both natural and refilled) lenses have been evaluated using this approach. It is important to note the limitations of lens stretching. For example, the total force measured by the instrument does not necessarily correspond to the force experienced by the lens: circumferential stresses arising in intervening tissues diminish the radial forces distributed to the lens via zonular tension.133 Lens stretching does not fully recapitulate the in vivo environment involved in accommodation. This may alter the force vectors due to zonular and vitreous interactions with the lens capsule. It is also important to recognize that stretching the lens simulates disaccommodation rather than accommodation, and that simply measuring a change in optical power due to the application of force may not correspond to a useful measure of the accommodative ability of a given lens. The accommodative ability of a given lens is determined solely by the optical power of the residually loaded state, i.e., when the stretching force is zero.11 Thus, even if a significant change in optical power is noted following stretching, this does not necessarily imply useful accommodation. Despite these caveats, lens stretching remains the best in-vitro method for evaluating lens refilling materials prior to animal testing. Presumably, if a young human lens and a refilled lens capsule perform similarly under a lens stretching test, the refilling procedure and material would be good candidates for animal testing. 4.3. Prosthetic materials Lens refilling materials have generally been silicone-based to allow flexibility and a high refractive index. However, these materials have been uniform in both optical and mechanical properties. The young, pre-presbyopic lens exhibits opposing gradients in refractive index (high at the center decreasing towards the surface)134 and shear modulus (low at the center and increasing towards the surface)51. If these gradients are found to be essential to high-quality vision during accommodation, then lens refilling materials must attempt to recapitulate them to be successful. This combination is particularly challenging since, in hydrogel systems, the refractive index and shear modulus both increase with concentration. Thus, even if it were possible to

302

M.A. Reilly

generate an appropriate optical property gradient, the corresponding elasticity gradient would be similar to that of a presbyopic human lens. One possible solution to this problem is the development of a biomimetic nanocomposite system based on a conceptual model of the natural lens in which the cytoskeleton is primarily responsible for the elastic properties75 while the cytoplasm is highly viscous in nature.57 These properties could theoretically be recapitulated in a hydrogel having a crosslink density gradient135 in combination with concentrated nanoparticles having an opposing concentration gradient.136 While no such material has yet been produced, and developing such a composite will be extremely challenging, it may represent the ideal solution for restoring accommodation. Significant age-related changes in other tissues involved in accommodation must also be noted: the vitreous liquefies with age,137 Bruch’s membrane may lose its elasticity,13 and the zonules stiffen with age.14 Some progress has already been made in restoring youthful mechanical properties to the vitreous,138 although repairing aged elastin may prove to be a larger obstacle.

5. Future directions Considerable progress in the understanding of accommodation and presbyopia has been made in recent years, even though significant questions persist. The relative contributions of lens growth, lens stiffening, and changes in the lens capsule remain to be elucidated. In particular, the optomechanical interaction between the capsule and the lens has been largely neglected up to this point. The role of ion and antioxidant transport has been studied extensively with respect to age-related nuclear cataract. However, the implications for presbyopia have not been explored to the same degree. There is increasing evidence that presbyopia is the first clinical symptom of age-related nuclear cataract.139 Most investigators studying the lens seek to understand, prevent, or treat cataract due to its ability to cause blindness. However, it is important to recognize that integration of what is known about both presbyopia and cataract may produce a more complete picture of lens aging. Development of new computational models of accommodation promises to catalyze understanding and treatments for presbyopia. Full realization of the potential of these models will require the collaborative efforts of engineers, clinicians, and scientists.

References 1. 2. 3.

Copyright © 2018. Kugler Publications. All rights reserved.

4.

5. 6.

7.

Gullstrand A. Helmholtz’s treatise on physiological optics. translated ed: The Optical Society of America; 1924. Helmholtz H. Uber die akkommodation des auges. Arch Ophthalmol. 1855;1:1-74. Kessler J. Experiments in refilling the lens. Arch Ophthalmol. 1964;71(1):412-417. Anderson HA, Gloria H, Adrian G, Stuebing Karla K, Manny Ruth E. Minus-lens-stimulated accommodative amplitude decreases sigmoidally with age: a study of objectively measured accommodative amplitudes from age 3. Invest Ophthalmol Vis Sci. 2008;49(7):2919-2926. Fisher RF. Presbyopia and the changes with age in the human crystalline lens. J Physiol. 1973;228(3):765-779. Dubbelman M, Heijde vd. The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox. Vision Res. 2001;41:1867-1877. Dubbelman M, van der Heijde GL, Weeber HA. Change in shape of the aging human crystalline lens with accommodation. Vision Res. 2005;45:117-132.

8.

9.

10. 11.

12. 13.

Glasser A, Campbell MC. Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia. Vision Res. 1999;39(11):1991-2015. Koretz JF, Cook CA, Kaufman PL. Accommodation and presbyopia in the human eye. Changes in the anterior segment and crystalline lens with focus. Invest Ophthalmol Vis Sci. 1997;38(3):569-578. Weale RA. On potential causes of presbyopia. Vision Res. 1999;39(7):1263-1272. Reilly MA. A quantitative geometric mechanics lens model: insights into the mechanisms of accommodation and presbyopia. Vision Res. 2014;103:20-31. Coleman DJ, Fish SK. Presbyopia, accommodation, and the mature catenary. Ophthalmology. 2001;108(9):1544-1551. Croft MA, McDonald JP, Katz A, Lin TL, Lutjen-Drecoll E, Kaufman PL. Extralenticular and lenticular aspects of accommodation and presbyopia in human versus monkey eyes. Invest Ophthalmol Vis Sci. 2013;54(7):5035-5048.

Copyright © 2018. Kugler Publications. All rights reserved.

Accommodation and presbyopia 14. Michael R, Marek M, Carlos G, Montenegro Gustavo A, Pinilla CL, Barraquer Rafael I. Elastic properties of human lens zonules as a function of age in presbyopes. Invest Ophthalmol Vis Sci. 2012;53(10):6109-6114. 15. Croft MA, Nork TM, McDonald JP, Katz A, Lutjen-Drecoll E, Kaufman PL. Accommodative movements of the vitreous membrane, choroid, and sclera in young and presbyopic human and nonhuman primate eyes. Invest Ophthalmol Vis Sci. 2013;54(7):5049-5058. 16. Executive Summary. Vision Research – A National Plan:19992003. Bethesda, MD. National Eye Institute; 1999. 17. Macsai MS, Fontes BM. Refractive enhancement following presbyopia-correcting intraocular lens implantation. Curr Opin Ophthalmol. 2008;19(1):18-21. 18. Menapace R, Findl O, Kriechbaum K, Ch L-K. Accommodating intraocular lenses: a critical review of present and future concepts. Graefe’s Arch Clin Exp Ophthalmol. 2007;245:473489. 19. Arlt E, Krall E, Moussa S, Grabner G, Dexl A. Implantable inlay devices for presbyopia: the evidence to date. Clin Ophthalmol. 2015;9:129-137. 20. Parel JM, Gelender H, Trefers WF, Norton EW. Phaco-Ersatz: cataract surgery designed to preserve accommodation. Graefes Arch Clin Exp Ophthalmol. 1986;224(2):165-173. 21. Nishi O, Nishi K, Mano C, Ichihara M, Honda T. Controlling the capsular shape in lens refilling. Arch Ophthalmol. 1997;115(4):507-510. 22. Koopmans SA, Terwee T, Glasser A, et al. Accommodative Lens Refilling in Rhesus Monkeys. Invest Ophthalmol Vis Sci. 2006;47(7):2976-2984. 23. Koopmans SA, Terwee T, Barkhof J, Haitjema HJ, Kooijman AC. Polymer refilling of presbyopic human lenses in vitro restors the ability to undergo accommodative changes. Invest Ophthalmol Vis Sci. 2003;44:250-257. 24. Koopmans SA, Thom T, Haitjema Henk J, Henk D, Sonja A, Kooijman Aart C. Relation between injected volume and optical parameters in refilled isolated porcine lenses. Ophthalmic Physiol Opt. 2004;24(6):572-579. 25. Reilly MA, Hamilton Paul D, Gavin P, Nathan R. Comparison of the behavior of natural and refilled porcine lenses in a robotic lens stretcher. Exp Eye Res. 2009;88(3):483-494. 26. Powell TA, Amini R, Oltean A, et al. Elasticity of the porcine lens capsule as measured by osmotic swelling. J Biomech Eng. 2010;132(9):91008. 27. Shi Y. The penny pusher: a cellular model of lens growth. Invest Ophthalmol Vis Sci. 2015;56(2):799-809. 28. Bassnett S, Shi Y. A method for determining cell number in the undisturbed epithelium of the mouse lens. Mol Vis. 2010;16:2294-2300. 29. Zhao H, Yang T, Madakashira BP, et al. Fibroblast growth factor receptor signaling is essential for lens fiber cell differentiation. Dev Biol. 2008;318(2):276-288. 30. Bassnett S. Three-dimensional reconstruction of cells in the living lens: the relationship between cell length and volume. Exp Eye Res. 2005;81(6):716-723.

303 31. Beebe DC, Vasiliev O, Guo J, Shui YB, Bassnett S. Changes in adhesion complexes define stages in the differentiation of lens fiber cells. Invest Ophthalmol Vis Sci. 2001;42(3):727734. 32. Bassnett S, Missey H, Vucemilo I. Molecular architecture of the lens fiber cell basal membrane complex. J Cell Sci. 1999;112(13):2155-2165. 33. Kuszak J, Zoltoski RK, Sivertson C. Fibre cell organization in crystalline lenses. Exp Eye Res. 2004;78(3):673-687. 34. Bassnett S. On the mechanism of organelle degradation in the vertebrate lens. Exp Eye Res. 2009;88(2):133-139. 35. Bassnett S. Fiber cell denucleation in the primate lens. Invest Ophthalmol Vis Sci. 1997;38(9):1678-1687. 36. Bassnett S. Lens organelle degradation. Exp Eye Res. 2002;74(1):1-6. 37. Hughes JR, Levchenko VA, Blanksby SJ, Mitchell TW, Williams A, Truscott RJ. Correction: No turnover in lens lipids for the entire human lifespan. Elife. 2015;4:e08186. 38. Truscott RJ, Zhu X. Presbyopia and cataract: a question of heat and time. Prog Retin Eye Res. 2010;29(6):487-499. 39. Bassnett S, Beebe DC. Coincident loss of mitochondria and nuclei during lens fiber cell differentiation. Dev Dyn. 1992;194(2):85-93. 40. Huang J, Rajagopal R, Liu Y, et al. The mechanism of lens placode formation: a case of matrix-mediated morphogenesis. Dev Biol. 2011;355(1):32-42. 41. Augusteyn RC. On the growth and internal structure of the human lens. Exp Eye Res. 2010;90(6):643-654. 42. Beers AP, van der Heijde RGL. In vivo determination of the biomechanical properties of the component elements of the accommodation mechanism. Vision Res. 1994;34:2897-2905. 43. Fincham EF. The mechanism of accommodation. Br J Ophthalmol. 1937;21:1-80. 44. Koretz JF, Handelman GH. How the human eye focuses. Sci Am. 1988;259(1):92-9. 45. Augusteyn RC. Growth of the human eye lens. Mol Vis. 2007;13:252-257. 46. Urs R, Manns F, Ho A, et al. Shape of the isolated ex-vivo human crystalline lens. Vision Res. 2009;49:74-83. 47. Fisher RF. The elastic constants of the human lens. J Physiol. 1971;212(1):147-180. 48. Heys KR, Leigh CS, Willis TRJ. Massive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia? Mol Vis. 2004;10:956-963. 49. Weeber HA, Gabriele E, Wolfgang P. Stiffness gradient in the crystalline lens. Graefes Arch Clin Exp Ophthalmol. 2007;245(9):1357-1366. 50. Weeber HA, Eckert G, Soergel F, Meyer CH, Pechhold W, van der Heijde RGL. Dynamic mechanical properties of human lenses. Exp Eye Res. 2005;80(2):425-434. 51. Wilde GS, Burd HJ, Judge SJ. Shear modulus data for the human lens determined from a spinning lens test. Exp Eye Res. 2012;97(1):36-48. 52. Chai CK, Burd HJ, Wilde GS. Shear modulus measurements on isolated human lens nuclei. Exp Eye Res. 2012;103:78-81.

Copyright © 2018. Kugler Publications. All rights reserved.

304 53. Soergel F, Meyer C, Eckert G, Abele B, Pechhold W. Spectral Analysis of Viscoelasticity of the Human Lens. J Refract Surg. 1999;15:714-716. 54. Ejiri M, Thompson HE, O’Neill WD. Dynamic Visco-Elastic Properties of the Lens. Vision Res. 1969;9:233-344. 55. Itoi M, Ito N, Kaneko H. Visco-elastic Properties of the Lens. Exp Eye Res. 1965;4(3):168-173. 56. Reilly MA, Nathan R. Microindentation of the young porcine ocular lens. J Biomech Eng. 2009;131(4):044502. 57. Reilly MA, Brian R, Hamilton Paul D, Shen Amy Q, Nathan R. Material characterization of porcine lenticular soluble proteins. Biomacromolecules. 2008;9(6):1519-1526. 58. Krag S, Andreassen TT. Mechanical properties of the human lens capsule. Prog Retin Eye Res. 2003;22:749-767. 59. Fisher RF. Elastic constants of the human lens capsule. J Physiol. 1971;201(1):1-19. 60. Dubbelman M, van der Heijde GL, Weeber HA. The thickness of the aging human lens obtained from corrected Scheimpflug images. Optom Vis Sci. 2001;78(6):411-416. 61. Smith WJ. Modern optical engineering: The design of optical systems. McGraw-Hill Inc.; 1990. 62. Shearer D, Ens W, Standing K, Valdimarsson G. Posttranslational modifications in lens fiber connexins identified by off-lineHPLC MALDI-quadrupole time-of-flight mass spectrometry. Invest Ophthalmol Vis Sci. 2008;49(4):1553-1562. 63. Slavi N, Rubinos C, Li L, et al. Connexin 46 (cx46) gap junctions provide a pathway for the delivery of glutathione to the lens nucleus. J Biol Chem. 2014;289(47):32694-32702. 64. Sweeney MH, Truscott RJ. An impediment to glutathione diffusion in older normal human lenses: a possible precondition for nuclear cataract. Exp Eye Res. 1998;67(5):587-595. 65. Grey AC, Schey KL. Age-related changes in the spatial distribution of human lens alpha-crystallin products by MALDI imaging mass spectrometry. Invest Ophthalmol Vis Sci. 2009;50(9):43194329. 66. Grey AC, Chaurand P, Caprioli RM, Schey KL. MALDI imaging mass spectrometry of integral membrane proteins from ocular lens and retinal tissue. J Proteome Res. 2009;8(7):3278-3283. 67. Thibault DB, Gillam CJ, Grey AC, Han J, Schey KL. MALDI tissue profiling of integral membrane proteins from ocular tissues. J Am Soc Mass Spectrom. 2008;19(6):814-822. 68. Truscott RJ, Comte-Walters S, Ablonczy Z, et al. Tight binding of proteins to membranes from older human cells. Age (Dordr). 2011;33(4):543-554. 69. Raguz M, Mainali L, O’Brien WJ, Subczynski WK. Lipid domains in intact fiber-cell plasma membranes isolated from cortical and nuclear regions of human eye lenses of donors from different age groups. Exp Eye Res. 2015;132:78-90. 70. Raguz M, Mainali L, O’Brien WJ, Subczynski WK. Lipid-protein interactions in plasma membranes of fiber cells isolated from the human eye lens. Exp Eye Res. 2014;120:138-151. 71. Mainali L, Raguz M, O’Brien WJ, Subczynski WK. Properties of membranes derived from the total lipids extracted from clear and cataractous lenses of 61-70-year-old human donors. Eur Biophys J. 2015;44(1-2):91-102.

M.A. Reilly 72. Mainali L, Raguz M, O’Brien WJ, Subczynski WK. Properties of membranes derived from the total lipids extracted from the human lens cortex and nucleus. Biochim Biophys Acta. 2013;1828(6):1432-1440. 73. Heys KR, Friedrich MG, Truscott RJ. Presbyopia and heat: changes associated with aging of the human lens suggest a functional role for the small heat shock protein, alpha-crystallin, in maintaining lens flexibility. Aging Cell. 2007;6(6):807815. 74. Reilly MA, Hamilton Paul D, Nathan R. Dynamic multi-arm radial lens stretcher: a robotic analog of the ciliary body. Exp Eye Res. 2008;86(1):157-164. 75. Candia OA. Surface and volume changes in the lens during accommodation. Invest Ophthalmol Vis Sci. 2011;52(6):3698. 76. Sheppard AL, Evans CJ, Singh Krish D, Wolffsohn James S, Dunne Mark CM, Davies Leon N. Three-dimensional magnetic resonance imaging of the phakic crystalline lens during accommodation. Invest Ophthalmol Vis Sci. 2011;52(6):3689-3697. 77. Gerometta R, Zamudio AC, Escobar DP, Candia OA. Volume change of the ocular lens during accommodation. Am J Physiol Cell Physiol. 2007;293(2):C797-C804. 78. Burd HJ, Wilde GS, Judge SJ. Can reliable values of Young’s modulus be deduced from Fisher’s (1971) spinning lens measurements? Vision Res. 2006;46(8-9):1346-1360. 79. Burd HJ, Wilde GS, Judge SJ. An improved spinning lens test to determine the stiffness of the human lens. Exp Eye Res. 2011;92(1):28-39. 80. Reilly MA, Martius P, Kumar S, Burd HJ, Stachs O. The mechanical response of the porcine lens to a spinning test. Zeitschrift für Medizinische Physik. 2016;26(2):127-135. 81. Sneddon IN. The Relation Between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile. Int J Eng Sci. 1965;3:47-57. 82. Huajian G, Chiu C-H, Lee J. Elastic contact versus indentation modeling of multi-layered materials. Int J Solids Struct. 1992;29(20):2471-2492. 83. King RB. Elastic analysis of some punch problems for a layered medium. Int J Solids Struct. 1987;23(12):1657-1664. 84. Ziebarth NM, Wojcikiewicz EP, Manns F, Moy VT, Parel JM. Atomic force microscopy measurements of lens elasticity in monkey eyes. Mol Vis. 2007;13:504-510. 85. Baradia H, Negin N, Adrian G. Mouse lens stiffness measurements. Exp Eye Res. 2010;91(2):300-307. 86. Gokhin DS, Nowak RB, Kim NE, et al. Tmod1 and CP49 synergize to control the fiber cell geometry, transparency, and mechanical stiffness of the mouse lens. PLoS One. 2012;7(11):e48734. 87. Fudge DS, McCuaig JV, Van Stralen S, et al. Intermediate filaments regulate tissue size and stiffness in the murine lens. Invest Ophthalmol Vis Sci. 2011;52(6):3860-3867. 88. Kumari SS, Gupta N, Shiels A, et al. Role of aquaporin 0 in lens biomechanics. Biochem Biophys Res Commun. 2015;462(4):339-345. 89. Vilupuru AS, Glasser A. Optical and biometric relationships of the isolated pig crystalline lens. Ophthalmic Physiol Opt. 2001;21(4):296-311.

Copyright © 2018. Kugler Publications. All rights reserved.

Accommodation and presbyopia 90. Reiss S, Burau G, Stachs O, Guthoff R, Stolz H. Spatially resolved Brillouin spectroscopy to determine the rheological properties of the eye lens. Biomed Opt Express. 2011;2(8):2144-2159. 91. Bailey ST, Twa MD, Gump JC, Venkiteshwar M, Bullimore MA, Sooryakumar R. Light-scattering study of the normal human eye lens: elastic properties and age dependence. IEEE Trans Biomed Eng. 2010;57(12):2910-2917. 92. Reiss S, Stachs O, Guthoff R, Stolz H. Non-invasive, spatially resolved determination of tissue properties of the crystalline lens with regard to rheology, refractive index, density and protein concentration by using Brillouin spectroscopy. Klin Monbl Augenheilkd. 2011;228(12):1079-1085. 93. Scarcelli G, Kim P, Yun SH. In vivo measurement of age-related stiffening in the crystalline lens by Brillouin optical microscopy. Biophys J. 2011;101(6):1539-1545. 94. Randall J, Vaughan JM. The measurement and interpretation of Brillouin scattering in the lens of the eye. Proc R Soc Lond B Biol Sci. 1982;214(1197):449-470. 95. Scarcelli G, Yun SH. In vivo Brillouin optical microscopy of the human eye. Opt Express. 2012;20(8):9197-9202. 96. Erpelding TN, Hollman KW, O’Donnell M. Mapping age-related elasticity changes in porcine lenses using bubble-based acoustic radiation force. Exp Eye Res. 2007;84(2):332-341. 97. Erpelding TN, Hollman KW, O’Donnell M. Spatially mapping the elastic properties of the lens using bubble-based acoustic radiation force. IEEE Ultrasonics Symp. 2005;1:613-616. 98. Yoon S, Aglyamov S, Karpiouk A, Emelianov S. A high pulse repetition frequency ultrasound system for the ex vivo measurement of mechanical properties of crystalline lenses with laser-induced microbubbles interrogated by acoustic radiation force. Phys Med Biol. 2012;57(15):4871-4884. 99. Wu C, Han Z, Wang S, et al. Assessing age-related changes in the biomechanical properties of rabbit lens using a coaligned ultrasound and optical coherence elastography system. Invest Ophthalmol Vis Sci. 2015;56(2):1292-1300. 100. Yoon S, Aglyamov S, Karpiouk A, Emelianov S. The mechanical properties of ex vivo bovine and porcine crystalline lenses: age-related changes and location-dependent variations. Ultrasound Med Biol. 2013;39(6):1120-1127. 101. Krag S, Andreassen TT. Biomechanical measurements of the porcine lens capsule. Exp Eye Res. 1996;62:253-260. 102. Krag S, Olsen T, Andreassen TT. Biomechanical characteristics of the human anterior lens capsule in relation to age. Invest Ophthalmol Vis Sci. 1997;38(2):357-63. 103. Fisher RF. The significance of the shape of the lens and capsular energy changes in accommodation. J Physiol. 1969;201:21-47. 104. Burd HJ. A structural constitutive model for the human lens capsule. Biomech Model Mechanobiol. 2009;8:217-231. 105. Gyoneva L, Segal Y, Dorfman KD, Barocas VH. Mechanical response of wild-type and Alport murine lens capsules during osmotic swelling. Exp Eye Res. 2013;113:87-91. 106. David G, Pedrigi RM, Heistand MR, Humphrey JD, Delange SL, Dziezyc J. Regional multiaxial mechanical properties of the porcine anterior lens capsule. J Biomech Eng. 2007;129(1):97104.

305 107. Heistand MR, Pedrigi RM, Delange SL, Dziezyc J, Humphrey JD. Multiaxial mechanical behavior of the porcine anterior lens capsule. Biomechan Model Mechanobiol. 2005;4:168177. 108. Pedrigi RM, Staff E, David G, Glenn S, Humphrey JD. Altered multiaxial mechanical properties of the porcine anterior lens capsule cultured in high glucose. J Biomech Eng. 2007;129(1):121-125. 109. Pedrigi RM, David G, Dziezyc J, Humphrey JD. Regional mechanical properties and stress analysis of the human anterior lens capsule. Vision Res. 2007;47:1781-1789. 110. Burd HJ, Regueiro RA. Finite element implementation of a multiscale model of the human lens capsule. Biomech Model Mechanobiol. 2015. 111. O’Neill WD, Doyle JM. A thin shell deformation analysis of the human lens. Vision Res. 1968;8(2):193-206. 112. Burd HJ, Judge SJ, Cross JA. Numerical modelling of the accommodating lens. Vision Res. 2002;42(18):2235-2251. 113. Hermans EA, Dubbelman M, van der Heijde GL, Heethaar RM. Estimating the external force acting on the human eye lens during accommodation by finite element modelling. Vision Res. 2006;46(21):3642-3650. 114. Hermans EA, Dubbelman M, van der Heijde GL, Heethaar RM. Change in the accommodative force on the lens of the human eye with age. Vision Res. 2008;48(1):119-126. 115. Weeber HA. On the relationship between lens stiffness and accommodative amplitude. Exp Eye Res. 2007;85(5):602-607. 116. Ljubimova D, Eriksson A, Bauer S. Aspects of eye accommodation evaluated by finite elements. Biomech Model Mechanobiol. 2008;7(2):139-150. 117. Ljubimova D. Numerical modelling of the human eye accommodation. 2005. 118. Chien CHM, Huang T, Schachar RA. Analysis of human crystalline lens accommodation. J Biomech. 2006;39:672-680. 119. Reilly MA, Nathan R. A geometric model of ocular accommodation. Vision Res. 2010;50(3):330-336. 120. Wilkes R, MatthewA R. A pre-tensioned finite element model of ocular accommodation and presbyopia. Int J Adv Eng Sci Appl Math. 2015:1-14. 121. Wilkes RP. A whole eye finite element analysis of accommodation [dissertation]. [San Antonio (TX)]: The University of Texas at San Antonio; 2014. 148 p. 122. Glasser A, Kaufman PL. The Mechanism of Accommodation in Primates. Ophthalmology. 1999;106:863-872. 123. Glasser A, Troilo D, Howland HC. The mechanism of corneal accommodation in chicks. Vision Res. 1994;34(12):1549-1566. 124. Strenk SA, Strenk LM, Koretz JF. The mechanism of presbyopia. Prog Retin Eye Res. 2005;24:379-393. 125. Sunderland HR, O’Neill WD. Functional Dependence of Optical Parameters on Circumferential Forces in the Cat Lens. Vision Res. 1976;16:1151-1158. 126. Roorda A, Glasser A. Wave aberrations of the isolated crystalline lens. J Vision. 2004;4(4):250-261. 127. Fisher RF. The Force of Contraction of the Human Ciliary Muscle During Accommodation. J Physiol. 1977;270:51-74.

306

Copyright © 2018. Kugler Publications. All rights reserved.

128. Pierscionek BK. Age-related Response of Human Lenses to Stretching Forces. Exp Eye Res. 1995;60:325-332. 129. Pierscionek BK. In Vitro Alteration of Human Lens Curvatures by Radial Stretching. Exp Eye Res. 1993;57:629-635. 130. Augusteyn RC, Mohamed A, Nankivil D, et al. Age-dependence of the optomechanical responses of ex vivo human lenses from India and the USA, and the force required to produce these in a lens stretcher: the similarity to in vivo disaccommodation. Vision Res. 2011;51(14):1667-1678. 131. Manns F, Parel JM, Denham D, et al. Optomechanical Response of Human and Monkey Lenses in a Lens Stretcher. Invest Ophthalmol Vis Sci. 2007;48:3260-3268. 132. Schachar RA. Qualitative effect of zonular tension on freshly extracted intact human crystalline lenses: implications for the mechanism of accommodation. Invest Ophthalmol Vis Sci. 2004;45:2691-2695. 133. Pinilla Cortes L, Burd HJ, Montenegro GA, et al. Experimental protocols for ex vivo lens stretching tests to investigate the biomechanics of the human accommodation apparatus. Invest Ophthalmol Vis Sci. 2015;56(5):2926-2932.

M.A. Reilly 134. Moffat BA, Atchison DA, Pope JM. Age-related changes in refractive index distribution and power of the human lesn as measured by magnetic resonance micro-imaging in vitro. Vision Res. 2002;42(13):1683-1693. 135. Ravi N, Hamilton PD, Reilly MA. Characterization of a new nanocomposite projected as an accommodative lens refilling material. Invest Ophthalmol Vis Sci. 2007;48:E-abstract 980. 136. Ravi N, Aliyar H, Hamilton PD. Hydrogel nanocomposite as a synthetic intra-ocular lens capable of accommodation. Macromol Symp. 2005;227:191-201. 137. Sebag J. Age-related changes in human vitreous structure. Graefes Arch Clin Exp Ophthalmol. 1987;225(2):89-93. 138. Zhang Q, Filas BA, Roth R, et al. Preservation of the structure of enzymatically-degraded bovine vitreous using synthetic proteoglycan mimics. Invest Ophthalmol Vis Sci. 2014;55(12):81538162. 139. McGinty SJ, Truscott RJ. Presbyopia: the first stage of nuclear cataract? Ophthalmic Res. 2006;38(3):137-148.

21. Biomechanics of the lens and its role in accommodation Noël M. Ziebarth1, Vivian M. Sueiras1, Vincent T. Moy2, Fabrice Manns1,3, Jean-Marie Parel1,3 Department of Biomedical Engineering, University of Miami College of Engineering, Miami, FL, USA; 2Department of Physiology and Biophysics, University of Miami Miller School of Medicine, Miami, FL, USA; 3Ophthalmic Biophysics Center, Bascom Palmer Eye Institute, University of Miami Miller School of Medicine, Miami, FL, USA

1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction Accommodation is the ability of the eye to dynamically change its focus to view near objects. According to the Helmholtz theory of accommodation, the ciliary muscles contract and the lens suspensory ligaments, called the zonules, relax during near vision.1 This combined action releases the tension on the lens capsule, enabling it to contract and increase the anterior and posterior curvatures of the lens. The refractive power of the lens increases as a result of the increase in lens curvatures. This higher power lens is now able to successfully focus on objects located at closer distances. As a person ages, the ability to accommodate gradually diminishes until it is completely lost. The loss of accommodation commences at birth, but it does not become symptomatic until around the age of 40. The loss of accommodation is referred to as presbyopia when it leads to the loss of near vision.2,3 It is generally accepted that the loss of accommodation is due to normal, age-related optical and physical changes of the lens, lens capsule, ciliary muscle, and zonules. It is known that the lens undergoes many profound changes with age: increased mass,4 increased thickness,5-10 increased stiffness,11-20 and changes in posterior and anterior curvatures8,21 and refractive index distribution.22,23 The capsule also undergoes many changes during the aging process: it increases in thickness,2,24-26 becomes less elastic, and has decreased tensile strength.25,27 Lens and capsule-based theories of

presbyopia assume that the age-related changes of the ciliary muscle and zonules are insignificant compared to those changes in the lens and capsule. These theories of presbyopia suggest that a main factor in the loss of accommodation is the decreased elasticity of both the lens and capsule with age. As the stiffness of the lens increases, the capsule is no longer an effective transmitter of the forces from ciliary muscle contraction during accommodation.1,2,28-31

2. The lens 2.1. Basic anatomy The lens is a transparent, avascular body located between the iris and the vitreous.32 Development of the lens begins as early as day 28 of human gestation with the formation of the lens placode.33 The placode eventually closes off to form the lens vesicle, an enclosed bag lined with ectodermal cells. This bag will become the lens capsule of the developed lens. Differentiation of the ectodermal cells results in a layer of epithelial cells in the anterior and peripheral regions, and primary lens fiber cells in the posterior region. The lens epithelial cells at the lens periphery continue to proliferate after birth, differentiating into the lens fiber cells that make up the bulk of the lens material.33 As new fiber cells are added to the lens, the older cells are displaced towards the center of the lens. These older fiber cells eventually lose their cellular organelles and,

Correspondence:Noël M. Ziebarth, PhD, McArthur Engineering Annex, Room 219, 1251 Memorial Drive, Coral Gables, FL 33146, USA E-mail: [email protected] Biomechanics of the Eye, pp. 307-318 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

N.M. Ziebarth et al.

308

Copyright © 2018. Kugler Publications. All rights reserved.

Table 1. Summary of human lens elasticity measurements. Only studies where Young’s modulus of elasticity was directly measured or could be calculated from the presented results are included. Study

Method

Age range (years)

Young’s Modulus (Pa)

Itoi et al.44

Rheometry

85

10,000-100,000

Fisher16

Lens spinning

0-67

432-3,634

Van alphen and Graebel52

Uniaxial stretching

18, 49

4400, 10,900

Heys et al.11

DMA

14-76

146-7,731 (cortex) 77-71,862 (nucleus)

Weeber et al.14

DMA

18-90

533-950,000 (cortex)

Hollman et al.53

Bubble-based acoustic radiation force

40, 63-70

5200, 10,600

consequently, metabolic activity comes to an end.33,34 With age, the older fiber cells form a dense nucleus with a decreased concentration of water, a condition known as sclerosis.35 The continued proliferation of lens fiber cells throughout life results in several changes in the lens biometry. Studies on human lens dimensions both in vivo and in vitro using magnetic resonance imaging,7,10 digital imaging,5,8 and optical coherence tomography9 concur that the lens diameter increases significantly with age. The lens thickness decreases until approximately 13 years of age, and then begins to increase.5-10 Growth of the lens also results in an increase in anterior and posterior curvature of the relaxed lens in vivo.5,8,36,37 Despite the increased lens curvature, the power of the lens remains constant with age, a phenomenon known as the lens paradox.38-40 Many studies suggest that the lens paradox is due to changes in the refractive index distribution.7,39 The refractive index profiles become flatter in the central region of the lens with increasing age.7,33 The increasing refractive index plateau in the lens center provides evidence for an increasing nuclear region.33 2.2. Lens biomechanics 2.2.1. Significance Continued growth of the lens with age creates a densely packed structure contained within the lens capsule. Consequently, the lens becomes less compliant with age. In fact, studies have found unequivocally that the

lens stiffness increases by several orders of magnitude throughout the lifetime of an individual.11,13,14,16 Accommodation cannot occur if the lens cannot undergo the necessary changes in thickness and curvature.1,2,28,29 In the young eye, the modulus of elasticity of the lens is several orders of magnitude less than that of the capsule.11,14,16,25,30 Therefore, the lens capsule is effective at transmitting the forces of contraction of the ciliary body.30,31,41,42 With age, the lens modulus of elasticity increases at a much faster rate than that of the lens capsule, and the capsule modulus of elasticity eventually becomes lower than that of the inner lens material. The onset of presbyopia may represent the point in an individual’s lifetime when Young’s modulus of the lens exceeds that of the capsule, and the capsule can no longer effectively transmit forces from the ciliary muscle.30,31 2.2.2. Lens elasticity and viscoelasticity The elasticity and viscoelasticity of the lens have been extensively studied ex vivo. Methods employed include rheometry,43-46 spinning,16,47-49 squeezing,5,15,50,51 uniaxial stretching,52 bubble-based acoustic radiation force,53-56 ultrasonic attenuation,57 dynamic mechanical analysis,11-14,58,59 atomic force microscopy,60,61 optical coherence elastography,20 and Brillouin microscopy.17,62 The measured elasticity of the human lens is presented in Table 1 for those studies in which Young’s modulus of elasticity, a standard mechanical property, was directly measured or could be calculated from the presented results. Due to variations introduced by the tissue

Copyright © 2018. Kugler Publications. All rights reserved.

Biomechanics of the lens and its role in accommodation

preparation, storage, changes in hydration, handling, postmortem time, as well as inherent differences in the methodologies themselves, the measured values of lens elasticity vary by orders of magnitude. Therefore, it is not possible to directly compare quantitative measurements found by different investigators. However, when comparing results obtained by the same researchers using the same techniques, relative values of lens elasticity can be used to study age-related changes in lens compliance. All these previous studies, despite differences in methodologies, have shown that the lens becomes significantly stiffer with age. This phenomenon is most likely a major factor in the development of presbyopia. As is the case with many soft biological tissues, the lens has been demonstrated to exhibit typical viscoelastic behavior.43-45 During compression, the lens deformation increases with time after the applied stress, a phenomenon known as creep.44 Once the stress is unloaded, the lens gradually recovers over time. Previous studies have found that the lens behaves as a linear viscoelastic body up to deformations of 0.03 mm, after which point it starts to behave in a non-linear fashion.43,44 Since the maximal deformation of the human lens during accommodation is approximately 0.5 mm, the lens most likely behaves as a non-linear viscoelastic body in vivo.44,63 The observed viscoelastic behavior is due to the interactions between the fiber cell component (elastic response) and the intra and intercellular fluid (viscous response).45 The earliest viscoelastic measurements of human lenses found that young lenses are more viscous than older lenses.43 This conclusion was later confirmed by Soergel et al.,58 who measured that the dynamic response of younger lenses included a significant viscous flow component. Czygan and Hartung45 found specifically that the creep response of the lens exhibited two time constants, on the order of 0.5 s and 100 s. However, later investigations used a Maxwell mechanical model, a spring and a dashpot in series, to describe the dynamic behavior of the lens. Using this model, three time constants, corresponding to three Maxwell elements connected in parallel, were necessary to most accurately describe the behavior of the lens.14,15,58 All three of these time constants decrease with age, signifying that the relaxation process of the lens becomes faster with age.14,15 In addition, Soergel

309

Fig. 1. Shear modulus trend as a function of distance from the lens center for different aged individuals.13

et al.58 detected that the three different types of relaxation processes shift towards lower frequencies in stiffer lenses, indicating that stiffer lenses have a slower accommodation response. 2.2.3. Gradient mechanical properties of the lens Lens growth continues throughout the lifetime of the individual, creating a gradient of fiber cell age.64 Older fiber cells that have already lost their organelles and undergone sclerosis are in the center, and young fiber cells that have recently differentiated are toward the outside. It would therefore be expected that the lens mechanical properties across its axes vary with position. In fact, previous studies have demonstrated that the lens has a gradient of mechanical properties across its longitudinal axis, and that this gradient changes with age. At a young age, the lens cortex and nucleus have similar values of Young’s modulus of elasticity.11,13 With increasing age, this elasticity profile changes, resulting in a lens nucleus that is much stiffer than the lens cortex.11,13,17,53 In addition, the central stiffer region becomes wider with increasing age, creating a plateau of higher stiffness (Fig. 1). We have also performed experiments using atomic force microscopy to investigate the lens stiffness gradient. We demonstrated that the stiffness of the lens cortex increases as you moved towards the center (unpublished results). The outer lens cortex elasticity of 14 lenses from 11 humans (age range: 34-79 years) was measured in the central anterior pole of the lens after performing a capsulorhexis. The measured Young’s

N.M. Ziebarth et al.

310

Copyright © 2018. Kugler Publications. All rights reserved.

Table 2. Summary of human lens capsule elasticity measurements. Only studies where Young’s modulus of elasticity was directly measured or could be calculated from the presented results are included. Study

Method

Age range (years)

Young’s Modulus, Anterior (MPa)

Fisher30

Pressure loading

1-80

2.0-6.0

Krag et al.25

Uniaxial stretching

1-98

0.4-2.5

Danielsen84

Pressure loading

80 ± 10

2.4 ± 0.27

Candiello et al.88

Atomic force microscopy

40-80

2.70-4.37

Ziebarth et al.89

Atomic force microscopy

33-79

0.022-0.131

Haritoglou et al.90

Atomic force microscopy

from cataract patients

average: 0.207

Tsaousis et al.91

Atomic force microscopy

75±4

0.1-0.85

modulus of elasticity of the outer lens cortex was independent of age. For one representative lens from a 62-year-old human, a femtosecond laser was used to section the lens at a depth of 1.5 mm, corresponding to approximately 25% of the total thickness of the lens. At this depth, the lens cortex was approximately nine times stiffer than in the outer region. It is known that the proliferation and differentiation of lens epithelial cells continues throughout life, producing new fiber cells. The newest fiber cells create the outermost layer of the lens cortex. The measurements of outer lens cortex will always correspond to the youngest fiber cells, independent of age, so it therefore would be expected that the elasticity of the new fiber cells would be constant. The stiffer value obtained for the cortex at a depth of 25% in the lens material demonstrates the presence of a gradient of mechanical properties. The significant changes in the lens mechanical property profile with age have been directly correlated to accommodative amplitude.65 Using finite element modeling, Weeber and van der Heijde65 showed that the increase in overall lens stiffness with age is not sufficient to explain the corresponding loss of accommodation in vivo. A lens with uniformly increasing stiffness will only result in a linear decrease in accommodative amplitude. When the lens stiffness gradient is introduced into the model, it can now accurately predict the accelerated loss of accommodative amplitude after 40 years of age. This finding is important because it shows that it is the changing stiffness gradient, not the changing stiffness, which is responsible for the loss of accommodation with age. This finding also has significance for surgeries

and implants under development for the correction of presbyopia. Weeber and van der Heijde’s65 findings suggest that approaches that attempt to restore accommodation by replacing the lens with a homogeneous material or by softening the lens need to either preserve the gradient or find an “equivalent” stiffness. A recent finite element modeling study demonstrated that accommodative amplitude can be mathematically expressed as a function of a uniform refractive index and uniform elasticity. This signifies that infinite combinations of elasticity and refractive index exist to provide a certain degree of accommodation.66

3. The lens capsule 3.1. Basic anatomy The structural integrity of the lens is maintained by the lens capsule, which completely encloses the lens material. The lens capsule is classified as the thickest basement membrane in the body, forming the substratum of the lens epithelial cells in the anterior region. Its thickness is not uniform, however: the lens capsule is thickest anteriorly, and the anterior and posterior portions become thicker towards the periphery.2 Researchers have found that the thickness of the anterior lens capsule increases with age,24-26 although there is some debate as to whether or not the thickness begins to decrease again later in life.24,25 The posterior capsule does not exhibit dependence with age.26,27 The lens capsule is composed of networks of laminin,67-71 collagen IV,67,72,73 entactin/nidogen,67,68,74

Biomechanics of the lens and its role in accommodation

311

perlecan,67,75-77 collagen XVIII,78 collagen XV,79 and agrin.80 Collagen type IV is the most abundant component,73 making up 30-40% of the lens capsule’s dry weight.81 3.2. Lens capsule biomechanics

Copyright © 2018. Kugler Publications. All rights reserved.

3.2.1. Significance Since it is the capsule that maintains the shape of the lens, it plays an important role in accommodation. The lens capsule distributes the forces of contraction from the ciliary muscle during accommodation to the underlying lens material. Studies that measured the lens profiles of decapsulated lenses at different ages demonstrate the capsule’s impact on accommodation. In younger eyes, the capsule maintains the lens in the fully accommodated state; removing it results in an unaccommodated lens form. In contrast, removing the capsule from an older lens has virtually no effect on lens shape.5,35 Lens and capsule-based theories of presbyopia agree that the mechanical properties of the capsule, and their changes with age, play an important role in changing lens shape during accommodation.1,2,28-31 3.2.2. Lens capsule elasticity and viscoelasticity As with the lens, the lens capsule is known to exhibit a viscoelastic, time-dependent behavior.82 The capsule is more compliant when it is stretched slowly than when it is stretched quickly. The capsule will return to its original shape after the deforming force has been removed (elastic response), but it will take time for this to occur (viscous response). The elasticity of the lens capsule is due predominately to the organization of the collagen molecules: the N- and C- terminal ends of the molecules interact to form a continuous beehive structure.83 The viscous response is due to the matrix, which contains water, proteoglycans, and glycoproteins.82 The strength and elasticity of the lens capsule have been previously investigated using pressure loading,30,84,85 uniaxial stress-strain analysis,86,87 atomic force microscopy,88-91 swelling,92 and by stretching capsular rings25 or openings93-97. Classic experiments by Fisher30 measured Young’s modulus of elasticity using a volume-strain principle. In these experiments, the capsule was clamped between two plates and distended by injecting balanced salt solution; the pressure-volume relationship was then recorded.

Fig. 2. Young’s modulus of elasticity of the human and non-human anterior lens capsule. The data from all three species was analyzed together using a scaling factor of one monkey year to three human years. Young’s modulus of elasticity of the combined data significantly increases with age.89

Using this setup, Fisher determined that Young’s modulus of elasticity decreases from 6.0 MPa to 1.5 MPa with age. Subsequent investigations using the same technique84,85 determined that Fisher’s measurements were performed in the non-linear regime of the stress-strain curve (> 10% strain). Therefore, the values obtained were not accurate indicators of Young’s modulus of elasticity of the capsule. Various researchers using a number of different techniques all concur that the Young’s modulus of elasticity of the anterior lens capsule increases significantly with age. The elasticity of the posterior lens capsule has only been studied by Krag et al.,27 but these measurements show that the posterior lens capsule also becomes stiffer with age. Values of Young’s modulus of the human anterior lens capsule reported in the literature are given in Table 2. Our results on human and non-human primate lens capsules using atomic force microscopy are shown in Figure 2. The increase in stiffness of the lens capsule with age can be explained by its beehive structure, consisting of collagen molecules. This structure is stabilized by sulfide bridges and intermolecular crosslinks at the ends of the molecules. With the aging process, the number of disulfide bridges increases, which may help to explain the capsule’s loss of elasticity with age.83 A recent study using atomic force microscopy found that the interfibrillar spacing of the collagen fibers of the primate anterior lens capsule significantly decreased

312

N.M. Ziebarth et al.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. Images of the human lens capsule for donors ranging in age from 36 years old to 88 years old. The structure becomes less ordered with age. In addition, with increasing age, the distance between collagen fibers decreases, indicating compaction of the material.

with age, indicating that the structure becomes more compact.98 Figure 3 shows representative images of the lens capsule for human cadaver eyes ranging in age from 36 to 88 years, illustrating that the structure becomes less organized and more compact. It is likely that these variations in lens capsule structure with age impact the measured mechanical properties. Previous measurements of lens capsule elasticity measured the bulk response or the response at a discrete location on the surface. A study by Pedrigi et al.85 investigated the anisotropy of the lens capsule mechanical properties. They found that lens capsule stiffness is greater as you move towards the lens equator in the circumferential direction when compared to the meridional direction. They hypothesize that the regional variations in lens capsule mechanical properties help homogenize the stress coming from the ciliary muscle during accommodation. Experience during cataract surgery provided the first evidence of the viscoelastic behavior of the lens capsule. Slowly stretching the capsulorhexis during phacoemulsification results in increased compliance of the capsule. Krag et al.82 suggested that this viscoelastic response of the lens capsule makes it ideal to transform locally applied forces from the ciliary muscle into a uniform force at the lens surface during accommodation. Krag and colleagues quantified the viscoelasticity of the human anterior lens capsule during uniaxial stress relaxation experiments. When comparing the results from 14 anterior lens capsules from donors ranging in age from 4 years to 82 years, no association could be found with age. This result suggests that, with age, the capsule maintains its ability to absorb and relax stress accumulations during accommodation. We developed a special mathematical model of accommodation (unpublished results), based on that of

O’Neill and Doyle.99 Simulating accommodation using the mathematical model showed that the predicted change in the anterior surface power during accommodation decreases significantly with age. However, when accommodation is completely lost at 50 years old, the predicted change in anterior surface power is still nearly 5 diopters. This demonstrates that the lens capsule mechanical properties do not greatly limit the accommodative ability of the lens. These results mean that accommodative ability will be lost even if the mechanical properties of the capsule remain constant.

4. Lens and lens capsule mechanical properties in accommodation Previous research has shown that the mechanical properties of the lens and the lens capsule change significantly with age. Finite element modeling studies have linked the loss of accommodative amplitude to the increase in stiffness of the lens as well as the shift in the stiffness profile. Conversely, models have shown that the changing lens capsule mechanical properties do not significantly impact the ability of the lens to accommodate. Through ex-vivo simulation of accommodation, several researchers have been able to link the increased stiffness of the lens and the loss of accommodative amplitude. To gain insight into the mechanism of accommodation, several researchers have developed devices that can simulate accommodation ex vivo while measuring lens shape, power, and the force of contraction of the ciliary body. One of the first such devices, designed by Fisher,100 radially stretched human lenses from eight quadrants to simulate the forces applied on the lens during accommodation. The results of this study

Biomechanics of the lens and its role in accommodation

313

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. General view of the lens-stretching system (top) and close-up view of the tissue chamber (bottom). The sclera is stretched using a system of pulleys. The optical power is measured using an optical system that relies on the Scheiner principle. The lens diameter is measured on digitized video images acquired using a frame grabber.103

showed that 50% more force applied to the ciliary muscle is required to produce power changes in older lenses. Van Alphen and Graebel52 found similar results during uniaxial simulation of accommodation applied to the ciliary body-lens-ciliary body combination: the force required for 10% elongation of lens increased one order of magnitude by 50 years of age. Pierscionek101,102 designed a motorized device to measure changes in lens thickness and curvature during stretching using eight stepper motors to exert radial pulling forces on human lens specimens consisting of the lens, zonules, and ciliary body. Results from this study indicate that younger lenses have a greater response to stretching forces than older lenses, meaning that older lenses cannot undergo the shape changes required during accommodation. Similar results were later found by Glasser and Campbell103 using their stretching apparatus: older lenses showed no changes in focal length with stretching. Since force was not measured in either of these studies, the results cannot be directly linked to lens mechanical properties. Additional lens stretching systems have been developed in recent years. Rafael Barraquer and colleagues constructed a system with hooks that connect to the tissue and exert radial stretching forces on the tissue.104,105 Using a webcam, radial changes in the crystalline lens and the ciliary body during stretching could be determined. Preliminary results on

human lenses showed that the force versus displacement response was different for lenses aging from 45 to 82 years. Their study also found a relationship between response and postmortem time, which is an important consideration for these types of experiments.105 Reilly et al. developed a similar stretcher, but the tissue was stretched with eight independent, motorized arms.106-108 Anterior and posterior radii of curvature, thickness, and diameter of the lens were recorded during stretching. The studies by Reilly and colleagues were only performed on porcine eyes, mainly to see differences between natural vs refilled lenses.108 We developed a system that combines the capabilities of these previous systems: changes in lens power, diameter, and thickness can be quantified while simultaneously recording the force required to stretch the ciliary body-lens-ciliary body combination (Figs. 4 and 5).109 We found that the force required to change the shape and power of the lens increases with age. Since the change in inner ciliary body diameter per unit force was independent of age, the age-related changes in the force required to stretch the lenses must be due to changes in the mechanical properties of the lens. These results were later confirmed by Augusteyn et al.110 using the same lens stretching system, but on a larger group of samples from both the United States and India. Our lens stretching system was also used to quantify the ability of the lens capsule to stretch during

N.M. Ziebarth et al.

314

10 8

Cynomolgus #20-OS Age: 10 years Average of 3 runs

12.0 11.5

Cynomolgus #20-OS Age: 10 years Average of 3 runs

Diameter (mm)

Load (g)

11.0

6 4 2

10.5 10.0 9.5 Ciliary Body

9.0 8.5 8.0

0

Lens

7.5

0.0

0.5

1.0

1.5

2.0

0.0

10

12.0

Eye Bank Eye #07-OD Age: 14 years Average of 3 runs

11.5

Diameter (mm)

Load (g)

1.0

1.5

2.0

Displacement (mm)

Displacement (mm)

8

0.5

6 4 2

Eye Bank Eye #07-OD Age: 14 years Average of 3 runs Ciliary Body

11.0 10.5 10.0 9.5 9.0 8.5

Lens

8.0

0

7.5

0.0

0.5

1.0

1.5

2.0

Displacement (mm)

0.0

0.5

1.0

1.5

2.0

Displacement (mm)

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. Typical changes in load (left) and lens and inner ciliary body diameter (right) as a function of the displacement of the translation stage for a cynomolgus monkey (top) and a young human (bottom) eye. Each curve corresponds to the average of three or five successive stretching cycles. Error bars show the standard deviation.103

simulation of accommodation.111 Ex-vivo measurements of lens capsule elasticity have demonstrated that it becomes stiffer with age. However, it was not known if these changes in mechanical properties are relevant during accommodation. This information is especially important for the success of procedures designed to restore accommodation, such as lens refilling. These procedures rely on the assumption that the loss of elasticity of the lens capsule with age does not have a significant effect on the loss of accommodative amplitude. The results showed that there was no relationship between the force necessary to stretch

the empty lens capsule and age, indicating that the lens capsule may retain the potential to produce accommodation if the lens retains its ability to undergo accommodation.111

5. Summary and conclusions The decreased elasticity of the lens and capsule is thought to be an important cause of the age-related loss of accommodation. The loss of lens and capsule elasticity results in the inability of the lens capsule to

Biomechanics of the lens and its role in accommodation

mold the lens material, which is necessary for the lens shape changes during accommodation. Studies have shown that both the lens and lens capsule stiffness increase significantly with age. Studies have further demonstrated that the lens possesses a stiffness gradient and that this gradient changes with age. Ex-vivo simulation of accommodation has shown that even increased force applied to the lens from older individuals is insufficient to change it shape. These experimental observations coincide with findings using finite element modeling: stiffer lens material cannot change shape, especially when the gradient mechanical properties are introduced into the model. On the other hand, ex-vivo simulation of accommodation and mathematical models of accommodation have shown that the lens capsule maintains its ability to stretch during accommodation, despite changes

References

Copyright © 2018. Kugler Publications. All rights reserved.

1.

Glasser A, Kaufman PL. Accommodation and presbyopia. In: Kaufman PL, Alm A, eds. Adler’s Physiology of the Eye, Clinical Applications. Vol 10th. St. Louis, MO: Mosby; 2003:197. 2. Fincham EF. The mechanism of accommodation. British Journal of Ophthalmology. 1937;Monograph Supplement VIII. 3. Wyatt HJ. Some aspects of the mechanics of accommodation. Vision Res. 1988;28(1):75-86. 4. Scammon REH, M.S. Growth in mass and volume of the human lens in postnatal life. Arch Ophthalmol. 1937;17:104-112. 5. Glasser A, Campbell MC. Biometric, optical and physical changes in the isolated human crystalline lens with age in relation to presbyopia. Vision Res. 1999;39(11):1991-2015. 6. Dubbelman M, Van der heijde GL, Weeber HA. The thickness of the aging human lens obtained from corrected Scheimpflug images. Optom Vis Sci. 2001;78(6):411-416. 7. Jones CE, Atchison DA, Meder R, Pope JM. Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI). Vision Res. Aug 2005;45(18):2352-2366. 8. Rosen AM, Denham DB, Fernandez V, et al. In vitro dimensions and curvatures of human lenses. Vision Res. 2006;46(6-7):10021009. 9. Uhlhorn SR, Borja D, Manns F, Parel JM. Refractive index measurement of the isolated crystalline lens using optical coherence tomography. Vision Res. Dec 2008;48(27):2732-2738. 10. Strenk SA, Semmlow JL, Strenk LM, Munoz P, Gronlund-jacob J, Demarco JK. Age-related changes in human ciliary muscle and lens: a magnetic resonance imaging study. Invest Ophthalmol Vis Sci. 1999;40(6):1162-1169.

315

in mechanical properties with age. These findings are hopeful for groups developing lens substitutes or methods to soften the lens for restoration of accommodation. However, the viscoelasticity of the lens and lens capsule remain poorly understood due to the need to employ destructive or indirect measurement techniques which may alter the tissue’s mechanical properties and the complexity of the accommodative structures. The contribution of age-related changes in lens and capsule biomechanics in accommodation and presbyopia is also still poorly understood. More reliable measurements and more comprehensive mechanical models that take into account the complex geometry and heterogeneous nature of the accommodative tissues, their microstructure, and their changes with age are needed.

11. Heys KR, Cram SL, Truscott RJ. Massive increase in the stiffness of the human lens nucleus with age: the basis for presbyopia? Mol Vis. 2004;10:956-963. 12. Heys KR, Truscott RJ. The stiffness of human cataract lenses is a function of both age and the type of cataract. Exp Eye Res. 2008;86(4):701-703. 13. Weeber HA, Eckert G, Pechhold W, van der Heijde RG. Stiffness gradient in the crystalline lens. Graefe’s archive for clinical and experimental ophthalmology = Albrecht von Graefes Archiv fur klinische und experimentelle Ophthalmologie. 2007;245(9):1357-1366. 14. Weeber HA, Eckert G, Soergel F, Meyer CH, Pechhold W, van der Heijde RG. Dynamic mechanical properties of human lenses. Exp Eye Res. 2005;80(3):425-434. 15. Sharma PK, Busscher HJ, Terwee T, Koopmans SA, van Kooten TG. A comparative study on the viscoelastic properties of human and animal lenses. Exp Eye Res. Nov 2011;93(5):681-688. 16. Fisher RF. The elastic constants of the human lens. J Physiol. Jan 1971;212(1):147-180. 17. Besner S, Scarcelli G, Pineda R, Yun SH. In Vivo Brillouin Analysis of the Aging Crystalline Lens. Invest Ophthalmol Vis Sci. Oct 01 2016;57(13):5093-5100. 18. Pau H, Kranz J. The increasing sclerosis of the human lens with age and its relevance to accommodation and presbyopia. Graefes Arch Clin Exp Ophthalmol. 1991;229(3):294-296. 19. Yoon S, Aglyamov S, Karpiouk A, Emelianov S. The mechanical properties of ex vivo bovine and porcine crystalline lenses: age-related changes and location-dependent variations. Ultrasound Med Biol. Jun 2013;39(6):1120-1127.

Copyright © 2018. Kugler Publications. All rights reserved.

316 20. Wu C, Han ZL, Wang S, et al. Assessing Age-Related Changes in the Biomechanical Properties of Rabbit Lens Using a Coaligned Ultrasound and Optical Coherence Elastography System. Invest Ophthalmol Vis Sci. Feb 2015;56(2):1292-1300. 21. Borja D, Manns F, Ho A, et al. Optical power of the isolated human crystalline lens. Invest Ophthalmol Vis Sci. Jun 2008;49(6):2541-2548. 22. de Castro A, Siedlecki D, Borja D, et al. Age-dependent variation of the Gradient Index profile in human crystalline lenses. J Mod Opt. 2011;58(19-20):1781-1787. 23. Birkenfeld J, de Castro A, Marcos S. Astigmatism of the ex vivo human lens: surface and gradient refractive index age-dependent contributions. Invest Ophthalmol Vis Sci. Aug 2015;56(9):5067-5073. 24. Salzmann M. Anatomy and histology of the human eyeball in the normal state: Its development and senescence. Chicago: University of Chicago Press; 1912. 25. Krag S, Olsen T, Andreassen TT. Biomechanical characteristics of the human anterior lens capsule in relation to age. Invest Ophthalmol Vis Sci. 1997;38(2):357-363. 26. Barraquer RI, Michael R, Abreu R, Lamarca J, Tresserra F. Human lens capsule thickness as a function of age and location along the sagittal lens perimeter. Invest Ophthalmol Vis Sci. May 2006;47(5):2053-2060. 27. Krag S, Andreassen TT. Mechanical properties of the human posterior lens capsule. Invest Ophthalmol Vis Sci. Feb 2003;44(2):691-696. 28. Kessler J. Refilling the rabbit lens. Further experiments. Arch Ophthalmol. 1966;76(4):596-598. 29. Kessler J. Experiments in Refilling the Lens. Arch Ophthalmol. 1964;71:412-417. 30. Fisher RF. Elastic constants of the human lens capsule. J Phys. 1969;201(1):1-19. 31. Gilmartin B. The aetiology of presbyopia: a summary of the role of lenticular and extralenticular structures. Ophthalmic Physiol Opt. 1995;15(5):431-437. 32. Remington LA. Clinical Anatomy of the Visual System. Boston, MA: Butterworth-Heinemann; 1998. 33. Augusteyn RC. Growth of the lens: in vitro observations. Clin Exp Optom. 2008;91(3):226-239. 34. Bassnett S. On the mechanism of organelle degradation in the vertebrate lens. Exp Eye Res. Feb 2009;88(2):133-139. 35. Pandey SK, Thakur J, Werner L, et al. The human crystalline lens, ciliary body, and zonules: their relevance to presbyopia. In: Agarwal A, ed. Presbyopia: a surgical textbook. Thorofare, NJ: Slack Incorporated; 2002. 36. Dubbelman M, Van der Heijde GL. The shape of the aging human lens: curvature, equivalent refractive index and the lens paradox. Vision Res. Jun 2001;41(14):1867-1877. 37. Moffat BA, Pope JM. Anisotropic water transport in the human eye lens studied by diffusion tensor NMR micro-imaging. Exp Eye Res. 2002;74(6):677-687. 38. Brown N. The change in lens curvature with age. Exp Eye Res. Aug 1974;19(2):175-183.

N.M. Ziebarth et al. 39. Moffat BA, Atchison DA, Pope JM. Age-related changes in refractive index distribution and power of the human lens as measured by magnetic resonance micro-imaging in vitro. Vision Res. Jun 2002;42(13):1683-1693. 40. Koretz JF, Handelman GH. Model of the accommodative mechanism in the human eye. Vision Res. 1982;22(8):917-927. 41. Tscherning M. Le mecanisme de l’accommodation. Annals Oculiat. 1904;131:168. 42. Fincham EF. The changes in the form of the crystalline lens in accommodation. Transactions of the Optical Society. 1925;26:239. 43. Fukuda M. Rheological characteristics of human crystalline lens. Jpn J Ophthalmol. 1963;7:47-55. 44. Itoi M, Ito N, Kaneko H. Visco-elastic properties of the lens. Exp Eye Res. Sep 1965;4(3):168-173. 45. Czygan G, Hartung C. Mechanical testing of isolated senile human eye lens nuclei. Med Eng Phys. Jul 1996;18(5):345-349. 46. Cui J, Lee CH, Delbos A, McManus JJ, Crosby AJ. Cavitation rheology of the eye lens. Soft Matter. 2011;7(17):7827-7831. 47. Burd HJ, Wilde GS, Judge SJ. An improved spinning lens test to determine the stiffness of the human lens. Exp Eye Res. Jan 2011;92(1):28-39. 48. Ripken T, Oberheide U, Fromm M, Schumacher S, Gerten G, Lubatschowski H. fs-Laser induced elasticity changes to improve presbyopic lens accommodation. Graefes Arch Clin Exp Ophthalmol. Jun 2008;246(6):897-906. 49. Reilly MA, Martius P, Kumar S, Burd HJ, Stachs O. The mechanical response of the porcine lens to a spinning test. Z Med Phys. 2016;26(2):127-135. 50. Nordmann J, Mack G. Nucleus of Human Lens .3. Its Separation, Its Hardness. Ophthalmic Research. 1974;6(2-4):216-222. 51. Kikkawa Y, Sato T. Elastic Properties of the Lens. Exp Eye Res. 1963;2(2):210-215. 52. Vanalphen GWHM, Graebel WP. Elasticity of tissues involved in accommodation. Vision Res. 1991;31(7-8):1417-1438. 53. Hollman KW, O’Donnell M, Erpelding TN. Mapping elasticity in human lenses using bubble-based acoustic radiation force. Exp Eye Res. Dec 2007;85(6):890-893. 54. Erpelding TN, Hollman KW, Juhasz T, O’Donnell M. Bubble-based acoustic radiation force for monitoring intraocular lens elasticity. Ultrason. 2004:732-735. 55. Erpelding TN, Hollman KW, O’Donnell M. Spatially mapping the elastic properties of the lens using bubble-based acoustic radiation force. Ultrason. 2005:613-616. 56. Erpelding TN, Hollman KW, O’Donnell M. Mapping age-related elasticity changes in porcine lenses using bubble-based acoustic radiation force. Exp Eye Res. Feb 2007;84(2):332-341. 57. Huang CC, Zhou QF, Ameri H, et al. Determining the acoustic properties of the lens using a high-frequency ultrasonic needle transducer. Ultrasound in Medicine and Biology. Dec 2007;33(12):1971-1977. 58. Soergel F, Meyer C, Eckert G, Abele B, Pechhold W. Spectral analysis of viscoelasticity of the human lens. J Refract Surg. Nov-Dec 1999;15(6):714-716.

Copyright © 2018. Kugler Publications. All rights reserved.

Biomechanics of the lens and its role in accommodation 59. Weeber HA, Eckert G. Stiffness distribution within the human crystalline lens and its function with age. Invest Ophthalmol Vis Sci. Apr 2004;45:U604-U604. 60. Ziebarth NM, Wojcikiewicz EP, Manns F, Moy VT, Parel JM. Atomic force microscopy measurements of lens elasticity in monkey eyes. Mol Vis. 2007;13:504-510. 61. Hozic A, Rico F, Colom A, Buzhynskyy N, Scheuring S. Nanomechanical characterization of the stiffness of eye lens cells: a pilot study. Invest Ophthalmol Vis Sci. Apr 06 2012;53(4):21512156. 62. Vaughan JM, Randall JT. Brillouin-scattering, density and elastic properties of the lens and cornea of the eye. Nature. 1980;284(5755):489-491. 63. Ejiri M, Thompson HE, O’Neill WD. Dynamic visco-elastic properties of the lens. Vision Res. Feb 1969;9(2):233-244. 64. Donaldson PJ, Grey AC, Maceo Heilman B, Lim JC, Vaghefi E. The physiological optics of the lens. Prog Retin Eye Res. Jan 2017;56:e1-e24. 65. Weeber HA, van der Heijde RG. On the relationship between lens stiffness and accommodative amplitude. Exp Eye Res. 2007;85(5):602-607. 66. Mohammad-Pour H, Kanapathipillai S, Manns F, Ho A. Determining the Optomechanical Properties of Accommodating Gel for Lens Refilling Surgery using Finite Element Analysis and Numerical Ray-tracing. Proc Spie. 2015;9307. 67. Cammarata PR, Cantu-crouch D, Oakford L, Morrill A. Macromolecular organization of bovine lens capsule. Tissue Cell. 1986;18(1):83-97. 68. Cammarata PR, Spiro RG. Identification of noncollagenous components of calf lens capsule: evaluation of their adhesion-promoting activity. J Cell Physiol. Dec 1985;125(3):393402. 69. Kohno T, Sorgente N, Ishibashi T, Goodnight R, Ryan SJ. Immunofluorescent studies of fibronectin and laminin in the human eye. Invest Ophthalmol Vis Sci. Mar 1987;28(3):506-514. 70. Muraoka M, Hayashi T. Three polypeptides with distinct biochemical properties are major alpha chain-size components of type IV collagen in bovine lens capsule. J Biochem. Sep 1993;114(3):358-362. 71. Parmigiani C, McAvoy J. Localisation of laminin and fibronectin during rat lens morphogenesis. Differentiation; research in biological diversity. 1984;28(1):53-61. 72. Brinker JM, Pegg MT, Howard PS, Kefalides NA. Immunochemical characterization of type IV procollagen from anterior lens capsule. Coll Relat Res. Jun 1985;5(3):233-244. 73. Kelley PB, Sado Y, Duncan MK. Collagen IV in the developing lens capsule. Matrix Biol. Aug 2002;21(5):415-423. 74. Dong L, Chen Y, Lewis M, et al. Neurologic defects and selective disruption of basement membranes in mice lacking entactin-1/ nidogen-1. Lab Invest. 2002;82(12):1617-1630. 75. Laurent M, Lonchampt MO, Regnault F, Tassin J, Courtois Y. Biochemical, ultrastructural and immunological study of in vitro production of collagen by bovine lens epithelial cells in culture. Exp Cell Res. 1978;115(1):127-142.

317 76. Rossi M, Morita H, Sormunen R, et al. Heparan sulfate chains of perlecan are indispensable in the lens capsule but not in the kidney. EMBO J. Jan 15 2003;22(2):236-245. 77. Peterson PE, Pow CS, Wilson DB, Hendrickx AG. Localisation of glycoproteins and glycosaminoglycans during early eye development in the macaque. J Anat. 1995;186 ( Pt 1):31-42. 78. Fukai N, Eklund L, Marneros AG, et al. Lack of collagen XVIII/ endostatin results in eye abnormalities. EMBO J. Apr 2 2002;21(7):1535-1544. 79. Ylikarppa R, Eklund L, Sormunen R, et al. Double knockout mice reveal a lack of major functional compensation between collagens XV and XVIII. Matrix Biol. Sep 2003;22(5):443-448. 80. Fuerst PG, Rauch SM, Burgess RW. Defects in eye development in transgenic mice overexpressing the heparan sulfate proteoglycan agrin. Dev Biol. 2007;303(1):165-180. 81. Marshall GE, Konstas AG, Bechrakis NE, Lee WR. An immunoelectron microscope study of the aged human lens capsule. Exp Eye Res. 1992;54(3):393-401. 82. Krag S, Andreassen TT. Mechanical properties of the human lens capsule. Prog Retin Eye Res. Nov 2003;22(6):749-767. 83. Courtois Y. The Capsule of the Crystalline Lens. In: Obrecht LSaG, ed. Presbyopia: Recent research and reviews from the third international symposium: Professional Press Books/ Fairchild Publications Division of Capital Cities Media, Inc.; 1987. 84. Danielsen CC. Tensile mechanical and creep properties of Descemet’s membrane and lens capsule. Exp Eye Res. 2004;79(3):343-350. 85. Pedrigi RM, David G, Dziezyc J, Humphrey JD. Regional mechanical properties and stress analysis of the human anterior lens capsule. Vision Res. 2007;47(13):1781-1789. 86. Yang X, Zou L, Binrong M, Dong D, Dai H, Lu X. Tensile strength of lens capsules in eye-bank eyes. J Cataract Refract Surg. Apr 1998;24(4):543-546. 87. Dyksterhuis LB, Dyksterhuis LD, White JF, et al. Impact of heparan sulfate chains and sulfur-mediated bonds on the mechanical properties of bovine lens capsule. Biophys J. 2011;100(9):2077-2083. 88. Candiello J, Cole GJ, Halfter W. Age-dependent changes in the structure, composition and biophysical properties of a human basement membrane. Matrix Biol. Jun 2010;29(5):402-410. 89. Ziebarth NM, Arrieta E, Feuer WJ, Moy VT, Manns F, Parel JM. Primate lens capsule elasticity assessed using Atomic Force Microscopy. Exp Eye Res. Jun 2011;92(6):490-494. 90. Haritoglou C, Mauell S, Schumann RG, et al. Increase in lens capsule stiffness caused by vital dyes. J Cataract Refract Surg. Nov 2013;39(11):1749-1752. 91. Tsaousis KT, Karagiannidis PG, Kopsachilis N, et al. Measurements of elastic modulus for human anterior lens capsule with atomic force microscopy: the effect of loading force. Int Ophthalmol. Jun 2014;34(3):519-523. 92. Powell TA, Amini R, Oltean A, et al. Elasticity of the Porcine Lens Capsule as Measured by Osmotic Swelling. J Biomech Eng-T Asme. Sep 2010;132(9).

318

Copyright © 2018. Kugler Publications. All rights reserved.

93. Assia EI, Apple DJ, Barden A, Tsai JC, Castaneda VE, Hoggatt JS. An Experimental-Study Comparing Various Anterior Capsulectomy Techniques. Arch Ophthalmol. May 1991;109(5):642-647. 94. Andreo LK, Wilson ME, Apple DJ. Elastic properties and scanning electron microscopic appearance of manual continuous curvilinear capsulorhexis and vitrectorhexis in an animal model of pediatric cataract. J Cataract Refract Surg. Apr 1999;25(4):534539. 95. Parel JM, Ziebarth N, Denham D, et al. Assessment of the strength of minicapsulorhexes. J Cataract Refract Surg. Aug 2006;32(8):1366-1373. 96. Morgan JE, Ellingham RB, Young RD, Trmal GJ. The mechanical properties of the human lens capsule following capsulorhexis or radiofrequency diathermy capsulotomy. Arch Ophthalmol. Sep 1996;114(9):1110-1115. 97. Wood MG, Schelonka LP. A porcine model predicts that a can-opener capsulotomy can be done safely in pediatric patients. J Aapos. Dec 1999;3(6):356-362. 98. Sueiras VM, Moy VT, Ziebarth NM. Lens capsule structure assessed with atomic force microscopy. Mol Vis. 2015;21:316323. 99. O’Neill WD, Doyle JM. A thin shell deformation analysis of the human lens. Vision Res. Feb 1968;8(2):193-206. 100. Fisher RF. The force of contraction of the human ciliary muscle during accommodation. J Physiol. Aug 1977;270(1):51-74. 101. Pierscionek BK. In vitro alteration of human lens curvatures by radial stretching. Exp Eye Res. Nov 1993;57(5):629-635. 102. Pierscionek BK. Age-related response of human lenses to stretching forces. Exp Eye Res. Mar 1995;60(3):325-332. 103. Glasser A, Campbell MC. Presbyopia and the optical changes in the human crystalline lens with age. Vision Res. Jan 1998;38(2):209-229.

N.M. Ziebarth et al. 104. Michael R, Mikielewicz M, Gordillo C, Montenegro GA, Cortes LP, Barraquer RI. Elastic properties of human lens zonules as a function of age in presbyopes. Invest Ophthalmol Vis Sci. Sep 2012;53(10):6109-6114. 105. Cortes LP, Burd HJ, Montenegro GA, et al. Experimental protocols for ex vivo lens stretching tests to investigate the biomechanics of the human accommodation apparatus. Invest Ophthalmol Vis Sci. May 2015;56(5):2926-2932. 106. Reilly MA, Ravi N. Equibiaxial stretching device for the determination of polymeric film properties. Abstr Pap Am Chem S. Mar 26 2006;231. 107. Reilly MA, Hamilton PD, Ravi N. Dynamic multi-arm radial lens stretcher: A robotic analog of the ciliary body. Exp Eye Res. Jan 2008;86(1):157-164. 108. Reilly MA, Hamilton PD, Perry G, Ravi N. Comparison of the behavior of natural and refilled porcine lenses in a robotic lens stretcher. Exp Eye Res. Mar 2009;88(3):483-494. 109. Manns F, Parel JM, Denham D, et al. Optomechanical response of human and monkey lenses in a lens stretcher. Invest Ophthalmol Vis Sci. Jul 2007;48(7):3260-3268. 110. Augusteyn RC, Mohamed A, Nankivil D, et al. Age-dependence of the optomechanical responses of ex vivo human lenses from India and the USA, and the force required to produce these in a lens stretcher: The similarity to in vivo disaccommodation. Vision Res. Jul 15 2011;51(14):1667-1678. 111. Ziebarth NM, Borja D, Arrieta E, et al. Role of the lens capsule on the mechanical accommodative response in a lens stretcher. Invest Ophthalmol Vis Sci. Oct 2008;49(10):4490-4496.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

VITREOUS AND VITREORETINAL DISEASE

Copyright © 2018. Kugler Publications. All rights reserved.

22. Biomechanics of the vitreous humor Rodolfo Repetto1, Jennifer H. Tweedy2 Department of Civil, Chemical and Environmental Engineering, University of Genoa, Genoa, Italy; 2Department of Bioengineering, Imperial College London, London, UK

1

1. Introduction

Copyright © 2018. Kugler Publications. All rights reserved.

The vitreous humor and vitreous body, or vitreous, is the gel-like material that fills the vitreous chamber of the eye. This chamber occupies the space between the lens and the retina, and it is the largest structure in the eye globe with a volume of approximately 4 ml (Fig. 1).  The vitreous is a transparent gel that is both avascular and acellular, containing between 98 and 99.7% water, and approximately 0.9% salts. Two additional ingredients, collagen and hyaluronan, are present only in small quantities, but account for the distinct biomechanics of the vitreous. The vitreous contains an array

Fig. 1. Sketch of the cross-section of a human eye. Drawing by Dr. Federica Grillo, University of Genoa, Italy.

of proteins; Sebag gives a comprehensive description of vitreous structure and composition.1 Collagen, which is present primarily as type II collagen, forms a delicate network of fibrils with a diameter of 10–20 nm that run through the vitreous humor and whose concentration is estimated to be approximately 60 mg/ml in bovine eyes and 300 mg/ml in human eyes.2 Hyaluronan increases the viscosity of the aqueous solution and also swells when hydrated, which forces the collagen fibers apart.1,2 The vitreous chamber is bounded by several layers of tissue, the innermost of which is the retina. The most superficial layer of the retina is known as the internal limiting lamina, and the outermost layer of the vitreous humor is the vitreous cortex; there is no vitreous cortex over the optic nerve head and it is thinner over the macula. The vitreous cortex is weakly attached to the retina by collagen fibrils that extend through the cortex into the internal limiting lamina; however, the molecular basis of this attachment is poorly understood. The anterior boundary of the vitreous cortex is the vitreous base, which extends over the anterior limit of the retina and the posterior part of the ciliary body; this region of the vitreous cortex is particularly strongly attached to these structures. The hyaloid membrane, the anterior surface of the vitreous, is separated from the lens by a thin layer of aqueous humor. The collagen fibrils within the vitreous tend to be oriented in the anterior– posterior direction and tend to group into bundles of fibers. The branching between the bundles gives the vitreous its mechanical properties. The density of the fibers is particularly high at the vitreous base and the vitreous cortex, with a lower density in the interior,

Correspondence: Rodolfo Repetto, Department of Civil, Chemical and Environmental Engineering, University of Genoa, Via Montallegro 1, 16145 Genova, Italy. E-mail: [email protected] Biomechanics of the Eye, pp. 323-342 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

Copyright © 2018. Kugler Publications. All rights reserved.

324

which leads to heterogeneous mechanical properties. There has been some debate in the literature about the role of the vitreous humor. In particular, replacement of the vitreous by water or other substitute does not necessarily impede the function of the eye, raising the question of why the gel-like rheology is necessary.3 The elastic properties of the vitreous could help protect the eye globe from collapsing in the event of a penetrating injury. Another important function of the vitreous is regulating mass transport, since the collagen fibers impede or stop the motion of molecules and cells within it, and the vitreous has the particular role of regulating oxygen transport and distribution within the eye. If the vitreous is removed and replaced, which is done in a surgical procedure known as vitrectomy, the intraocular oxygen tension increases. This could contribute to some retinal diseases while also increasing the oxidative stress within the eye, which could in turn contribute to the formation of nuclear cataracts and primary open-angle glaucoma.4  With advancing age, vitreous liquefaction, i.e., synchysis, often occurs, in which the delicate structure of the collagen fibrils is disrupted and the gel structure disintegrates. Often the vitreous humor also shrinks, i.e., syneresis, leading to the formation of liquid gaps within the gel and/or posterior vitreous detachment (PVD), in which the vitreous cortex comes away from the internal limiting lamina of the retina, which tends to happen in the posterior vitreous chamber. This degradation process is thought to produce retinal tears if a region of the vitreous cortex is particularly strongly attached to the internal limiting lamina, so instead of detaching from the retina, the strongly attached vitreous pulls the retina away from the choroid. Retinal tears are potentially dangerous, as they can lead to retinal detachment (RD) when liquefied vitreous enters into the potential space between the retina and the choroid through the tear. Since the choroid contains the majority of the retinal blood supply, RD is considered an ophthalmic emergency which should be treated quickly in order to save sight. Although many aspects of vitreous biomechanics are poorly understood, it is now well accepted that mechanical effects play a fundamental role in vitreous function in health and disease, as well as in several treatments of various ocular pathologies. In this chapter, we outline some of the major work that has

R. Repetto and J.H. Tweedy

been undertaken to understand vitreous biomechanics, and we conclude with some open problems in this area.

2. Mechanical properties of vitreous humor 2.1. Basic mechanical concepts Before discussing mechanics specific to the vitreous humor, we introduce some relevant general concepts in this section. We start with the continuum formulation, which has proved a remarkably successful way of describing material phenomena on scales much larger than the molecular scale. In this description, all properties of interest, such as density or velocity, are assumed to be continuously distributed in space, that is, we can define their values at any point within the material, even though this is clearly an abstraction owing to the molecular nature of matter. In this way, we avoid needing to know or consider the microstructural details of the material, even though they are integral to its macroscopic behavior. One of the most important concepts in continuum mechanics is that of stress, which is a measure of the force per unit area (with dimensions of pressure) acting on a small material surface centered on the point of interest, and in general, depends on the orientation of the surface, as well as on the location and time. This means that the stress can vary from point to point in a body and, at a particular point, depends on the orientation of the surface considered. Shear stress refers to the components tangential to the surface considered; normal stress refers to the component that is orthogonal to the surface. In a solid, it is typical to compute the deformation with respect to a reference configuration, normally the relaxed one. A dimensionless measure of the local deformation of a material is called strain. In a fluid, however, the concept of strain has little significance, since the fluid particles have no preferential position relative to one another, and instead the rate of change of the strain with respect to time is a more useful measure. This is a matter of everyday experience in that deforming an elastic solid by a large amount (high strain) requires more effort (high stress), whereas in order to maintain a high stress in a fluid, a high rate of

Copyright © 2018. Kugler Publications. All rights reserved.

Biomechanics of the vitreous humor

strain must be applied (e.g., by rapidly stirring the fluid). Properties of fluids are usually determined using instruments called rheometers; in general, these test the material by applying a prescribed rate of strain and measuring the resulting stress, or by applying a stress and measuring the rate of strain. A linear elastic solid is a material in which the stress depends linearly on the strain (the constant of proportionality is known as the elastic modulus). Thus, an elastic solid has an infinite memory in the sense that it remembers its relaxed reference shape forever. A linear, viscous fluid, otherwise known as a Newtonian fluid, is one in which the stress depends linearly on the rate of strain. The constant of proportionality is the dynamic viscosity, typically denoted μ (with dimensions of pressure*time). Many fluids have almost perfectly Newtonian behavior over a wide range of pressures and temperatures; for example, both water and the aqueous humor can often be successfully characterized as Newtonian fluids. A perfectly Newtonian fluid has no memory in the sense that its state of (viscous) stress at a particular time depends on the rate of deformation at that time, but not on the past history of motion. In addition to viscous stresses, the state of stress in a fluid is also characterized by the pressure. This is defined as the average of the normal stress on three mutually orthogonal surfaces centered on the point of interest (which can be shown to be independent of the orientation of those surfaces). It occurs due to compression of the molecules, although in liquids this compression is usually so slight as to cause negligible volume change, even though huge pressures can be generated. An everyday experience of such a pressure change is that water pressure increases by about one atmosphere for every 10  m of depth; however, the density of the water changes little with depth. In reality, many materials cannot be classified as one of these two types (elastic solids or viscous fluids), and of interest to us are so-called viscoelastic materials that have both fluid and solid properties. They have a fading memory, meaning that the state of stress at a certain time depends on all past states of motion, with the strength decreasing for states further back in the past. Such materials are typically characterized by several time scales, meaning that their response to a pattern of forcing can have different characteristics depending on the time scale over which the observations are made.

325

A typical way to test the fast response of viscoelastic materials is to subject them to harmonic periodic strains of small amplitude and measure the corresponding stress (or vice versa). Since the oscillations are small, the corresponding stress is also harmonic. Now, in an elastic solid, stress is proportional to strain, and thus the stress and strain oscillations would be in phase with one another. On the other hand, in a viscous fluid, the stress depends on the rate of strain, and thus strain and stress will be out of phase by 90°. In a viscoelastic material, the phase difference is neither 0° nor 90°. In this case, the response can be completely defined using two moduli, called the elastic (G’) and loss (G’’) moduli. The elastic modulus characterizes the elasticity of the body (with higher values of G’ corresponding to stiffer materials), and the loss modulus characterizes its viscosity. For mathematical convenience, these quantities are typically combined in the form of the complex modulus G*,  given by  G* = G’ + iG’’, where ​i =​ _ √ ‒1 ​​.  For technical details about the use of the complex modulus, see Tanner.5 The notion of complex modulus will be used extensively in Section 3 of this chapter, which discusses vitreous humor motion induced by eye rotations. The healthy vitreous body is often described as a viscoelastic material, although the details of its properties remain unclear. We describe several studies concerning short duration saccadic rotations of the eye in this chapter, so we now describe how to characterize the short time scale behavior of a viscoelastic fluid. 2.2. Studies of vitreous rheology The study of fluid mechanical properties is called rheology, and a variety of techniques have been used in the case of the vitreous body, including bulk measurement techniques,6,7 magnetic microrheology,8,9 in-vivo visual tracking,10 acoustic,11 and magnetic resonance imaging (MRI)-based12 techniques. Most experiments have been conducted on animal vitreous, typically bovine and porcine specimens. In spite of the significant quantitative differences in the mechanical properties estimated with different methods, all authors characterize the vitreous as a viscoelastic material. However, measurement of the complex modulus using a rheometer is extremely challenging, owing to a thin layer of lubricating aqueous fluid that forms between the vitreous and

326

R. Repetto and J.H. Tweedy

(a) 10 8 G' (Pa)

Sharif-Kashani et al. also performed creep tests, in which the material is subjected to a constant stress over time while the strain is measured, on vitreous samples.14 They observed that two characteristic time scales exist and hypothesized that the short-duration viscoelastic response is associated with the collagen structure, while the longer time scale response is due to the microfibrils and hyaluronan network.

N-st N-in SK eye 1 SK eye 2 SK eye 3 S

6 4 2 0

(b)

0.1 4

3.5

G'' (Pa)

3 2.5

1

Frequency (rad/s)

10

N-st N-in SK eye 1 SK eye 2 SK eye 3 S

2 1.5 1 0.5 0

0.1

1 10 Frequency (rad/s)

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 2. Elastic (a) and loss (b) moduli as a function of the testing frequency. N-st: steady-state values;13 N-in: initial values;13 SK;14 S.15 Strain: γ = 0.03.

the rheometer, causing slippage. Moreover, the delicate gel structure of the vitreous rapidly degrades after dissection. Some measurements of the moduli found using dynamic oscillatory tests are presented in Figure 2, and these are plotted as a function of the testing frequency. For frequencies under approximately 5  rad/s, both moduli are almost independent of frequency; for higher frequencies, both moduli increase with frequency, especially the elastic modulus G’, which is typical of gels. Nickerson et al. also reported that the mechanical properties of vitreous change significantly with time after excision.13 Specifically, in Figure 2, the blue curve with solid circles corresponds to the equilibrium state that is reached long after excision, while the single blue squares at 10  rad/s correspond to the results immediately after excision. This suggests that the in-vivo moduli are closer to the higher values indicated by the squares.

3. Vitreous motion induced by eye rotations Stresses are generated on the retina when the vitreous body is in relative motion with respect to the eye wall. It is well accepted that such stresses are related to the occurrence of retinal breaks and possibly to RD, especially if the rheological properties of the vitreous are inhomogeneous, as discussed in Section  5 of the present chapter and elsewhere.16 It has also been postulated that, over long time scales, mechanical stretching of the vitreous body induced by rotations of the eye might contribute to the disruption of the gel structure, leading to vitreous liquefaction.1,17 We therefore focus on the dynamics of the vitreous body in this section. Possible causes of vitreous motion include eye rotations, thermal effects, dynamic accommodation of the lens, and the slow flow that occurs from the anterior to the posterior of the vitreous chamber that is driven by the pressure difference between the interior and exterior of the eye (retinal pumping). Thermally driven flow is known to be very important in the anterior chamber due to the relatively large temperature differences;18,19 however, Dyson et al. used order-of-magnitude estimations to show that the intensity of any thermally driven flow in the vitreous chamber is likely to be negligible compared to that produced by eye rotations.20 In this chapter, we mainly focus on motion driven by eye rotations and especially by saccades, which are eye rotations of short duration whose purpose is to redirect sight from one target to another and whose characteristics have been extensively studied.21

Biomechanics of the vitreous humor

327

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3a,b. Examples of two 2-D flow fields measured during a saccadic movement.23 The two images are taken at two different times during the eye rotation. (c-f) Examples of the vitreous deformation during eye rotations.12

3.1. In-vivo measurements of vitreous dynamics Very few direct, in-vivo observations of vitreous humor motion induced by eye rotations are available, partly due to the challenge of visualization, which is made particularly difficult as the vitreous is designed to be invisible.22 Some authors have attempted to investigate vitreous humor dynamics by tracking speckles or other echogenic objects in the vitreous body. Zimmerman  recorded the movement of the scattering pattern induced by a point source of light during the relaxation movement of the vitreous humor following an impulsive eye rotation,10 and Walton et al. used ultrasound films of eyes performing impulsive rotations and tracked the speckles present in the vitreous humor.11 More recently, Rossi et al. applied an ultrasound image velocimetry technique to reconstruct 2-D flow fields of vitreous humor motion during saccadic rotations.23 For this study, patients were asked to perform large-amplitude eye rotations while dynamic ultrasound films were taken on planes approximately orthogonal to the axis of rotation of the eye. The authors analyzed the films by

applying robust image velocimetry,24 which is a modification of the standard Particle Image Velocimetry (PIV) that has been in use for several years in experimental fluid mechanics.25 The basic idea is to subdivide the images into subregions called interrogation windows, and compare images of the interrogation windows at different times. Assuming the echogenic objects move with the local velocity of the fluid and do not affect that velocity, the displacement that maximizes the correlation between two interrogation windows is assumed to be representative of the actual vitreous displacement in that subregion. An estimate of the local vitreous velocity is obtained by dividing the local displacement by the time difference between the two images. Use of this method allowed Rossi et al. to reconstruct 2-D velocity vector fields of vitreous motion.23 Examples of two such vector fields are shown in Figure 3. The velocity field shown in Figure 3a approximately corresponds to the time at which the angular velocity of the eye is maximum, while that in Figure 3b is taken at a representative time during the deceleration phase. The figure shows that a good spatial resolution

328

R. Repetto and J.H. Tweedy

(a)

(b) vq

y

0

-0.5

-1

-1

-0.5

0

x

0.5

1

vq

0.5

0

y

0.5

0.000 -0.095 -0.189 -0.284 -0.379 -0.474 -0.568 -0.663 -0.758 -0.853 -0.947 -1.042 -1.137 -1.232 -1.326 -1.421 -1.516 -1.611 -1.705 -1.800

-0.5

-1

-1

-0.5

0

x

0.5

1

0.000 -0.095 -0.189 -0.284 -0.379 -0.474 -0.568 -0.663 -0.758 -0.853 -0.947 -1.042 -1.137 -1.232 -1.326 -1.421 -1.516 -1.611 -1.705 -1.800

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. Velocity fields and contours of the magnitude of the azimuthal velocity component on the horizontal plane (orthogonal to the rotation axis) in a viscoelastic fluid at the time of maximum (negative) angular velocity. The rotation amplitude is A = 0.035 rad in both cases, and the frequency is (a) ω = 6.28 rad/s and (b) ω = 43.98 rad/s. The velocity is scaled with the maximum magnitude of the wall velocity and distances with the eye model radius.29

of the flow field can be obtained using this method. Using the velocity fields, the authors computed several quantities of potential clinical relevance, such as the ratio of the peak spatially averaged kinetic energy per unit mass to the maximum squared scleral angular velocity, which characterizes the efficiency of kinetic energy transfer from the sclera to the vitreous. Rossi et al. showed that this parameter correlates inversely with age and refractive error,23 which implies that energy transmission is less efficient in older and highly myopic eyes, likely due to vitreous liquefaction. This technique is very promising, since it allows us to obtain quantitative measurements of vitreous humor movement. Its widespread use is, however, hampered by the fact that it is only applicable if the vitreous is sufficiently echogenic, which typically happens in cases of syneresis, haeme, or inflammation. Moreover, obtaining an accurate estimate of the elastic and loss moduli requires many images per saccade, and this restricts the time resolution of the ultrasound scan to high frequencies since saccades are relatively fast. An alternative MRI-based technique to measure vitreous motion in vivo in humans was recently proposed by Piccirelli et al.12 Subjects were asked to gaze at a harmonically moving target during MRI acquisition. Axial 2-D ‘complementary spatial modulation of magnetization’ tagged images26 were acquired; vitreous deformation

was then tracked using a dedicated algorithm and successfully quantified in all volunteers. Some images of vitreous deformation during periodic eye movements are shown in Figure  3c-f. A post-processing technique based on the mesh-tracking algorithm introduced by Piccirelli et al.27  was used to analyze the acquired images. The authors fitted their measurements to a theoretical model28 (see also Section 3.3.) to obtain indirect measurements of the mechanical properties of the vitreous. The value of the complex modulus obtained by the authors is significantly higher than all other existing measurements discussed in Section 2.2. 3.2. In-vitro experimental studies of vitreous motion In-vitro experiments have been used successfully to understand some aspects of the vitreous dynamics, and are popular as they avoid the difficulties associated with measuring vitreous motion. Bonfiglio et al.  performed measurements of the flow of a viscoelastic fluid within a rotating sphere.29 Their setup consisted of a Perspex cylinder in which a spherical cavity representing the vitreous chamber had been carved. The cavity was filled with an artificial vitreous humor made of a solution of agar powder and hyaluronic acid sodium salt in deionized water,30 which has viscoelastic properties similar to those measured for real vitreous. The eye model was mounted on the

Biomechanics of the vitreous humor

(b)

2.5 2.0

N orm alized azim uthalvelocity

N orm alized azim uthalvelocity

(a)

329

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 0

0.2

0.4

0.6

0.8

1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.5 0

1

N orm alized radialcoordinate

(d)

2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0 -2.5 0

2.0

-2.0

N orm alized azim uthalvelocity

N orm alized azim uthalvelocity

(c)

2.5

0.2

0.4

0.6

0.8

1

N orm alized radialcoordinate 2.5 2.0 1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0

0.2

0.4

0.6

0.8

1

N orm alized radialcoordinate

-2.5 0

0.2

0.4

0.6

0.8

1

N orm alized radialcoordinate

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. Azimuthal velocity profiles for various experimental conditions, showing the effect of passing through a resonant frequency from (a) to (d). The fluid used is the same in each case, but the amplitude and driving frequency are different. The velocity magnitude is scaled with the maximum wall velocity and the radial co-ordinate with the radius of the eye model. Modified from Bonfiglio et al.29

shaft of a computer-controlled motor that could rotate it according to a prescribed time law. For simplicity, Bonfiglio et al. focused on periodic harmonic rotations of the domain, choosing frequencies and amplitudes representative of a sequence of real saccadic eye movements.29 The fluid was seeded with small, neutrally buoyant, hollow glass spheres, and PIV measurements were taken on the plane orthogonal to the axis of rotation. Figure 4 shows two flow fields measured at the time of maximal angular velocity of the eye model. The

fluid motion is forced by the motion of the boundary, which is in contact with the fluid, and thus, owing to the no-slip boundary condition at the wall, the fluid particles at the wall are forced to move at the same velocity as the wall, driving an overall motion of the fluid. Repetto et al. studied the case of a Newtonian fluid, finding that, at the time of the maximal angular velocity of the container, the maximal velocity in the fluid is obtained at the wall (Fig. 3a).31 Using a viscoelastic fluid, the velocity field can likewise have a maximum at the outer boundary, as shown in Figure 4a, but the

Copyright © 2018. Kugler Publications. All rights reserved.

maximum can also occur in the interior of the domain, as shown in Figure 4b. The phenomenon of an internal maximum occurs at particular frequencies and is due to resonant excitation. Resonance is a well-known phenomenon in mechanics, which occurs when a mechanical system can store and transfer energy between two different modes of energy. In the case of oscillatory motion, viscoelasticity is necessary for resonance to occur because elastic energy must be stored during part of the motion and converted into kinetic energy at other times, which is not possible for a viscous fluid as it has no elasticity. Resonant excitation occurs when a system is forced at frequencies that are near to the natural frequencies of the fluid, which are dependent on both fluid rheology and container shape. Figure  5 shows velocity profiles measured in four different experiments,29 illustrating the effect of resonance in a viscoelastic fluid. Each of the subparts shows the velocity profiles at various time points for a particular amplitude and frequency. Figure  5b is very close to a natural frequency, and a significant resonant effect can be observed as the velocity in the interior is significantly greater than the boundary forcing. The velocity profiles for different frequencies are qualitatively very different, depending on both the rotation frequency and on the rheology of the fluid given by the complex modulus, but resonance can be observed over a wide range of frequencies; for example, Figure 5d is for a frequency 25% higher than Figure 5c. To further highlight the effect of resonance, Bonfiglio et al. also calculated the normalized, time-averaged total kinetic energy of the fluid during the oscillations, 29 , which acts as a dimensionless measure of the intensity of the fluid flow. Figure  6 shows  vs the oscillation frequency, and most curves show a peak in  that closely corresponds to the natural frequency of the solution plus container. This is particularly striking, given that a purely viscous fluid would always have  less than 1. The authors also showed that the resonant frequencies can lie within the range of frequencies of natural eye rotations, and suggest that resonant excitation of vitreous motion could therefore be possible during real eye rotations. This might have important clinical implications, as the vitreous humor deformations are significantly larger at resonance, which could produce abnormally high stresses on the

R. Repetto and J.H. Tweedy Normalized average kinetic energy

330 9 8 7 6 5 4 3 2 1

10

20

30

40

50

Rotation frequency (rad/s)

60

70

Fig. 6. Normalized, time-averaged kinetic energy of the fluid, K ̅ , vs the frequency of oscillations, ω, for different values of the rotation amplitude and different solutions. Each curve corresponds to a different solution and a different amplitude of the oscillation. Modified from Bonfiglio et al.29

retina or abnormally large strains within the vitreous that disrupt its structure. Vitrectomy refers to the surgical removal of the natural vitreous, which is used to release vitreoretinal tractions and seal retinal breaks. There has been much discussion in recent literature about artificial fluids whose mechanical properties allow them to be used as vitreous replacements. Several authors highlight the benefits of using a viscoelastic fluid with a significant elastic component. For example, Soman and Banerjee  suggest it avoids excessive flow within the vitreous chamber,32 and Foulds  points out that the elastic component absorbs energy and could protect the retina from external injury.16 However, the possibility of resonance and its associated risks were not discussed. The work of Bonfiglio et al.29 relies on several simplifying assumptions, in particular the idealization of the domain shape as spherical and of the eye rotations as harmonic. The most significant departure of the real vitreous chamber is that the anterior part has an indentation due to the lens. The effect of the shape of the domain was investigated in a series of experiments conducted by Stocchino et al., in which the authors adopted an experimental setup similar to that described in Bonfiglio et al.,29 but used a non-spherical cavity instead of a spherical one, as well as only purely viscous fluids.33  Their work shows that the shape change leads to significantly more complicated flow fields than in the

Biomechanics of the vitreous humor

Copyright © 2018. Kugler Publications. All rights reserved.

3.3. Theoretical studies Much insight on the dynamics of vitreous motion induced by saccadic rotations of the eye has also been provided by a number of theoretical studies, starting from the seminal work of David et al.28 The authors used a mathematical model to investigate the motion of a viscoelastic fluid within a periodically rotating sphere, adopting mechanical properties of the fluid measured by Lee.8 This study was extended by Meskaukas et al. to include the possible occurrence of resonant excitation of the fluid motion, and they found that the natural frequencies of the vitreous are within the range possible frequencies of real eye rotations for all sets of mechanical properties of the vitreous body existing in the literature, 34 which were discussed in Section  2.2. This means that resonant excitation is likely to occur, in agreement with the experimental results by Bonfiglio et al.29 described above, and the results of the two papers agree well both quantitatively and qualitatively. Repetto and colleagues extended this work to consider the case of a sequence of real saccadic rotations in opposite directions, separated by a resting time, and showed that resonance is also possible in this case when the period of oscillations is close to a multiple of a natural frequency of the system.35 Numerical simulations of vitreous dynamics within a realistic domain have been performed by Modarreszadeh and Abouali, who modeled the vitreous humor as a non-linear viscoelastic fluid.36 The authors considered harmonic oscillations of the eye and computed the shear stress on the retina, showing that stresses can

be around ten times higher in the normal vitreous compared to liquefied vitreous. 3.4. The case of myopic eyes The incidence of RD is known to correlate with myopia, although the reasons are not understood. The risk of RD is reported as four times higher in myopic eyes whose refractive error is −1 to −3  diopters (D) than in emmetropic eyes, and up to ten times higher if the refractive error is more than 3 D.37 Moreover, risk factors for RD such as PVD and lattice degeneration are more common in myopic subjects.38,39 In myopia, the eye is, on average, longer in the anterior–posterior direction than in emmetropic eyes.40,41 Meskauskas et al. modeled the vitreous chamber as an ellipsoid with principal radii,42 as measured experimentally in Atchison;41 their results are reported in Figure  7, which shows the cases of an emmetropic eye and eyes with refractive errors of −10 D and −20 D. Their results suggest that the vitreous humor and retina in highly myopic eyes are continuously subjected to significantly larger shear stresses than those in emmetropic eyes, which might explain the more frequent occurrence of vitreous liquefaction, PVD, and RD in myopic eyes. Maximum wall shear stress (Pa)

sphere, and the flow is characterized by circulations that are generated behind the lens during the rotation cycle which progressively migrate towards the core of the domain (see Figs. 2 and 3 in Stocchino et al.).33  The effect of real eye rotations, as opposed to harmonic periodic rotations, was considered by Repetto et al., although they too only considered purely viscous fluids.31 Remarkably, their results show that the maximum stress generated on the retina during a single saccadic eye movement increases significantly with the viscosity of the fluid, but depends only weakly on the amplitude of the rotation. This seems to suggest that small-amplitude eye rotations, which are far more frequent than large ones, are responsible for generating the majority of the stress on the retina.

331

6.5 6

0D -10D -20D

5.5 5 4.5 4 3.5

10

15 20 25 Saccade amplidure (deg)

30

Fig. 7. Maximum shear stress on the retina versus saccade amplitude for emmetropic eyes and two different myopic cases (see legend). The rheological values of the vitreous humor are taken from Swindle;15 the figure has been modified from Meskauskas et al.42

332

Copyright © 2018. Kugler Publications. All rights reserved.

4. Mass transport and drug delivery in the vitreous chamber Mass transport in and across the eye is crucial for maintaining the balance of species in the retina and vitreous humor. Naturally occurring mass transport from the blood to the retina and vitreous humor is regulated by the blood–retinal barrier, which is composed of the retinal pigment epithelium and Bruch’s membrane.43,44 Severe vision loss from posterior segment diseases, such as age-related macular degeneration, diabetic retinopathy, glaucoma, and retinitis pigmentosa account for most cases of irreversible blindness worldwide. While topical application of drugs is relatively successful in treating disease in the anterior chamber, it is more difficult to deliver sufficiently high concentrations of drug to the vitreous chamber to treat posterior segment diseases. Systemic injection is an alternative method, although this suffers from the same drawback in terms of reaching sufficiently high concentrations. A third approach is periocular delivery, in which the drug is placed either sub-conjunctivally in Tenon’s space or at the posterior of the eye, meaning that the drug must pass through the sclera and choroid before reaching the retina. The method is growing in popularity because, unlike the cornea, the sclera is typically relatively permeable to drugs;45 however, some of the drug will be absorbed by the choroidal circulation, which could be undesirable. A fourth alternative is intravitreal injection of pharmacological agents, which has become a common therapeutic option for treating a wide spectrum of retinal and chorio-retinal diseases. This method tends to result in rapid dispersion of the drug and thus a short delivery time, which is not always desirable as it can necessitate frequent repeated injections for chronic conditions. To avoid this, intravitreal sustained-release devices can be used.45 For all these methods, an understanding of the transport processes in the vitreous is essential to predict the concentrations of drug reaching different spatial regions of the retina; this could also provide clinical indications to optimize drug delivery modalities and improve regional therapeutic efficacy. One of the major issues is achieving a sufficiently steady concentration of the drug, sufficiently uniformly distributed over the retina, and acting over a sufficiently long period

R. Repetto and J.H. Tweedy

of time for the drug to be effective. This is particularly important, as many of the drugs in use have a relatively narrow concentration window over which they are effective, with higher concentrations being toxic and lower ones being ineffective.46 Achieving the proper balance is difficult, but the many studies described in this section are pointing the way to improved drug delivery. Mass transport in a fluid occurs as a result of two physical mechanisms. One is molecular diffusion, described by Fick’s law, which states that mass transport occurs from regions of high concentration of the solute to regions of low concentration at a rate proportional to the gradient of concentration, with the constant of proportionality given by the diffusion coefficient or diffusivity, D (with dimension squared length divided by time). The other is convection, which arises due to bulk motion of the fluid. The relative importance of convection and diffusion is quantified by the Péclet number, defined as UL/D, where U is a characteristic velocity of the flow and L is a characteristic length scale. Thus, mass transport in the vitreous is driven by both convection and diffusion, with convection occurring as a result of any type of fluid motion (whether driven by saccades, thermal convection, anterior–posterior flow, or lens accommodation). 4.1. Parameter estimation using ex-vivo models Xu and colleagues used a poroviscoelastic model of the vitreous humor to develop a method to estimate the diffusion coefficient and hydraulic conductivity of any species in samples of bovine vitreous humor using acid orange 8 as a model diffusant.47 They used their model to compare diffusive transport to convective transport arising from the constant flow from the anterior to the posterior vitreous chamber due to the pressure difference between the interior and exterior of the eye. They showed that the Péclet number in humans is 0.41, meaning that both convection and diffusion are important. Since acid orange 8 is a relatively small molecule, convection will be dominant for very large molecules that diffuse more slowly. On the other hand, in mice, which have smaller length scales, diffusion is dominant for acid orange 8. Penkova et al. developed a sophisticated technique for estimating the diffusion coefficient of drugs or drug surrogates in the vitreous humor of an ex-vivo eye by

Fluorescein concentration (ml)

Biomechanics of the vitreous humor

333

0.6

treat retinitis pigmentosa, and the authors found that both the passive and unidirectional permeabilities decreased after treatment with this drug, suggesting its efficacy is partly due to a reduction in mass transport brought about by reducing these permeabilities.  The authors also found that mass transport processes are much more intense in liquefied than in normal vitreous, due to the fact that convection becomes dominant over diffusion in liquefied vitreous.

7 h 30 h

0.5 0.4 0.3 0.2 0.1 0

matching observations of the drug concentrations to theoretical predictions.48 The technique has the advantage that there is no disruption of the vitreous gel, but it is limited to molecules visible through imaging techniques such as MRI or fluorescence.

4.3. In-vitro experiments Some authors have studied mass transport in the eye using in-vitro models due to the difficulty of measuring concentrations in vivo. Awwad et al. successfully designed and tested a life-size eye model consisting of an anterior and a posterior chamber.51 The chambers were filled with fluids representing the aqueous and vitreous humors, and the aqueous humor could optionally be made to flow, allowing estimation of drug concentrations after intraocular injection. Their results suggest that aqueous flow is necessary to clear drugs from the vitreous humor.

4.2. In-vivo studies There are relatively few in-vivo studies of drug delivery in the eye that quantify drug concentration measurements over time after drug delivery. An extensive review of fluoremetry techniques to measure in-vivo concentrations of fluorophores was performed by Cunha-Vaz.49 Moldow et al. measured concentrations of fluorescein in patients with retinitis pigmentosa and macula edema.50 The fluorescein was delivered intravenously and the concentration in the blood plasma within the retina as well as the concentration in the vitreous were measured as a function of distance from the retina (Fig. 8). They rejected patients with vitreous liquefaction or other complications, and reported both the passive permeability and the unidirectional permeability. The passive permeability is transport that occurs due to diffusion only, and which would remain in an ex-vivo sample, whereas the unidirectional permeability was defined as the effective permeability due to active transport processes (the remainder once the passive effects have been subtracted). This was done seven hours after the injection, by which time the direction of net transport is from the retina to the bloodstream (Fig.  8). Acetazolamide is a drug commonly used to

4.4. Theoretical studies A number of authors studied mass transport in the vitreous chamber with application to intravitreal injection or insertion of a drug-filled implant, and included both the transport due to diffusion of the drug and the transport due to the slow flow in the posterior direction that occurs from the hyaloid membrane at the anterior boundary of the vitreous chamber. Missel52 and Stay et al.53  both performed numerical simulations of drug dispersal in the posterior chamber which included the effect of the slow flow and the effects of diffusion, and both treated the vitreous humor as a porous medium. Like Xu et al.,47  Stay et al.  also found that the flow has a significant influence on mass transport for small molecules, and a larger influence for large molecules.53 Stay et al. also investigated the same problem in mice, and showed that the dynamics are very different owing to the different length scales involved53; in that case, the slow flow hardly affects the mass transport at all, meaning the dispersal is diffusion-dominated in all cases. Park et al. developed a similar model for a rabbit eye, but included additional anatomical details of the eye, which allowed the amount of drug exiting through the aqueous humor and

-1

0

1

2

3

4

5

6

Distance from retina (mm)

7

8

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 8. Pre-retinal vitreous concentration profiles for fluorescein measured after 30 minutes and 7 hours, which enable determination of the passive and unidirectional permeabilities. Recorded in the left eye of Patient 3 in the study by Moldow et al.;50 replotted from the original figure.

334

into Schlemm’s canal to be estimated as well.54 They treated the vitreous and aqueous humors as Newtonian fluids, meaning their results might be more applicable to eyes that have undergone a vitrectomy procedure. They investigated both injecting the drug as a bolus and using an implant to allow for a slower release, and they found that the implant does sustain the release of the drug over a longer period while also reducing the peak concentrations of the drug, both of which could be beneficial for treating some conditions. Kathawate and Acharya  also developed a model to investigate the flow in post-vitrectomy eyes using a Newtonian fluid model.55 Balachandran and Barocas performed a careful numerical study similar to those just described, but considering transcleral application of the drug (fluorescein) instead of intravitreal injection or an implant.46 They used a porous medium to represent the vitreous humor, including absorption by the choroidal circulation and active transport by the retinal pigment epithelium. They employed this model to find the values of unknown parameters, including the amount of drug that would enter the choroidal circulation and the amount that would exit the eye via the sclera. In the case of a molecule with similar properties to fluorescein, they found that less of the drug enters the choroidal circulation than had previously been thought, and also that active transport by the retinal pigment epithelium could be significant and should therefore be taken into account in future models.

Copyright © 2018. Kugler Publications. All rights reserved.

4.5. Effect of eye rotations on mass transport 4.5.1. In-vitro experiments As discussed above, eye rotations can contribute significantly to convective mass transport in the eye, especially when the vitreous is partially or completely liquefied. Loch et al. developed a model consisting of a glass bulb representing the vitreous chamber mounted on a rotating motor to replicate eye movements.56 They performed sets of experiments using artificial vitreous humor that either completely filled the bulb or partially filled it, with the remainder being filled by a buffer solution representing liquefied vitreous. They then injected dye representing a drug into the center of the model and measured the concentration after three hours with or without simulated saccades. Their results showed that saccades make a significant difference to

R. Repetto and J.H. Tweedy

the distribution of the drug, especially in the case in which there is partially liquefied vitreous humor. Stocchino et al. used a perspex eye model,57 similar to that used in Bonfiglio et al.29 as described in Section  3.2., that was subjected to periodic harmonic torsional oscillations. The authors focused on the flow on the horizontal plane of the model (orthogonal to the axis of rotation), and quantified only the time-averaged flow, also called the steady streaming flow. Although this is not the largest component of the velocity by magnitude, the steady streaming flow is dominant in its effect on mass transport due to the fact that the effect of oscillatory flow components tends to cancel out over whole periods. They found that the lens indentation into the vitreous cavity has a significant effect on the steady flow, with large circulations developing posterior to the lens. 4.5.2. Theoretical studies For small harmonic oscillations and a spherical (or near-spherical) vitreous chamber, it is possible to make some progress analytically. Repetto et al. developed a theoretical model of the vitreous chamber undergoing periodic torsional oscillations, modeling the chamber as a sphere and the vitreous humor as a Newtonian fluid, and focusing on the steady streaming flow.58 They showed that the steady streaming flow consists of two toroidal circulation cells (one in each hemisphere), such that particles close to the horizontal plane orthogonal to the rotation axis move towards the center of the sphere, then towards the poles, and finally back again towards the horizontal plane along the rigid wall of the domain. That work was extended in a subsequent study59 to include the effect of a non-spherical chamber, which made a significant qualitative difference to the flow, in agreement with the results of Stocchino and colleagues.57 The work of Repetto et al.58 was also later extended by the same group to allow consideration of a viscoelastic fluid.60 The authors showed that viscoelasticity significantly complicates the characteristics of the steady streaming flow. Theoretical studies of mass transport in the presence of eye rotations are made difficult by the fact that the time scale of a saccade is very short compared to the time scale of interest for drug transport, so many saccades need to be simulated to find the distribution. Balachandran et al. developed a technique to overcome

Biomechanics of the vitreous humor

this, which they called telescopic time bridging.61 In this method, a few saccadic cycles are simulated in detail, and then the solution is projected forward over many periods using the information gained from the initial detailed simulation, followed by a detailed simulation over a few periods, and so on. Balachandran and Barocas  used this approach with a Newtonian fluid model of the vitreous humor, which allowed them to investigate the dispersion of a drug injected into the vitreous humor of an eye performing repeated saccades.62 Their results show significant differences between the cases with and without saccades, with the time scale for drug transport being reduced from hours to minutes, highlighting the importance of including saccadic motion in models of drug transport. Abouali et al. performed numerical simulations of the motion of a Newtonian model of the vitreous humor, investigating in particular the effect of the indentation in the vitreous chamber due to the presence of the lens.63 Modareszadeh et al. also simulated dispersion of a drug in a Newtonian model of the vitreous humor, with saccadic motions included for various injection locations and drug diffusivities, and agreed that saccades have a dramatic effect on the time scales.64 This again showed that he diffusivity of the drug does not make a significant difference after a few cycles, whereas the details of the saccade dynamics have a big effect. In conclusion, saccadic eye motion has a dominant effect and should be accounted for in models to investigate mass transport. However, the details of this effect are not well understood, though they certainly seem to be complicated. This is thus an area in which future research is needed.

Copyright © 2018. Kugler Publications. All rights reserved.

5. Retinal detachment RD occurs when fluid enters the space between the neurosensory retina and the retinal pigment epithelium (RPE), the outer layer to which the retina is normally adhered. Rhegmatogenous retinal detachment (RRD) is the most common type of RD, and it occurs when the liquefied vitreous enters the subretinal space through a retinal tear. The tears are primarily produced as a result of PVD, which leads to tractions on the retina, especially if there are regions of vitreous that have especially tight adhesions that could lead to concentrated mechanical

335

stimuli and subsequent non-traumatic tearing.16 In the general population, RRD occurs in about 10 out of 100,000 people65 and is among the most frequent causes of blindness in Western countries. At the beginning of the 20th century, Jules Gonin, who performed the first intervention for treatment of RRD employing trans-scleral cautery to seal a retinal break, wrote in the French Encyclopedia of Ophthalmology: “In order to effectively fight a pathological process, we must know its nature and anatomic conditions. Only the study of pathogenesis of spontaneous (retinal) detachment, based on facts and not on hypothesis, will make it possible to find the treatment of this disease”.66 Indeed, it is widely accepted that mechanics plays a fundamental role both in the generation of retinal tears and in the subsequent process of RD. However, more than a century after these words were written, the mechanical processes underlying RD are still poorly understood and only a relatively small number of papers have been published in the field. Despite this lack of understanding, the success rate in treating RDD has significantly increased in recent years, mainly due to the use of scleral buckling and vitrectomy, both of which rely on mechanical principles, and are discussed in Sections 5.4 and 5.5., respectively. 5.1. Vitreoretinal adhesive force The probability of RD depends on the balance between vitreous tractions and the strength of the adhesion between the retina and the RPE. Hence, in order to understand the mechanical processes leading to a RD and improve its management, it is important to estimate the forces maintaining the retinal apposition to the RPE, which include both active and passive forces. The latter arise as a result of the structure of the retina,16 and it is thought that the active forces appear to play the dominant role in retinal adhesion. These active forces are essentially related to a flux of water from the vitreous to the choroid across the retina, RPE, and Bruch’s membrane,67 which is driven by mechanical pressure differences, colloid osmotic pressure, and diffusion.16 Various authors have attempted to measure the strength of retinal adhesion to the RPE employing different techniques. Ex-vivo peeling experiments on rabbit eyes performed by deGuillebon et al. measured the force needed to peel strips of the retina off the

Copyright © 2018. Kugler Publications. All rights reserved.

336

pigment epithelium at a constant rate, finding that the adhesion is greater at the equator.68 A subsequent study by deGuillebon and Zauberman used a similar technique to show that the peeling force required increases with the rate of peeling, and moreover, the rate of peeling was smooth for low peeling rates but jerky for higher rates.69 Marmor et al. also performed ex-vivo peeling experiments while the sample was immersed in a physiologic medium, which allowed them to observe the effects of various environmental factors.70 The adhesive forces measured in these ex-vivo tests could be substantially different from those in vivo since the active processes are not present in the ex-vivo experiments. To overcome this, Kita et al. proposed a new method to measure the adhesive force in vivo by inducing non-rhegmatogenous RDs in rabbit eyes.71 They did this by inserting a glass micropipette through a scleral slit and advancing it through the vitreous until it penetrated through the retina at the posterior pole. A balanced salt solution was then injected through the pipette into the subretinal space in order to create a dome-shaped RD (bleb). The authors measured the pressure within the bleb and used this to estimate the retinal adhesive force as follows. They assumed the bleb was spherical and used the law of Laplace to estimate the force of the retina at the edge of the bleb acting orthogonally to the retinal surface, which leads to T = R(Ps – Pv)/2. In this equation (and adopting the authors’ original notation), T is the estimated force per unit length exerted on the eye wall, R is the bleb radius, Pv is the intravitreal pressure and Ps the subretinal pressure within the bleb, with Ps > Pv. As fluid is injected into the bleb, Ps increases, and so T also increases up to the limit at which failure occurs, and the value of T at this limit is the estimated force per unit length required to achieve failure of the adhesion along the bleb margin. Using this method, the authors found forces of 0.18 ± 0.02 N/m, which were approximately five times larger than those estimated with in-vitro peeling methods. Kita et al. used the same method to test the eyes of rabbits, cats, and monkeys, finding similar values for the adhesive force.72 5.2. Models of vitreo-retinal tractions In the presence of PVD, the gel-like vitreous volume shrinks and the remainder of the volume in the vitreous chamber is filled with liquefied vitreous humor. The

R. Repetto and J.H. Tweedy

posterior vitreous cortex continues to bound the gel-like vitreous and acts as the boundary between the two fluids. Vitreoretinal tractions, which may be either static or dynamic in nature, can be generated under these conditions. Dynamic mechanical stimuli are due to saccadic eye rotations that produce oscillations of the detached vitreous, and consequently, tractions on the retina, particularly at the attachment points of the gel-like vitreous to the retina. Static forces on the retina are induced by the quasi-static shrinkage of the vitreous humor produced by vitreous syneresis. Both types of force are thought to have the potential to lead to retinal breaks. Repetto et al. proposed an idealized mathematical model to estimate retinal tractions during eye rotations in the presence of a PVD.73 The authors considered a 2-D domain, representing the vitreous chamber as a circle. The domain was subdivided into two regions, one occupied by a viscoelastic solid material representing the vitreous in the gel state, and the other occupied by a purely viscous fluid representing the liquefied vitreous. The approach accounted for the presence of the posterior vitreous cortex by assuming the presence of an elastic membrane (stiffer than the solid) separating the two regions. The domain was rotated to represent saccadic rotations of the eye globe, and the deformation of the solid as well as the motion of the fluid were studied numerically using a finite element method. The authors considered various different shapes of the detached vitreous, which represented idealizations of possible progressions of PVD. In all cases, they found large tractions are generated on the retina close to the attachment points of the membrane, identifying PVD configurations that exhibited particularly high tractions. Interestingly enough, the numerical simulations suggested that the tractions are likely to be of the same order of magnitude as the adhesive force between the retina and the RPE, providing evidence that saccadic eye rotations in the presence of PVD could be responsible for RD. Di Michele et al.  recently developed a mathematical model of quasi-static generation of tractions on the retina produced by shrinkage of the vitreous, i.e., syneresis.74 The vitreous body was modeled as a hyperelastic, viscous solid, and the authors also accounted for the presence of the vitreous cortex, described as a membrane wrapping the vitreous, with a higher

Copyright © 2018. Kugler Publications. All rights reserved.

Biomechanics of the vitreous humor

elastic modulus than the bulk vitreous. The process of syneresis was simulated by imposing a uniform and isotropic contraction of the relaxed state of the vitreous and the vitreous cortex in time. The authors modeled the vitreous chamber as a sphere, and imposed an attachment traction field between the vitreous and the wall of the chamber that varies over the surface of the sphere to represent the real physiological adhesion. They modeled the evolution of the vitreous using a finite element model, assuming that the vitreous gel initially filled the vitreous chamber completely. If the vitreous were able to freely shrink, without any external tractions applied to it, it would do so without generating stresses. However, the existence of a spatially variable adhesion on the retina breaks the spherical symmetry, and the contracting vitreous experiences stresses. Figure  9 shows two examples of 3-D configurations of the detached vitreous body attained during the progression of PVD. The first case (Fig.  9a) is relative to a complete vitreous detachment, and was obtained by assuming that the limit adhesive traction between the vitreous and the retina grows from the back (right) to the front (left) of the vitreous chamber. In contrast, Figure  9b shows the case of a PVD in the presence of a focal vitreoretinal adhesion at the back of the vitreous chamber. This case is known to be potentially dangerous, since large tractions can be generated on the retina. In this case, during the contraction process, the vitreous undergoes large amplitude deformations, which are associated with large values of stress. Shapes of the contracting vitreous body very similar to those shown in Figure 9 can be observed clinically. The model shows that once the spatial variation of the adhesive traction at the boundary is proscribed, the shape of the detaching vitreous is determined by two dimensionless parameters. The first is the ratio between the elastic moduli of the bulk solid and the skin; the second is the ratio between the elastic modulus of the solid and the limiting adhesive traction at the wall. The model can be used to identify shapes of the detaching vitreous associated with the existence of strong focal adhesions on the retina, which is a risk factor for the generation of retinal tears. 5.3. Models of RD Once a retinal break is present, the development of RD is thought to be due to motion of the liquefied vitreous,

337

Fig. 9. Shapes of the contracting vitreous predicted by the model. (a) Complete detachment: in this case, the limiting adhesion traction increases from the back (right) to the front (left) of the posterior chamber. (b) Focal adhesion: in this case, it has been assumed that the vitreous has a focal adhesion to the retina at the back of the vitreous chamber.

which can enter the subretinal space, as well as to vitreoretinal tractions.3 Mechanics is obviously heavily involved in both of these mechanisms. The possible occurrence of fluid currents from the vitreous cavity to the subretinal space has been studied by Lindner,75 who performed seminal experiments with the aim of understanding the mechanical processes leading to RRD once a retinal break is formed. The authors used an experimental apparatus consisting of a cylindrical glass container filled with water whose inner wall was covered by a thin membrane that had a small tear in it. They found that translational movements of the container did not lead to the detachment of the membrane, although rotations might have contributed. The mechanics of RD induced by vitreoretinal tractions has also been studied by Bottega et al.76 and Lakawicz et al.77 They modeled the retina, sclera, and choroid as spherical shells, with the retina being elastic and the choroid and sclera as rigid. The vitreous gel was modeled as a contracting sphere connected to the retina through elastic fibrils that stretch progressively as the vitreous contracts. They considered the case with no retinal break and also the case with a circular hole in the retina, finding that the retina could come away from the choroid catastrophically in either case. However, it was more likely in the case with no hole, indicating that a retinal hole might stabilize the RD in some cases. 5.4. Treatments for retinal detachment: vitrectomy The main surgical techniques currently employed to treat RRD are vitrectomy and scleral buckling, and we briefly discuss them in this section and the next,

Copyright © 2018. Kugler Publications. All rights reserved.

338

respectively. Vitrectomy involves removal of the degraded vitreous humor aimed at relieving vitreoretinal tractions. The vitreous chamber is then filled with tamponade fluids that can be liquid (typically silicone oils) or gases. The patient must keep a prescribed head position for several hours or days, so that the liquid/ gas bubble floats against the retinal tear and pushes the retina back in contact with the pigment epithelium, favoring reattachment. Foster and Chou  compared the effect of the two major forces involved in the reattachment process with retinopexy by estimating the buoyancy and surface tension forces induced on the retinal tear by the gas bubble.77 The authors discuss the possible physical mechanisms that can contribute to retinal reattachment. In the case of a large bubble inserted in the eye, which is the typical scenario, they argue that reattachment takes place primarily as a result of surface tension effects. When a tamponade fluid is injected, a layer of aqueous humor forms between the tamponade fluid and the retina. Isakova et al. developed a mathematical model in which they showed that this layer significantly decreases the shear stress exerted on the retina.79 They also investigated the stability of the interface between the two fluids during eye rotations (see also Isakova et al.),80 and their results suggest that the interface could be unstable over a range of physiological parameters. Eames et al. developed a mathematical model to find the shape of a gas bubble in the vitreous chamber, showing that it depended only on the Bond number, which expresses the relative strengths of buoyancy forces and surface tension, as well as on the volume fraction of gas added.81 Angunawela et al. numerically simulated a spherical eye model filled with a mixture of air and water during both horizontal and vertical saccade movements.81 They calculated the shear stress, showing that the highest magnitude shear stresses are achieved when the eye is approximately 50% full of air and that rectilinear (as opposed to angular) motion produced higher stresses in this case. This is in contrast to the case of an eye filled with a homogeneous material, in which rectilinear acceleration produces only a change in pressure and does not give rise to fluid motion and shear stress. Amini et al. studied a mathematical model of an eye with an intravitreal gas bubble that is undergoing

R. Repetto and J.H. Tweedy

altitude changes over time, giving rise to pressure changes similar to those experienced during airplane flight.83 They checked their results against in-vivo measurements and investigated the alleviation of the pressure change that might be produced by increasing the outflow facility for the aqueous humor or decreasing the aqueous humor production rate. 5.5. Treatments for RD: scleral buckling Scleral buckling is a treatment for RRD consisting of a surgically induced change in the curvature of the sclera in correspondence to the retinal hole, which clinical practice has shown helps promote reattachment of the retina to the RPE. The mechanism by which the retina reattaches during buckling remains obscure, although a number of studies have been conducted that confirm the observations or add to our understanding in other ways, and these are reported in this section. Clemens et al. developed an in-vitro model of an eye with a detached retina by attaching a piece of fabric to the bottom of a glass tank, creating a hole in the fabric, and injecting fluid through the hole to simulate RD.83 The authors had also placed a plastic tube, simulating a scleral buckle, underneath the fabric. They then filled the tank with fluid and rocked it back and forth on rollers to simulate saccades of the eye. The fabric moved downwards so that it tightly covered the plastic tube, simulating reattachment of the retina and agreeing with clinical observations. Keeling et al. used an energy minimization procedure subject to a volume constraint to find the shape of the eye wall during scleral buckling, finding the maximum postoperative appositional pressure that would be attained as well as the pressure that would be achieved in the longer term.85 Foster developed a simplified numerical model of a detached retina with a hole and a scleral buckle under the hole.86 Their results showed a decrease in subretinal pressure, agreeing with the observation that the scleral buckle promotes appositional pressure and reattachment. Meskauskas et al. used an analytical model approximating the shape of the eye with a scleral buckle as a weakly deformed sphere.42 They modeled the vitreous humor as a viscoelastic material, calculating the pressure and shear stress during saccades of the eye, which they found were significantly changed by

Biomechanics of the vitreous humor

the presence of the buckle, although the results did not give significant insight as to why the scleral buckle procedure is successful. Ge et al.  used an energy conservation approach to predict the effect of a scleral buckle on a detached flap of retina, showing that when the buckle is in position, the flap tends to move towards the outer wall, indicating a possible mechanism for healing.87

339

2.

Copyright © 2018. Kugler Publications. All rights reserved.

6. Conclusions and future research directions We hope to have shown that the biomechanics of the vitreous humor is a fruitful and interesting area of study that presents many problems that are amenable to experimental, numerical, or analytical studies. Although progress has been made, the lack of correspondence between modeling and clinical practice remains of concern. On the one hand, many treatments are performed that would benefit from an improved understanding of the underlying mechanical principles, and on the other hand, our current understanding of the mechanics is insufficient to have a useful impact on clinical practice. We are thus left with a number of challenges that we would encourage the researcher in biomechanics to pursue:  1. Motion of the vitreous humor: Vitreous motion is now understood to play a crucial role in all areas of vitreous biomechanics discussed in this chapter. Significant progress in our understanding of this area has been made recently, and experiments, numerical work, and theoretical studies all agree very well. However, an agreement between our understanding of these predictions and the reality of what happens in the eye has not yet been conclusively demonstrated. Crucially, this depends on the rheology of the vitreous humor, which is still relatively poorly understood, owing to the difficulty of experimental approaches to

3.

4.

5.

determine the appropriate parameters.  Mass transport: Mass transport plays a major role in many processes, including transport of nutrients through the retina and of oxygen through the vitreous humor, the latter which is thought to lead to cataracts. Our understanding of this is limited. In particular, drug transport is a significant area of interest, owing to the large number of intravitreal injections that are performed in current clinical practice. The studies so far highlight the significant effect of saccadic motions in the distribution of the drug over time. However, our understanding of the time scales for drug distribution and the locations at which the drug is absorbed remains confined to modeling highly idealized scenarios rather than complex in-vivo conditions.  RD: Our understanding of the process of RD is patchy, and we have little ability to predict the areas of the retina that are at risk of damage from data that is obtainable in the clinic. A lack of understanding of the precise forces involved, as well as the physiological variability in these systems inherent in both aging and disease processes, hampers these efforts. Treatments for RD: The mechanical principles underlying the effectiveness of retinopexy and scleral buckling are not well understood. A better knowledge in these areas could lead to improvement in the treatments themselves, and could also point the way to more effective approaches in the future. One of the main problems associated with the long-term use of tamponade fluids, particularly silicone oils, is the typical occurrence of emulsification. Although there has been some research in this area, the mechanisms causing this are not understood. A better understanding of the mechanics would inform the development of tamponades resistant to emulsification. 

340

R. Repetto and J.H. Tweedy

References 1. 2. 3. 4. 5. 6. 7. 8.

9.

10. 11.

12.

13.

14.

15.

Copyright © 2018. Kugler Publications. All rights reserved.

16.

17.

18.

19.

20.

J. Sebag. The vitreous: structure, function and pathobiology. Springer and Verlag;1989. Le Go MM, Bishop PN. Adult vitreous structure and postnatal changes. Eye (Lond). 2008;22(10):1214-1222. PMID: 18309340. Foulds W. Is your vitreous really necessary? Eye. 1987;1:641175. E. Steffansson. Physiology of vitreous surgery. Graefes Arch Clin Exp Ophthalmol. 2009:247:147-163, 2009. Tanner RI. Engineering Rheology. 2nd ed. Oxford University Press; 2000. Bettelheim FA, TJY Wang. Dynamic viscoelastic properties of bovine vitreous. Exp Eye Res. 1976;23(4):435-441. Tokita M, Fujiya Y, Hikichi K. Dynamic viscoelasticity of bovine vitreous body. Biorheology. 1983;21(6):751-756. Lee B, Litt M, Buchsbaum G. Rheology of the vitreous body. Part I: viscoelasticity of human vitreous. Biorheology. 1992;29:521533. Lee B, Litt M, Buchsbaum G. Rheology of the vitreous body: Part 2. viscoelasticity of bovine and porcine vitreous. Biorheology. 1994;31(4):327-338. PMID: 7981433. Zimmerman RL. In vivo measurements of the viscoelasticity of the human vitreous humor. Biophys J. 1980;29:539-544. Walton KA, Meyer CH, Harkrider CJ, Cox TA, Toth CA. Age-related changes in vitreous mobility as measured by video b scan ultrasound. Exp Eye Res. 2002;74(2):173-180. PMID: 11950227. Piccirelli M, Bergamin O, Landau K, Boesiger P, Luechinger R. Vitreous deformation during eye movement. NMR Biomed. 2012;25(1):59-66. Nickerson CS, Park J, Korn JA eld, Karageozian H. Rheological properties of the vitreous and the role of hyaluronic acid. J Biomech. 2008;41(9):1840-1846. Sharif-Kashani P, Hubschman J-P, Sassoon D, Kavehpourlee HP. Rheology of the vitreous gel: effects of macromolecule organization on the viscoelastic properties. J Biomech. 2011;44(3):419-423. PMID: 21040921. Swindle KE, Hamilton PD, Ravi N. In situ formation of hydrogels as vitreous substitutes: Viscoelastic comparison to porcine vitreous. J Biomed Mater Res A. 2008;87A(3):656-665. Foulds WS. Role of vitreous in the pathogenesis of retinal detachment. In: Sebag J., Ed. Vitreous in Health and Disease, p. 375-393. Springer-Verlag; 2014. Bishop PN, Holmes DF, Kadler KE, McLeod D, Bos KJ. Age-related changes on the surface of vitreous collagen fibrils. Invest Ophthalmol Vis Sci. 2004;45(4):1041-1046. Canning CR, Greaney MJ, Dewynne JN, Fitt A. Fluid flow in the anterior chamber of a human eye. IMA J Math Appl Med Biol. 2002;19:31-60. Heys JJ, Barocas VH. A Boussinesq model of natural convection in the human eye and formation of Krunberg’s spindle. Ann Biomed Eng. 2002;30:392-401. Dyson R, Fitt AJ, Jensen OE, et al. Post re-attachment retinal re-detachment. In: Proceedings of the Fourth Medical Study Group. University of Strathclyde: Glasgow; 2004.

21. W. Becker W. Metrics. In R.H. Wurtz and M.E. Goldberg, editors, The neurobiology of saccadic eye movements. Elsevier Science Publisher BV (Biomedical Division); 1989. 22. Sebag J. Seeing the invisible: the challenge of imaging vitreous. J Biomed Opt. 2004;9(1):38-46. 23. Rossi T, Querzoli G, Pasqualitto G, et al. Ultrasound imaging velocimetry of the human vitreous. Exp Eye Res. 2012;99(1):98104. PMID: 22516112. 24. Falchi M, Querzoli G, Romano GP. Robust evaluation of the dissimilarity between interrogation windows in image velocimetry. Exp Fluids. 2006;41(2):279-293. 25. Adrian RJ. Twenty years of particle image velocimetry. Exp Fluids. 2005;39(2):159-169,. 26. Fischer SE, McKinnon GC, Maier SE, Boesiger P. Improved myocardial tagging contrast. Magn Reson Med. 1993;30(2):191-200. 27. Piccirelli M, Luechinger R, Sturm V, et al. Local deformation of extraocular muscles during eye movement. Invest Ophthalmol Vis Sci. 2009;50(11):5189-5196. 28. David T, Smye S, Dabbs T, James T. A model for the fluid motion of vitreous humour of the human eye during saccadic movement. Phys. Med. Biol. 1998;43:1385-1399. 29. Bonfiglio A, Lagazzo A, Repetto R, Stocchino A. An experimental model of vitreous motion induced by eye rotations. Eye Vis (Lond). 2015;2(1):10. 30. Kummer MP, Abbott JJ, Dinser S, Nelson BJ. Artificial vitreous humor for in vitro experiments. In: Engineering in Medicine and Biology Society, 2007. EMBS 2007. 29th Annual International Conference of the IEEE;2007:6406-6409. 31. Repetto R, Stocchino A, Cafferata C. Experimental investigation of vitreous humour motion within a human eye model. Phys Med Biol. 2005;50:4729-4743. 32. Soman N, Banerjee R. Artificial vitreous replacements. Biomed Mater Eng. 2003;13(1):59-74 33. Stocchino A, Repetto R, Cafferata C. Eye rotation induced dynamics of a Newtonian fluid within the vitreous cavity: the effect of the chamber shape. Phys Med Biol. 2007;52:2021-2034. 34. Meskauskas J, Repetto R, Siggers JH. Oscillatory motion of a viscoelastic fluid within a spherical cavity. J Fluid Mech. 2011;685:1-22. 35. Repetto R, Siggers JH, Meskauskas J. Fluid mechanics of the vitreous chamber. In: Causin P, Guidoboni G, Sacco R, Harris A, eds. Integrated multidisciplinary approaches in the study and care of the human eye. Amsterdam: Kugler Publications; 2014. 36. Modarreszadeh A, Abouali O. Numerical simulation for unsteady motions of the human vitreous humor as a viscoelastic substance in linear and non-linear regimes. J Nonnewton Fluid Mech. 2014;204:22-31. 37. The Eye Disease Case-Control Study Group. Risk factors for idiopathic rhegmatogenous retinal detachment. Am J Epidemiol. 1993;137:749-757. 38. Akiba J. Prevalence of posterior vitreous detachment in high myopia. Ophtalmology. 1993;100(9):1384-1388. 39. Morita H, Funata M, Tokoro T. A clinical study of the development of posterior vitreous detachment in high myopia. J Ret Vit Dis. 1995;15(2):117-124.

Copyright © 2018. Kugler Publications. All rights reserved.

Biomechanics of the vitreous humor 40. Atchison DA, Jones CE, Schmid KL, et al. Eye shape in emmetropia and myopia. Invest Ophthalmol Vis Sci. 2004;45(10):33803386. 41. Atchison DA, Pritchard N, Schmid KL, et al. Shape of the retinal surface in emmetropia and myopia. Invest Ophthalmol Vis Sci. 2005;46(8):2698-2707. 42. Meskauskas J, Repetto R, Siggers JH. Shape change of the vitreous chamber influences retinal detachment and reattachment processes: Is mechanical stress during eye rotations a factor? Invest Ophthalmol Vis Sci. 2012;53(10):6271-6281. PMID: 22899755. 43. Ethier CR, Johnson M, Ruberti J. Ocular biomechanics and biotransport. Annu Rev Biomed Eng. 2004;6:249-273. 44. Cunha-Vaz JG. The blood-retinal barriers system. Basic concepts and clinical evaluation. Exp Eye Res.2004;78:715-721. 45. Geroski DH, Edelhauser HF. Drug delivery for posterior segment eye disease. Invest Ophthalmol Vis Sci. 2000;41(5):961-964. 46. Balachandran R, Barocas V. Computer modeling of drug delivery to the posterior eye: Effect of active transport and loss to choroidal blood flow. Pharm Res. 2008;25(11):2685-2696. 47. Xu J, Heys JJ, Barocas VH, Randolph TW. Permeability and diffusion in vitreous humor: implications for drug delivery. Pharm Res. 2000;17(6):664-669. 48. Penkova A, Rattanakijsuntorn K, Sadhal SS, et al. A technique for drug surrogate diffusion coefficient measurement by intravitreal injection. Int J Heat Mass Transfer. 2014;70:504-514. 49. J. G. Cunha-Vaz. Optical sensors for clinical ocular fluorometry. Prog Ret Eye Res. 1997;16(2):243-270. 50. Moldow B, Sander B, Larsen M, et al. The effect of acetazolamide on passive and active transport of fluorescein across the blood-retina barrier in retinitis pigmentosa complicated by macular oedema. Graefe’s Arch Clin Exp Ophthalmol. 1998;236:881-889. 51. Awwad S, Lockwood A, Brocchini S, Khaw PT. The pk-eye: A novel in vitro ocular flow model for use in preclinical drug development. J Pharmaceut Sci. 2015;104(10):3330-3342 52. Paul J Missel. Hydraulic flow and vascular clearance influences on intravitreal drug delivery. Pharm Res. 2002;19(11):16361647. PMID: 12458669. 53. Stay MS, Xu J, Randolph TW, Barocas VH. Computer simulation of convective and diffusive transport of controlled-release drugs in the vitreous humor. Pharm Res. 2003;20(1):96-102. PMID: 12608542. 54. Park J, Bungay PM, Lutz RJ, et al. Evaluation of coupled convective-diffusive transport of drugs administered by intravitreal injection and controlled release implant. J Control Release. 2005;105(3):279-295. 55. Kathawate J, Acharya S. Computational modeling of intravitreal drug delivery in the vitreous chamber with different vitreous substitutes. Int J Heat Mass Transf. 2008;51(23-24):5598-5609. 56. Loch C, Bogdahn M, Stein S, et al. Simulation of drug distribution in the vitreous body after local drug application into intact vitreous body and in progress of posterior vitreous detachment. Pharmaceut Drug Deliv Pharmaceut Tech. 2014;103:517526.

341 57. Stocchino A, Repetto R, Siggers JH. Mixing processes in the vitreous chamber induced by eye rotations. Phys Med Biol. 2010;55(2):453-467. 58. Repetto R, Siggers JH, Stocchino A. Steady streaming within a periodically rotating sphere. J Fluid Mech. 2008;608:71-80. 59. Repetto R, Siggers JH, Stocchino A. Mathematical model of flow in the vitreous humor induced by saccadic eye rotations: effect of geometry. Biomech Mod Mechanobiol. 2010;9(1):65-76. 60. Repetto R, Siggers JH, Meskauskas J. Steady streaming of a viscoelastic fluid within a periodically rotating sphere. J Fluid Mech. 2014;761:329-347. 61. Balachandran RK, Roychowdhury J, Dorfman KD, Barocas VH. Telescopic timescale bridging for modeling dispersion in rapidly oscillating flows. AIChE J. 2011;58:1987-1997. 62. Balachandran RK, Barocas VH. Contribution of saccadic motion to intravitreal drug transport: Theoretical analysis. Pharm Res. 2011;28(5):1049-1064. 63. Abouali O, Modareszadeh A, Ghaffariyeh A, Tu J. Numerical simulation of the fluid dynamics in vitreous cavity due to saccadic eye movement. Med Eng Phys. 2012;34(6):681-692. 64. Modareszadeh A, Abouali O, Ghaffariyeh A, Ahmadi G. Saccade movements effect on the intravitreal drug delivery in vitreous substitutes: a numerical study. Biomech Mod Mechanobiol. 2012;12(2):281-90. 65. Mitry D, Chalmers J, Anderson K, et al. Temporal trends in retinal detachment incidence in Scotland between 1987 and 2006. Br J Ophthalmol. 2009;95(3):365-369. 66. Gonin J. Décollement rétinien. Encycl Franη Ophtalmol 1906;6:947-1025. 67. Moseley H, Foulds WS, Allan D, Kyle PM. Routes of clearance of radioactive water from the rabbit vitreous. Br J Ophthalmol. 1984;68(3):145-151. 68. deGuillebon H, de la Tribonniere MM, Pomerantze O. Adhesion between retina and pigment epithelium: measurement by peeling. Arch Ophthalmol. 1971;86(6):679. 69. deGuillebon H, Zauberman H. Experimental retinal detachment: Biophysical aspects of retinal peeling and stretching. Arch Ophthalmol. 1972;87(5):545. 70. Marmor MF, Abdul-Rahim AS, Cohen DS. The effect of metabolic inhibitors on retinal adhesion and subretinal fluid resorption. Invest Ophthalmol Vis Sci. 1980;19(8):893-903. 71. Kita M, Negi A, Kawano S, Honda Y, Maegawa S. Measurement of retinal adhesive force in the in vivo rabbit eye. Invest Ophthalmol Vis Sci. 1990;31(4):624-628. 72. Kita M, Marmor MF. Retinal adhesive force in living rabbit, cat, and monkey eyes. normative data and enhancement by mannitol and acetazolamide. Invest Ophthalmol Vis Sci. 1992;33(6):1879-1882. 73. Repetto R, Tatone A, Testa A, Colangeli E. Traction on the retina induced by saccadic eye movements in the presence of posterior vitreous detachment. Biomech Mod Mechanobiol. 2010;10:191-202. 74. Di Michele F, Repetto R, Tatone A. A mathematical model of posterior vitreous detachment and generation of vitreoretinal tractions. In: Book of Abstracts: “Summer Biomechanics, Bio-

342

75.

76. 77.

78.

79.

80.

Copyright © 2018. Kugler Publications. All rights reserved.

81.

R. Repetto and J.H. Tweedy engineering, and Biotransport Conference”, National Harbor, Maryland, June 29 - July 2 2016. Submitted. Lindner K. Uber die Herstellung von Modellen zu Modellversuchen der Netzhautabhebung. Klin. Mbl. Augenheilk, 1933;90:289-300. Bottega WJ, Bishay PL, Prenner JL, Fine HF. On the mechanics of a detaching retina. Math Med Biol. 2013;30:287-310. Lakawicz JM, Bottega WJ, Prenner JL, Fine HF. An analysis of the mechanical behaviour of a detached retina. Math Med Biol. 2015;32:137-161. Foster W, Chou T. Physical mechanisms of gas and perfluoron retinopexy and subretinal uid displacement. Phys Med Biol. 2004;49:2989-2997. Isakova K, Pralits JO, Repetto R, Romano MR. Mechanical models of the dynamics of vitreous substitutes. Biomed Res Int. 2014;2014:672926. Isakova K, Pralits JO, Repetto R, Romano MR.. A model for the linear stability of the interface between aqueous humor and vitreous substitutes after vitreoretinal surgery. Phys Fluids. 2014;26(12):124101. Eames I, Angunawela RI, Aylward GW, Azarbadegan A. A theoretical model for predicting interfacial relationships of retinal tamponades. Invest Ophthalmol Vis Sci. 2010;51(4):2243-2247. PMID: 19933190.

82. Angunawela RI, Azarbadegan A, Aylward GW, Eames I. Intraocular fluid dynamics and retinal shear stress after vitrectomy and gas tamponade. Invest Ophthalmol Vis Sci. 2011;52(10):70467051. PMID: 21310904. 83. Amini R, Barocas VH, Kavehpour HP, Hubschman JP. Computational simulation of altitude change-induced intraocular pressure alteration in patients with intravitreal gas bubbles. Retina. 2011;31(8):1656-1663. 84. Clemens S, Kroll P, Stein E, Wagner W, Wriggers P. Experimental studies on the disappearance of subretinal fluid after episcleral buckling procedures without drainage. Graefes Arch Clin Exp Ophthalmol. 1987;225(1):16-18. PMID:3569945. 85. Keeling SL, Propst G, Stadler G, Wackernagel W. A mathematical model for the deformation of the eyeball by an elastic band. Math Med Biol. 2009;26(2):165-185. PMID: 19351791. 86. Foster WJ. Bilateral patching in retinal detachment: fluid mechanics and retinal “settling”. Invest Ophthalmol Vis Sci. 2011;52(8):5437-5440. PMID:21666245. 87. Ge P, Bottega WJ, Prenner JL, Fine HF. On the influence of an equatorial cerclage on closure of posterior retinal detachment. Math Med Biol. 2016;(4):417-433.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

Copyright © 2018. Kugler Publications. All rights reserved.

OPTIC NERVE HEAD, LAMINA CRIBROSA, AND SCLERA

Copyright © 2018. Kugler Publications. All rights reserved.

23. Introduction to posterior pole biomechanics J. Crawford Downs1, Thao D. Nguyen2 Department of Ophthalmology, University of Alabama at Birmingham School of Medicine Birmingham, AL, USA; 2Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD, USA

1

1. The eye as a pressure vessel The reaction of a body to a force is determined by three critical features: the magnitude and time course of the load itself, the geometry of the body under load, and the material properties of the body’s constituent parts. In the case of the eye, an exquisitely designed organ responsible for our critical sense of sight, these seemingly simple qualities are incredibly complex, so much so that we are likely decades or more away from truly understanding ocular biomechanics to the level necessary to combat blinding diseases and conditions such as retinal tears, myopia, and glaucoma. This chapter of Biomechanics of the Eye is focused on introducing the current state of the field in biomechanics of the posterior pole, with in-depth chapters focused on loading, tissue geometries, material properties, and observations, simulations, and experiments designed to elucidate the biomechanical response of critical aspects of the eye later in the book.

Copyright © 2018. Kugler Publications. All rights reserved.

2. Loading Intraocular pressure, or IOP, is the fluid pressure inside the eye that is maintained through the secretion and outflow of aqueous humor. Aqueous humor is a nutrient- and oxygen-rich clear fluid that is secreted by the ciliary body, flows through the pupil into the anterior chamber, bathes the cornea, then flows out of the eye through the conventional (~2/3) and unconventional (~1/3) pathways. While aqueous humor inflow and outflow change throughout the day, they

are always in balance, and the resistance to aqueous outflow determines the IOP set point. While both clinical practice and clinical research have largely relied on infrequent snapshot IOP measurements, hourly at most frequent for research studies, IOP has been shown to be very dynamic, changing on the day-to-day, hour-to-hour, minute-to-minute and second-to-second timescales. It is clear that blinks, saccadic eye movements, and the change in intraocular volume with every heartbeat, common occurrences in all eyes, generate substantial transient IOP fluctuations that likely affect all the physiologic systems critical to ocular function, from aqueous outflow pathways, to mixing of the vitreous, to blood flow, to optic nerve head deformation. Aside from maintaining an inflation load sufficient to maintain eye shape, IOP is a primary risk factor in glaucoma, a prevalent blinding disease. Hence, ocular loading is critical to both the physiology and pathophysiology of the eye. The eye is subjected to additional loading generated by the cerebrospinal fluid (CSF) within the subarachnoid space of the optic nerve, extraocular muscles tugging at the eye wall during eye movements, and tethering of the optic nerve during extreme horizontal gaze. Cerebrospinal fluid pressure is typically measured by lumbar puncture and correlates with intracranial pressure as well as the retrolaminar tissue pressure, though the pressure acting directly on the lamina cribrosa has not been directly measured in humans. While the CSF pressure is smaller than IOP under normal conditions, its direct action on the lamina cribrosa (but not the surrounding sclera) has generated renewed interest in its role in lamina cribrosa biomechanics.

Correspondence:J. Crawford Downs, PhD, Professor, Department of Ophthalmology, University of Alabama at Birmingham School of Medicine, 1670 University Blvd., VH 390A, Birmingham, AL 35294, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 347-350 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

348

Copyright © 2018. Kugler Publications. All rights reserved.

3. Geometry The ocular structures are optimized to maintain the visual pathway under diverse and challenging conditions. The eye is a soft tissue structure and the load-bearing ocular coats are responsible for maintaining a constant distance between the cornea and lens, the primary refractive elements in the eye, and the retina, the photo transduction layer responsible for capturing the visual signal and translating it into electrical pulses that can be reconstructed into a moving picture of our surroundings. The eye is not spherical, but a prolate ellipsoid resting in a boney orbit, cushioned by orbital fat and tethered to a complex musculature capable of precisely moving the axis of vision of both eyes in perfect tandem. There are several conditions, such as myopia and keratoconus, in which the shape of the ocular coats become malformed in a manner that interferes with focused vision. In the case of myopia, growth and remodeling processes run amok, leading to an eye that is too long and a focal plane that is in front of the retina rather than on the photoreceptor layer as nature intended. In keratoconus, the cornea develops a characteristic cone-shaped bulge, which changes the refractive power of this clear portion of the ocular coat, thereby disrupting focus in a different way. The cornea, like the sclera, is primarily composed of collagen fibrils, packed in a gelatinous matrix with cells embedded to maintain homeostasis. Unlike the white sclera, the clear corneal collagen fibrils are of very uniform diameter, with precisely controlled packing density, allowing the visible wavelengths of light to penetrate undisturbed. The light entering the eye must travel though the cornea, aqueous humor, the pupil of the iris, the lens, and the vitreous humor on its path to the retina. Each of these elements must provide a clear path for the light signal, as well as precise refractive power, such that the visual focal plane rests precisely on the retina. The biomechanical and optical characteristics of these distinct structures and fluids are critical to eye function. The cornea, for example, is avascular, and so the cells of the cornea must be nourished by a constant flow of nutrient and oxygen-rich aqueous humor that moves through the anterior chamber by diffusion, convection, and mixing flow driven by ocular motion and IOP dynamics. The nerve fibers that transmit the visual information from the retina inside the eye to the brain, also known

J.C. Downs and T.D. Nguyen

as retinal ganglion cell axons, penetrate the sclera at the optic nerve head through a hole in the sclera known as the scleral canal. These neural tissues are very weak mechanically, so the scleral canal is spanned by a fenestrated connective tissue structure known as the lamina cribrosa that provides both structural and nutrient support to the axons coursing through its pores. It is generally accepted that the laminar region of the optic nerve head is the site of damage to the axons in glaucoma, and the lamina cribrosa is thought to play a central role in the disease pathophysiology.

4. Material properties Collagen fibrils in both the cornea and sclera are arranged in stacked sheets (lamellae) and the fibrils within individual lamellae are arranged in a predominant fibril direction that lies in the plane of the eye wall. The directional arrangement of the fibrils resists the in-wall hoop stresses present in every pressure vessel, and any preferential directionality determines the relative directional stiffness of the ocular coat at each location. When measured through the thickness and assessed in toto, the corneal fibrils are arranged with preferential orientation in the vertical and horizontal directions centrally, as well as arranged in a highly anisotropic, circumferential orientation near the corneal junction with the sclera, where hoop stresses are high. Similarly, the scleral canal is a relatively weak spot in the otherwise strong corneoscleral envelope, as the lamina cribrosa is approximately one-third the thickness of the surrounding sclera and is filled with pores through which the axons weave on their path from the retina to the brain. The peripapillary sclera around the scleral canal is thicker than the surrounding sclera, and includes a reinforcing ring of circumferentially-aligned collagen fibers to resist IOP-induced canal expansion and excessive laminar strain (stretch, compression, and/or shear). The collagen fibrils in the ocular coats exhibit a crimp at normal mechanical strain levels, which acts like the coils of a spring. At low strains, the collagen fibrils stretch with relative ease as the crimp is pulled out, but the fibrils stiffen once straightened at high strain levels, providing increased resistance to further deformation. This results in a resilient, elastic pressure vessel that maintains its shape after repeated

Introduction to posterior pole biomechanics

loading and unloading cycles. The viscoelastic response of the corneoscleral envelope also plays a critical role, in that the eye wall dissipates energy when deformed, thereby damping IOP fluctuations.

5. The eye is a living, changing, structural system

Copyright © 2018. Kugler Publications. All rights reserved.

The cells in the eye maintain the ocular load-bearing structures, repairing and remodeling the tissues in response to all manner of stimuli. The cells in the load-bearing ocular coats are typically fibroblastic in nature and are tethered to the surrounding extracellular matrix of collagen and elastin fibers; they thereby sense mechanical deformation of the fibers via a process known as mechanotransduction. Understanding the mechanobiology of the cells of the cornea, sclera, and lamina cribrosa is critical for uncovering the mechanisms underlying diseases including keratoconus, myopia, and glaucoma. The research community has generally relied on experimental systems that apply hydrostatic pressure, constant applied strain, or monotonous cyclic strain to cells grown in culture to deduce their responses to mechanical load. However, recent studies on cell responses to mechanical strain have indicated that cells respond very differently to monotonous and variable cyclic strains, and therefore our current experimental paradigms may be inadequate to simulate cellular responses in vivo.

349

Misconception The eye is often thought of as a static biomechanical structure and researchers often study it as such, but it is not. Intraocular pressure, the principle loading of the eye is very dynamic, and both the geometry and material properties of the ocular coats change with both natural processes, such as aging, and pathophysiologic processes, such as scleral elongation in myopia and optic nerve head remodeling in glaucoma.

The loading of the eye interacts with its tissue geometry and material properties to determine its biomechanical response. Many researchers have studied this complex system assuming that the eye is a static structure. It has become clear however, that the geometry and material properties of the ocular coats differ with racial heritage, and change markedly with both aging and disease pathophysiology, all of which interact to constantly change the structural response of the system. Future research will certainly begin to unravel the intricacies of these changes and their effects on the eye as a biomechanical pressure vessel with the critical function of providing our sense of sight.

Copyright © 2018. Kugler Publications. All rights reserved.

24. Intraocular pressure Daniel C. Turner1, Jessica V. Jasien1, J. Crawford Downs2 Department of Vision Sciences, School of Optometry, University of Alabama at Birmingham, Birmingham, AL, USA; Department of Ophthalmology, School of Medicine, University of Alabama at Birmingham, Birmingham, AL, USA

1

2

Copyright © 2018. Kugler Publications. All rights reserved.

1. Intraocular pressure overview Intraocular pressure (IOP), the fluid pressure inside the eye, is approximately 16 mmHg in healthy humans, but is widely variable and ever-changing at multiple timescales. IOP can be considered as a combination of two components: steady-state IOP and transient IOP fluctuations. The steady-state component of IOP, classically described in Goldmann’s Equation and subsequent revisions by many other researchers, describes IOP as a steady-state function of aqueous inflow (µl/min) and aqueous outflow resistance (µl/ min/mmHg IOP), plus episcleral venous pressure (EVP in mmHg).1 On average, aqueous inflow and outflow are equivalent; the steady-state IOP is a function of the IOPrelated outflow resistance at which that equivalence occurs. As steady state IOP increases, aqueous outflow likewise increases, until aqueous inflow and outflow are in perfect balance. Goldmann’s Equation and its derivatives only act on the timescales of 4-5 seconds and longer due to the lag in outflow- and EVP-driven changes in IOP in response to perturbations, Hence, outflow-driven determinants of IOP cannot explain transient IOP fluctuations due to external forces, such as extraocular muscle contractions and blinks, or rapid changes in intraocular volume, such as choroidal/blood vessel volume variation with the cardiac cycle, also known as ocular pulse amplitude (OPA). The Goldmann description of steady-state or mean IOP forms the basis for understanding ocular hypertension (chronically elevated IOP) as described clinically, as well as current pharmacological or surgical treatment to lower IOP in glaucoma.1 As such, all glaucoma treatments are

focused solely on lowering mean or steady-state IOP2 and ignore transient IOP fluctuations.

Misconception IOP is often thought to be generally stable with slow changes, but IOP is very dynamic, and changes from second-to-second in a manner that single-time-point clinical measurements do not capture. 1.1. EVP: steady-state IOP EVP, arises from aqueous humor that has entered the episcleral veins from the trabecular meshwork (TM), as well as some resistance inherent in that vascular network. It is known that EVP circadian variations follow the same circadian variations of IOP.3 Several variables account for changes in EVP, such as changes in body position, inhalation of oxygen, vasoactive drugs, and cold temperatures.4-7 EVP increases with a change in body position from seated to supine and is stable when body position is unchanged.4 A change of 0.8 mmHg EVP results in an IOP change of 1 mmHg. Mean EVP is approximately 8 mmHg, while mean IOP is approximately 16 mmHg. Hence there is an ~8 mmHg pressure drop from the anterior chamber to the episcleral veins attributable to resistance within the conventional outflow pathways.8,9 The pressure of the retinal veins is also linked to IOP, as retinal venous pressure must be higher than IOP except for short periods to avoid continuous vessel collapse and occlusion. The episcleral veins and central retinal vein

Correspondence:J. Crawford Downs, PhD, Professor and Director, Ocular Biomechanics and Mechanobiology Program, Department of Ophthalmology, University of Alabama at Birmingham School of Medicine, 1670 University Blvd., VH 390A, Birmingham, AL 35294, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 351-362 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

352

D.C. Turner, J. Jasien and J.C. Downs

Copyright © 2018. Kugler Publications. All rights reserved.

(CRV) drain to the ophthalmic vein, which has a lower pressure than EVP. Pulsatile flow in the episcleral veins stops when IOP is decreased below the physiological point, but flow returns when IOP rises to the homeostatic pressure.8,10,11 1.2. IOP-volume relationship Transient IOP fluctuations shorter than 3-4 seconds in duration can be described as a function of IOP and volume in the Friedenwald framework: as the intraocular volume increases instantaneously, so does IOP, and viceversa. In essence, the pressure-volume (P-V) relationship is an exponential function relating the total intraocular volume to IOP, modulated by the elasticity of the corneoscleral shell.12 The magnitude of the IOP rise that occurs with changes in intraocular volume, as well the rate at which the pressure rises, can be related to ocular elasticity and viscoelasticity depending on the time scale of application (near instantaneous to several seconds). For near-instantaneous, equal volume increases, a stiffer eye will have a larger rise in IOP compared to a more compliant eye.13,14 Jonas Friedenwald used this relationship to create the basis for indentation tonometry as an IOP measurement.12 While developing the data upon which his findings were based, he discovered that ocular coat stiffness in human eyes was more variable than previously appreciated. He also noted that the P-V curve becomes linear when plotted on a semi-logarithmic scale based on ocular coat hyperelasticity within eyes, and the slope of the P-V line, known as the ocular rigidity coefficient, varies with the elasticity of the ocular coats between eyes. This model is the theoretical basis for indentation tonometry, and has been widely studied. W. Morton Grant later used this same approach as the basis of tonography, or the study of IOP-induced perturbations of the aqueous outflow of the eye and subsequent recovery after the perturbation removal. This approach involves applying a steady external pressure to the eye to increase steady-state aqueous outflow and induce hypotony to generate approximate outflow rates to then produce a pressure coefficient of outflow.15 Furthermore, the concept of ocular coat stiffening with stretch (hyperelasticity) has been studied by many investigators.16,17–20,21 These studies shed light on the biomechanics of the ocular coats, in particular on the

Fig 1. Hyperelastic ocular coat response due to collagen fiber stiffening. Uncrimping of the collagen fibers induces scleral stiffening at the macroscopic level. Initially, the collagen fibers are buckled, then they uncrimp and eventually become straight due to acute elevations of IOP, thus limiting scleral deformations at high IOP values. Adapted from Girard et al.16

change in ocular coat stiffness with strain (or IOP), and the inhomogeneity of both scleral material properties and collagen fiber alignment. As IOP increases, scleral deformation increases non-linearly; the rate of scleral deformation slows as IOP increases and the ocular coat becomes stretched. This behavior arises from the basic mechanical properties of collagen fibers in soft tissues, in which the collagen fibers are in a crimped, compliant state at normal IOPs and lower collagen stretch levels, and stiffen as they uncrimp and straighten at higher IOPs/stretch levels (Fig. 1). This behavior provides a mechanistic explanation of Friedenwald’s findings, as well as the observation that the ocular coats are less compliant at higher IOPs. Ophthalmic clinical practice generally involves measuring IOP approximately once every 3-12 months using a single-time-point tonometer during clinic hours, although more frequent IOP measurements are often taken in progressing glaucoma patients. The most commonly used device is the clinical gold-standard Goldmann Applanation Tonometer (GAT, Haag-Streit, Essex, UK), which measures IOP using the Imbert-Fick Law by pressing on the corneal surface with a known weight until the cornea is flattened, and measuring the force at which the cornea “pushes” back.22 The GAT and other tonometers are accurate to ~2 mmHg and measure steady-state or mean IOP. While assessment of mean IOP is important, all of these devices fail to

Intraocular pressure

Fig. 2. High- and low-frequency IOP fluctuation in the human eye. Recording of continuous IOP from an unrestrained awake patient with baseline mean IOP of ~16 mmHg and IOP fluctuations up to 10 and 14 mmHg associated with blinks and saccadic eye movements, respectively. Adapted from Coleman and Trokel.25

capture exposure to potentially injurious transient IOP fluctuations that may contribute to the development or progression of glaucomatous optic neuropathy. We know relatively little about the true IOP in patients due to a lack of accurate continuous IOP-monitoring technology. Single-time-point IOP measurements obtained during office hours are very limited, as IOP varies considerably over 24-hour periods and the daily pattern is not repeatable.23,24 The lack of continuous IOP-monitoring technology in humans results in a lack of understanding of how mean IOP and transient IOP fluctuations are involved in ocular homeostasis, and also prevent studies aimed at determining if transient IOP fluctuations contribute to glaucoma development and progression.

Copyright © 2018. Kugler Publications. All rights reserved.

2. IOP dynamics IOP has been recorded continuously in humans on at least two occasions: Coleman and Trokel recorded continuous IOP using anterior chamber manometry just prior to enucleation in two eyes (Fig. 2),25 and Hoh and Schwanengel implanted a Codman Micro Sensor (DePuy Synthes, Raynham, MA, USA) in the eye of two patients (one normal, and one glaucomatous) in a second study.26 In the latter study, IOP data were recorded via the Codman sensor in three eyes of two patients for 1, 1, and 5 days, respectively. These studies confirm that IOP is highly dynamic in humans, and transient IOP fluctuations of 100-250 millisecond duration and up to twice the magnitude of baseline IOP occur frequently with

353

normal ocular function. The main limitation of these studies was the extremely small sample size and the short duration of continuous IOP measurement; hence, it is unlikely that these data are sufficient to fully characterize the highly dynamic nature of IOP. McLaren and colleagues showed that IOP was very dynamic over long periods in studies using implanted IOP transducers and radiotelemetry in unrestrained rabbits.27 Similarly, Downs et al. later reported continuous IOP measurements in non-human primates (NHP) for long periods using a wireless telemetry system.28 These studies concluded that real-time IOP fluctuates as much as 20 mmHg from second-to-second, and mean IOP fluctuates 10 mmHg from day-to-day and hour-to-hour in awake, behaving rabbits and NHPs (Figs. 3 and 4). 2.1. IOP changes with body position IOP changes with changes in body position, and studies have shown a non-linear relationship between IOP increase and body position change from 60° semi-upright to 30° head-down tilt.29 Lee et al. studied the effect of the lateral decubitus position (LDP) on IOP in healthy young subjects,30 demonstrating significant changes in IOP between the dependent eye in LDP compared to that in the supine position. J-W Hwang and coworkers found similar results and reported that the mean differences in IOP between eyes in the LDP ranged from 2.9 to 4.1 mmHg.31 They concluded that IOP was higher in the dependent eye, and that IOPs in anesthetized patients were higher than in those who were awake. Carlson and colleagues measured IOP changes in patients in response to a change in body tilt from 15° from horizontal to 50° from horizontal, and also measured aqueous humor flow with fluorophotometry.32 They concluded that aqueous formation is relatively insensitive to IOP. Malihi and Sit showed that IOP is lowest when measured while sitting with the neck in the neutral position. All other head and body positions resulted in an elevation of IOP compared with the position used for typical clinical measurements (seated). They also noted that the dependent eye IOP was higher in the LDP, and found an inter-eye IOP difference in the LDP of 0.7 to 1.1 mmHg.33 Eklund and coworkers studied the postural influence on simultaneously measured IOP and intracranial pressure (ICP), and reported similar results on IOP changes

354

D.C. Turner, J. Jasien and J.C. Downs

Fig. 3. High- and low-frequency IOP fluctuation in the NHP. Screen capture of ~7 s of continuous telemetric IOP trace from an unrestrained awake NHP with baseline mean IOP of ~8-14 mmHg and IOP fluctuations up to 12 and 8 mmHg associated with blinks and saccadic eye movements, respectively. IOP fluctuations can be much larger and of longer duration, especially when the animal squints, or is agitated or stressed. Adapted from Downs et al.28

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. IOP fluctuates throughout the day in the NHP. (A) Plot of the 10-minute time-window average of 24 hours of continuous IOP showing low-frequency IOP fluctuation from a typical NHP eye. Note that room lights were on from 6 AM to 6 PM daily. The color of the plot points and lines indicate how much data remained in each 10-min window after post-hoc digital filtering of signal dropout and noise. Green indicates that 100% of the continuous IOP data were used in the 10-minute average IOP plotted in each point, and yellow indicates that 50% were eliminated due to signal dropout or noise. Note the fluctuations in IOP are substantial even when the high-frequency IOP spikes seen in Figure 2 are averaged out. Adapted from Downs et al.28 (B) Histogram of IOP for the 24-hour period presented in (A). Note the width of the IOP distribution within this single 24-hour period relative to the median value of 11 mmHg .28

with body position in the sitting and supine positions. They calculated the trans-lamina cribrosa pressure difference (TLCPD) in different body positions by subtracting ICP from IOP. ICP was lowest in the sitting position, resulting in the largest TLCPD compared to the supine and head-down tilt positions.34 2.2. OPA One primary source of transient IOP fluctuations is OPA, or the fluctuation in IOP associated with the cardiac cycle. The relationship between IOP and OPA has been studied recently in humans with dynamic contour tonometry (DCT) (Fig. 5).35 DCT can provide accurate measurement of IOP and its fluctuations, but only for the short periods that a patient can tolerate corneal

contact without blinking. OPA has the potential to be very useful as a measure of ocular coat stiffness when coupled with blood pressure measurements and ophthalmodynamometry to increase IOP acutely. The change in OPA magnitude per mmHg IOP change could be used as a measure of both the elastic and hyperelastic properties of the ocular coats, and as a surrogate for the amplitude of short-duration transient IOP fluctuations due to blinks and saccades that are now impossible to measure non-invasively. OPA fluctuations are one of the best sources of transient IOP fluctuations to study due to the consistency of amplitude, as opposed to blinks of varying force, and saccades of varying acceleration and angle. The ocular coat stiffness estimates gleaned

Intraocular pressure

Fig. 5. Ocular pulse waves measured with dynamic contour tonometry. OPA is a numerical representation of the difference between the minimum (broken line) and maximum (dotted line) of the pulse wave contour. With dynamic contour tonometry, the level of the mean minimum values is displayed as IOP. Adapted from Kaufmann et al.35

from assessing OPA at different IOPs could prove vital to elucidating the role of transient IOP fluctuations in glaucoma.36 OPA increases with IOP (Fig. 6), and when combined with other risk factors, OPA may eventually prove to be important in glaucoma diagnosis and treatment.

Copyright © 2018. Kugler Publications. All rights reserved.

3. The influence of ocular coat stiffness on transient IOP fluctuation magnitude The structural stiffness of the ocular coat is a dominant factor in modulating the amplitude of transient IOP fluctuations.13,14 The ocular coat acts as an elastic shock absorber that serves to decrease the amplitude IOP fluctuations due to ocular perturbations such as blinks, saccades, and systolic vascular filling (OPA). Hence, when the ocular coat is stiff, transient IOP fluctuation magnitude will be greater due to the inability of the eye to elastically expand and absorb the perturbation. Transient IOP fluctuations can be caused by internal forces (ocular pulse due to vascular volume change), or external forces (blinks, saccades, and eye rubs).25,35,36 Thus, greater ocular stiffening of the corneoscleral shell and ONH will result in larger transient IOP fluctuations, potentially resulting in increased IOP-induced injury.38,39 Also, greater IOP fluctuation can occur at normal IOP mean levels in stiffer eyes, or the IOP fluctuation can be

355

Fig. 6. OPA increases with baseline IOP. The amplitude of IOP fluctuations associated with systolic vascular filling, known as OPA, plotted as a function of baseline IOP in one eye of four NHPs. These data show that IOP fluctuations increase significantly in magnitude as IOP increases, presumably driven by the stretching and stiffening of the ocular coats with increasing IOP. 37

lower at higher IOPs in more compliant eyes. Larger transient IOP fluctuations are associated with stiffening of the corneoscleral shell and ONH, which has been shown to occur with aging,16,40–42 in people of African heritage,42,43 in response to chronic exposure to elevated IOP in NHPs,38,39 and in glaucomatous human donor eyes.19 Ocular rigidity has also been shown to be higher in clinical glaucoma patients compared to healthy controls.44 The characterization and findings of how IOP and ocular perfusion pressure (OPP) fluctuations relate to biomechanical changes in ocular coat stiffness may have important clinical ramifications, in that modulation of ocular coat stiffness and/ or blockade of IOP-induced remodeling may reduce injurious IOP and OPP fluctuations. The characterization of IOP and OPP fluctuations in comparison to mean IOP and OPP would yield a better understanding of risk of disease onset and progression, and may lead to new clinical diagnostics and treatments for glaucoma. This will be discussed fully in the following sections.

4. The effects of IOP dynamics on ocular physiology 4.1. The conventional outflow pathway Aqueous humor is produced in the ciliary body, traveling through the pupil into the anterior chamber and out of the eye through the conventional (primary)

Copyright © 2018. Kugler Publications. All rights reserved.

356

and unconventional (secondary) pathways. In conventional outflow, aqueous flows through the trabecular meshwork (TM) into Schlemm’s canal (SC), and then through collector channels into the episcleral veins.45 The rate of aqueous humor outflow facility in a healthy human eye is between 0.1 to 0.4 µL/min/mmHg.4,46–50 The flow of aqueous humor is synchronous with the ocular and cardiac pulse.45,51,52 A relationship has been found between primary open-angle glaucoma (POAG) and increased TM tissue stiffness,8,10,53,54 which creates an increase in outflow resistance and a subsequent increase in IOP.8,55 As mentioned previously, the ocular coats are stiffer at higher IOPs, which results in higher magnitude transient IOP fluctuations (Fig. 6). Transient IOP fluctuations have a prominent effect on aqueous humor outflow facility through structural deformation in the TM and SC, thereby altering aqueous outflow, increasing cellularity, and increasing contractility of TM cells.8,45,56,57 These transient changes in IOP result in the alteration of the biomechanics of the TM on a cellular level, specifically the SC endothelium, juxtacanalicular cells, and extracellular matrix of the TM.8,58–62 It has been recently recognized that transient IOP fluctuations play a role in conventional aqueous outflow, although the magnitude of this effect is not fully understood.45 Johnstone and colleagues have proposed that the pulsatile flow of aqueous through the TM and SC generates shear stress and wall stress in the outflow pathway in a feedback mechanism to maintain homeostasis. This is similar to the mechanotransduction response known to be present throughout the vasculature.8 This response optimizes vessel wall elasticity, compliance, and lumen size to maintain healthy blood flow to tissues.45,564.2.,57 Deformation of the TM and SC from OPA can be measured using newer imaging techniques, such as phase-sensitive optical coherence tomography, and may therefore be a biomarker of TM stiffness and functional health.8 4.2. OPP: an IOP-dependent variable OPP is defined as ocular arterial blood pressure minus IOP, and hence IOP is a major driver of blood flow in the eye. A reduction in OPP may be due increased IOP or decreased blood pressure. The two main supplies of blood to the eye are the central retinal artery (CRA) and

D.C. Turner, J. Jasien and J.C. Downs

orbital ciliary arteries, both branches of the ophthalmic artery. Systolic filling of intraocular blood vessels changes the intraocular volume slightly with every heartbeat, and changes IOP via the pressure-volume relationship (OPA). Low OPP has been found to be associated with the development of glaucoma that occurs at both elevated IOP and clinically-measured normal IOP in patients.63,64 A prevalence of vascular hypotension has been reported in patients with glaucoma that occurs at normal IOP levels (oftentimes labeled normal-tension glaucoma), where lower systolic and diastolic pressures are found particularly during the night in progressive disease.65 It has been proposed that systemic vascular hypotension reduces OPP and blood flow to the ONH, causing ischemia as well as retinal ganglion cell (RGC) layer and axon damage.66 Evidence suggests that these relationships are complex, however, as one study found that systemic vascular hypertension was protective of glaucoma in young patients, but damaging in older patients.67 Autoregulation of ocular blood flow is maintained by changing perfusion pressure through active regulation of vessel caliber to maintain a steady nutrient supply to intraocular tissues. Hence, the retina and ciliary body do not experience blood flow reduction with a change in IOP within physiologic IOP and blood pressure ranges.68 Blood flow autoregulation is altered in glaucoma however, which may increase the sensitivity of intraocular tissues to IOP-related ischemic insult as disease progresses. 68 Healthy blood flow autoregulation is critical, as a reduction in ocular blood flow can cause ischemic damage, whereas an increase in ocular blood flow may damage or rupture ocular capillaries.69 However, there is no blood flow autoregulation in the choroid, and hence choroidal blood flow fluctuates with IOP.70 OPP is a critical variable in these systems, and is somewhat modulated by IOP dynamics.

5. IOP, IOP dynamics, and glaucoma Glaucoma is an ocular neurodegenerative disease and a leading cause of irreversible blindness in the developed world. The results of several randomized prospective trials have identified risk factors associated with the development or progression of glaucoma.78–80 Across

Copyright © 2018. Kugler Publications. All rights reserved.

Intraocular pressure

these studies, IOP, age, central corneal thickness, increased optic disc cupping, and African ancestry were independently associated with glaucomatous progression.67,71–77 Importantly, age and race (Ocular Hypertension Treatment Study (OHTS); univariate only) are the only risk factors other than IOP that are independently associated with the onset and progression of glaucoma across all major prospective clinical trials conducted over the past twenty years.78–82 In addition, the degree of visual field loss (indicating the severity of existing glaucoma) was a risk factor for disease progression in all but one of these large prospective trials.82 In addition to data from prospective trials in glaucoma and ocular hypertension, every population-based survey conducted to date has demonstrated a strong relationship between the prevalence of glaucoma with advancing age,83 despite almost all studies showing no changes in IOP with age.84–88 Furthermore, while normal-tension glaucoma is not uncommon within elderly populations and people of African ancestry,89,90 it is rarely seen in children or young adults.91 Glaucoma is primarily a disease of aging78,79 and is one of the leading causes of blindness in the developed world.92 IOP, age, central corneal thickness (CCT), increased optic disc cupping, and African ancestry are independent risk factors for glaucoma progression,71,93– 95 all of which have a plausible association with IOP, severity of disease based on visual field defect, and the biomechanical properties of the ocular coats and ONH.16,38,40–42,96–99 Lacking continuous IOP data, previous studies have wholly relied on infrequent snapshot measurements of mean IOP to associate this dynamic variable to glaucoma onset and progression.100–103 Lowering IOP is the only clinical treatment that has been shown to retard the onset and progression of glaucoma, but once damaged, the ONH is thought to be more susceptible to further glaucomatous progression even after clinical intervention has lowered mean IOP to normal levels. IOP is a mechanical load, and ONH and scleral biomechanics are also thought to be centrally involved in glaucoma susceptibility, as well as disease onset and progression (Fig. 1).104–108 There is a large and controversial literature surrounding the importance of low frequency fluctuations of clinically measured mean IOP in ­glaucoma.100– 102,109 These studies all rely on snapshot (single-time-

357

point) measurements of IOP that yield a mean baseline value at each time point, and those measurements are taken at relatively infrequent intervals (hourly at the most frequent). Recently however, there has been some interest in OPA, or the fluctuation in IOP associated with the cardiac cycle, which can be measured for short periods by dynamic contour tonometry or DCT (Fig. 5)110-113 (PASCAL DCT, Ziemer Ophthalmic Systems AG, Port Switzerland). However, DCT measurement requires the patient to avoid eye movement or blinking, which have been shown to be the most common sources of large transient IOP fluctuations according to telemetric IOP data collected in humans114 and NHPs.28 IOP is a pressure, and hence, it is a mechanical load that must be borne by the ocular coats and ONH. IOP can cause glaucomatous damage even at statistically defined ‘normal’ IOPs of less than 21 mmHg if a particular eye is unusually susceptible to IOP insult, regardless of its mechanism of action. IOP fluctuations could harm the tissues of the ONH in a similar manner as mean IOP, and there is some evidence that transient IOP fluctuations may be more harmful to resident cells than steady-state IOP.115 As with any solid structure, the degree of instantaneous deformation (strain) experienced by the ONH under a given level of stress (IOP) is dependent upon its 3-D architecture and material properties.106 The stress and strain in the corneoscleral shell and ONH is dependent on the forces applied (IOP), the geometry of the load-bearing structure, and the material properties (stiffness) of the constituent tissues.106 IOP fluctuations down to the millisecond may induce potentially pathological stresses and strains on the ONH. Prior research has also suggested that mechanical stress and strain in the lamina cribrosa and peripapillary sclera could lead to ONH damage in some eyes, even at statistically normal IOP levels.116–118 Eye-specific variation in transient IOP fluctuation magnitude and resulting mechanical strain could explain why some patients develop glaucoma at statistically normal mean IOP, while other patients with high IOP (ocular hypertension) do not develop clinical signs of the disease.119,120 Mean IOP has traditionally been thought of as the driver of biomechanical insult to the ONH in glaucoma, even when reported in terms of hourly fluctuations. However, it has not been truly appreciated that IOP is very dynamic, and the structural stiffness of the corneo-

358

D.C. Turner, J. Jasien and J.C. Downs

scleral shell is a strong determinant of the amplitude of transient IOP fluctuations that occur when the eye is perturbed.13,14 These findings may have important clinical ramifications in that, for a given mean IOP, the ocular coats are stiffer and transient IOP fluctuations are greater in the elderly, persons of African heritage, and/or those with a history of elevated IOP, which may account for some portion of the increased susceptibility to IOP-induced injury in these at-risk populations. In addition to these longer-term causes of increased structural stiffness, the ocular coats are non-linear in terms of material properties, such that the coats stiffen as they become stretched when subjected to acutely elevated IOP.16 This IOP-related stiffening is an acute phenomenon, in that high-frequency IOP fluctuations have higher magnitudes when mean IOP is higher28,36 for identical perturbations (Fig. 6), which may contribute to a higher risk of IOP-related glaucomatous damage in ostensibly ‘normotensive’ patients with high baseline mean IOP for some part of the day or night. IOP is an important risk factor for glaucoma, and lowering IOP, even when IOP is in the normal range

References 1.

2.

Copyright © 2018. Kugler Publications. All rights reserved.

3.

4. 5.

6.

7.

Barany EH. A mathematical formulation of intraocular pressure as dependent on secretion, ultrafiltration, bulk outflow, and osmotic reabsorption of fluid. Invest Ophthalmol. 1963;2:584590. Boland M V, Ervin A-M, Friedman DS, et al. Comparative effectiveness of treatments for open-angle glaucoma: a systematic review for the U.S. Preventive Services Task Force. Ann Intern Med. 2013;158(4):271-279. Blondeau P, Tetrault JP, Papamarkakis C. Diurnal variation of episcleral venous pressure in healthy patients: a pilot study. J Glaucoma. 2001;10(1):18-24. Shaarawy T, Sherwood MB, Crowston JG. Glaucoma: Medical Diagnosis & Therapy. Saunders/Elsevier; 2009. Philadelphia, PA Yablonski ME, Gallin P, Shapiro D. Effect of oxygen on aqueous humor dynamics in rabbits. Invest Ophthalmol Vis Sci. 1985;26(12):1781-1784. Ortiz GJ, Cook DJ, Yablonski ME, Masonson H, Harmon G. Effect of cold air on aqueous humor dynamics in humans. Invest Ophthalmol Vis Sci. 1988;29(1):138-140. Toris CB, Tafoya ME, Camras CB, Yablonski ME. Effects of apraclonidine on aqueous humor dynamics in human eyes. Ophthalmology. 1995;102(3):456-461.

as defined epidemiologically, remains the only proven-effective treatment for the disease. However, our knowledge of the true character and dynamics of IOP in humans and how it contributes to the health and disease in ocular tissues is limited by the lack of continuous IOP-monitoring technology for patients. Hence, the relationship between IOP and glaucoma remains murky, and more research is needed to characterize IOP dynamics in ocular health and pathophysiological disease processes.

Acknowledgements This work was supported by: US National Institutes of Health Grant R01-EY026035 (J. Crawford Downs); P30-EY003039 (University of Alabama at Birmingham Instrumentation Core Facilities, AL, USA); EyeSight Foundation of Alabama (AL, USA); and Research to Prevent Blindness (NY, USA).

8.

9. 10.

11. 12. 13.

14.

15.

Johnstone MA. Intraocular pressure regulation: findings of pulse-dependent trabecular meshwork motion lead to unifying concepts of intraocular pressure homeostasis. J Ocul Pharmacol Ther. 2014;30(2-3):88-93. Kaufman PL, Adler FH, Levin LA, Alm A. Adler’s Physiology of the Eye. Saunders/Elsevier; 2011. Philadelphia, PA. Johnstone M, Martin E, Jamil A. Pulsatile flow into the aqueous veins: manifestations in normal and glaucomatous eyes. Exp Eye Res. 2011;92(5):318-327. Ascher KW. The Aqueous Veins: Biomicroscopic Study of the Aqueous Humor Elimination. Thomas; 1961. Springfield, IL. Friedenwald J. Contribution to the theory and practice of tonometry. Am J Ophthalmol. 1937;20(10):985-1024. Morris HJ, Tang J, Perez BC, et al. Correlation between biomechanical responses of posterior sclera and IOP elevations during micro intraocular volume change. Invest Ophthalmol Vis Sci. 2013;54(12):7215-7222. Liu J, He X. Corneal stiffness affects IOP elevation during rapid volume change in the eye. Invest Ophthalmol Vis Sci. 2009;50(5):2224-2229. Grant WM. Tonographic method for measuring the facility and rate of aqueous flow in human eyes. Arch Ophthalmol. (Chicago, Ill 1929). 1950;44(2):204-214.

Copyright © 2018. Kugler Publications. All rights reserved.

Intraocular pressure 16. Girard MJA, Suh JKF, Bottlang M, Burgoyne CF, Downs JC. Scleral biomechanics in the aging monkey eye. Invest Ophthalmol Vis Sci. 2009;50(11):5226-5237. 17. Downs JC, Suh JKF, Thomas KA, Bellezza AJ, Burgoyne CF, Hart RT. Viscoelastic characterization of peripapillary sclera: material properties by quadrant in rabbit and monkey eyes. J Biomech Eng. 2003;125(1):124-131. 18. Grytz R, Fazio MA, Libertiaux V, et al. Age-and race-related differences in human scleral material properties. Invest Ophthalmol Vis Sci. 2014;55(12):8163-8172. 19. Coudrillier B, Tian J, Alexander S, Myers KM, Quigley HA, Nguyen TD. Biomechanics of the human posterior sclera: age- and glaucoma-related changes measured using inflation testing. Invest Ophthalmol Vis Sci. 2012;53(4):1714-1728. 20. Ethier CR. Scleral biomechanics and glaucoma--a connection? Can J Ophthalmol. 2006;41(1):9-12,14. 21. Nguyen TD, Jones RE, Boyce BL. A nonlinear anisotropic viscoelastic model for the tensile behavior of the corneal stroma. J Biomech Eng. 2008;130(4):41020. 22. Mark HH. Armand Imbert, Adolf Fick, and their tonometry law. Eye (Lond). 2012;26(1):13-16. 23. Realini T, Weinreb RN, Hobbs G. Correlation of intraocular pressure measured with Goldmann and dynamic contour tonometry in normal and glaucomatous eyes. J Glaucoma. 2009;18(2):119-123. 24. Liu JHK, Sit AJ, Weinreb RN. Variation of 24-hour intraocular pressure in healthy individuals: right eye versus left eye. Ophthalmology. 2005;112(10):1670-1675. 25. Coleman DJ, Trokel S. Direct-recorded intraocular pressure variations in a human subject. Arch Ophthalmol (Chicago, Ill 1960). 1969;82(5):637-640. 26. Hoh H, Schwanengel M. Continuous intraocular pressure measurement over several days with the Codman Microsensor--a case report. Klin Monbl Augenheilkd. 1999;215(3):186-196. 27. Mclaren JW, Brubaker RF, Fitzsimon S. Continuous measurement of intraocular pressure in rabbits by telemetry. IOVS. 1996;37(6):966-975. 28. Downs JC, Burgoyne CF, Seigfreid WP, Reynaud JF, Strouthidis NG, Sallee V. 24-hour IOP telemetry in the nonhuman primate: implant system performance and initial characterization of IOP at multiple timescales. Invest Ophthalmol Vis Sci. 2011;52(10):7365-7375. 29. Krieglstein GK, Waller WK, Leydhecker W. The vascular basis of the positional influence of the intraocular pressure. Albrecht Von Graefes Arch Klin Exp Ophthalmol. 1978;206(2):99-106. 30. Lee JY, Yoo C, Jung JH, Hwang YH, Kim YY. The effect of lateral decubitus position on intraocular pressure in healthy young subjects. Acta Ophthalmol. 2012;90(1):e68-72. 31. Hwang J-W, Jeon Y-T, Kim J-H, Oh Y-S, Park H-P. The effect of the lateral decubitus position on the intraocular pressure in anesthetized patients undergoing lung surgery. Acta Anaesthesiol Scand. 2006;50(8):988-992. 32. Carlson KH, McLaren JW, Topper JE, Brubaker RF. Effect of body position on intraocular pressure and aqueous flow. Invest Ophthalmol Vis Sci. 1987;28(8):1346-1352.

359 33. Malihi M, Sit AJ. Effect of head and body position on intraocular pressure. Ophthalmology. 2012;119(5):987-991. 34. Eklund A, Johannesson G, Johansson E, et al. The pressure difference between eye and brain changes with posture. Ann Neurol. 2016;80(2):269-276. 35. Kaufmann C, Bachmann LM, Robert YC, Thiel M a. Ocular pulse amplitude in healthy subjects as measured by dynamic contour tonometry. Arch Ophthalmol. 2006;124:1104-1108. 36. Dastiridou AI, Ginis HS, de Brouwere D, Tsilimbaris MK, Pallikaris IG. Ocular rigidity, ocular pulse amplitude, and pulsatile ocular blood flow: The effect of intraocular pressure. Investig Ophthalmol Vis Sci. 2009;50(12):5718-5722. 37. Downs JC. IOP telemetry in the nonhuman primate. Exp Eye Res. 2015;141:91-98. 38. Girard MJA, Francis Suh JK, Bottlang M, Burgoyne CF, Crawford Downs J. Biomechanical changes in the sclera of monkey eyes exposed to chronic IOP elevations. Investig Ophthalmol Vis Sci. 2011;52(8):5656-5669. 39. Downs JC, Suh JKF, Thomas KA, Bellezza AJ, Hart RT, Burgoyne CF. Viscoelastic material properties of the peripapillary sclera in normal and early-glaucoma monkey eyes. Investig Ophthalmol Vis Sci. 2005;46(2):540-546. 40. Albon J, Purslow PP, Karwatowski WS, Easty DL. Age related compliance of the lamina cribrosa in human eyes. Br J Ophthalmol. 2000;84:318-323. 41. Cartwright NEK, Tyrer JR, Marshall J. Age-related differences in the elasticity of the human cornea. Investig Ophthalmol Vis Sci. 2011;52(7):4324-4329. 42. Fazio MA, Grytz R, Morris JS, et al. Age-related changes in human peripapillary scleral strain. Biomech Model Mechanobiol. 2014;13(3):551-563. 43. Fazio MA, Grytz R, Morris JS, Bruno L, Girkin CA, Downs JC. Human scleral structural stiffness increases more rapidly with age in donors of African descent compared to donors of European descent. Invest Ophthalmol Vis Sci. 2014;55(11):71897198. 44. Ebneter A, Wagels B, Zinkernagel MS. Non-invasive biometric assessment of ocular rigidity in glaucoma patients and controls. Eye (Lond). 2009;23(3):606-611. 45. Johnstone MA. The aqueous outflow system as a mechanical pump: evidence from examination of tissue and aqueous movement in human and non-human primates. J Glaucoma. 2004;13(5):421-438. 46. Toris CB, Yablonski ME, Wang YL, Camras CB. Aqueous humor dynamics in the aging human eye. Am J Ophthalmol. 1999;127(4):407-412. 47. Toris CB, Koepsell SA, Yablonski ME, Camras CB. Aqueous humor dynamics in ocular hypertensive patients. J Glaucoma. 2002;11(3):253-258. 48. Grant WM. Clinical measurements of aqueous outflow. AMA Arch Ophthalmol. 1951;46(2):113-131. 49. Becker B. The decline in aqueous secretion and outflow facility with age. Am J Ophthalmol. 1958;46(5 Part 1):731-736. 50. Gaasterland D, Kupfer C, Milton R, Ross K, McCain L, MacLellan H. Studies of aqueous humour dynamics in man. VI. Effect of

360

51. 52. 53.

54.

55. 56.

57.

58.

59.

60.

61.

62.

63.

Copyright © 2018. Kugler Publications. All rights reserved.

64.

65. 66.

67.

D.C. Turner, J. Jasien and J.C. Downs age upon parameters of intraocular pressure in normal human eyes. Exp Eye Res. 1978;26(6):651-656. Ascher K. Physiologic importance of the visible elimination of intraocular fluid. Am J Ophthalmol. 1942;25:1174-1209. Ascher K. Glaucoma and aqueous veins. Am J Ophthalmol. 1942;25:1309-1315. Suson EB, Schultz RO. Blood in schlemm’s canal in glaucoma suspects. A study of the relationship between blood-filling pattern and outflow facility in ocular hypertension. Arch Ophthalmol (Chicago, Ill 1960). 1969;81(6):808-812. Johnstone MA. A New Model Describes an Aqueous Outflow Pump and Explores Causes of Pump Failure in Glaucoma. In: Grehn F, Stamper R, eds. Glaucoma. Berlin, Heidelberg: Springer Berlin Heidelberg; 2006:3-34. Ellingsen BA, Grant WM. Trabeculotomy and sinusotomy in enucleated human eyes. Invest Ophthalmol. 1972;11(1):21-28. Ramos RF, Stamer WD. Effects of cyclic intraocular pressure on conventional outflow facility. Invest Ophthalmol Vis Sci. 2008;49(1):275-281. Ramos RF, Sumida GM, Stamer WD. Cyclic mechanical stress and trabecular meshwork cell contractility. Invest Ophthalmol Vis Sci. 2009;50(8):3826-3832. Johnstone MA, Grant WG. Pressure-dependent changes in structures of the aqueous outflow system of human and monkey eyes. Am J Ophthalmol. 1973;75(3):365-383. Johnstone MA. Pressure-dependent changes in nuclei and the process origins of the endothelial cells lining Schlemm’s canal. Invest Ophthalmol Vis Sci. 1979;18(1):44-51. Grierson I, Lee WR. Pressure-induced changes in the ultrastructure of the endothelium lining Schlemm’s canal. Am J Ophthalmol. 1975;80(5):863-884. Bradley JMB, Kelley MJ, Rose A, Acott TS. Signaling pathways used in trabecular matrix metalloproteinase response to mechanical stretch. Invest Ophthalmol Vis Sci. 2003;44(12):51745181. Vittal V, Rose A, Gregory KE, Kelley MJ, Acott TS. Changes in gene expression by trabecular meshwork cells in response to mechanical stretching. Invest Ophthalmol Vis Sci. 2005;46(8):2857-2868. Leske MC, Nemesure B, He Q, Wu SY, Fielding Hejtmancik J, Hennis A. Patterns of open-angle glaucoma in the Barbados Family Study. Ophthalmology. 2001;108(6):1015-1022. De Moraes CG, Liebmann JM, Greenfield DS, Gardiner SK, Ritch R, Krupin T. Risk factors for visual field progression in the low-pressure glaucoma treatment study. Am J Ophthalmol. 2012;154(4):702-711. Graham SL, Drance SM. Nocturnal hypotension: role in glaucoma progression. Surv Ophthalmol. 1999;43 Suppl 1:S10-6. Memarzadeh F, Ying-Lai M, Chung J, Azen SP, Varma R. Blood pressure, perfusion pressure, and open-angle glaucoma: The Los Angeles Latino eye study. Investig Ophthalmol Vis Sci. 2010;51(6):2872-2877. Tielsch JM, Katz J, Sommer A, Quigley HA, Javitt JC. Hypertension, perfusion pressure, and primary open-angle glaucoma. A population-based assessment. Arch Ophthalmol (Chicago, Ill 1960). 1995;113(2):216-221.

68. Wang L, Burgoyne CF, Cull G, Thompson S, Fortune B. Static blood flow autoregulation in the optic nerve head in normal and experimental glaucoma. Invest Ophthalmol Vis Sci. 2014;55(2):873-880. 69. Flammer J. The vascular concept of glaucoma. Surv Ophthalmol. 1994;38 Suppl:S3-6. 70. Kiel JW. Choroidal myogenic autoregulation and intraocular pressure. Exp Eye Res. 1994;58(5):529-543. 71. Station W. Predictive Factors for Open-Angle Glaucoma among Patients with Ocular Hypertension in the European Glaucoma Prevention Study. Ophthalmology. 2007;114(1):3-9. 72. Sommer A, Tielsch JM, Katz J, et al. Relationship between intraocular pressure and primary open angle glaucoma among white and black Americans. The Baltimore Eye Survey. Arch Ophthalmol (Chicago, Ill 1960). 1991;109(8):1090-1095. 73. Tielsch JM, Katz J, Sommer A, Quigley HA, Javitt JC. Family history and risk of primary open angle glaucoma. The Baltimore Eye Survey. Arch Ophthalmol (Chicago, Ill 1960). 1994;112(1):69-73. 74. Leske MC, Connell AM, Wu SY, Hyman LG, Schachat AP. Risk factors for open-angle glaucoma. The Barbados Eye Study. Arch Ophthalmol (Chicago, Ill 1960). 1995;113(7):918-924. 75. Leske MC, Wu SY, Hennis A, Honkanen R, Nemesure B. Risk Factors for Incident Open-angle Glaucoma. The Barbados Eye Studies. Ophthalmology. 2008;115(1):85-93. 76. Bonomi L, Marchini G, Marraffa M, Bernardi P, Morbio R, Varotto A. Vascular risk factors for primary open angle glaucoma: the Egna-Neumarkt Study. Ophthalmology. 2000;107(7):12871293. 77. Leske MC, Wu S-Y, Nemesure B, Hennis A. Incident open-angle glaucoma and blood pressure. Arch Ophthalmol (Chicago, Ill 1960). 2002;120(7):954-959. 78. Gordon MO, Beiser JA, Brandt JD, et al. The Ocular Hypertension Treatment Study: baseline factors that predict the onset of primary open-angle glaucoma. Arch Ophthalmol (Chicago, Ill 1960). 2002;120(6):714-730. 79. Leske MC, Heijl A, Hussein M, Bengtsson B, Hyman L, Komaroff E. Factors for glaucoma progression and the effect of treatment: the early manifest glaucoma trial. Arch Ophthalmol (Chicago, Ill 1960). 2003;121(1):48-56. 80. Miglior S, Torri V, Zeyen T, Pfeiffer N, Vaz JC, Adamsons I. Intercurrent factors associated with the development of open-angle glaucoma in the European glaucoma prevention study. Am J Ophthalmol. 2007;144(2):266-275. 81. Pfeiffer N, Torri V, Miglior S, Zeyen T, Adamsons I, Cunha-Vaz J. Central corneal thickness in the European Glaucoma Prevention Study. Ophthalmology. 2007;114(3):454-459. 82. Musch DC, Gillespie BW, Lichter PR, Niziol LM, Janz NK. Visual field progression in the Collaborative Initial Glaucoma Treatment Study the impact of treatment and other baseline factors. Ophthalmology. 2009;116(2):200-207. 83. Rudnicka AR, Mt-Isa S, Owen CG, Cook DG, Ashby D. Variations in primary open-angle glaucoma prevalence by age, gender, and race: a Bayesian meta-analysis. Invest Ophthalmol Vis Sci. 2006;47(10):4254-4261.

Copyright © 2018. Kugler Publications. All rights reserved.

Intraocular pressure 84. Klein BE, Klein R, Linton KL. Intraocular Pressure in an American Community. Invest Ophthalmol. 1992;33(7):2224-2228. 85. Nomura H, Shimokata H, Ando F, Miyake Y, Kuzuya F. Age-related changes in intraocular pressure in a large Japanese population: a cross-sectional and longitudinal study. Ophthalmology. 1999;106(10):2016-2022. 86. Weih LM, Mukesh BN, McCarty C a, Taylor HR. Association of demographic, familial, medical, and ocular factors with intraocular pressure. Arch Ophthalmol. 2001;119(6):875-880. 87. Nomura H, Ando F, Niino N, Shimokata H, Miyake Y. The relationship between age and intraocular pressure in a Japanese population: the influence of central corneal thickness. Curr Eye Res. 2002;24(2):81-85. 88. Rochtchina E, Mitchell P, Wang JJ. Relationship between age and intraocular pressure: the Blue Mountains Eye Study. Clin Experiment Ophthalmol. 2002;30(3):173-175. 89. Chumbley LC, Brubaker RF. Low-tension glaucoma. Am J Ophthalmol. 1976;81(6):761-767. 90. Levene R. Low tension glaucoma: a critical review and new material. Surv Ophthalmol. 1980;24(6):621-664. 91. Geijssen HC, Greve EL. Focal ischaemic normal pressure glaucoma versus high pressure glaucoma. Doc Ophthalmol. 1990;75(3-4):291-301. 92. Quigley HA, Broman AT. The number of people with glaucoma worldwide in 2010 and 2020. Br J Ophthalmol. 2006;90(3):262-267. 93. Blackwell B, Gaasterland D, Ederer F, et al. The Advanced Glaucoma Intervention Study (AGIS): 12. Baseline risk factors for sustained loss of visual field and visual acuity in patients with advanced glaucoma. Am J Ophthalmol. 2002;134(4):499-512. 94. Gordon MO. The Ocular Hypertension Treatment Study. Arch Ophthalmol. 2002;120(6):714. doi:10.1001/archopht.120.6.714. 95. Leske MC. Factors for Glaucoma Progression and the Effect of Treatment. Arch Ophthalmol. 2003;121(1):48. doi:10.1001/ archopht.121.1.48. 96. Dandona L, Quigley HA, Brown AE, Enger C. Quantitative regional structure of the normal human lamina cribrosa. A racial comparison. Arch Ophthalmol (Chicago, Ill 1960). 1990;108(3):393-398. 97. Girkin CA, McGwin G, Xie A, Deleon-Ortega J. Differences in optic disc topography between black and white normal subjects. Ophthalmology. 2005;112(1):33-39. doi:10.1016/j. ophtha.2004.07.029. 98. Lesk MR, Hafez AS, Descovich D. Relationship between central corneal thickness and changes of optic nerve head topography and blood flow after intraocular pressure reduction in open-angle glaucoma and ocular hypertension. Arch Ophthalmol (Chicago, Ill 1960). 2006;124(11):1568-1572. 99. Yang H, Downs JC, Bellezza A, Thompson H, Burgoyne CF. 3-D histomorphometry of the normal and early glaucomatous monkey optic nerve head: Prelaminar neural tissues and cupping. Investig Ophthalmol Vis Sci. 2007;48(11):5068-5084. 100. Bengtsson B, Heijl A. Diurnal IOP fluctuation: Not an independent risk factor for glaucomatous visual field loss in highrisk ocular hypertension. Graefe’s Arch Clin Exp Ophthalmol. 2005;243(6):513-518.

361 101. Bengtsson B, Leske MC, Hyman L, Heijl A. Fluctuation of Intraocular Pressure and Glaucoma Progression in the Early Manifest Glaucoma Trial. Ophthalmology. 2007;114(2):205209. 102. Medeiros FA, Weinreb RN, Zangwill LM, et al. Long-term Intraocular Pressure Fluctuations and Risk of Conversion from Ocular Hypertension to Glaucoma. Ophthalmology. 2008;115(6):934940. 103. Saccà SC, Rolando M, Marletta A, Macrì A, Cerqueti P, Ciurlo G. Fluctuations of intraocular pressure during the day in open-angle glaucoma, normal-tension glaucoma and normal subjects. Ophthalmologica. 1998;212(2):115-119. 104. Zeimer RC, Ogura Y. The relation between glaucomatous damage and optic nerve head mechanical compliance. Arch Ophthalmol (Chicago, Ill 1960). 1989;107(8):1232-1234. 105. Burgoyne CF, Crawford Downs J, Bellezza AJ, Francis Suh JK, Hart RT. The optic nerve head as a biomechanical structure: A new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage. Prog Retin Eye Res. 2005;24(1):39-73. 106. Downs JC, Roberts MD, Burgoyne CF. Mechanical environment of the optic nerve head in glaucoma. Optom Vis Sci. 2008;85(6):425-435. 107. Sigal IA, Ethier CR. Biomechanics of the optic nerve head. Exp Eye Res. 2009;88(4):799-807. 108. Sigal IA, Yang H, Roberts MD, Downs JC. Morphing methods to parameterize specimen-specific finite element model geometries. J Biomech. 2010;43(2):254-262. 109. Sacca SC, Rolando M, Marletta A, Macri A, Cerqueti P, Ciurlo G. Fluctuations of intraocular pressure during the day in open-angle glaucoma, normal-tension glaucoma and normal subjects. Ophthalmol J Int d’ophtalmologie Int J Ophthalmol Zeitschrift fur Augenheilkd. 1998;212(2):115119. 110. Hoffmann EM, Grus F-H, Pfeiffer N. Intraocular pressure and ocular pulse amplitude using dynamic contour tonometry and contact lens tonometry. BMC Ophthalmol. 2004;4:4. 111. Punjabi OS, Ho H V, Bostrom AG, Stamper RL, Lin SC. Intraocular Pressure and Ocular Pulse Amplitude Comparisons in Different Types of Glaucoma Using Dynamic Contour Tonometry. 2006;3683(October 2016):851-862. 112. Pourjavan S, Boëlle PY, Detry-Morel M, De Potter P. Physiological diurnal variability and characteristics of the ocular pulse amplitude (OPA) with the dynamic contour tonometer (DCT-Pascal®). Int Ophthalmol. 2007;27(6):357-360. 113. Kotecha A, White E, Schlottmann PG, Garway-Heath DF. Intraocular Pressure Measurement Precision with the Goldmann Applanation, Dynamic Contour, and Ocular Response Analyzer Tonometers. Ophthalmology. 2010;117(4):730-737. 114. Coleman DJ, Trokel S. Direct-recorded intraocular pressure variations in a human subject. Arch Ophthalmol (Chicago, Ill 1960). 1969;82(5):637-640. 115. Suki B, Parameswaran H, Imsirovic J, Bartolak-Suki E. Regulatory Roles of Fluctuation-Driven Mechanotransduction in Cell Function. Physiology (Bethesda). 2016;31(5):346-358.

362

Copyright © 2018. Kugler Publications. All rights reserved.

116. Roberts MD, Sigal IA, Liang Y, Burgoyne CF, Crawford Downs J. Changes in the biomechanical response of the optic nerve head in early experimental glaucoma. Investig Ophthalmol Vis Sci. 2010;51(11):5675-5684. 117. Roberts MD, Liang Y, Sigal IA, et al. Correlation between local stress and strain and lamina cribrosa connective tissue volume fraction in normal monkey eyes. Investig Ophthalmol Vis Sci. 2010;51(1):295-307. 118. Roberts MD, Grau V, Grimm J, et al. Remodeling of the connective tissue microarchitecture of the lamina cribrosa in early experimental glaucoma. Investig Ophthalmol Vis Sci. 2009;50(2):681-690.

D.C. Turner, J. Jasien and J.C. Downs 119. Punjabi OS, Stamper RL, Bostrom AG, Lin SC. Does treated systemic hypertension affect progression of optic nerve damage in glaucoma suspects? Curr Eye Res. 2007;32(2):153160. 120. Jeong JH, Park KH, Jeoung JW, Kim DM. Preperimetric normal tension glaucoma study: long-term clinical course and effect of therapeutic lowering of intraocular pressure. Acta Ophthalmol. 2014;92(3):e185-93.

25. Collagen anisotropy in scleral mechanics Neeraj Vij Jr.1, Jonathan Vande Geest2 Department of Biomedical Engineering, University of Arizona, Tucson, Arizona, USA; 2Departments of Bioengineering and Ophthalmology, University of Pittsburgh, Pittsburgh, PA, USA

1

1. Abstract As the second leading cause of blindness worldwide, glaucoma will affect an estimated 60 million people in 2010 and 80 million by 2020.1 The extracellular matrix of the sclera is primarily composed of type I collagen, and may play an influential role in the development of primary open-angle glaucoma (POAG).2-5 The purpose of this chapter is to summarize the current state of knowledge on scleral anisotropy determined from mechanical testing, microstructural imaging, and inverse finite element methods. Future directions in scleral mechanics are also discussed.

Copyright © 2018. Kugler Publications. All rights reserved.

2. Introduction Soft tissues are composed of cells embedded in an extracellular fibrillar matrix. The sclera is composed primarily of fibroblasts embedded within a dense and well-organized collagen matrix. The focus of this chapter will be on the collagen microstructural and mechanical anisotropy of the sclera. There are three main types of collagen, and each type differs in its physical properties and function. Type II collagen is found in the cartilage and the vitreous humor in the eye, while type III fibers are found in the skin, as well as muscles, arteries, and veins. Type I collagen fibers are the most abundant in the human body, both in quantity and number of different locations: skin, tendons/ligaments, bones, and the eye. Type I collagen is the most abundant collagen type in the sclera and is the primary source of its microstruc-

tural and mechanical anisotropy. The complex hierarchical organization of type I collagen leads to its characteristic crimp and strain-stiffening mechanical behavior. The fundamental unit of collagen, tropocollagen, is a long, thin protein molecule comprised of three alpha chains: two alpha-1 chains and one alpha-2 chain. The left-handed helical nature of this molecule allows it to be packed together in a spatially efficient manner, giving it increased stability through intramolecular interactions. Tropocollagen molecules are tightly packed and assembled into the next level of collagen microstructure — a fibril. Typically, fibrils are 50-200 nm in width, with collagen molecules themselves spaced 67 nm apart.6 These fibrils are then interwoven into collagen fiber bundles, which are organized in an optimal anisotropic manner throughout the sclera to provide resistance to stretching and protection of delicate intraocular tissues. The purpose of this chapter is to summarize the current state of knowledge on the microstructural and mechanical anisotropy of the sclera. Scleral anisotropy is of interest in ocular biomechanics for many reasons, including its potential role in myopia and POAG. For example, it is hypothesized that the sclera is responsible for transmitting forces and deformations associated with elevated intraocular pressure (IOP) to the lamina cribrosa (LC), the primary site of cell death in POAG. Changes in scleral properties may therefore negatively influence the health of retinal ganglion cells passing through the LC.2,7-10 In this chapter, mechanical anisotropy will be defined as any evidence demonstrating how the mechanical

Correspondence: Prof. Jonathan Vande Geest, 409 Center for Bioengineering, 300 Technology Drive, Swanson School of Engineering, University of Pittsburgh, Pittsburgh, PA 15219, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 363-376 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

364

N. Vij Jr. and J. Vande Geest

behavior of the sclera is directionally dependent. For example, this might manifest in the ratio of directional material stiffness constants, where each constant controls the biomechanical response of the sclera in a particular anatomical direction. Microstructural anisotropy, on the other hand, will be defined as any directional dependence of the collagen organization within the sclera. The third section of this review will discuss mechanical anisotropy, while the fourth will discuss microstructural results obtained either through indirect computational methods (Section 4.1.) or through imaging techniques including small-angle light scattering (SALS), wide-angle X-ray scattering (WAXS), and multiphoton microscopy (Section 4.2.).

Copyright © 2018. Kugler Publications. All rights reserved.

3. Experimentally measured scleral mechanical anisotropy and heterogeneity Scleral anisotropy is hypothesized to play a role in ocular disease, and there are two primary methods by which scleral anisotropy is typically measured. The first is to impose physiological loading conditions on the sclera (e.g., IOP) and analyze the directional dependence of the mechanical response (mechanical anisotropy); the second is to determine the microstructural organization of the collagen within the sclera using an indirect (computational) or direct (imaging) technique (microstructural anisotropy). In this section, we will summarize features of scleral mechanical anisotropy that were determined by the first method, specifically those that were determined experimentally directly from mechanical tests. The heterogeneity (regional differences) in scleral mechanical deformation will also be highlighted. One of the first researchers to explore the directional dependence of scleral mechanical properties was Eilaghi et al.11 They performed planar biaxial tensile tests on human sclerae, and concluded the sclera was mildly mechanically anisotropic, with the ratio of the stiffness in the circumferential and meridional directions being 1.065 (Fig. 1).11 These results were on very large samples of the posterior sclera that were isolated in a planar configuration to directly assess the anisotropy of the sclera averaged over samples spanning a large mid-peripheral scleral area.

Fig. 1. Degree of scleral mechanical anisotropy as measured using planar biaxial testing.11

The mild directional dependence seen above in Eilaghi et al. was more prominent in planar biaxial tests performed by Perez et al.12 They showed that the porcine sclera exhibits a stronger anisotropic behavior when biaxial testing was performed using ultrasound speckle tracking. They found that the meridional direction showed significantly higher tensile strains than the equatorial direction when exposed to equibiaxial load. Similarly, the stiffness in the meridional and equatorial directions were also significantly different.12 Perez and Eilaghi have thus both provided direct evidence of the mechanical anisotropy of the sclera, in particular with a more deformable response in the meridional direction. This mechanical anisotropy is likely due to the microstructural anisotropy present in the sclera, which shall be discussed subsequently. The heterogeneity in mechanical response of the bovine sclera was studied by Myers et al.13 using digital image correlation (DIC). These researchers showed that displacements are largest in the peripapillary region and that maximum displacements were found at the site of the optic nerve head (ONH). The authors also quantified the time-dependent behavior of the sclera, providing important evidence for many researchers on the inherent viscoelastic properties of this tissue.13 Since the pressures associated with glaucoma may affect scleral properties, it is not surprising that

Collagen anisotropy in scleral mechanics

365

Elevated IOP that is typically associated with POAG may have an effect on how scleral tissue mechanically responds to physiological loading. Coudrillier et al.17 used DIC to study the inflation strain response of the sclera from both glaucomatous and normal human donor eyes. They found that glaucomatous eyes have lower meridional strains in the peripapillary sclera than normal eyes. This increased meridional stiffness may be indicative of the microstructural changes that accompany glaucoma, which were also studied in this paper and will be discussed in Section 4. While no clear conclusions were made on the mechanical anisotropy in response to elevated IOP, Girard et al.3 did demonstrate that scleral shells that are originally stiffer may resist scleral remodeling, leading to further changes in scleral biomechanical properties. These experimentally derived mechanical testing data confirm that the sclera undergoes large deformations, is mechanically anisotropic, and that remodeling of the sclera may play a role in the initiation, onset, or progression of ocular diseases including glaucoma.

4. Microstructural anisotropy

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 2. Strains as a function of IOP in both the peripapillary and mid-peripheral region.14

researchers have studied the effects of elevated IOP on the extracellular matrix in soft tissues. Girard et al.3 sought to determine how the mechanical properties and computationally derived microstructure of the sclera change in response to elevated IOP in non-human primates. The heterogeneity of the sclera was evidenced in this work, as the peripheral sclera had a higher tangent modulus than the peripapillary sclera in normal eyes. This result was corroborated by Grytz et al. in 2014,14 who studied IOP-induced scleral deformations using laser speckle interferometry, showing that the in-plane strains are higher in the peripapillary sclera than in the peripheral sclera (Fig. 2). Girard et al.15 and Fazio et al.16 verified the claim that the principal strain is highest directly adjacent to the scleral canal. Fazio et al.16 also demonstrated that scleral strain response is regionally dependent, specifically, that the infero-temporal sector was associated with the highest strain, while the superior sector was associated with the lowest strain.16

4.1. Microstructural anisotropy from computational simulation In this section, we summarize predictions of scleral anisotropy as derived using inverse finite element analyses (iFEM). In this approach, automated search algorithms are used to determine the values of the microstructurally based material parameters (fiber direction, fiber splay) that drive a computational simulation to match the experimentally measured deformational response of sclera. This type of approach indirectly predicts the underlying heterogeneous microstructural organization of the sclera. The existence of a circumferential ring of collagen around the ONH has been shown both directly and indirectly by many researchers in the literature.3,14,1828 Girard et al.18 used an iFEM to show that collagen fibers are circumferentially oriented around the ONH in three out of the four peripapillary regions (Fig. 3). Furthermore, this study found that the collagen fibers in the peripapillary region were significantly more anisotropic than those in the peripheral sclera. This result again suggests that the peripapillary sclera helps

366

N. Vij Jr. and J. Vande Geest

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. Thickness, microstructural, and mechanical deformation of a rhesus macaque posterior pole.18

to protect the ONH by limiting IOP-induced scleral canal expansion. This study also showed that the peripapillary sclera is thicker and has a lower tangent modulus than the peripheral sclera. According to this study, scleral tangent modulus increases in a non-linear fashion with both chronic and acute increases in IOP. More interestingly, however, the study showed that scleral thickness and tangent modulus have an inversely proportional relationship, which allows the eye to expand uniformly as IOP is increased.18 The same of group of researchers corroborated the above results within the same year through an iFEM with a fiber-reinforced constitutive model. Girard et al.19 showed that, regardless of age, tangent modulus is higher in the peripheral sclera than in the peripapillary sclera, and thus, the peripheral sclera is more resistant to stretching (Fig. 4). Their inverse computational analysis predicted the existence of a preferred collagen fiber orientation tangent to the scleral canal around the ONH (Fig. 4).19 Interestingly, in non-human primates, there was no influence of age on this predicted microstructural anisotropy, perhaps suggesting that the fiber reinforcement of the peripapillary sclera is critical for proper visual function throughout one’s lifespan. As mentioned, many other articles support the conclusion of a preferred collagen fiber reinforcement

Fig. 4. (Top) Tangent modulus and strain as a function of IOP. (Bottom) Preferred fiber orientation as, on average, tangent to the optic nerve head.19

Copyright © 2018. Kugler Publications. All rights reserved.

Collagen anisotropy in scleral mechanics

around the ONH. Through finite element modeling, Girard et al.3 showed that the mean preferred fiber orientation is tangent to the scleral canal. This was seen in both the peripapillary and peripheral sclera; however, the effect was larger in the peripapillary sclera. This may imply that the fibers closest to the ONH play a role in protecting the retinal ganglion cells that pass through the LC. They also showed that the peripapillary sclera is thicker and has a higher K factor, which corresponds to a higher fiber concentration and a greater degree of anisotropy. Furthermore, tangent modulus was found to be higher in the peripheral sclera than peripapillary sclera, which shows that peripheral fibers resist stretching more than peripapillary fibers. Interestingly, these authors also concluded that the predicted collagen fiber orientations do not change in glaucomatous non-human primate eyes.3 In contrast to the approach used above, Coudrillier et al.24 used an iFEM that incorporated wide-angle X-ray scatter (WAXS) results as seen in Section 4.2.; however, the effects of differences in scleral anisotropy are more relevant to this section. From the model, the average level of anisotropy was found to be 1.096. This corroborates the experimental results from Eilaghi et al.,11 which reported an average anisotropy ratio of 1.065.11 The difference between these magnitudes can perhaps be attributed to the manner in which anisotropy is defined in these two studies. The former defines anisotropy as the ratio of maximum stress in two orthogonal directions; the latter defines anisotropy as the ratio of the maximum strains in two orthogonal directions. In this study, increasing anisotropy in the peripapillary sclera was correlated with increases in scleral canal expansion, LC strain, and posterior LC deformation (Fig. 5). Conversely, their models also predicted that increasing the isotropy of the mid-posterior sclera does not largely influence the mechanical deformations of the ONH. This work implies that there may be an optimum level of regionally dependent scleral anisotropy, and any deviance from this optimum may initiate or exacerbate disease.24 Whereas Coudrillier et al.24 showed the existence of a highly aligned ring-like structure of fibers around the ONH through imaging (see Section 4.2.), Grytz et al.14 was also able to predict this result through eye-specific iFEM fitted to match strain maps generated with laser speckle interferometry. Consistent with other

367

Fig. 5. (Top) Anisotropic ratio values for the peripapillary and mid-posterior sclera in the left and right eye. (Middle) Degree of fiber alignment as a function of distance from the ONH. (Bottom) Scleral canal expansion and LC posterior deformation as functions of the anisotropic ratio.24

Copyright © 2018. Kugler Publications. All rights reserved.

368

Fig. 6. (Top) Degree of fiber alignment as a function of location. A circumferential ring of fibers can be traced out around the ONH. (Middle) Mechanical anisotropy variations throughout the regions of the peripapillary sclera. (Bottom) Degree of fiber alignment as a function of age in all four regions, with the general trend being increasing age decreases fiber alignment.27

N. Vij Jr. and J. Vande Geest

mechanical data in the literature, these authors also confirmed that the in-plane strains in the peripapillary sclera are larger than those in the mid-peripheral region. Coudrillier et al.27 also used a specimen-specific iFEM, which was based on an initial fiber mapping done via WAXS. Whereas the WAXS data helped determine fiber alignment as a function of quadrant (see Section 3.2.), the finite element model allowed relationships between fiber alignment and age to be highlighted. This study found that the fibers of older sclerae are less aligned with one another in the peripapillary sclera (Fig. 6). This contributes to older peripapillary sclerae being less anisotropic than younger sclerae, which is not consistent with the data on scleral anisotropy reported in non-human primates by Girard et al.19 Since it is hypothesized that peripapillary scleral anisotropy may protect the LC against strains, perhaps this finding plays a role in the increased incidence of glaucoma with age.27 Similar to Coudrillier et al.,24 Zhang et al.29 used computational simulations informed with experimental data from WAXS to show the relationships between degree of fiber alignment in the sclera/LC and the distribution of strain. Not surprisingly, preferred fiber orientation in the sclera affected strain distributions in many regions, highlighting the physiological importance of an optimum or preferred level of scleral anisotropy. A high degree of collagen alignment located 400-500 μm from the LC produced rings of ideally low strains in regions adjacent to the LC. Varying the scleral preferred fiber orientation to meridional was shown to drastically increase the principal strain near the LC and decrease the effective strain in the outer peripapillary sclera (Fig. 7). On the other hand, adjusting the model to incorporate perfectly circumferential fibers in both the peripapillary and peripheral sclera led to minimal changes. This reconfirms the notion that an ideal level of anisotropy is one that corresponds to a circumferential ring-like structure in the sclera, and altering this level can affect the biomechanical environment near the ONH, which may be a precursor to disease.29 Coudrillier et al.17 used an iFEM very similar to to their previous study27 to investigate the relationship between glaucoma and matrix/fiber stiffness. They found that damaged glaucomatous eyes had the highest matrix and fiber stiffness, while normal eyes the least stiff. As one might expect, undamaged glaucomatous sclerae

Collagen anisotropy in scleral mechanics

369

had a matrix and fiber stiffness in between the two (Fig. 8). The relationships regarding fiber alignment and glaucoma, which came solely out of WAXS data and may be of greater importance to a reader interested in scleral anisotropy, are discussed in the next section.17 4.2. Direct assessment of microstructural anisotropy using imaging techniques The following section will summarize the micro-

structural anisotropy of scleral tissue as quantified using imaging techniques including SALS, WAXS, and multiphoton microscopy. SALS and WAXS both rely on the preferred scattering of light (SALS) or X-rays (WAXS) based on the local orientation of collagen, typically measured in a thinly cryosectioned, dehydrated slice of sclera. Multiphoton imaging, on the other hand, can be performed on fresh and otherwise untreated scleral samples. In these experiments, it is common to

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 7. (Left) Preferred fiber orientation (far left) and resulting scleral and LC strain. Effective strain and first principal strain are also shown. (Right) Strain values when the preferred fiber orientation is changed from original to circumferential (cir), to meridional (mer). 29

Fig. 8. (Left) Degree of fiber alignment of normal (non-glaucomatous) and undamaged/damaged glaucomatous peripapillary sclerae for all four quadrants. (Right) Matrix stiffness and fiber stiffness for normal (non-glaucomatous), undamaged, and damaged sclerae.17

Copyright © 2018. Kugler Publications. All rights reserved.

370

quantify the second harmonic generation (SHG) signal of collagen by collecting light at half the wavelength of a short pulsed femtosecond excitation laser. In all cases, the heterogeneous preferred orientation of collagen and associated collagen splay can be quantified. As alluded to in previous sections, the microstructural organization of the sclera will have a direct influence on the biomechanical environment of the ONH, and thus may potentially participate in the initiation and/or progression of POAG. Age and glaucoma may not be the only factors that influence scleral anisotropy. Yan and colleagues21 were able to establish interesting relationships between a donors’ racioethnic background and scleral anisotropy using SALS. This study showed that African Americans had less equatorially aligned fibers than Caucasians (Fig. 9). This reduced level of equatorial support may contribute to larger scleral canal expansions in individuals of African descent, and as such, may play a role in the known higher incidence of POAG in this population. In concordance with the discussion of the presence of a circumferentially-oriented ring around the ONH earlier in this chapter, Yan et al. found that fiber orientation is equatorial around the ONH, regardless of age or sex (Fig. 9). This study also showed that, regardless of race, scleral microstructural anisotropy was depth-dependent, with an increase in the percentage of meridionally aligned fibers moving from the outer layer to the inner layer of the sclera (Fig. 9).21 Girard et al.20 showed that collagen fibers form a circumferentially aligned ring at the junction of the cornea and the sclera using SALS. Circumferentially aligned fibers were also found in the peripapillary and peripheral scleral subsection (Fig. 10), which is consistent with many other studies. However, meridionally aligned fibers were found in the equatorial region. The author suggested that this is likely present in order to resist axial length increases due to the effects of muscles in the eye. The scleral canal was one of the regions in which fibers had the highest degree of alignment, in agreement with the aforementioned studies. However, Girard et al. also found a high degree of fiber alignment at the limbus and the equator (Fig. 10).20 Pijanka et al.22 yet again showed that the peripapillary sclera collagen fibers are aligned parallel to the scleral canal; this characteristic feature further points

N. Vij Jr. and J. Vande Geest

Fig. 9. (Top) Percentage of occurrence of fibers within the meridional range and equatorial range for African American and Caucasian donor tissues. (Middle) Percentage of occurrence of fibers in the meridional range and equatorial range at three different depths. (Bottom) Percentage of occurrence of fibers in the meridional range and equatorial range for three different age groups.21

Collagen anisotropy in scleral mechanics

371

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 11. Higher alignment of collagen in the peripapillary sclera than in the mid-posterior sclera.22

Fig. 10. (Top) Preferred fiber orientation to be circumferential to the ONH in the peripapillary and peripheral sclera. (Bottom) High degree of fiber alignment at the limbus and the equator.20

towards the existence of a ring-like structure around the ONH. They also showed some other interesting features of scleral anisotropy through WAXS. Scleral anisotropy was significantly higher in the peripapillary sclera than in the mid-posterior sclera (Fig. 11). By quadrant, the superior-nasal subsection of the sclera was the least anisotropic out of all the scleral subsections. Interest-

ingly, Pijanka et al. showed that eyes with glaucoma showed significantly lower levels of anisotropy in both the superior-temporal and inferior-nasal regions than normal eyes, which bolsters the idea of an optimum level of anisotropy. Although this finding confirms that glaucomatous eyes have lost the scleral anisotropy that may protect the biomechanical environment near the ONH, it does not elucidate whether this is a precursor to or result of glaucoma. This study also used multiphoton microscopy to further characterize depth-dependent collagen organization. They report that the sclera exhibits less interwoven fibers, yet a higher fiber alignment in the innermost five-sixths of the sclera when moving radially away from the ONH; the alignment decreases in the outer one-sixth of the sclera.22 These results support the notion that scleral microstructural organization and anisotropy are not

372

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 12. Displacement of the circumferentially aligned ring of collagen in the superior region away from the ONH.23

entirely homogeneous throughout the depth of the sclera. In an effort to further understand depth-dependent collagen organization and how this may affect ONH health, Pijanka et al.25 used WAXS and SHG multiphoton microscopy to further look at fibrillar structures. In addition to confirming the presence of a circumferential ring of fibers in the peripapillary sclera, this study added to our body of knowledge that the strongest correlation of the aforementioned ring is in the mid-stromal region. It is also important to note that fibrous bundles were found to run from the superior and inferior portion of the peripapillary collagen ring out into the mid-posterior sclera. These bundles may serve to anchor the peripapillary ring and support it in carrying out its potential function of protecting the LC from scleral strains.25 Through SHG, Cone-Kimball et al.23 showed that the external sclera has fibrils that are more randomly oriented than the interior sclera, and that the fibers are oriented circumferentially around the scleral canal in mice. This is expected; however, what was more

N. Vij Jr. and J. Vande Geest

notable about this study was that the ring comprised of collagen was further from the scleral canal, and specifically, in the superior region in mice that were exposed to chronic IOP elevation (Fig. 12). This finding implies that the pressures associated with glaucoma may effect the fibrillar organization at the scleral canal, which in turn might be harmful to the health of retinal ganglion cells. Glaucomatous eyes were also associated with an increase in the number of small fibrils compared to larger fibrils, which further points towards the effects of elevated IOP exposure on scleral collagen microstructural organization.23 Danford et al.30 used SALS to show that the normal sclera has a higher fibril eccentricity than glaucomatous tissue in the superior and inferior regions, and a lower eccentricity than glaucomatous tissue in the nasal and temporal regions (Fig. 13). This study also demonstrated that the glaucomatous sclera has a greater inclination to have equatorially oriented fibers than the non-glaucomatous sclera (Fig. 13). These findings support the notion that healthy (non-glaucomatous) eyes have a certain distribution of scleral anisotropy, and that alterations in this distribution may be associated with poor retinal ganglion cell health.30 Moreover, this study showed some interesting relationships regarding microstructural information as a function of scleral depth. Like the Cone-Kimball et al. study, the Danford study showed that the nasal region had a higher eccentricity at shallow depths (the fibers were more highly oriented) than the inferior and superior regions; however, as the depth increased, the eccentricity values for all of the regions merged to a convergent value (Fig. 13). Elucidating the relationship between depth and collagen organization is of interest because it may provide further insight as to why POAG affects scleral tissue remodeling. Danford et al. also confirmed a lower percentage of equatorially aligned fibers is associated with sclera farther away from the scleral canal. This depth-dependent fibrillar organization was originally established in 2011 by Yan et al., a study done in the same laboratory two years prior. Lastly, all of the regions exhibited increasing fiber splay and a lower percentage of equatorial fibers with increasing depth (Fig. 13). These results add to the limited body of knowledge regarding relationships between depth and fibril microstructure, and confirm that scleral tissue is inhomogeneous both regionally

Collagen anisotropy in scleral mechanics

373

Copyright © 2018. Kugler Publications. All rights reserved.

and through the scleral thickness. The changes seen in fiber splay and equatorial alignment may be functionally important because of the sclera’s role in adjusting to alterations in pressure. Because glaucoma has been shown to disrupt eccentricity and fiber alignment, an interesting future direction would be to explore how the depth-dependent fibrillar organization is affected by acute IOP elevations.30 Evidence of the circumferential ring in the peripapillary sclera was seen again in Coudrillier et al. through WAXS.24 The peripapillary sclera was shown to be more aligned and more anisotropic than mid-posterior collagen (Fig. 5). Within the peripapillary sclera, higher fiber alignment was seen closer to the ONH (Fig. 5), which reinforces the notion that the fibers near the ONH have a protective function. Furthermore, WAXS revealed that the superior-temporal quadrant displayed the highest degree of anisotropy and the nasal-superior quadrant displayed the lowest level of anisotropy, in agreement with Pijanka et al.22 Continuing with the work done two years prior, Pijanka et al.26 showed that collagen was circumferentially oriented around the ONH through WAXS (Fig. 14). Furthermore, this study reconfirmed that collagen is more anisotropic in the peripapillary sclera than in the peripheral sclera. This implies that the level of

Fig. 13. (Top) Eccentricity (Ecc) in glaucomatous and non-glaucomatous human donor tissues. (Middle) Percent Equatorial Fibers (PEF) in glaucomatous and non-glaucomatous human donor tissues. (Bottom) Percent Equatorial Fibers as a function of depth for the Inferior (I), Nasal (N), Superior (S) and Temporal (T) regions. 30

Fig. 14. (Top) Circumferential ring of collagen in both the bead-induced glaucoma and control mice. (Bottom) Anisotropy in the bead-induced glaucoma and control mice; a notably higher level of anisotropy can be seen in the control mice.26

374

N. Vij Jr. and J. Vande Geest

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 15. (Top) Mean collagen fiber orientation at six different depths of the sclera. (Bottom) Collagen anisotropy as a function of depth for the four quadrants.31

anisotropy near the ONH is related to the function of the ONH and health of retinal ganglion cells. Pijanka et al. found that the collagen, in general, was less anisotropic in bead-induced ocular hypertensive mice (Fig. 14). This finding supports the notion from Cone-Kimball et al. that the effects of pressure inflation in the eye may alter the anisotropy near the ONH, and may thus have negative effects on retinal ganglion cells that pass through the LC.26 In addition to once again corroborating the existence of a ring of circumferentially aligned collagen fibers in the peripapillary sclera, Coudrillier et al.27 also showed a pair of symmetrical oblique bundles which originated at the temporal peripapillary sclera and moved towards the superior-nasal and inferior-nasal poles in the mid-posterior sclera. This is very similar to the result obtained by Pijanka et al.,25 and is potentially indicative of more peripheral anchors for the circumpapillary ring surrounding the ONH. Furthermore, this study showed that collagen fibers are least aligned in the nasal-superior quadrant and most aligned in the temporal-superior quadrant (Fig. 7), which confirms the results seen in

Coudrillier et al.27 Similar to Yan et al.,21 which used SALS to study depth-dependent anisotropy, Pijanka et al.31 characterized depth-dependent anisotropy through WAXS. This study found that the innermost one-third of the sclera, nearest to the choroid, was found to have fibrils oriented radially. This is consistent with another recent study showing radially aligned scleral fibers in sheep sclera.32 Conversely, the outermost two-thirds of the sclera were found to have fibrils oriented in a circumferential fashion around the ONH (Fig. 15). The sclera became more isotropic as the depth (distance from the outer surface) decreased, while maximum circumferential anisotropy was noted at a depth of 300-450 μm from the outer surface.31 These results confirm those of Yan et al.,21 who showed an increase in the percentage of meridionally aligned fibers moving from the outermost to innermost layers of the sclera, as well as an increase in the degree of fiber splay closer to the choroidal interface. Jones et al.28 showed that the degree of fiber alignment was highest in the peripapillary sclera

Collagen anisotropy in scleral mechanics

375

damage displayed the lowest variation in degree of fiber alignment (Fig. 8), while normal sclerae had the highest variation. As one might expect, sclerae from eyes reported to be glaucomatous but with no optic nerve damage were in between the two extremes. Coudriller et al.27 showed fiber alignment and mechanical anisotropy to be directly correlated, and this finding once again supports the potential importance of scleral anisotropy in ONH health, and ultimately, glaucoma. Lastly, Coudriller et al.17 found diabetic eyes to have a more anisotropic peripapillary sclera compared to normal eyes. Because peripapillary scleral anisotropy may protect the ONH — the site of retinal ganglion cell death in glaucoma — from tensile strains, , this finding may be related to diabetic patients being twice as likely to develop glaucoma.17

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 16. Mean preferred fiber orientation of the peripapillary sclera to be circumferential.28

and lowest in the LC using both SHG microscopy and SALS. Fibers were circumferentially oriented around the scleral canal once again (Fig. 16); the relationship between the degree of fiber alignment and age or glaucoma that emerged from this study is more interesting. Older donor sclerae exhibited a higher degree of fiber alignment in the peripapillary region, whereas glaucomatous donor peripapillary scleral samples exhibited a lower degree of fiber alignment than normal donor tissues. This provides evidence of scleral remodeling with glaucoma and aging, which may be an interesting focus of future research.28 Coudrillier et al.17 used WAXS to study fiber alignment as a function of scleral region, but also to determine the effect of glaucoma on fiber alignment. Firstly, Coudriller et al.17 corroborated the regionally dependent fiber alignment seen in Coudriller et al.27 in 2015. What is more interesting however, are the differences in fiber alignment in glaucoma eyes. By quadrant, sclerae from eyes reported to be glaucomatous with optic nerve

4. Summary The scleral shell first and foremost provides a structural protective function for the delicate intraocular tissues responsible for achieving functional vision. There is now a wealth of evidence to suggest that collagen microstructural organization and the associated mechanical anisotropy of the posterior scleral shell are optimized to protect the axons of the retinal ganglion cells as they exit the posterior pole to transmit visual information to the brain. Paramount in this organization is the formation of a circumferentially oriented ring of collagen around the scleral canal that limits expansion of the scleral canal and the contained lamina cribrosa, presumably establishing a homeostatic biomechanical environment promoting proper visual transmission. Evidence is now also available indicating that elevated IOP and/or the presence of glaucoma result in a disorganization and remodeling of the sclera. Future research should be focused on delineating what role this remodeling plays in the initiation and/or progression of ocular diseases including POAG.

376

N. Vij Jr. and J. Vande Geest

References 1. 2.

3.

4.

5.

6.

7.

8.

9.

10. 11.

Copyright © 2018. Kugler Publications. All rights reserved.

12.

13.

14.

15.

16.

Quigley HA, Broman AT, The number of people with glaucoma worldwide in 2010 and 2020. Br J Ophthalmol. 2006;90(3):262-267. Burgoyne CF, Downs JC, Bellezza AJ, Suh JK, Hart RT. The optic nerve head as a biomechanical structure: a new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage. Prog Retin Eye Res. 2005;24(1):39-73. Girard MJ, Suh JK, Bottlang M, Burgoyne CF, Downs JC. Biomechanical changes in the sclera of monkey eyes exposed to chronic IOP elevations. Invest Ophthalmol Vis. Sci. 2011;52(8):5656-5669. Norman RE, Flanagan JG, Sigal IA, Rausch SM, Tertinegg I, Ethier CR. Finite element modeling of the human sclera: influence on optic nerve head biomechanics and connections with glaucoma. Exp Eye Res. 2011;93(1):4-12. Sigal IA, Yang H, Roberts MD, Burgoyne CF, Downs JC. IOP-induced lamina cribrosa displacement and scleral canal expansion: an analysis of factor interactions using parameterized eye-specific models. Invest Ophthalmol Vis Sci. 2011;52(3):1896-1907. Lodish H, Berk A, Zipursky SL, Matsudaira P, Baltimore D, Darnell J. Molecular Cell Biology. 4th ed. 2000. New York, NY: W. H. Freeman; 2000. Burgoyne CF, Morrison JC. The anatomy and pathophysiology of the optic nerve head in glaucoma. J Glaucoma. 2001;10(5 Suppl 1):S16-8. Quigley HA, Addicks EM, Green WR, Maumenee AE. Optic nerve damage in human glaucoma. II. The site of injury and susceptibility to damage. Arch Ophthalmol. 1981;99(4):635-649. Holländer H, Makarov F, Stefani FH, Stone J. Evidence of constriction of optic nerve axons at the lamina cribrosa in the normotensive eye in humans and other mammals. Ophthalmic Res. 1995;27(5):296-309. Quigley HA. Neuronal death in glaucoma. Prog Retin Eye Res. 1999;18(1):39-57. Eilaghi A, Flanagan JG, Tertinegg I, Simmons CA, Brodland GW, Ethier CR. Biaxial mechanical testing of human sclera. J Biomech. 2010;43(9):1696-701. Cruz Perez B, Tang J, Morris HJ, et al. Biaxial mechanical testing of posterior sclera using high-resolution ultrasound speckle tracking for strain measurements. J Biomech. 2014;47(5):1151-1156. Myers KM, Coudrillier B, Boyce BL, Nguyen TD. The inflation response of the posterior bovine sclera. Acta Biomater. 2010;6(11):4327-4335. Grytz R, Fazio MA, Girard MJ, et al. Material properties of the posterior human sclera. J Mech Behav Biomed Mater. 2014;29:602-17. Girard MJ, Downs JC, Burgoyne CF, Suh JK, Experimental surface strain mapping of porcine peripapillary sclera due to elevations of intraocular pressure. J Biomech Eng. 2008;130(4):041017. Fazio MA, Grytz R, Bruno L, et al. Regional variations in mechanical strain in the posterior human sclera. Invest Ophthalmol Vis Sci. 2012;53(9):5326-5333.

17. Coudrillier B, Pijanka JK, Jefferys J, et al. Glaucoma-related changes in the mechanical properties and collagen micro-architecture of the human sclera. PLoS One. 2015;10(7):e0131396. 18. Girard MJ, Downs JC, Bottlang M, Burgoyne CF, Suh JK. Peripapillary and posterior scleral mechanics--part II: experimental and inverse finite element characterization. J Biomech Eng. 2009;131(5):051012. 19. Girard MJ, Suh JK, Bottlang M, Burgoyne CF, Downs JC. Scleral biomechanics in the aging monkey eye. Invest Ophthalmol Vis Sci. 2009;50(11):5226-5237. 20. Girard MJ, Dahlmann-Noor A, Rayapureddi S, et al. Quantitative mapping of scleral fiber orientation in normal rat eyes. Invest Ophthalmol Vis Sci. 2011;52(13):9684-9693. 21. Yan D, McPheeters S, Johnson G, Utzinger U, Vande Geest JP, Microstructural differences in the human posterior sclera as a function of age and race. Invest Ophthalmol Vis Sci. 2011;52(2): 821-829. 22. Pijanka JK, Coudrillier B, Ziegler K, et al. Quantitative mapping of collagen fiber orientation in non-glaucoma and glaucoma posterior human sclerae. Invest Ophthalmol Vis Sci. 2012;53(9):5258-5270. 23. Cone-Kimball E, Nguyen C, Oglesby EN, Pease ME, Steinhart MR, Quigley HA. Scleral structural alterations associated with chronic experimental intraocular pressure elevation in mice. Mol Vis. 2013;19:2023-2039. 24. Coudrillier B, Boote C, Quigley HA, Nguyen TD. Scleral anisotropy and its effects on the mechanical response of the optic nerve head. Biomech Model Mechanobiol. 2013;12(5):941-963. 25. Pijanka, J, Sorensen T, Nguyen TD, Quigley HA, Boote C. Three-dimensional quantitative analysis of collagen fibre architecture in human peripapillary sclera. Invest Ophthalmol Vis Sci. 2013; 2013;4:2299. 26. Pijanka JK, Kimball EC, Pease ME, et al. Changes in scleral collagen organization in murine chronic experimental glaucoma. Invest Ophthalmol Vis Sci. 2014;55(10):6554-6564. 27. Coudrillier B, Pijanka J, Jefferys J, et al. Collagen structure and mechanical properties of the human sclera: analysis for the effects of age. J Biomech Eng. 2015;137(4):041006. 28. Jones HJ, Girard MJ, White N, et al. Quantitative analysis of three-dimensional fibrillar collagen microstructure within the normal, aged and glaucomatous human optic nerve head. J R Soc Interface. 2015;12(106):20150066. 29. Zhang L, Albon J, Jones H, et al. Collagen microstructural factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2015;56(3):2031-2042. 30. Danford FL, Yan D, Dreier RA, Cahir TM, Girkin CA, Vande Geest JP. Differences in the region- and depth-dependent microstructural organization in normal versus glaucomatous human posterior sclerae. Invest Ophthalmol Vis Sci. 2013;54(13):7922-7932. 31. Pijanka JK, Spang MT, Sorensen T, et al. Depth-dependent changes in collagen organization in the human peripapillary sclera. PLoS One. 2015;10(2):e0118648. 32. Jan NJ, Lathrop K, Sigal IA. Collagen architecture of the posterior pole: high-resolution wide field of view visualization and analysis using polarized light microscopy. Invest Ophthalmol Vis Sci. 2017;58(2):735-744.

26. The dynamic response of the corneoscleral shell Jun Liu, Keyton L. Clayson, Elias R. Pavlatos Department of Biomedical Engineering, The Ohio State University, Columbus, OH, USA

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction Intraocular pressure (IOP) is a primary risk factor for glaucoma. However, the extent of optic nerve damage can vary substantially among individuals with similar IOPs. Since IOP magnitude is not a sufficient predictor for glaucoma development and progression, other predictive factors are needed to identify high-risk individuals that may benefit from aggressive treatment to prevent vision loss. Emerging evidence has suggested a potential link between corneoscleral biomechanical properties and glaucoma risk. For example, central corneal thickness (CCT) was identified as a potent clinical risk factor for the development of glaucoma in the Ocular Hypertension Treatment Study,1 and was later confirmed as an independent risk factor, even after accounting for its influence on IOP measurement.2 A compliant peripapillary sclera has been proposed as a risk factor for glaucoma3 because it may result in larger optic nerve head deformation under similar IOPs based on computational modeling.4 Additionally, several known or suggested glaucoma risk factors such as age, race, myopia, and diabetes plausibly have some association with corneoscleral biomechanical alterations or abnormalities,5-8 and these associations may represent a common pathway for their impact on glaucoma risk. These results indicate there may be individual differences or disease-related changes in corneoscleral biomechanical properties that influence the susceptibility to glaucomatous damage. This intriguing link between corneoscleral biomechanics and glaucoma risk has motivated our group and others to

examine how corneoscleral biomechanical properties are involved in regulating the primary risk factor, IOP, and more specifically, the dynamic profile of IOP.

2. IOP fluctuation and its physiological processes IOP is a dynamic parameter and fluctuates across different time scales.9 For example, it fluctuates at each heartbeat due to the pulsatile blood flow into the choroid in sync with the systemic blood pressure pulsation. IOP also fluctuates during incidental activities such as blinking, eye movement, postural change, fluid intake, or Valsalva maneuver. These short-term, rapid IOP fluctuations could be large and may vary substantially between individuals. An early study showed that forcible squeezing or rubbing of the eye could raise IOP to over 80 mmHg.10 Postural change from sitting to supine could raise IOP by 2 mmHg in one individual, but over 10 mmHg in another.11-13 Although in current clinical practice IOP is often recorded as a single value, it is in fact responsive to many physiological and biological factors, and can have transient ups and downs within a very large dynamic range. The detailed physiological processes involved in short-term IOP variations are not fully characterized. It is currently understood that IOP variations can be caused by aqueous flow changes associated with aqueous production or outflow facility,14 blood flow

Correspondence:Jun Liu, Department of Biomedical Engineering, The Ohio State University, 270 Bevis Hall, 1080 Carmack Road, Columbus, OH 43210, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 377-382 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

378

J. Liu, K.L. Clayson and E.R. Pavlatos

Fig. 1. Corneoscleral viscoelastic properties modulate the parameters (magnitude, speed, and duration) of IOP fluctuations, and may be used as new risk factors to improve glaucoma management.

Copyright © 2018. Kugler Publications. All rights reserved.

(volume or pressure) changes,15 and/or intraocular fluid displacement associated with external forces acting on the eye (e.g., blinking or eye rubbing).10 In the case of postural effects, when the body changes from sitting to supine, there is an increase in episcleral venous pressure which impairs aqueous outflow, leading to IOP elevation.15 There may also be rapid blood filling in the intraocular blood vessels (i.e., choroidal vessels) when a person is lying down,16 suggested by the fact that the postural effect on IOP is almost instantaneous.17 Changes in both aqueous flow and blood flow effectively alter the total volume within the corneoscleral shell, which presumably is the direct cause of IOP change. It is therefore reasonable to expect that the biomechanical properties of the ocular coat that encloses the intraocular volume play an important role in governing the dynamics of IOP. As shown in Figure 1, an eye with a compliant ocular coat and fast viscoelastic relaxation is more capable of damping IOP (i.e., smaller, slower, and/or shorter elevations), resulting in a lower degree of IOP fluctuation. Conversely, a stiff corneoscleral shell, often seen in aged eyes, could result in more frequent and larger fluctuations of IOP.

3. The relevance of IOP fluctuation in glaucoma It is unclear to what extent IOP fluctuations are harmful. Several clinical trials have reported a positive correlation between larger IOP fluctuation and a poorer glaucoma prognosis. Asrani et al. found that the diurnal IOP range and the IOP range over a time period of five days were significant risk factors for visual field loss in patients with open-angle glaucoma using home tonometry five times daily (Fig. 2).18 In a retrospective analysis of IOP

Fig. 2. Asrani et al. showed that open-angle glaucoma patients with a smaller diurnal IOP range were less likely to experience visual field loss.18

measurements obtained every six months for approximately seven years, Caprioli and Coleman concluded that long-term IOP fluctuation was associated with visual field progression for patients in the lowest tercile of mean IOP.19 Hong et al. have retrospectively studied patients with primary open-angle glaucoma and primary angle-closure glaucoma over a postoperative period of at least three years and reported an increased likelihood of visual field loss for a standard deviation in IOP larger than 2 mmHg.20,21 However, others have reported conflicting outcomes showing lack of a definitive correlation between IOP fluctuation and glaucoma progression. Medeiros et al. retrospectively evaluated a cohort of untreated ocular hypertensives over an average of seven years. Their results (Fig. 3) showed that mean IOP, rather than IOP fluctuation, was a risk factor for conversion from ocular hypertension to glaucoma judged by reproducible visual field defects or glaucomatous changes in the appearance of the optic disc.22 In patients with unilateral glaucoma, Wang et al. found no significant difference in IOP fluctuation between the glaucomatous eye and the healthy eye after six measurements at four-hour intervals.23 These contradictory findings may be due to the fact

The dynamic response of the corneoscleral shell

379

and found that a slow pressure rise to 50 mmHg at 3 mmHg/min resulted in no detectable cellular injury, while pressure spikes of the same magnitude but which rose much faster (i.e., 8 mmHg/sec) induced appreciable cellular injury, even when the spike only lasted for one min.25 They also found that the cellular injury was accumulative over the number and magnitude of the spikes. Similar effects were observed in vivo. These results suggest that the dynamic aspects of IOP, such as the peak magnitude, speed of rise to peak, and duration may all play a role in the pathophysiological outcomes of IOP fluctuation.

Fig. 3. Medeiros et al. found that the level of long-term IOP fluctuation did not result in a significant difference in the risk of progression from ocular hypertension to glaucoma.22

Copyright © 2018. Kugler Publications. All rights reserved.

that different studies use different definitions of IOP fluctuation: some define fluctuation as the difference between maximum and minimum IOP values during a designated period of time, while others define it as the standard deviation of repeated IOP measurements. IOP fluctuation is also less robust to measure than mean pressure because it is more sensitive to transient noise, such as holding one’s breath during measurements. It is also well recognized that clinical office hours likely do not capture the peak IOP.24 We currently have a limited understanding of the impact of IOP fluctuations at the cellular level. Resta et al. studied retinal ganglion cells in mounted rat retinas

4. Corneal and scleral stiffness impacts rapid IOP elevations It is challenging to evaluate the role of corneoscleral biomechanics in regulating IOP in vivo because other factors such as blood flow and aqueous flow are simultaneously impactful, potentially interactive, and difficult to control. In order to separate out the factors associated with corneoscleral biomechanics, we have designed experiments on animal or human donor eyes in which the total intraocular fluid (aqueous humor, or blood, or a combination of the two) change is simulated by a controlled fluid infusion to investigate how IOP elevations are influenced by corneal and scleral stiffness. We first investigated IOP elevations due to rapid intraocular volume change before and after corneal

Fig. 4. (a) Mean IOP elevation change with 200 µL infusion at 200 µL/min before and after glutaraldehyde treatment of the cornea (p > 0.4 for 0% group, p < 0.001 for 1% and 4% group). (b) IOP elevation was positively correlated with the secant tensile modulus of the cornea obtained at 5% strain (R = 0.84, fit line not shown).26

380

J. Liu, K.L. Clayson and E.R. Pavlatos

These studies reported the separate effects of corneal or scleral stiffness on IOP elevations during rapid microvolumetric changes in the eye. Investigations are currently underway to examine how the relative stiffness of the cornea and sclera affect the response, and which area of the ocular coat may dominate the process.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. IOP elevation at the “fast” infusion rate was significantly correlated with radial strains in the peripapillary sclera measured at 20.6 mmHg.27

stiffening.26 A volume of 200 µL was infused in porcine globes at a rate of 200 µL/min, and the IOP change from a baseline of 10 mmHg was recorded. This procedure was repeated after corneas were treated with 0%, 1%, or 4% concentration of glutaraldehyde in isotonic phosphate buffered saline. The corneas were then dissected and subjected to mechanical testing via strip extensiometry to measure tensile modulus. IOP elevations were significantly increased after glutaraldehyde treatment in a dose-dependent manner (Fig. 4a). Strip testing confirmed that increased glutaraldehyde treatment corresponded to a higher tensile modulus and that corneal modulus was significantly correlated with IOP elevations (Fig. 4b). This study showed that corneal stiffness had a significant impact on the magnitude of IOP fluctuations during short-term volumetric change. In a more recent study, we examined the relationship between scleral stiffness and IOP elevations.27 A 15 µL volume of fluid was infused into porcine globes at fast, intermediate, and slow rates (15, 1, and 0.1 µL/ sec, respectively). The peripapillary sclera of these globes was imaged with high-frequency ultrasound to measure the inflation strains using speckle tracking. Scleral strains were shown to vary between specimens, and were inversely correlated with IOP elevations (p = 0.02) (Fig. 5), suggesting that a stiffer sclera was associated with higher IOP elevations. IOP elevation was also found to proportionally increase as infusion rate increased, showing a viscoelastic behavior of the corneoscleral shell. These results suggest that the IOP elevation magnitude is related to both the rate of infusion and the scleral stiffness during short-term volumetric change.

5. The viscoelastic properties of the corneoscleral shell It is important to understand the time-dependent viscoelastic properties of the corneoscleral shell in order to model and characterize how corneoscleral biomechanics influences the dynamic profile of IOP. Both the cornea and sclera are known to exhibit viscoelastic properties such as creep and stress relaxation.28-30 The instantaneous modulus and the equilibrium modulus constitute two principal parameters for characterizing the stress relaxation behavior of a viscoelastic material. The instantaneous modulus is a measure of the immediate response of the tissue. The equilibrium modulus is a measure of the tissue’s long-term stiffness (i.e., after it has fully relaxed after a rapid deformation). In addition, a variety of time constants are needed to capture the detailed viscoelastic behavior, among which are the short- and long-term time constants for stress relaxation. The short- and long-term time constants are measures of the shortest and longest time-dependent components of the tissue’s stress relaxation response. They describe how quickly the tissue relaxes to an equilibrium stress after a rapid deformation. All four principal viscoelastic parameters can be derived from standard stress relaxation tests. Viscoelastic characterization of porcine cornea and sclera has been scarcely reported in the literature. We developed a finite element model to study the viscoelastic responses of the eye during microvolumetric changes at different rates.31 By matching the model output with experimental data27, the viscoelastic properties of the porcine eye were estimated (Table 1). The model showed that the long-term time constant primarily influenced the fast rate, whereas the short-term time constant directly affected the intermediate and slow rates (Fig. 6). The equilibrium modulus was also shown to primarily affect the slow rate, while

The dynamic response of the corneoscleral shell

381

Table 1. Viscoelastic material parameters of the porcine eye estimated from finite element modeling of infusion experiments. 31 Sclera

Cornea

Material properties

Baseline

Range

Baseline

Range

Instantaneous modulus

5.5 MPa

3.1 – 7.9 MPa

1.1 MPa

0.62 – 1.6 MPa

Equilibrium modulus

1.325 MPa

0.325 – 2.325 MPa

0.265 MPa

0.065 – 0.465 MPa

Short term time constant

0.35 sec

0.05 – 0.65 sec

0.35 sec

0.05 – 0.65 sec

Long term time constant

68 sec

18 – 128 sec

68 sec

18 – 128 sec

Fig. 6. Effect of viscoelastic parameters on IOP elevations at the fast (left), intermediate (center), and slow (right) infusion rates scaled from the minimum value (-1) to the maximum (+1) value. 31

the instantaneous modulus had a larger influence on the fast and intermediate rates. This suggests that different viscoelastic parameters may have a different effect on IOP elevation depending on the rate of change in the intraocular volume.

Copyright © 2018. Kugler Publications. All rights reserved.

6. Outlook Certain characteristics or alterations in corneoscleral biomechanical properties may increase a person’s susceptibility to the adverse impact of IOP fluctuations, leading to glaucomatous optic neuropathy. If proven to be independent risk factors, corneoscleral biomechanical properties may expand treatment strategies as potentially modifiable factors beyond IOP reduction. Non-invasive and clinically feasible techniques are needed to measure corneal and scleral biomechanical properties in vivo. Investigating the role of these properties in glaucoma risk may potentially translate the outcome to the standard of care in glaucoma by optimizing treatment strategies in patients whose progression rates are currently difficult to ascertain. In summary, the understanding of corneoscleral

biomechanics and its role in affecting dynamic IOP, and thus glaucomatous damage, combined with the knowledge of other more established factors such as IOP, optic nerve head biomechanics, and aqueous outflow, will likely improve our ability to implement effective management for individual glaucoma suspects and patients.

382

J. Liu, K.L. Clayson and E.R. Pavlatos

References 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Copyright © 2018. Kugler Publications. All rights reserved.

12.

13.

14.

15.

Gordon MO, Beiser JA, Brandt JD, et al. The Ocular Hypertension Treatment Study: baseline factors that predict the onset of primary open-angle glaucoma. Arch Ophthalmol. 2002;120:714-20; discussion_829-830. Francis BA, Varma R, Chopra V, Lai MY, Shtir C, Azen SP. Intraocular pressure, central corneal thickness, and prevalence of open-angle glaucoma: the Los Angeles Latino Eye Study. Am J Ophthalmol. 2008;146:741-746. Nguyen C, Cone FE, Nguyen TD, et al. Studies of scleral biomechanical behavior related to susceptibility for retinal ganglion cell loss in experimental mouse glaucoma. Invest Ophthalmol Vis Sci. 2013;54:1767-1780. Sigal IA, Flanagan JG, Ethier CR. Factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2005;46:41894199. Coudrillier B, Tian J, Alexander S, Myers KM, Quigley HA, Nguyen TD. Biomechanics of the human posterior sclera: age- and glaucoma-related changes measured using inflation testing. Invest Ophthalmol Vis Sci. 2012;53:1714-1728. Fazio MA, Grytz R, Morris JS, Bruno L, Girkin CA, Downs JC. Human scleral structural stiffness increases more rapidly with age in donors of African descent compared to donors of European descent. Invest Ophthalmol Vis Sci. 2014;55:71897198. Mitchell P, Hourihan F, Sandbach J, Wang JJ. The relationship between glaucoma and myopia: the Blue Mountains Eye Study. Ophthalmology. 1999;106:2010-2015. Mitchell P, Smith W, Chey T, Healey PR. Open-angle glaucoma and diabetes: the Blue Mountains eye study, Australia. Ophthalmology. 1997;104:712-718 Downs JC, Burgoyne CF, Seigfreid WP, Reynaud JF, Strouthidis NG, Sallee V. 24-hour IOP telemetry in the nonhuman primate: implant system performance and initial characterization of IOP at multiple timescales. Invest Ophthalmol Vis Sci. 2011;52:7365-7375. Coleman DJ, Trokel S. Direct-recorded intraocular pressure variations in a human subject. Arch Ophthalmol. 1969;82:637640. Anderson DR, Grant WM. The influence of position on intraocular pressure. Invest Ophthalmol. 1973;12:204-212. Krieglstein G, Langham ME. Influence of body position on the intraocular pressure of normal and glaucomatous eyes. Ophthalmologica. 1975;171:132-145. Parsley J, Powell RG, Keightley SJ, Elkington AR. Postural response of intraocular pressure in chronic open-angle glaucoma following trabeculectomy. Br J Ophthalmol. 1987;71:494-496. Stamer WD, Acott TS. Current understanding of conventional outflow dysfunction in glaucoma. Curr Opin Ophthalmol. 2012;23:135-143. Friberg TR, Sanborn G, Weinreb RN. Intraocular and episcleral venous pressure increase during inverted posture. Am J Ophthalmol. 1987;103:523-526.

16. Longo A, Geiser MH, Riva CE. Posture changes and subfoveal choroidal blood flow. Invest Ophthalmol Vis Sci. 2004;45:546-551. 17. Krieglstein GK, Waller WK, Leydhecker W. The vascular basis of the positional influence of the intraocular pressure. Albrecht Von Graefes Arch Klin Exp Ophthalmol. 1978;206:99-106. 18. Asrani S, Zeimer R, Wilensky J, Gieser D, Vitale S, Lindenmuth K. Large diurnal fluctuations in intraocular pressure are an independent risk factor in patients with glaucoma. J Glaucoma. 2000;9:134-142. 19. Caprioli J, Coleman AL. Intraocular pressure fluctuation a risk factor for visual field progression at low intraocular pressures in the advanced glaucoma intervention study. Ophthalmology. 2008;115:1123-1129.e3. 20. Hong S, Seong GJ, Hong YJ. Long-term intraocular pressure fluctuation and progressive visual field deterioration in patients with glaucoma and low intraocular pressures after a triple procedure. Arch Ophthalmol. 2007;125:1010-1013. 21. Hong S, Kim CY, Seong GJ. Long-term intraocular pressure fluctuation and visual field progression in glaucoma patients with low intraocular pressure after post-trabeculectomy phacoemulsification. J Ocul Pharmacol Ther. 2007;23:571-576. 22. Medeiros FA, Weinreb RN, Zangwill LM, et al. Long-term intraocular pressure fluctuations and risk of conversion from ocular hypertension to glaucoma. Ophthalmology. 2008;115:934-940. 23. Wang NL, Friedman DS, Zhou Q, et al. A population-based assessment of 24-hour intraocular pressure among subjects with primary open-angle glaucoma: The Handan Eye Study. Invest Ophthalmol Vis Sci. 2011;52:7817-7821. 24. Leidl MC, Choi CJ, Syed ZA, Melki SA. Intraocular pressure fluctuation and glaucoma progression: what do we know? Br J Ophthalmol. 2014;98:1315-1319. 25. Resta V, Novelli E, Vozzi G, et al. Acute retinal ganglion cell injury caused by intraocular pressure spikes is mediated by endogenous extracellular ATP. Eur J Neurosci. 2007;25:2741-2754. 26. Liu J, He X. Corneal stiffness affects IOP elevation during rapid volume change in the eye. Invest Ophthalmol Vis Sci. 2009;50:2224-2249. 27. Morris HJ, Tang J, Cruz Perez B, et al. Correlation between biomechanical responses of posterior sclera and IOP elevations during micro intraocular volume change. Invest Ophthalmol Vis Sci. 2013;54:7215-7222. 28. Downs JC, Suh JK, Thomas KA, Bellezza AJ, Hart RT, Burgoyne CF. Viscoelastic material properties of the peripapillary sclera in normal and early-glaucoma monkey eyes. Invest Ophthalmol Vis Sci 2005;46:540-546. 29. Boyce BL, Jones RE, Nguyen TD, Grazier JM. Stress-controlled viscoelastic tensile response of bovine cornea. J Biomech. 2007;40:2367-2376. 30. Downs JC, Suh JKF, Thomas KA, Bellezza AJ, Burgoyne CF, Hart RT. Viscoelastic characterization of peripapillary sclera: material properties by quadrant in rabbit and monkey eyes. J Biomech Eng. 2003;125:124-131. 31. Perez BC, Morris HJ, Hart RT, Liu J. Finite element modeling of the viscoelastic responses of the eye during microvolumetric changes. J Biomed Sci Eng. 2013;6:29-37.

27. Scleral remodeling in myopia Rafael Grytz Department of Ophthalmology and Visual Sciences, University of Alabama at Birmingham, Birmingham, AL, USA

1. Introduction

Copyright © 2018. Kugler Publications. All rights reserved.

Myopia, also known as nearsightedness, is the most common type of refractive error, affecting about 1.5 billion people representing 22% of the current world population.1 A normal eye with clear vision is emmetropic, and emmetropia is achieved when light rays focus precisely on the retina in an eye that is not accommodating (Fig. 1A). A myopic eye is too long for its optical system, and light rays focus in front of the retina, which causes the blurry vision in myopia (Fig. 1B). In 1899, Heine had the rare opportunity to compare a myopic eye with its fellow emmetropic eye in the same human donor. He observed that the increased axial length of the myopic eye was due to an elongated posterior segment (Fig. 1C).2 Many studies have since confirmed that myopia, especially juvenile-onset myopia, is typically characterized by an elongated posterior scleral shell, and less commonly, by abnormalities of the lens.3 The underlying cause of axial

elongation in myopia is thought to be a combination of genetic and environmental factors.4 Juvenile-onset myopia develops during the years before adulthood, when the eye uses visual signals to match its axial length to the focal plane. Increasing evidence from animal studies suggests that this emmetropization process relies on scleral remodeling to adapt the axial length of the eye.5-8 This book chapter provides insight into the emmetropization process and the critical role of scleral remodeling during emmetropization and myopia development. The prevalence of myopia has been increasing dramatically over the past 50 years.10,11 Epidemic increases have been recorded in some Asian populations, where the prevalence of myopia has risen from 20% to nearly 90% in teenagers and young adults. This is not a geographically isolated phenomenon, as the prevalence of myopia is high and rising in North America and

Fig. 1. (A) Emmetropia is the visual condition of the normal eye, where faraway objects appear in sharp focus. This condition is achieved when the axial length of the eye matches the refractive power of the cornea and lens, such that light rays are focused exactly on the retina. (B) A myopic eye is too long for its optical system, focusing light in front of the retina instead of on the retina, causing faraway objects to appear blurry. (C) Histologic sections of the emmetropic eye and the contralateral, highly myopic eye (-15 diopters (D)) of the same donor showing the longer axial length of the myopic eye. The anatomy of the anterior segment is nearly identical between the two eyes. In contrast, the vitreous chamber of the myopic eye is elongated compared to the emmetropic eye, causing the typical increase in axial length in the myopic eye. Modified from Heine;2 © Springer. Correspondence: Rafael Grytz, PhD, University of Alabama at Birmingham, Department of Ophthalmology and Visual Sciences, 1670 University Blvd, Birmingham, AL 35294, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 383-403 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

384

R. Grytz

Fig. 2. Prevalence and distribution of people estimated to have myopia across age groups in 2000 and 2050. reproduced from Holden et al.;9 © American Academy of Ophthalmology

E ­ urope.12-16 In parallel with the increasing prevalence of myopia and, in particular, high degrees of myopia (-5.0 diopters (D) or less), are increases in blinding ocular co-morbidities including glaucoma, retinal detachment, and macular degeneration.17-20 While myopia develops early in life (childhood and adolescence), associated co-morbidities typically develop later in life. Recent estimates suggest significant increases in myopia and high myopia prevalence in the elderly world population from 2000 to 2050 (Fig. 2),9 making myopia an acute global health concern.

Copyright © 2018. Kugler Publications. All rights reserved.

2. Emmetropization and myopization Human and animal studies have confirmed the existence of an active emmetropization process that uses visual cues to match the axial length of the eye to its focal length.4,6,7,21,23,24 As the eye develops during childhood, the emmetropization mechanism uses visual cues to adjust the axial length to match the focal plane. This emmetropization process has also been seen in human population studies. While newborns show a broad distribution of refractive errors, this distribution narrows postnatally and continues to narrow until adulthood (Fig. 3).21,22,25 Mutti et al. have shown that the narrowing of the refractive error distribution correlates with the adjustment of the axial elongation rate. Hyperopic eyes of infants emmetropize faster at three months of age compared to those that were already close to emmetropia.21 This adjustment of the axial elongation rate is guided by vision, and therefore requires a visual stimulus. If the visual stimulus is absent or obstructed,

Fig.3. Refractive error distribution at three months and nine months of age, and in adults. At three months, the distribution is broad and the majority of infants are hyperopic (the eye is too short). This distribution narrows at nine months towards emmetropia (zero refractive error). In adults, the distribution narrows further around emmetropia, but myopia has become more prevalent. Replotted from data presented in Mutti et al.21 and Stenstrom.23

as in corneal opacification,26 congenital cataract,27 or ptosis,28 the eye elongates faster than normal and typically becomes myopic. This is also seen in animals when a diffuser is placed in front of the eye to produce a blurry visual stimulus and induce myopia.29,30 The emmetropization process has been observed in animals across many species.6 Similar to humans, many animals are hyperopic at birth, and the refractive error diminishes as the eye emmetropizes. The eye size of animals can be experimentally modulated by shifting the focal plane posterior and anterior to the retina using negative- and positive-power lenses, respectively.31-35 Figure 4 shows the refractive development in tree shrews and how this process is modulated when using negative- or positive-power lenses. The eyes of infantile animals are able to detect lens-induced change in defocus and adapt the axial elongation rate to match the eye size to the new focal plane. A positive-power lens slows the axial elongation rate, while a negative-power lens increases it. However, the tree shrew eye loses its ability to adapt to the positive lenses at juvenile ages,32 while it remains able to adapt to negative-power lenses through adulthood.34 Similar to positive-lens treatment, the tree shrew eye can recover from negative-power lens-induced myopia by slowing axial elongation. Animal experiments that study recovery from lens-induced myopia typically involve removal of

Scleral remodeling in myopia

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. Refractive error development in normal (untreated) tree shrews and tree shrews treated with negative- or positive-power lenses at infantile and juvenile ages. Tree shrews are highly hyperopic at birth (~25 D at the day of eye opening). The refractive error decreases very rapidly during the first ten days after eye opening and then continues more slowly as the eye approaches emmetropia (black line). Putting a negative-power lens in front of the animal’s eye shifts the focal plane posteriorly, initially increasing hyperopia. The eye detects the increased hyperopia and increases its axial elongation rate to match the new focal plane, which reduces the lens-induced refractive error (red lines). Conversely, a positive power lens moves the focal plane anteriorly; in infantile tree shrews, the axial elongation rate is slowed to match the eye size to the more anterior focal plane (blue squares). However, older animals of juvenile age lose the ability to adapt to positive lenses while they remain able to increase the axial elongation rate and adapt to negative power lenses. Reproduced from Siegwart and Norton;4 © Lippincott Williams & Wilkins.

385

the lens after the animal develops myopia. Interestingly, the tree shrew eye can recover from lens-induced myopia at all ages, while it cannot adapt to a positive lens once it reaches juvenile age (Fig. 4).32 The cause of this age- and treatment-dependent response to myopic defocus has not been resolved. Little evidence exists demonstrating that the eye can shorten during the emmetropization process.36 Most animal experiments indicate that the eye compensates for myopic defocus by slowing axial elongation while the optical system (cornea and lens) continues to develop. Note that the eye is still increasing in size after it reaches emmetropia at juvenile age. Consequently, slowing down the axial elongation process is sufficient to compensate for a myopic defocus. On the other hand, the emmetropization process must continue to adjust the axial elongation rate to maintain emmetropia until the eye is fully developed. In conclusion, the emmetropization process can slow or accelerate axial elongation, and this process is driven by visual stimuli. Additional details on the emmetropization process can be found in Siegwart and Norton.4 The exact mechanisms underlying the emmetropization process are still unclear. Figure 5 provides an overview of potential mechanisms and factors that impact the emmetropization process. Emmetropization can be understood as a feedback mechanism where the axial elongation rate is modulated until clear vision is achieved and the axial length matches the focal plane. Scleral remodeling plays a key role within

Fig. 5. The emmetropization process and factors that impact the refractive development of the eye. Mechanisms highlighted in yellow represent visual stimuli and environmental factors that impact the refractive development of the eye. Mechanisms highlighted in blue are thought to be involved in the feedback mechanism that leads to emmetropia. Mechanisms highlighted in green are thought to impact the refractive development of the eye, but are not modulated by the feedback mechanism.

386

R. Grytz

this feedback process, as its modulation determines the final size of the eye. Other factors, such as accommodation, impact the emmetropization process but are not modulated by the feedback mechanism. The remaining sections of this chapter will provide insight into the different mechanisms shown in Figure 5, with special emphasis on scleral remodeling and related biomechanical changes.

Copyright © 2018. Kugler Publications. All rights reserved.

3. The moving target The development of the focal plane seems to be entirely defined by genetics. Like other body dimensions, the power of the lens and cornea, as well as the anterior chamber depth are normally distributed, suggesting that development of these eye components is genetically determined.22,37 Animal studies using mammals (non-human primates, tree shrews) have found little changes in either corneal and lens parameters or anterior chamber depth during lens-induced acceleration or slowing of the axial elongation rate.38,39 These findings support the idea that the development of the focal plane is mostly defined by genetics and not significantly influenced by environmental factors. During eye development in humans, the focal plane moves posteriorly (away from the cornea) as the cornea flattens, the lens power decreases, and the anterior chamber depth increases.21,40-42 The distance between the focal plane and the cornea increases most rapidly during early infantile age and settles over time. The development of corneal power settles first at ~6 years of age.43 Lens power continues to decrease, while the anterior chamber depth increases slightly between 6 and 14 years of age.43 As the focal plane undergoes genetically-defined changes from birth until adulthood, it represents a “moving target” for the emmetropization process. The same pattern has been observed in multiple animal models. Figure 6 illustrates the development of the focal plane and axial length in tree shrews. Every tree shrew is born hyperopic, which means that the axial length is shorter than the focal length. During normal eye development, the emmetropization process matches the axial length to the simultaneously developing focal length. Many animal studies have confirmed that the emmetropization process is guided by vision and actively controlled.6,24,34,44-46 The broken

Fig. 6. The development of the focal plane and axial length in normal tree shrews and animals that were treated with a -5 D lens at 24 days after eye opening. At the day of eye opening, the axial length (blue curve) is shorter than the focal plane (black curve). The emmetropization process actively adjusts the axial elongation rate of the eye to match the axial length to the simultaneously developing focal plane (the “moving target”). A negative power lens moves the focal plane posteriorly and shifts the “moving target” (broken black curve). The feedback mechanism detects the modified visual stimulus and adjusts the axial elongation process to match the axial length to the shifted focal plane (broken red curve). Curves were estimated using a simplified optical eye model42 and a computational model47 of the emmetropization process that were fitted to data34 from tree shrews across a wide age range.

red curve in Figure 6 illustrates that the emmetropization feedback process actively adapts the axial elongation rate to match a lens-induced shift of the focal length. This feedback process involves a precise detection of the visual stimulus and fine adjustments of the axial elongation rate, as 1 D in refractive error relates to a mismatch between the axial length and the focal plane of about 30 µm in tree shrews and 333 µm in humans. Note that that the emmetropization process does not stop once the axial length matches the focal plane, but continues until the focal plane is fully developed. Ideally, the emmetropization process continues to adjust the eye’s axial length in concert with the simultaneously developing focal plane to maintain emmetropia until the eye is fully developed.

Scleral remodeling in myopia

387

Copyright © 2018. Kugler Publications. All rights reserved.

4. Visual stimuli and environmental factors Multiple visual stimuli and environmental factors have been identified to impact the emmetropization process, where some stimuli accelerate the axial elongation process and others slow it. The axial elongation response to some visual stimuli depends on other conditions, such as age. One of the most studied visual stimuli is the defocus along the central axis of the eye. Extensive evidence from animal studies suggests that the emmetropization process can detect defocus and whether the focal plane is in front or behind the retina.32,48,49 Human infants50-54 and many other species41,42,55,56 are typically, but not universally, born hyperopic. Consequently, most eyes start the emmetropization process with a hyperopic defocus (i.e., the eye is too short at birth). A hyperopic defocus provides a consistent response across different species and ages that accelerates the axial elongation process.6,34,57-59 While the emmetropization process can distinguish a hyperopic defocus (the eye is too short) from a myopic defocus (the eye is too long), the success of slowing the axial elongation rate in response to a myopic defocus depends on age, refractive history, degree of myopic defocus, and peripheral defocus of the subject. Tree shrews can adapt to lens-induced myopic defocus using positive-power lenses at very young ages, but fail to do so at older ages (Fig. 4). In contrast, tree shrews are consistently able to recover from lens-induced myopia (removing a negative-power lens after the animal adapted to it) at all ages. Note that removing a negative-power lens after the animal has adapted to it produces a myopic defocus similar to a positive power lens. Metlapally and McBrien showed that young tree shrews can adapt to +4 D lenses, but not to higher positive-power lenses, suggesting that the emmetropization process is only functional within a range of refractive errors.60 Clinical trials attempted to impose a central myopic defocus to slow axial elongation by slightly undercorrecting children’s vision by prescribing a lens that is less powerful than needed to correct for the existing myopia, but without success. In contrast to findings in many animal models, the undercorrection of children’s vision actually accelerated myopia progression in two clinical trials.61,62

Fig. 7. Schematic of the focal surface in a myopic eye that was corrected with a single-vision lens. The single-vision lens corrects the central myopic defocus but fails to correct the peripheral hyperopic defocus. The peripheral defocus is thought to provide a visual stimulus that locally drives scleral remodeling, and promotes further axial elongation and myopization.

Targeting central defocus without accounting for the defocus in the periphery of the visual field may be insufficient for effective myopia control in humans.63,64 Correcting or undercorrecting central myopia using single-vision glasses does not necessarily account for any peripheral defocus. Even if the central defocus is corrected, human eyes may be exposed to a hyperopic defocus in the periphery of the visual field, particularly in myopic eyes (Fig. 7). As myopia progresses in a child, eye shape becomes more prolate, increasing any existing hyperopic defocus in the periphery. Clinical trials that treated the peripheral defocus using spectacles,65 contact lenses,66-68 and orthokeratology69-74 showed variable degrees of success, but all studies showed a reduction in axial elongation. Animal studies support the importance of the peripheral defocus, showing that optically imposed peripheral myopia75,76 and hyperopia77,78 can slow and accelerate the axial elongation process, respectively. It has been suggested that visual stimuli and environmental factors other than optical defocus influence the emmetropization process (Fig. 5). The first animal models of myopia used different methods to degrade the visual images by performing lid-suture or placing diffusers in front of the animal’s eye.30,79-81 Form deprivation has remained a common visual stimulus to induce axial elongation and to study myopia in animals.57-59 Form deprivation reduces the image contrast — especially for high spatial frequencies — and prevents focused images from forming on the retina, and thus provides a constant visual stimulus that is independent of the actual position of the focal plane and the eye’s axial length. Across all studied

Copyright © 2018. Kugler Publications. All rights reserved.

388

animal models, form deprivation leads to uncontrolled axial elongation and can be used to induce substantial degrees of myopia.29,44,82 The contrast of an image on the retina depends on multiple factors in addition to the current optical defocus of the eye.83 Therefore, studying individual environmental factors independently remains a challenge. Schmid et al. have shown that image contrast below a certain threshold accelerates axial elongation in chicks.84 This group concluded that image contrast must reach a threshold value for the emmetropization process to function. In comparison to emmetropes, human myopes were found to exhibit reduced sensitivity to central contrast, where contrast sensitivity decreases with increasing degrees of myopia.85 Kerber et al. showed that myopes experience a greater decrease in peripheral contrast sensitivity than emmetropes.86 Transient contrast adaptation has been found when positive lenses were worn, but not with negative lenses.83 Thus, it has been suggested that contrast sensitivity and adaptation can impact the emmetropization process, but its role remains unclear.87 Light levels have also been shown to impact the emmetropization process. For example, children who spend less time outdoors were shown to be at greater risk of developing myopia.88,89 It has been speculated that the increased exposure to outdoor light was protective in children, and animal experiments support this hypothesis. The axial elongation process during experimentally-induced myopia was significantly slowed in chicks, tree shrews, and macaque monkeys that were exposed to high illumination levels (similar to outdoor light) compared to animals that were exposed to typical indoor light conditions.90-93 Smith et al. found that high illumination levels had a protective effect against form-deprivation myopia, but not against minus lens-induced myopia in macaque monkeys, suggesting that the mechanisms responsible for form-deprivation myopia and lens-induced myopia are not identical.94 Additional visual stimuli that alter the emmetropization process have been identified, such as the light color (wavelength) of visual signals. Animal experiments showed that modifying the chromaticity of the ambient light impacts the emmetropization process. However, experimental results differ significantly between species. Rearing chicks in red light causes

R. Grytz

progressive myopia, while rearing them in blue light causes progressive hyperopia.95 In contrast, exposing the eyes of infant monkeys96 or tree shrews97 to red light produced hyperopia. The temporal modulation of ambient lighting, such as flickering light, also impacts the emmetropization process.97-104 The goal of the emmetropization process is to match the eye’s size to the “moving target” (the focal plane), but as discussed in this section, many visual stimuli besides the optical defocus can impact this process.

5. Visual stimulus detection and signaling The detection of the magnitude and sign of the optical defocus is critical in guiding the emmetropization process towards clear vision. However, the mechanism by which the eye detects the optical defocus is still debated. Animal studies have shown that the emmetropization process occurs within the eye and does not require a functional connection to the brain.105 Instead, the retina seems to be responsible for the detection of defocus and other visual stimuli that ultimately alter scleral remodeling and axial elongation. Wildsoet and co-authors suggested that the retina uses chromatic aberration, accommodation, and optical vergence to decode the degree and sign of optical defocus.48,106 Normal daylight is composed of multiple wavelengths, creating a disparity in the focal planes of each wavelength: the focal plane of long wavelengths is more posterior than shorter wavelengths. This effect is called longitudinal chromatic aberration. Many studies have suggested that the eye uses longitudinal chromatic aberration to detect the degree and sign of optical defocus, and guide the emmetropization p ­ rocess.106-113 However, a consensus has not been reached and scientific investigations are ongoing to elucidate the mechanism by which the retina detects defocus. After the retina detects the visual stimulus, biochemical signals are sent to the sclera to alter its remodeling rate, which adjusts the eye’s elongation rate. The details of the signaling pathway underlying the emmetropization process are not well understood. Thus, only a few important aspects of the signaling cascade are summarized in this section. Retinal signals

Copyright © 2018. Kugler Publications. All rights reserved.

Scleral remodeling in myopia

must pass through the choroid and the retinal pigment epithelium before they reach the sclera and alter its remodeling rate. Tree shrew experiments show that the gene expression signatures are similar within each tissue type for the different visual stimuli that accelerate scleral remodeling (minus lens, form deprivation, darkness), but different across tissues (retina, choroid, sclera).114-116 The gene expression signature was very different in animal eyes that were exposed to visual stimuli that slowed scleral remodeling compared to stimuli that accelerated scleral remodeling.117,118 As pointed out in Figure 7, the retina can be exposed to a variable visual stimulus across the posterior segment. In humans, it is believed that a peripheral defocus may still exist after correcting the axial defocus of a myope with single-vision lenses. This peripheral defocus can be detected by the peripheral retina, which sends signals to the peripheral sclera to accelerate remodeling in that particular area of the eye. Animal studies support the notion that visual stimulus detection and the signaling cascade occur locally. If diffusers or negative lenses cover only half of the retina, only the corresponding half of the sclera remodels and half of the eye enlarges.119-121 Both spatial and temporal differences in the visual stimulus have an impact on the emmetropization process. Visual stimuli are not constant in time, and local defocus changes constantly as we look around, with some objects being in front of the focal surface while others are behind it. Visual stimulus changes occur frequently throughout the day, and at a much faster rate than scleral remodeling can be adjusted. The visual stimulus detection and signaling process must integrate the visual signals over time to infer if scleral remodeling should be accelerated or slowed. This temporal integration is asymmetric and non-linear. If negative lenses are removed for one hour each day, the rate by which the eye develops myopia is halved in several animal models.122-125 It is still unclear whether the temporal integration process of the defocus signal is neural, biochemical, or some combination of both. As noted previously, the mechanism used for visual stimulus detection and signaling are complex and not well understood at present. More research is needed to gain fundamental insight into these mechanisms.

389

Fig. 8. Human scleral thickness maps obtained from micro-magnetic resonance imaging and mapped onto a 3-D model of the eye showing a posterior view centered around the optic nerve head (left) and a temporal view (right). The sclera is thickest at the posterior pole, becomes thinner towards the equator, and thickens again slightly towards the limbus, where the sclera connects to the cornea. Reproduced from Norman et al.;129 © Elsevier

6. Scleral structure and composition The sclera is an avascular tissue126 which surrounds the posterior eye and serves as the principal load-bearing tissue of the posterior segment. It is a structurally robust connective tissue that protects the delicate intraocular tissues and resists intra- and extraocular forces. The critical functions of the sclera are to establish appropriate eye shape during the emmetropization process so that the retinal image is undisturbed, and to maintain this shape when the eye is exposed to changes in extraocular (e.g., muscle forces, saccades, blinking) and intraocular forces (e.g., intraocular pressure fluctuations). The sclera is thickest at the posterior pole and thinnest around the equator (Fig. 8). The human sclera consists of water (68%), collagen (28.8%), proteoglycans (< 1%), elastin (0.64%), and other proteins, as well as intracellular components (< 3% wet weight).127 The scleral extracellular matrix exhibits a complex hierarchical structure which varies across species. The sclera of eutherian mammals, including humans, is mainly composed of collagen fibrils. Multiple collagen types (I, III, V, VI, XII) are present in the sclera, but 99% of the scleral collagen is type I fibrillar collagen. 127 These collagen fibrils aggregate into lamellae, which interweave and form a complex 3-D network (Figs. 9A and B). The collagen fibrils and lamellae can crimp and appear wavy,128 in particular when the tissue is unloaded (Fig. 9C). The collagen fibril crimp has a profound impact on scleral biomechanics, which will be discussed in more detail in the next section. Collagen

390

R. Grytz

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 9. (A) Lamellar structure of the outer layer of the human sclera. Scleral lamellae run in various directions, forming a highly interwoven 3-D network. reproduced from Komai and Ushiki;130 © Association for Research in Vision and Ophthalmology. (B) Each lamella consists of collagen fibrils that follow the lamellar orientation. Shown are scleral lamellae with collagen fibrils that run longitudinal (Lc), oblique (Oc), or transversal (Tc) to the image section. Scleral fibroblasts (F) are seen between the lamellae. Bar: um. Reproduced from Meek;127 © Springer. (C) Wavy collagen lamellae with crimped collagen fibrils in the unloaded tree shrew sclera. Bar: 50 μm.

Fig. 10. Histologic sections of the human (A) and chick (B) sclera. The human sclera consists of a single layer of fibrous sclera (FS), while the chick sclera is composed of two layers, a cartilaginous sclera (CS) and a fibrous sclera (FS). Sections are oriented such that the choroid is at the top (indicated by arrow in A). Reproduced from Harper and Summers;131 © Elsevier

Fig. 11. Immunohistochemical localization of type I collagen and aggrecan in tree shrew sclera showing that aggrecan is located primarily between the collagen lamella and near fibroblasts. Areas of discrete collagen labeling (red) and discrete aggrecan labeling (green) as well as areas where collagen and aggrecan appear to co-localize in thin bands (yellow) are shown. Unstained voids with no collagen or aggrecan labeling (arrows) are likely fibroblast bodies and processes. Reproduced from Siegwart and Strang;136 © Molecular Vision.

fibril diameters range in the sclera between 30 and 260 nm, while scleral lamellae are between 0.5 and 6 µm thick. The sclera of eutherian mammals such as humans consists of only one layer, as opposed to the sclera of most other vertebrates, which is composed of two layers: an inner layer of cartilage and an outer, fibrous layer similar to the single layer of the human sclera (Fig. 10). This book chapter focuses on the fibrous sclera.

The scleral extracellular matrix contains several proteoglycans. Decorin and biglycan are small proteoglycans that are believed to regulate collagen fibril diameter, assembly, and interactions. The quantity of these two proteoglycans increases steadily in the human sclera from childhood through young adulthood, but declines after the fourth decade.132,133 The role of these proteoglycans in scleral remodeling

Scleral remodeling in myopia

391

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 12. (A) Scattergram showing the significant correlation between axial length and scleral thickness in Chinese eyes, stratified into two age groups. Reproduced from Shen et al.;143 © Association for Research in Vision and Ophthalmology. (B) Scattergram showing the correlation between axial length and scleral volume at the posterior pole in Chinese participants aged 5+ years. The relationship was not statistically significant. Reproduced from Shen et al.;142© Springer.

and scleral biomechanics will be discussed in the next section.134,135 Surprisingly, the human (fibrous) sclera also contains aggrecan, a large proteoglycan normally found in cartilage. Due to its many attached glycosaminoglycan sidechains (chondroitin sulfate and keratan sulfate), aggrecan provides osmotic properties that produce a swelling pressure. In cartilage, this swelling pressure plays a critical role in withstanding compression forces, but the importance of this swelling pressure in the sclera is unclear. In contrast to the age-related loss of the small proteoglycans (decorin and biglycan), the amount of aggrecan found in the sclera remains constant at all ages.131 The function of aggrecan in the sclera is unclear. Aggrecan was found to be located primarily between the collagen lamella and near the fibroblasts (Fig. 11).136 Decorin and biglycan are attached to collagen fibrils and are present throughout the entire sclera, while aggrecan is predominantly found in the posterior sclera.132,137 Sclera also contains hyaluronan, which is a non-sulphated glycosaminoglycan that does not associate with a core protein. As any other soft tissue, the sclera also contains collagen crosslinks that accumulate with age.138 Crosslinks are thought to impact the integrity of the extracellular matrix and scleral biomechanics. The sclera is populated with fibroblasts that maintain the extracellular matrix and drive scleral remodeling. Scleral fibroblasts are located between the scleral lamellae (Fig. 9B). Scleral fibroblasts can express matrix metalloproteinases and inhibitors that promote and

inhibit the degradation of collagen, respectively, as well as other extracellular matrix constituents.139-141 The amount (volume) of scleral tissue increases from birth to the end of the second year of life, but remains constant thereafter, suggesting that scleral growth ceases early in life.142 Several changes in scleral structure and composition have been observed in human myopia and experimental animal myopia, such as scleral thickness decreasing with increasing axial length (Fig. 12A).143 In the most severe cases of myopia, the scleral thickness can be as thin as 31% of normal scleral thickness.144 While the sclera thins in myopia, histologic studies suggest that the amount of scleral tissue (volume) remains unchanged (Fig. 12B).142,145,146 This finding supports the notion that volume-preserving remodeling deformations underlie myopia progression, which will be explored in more detail in Section 8. Animal studies have confirmed that the sclera thins significantly during experimental myopia.147,148 Similar to human myopia, the amount of sclera changes little (dry weight reduction of 3-5%) during experimental myopia.148-150 McBrien et al. have reported that the scleral ultrastructure remained unchanged after short-term myopia treatment (12 days) in tree shrews.148 Only long-term myopia treatment (> 3 months) caused a significant change in the scleral ultrastructure, showing a reduction of the collagen fibril diameter at the posterior pole. This suggests that these ultrastructural changes are a long-term consequence of accelerated scleral remodeling, but not

392

R. Grytz

Fig. 13. (A) Stress–strain curves (ascending and descending load response) of control, buffer-treated, and enzyme-treated porcine scleral shells that were inflation tested. Enzyme treatment digested about 80% of the scleral glycosaminoglycans. Stress represents the amount of normalized force acting on the tissue, while strain represents relative tissue deformation. Modified from Murienne et al;135 © Elsevier. (B) Typical stress-strain curves obtain from strip testing of tree shrew sclera. One eye was lens treated (4 days of -5 D lens wear from 24 to 28 days after eye opening) to induce scleral remodeling and myopia. The contralateral eye served as an untreated control. Plot generated from data presented in Grytz and Siegwart.134 Both plots (A,B) show the typical scleral stiffening effect with increasing load due to the uncrimping of collagen fibrils, where regions with crimped vs straightened collagen fibrils are marked in (B). Both plots (A,B) show a similar rightward shift in the locking stretch of the ascending stress-strain curve, indicating an extended collagen fibril straightening response after glycosaminoglycan removal (A) and experimental myopia induction (B).

its cause.148 This reduction in collagen fibril diameter is consistent with ultrastructural observations in high myopic human eyes as well.151 Scleral composition is also changed during experimental myopia, with lower hyaluronan and sulfated glycosaminoglycan levels;150 upregulated enzymatic degradation;114,152-155 downregulated collagen type I synthesis;156 and downregulation of aggrecan.136 These changes in scleral composition have potential implications and interactions for scleral biomechanics and remodeling, which are discussed in the following two sections.

Copyright © 2018. Kugler Publications. All rights reserved.

7. Scleral biomechanics The biomechanical properties of the sclera are tightly related to its composition and structure. As the composition and structure of the sclera are changed during the emmetropization process and myopia development, so are its biomechanical properties. The mechanical response of the sclera is defined by its load-bearing constituents, collagen fibrils in particular. These fibrils crimp and buckle when the tissue is unloaded (Fig. 9C) and straighten with increasing intraocular pressure. This uncrimping effect causes the

elastic response of the sclera to be non-linear (Fig. 13B), where the sclera stiffens with increasing intraocular pressure as the collagen fibrils straighten and stiffen.157-161 Elastin is more compliant than collagen, and contributes mainly to the scleral stiffness at low intraocular pressure levels. The biomechanical role of proteoglycans and glycosaminoglycans in the sclera is still a matter of debate. Murienne et al. artificially digested glycosaminoglycans in pig sclerae, causing a significant shift in the so-called transition strain (Fig. 13A).135 This transition strain is also called locking stretch, and has been related to the collagen fibril crimp and the amount of deformation needed to straighten (or lock) the crimped collagen fibrils.158,159 A similar shift in this collagen fibril locking stretch was observed in tree shrew sclera after inducing experimental myopia (Fig. 13B).134 The crimp of scleral collagen fibrils was estimated to increase and decrease in concert with the increase and decrease of the axial elongation rate.134 It has been suggested that scleral remodeling involves micro-deformations, such as interfibrillar sliding, and that these micro-deformations underlie the increased collagen crimping response. Furthermore, these biomechanical changes may be driven by changes in the extracellular matrix

Scleral remodeling in myopia

393

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 14. Regulation of the scleral creep rate in tree shrews during experimentally accelerated and slowed axial elongation. Axial elongation was accelerated in the treated eye during monocular -5 D lens treatment and slowed during recovery from -5 D lens wear (the lens was removed). Creep rate increased and decreased in the treated eye during lens treatment and recovery, respectively. Creep rate of control and normal eyes are shown for comparison. Replotted from Siegwart and Norton.177

composition, specifically the decrease in proteoglycan and glycosaminoglycan levels. 134 Rada et al. suggested that biochemical alterations, such as the reduction in aggrecan, could make it easier for scleral lamellae to slide across each other.5 However, controversial opinions exist in the literature on the role of proteoglycans and their glycosaminoglycan sidechains in soft tissue mechanics. It has been suggested that the small proteoglycan decorin mechanically couples neighboring collagen fibrils and more of these “mechanical links” will reduce collagen sliding.162-168 An alternative hypothesis suggests that decorin and its attached glycosaminoglycan chain are mainly responsible for controlling the distance between collagen fibrils, and decreased amounts will lead to increased friction between fibrils, slowing collagen sliding.169,170 Multiple authors have shown that the hyperelastic and viscoelastic material properties remain unchanged in tendons171-173 and ligaments174,175 after enzymatic glycosaminoglycan depletion. These findings conflict with the significant changes seen in the mechanical response of the sclera after glycosaminoglycan depletion.135 These contradictory results may relate to the unique composition of the sclera, which contains the large proteoglycan aggrecan that other collagenous soft tissues lack. Ahmadzadeh

et al. proposed a mechanical model where glycosaminoglycan depletion promotes collagen sliding only if collagen fibrils are shorter than a certain characteristic length.176 More research is needed to fully understand the role of proteoglycans and glycosaminoglycan in scleral biomechanics and remodeling. The first documented vision-induced alteration of scleral biomechanics was a change in scleral creep rate.177,178 The creep rate represents the rate by which the sclera stretches over time under a constant load. Similar to the changes in the collagen crimping response, it was shown that the creep rate in tree shrews increases and decreases during time periods, where the emmetropization process increases and decreases the axial elongation rate, respectively (Fig. 14).177 McBrien et al. suggested that the increase in creep rate during myopia development is due to a biomechanical weakening of the sclera.179 Siegwart and Norton suggested that increased scleral creep involves sliding between scleral lamellae, 177 a remodeling mechanism that will be discussed in more detail in the next section. Collagen crosslinks also impact the biomechanics of the sclera. Studies using human donor tissues have shown that the sclera stiffens with age,180-182 partially due to an increased shear stiffness of the ground substance

394

R. Grytz

rate or cyclic softening are a consequence or cause of changes in the sclera remodeling rate. A detailed discussion on potential remodeling mechanisms that are involved in the emmetropization process are presented in the next section.

8. Scleral growth vs scleral remodeling

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 15. The mechanical response of tree shrew scleral strips subjected to cyclic tensile loading. Scleral strips were taken from juvenile animals where one eye was form deprived (FD) for four days to induce myopia while the other eye was left untreated as a control. The strips were incubated for 24 hours at 37°C in physiologic phosphate buffered saline solution (PBS) or PBS supplemented with the crosslink agent genipin at 0.25 mM. After the incubation time, 50 load cycles at physiological loads were performed and the incremental increase in deformation (strain) from one cycle to the next cycle was studied (cyclic softening). (A) Representative stress-strain graphs. (B) Boxplots of the cyclic increase in strain. Compared to the control sclera, the cyclic increase in strain is significantly higher in FD sclera that was incubated in PBS and significantly lower in FD sclera that was incubated in PBS supplemented with genipin (*: p < 0.05; **: p < 0.01). Replotted from Levy et al.194

and partially due to a decrease in the collagen fibril crimp.183 It was suggested that both of these age-dependent stiffening mechanisms are partially due to natural accumulation of collagen crosslinks with age. Artificial scleral crosslinking was shown to increase scleral stiffness184-188 and to slow experimental myopia.189-193 Recently, it was discovered that the biomechanical response of the sclera to cyclic loading changes during experimental myopia and after crosslinking (Fig. 15). In juvenile tree shrew sclera, the repeated application of loading and unloading leads to progressive deformations, called cyclic softening.134,194 Experimental myopia leads to a significant increase in the cyclic softening rate, which can be completely inhibited by pharmacologic collagen crosslinking (Fig. 15). Like the modulation of the creep rate and collagen fibril crimping, the increased cyclic softening response supports the notion that accelerated scleral remodeling involves biomechanical weakening of the sclera. Furthermore, pharmacologic collagen crosslinking strengthens the sclera, which seems to slow scleral remodeling. The findings reported in this section show that scleral biomechanics are tightly connected to alterations in the scleral remodeling rate, which is altered during the emmetropization feedback process. It is currently unclear if biomechanical changes such as the creep

We have discussed in the previous sections that the “moving target” (the focal plane) is detected by the retina, and signals are then sent from the retina through the choroid and the retinal pigment epithelium to the sclera, where scleral fibroblasts receive the signal and alter the scleral remodeling rate to match the axial length to the “moving target” focal plane. The emmetropization feedback process can accelerate or slow scleral remodeling to accelerate or slow the axial elongation process. In this section, we illustrate the difference between scleral growth and scleral remodeling. Furthermore, we provide evidence that the emmetropization process uses scleral remodeling and not growth for the vision-guided adjustment of the axial elongation rate.

Misconception 1: Scleral growth vs scleral remodeling Scleral growth has been thought to drive eye elongation in myopia, but emerging evidence suggests that scleral remodeling is the most active component of globe elongation, defining the final size of the eye. To appreciate the dynamic and interactive process that determines the size of the eye during emmetropization, it is critical to differentiate scleral growth from scleral remodeling, as both mechanisms can alter the size of the eye. Tissue growth is a mechanism that increases the amount of tissue (tissue mass), which can occur through cell division (hyperplasia), cell enlargement (hypertrophy), and synthesis of extracellular matrix. Tissue growth leads to changes in tissue volume, as density changes are typically small in dense connective tissues like the sclera. Similar to other tissues in the body, all eye tissues, including

Copyright © 2018. Kugler Publications. All rights reserved.

Scleral remodeling in myopia

the sclera, grow as the organ develops. One could imagine that the emmetropization process accelerates or slows scleral growth to accelerate or slow axial elongation, as occurs in the cartilaginous sclera of chicks.195 However, as pointed out in Section 6, the tissue volume, or amount of sclera, is not significantly different between myopic and emmetropic human eyes.145,146 Furthermore, the volume of the sclera only increases from birth to the end of the second year of life and remains constant thereafter, suggesting that scleral growth ceases early in life (at two years of age) while the emmetropization process remains active until young adulthood.142 Moreover, scleral mass changes very little during induced myopia in animal experiments,147,148 where the tissue mass is actually reduced and not increased in the myopic eye when compared to the control eye. Note that only one study using the chick model of myopia reported increased scleral growth during experimentally induced myopia.195 It was later found that this increase in scleral growth was dominated by the growth of the cartilage layer of the bilayer chick sclera rather than growth in the fibrous layer,196 which is the only layer present in human sclera. As such, the scientific evidence strongly indicates that the emmetropization process does not use scleral growth (of the fibrous sclera) to match the size of the eye to the “moving target”, i.e., the focal plane. Nevertheless, scleral growth occurs as the eye develops, thus changing the axial length. The growth mechanism is thought to be genetically controlled and is not altered by visual stimuli.47 Therefore, scleral growth is highlighted in green in Figure 5 as a mechanism that impacts the refractive development outside the feedback mechanism. In contrast to growth, we define tissue remodeling as a mechanism that changes the tissue macro-structure without changing the amount (mass) of the tissue. While the sclera is known to thin in myopia, this thinning is likely a consequence of scleral remodeling that leads to scleral elongation tangential to the scleral plane. Soft tissues like the sclera are regarded as nearly incompressible within the physiological range of deformations due to their high water content. Because of this nearly incompressible property, remodeling deformations that elongate the sclera lead to scleral thinning based on the so-called Poisson’s effect. Multiple mechanisms can lead to remodeling deformations,

395

and the exact remodeling mechanism that underlies the emmetropization process is still unknown. Intraocular pressure is higher than atmospheric pressure, subjecting the sclera to continued tensile forces. Relative deformations between adjacent scleral lamellae (also called interlamellar sliding) have been suggested as a potential remodeling mechanism in myopia.136,154,177 McBrien et al. have suggested that scleral remodeling is a creep-like elongation process of the sclera at normal intraocular pressure.8 These creep-like deformations may be due to interlamellar sliding. Others have suggested that micro-deformations occur between collagen fibrils, and that these interfibrillar deformations (also called interfibrillar sliding) are modulated during the emmetropization process.47,134,197 Interfibrillar collagen sliding has been reported to occur in other soft tissues (e.g., tendons, anulus fibrosus).170,198,199 Accelerated interlamellar and/or interfibrillar sliding during myopia progression could be caused by a biomechanical weakening of the scleral extracellular matrix due to the increased enzymatic activity discussed in Section 6.153-155 The increase in matrix metalloproteinase and decrease in tissue inhibitors of metalloproteinase may reduce the integrity of the collagen network and promote interlamellar and/or interfibrillar collagen sliding to accelerate scleral remodeling. Rada et al. suggested that the reduction in aggrecan could make it easier for scleral lamellae to slide across each other during myopia.5 Collagen turnover can also lead to scleral remodeling. The synthesis and degradation of equal amounts of extracellular matrix, in particular of the load-bearing collagen fibrils, are thought to lead to macro-scale deformations that are volume-preserving.200 Synthesis and degradation of collagen fibrils occur in the eye while the sclera is subjected to tensile forces that are generated by the intraocular pressure. Fibroblasts are thought to pre-stretch newly synthesized collagen before its integration into the existing extracellular matrix.201 If this pre-stretch is smaller than the current stretch of existing collagen fibrils, collagen turnover should lead to an elongation of the sclera over time which could explain axial elongation. However, while collagen turnover seems to play an important role in other ocular diseases such as glaucoma,202,203 there is no strong evidence that collagen turnover is modulated

396

R. Grytz

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 16. (A) Computationally estimated scleral growth and remodeling rates in tree shrews. Scleral growth ceases earlier than scleral remodeling in tree shrews that are exposed to a normal visual environment. The maximum remodeling rate represents the maximum rate at which the sclera can remodel. This rate was estimated to decrease with age due to age-related collagen crosslinking. The actual remodeling rate is modulated by visual stimuli, but is always smaller than the maximum remodeling rate. The difference between the maximum and actual remodeling rate in normal animals represents the susceptibility to remodeling. (B) The susceptibility of tree shrews to scleral remodeling and myopia. The susceptibility to myopia and scleral remodeling peaks at juvenile age. The age-dependent trend of the susceptibility to scleral remodeling matches the trend of the susceptibility to myopia. The susceptibility to myopia was replotted from experimental data presented by Siegwart and Norton.38 All other curves are computational predictions by Grytz and El Hamdaoui.47

during the emmetropization process and used to adjust the axial length. A recent computational simulation of the emmetropization process in tree shrews illustrates the dynamic interplay between the developing focal plane (“moving target”), scleral growth, and scleral remodeling.47 Figure 16A shows the computationally estimated scleral growth and remodeling rates in normal tree shrews. The model was fitted to a large data set of normal and lens-treated animals at different ages. The results suggest that scleral growth ceases much faster with age than scleral remodeling (Fig. 16A). The model assumes that the sclera can remodel up to a certain maximum rate, which is genetically defined and diminishes with age. Hyperopic/myopic defocus accelerates/slows the scleral remodeling rate. It was estimated that scleral remodeling continues at a baseline rate after emmetropia is reached at juvenile age. This baseline remodeling rate is important for maintaining clear vision at this age, as the ocular refractive components are still developing and continued scleral remodeling is needed until the focal plane reaches the adult location. The difference between the maximum scleral remodeling rate and the remodeling rate of a normal eye represents the susceptibility of tree shrews to scleral remodeling (Fig. 16A). The model predicted that the susceptibility of tree shrews to myopia is low in very young animals, increases and peaks at juvenile age, and then decreases with increasing age. This finding is in good agreement with experimental observations by Siegwart and

Norton (Fig. 16B). 38 The model provides a mechanistic explanation for the increased susceptibility at juvenile age. As the normal tree shrew eye is highly hyperopic at birth, the hyperopic visual stimulus is very high even in normal animals. Any additional stimulus that could accelerate scleral remodeling has no additional effect, as the sclera is already remodeling at (almost) maximum speed at very young age (< 15 days after eye opening in tree shrews). Once the normal tree shrew eye is close to emmetropia (∼20 days after eye opening), the susceptibility to myopia increases as vision-guided stimuli have increased potential to accelerate scleral remodeling. At older ages, the susceptibility decreases as the maximum remodeling rate decreases with age, which is thought to be due to age-related accumulation of collagen crosslinks (Fig. 16B). This age-related reduction in the scleral remodeling rate is thought to determine the endpoint of the time window within which the emmetropization process can function.47 The exact role of scleral fibroblasts in modulating scleral remodeling is not fully understood. Clearly, the fibroblasts alter the composition of the sclera as outlined in the previous section, and these changes in scleral composition impact scleral biomechanics. However, it is unclear if the fibroblasts are actively rearranging the extracellular matrix of the sclera or just providing the required biochemical environment that can induce or inhibit creep-like micro-deformations and collagen sliding. It is also unclear whether biomechanical changes such increase in creep-rate, collagen fibril crimping, and cyclic softening are

Copyright © 2018. Kugler Publications. All rights reserved.

Scleral remodeling in myopia

the cause or a consequence of accelerated scleral remodeling. Most biomechanical investigations that studied the mechanical response of the sclera during emmetropization and myopization used scleral strips subjected to acute uniaxial loading over a short period of time (seconds or minutes).134,177,178 In vivo, the sclera is exposed to an omni-axial loading situation, and scleral remodeling occurs over a much longer time period (days or months). Cutting strips out of the sclera releases residual stresses, alters the integrity of scleral lamellae and collagen fibrils, and alters the mechanical response of the sclera compared to in-vivo conditions. To what extent the short-term mechanical tests are representative of the rather slow remodeling process in vivo is still unclear. Organ culture experiments that can replicate in-vivo conditions over a prolonged time are needed to better understand scleral biomechanics as well as the role of scleral fibroblasts during scleral remodeling and the emmetropization process.197 In the previous section, we propose that the accumulation of collagen crosslinks may change scleral biomechanics in multiple ways: decreased collagen fibril crimping, increased shear stiffness of the ground substance, and decreased cyclic softening rate. While there is no evidence that the collagen crosslink density changes in the sclera during the emmetropization process, collagen crosslinks can impact this process. Artificial collagen crosslinking of the sclera was shown to slow axial elongation and experimental myopia.189-193 In contrast, the prevention of natural crosslink formation was shown to accelerate experimental myopia, but had no effect on the refractive development under normal visual conditions.204 Based on these findings and computational simulations, it was suggested that collagen crosslinking alters the maximum remodeling rate and limits the range in which the emmetropization process can adjust the actual remodeling rate (Fig. 16).47 A common function of connective tissues is to bear load. Tissue growth and remodeling are common mechanisms across load-bearing tissues that are driven by alteration in their loading conditions. The sclera is unique compared to all load-bearing tissues, as scleral remodeling is driven not only by mechanical loading but also by visual stimuli. The goal of load-driven growth and remodeling is thought to establish or maintain a homeostatic loading condition. On the other hand, vision-guided remodeling aims at producing

397

eyes with clear vision and no refractive error. Similar to vision-guided remodeling, the exact stimulus that leads to load-driven growth and remodeling is not fully understood. Several recent experiments and computational studies suggest that mechanical homeostasis is defined at the collagen fibril level.202,205-207 Simulations have shown that tissue growth is a mechanism that changes the collagen fibril strain in a tissue that is subjected to tension, such as the sclera. Furthermore, load-driven modulation of growth can effectively regain mechanical homeostasis in an overloaded tissue (e.g., due to chronic intraocular pressure elevation).202,203 Conversely, computer simulations suggest that scleral remodeling due to collagen sliding has a minimal effect on the collagen fibril strain in tissues that are subjected to tension.203 Based on these findings, vision-guided scleral remodeling due to collagen sliding is thought to avoid impacting mechanical homeostasis during the emmetropization process. The remodeling mechanism used during emmetropization is decoupled and does not interfere with load-driven growth and remodeling. In summary, while scleral growth and remodeling occur simultaneously during eye development, scleral remodeling — not scleral growth — is actively modulated by the emmetropization process and defines the final size of the eye. Scleral remodeling is thought to involve micro-deformations within the tissue that elongate the sclera due to volume-preserving creep-like deformations at the macro-scale. The exact level — whether lamellar or collagen fibril — at which these micro-deformations occur is still unclear and remains under investigation.197 Similar to the development of the “moving target” focal plane, scleral growth is thought to be genetically defined, while scleral remodeling is driven by both genetic factors and visual stimuli.

Acknowledgements Preparation of this book chapter was made possible through support from the US National Institutes of Health (R01EY026588, R01EY027759), Research to Prevent Blindness (NY, USA), and the Eyesight Foundation of Alabama. I thank Dr. Thomas Norton, Dr. Mustapha El Hamdaoui, and Alexander Levy for many helpful comments.

398

R. Grytz

References 1.

2. 3. 4.

5. 6.

7. 8.

9.

10. 11.

12.

13.

14.

Copyright © 2018. Kugler Publications. All rights reserved.

15.

16.

17.

18.

19.

Holden B, Sankaridurg P, Smith E, Aller T, Jong M, He M. Myopia, an underrated global challenge to vision: where the current data takes us on myopia control. Eye (Lond). 2014;28:142-146. Heine L. Beitrage zur Anatomie des myopischen Auges. Archiv für Augenheilkunde. 1899;38:277-290. Lens A, Nemeth SC, Ledford JK. Ocular anatomy and physiology: Slack Incorporated; 2008. Siegwart JT Jr, Norton TT. Perspective: how might emmetropization and genetic factors produce myopia in normal eyes? Optom Vis Sci. 2011;88:E365-372. Rada JA, Shelton S, Norton TT. The sclera and myopia. Exp Eye Res. 2006;82:185-200. Norton TT, Siegwart JT. Animal models of emmetropization: matching axial length to the focal plane. J Am Optom Assoc. 1995;66:405-414. Wallman J, Winawer J. Homeostasis of eye growth and the question of myopia. Neuron. 2004;43:447-468. McBrien NA, Gentle A. Role of the sclera in the development and pathological complications of myopia. Prog Retin Eye Res. 2003;22:307-338. Holden BA, Fricke TR, Wilson DA, et al. Global Prevalence of Myopia and High Myopia and Temporal Trends from 2000 through 2050. Ophthalmology. 2016;123:1036-1042. Dolgin E. The myopia boom. Nature. 2015;519:276-278. Susanna R Jr, Vessani RM, Sakata L, Zacarias LC, Hatanaka M. The relation between intraocular pressure peak in the water drinking test and visual field progression in glaucoma. Br J Ophthalmol. 2005;89:1298-1301. Kempen JH, Mitchell P, Lee KE, et al. The prevalence of refractive errors among adults in the United States, Western Europe, and Australia. Arch Ophthalmol. 2004;122:495-505. Lee KE, Klein BE, Klein R, Wong TY. Changes in refraction over 10 years in an adult population: the Beaver Dam Eye study. Invest Ophthalmol Vis Sci. 2002;43:2566-2571. Zadnik K. The Glenn A. Fry Award Lecture (1995). Myopia development in childhood. Optom Vis Sci. 1997;74:603-608. Villarreal MG, Ohlsson J, Abrahamsson M, Sjostrom A, Sjostrand J. Myopisation: the refractive tendency in teenagers. Prevalence of myopia among young teenagers in Sweden. Acta Ophthalmol Scand. 2000;78:177-181. Midelfart A, Kinge B, Midelfart S, Lydersen S. Prevalence of refractive errors in young and middle-aged adults in Norway. Acta Ophthalmol Scand. 2002;80:501-505. Saw S-M, Gazzard G, Shih-Yen EC, Chua W-H. Myopia and associated pathological complications. Ophthalmic Physiol Opt. 2005;25:381-391. Mitchell P, Hourihan F, Sandbach J, Wang JJ. The relationship between glaucoma and myopia: the Blue Mountains Eye Study. Ophthalmology. 1999;106:2010-2015. Xu L, Wang Y, Wang S, Wang Y, Jonas JB. High myopia and glaucoma susceptibility the Beijing Eye Study. Ophthalmology. 2007;114:216-220.

20. Qiu M, Wang SY, Singh K, Lin SC. Association between myopia and glaucoma in the United States population. Invest Ophthalmol Vis Sci 2013;54:830-835. 21. Mutti DO, Mitchell GL, Jones LA, et al. Axial growth and changes in lenticular and corneal power during emmetropization in infants. Invest Ophthalmol Vis Sci 2005;46:3074-3080. 22. Stenstrom S. Investigation of the variation and the correlation of the optical elements of human eyes. Am J Optom Arch Am Acad Optom 1948;25:496-504. 23. Howlett MH, McFadden SA. Emmetropization and schematic eye models in developing pigmented guinea pigs. Vision Res 2007;47:1178-1190. 24. Wildsoet CF. Active emmetropization--evidence for its existence and ramifications for clinical practice. Ophthalmic Physiol Opt 1997;17:279-290. 25. Mayer DL, Hansen RM, Moore BD, Kim S, Fulton AB. Cycloplegic refractions in healthy children aged 1 through 48 months. Arch Ophthalmol 2001;119:1625-1628. 26. Meyer C, Mueller MF, Duncker GI, Meyer HJ. Experimental animal myopia models are applicable to human juvenile-onset myopia. Surv Ophthalmol 1999;44 Suppl 1:S93-102. 27. Rabin J, Van Sluyters RC, Malach R. Emmetropization: a vision-dependent phenomenon. Invest Ophthalmol Vis Sci 1981;20:561-564. 28. von Noorden GK, Lewis RA. Ocular axial length in unilateral congenital cataracts and blepharoptosis. Invest Ophthalmol Vis Sci 1987;28:750-752. 29. McBrien NA, Norton TT. The development of experimental myopia and ocular component dimensions in monocularly lid-sutured tree shrews (Tupaia belangeri). Vision Res 1992;32:843-852. 30. Sherman SM, Norton TT, Casagrande VA. Myopia in the lid-sutured tree shrew (Tupaia glis). Brain Res 1977;124:154-157. 31. Siegwart JT Jr, Norton TT. Goggles for controlling the visual environment of small animals. Lab Anim Sci 1994;44:292-294. 32. Siegwart JT Jr, Norton TT. Binocular lens treatment in tree shrews: Effect of age and comparison of plus lens wear with recovery from minus lens-induced myopia. Exp Eye Res 2010;91:660-669. 33. Smith EL III, Earl L, Hung L-F, Huang J, Blasdel TL, Humbird TL, Bockhorst KH. Effects of optical defocus on refractive development in monkeys: evidence for local, regionally selective mechanisms. Invest Ophthalmol Vis Sci 2010;51:3864-3873. 34. Norton TT, Amedo AO, Siegwart JT Jr. The effect of age on compensation for a negative lens and recovery from lens-induced myopia in tree shrews (Tupaia glis belangeri). Vision Res 2010;50:564-576. 35. Schaeffel F, Glasser A, Howland HC. Accommodation, refractive error and eye growth in chickens. Vision Res 1988;28:639657. 36. Zhu X, McBrien NA, Smith EL, Troilo D, Wallman J. Eyes in various species can shorten to compensate for myopic defocus. Invest Ophthalmol Vis Sci 2013. 37. Sorsby A, Leary GA, Fraser GR. Family studies on ocular refraction and its components. J Med Genet 1966;3:269-273.

Copyright © 2018. Kugler Publications. All rights reserved.

Scleral remodeling in myopia 38. Siegwart J, JT, Norton TT. The susceptible period for deprivation-induced myopia in tree shrew. Vision Res 1998;38:35053515. 39. Qiao-Grider Y, Hung LF, Kee CS, Ramamirtham R, Smith EL, 3rd. Nature of the refractive errors in rhesus monkeys (Macaca mulatta) with experimentally induced ametropias. Vision Res 2010;50:1867-1881. 40. Sorsby A, Benjamin B, Sheridan M, Stone J, Leary GA. Refraction and its components during the growth of the eye from the age of three. Memo Med Res Counc 1961;301(Special):1-67. 41. Bradley DV, Fernandes A, Lynn M, Tigges M, Boothe RG. Emmetropization in the rhesus monkey (Macaca mulatta): birth to young adulthood. Invest Ophthalmol Vis Sci 1999;40:214229. 42. Norton TT, McBrien NA. Normal development of refractive state and ocular component dimensions in the tree shrew (Tupaia belangeri). Vision Res 1992;32:833-842. 43. Zadnik K, Manny RE, Yu JA, et al. Ocular component data in schoolchildren as a function of age and gender. Optom Vis Sci 2003;80:226-236. 44. Wallman J, Adams JI. Developmental aspects of experimental myopia in chicks: susceptibility, recovery and relation to emmetropization. Vision Res 1987;27:1139-1163. 45. Smith EL, 3rd, Hung LF. The role of optical defocus in regulating refractive development in infant monkeys. Vision Res 1999;39:1415-1435. 46. Howlett MH, McFadden SA. Spectacle lens compensation in the pigmented guinea pig. Vision Res 2009;49:219-227. 47. Grytz R, El Hamdaoui M. Multi-scale Modeling of Vision-Guided Remodeling and Age-Dependent Growth of the Tree Shrew Sclera During Eye Development and Lens-Induced Myopia. J Elast 2017;129:171-195. 48. Wildsoet CF, Schmid KL. Emmetropization in chicks uses optical vergence and relative distance cues to decode defocus. Vision Res 2001;41:3197-3204. 49. Rucker FJ, Wallman J. Chicks use changes in luminance and chromatic contrast as indicators of the sign of defocus. J Vis 2012;12. 50. Mehra KS, Khare BB, Vaithilingam E. Refraction in Full-Term Babies. Br J Ophthalmol 1965;49:276-277. 51. Kuo A, Sinatra RB, Donahue SP. Distribution of refractive error in healthy infants. J AAPOS 2003;7:174-177. 52. Patel AR, Natarajan TS, Abreu R. Refractive errors in full-term newborn babies. J All India Ophthalmol Soc 1970;18:59-63. 53. Goldschmidt E. Refraction in the newborn. Acta Ophthalmol (Copenh) 1969;47:570-578. 54. Cook RC, Glasscock RE. Refractive and ocular findings in the newborn. Am J Ophthalmol 1951;34:1407-1413. 55. Pickett-Seltner RL, Sivak JG, Pasternak JJ. Experimentally induced myopia in chicks: morphometric and biochemical analysis during the first 14 days after hatching. Vision Res 1988;28:323-328. 56. Zhou X, Qu J, Xie R, et al. Normal development of refractive state and ocular dimensions in guinea pigs. Vision Res 2006;46:2815-2823.

399 57. Edwards MH. Animal models of myopia. A review. Acta Ophthalmol Scand 1996;74:213-219. 58. Norton TT. Animal models of myopia: learning how vision controls the size of the eye. ILAR J 1999;40:59-77. 59. Schaeffel F, Feldkaemper M. Animal models in myopia research. Clin Exp Optom 2015;98:507-517. 60. Metlapally S, McBrien NA. The effect of positive lens defocus on ocular growth and emmetropization in the tree shrew. J Vis 2008;8:1 1-12. 61. Adler D, Millodot M. The possible effect of undercorrection on myopic progression in children. Clin Exp Optom 2006;89:315321. 62. Chung K, Mohidin N, O’Leary DJ. Undercorrection of myopia enhances rather than inhibits myopia progression. Vision Res 2002;42:2555-2559. 63. Smith EL, 3rd. Optical treatment strategies to slow myopia progression: effects of the visual extent of the optical treatment zone. Exp Eye Res 2013;114:77-88. 64. Radhakrishnan H, Allen PM, Calver RI, et al. Peripheral refractive changes associated with myopia progression. Invest Ophthalmol Vis Sci 2013;54:1573-1581. 65. Sankaridurg P, Donovan L, Varnas S, et al. Spectacle lenses designed to reduce progression of myopia: 12-month results. Optom Vis Sci 2010;87:631-641. 66. Sankaridurg P, Holden B, Smith E, 3rd, et al. Decrease in rate of myopia progression with a contact lens designed to reduce relative peripheral hyperopia: one-year results. Invest Ophthalmol Vis Sci 2011;52:9362-9367. 67. Anstice NS, Phillips JR. Effect of dual-focus soft contact lens wear on axial myopia progression in children. Ophthalmology 2011;118:1152-1161. 68. Walline JJ, Greiner KL, McVey ME, Jones-Jordan LA. Multifocal contact lens myopia control. Optom Vis Sci 2013;90:12071214. 69. Charm J, Cho P. High myopia-partial reduction orthokeratology (HM-PRO): study design. Cont Lens Anterior Eye 2013;36:164-170. 70. Walline JJ, Jones LA, Sinnott LT. Corneal reshaping and myopia progression. Br J Ophthalmol 2009;93:1181-1185. 71. Cho P, Cheung SW. Retardation of myopia in Orthokeratology (ROMIO) study: a 2-year randomized clinical trial. Invest Ophthalmol Vis Sci 2012;53:7077-7085. 72. Chen C, Cheung SW, Cho P. Myopia control using toric orthokeratology (TO-SEE study). Invest Ophthalmol Vis Sci 2013;54:6510-6517. 73. Kakita T, Hiraoka T, Oshika T. Influence of overnight orthokeratology on axial elongation in childhood myopia. Invest Ophthalmol Vis Sci 2011;52:2170-2174. 74. Santodomingo-Rubido J, Villa-Collar C, Gilmartin B, Gutierrez-Ortega R. Myopia control with orthokeratology contact lenses in Spain: refractive and biometric changes. Invest Ophthalmol Vis Sci 2012;53:5060-5065. 75. Liu Y, Wildsoet C. The effective add inherent in 2-zone negative lenses inhibits eye growth in myopic young chicks. Invest Ophthalmol Vis Sci 2012;53:5085-5093.

Copyright © 2018. Kugler Publications. All rights reserved.

400 76. Tepelus TC, Vazquez D, Seidemann A, Uttenweiler D, Schaeffel F. Effects of lenses with different power profiles on eye shape in chickens. Vision Res 2012;54:12-19. 77. Liu Y, Wildsoet C. The effect of two-zone concentric bifocal spectacle lenses on refractive error development and eye growth in young chicks. Invest Ophthalmol Vis Sci 2011;52:1078-1086. 78. Smith EL, 3rd, Hung LF, Huang J. Relative peripheral hyperopic defocus alters central refractive development in infant monkeys. Vision Res 2009;49:2386-2392. 79. Wiesel TN, Raviola E. Myopia and eye enlargement after neonatal lid fusion in monkeys. Nature 1977;266:66-68. 80. Wallman J, Turkel J, Trachtman J. Extreme myopia produced by modest change in early visual experience. Science 1978;201:1249-1251. 81. Wilson JR, Sherman SM. Differential effects of early monocular deprivation on binocular and monocular segments of cat striate cortex. J Neurophysiol 1977;40:891-903. 82. Smith EL, 3rd, Harwerth RS, Crawford ML, von Noorden GK. Observations on the effects of form deprivation on the refractive status of the monkey. Invest Ophthalmol Vis Sci 1987;28:12361245. 83. Ohlendorf A, Schaeffel F. Contrast adaptation induced by defocus - a possible error signal for emmetropization? Vision Res 2009;49:249-256. 84. Schmid KL, Brinkworth DR, Wallace KM, Hess R. The effect of manipulations to target contrast on emmetropization in chick. Vision Res 2006;46:1099-1107. 85. Stoimenova BD. The effect of myopia on contrast thresholds. Invest Ophthalmol Vis Sci 2007;48:2371-2374. 86. Kerber KL, Thorn F, Bex PJ, Vera-Diaz FA. Peripheral contrast sensitivity and attention in myopia. Vision Res 2016;125:49-54. 87. Diether S, Schaeffel F. Long-term changes in retinal contrast sensitivity in chicks from frosted occluders and drugs: relations to myopia? Vision Res 1999;39:2499-2510. 88. Jones LA, Sinnott LT, Mutti DO, Mitchell GL, Moeschberger ML, Zadnik K. Parental history of myopia, sports and outdoor activities, and future myopia. Invest Ophthalmol Vis Sci 2007;48:3524-3532. 89. Rose KA, Morgan IG, Ip J, et al. Outdoor activity reduces the prevalence of myopia in children. Ophthalmology 2008;115:12791285. 90. Norton TT, Siegwart JT Jr. Light levels, refractive development, and myopia--a speculative review. Exp Eye Res 2013;114:48-57. 91. Ashby RS, Schaeffel F. The effect of bright light on lens compensation in chicks. Invest Ophthalmol Vis Sci 2010;51:5247-5253. 92. Ashby R, Ohlendorf A, Schaeffel F. The effect of ambient illuminance on the development of deprivation myopia in chicks. Invest Ophthalmol Vis Sci 2009;50:5348-5354. 93. Smith EL, 3rd, Hung LF, Huang J. Protective effects of high ambient lighting on the development of form-deprivation myopia in rhesus monkeys. Invest Ophthalmol Vis Sci 2012;53:421-428. 94. Smith EL, 3rd, Hung LF, Arumugam B, Huang J. Negative lens-induced myopia in infant monkeys: effects of high ambient lighting. Invest Ophthalmol Vis Sci 2013;54:2959-2969.

R. Grytz 95. Foulds WS, Barathi VA, Luu CD. Progressive myopia or hyperopia can be induced in chicks and reversed by manipulation of the chromaticity of ambient light. Invest Ophthalmol Vis Sci 2013;54:8004-8012. 96. Smith EL, 3rd, Hung LF, Arumugam B, Holden BA, Neitz M, Neitz J. Effects of long-wavelength lighting on refractive development in infant rhesus monkeys. Invest Ophthalmol Vis Sci 2015;56:6490-6500. 97. Gawne TJ, Siegwart JT Jr, Ward AH, Norton TT. The wavelength composition and temporal modulation of ambient lighting strongly affect refractive development in young tree shrews. Exp Eye Res 2016. 98. Crewther DP, Crewther SG. Refractive compensation to optical defocus depends on the temporal profile of luminance modulation of the environment. Neuroreport 2002;13:1029-1032. 99. Crewther SG, Barutchu A, Murphy MJ, Crewther DP. Low frequency temporal modulation of light promotes a myopic shift in refractive compensation to all spectacle lenses. Exp Eye Res 2006;83:322-328. 100. Kee CS, Hung LF, Qiao-Grider Y, et al. Temporal constraints on experimental emmetropization in infant monkeys. Invest Ophthalmol Vis Sci 2007;48:957-962. 101. Rohrer B, Iuvone PM, Stell WK. Stimulation of dopaminergic amacrine cells by stroboscopic illumination or fibroblast growth factor (bFGF, FGF-2) injections: possible roles in prevention of form-deprivation myopia in the chick. Brain Res 1995;686:169-181. 102. Rucker FJ. The role of luminance and chromatic cues in emmetropisation. Ophthalmic Physiol Opt 2013;33:196-214. 103. Schwahn HN, Schaeffel F. Flicker parameters are different for suppression of myopia and hyperopia. Vision Res 1997;37:2661-2673. 104. Yu Y, Chen H, Tuo J, Zhu Y. Effects of flickering light on refraction and changes in eye axial length of C57BL/6 mice. Ophthalmic Res 2011;46:80-87. 105. Troilo D, Gottlieb MD, Wallman J. Visual deprivation causes myopia in chicks with optic nerve section. Curr Eye Res 1987;6:993-999. 106. Wildsoet CF, Howland HC, Falconer S, Dick K. Chromatic aberration and accommodation: their role in emmetropization in the chick. Vision Res 1993;33:1593-1603. 107. Kroger RH, Wagner HJ. The eye of the blue acara (Aequidens pulcher, Cichlidae) grows to compensate for defocus due to chromatic aberration. J Comp Physiol A 1996;179:837-842. 108. Rohrer B, Schaeffel F, Zrenner E. Longitudinal chromatic aberration and emmetropization: results from the chicken eye. J Physiol 1992;449:363-376. 109. Rucker FJ, Kruger PB. Cone contributions to signals for accommodation and the relationship to refractive error. Vision Res 2006;46:3079-3089. 110. Rucker FJ, Wallman J. Cone signals for spectacle-lens compensation: differential responses to short and long wavelengths. Vision Res 2008;48:1980-1991. 111. Rucker FJ, Wallman J. Chick eyes compensate for chromatic simulations of hyperopic and myopic defocus: evidence that

Copyright © 2018. Kugler Publications. All rights reserved.

Scleral remodeling in myopia the eye uses longitudinal chromatic aberration to guide eyegrowth. Vision Res 2009;49:1775-1783. 112. Seidemann A, Schaeffel F. Effects of longitudinal chromatic aberration on accommodation and emmetropization. Vision Res 2002;42:2409-2417. 113. Schaeffel F, Howland HC. Properties of the feedback loops controlling eye growth and refractive state in the chicken. Vision Res 1991;31:717-734. 114. Guo L, Frost MR, He L, Siegwart JT Jr, Norton TT. Gene expression signatures in tree shrew sclera in response to three myopiagenic conditions. Invest Ophthalmol Vis Sci 2013;54:6806-6819. 115. He L. Gene expression signatures in tree shrew retina, {RPE}, and choroid during experimental myopia and recovery. Birmingham, Alabama: University of Alabama at Birmingham; 2014. 116. He L, Frost MR, Siegwart JT Jr, Norton TT. Gene expression signatures in tree shrew choroid in response to three myopiagenic conditions. Vision Res 2014;102:52-63. 117. He L, Frost MR, Siegwart JT Jr, Norton TT. Gene expression signatures in tree shrew choroid during lens-induced myopia and recovery. Exp Eye Res 2014;123:56-71. 118. Guo L, Frost MR, Siegwart JT Jr, Norton TT. Scleral gene expression during recovery from myopia compared with expression during myopia development in tree shrew. Mol Vis 2014;20:1643-1659. 119. Wallman J, Gottlieb MD, Rajaram V, Fugate-Wentzek LA. Local retinal regions control local eye growth and myopia. Science 1987;237:73-77. 120. Hodos W, Kuenzel WJ. Retinal-image degradation produces ocular enlargement in chicks. Invest Ophthalmol Vis Sci 1984;25:652-659. 121. Diether S, Schaeffel F. Local changes in eye growth induced by imposed local refractive error despite active accommodation. Vision Res 1997;37:659-668. 122. Napper GA, Brennan NA, Barrington M, Squires MA, Vessey GA, Vingrys AJ. The effect of an interrupted daily period of normal visual stimulation on form deprivation myopia in chicks. Vision Res 1997;37:1557-1564. 123. Schmid KL, Wildsoet CF. Effects on the compensatory responses to positive and negative lenses of intermittent lens wear and ciliary nerve section in chicks. Vision Res 1996;36:1023-1036. 124. Shaikh AW, Siegwart JT, Norton TT. Effect of interrupted lens wear on compensation for a minus lens in tree shrews. Optom Vis Sci 1999;76:308-315. 125. Smith EL, 3rd, Hung LF, Kee CS, Qiao Y. Effects of brief periods of unrestricted vision on the development of form-deprivation myopia in monkeys. Invest Ophthalmol Vis Sci 2002;43:291299. 126. Levin LA, Nilsson SF, Ver Hoeve J, Wu S, Kaufman PL, Alm A. Adler’s Physiology of the Eye: Elsevier Health Sciences; 2011. 127. Meek K. The cornea and sclera. Collagen: Springer; 2008:359396. 128. Jan NJ, Lathrop K, Sigal IA. Collagen architecture of the posterior pole: high-resolution wide field of view visualization and analysis using polarized light microscopy. Invest Ophthalmol Vis Sci 2017;58:735-744.

401 129. Norman RE, Flanagan JG, Rausch SM, et al. Dimensions of the human sclera: Thickness measurement and regional changes with axial length. Exp Eye Res 2010;90:277-284. 130. Komai Y, Ushiki T. The Three-Dimensional Organization of Collagen Fibrils in the Human Cornea and Sclera. Invest Ophthalmol Vis Sci 1991;32:2244-2258. 131. Harper AR, Summers JA. The dynamic sclera: extracellular matrix remodeling in normal ocular growth and myopia development. Exp Eye Res 2015;133:100-111. 132. Rada JA, Achen VR, Penugonda S, Schmidt RW, Mount BA. Proteoglycan composition in the human sclera during growth and aging. Invest Ophthalmol Vis Sci 2000;41:1639-1648. 133. Rada JA, Nickla DL, Troilo D. Decreased proteoglycan synthesis associated with form deprivation myopia in mature primate eyes. Invest Ophthalmol Vis Sci 2000;41:2050-2058. 134. Grytz R, Siegwart JT Jr. Changing material properties of the tree shrew sclera during minus lens compensation and recovery. Invest Ophthalmol Vis Sci 2015;56:2065-2078. 135. Murienne BJ, Jefferys JL, Quigley HA, Nguyen TD. The effects of glycosaminoglycan degradation on the mechanical behavior of the posterior porcine sclera. Acta Biomater 2015;12:195-206. 136. Siegwart JT, Strang CE. Selective modulation of scleral proteoglycan mRNA levels during minus lens compensation and recovery. Mol Vis 2007;13:1878-1886. 137. Rada JA, Achen VR, Perry CA, Fox PW. Proteoglycans in the human sclera. Evidence for the presence of aggrecan. Invest Ophthalmol Vis Sci 1997;38:1740-1751. 138. Schultz DS, Lotz JC, Lee SM, Trinidad ML, Stewart JM. Structural factors that mediate scleral stiffness. Invest Ophthalmol Vis Sci 2008;49:4232-4236. 139. Di Girolamo N, Lloyd A, McCluskey P, Filipic M, Wakefield D. Increased expression of matrix metalloproteinases in vivo in scleritis tissue and in vitro in cultured human scleral fibroblasts. Am J Pathol 1997;150:653-666. 140. Gaton DD, Sagara T, Lindsey JD, Gabelt BT, Kaufman PL, Weinreb RN. Increased matrix metalloproteinases 1, 2, and 3 in the monkey uveoscleral outflow pathway after topical prostaglandin F(2 alpha)-isopropyl ester treatment. Arch Ophthalmol 2001;119:1165-1170. 141. Yamaoka A, Matsuo T, Shiraga F, Ohtsuki H. TIMP-1 production by human scleral fibroblast decreases in response to cyclic mechanical stretching. Ophthalmic Res 2001;33:98-101. 142. Shen L, You QS, Xu X, et al. Scleral and choroidal volume in relation to axial length in infants with retinoblastoma versus adults with malignant melanomas or end-stage glaucoma. Graefes Arch Clin Exp Ophthalmol 2016;254:1779-1786. 143. Shen L, You QS, Xu X, et al. Scleral thickness in Chinese eyes. Invest Ophthalmol Vis Sci 2015;56:2720-2727. 144. Cheng HM, Singh OS, Kwong KK, Xiong J, Woods BT, Brady TJ. Shape of the myopic eye as seen with high-resolution magnetic resonance imaging. Optom Vis Sci 1992;69:698-701. 145. Jonas JB, Holbach L, Panda-Jonas S. Histologic differences between primary high myopia and secondary high myopia due to congenital glaucoma. Acta Ophthalmol 2016;94:147-153.

Copyright © 2018. Kugler Publications. All rights reserved.

402 146. Jonas JB, Holbach L, Panda-Jonas S. Scleral cross section area and volume and axial length. PLoS One 2014;9:e93551. 147. Norton TT, Rada JA. Reduced extracellular matrix in mammalian sclera with induced myopia. Vision Res 1995;35:1271-1281. 148. McBrien NA, Cornell LM, Gentle A. Structural and ultrastructural changes to the sclera in a mammalian model of high myopia. Invest Ophthalmol Vis Sci 2001;42:2179-2187. 149. McBrien NA, Lawlor P, Gentle A. Scleral remodeling during the development of and recovery from axial myopia in the tree shrew. Invest Ophthalmol Vis Sci 2000;41:3713-3719. 150. Moring AG, Baker JR, Norton TT. Modulation of glycosaminoglycan levels in tree shrew sclera during lens-induced myopia development and recovery. Invest Ophthalmol Vis Sci 2007;48:2947-2956. 151. Curtin BJ, Iwamoto T, Renaldo DP. Normal and Staphylomatous Sclera of High Myopia. Arch Ophthalmol 1979;97:912–-915. 152. Guggenheim JA, McBrien NA. Form-deprivation myopia induces activation of scleral matrix metalloproteinase-2 in tree shrew. Invest Ophthalmol Vis Sci 1996;37:1380-1395. 153. Gao H, Frost MR, Siegwart JT, Norton TT. Patterns of mRNA and protein expression during minus-lens compensation and recovery in tree shrew sclera. Mol Vis 2011;17:903-919. 154. Siegwart JT Jr, Norton TT. Selective regulation of MMP and TIMP mRNA levels in tree shrew sclera during minus lens compensation and recovery. Invest Ophthalmol Vis Sci 2005;46:3484-3492. 155. Siegwart JT, Norton TT. The time course of changes in mRNA levels in tree shrew sclera during induced myopia and recovery. Invest Ophthalmol Vis Sci 2002;43:2067-2075. 156. Gentle A, Liu Y, Martin JE, Conti GL, McBrien NA. Collagen gene expression and the altered accumulation of scleral collagen during the development of high myopia. J Biol Chem 2003;278:16587-16594. 157. Ho LC, Sigal IA, Jan NJ, et al. Magic angle-enhanced MRI of fibrous microstructures in sclera and cornea with and without intraocular pressure loading. Invest Ophthalmol Vis Sci 2014;55:5662-5672. 158. Grytz R, Meschke G. Constitutive modeling of crimped collagen fibrils in soft tissues. J Mech Behav Biomed Mater 2009;2:522533. 159. Grytz R, Fazio MA, Girard MJ, et al. Material properties of the posterior human sclera. J Mech Behav Biomed Mater 2014;29:602617. 160. Girard MJ, Downs JC, Bottlang M, Burgoyne CF, Suh JK. Peripapillary and posterior scleral mechanics--part II: experimental and inverse finite element characterization. J Biomech Eng 2009;131:051012. 161. Coudrillier B, Boote C, Quigley HA, Nguyen TD. Scleral anisotropy and its effects on the mechanical response of the optic nerve head. Biomech Model Mechanobiol 2013;12:941-963. 162. Cribb AM, Scott JE. Tendon response to tensile stress: an ultrastructural investigation of collagen:proteoglycan interactions in stressed tendon. J Anat 1995;187:423-428. 163. Liao J, Vesely I. A structural basis for the size-related mechanical properties of mitral valve chordae tendineae. J Biomech 2003;36:1125-1133.

R. Grytz 164. Liao J, Vesely I. Skewness angle of interfibrillar proteoglycans increases with applied load on mitral valve chordae tendineae. J Biomech 2007;40:390-398. 165. Scott JE. Proteoglycan:collagen interactions and subfibrillar structure in collagen fibrils. Implications in the development and ageing of connective tissues. J Anat 1990;169:2335. 166. Scott JE. Elasticity in extracellular matrix ‘shape modules’ of tendon, cartilage, etc. A sliding proteoglycan-filament model. J Physiol 2003;553:335-343. 167. Sasaki N, Odajima S. Elongation Mechanism of Collagen Fibrils and Force-Strain Relations of Tendon at Each Level of Structural Hierarchy. J Biomech 1996;29:1131-1136. 168. Robinson PS, Huang T-F, Kazam E, Iozzo RV, Birk DE, Soslowsky LJ. Influence of decorin and biglycan on mechanical properties of multiple tendons in knockout mice. J Biomech Eng 2005;127:181-185. 169. Rigozzi S, Müller R, Snedeker JG. Collagen fibril morphology and mechanical properties of the Achilles tendon in two inbred mouse strains. J Anat 2010;216:724-731. 170. Rigozzi S, Müller R, Stemmer A, Snedeker JG. Tendon glycosaminoglycan proteoglycan sidechains promote collagen fibril sliding-AFM observations at the nanoscale. J Biomech 2013;46:813-818. 171. Fessel G, Snedeker JG. Equivalent stiffness after glycosaminoglycan depletion in tendon--an ultra-structural finite element model and corresponding experiments. J Theor Biol 2011;268:77-83. 172. Fessel G, Snedeker JG. Evidence against proteoglycan mediated collagen fibril load transmission and dynamic viscoelasticity in tendon. Matrix Biol 2009;28:503-510. 173. Rigozzi S, Müller R, Snedeker JG. Local strain measurement reveals a varied regional dependence of tensile tendon mechanics on glycosaminoglycan content. J Biomech 2009;42:1547-1552. 174. Lujan TJ, Underwood CJ, Henninger HB, Thompson BM, Weiss JA. Effect of dermatan sulfate glycosaminoglycans on the quasi-static material properties of the human medial collateral ligament. J Orthop Res 2007;25:894-903. 175. Lujan TJ, Underwood CJ, Jacobs NT, Weiss JA. Contribution of glycosaminoglycans to viscoelastic tensile behavior of human ligament. J Appl Physiol (1985) 2009;106:423-431. 176. Ahmadzadeh H, Connizzo BK, Freedman BR, Soslowsky LJ, Shenoy VB. Determining the contribution of glycosaminoglycans to tendon mechanical properties with a modified shear-lag model. J Biomech 2013;46:2497-2503. 177. Siegwart JT, Norton TT. Regulation of the mechanical properties of tree shrew sclera by the visual environment. Vision Res 1999;39:387-407. 178. Phillips JR, Khalaj M, McBrien NA. Induced myopia associated with increased scleral creep in chick and tree shrew eyes. Invest Ophthalmol Vis Sci 2000;41:2028-2034. 179. McBrien NA, Jobling AI, Gentle A. Biomechanics of the sclera in myopia: extracellular and cellular factors. Optom Vis Sci 2009;86:E23-30.

Copyright © 2018. Kugler Publications. All rights reserved.

Scleral remodeling in myopia 180. Coudrillier B, Pijanka J, Jefferys J, et al. Collagen structure and mechanical properties of the human sclera: analysis for the effects of age. J Biomech Eng 2015;137:041006. 181. Coudrillier B, Pijanka J, Jefferys J, et al. Effects of age and diabetes on scleral stiffness. J Biomech Eng 2015;137. 182. Fazio MA, Grytz R, Morris JS, et al. Age-related changes in human peripapillary scleral strain. Biomech Model Mechanobiol 2014;13:551-563. 183. Grytz R, Fazio MA, Libertiaux V, et al. Age- and race-related differences in human scleral material properties. Invest Ophthalmol Vis Sci 2014;55:8163-8172. 184. Liu TX, Wang Z. Collagen crosslinking of porcine sclera using genipin. Acta Ophthalmol 2013;91:e253-257. 185. Wollensak G, Iomdina E. Crosslinking of scleral collagen in the rabbit using glyceraldehyde. J Cataract Refract Surg 2008;34:651-656. 186. Wollensak G, Iomdina E. Long-term biomechanical properties after collagen crosslinking of sclera using glyceraldehyde. Acta Ophthalmol 2008;86:887-893. 187. Wollensak G, Spoerl E. Collagen crosslinking of human and porcine sclera. J Cataract Refract Surg 2004;30:689-695. 188. Wollensak G, Iomdina E. Long-term biomechanical properties of rabbit sclera after collagen crosslinking using riboflavin and ultraviolet A (UVA). Acta Ophthalmol 2009;87:193-198. 189. Chu Y, Cheng Z, Liu J, Wang Y, Guo H, Han Q. The effects of scleral collagen cross-linking using glyceraldehyde on the progression of form-deprived myopia in guinea pigs. J Ophthalmol 2016;2016:3526153. 190. Dotan A, Kremer I, Gal-Or O, et al. Scleral Cross-linking Using Riboflavin and Ultraviolet-A Radiation for Prevention of Axial Myopia in a Rabbit Model. J Vis Exp 2016;e53201. 191. Dotan A, Kremer I, Livnat T, Zigler A, Weinberger D, Bourla D. Scleral cross-linking using riboflavin and ultraviolet-a radiation for prevention of progressive myopia in a rabbit model. Exp Eye Res 2014;127:190-195. 192. Liu S, Li S, Wang B, et al. Scleral cross-linking using riboflavin UVA irradiation for the prevention of myopia progression in a guinea pig model: blocked axial extension and altered scleral microstructure. PLoS One 2016;11:e0165792. 193. Wang M, Corpuz CC. Effects of scleral cross-linking using genipin on the process of form-deprivation myopia in the guinea pig: a randomized controlled experimental study. BMC Ophthalmol 2015;15:89. 194. Levy A, Baldivia SM, Grytz R. Collagen crosslinking using genipin diminishes cyclic softening of tree shrew sclera during lens-induced myopia development. Investigative Ophthalmology & Visual Science 2015;56:ARVO E-Abstract 2178.

403 195. Christensen AM, Wallman J. Evidence that increased scleral growth underlies visual deprivation myopia in chicks. Invest Ophthalmol Vis Sci 1991;32:2143-2150. 196. Marzani D, Wallman J. Growth of the two layers of the chick sclera is modulated reciprocally by visual conditions. Invest Ophthalmol Vis Sci 1997;38:1726-1739. 197. Baldivia S, Levy A, Hegde S, Aper SJ, Merkx M, Grytz R. A Novel Organ Culture Model to Quantify Collagen Remodeling in Tree Shrew Sclera. PLoS One 2016;11:e0166644. 198. Bruehlmann SB, Matyas JR, Duncan NA. ISSLS prize winner: Collagen fibril sliding governs cell mechanics in the anulus fibrosus: an in situ confocal microscopy study of bovine discs. Spine (Phila Pa 1976) 2004;29:2612-2620. 199. Cheng VW, Screen HR. The micro-structural strain response of tendon. Journal of Materials Science 2007;42:8957-8965. 200. Cyron CJ, Wilson JS, Humphrey JD. Mechanobiological stability: a new paradigm to understand the enlargement of aneurysms? J R Soc Interface 2014;11:20140680. 201. Cyron CJ, Humphrey JD. Vascular homeostasis and the concept of mechanobiological stability. Int J Eng Sci 2014;85:203-223. 202. Grytz R, Sigal IA, Ruberti JW, Meschke G, Downs JC. Lamina cribrosa thickening in early glaucoma predicted by a microstructure motivated growth and remodeling approach. Mech Mater 2012;44:99-109. 203. Grytz R, Girkin CA, Libertiaux V, Downs JC. Perspectives on biomechanical growth and remodeling mechanisms in glaucoma. Mech Res Commun 2012;42:92-106. 204. McBrien NA, Norton TT. Prevention of collagen crosslinking increases form-deprivation myopia in tree shrew. Exp Eye Res 1994;59:475-486. 205. Camp RJ, Liles M, Beale J, et al. Molecular mechanochemistry: low force switch slows enzymatic cleavage of human type I collagen monomer. J Am Chem Soc 2011;133:4073-4078. 206. Flynn BP, Bhole AP, Saeidi N, Liles M, Dimarzio CA, Ruberti JW. Mechanical strain stabilizes reconstituted collagen fibrils against enzymatic degradation by mammalian collagenase matrix metalloproteinase 8 (MMP-8). PLoS One 2010;5:e12337. 207. Flynn BP, Tilburey GE, Ruberti JW. Highly sensitive single-fibril erosion assay demonstrates mechanochemical switch in native collagen fibrils. Biomech Model Mechanobiol 2013;12:291-300.

Copyright © 2018. Kugler Publications. All rights reserved.

28. The connective tissue phenotype of glaucomatous cupping in the monkey eye* Hongli Yang,1,2 Juan Reynaud,1,2 Howard Lockwood,1,2 Galen Williams,1,2 Christy Hardin,1,2 Luke Reyes,1,2 Cheri Stowell,1,2 Stuart K. Gardiner,2 Claude F. Burgoyne1,2 Devers Eye Institute, Optic Nerve Head Research Laboratory, Legacy Research Institute, Portland, OR, USA; 2Devers Eye Institute, Discoveries in Sight Research Laboratories, Legacy Research Institute, Portland, OR, USA

1

Copyright © 2018. Kugler Publications. All rights reserved.

Abstract In a series of previous publications, we have proposed a framework for conceptualizing the optic nerve head (ONH) as a biomechanical structure. That framework proposes important roles for intraocular pressure (IOP), IOP-related stress and strain, cerebrospinal fluid pressure (CSFp), systemic and ocular determinants of blood flow, inflammation, auto-immunity, genetics, and other non-IOP related risk factors in the physiology of ONH aging and the pathophysiology of glaucomatous damage to the ONH. The present report summarizes 20 years of technique development and study results pertinent to the characterization of ONH connective tissue deformation and remodeling in the unilateral monkey experimental glaucoma (EG) model. In it, we propose that the defining pathophysiology of a glaucomatous optic neuropathy involves deformation, remodeling, and mechanical failure of the ONH connective tissues. We view this as an active process, driven by astrocyte, microglial, fibroblast, and oligodendrocyte mechanobiology. These cells, and the connective tissue phenomena they propagate, have primary and secondary effects on retinal ganglion cell (RGC) axon, laminar beam, and retrolaminar capillary homeostasis that may initially be ‘protective’, but eventually lead to RGC axonal injury, repair, and/or cell

death. The primary goal of this chapter is to summarize our 3-D histomorphometric and optical coherence tomography (OCT)-based evidence for the early onset and progression of ONH connective tissue deformation and remodeling in monkey EG. A second goal is to explain the importance of including ONH connective tissue processes in characterizing the phenotype of a glaucomatous optic neuropathy in all species.

1. Introduction While glaucomatous damage to the visual system likely includes pathophysiologies within the retinal photoreceptors,1-5 RGC soma,6-11 distal RGC axon,12 lateral geniculate/superior colliculus,12-17 and visual cortex,17 extensive evidence from ourselves18-25 and others26-29 suggests that damage to the RGC axons within the lamina cribrosa (LC) of the ONH is an early pathophysiology underlying glaucomatous neuronal loss in mice, rats, monkeys, and humans.30-40 However, while RGC axonal insult within the ONH is central to glaucomatous vision loss and its manifestations are the source of all current forms of clinical staging (visual field, retinal nerve fiber layer (RNFL) thickness,

*Reprinted from Progress in Retinal and Eye Research Vol. 59 Hongli Yang,Juan Reynaud,Howard Lockwood,Galen Williams,Christy Hardin,Luke Reyes,Cheri Stowell,Stuart K. Gardiner,Claude F. Burgoyne, The connective tissue phenotype of glaucomatous cupping in the monkey eye - Clinical and research implications. p. 1-59. Copyright 2017 with permission from Elsevier Correspondence: Claude F. Burgoyne MD, Optic Nerve Head Research Laboratory, Devers Eye Institute, Legacy Research Institute, 1225 NE 2nd Ave, Portland OR 97232, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 405-430 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

H. Yang et al.

Copyright © 2018. Kugler Publications. All rights reserved.

406

etc.), we propose that RGC axonal insult within the ONH is not the pathophysiology that defines the optic neuropathy of glaucoma. In making this statement, we acknowledge the essential need to preserve RGC axons, soma, and their peripheral connections in all glaucoma patients, because preservation of vision is the goal of all glaucoma therapy. However, we also emphasize that, to date, selectively killing RGC soma or axons alone, by whatever mechanism, has not been shown to create a glaucomatous optic neuropathy (i.e., glaucomatous ONH cupping).41-46 In this context, we propose that the defining pathophysiology of a glaucomatous optic neuropathy is the deformation, remodeling, and mechanical failure of the ONH connective tissues and the cells that are directly and indirectly linked to them. This report summarizes 20 years of technique development and study results pertinent to the characterization of ONH connective tissue deformation and remodeling in the unilateral monkey experimental glaucoma (EG) model. We view these phenomena as active, interactive processes, driven by and driving astrocyte, microglial, fibroblast, and oligodendrocyte mechanobiology. These cells, and the neural and connective tissue phenomena they propagate, have primary and secondary effects on RGC axon, laminar beam, retrolaminar capillary, and myelin homeostasis that may initially be ‘protective’, but eventually lead to RGC axonal injury, repair, and/or cell death. The following articles should be consulted for additional information: Burgoyne,47 for the monkey EG model; Yang et al.,48 for the 3-D histomorphometric reconstruction (HMRN) of the ONH; and Burgoyne,49 for the phenotype of glaucomatous connective tissue alteration in monkey and human glaucoma. Table 1 provides a list of abbreviations, acronyms, parameters, and definitions used in this report. By convention, all parameters are italicized so as to distinguish them from the anatomic landmark or structure they measure. Also by convention, we use the term ‘ONH’ to refer to the tissues that pass through and are contained within the scleral canal as well as those that are immediately adjacent to it (i.e., the peripapillary sclera (pp-sclera), choroid, retina, and retrolaminar optic nerve). This chapter is taken directly from portions of our recent review article,50 which should be consulted for greater details on the topics contained herein.

2. Monkey ONH anatomy and biomechanics In a series of previous publications,49,51-55 we have proposed a framework for conceptualizing the ONH as a biomechanical structure. That framework proposes important roles for IOP, IOP-related stress and strain, CSFp, systemic and ocular determinants of blood flow, as well as potential roles for inflammation, auto-immunity, genetics, and other non-IOP related risk factors in the physiology of ONH aging and the pathophysiology of glaucomatous damage to the ONH. This biomechanical paradigm specifically proposes that IOP-related stress and strain: 1. are substantial within the neural and connective tissues of the ONH at all levels of IOP, even when it is low; and 2. underlie the two central pathophysiologies of glaucomatous damage to the ONH: deformation, remodeling, and mechanical failure of the connective tissues and axonal compromise within the LC by a variety of IOP-related and IOP-independent mechanisms. Within the clinically-visible surface of the normal ONH (Fig. 1), central retinal vessels enter the eye and RGC axons appear pink due to their capillaries, which are principally supplied by branches from the posterior ciliary arteries. The primary site of RGC axon insult in glaucoma is within the LC, which is schematically depicted with axon bundles in Figure 1D, shown isolated by trypsin digest in a scanning electron micrograph in Figure 1E, and drawn with stippled extracellular matrix, central capillary, and surrounding astrocytes in Figure 1F. Blood flow within the ONH, while controlled by autoregulation, can be affected by non-IOP-related effects, such as systemic blood pressure fluctuation and vasospasm within the retrobulbar portion of the posterior ciliary arteries. Additional IOP-induced effects may include compression of posterior ciliary artery branches within the pp-sclera due to scleral stress and strain, and compression of LC beam capillaries reducing laminar capillary volume flow.56 There is no direct blood supply to the axons within the laminar region. Nor are there astrocyte processes to the LC beam capillaries, though prelaminar and retrolaminar astrocytes send processes to the septal capillaries, which are not surrounded by substantial connective tissue.57,58

The connective tissue phenotype of glaucomatous cupping

407

Table 1. Commonly used abbreviations/acronyms/terms and their description Acronyms/Terms

Meaning/Definition

3-D

Three-dimensional

ALCSD

Anterior lamina cribrosa surface depth

ALI

Anterior laminar insertion

Animal-Specific

Animal-specific EG vs Control eye difference

BD

Beam diameter

BM

Bruch’s membrane

BMO

Bruch’s membrane opening

Control Eye

Contralateral control eye of a unilateral optic neuropathy study animal – not assumed to be “normal”

CSFp

Cerebrospinal fluid pressure

CSLT

Confocal scanning laser tomography

CTV

Connective tissue volume – the sum of all connective tissue voxels

CTVF

Connective tissue volume fraction – the ratio of CTV/LV expressed without units

EG

Experimental glaucoma

HMRN

Histomorphometric reconstruction

IHC

Immunohistochemistry

IOP

Intraocular pressure

LC

Lamina cribrosa

LMA

Lamina cribrosa microarchitecture – as characterized by BD, PD, CTV, CTVF, LV

LV

Lamina cribrosa volume – the sum of all beam and pore voxels

MRW

Minimum rim width

OCT

Optical coherence tomography

ONH

Optic nerve head

ONT

Optic nerve transection

PD

Pore diameter

PID, PIDmax

Physiologic inter-eye difference (difference between the two eyes of a bilaterally normal monkey), and the maximum value of this difference among a group of bilaterally normal monkeys

PIPD, PIPDmax

Physiologic inter-eye percent difference, and its maximum value among a group (see PID, above)

PLI

Posterior laminar insertion

pp-sclera

Peripapillary sclera

RGC

Retinal ganglion cell

RNFL

Retinal nerve fiber layer

RNFLT

Retinal nerve fiber layer thickness

Copyright © 2018. Kugler Publications. All rights reserved.

Note that all parameters are italicized so as to distinguish them from the anatomic landmark or structure or phenomenon they measure.

408

H. Yang et al.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 1. ONH homeostasis is influenced by IOP-related stress and strain at all levels of IOP. (A) Prelaminar, laminar, and retrolaminar ONH regions. (B) The clinically visible surface of the normal ONH (referred to as the optic disc). Central retinal vessels enter the eye and RGC axons appear pink due to their capillaries. (C) The posterior ciliary arteries (PCA) are the principal blood supply to the ONH. Z-H: circle of Zinn-Haller; PCA: posterior ciliary arteries; NFL: nerve fiber layer; PLC: prelaminar region; LC: lamina cribrosa; RLC: retrolaminar region; ON: optic nerve; CRA: central retinal artery. (D) The LC is schematically depicted with axon bundles in (D), isolated by trypsin digest in a scanning electron micrograph in (E) and drawn with stippled extracellular matrix (ECM), central capillary (red), and surrounding astrocytes (yellow) with basement membranes (black) in (F). The clinical manifestation of IOP-induced damage to the ONH is most commonly ‘deep cupping’(G), but in some eyes cupping can be shallower, accompanied by pallor (H). (A) Reproduced from Anderson and Hoyt127 with permission from the American Medical Association; Copyright ©1969. All rights reserved. (B,G,H) Reprinted from Burgoyne and Downs 54 with permission from Wolters Kluwer Health, Inc. (C) Reprinted courtesy of J. Cioffi and M. Van Buskirk.128 (D) Reprinted courtesy of Harry Quigley.129 (E) Reproduced from Quigley et al.130 with permission from the American Medical Association; Copyright ©1989. All rights reserved. (F) Reproduced from Morrison et al.131 with permission from the American Medical Association; Copyright ©1990. All rights reserved.

IOP generates tensile forces within the sclera, generating an expansion of the scleral shell when IOP is acutely elevated. These forces act on the scleral canal wall, causing the scleral canal opening to expand, which in turn stretches the lamina within the canal. The magnitude of these effects depends upon the level of IOP change and the relative structural stiffnesses of the pp-sclera and lamina, respectively. If the structural stiffness of the sclera is more compliant than the lamina, the lamina will be pulled taut (more anteriorly positioned) and thinned in an eye at an IOP of 10 mmHg compared to the same eye at 0 mmHg. The effects of IOP within the sclera, and the scleral effects on the lamina, are predicted in most models to be greater than the direct effects of IOP on the lamina alone.51,59-76 IOP-related stress and strain influence the ONH connective tissues, the volume flow of blood (primarily), and the delivery of nutrients (secondarily), through chronic alterations in connective tissue stiffness and diffusion properties. Non-IOP related effects such as auto-immune or inflammatory insults and retrobulbar determinants of ocular blood flow can primarily

damage the ONH connective tissues and/or axons, leaving them vulnerable to secondary damage by IOPrelated mechanisms at normal or elevated levels of IOP. Once weakened, the ONH connective tissues deform in a predictable manner (Fig. 2) which underlies the laminar component of cupping (Fig. 3). ‘Deep’, ‘laminar’ or ‘glaucomatous’ cupping can be caused by IOP-related or non-IOP related insults, but once the ONH connective tissues are weakened, their deformation is driven by IOP-related connective tissue stress and strain regardless of IOP level. Thus, the presence of ONH connective tissue deformation in any optic neuropathy (Fig. 4) is evidence that the level of IOP at which it occurred (whether normal or elevated) is too high for the connective tissues in their present condition. Early IOP-related alterations in the monkey eye21-25,77 include posterior bowing of the lamina and pp-sclera, accompanied by scleral canal expansion, thickening of the lamina, and outward migration of the laminar insertion from the sclera into the pia mater (Fig. 2). In our studies to date, this appears to represent

Copyright © 2018. Kugler Publications. All rights reserved.

The connective tissue phenotype of glaucomatous cupping

Fig. 2. Connective tissue deformation, remodeling, and mechanical failure underlie the ‘laminar’ component of glaucomatous cupping. (A) Schematic of normal laminar thickness (x) within the scleral canal with scleral tensile forces acting on the scleral canal wall (arrows). (B) Early IOP-related damage in the monkey eye (Fig. 8) includes posterior bowing of the lamina and pp-sclera accompanied by scleral canal expansion (mostly within the posterior (outer) scleral portion), thickening (not thinning) of the lamina, (y) and outward migration of the laminar insertion from the sclera into the pia mater (not depicted here but seen in Fig. 5). (C) Progression to end-stage damage is thus along and within the canal wall, and includes profound scleral canal wall expansion (clinical excavation), and posterior deformation and thinning of the lamina (z). Reprinted from Yang et al.83 with permission from the Association for Research in Vision and Ophthalmology.

409

Fig. 3. All clinical ONH cupping, regardless of etiology, manifests ‘prelaminar’ and ‘laminar’ components. (A) Normal ONH. To understand the two pathophysiologic components of clinical cupping, start with (B) a representative digital central horizontal section image from a post-mortem 3-D reconstruction of this same eye (white section line in (A)): vitreous top, orbital optic nerve bottom, lamina cribrosa between the sclera and internal limiting membrane (ILM) delineated with green dots. (C) The same section is delineated into principal surfaces and volumes (black: ILM; purple: prelaminar neural and vascular tissue; cyan blue line: BMO-zero reference plane cut in section; green outline: Post-BMO Total Prelaminar area or a measure of the space below BMO and the anterior laminar surface). (D) Regardless of the etiology, clinical cupping can be shallow (E) or deep (F). Clinical photos (B-F) are representative and do not belong to the eye in (A). Reproduced from Yang et al.22 with permission from the Association for Research in Vision and Ophthalmology.

410

H. Yang et al.

is likely along and within the canal wall, and eventually includes profound scleral canal wall expansion (which underlies the clinical phenomenon of ‘excavation’), progressive posterior deformation, and eventual thinning of the lamina. We propose that the defining pathophysiology of a glaucomatous optic neuropathy is the deformation, remodeling, and mechanical failure of the ONH connective tissues described above. These phenomena have yet to be detected in any other human or experimental form optic neuropathy, as discussed in Section 4, below.49 We also propose that the cellular processes that underlie these morphologic connective tissue phenomena not only underlie the clinical appearance and behavior of glaucomatous cupping (i.e., the depth and excavation of the ‘cup’), but they also underlie the classic patterns of RGC axonal injury and visual field loss that define the neuropathy whether it occurs at normal or elevated IOP levels.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. The clinical appearance of cupping in a representative monkey EG (left) and optic nerve transection (ONT) eye. (Left) Representative EG eye at baseline (prior to laser – above) and near the time of euthanasia (below) from an old (16.1 years of age) animal with 58% axon loss at the time of death. (Right) Representative young adult ONT eye (7.8 years old) with 51% axon loss. Both eyes are shown in right eye orientation. In the EG eye, (left panels), note the posterior deformation and early excavation of the central retinal artery and veins as they leave the lamina and cross the clinical disc margin. Early ‘nasalization’ of the vessels and ‘bayoneting’ of the inferior vein as well as diffuse loss of the RNFL striations are also apparent. In the ONT eye, (right panels) diffuse pallor and RNFL loss (41% by OCT) is apparent, as is OCT-detected prelaminar and rim tissue thinning. While the presence of clinical cupping is not obvious, it is suggested by a slight change in the trajectory of the inferior temporal vessels (black arrows). No eye-specific change in anterior LC surface depth was detected by OCT in this eye. Reproduced from Ing et al.44 under the CC BY-NC-ND 4.0 license.

mechanical yield (permanent stretching) combined with mechanical failure (physical disruption) of the laminar beams. We propose that, while its onset may be diffuse, failure occurs focally within the anterior most laminar beam insertions (into the scleral canal wall and border tissues of Elschnig) and spreads to adjacent beams (both circumferentially and by depth within the canal wall), as the load from failed or disrupted beams is shifted to neighboring beams, making them more susceptible to failure. Progression to end-stage damage

3. Experimental evidence of ONH connective tissue deformation, remodeling, and mechanical failure in the monkey EG model 3.1. Background The connective tissue components of glaucomatous cupping in the monkey and human eye have been classically described to include laminar deformation, scleral canal expansion, and progressive laminar thinning.78-81 In a series of publications characterizing early ONH connective tissue change in monkeys with unilateral EG, we described posterior deformation and thickening of the lamina,21,22 accompanied by scleral canal expansion,23 outward bowing of the pp-sclera, 21,22 and outward migration of the laminar insertion into the retrobulbar pial sheath.18 Together, these phenomena suggest that the lamina does not just deform in response to chronic IOP elevation, but ‘remodels’ itself into a new shape in response to its altered biomechanical environment.18,20,55,82 This section summarizes 3-D histomorphometric, OCT, and scleral material property changes within the monkey unilateral EG model.

The connective tissue phenotype of glaucomatous cupping

411

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. Connective tissue deformation, remodeling and mechanical failure in the monkey EG model.49,83 Five morphologic phenomena underlie ONH cupping in monkey (EG): 1. laminar deformation; 2. scleral canal expansion; 3. laminar insertion migration; 4. laminar thickness change; and 5. posterior bowing of the pp-sclera. The following landmarks are delineated within representative superior-temporal (ST) to inferior-nasal (IN) digital sections from the control (left) and EG (right) eye of four representative unilateral EG animals (Monkeys 1, 12, 18, and 21, respectively, from the above study): anterior scleral/laminar surface (white dots), posterior scleral/laminar surface (black dots), neural boundary (green dots), BMO reference plane (red line) and BMO centroid (vertical blue line). For each animal, our parameter Post-BMO Total Prelaminar Volume is outlined in both the Control (light green, left) and EG (light blue) eye for qualitative comparison. EG eye Post-BMO Total Prelaminar Volume expansion is due to the combination of posterior laminar deformation, scleral canal expansion, and outward migration of the anterior laminar insertion. Because it captures three of the five deformation/remodeling phenomena, we use it as a surrogate measure of overall ONH laminar/scleral canal deformation within a given EG eye. Post-BMO Total Prelaminar Volume expansion is present within Monkey 1 and progresses through more advanced stages of connective tissue deformation and remodeling (Monkeys 12, 18, and 21). The phenomena that underlie Post-BMO Total Prelaminar Volume expansion are accompanied by laminar thickening in the EG eyes with the least Post-BMO Total Prelaminar Volume change (Monkeys 1 and 12), thickening that is progressively diminished in magnitude in eyes with moderate Post-BMO Total Prelaminar Volume change (Monkey 18), and laminar thinning in the eyes with the largest Post-BMO Total Prelaminar Volume change (Monkey 21). Outward migration of the laminar insertions from the sclera into the pia is apparent in Monkeys 12, 18, and 21 (blue ovals). Reprinted from Burgoyne 49 with permission from Wolters Kluwer Health, Inc.

3.2. 3-D Histomorphometric evidence to support the five morphologic connective tissue components of glaucomatous cupping83 Our method for 3-D HMRN parameterization of the monkey ONH has been described within a series of previous reports,18,21-24,84-87 and is summarized in detail in a recent book chapter.48 Our parameter Post-BMO Total Prelaminar Volume (light green in Figs. 3 and 5) is defined to be the volume beneath the Bruch’s membrane opening (BMO) zero reference plane, above the LC and within the neural canal wall. We use

EG vs control eye difference in this parameter as a single measure of the overall EG eye connective tissue component of cupping because it captures EG eye laminar deformation, laminar insertion migration, and scleral canal expansion in a single parameter. Figure 5 displays matched digital cross-section images from the control and EG eyes of monkeys spanning the full range of EG vs control eye Post-BMO Total Prelaminar Volume Difference (36% to 578%) present within the 21 EG eyes of a previous report.83 Taken together, these images depict the most consistent

412

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 6. 3-D HMRN Macroarchitectural EG Study — schematic depiction of the global data for the control (solid grey colors) and EG (dotted lines) (ONH) of each animal. Animals are ordered (1-21) by increasing overall ONH connective tissue deformation as characterized by the Post-BMO Total Prelaminar Volume parameter (see Fig. 5). The lamina is consistently thickened in the eyes with the least deformation and consistently thinned in the most profoundly deformed eyes. These changes are accompanied by anterior and posterior laminar insertion migration, scleral canal expansion, and pp-scleral bowing (Fig. 7). The relationship between overall deformation and these related phenomena can be better appreciated within the data plots of these figures. Reproduced from Yang et al.83 with permission from the Association for Research in Vision and Ophthalmology.

components of ONH connective tissue alteration in monkey EG: 1. posterior (outward) laminar deformation; 2. scleral canal expansion; 3. posterior (outward) migration of the anterior lamina insertion (ALI) and posterior laminar insertion (PLI) (from the sclera into the pial sheath); 4. laminar thickness change (increased in most eyes demonstrating the least deformation and less thickened or thinned in most eyes demonstrating the greatest deformation); and 5. posterior (outward) bowing of the pp-sclera and their range.

H. Yang et al.

Fig. 7. EG eye peripapillary scleral posterior bowing achieves its maximum value at moderate levels of Post-BMO Total Prelaminar Volume expansion and is not progressive beyond this point. Hatched color bars represent EG eyes perfusion-fixed at IOPs of 30 or 45 mmHg; solid color bars represent EG eyes perfusion-fixed at 10 mmHg. Asterisks (*) indicate the EG vs control eye difference exceeds the PIDmax for this parameter in this animal. By convention, a positive EG vs control eye difference (red bars) is present when the EG eye peripapillary sclera is more anterior relative to the BMO reference plane of the EG eye than in the control eye (see EG 11 and EG 21 data of Fig. 6). This finding is indirect evidence of posterior peripapillary scleral bowing in the EG eye because, as the sclera bows outward, BMO and its reference plane assume a position that is ‘more posterior to’ the peripapillary sclera. By convention, a negative EG vs control eye difference (blue bar) is present when the EG eye peripapillary sclera is more posterior relative to the BMO reference plane of the EG eye than in the control eye. Only one animal demonstrates this change (Monkey 14). Finally, of all of the connective tissue parameters, Peripapillary Scleral Position may have been most influenced by the level of IOP at the time of fixation. If the hatched bars are removed, the number of eyes demonstrating EG vs control eye differences exceeding 40 um is reduced from five to one (Monkey 21, only). While the large values among the IOP 30 and 45 mmHg may also represent fixed deformation (i.e., we cannot be certain they would be smaller at IOP 10 mmHg), they are compatible with the concept that the range of peripapillary scleral deformation we report may include a reversible component. Reproduced from Yang et al.83 with permission from the Association for Research in Vision and Ophthalmology.

Schematic plots of the global control and EG eye 3-D histomorphometric data for each animal are shown in Figure 5. These plots allow the differences among the 21 control eyes and the full range of EG vs control eye differences among the 21 study animals to be appreciated.

Copyright © 2018. Kugler Publications. All rights reserved.

The connective tissue phenotype of glaucomatous cupping

413

Fig. 8. EG Eye Post-BMO Total Prelaminar Volume expansion (A,B) captures three components of ONH connective tissue change in Monkey EG in a single parameter: 1. posterior laminar deformation (C); 2. scleral canal expansion (D,E); and 3. posterior (outward) migration of ALI (F). Animal order (1-21) for this study was determined by the magnitude of the EG vs control eye Post-BMO Total Prelaminar Volume % difference. Post-BMO Total Prelaminar Volume % difference progressively increases through all 21 EG eyes. While posterior laminar deformation (C) and ALI migration (F) also appear progressive through this range of Post-BMO Total Prelaminar Volume expansion, scleral canal expansion at the level of the anterior scleral canal opening (D) and ALI (E) appear to achieve their maximum values by the magnitude of Post-BMO Total Prelaminar Volume expansion present in Animal 12 (approximately 127%, (B)). Asterisks (*) indicate the EG vs control eye difference exceeds the PIDmax or PIPDmax value for this parameter in this animal. Data are hatched for the 7 animals in which the EG eye was perfusion-fixed at IOP 30 or 45 mmHg, and are solid for the 14 animals in which the EG eye was perfusion-fixed at IOP 10 mmHg. Positive EG vs control eye difference are red, negative are blue. Reproduced from Yang et al.83 with permission from the Association for Research in Vision and Ophthalmology.

Copyright © 2018. Kugler Publications. All rights reserved.

414

H. Yang et al.

Fig. 9. LC thickness alteration in monkey EG. (A-C) Schematic depiction of the lamina in a normal (A), early EG (B), and end stage EG (C) eye. EG vs control eye difference in LC thickness (D), ALI position (E), and PLI position (F) are also shown. While laminar thickness was increased in most EG eyes with early deformation, it was either less thickened or thinned in the most deformed eyes. Anterior (inward) migration of the anterior laminar insertion (E) was present in the two EG eyes with the least deformation. Progressive posterior (outward) migration of the anterior laminar insertion was detected in the 17 EG eyes demonstrating the largest deformation. Posterior laminar insertion migration (F) was outward in early deformation, though its magnitude diminished in moderate deformation, then progressively increased in the EG eyes with the greatest deformation. Hatched color bars in (D-F) represent EG eyes perfusion-fixed at 30 or 45 mmHg and solid color bars represent EG eyes perfusion-fixed at an IOP of 10 mmHg. Asterisks (*) indicate the EG vs control eye difference exceeds the PIDmax for this parameter in this animal. Positive EG vs control eye differences are red, negative are blue. Reprinted from Yang et al.83 with permission from Association for Research in Vision and Ophthalmology.

The connective tissue phenotype of glaucomatous cupping

415

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 10. LMA in early EG — Method overview.87 (Upper two rows) For both the control and EG eye of Animal 11 from the above study, segmented LC with beam and pore diameters assigned to each beam and pore voxel are cylinderized in right eye orientation. The global mean beam diameter (BD), mean pore diameter (PD), Connective Tissue Volume Fraction (CTVF), Connective Tissue Volume (CTV) and Laminar Volume (LV) are reported in white font for each eye on a grey or green scale background (grey and green scales not shown). For all connective tissue and pore parameters, scaling is adjusted so that white suggests more and black suggests less connective tissue. LV is depicted in green because it is not solely related to connective tissue. (Middle row) Global EG vs control eye differences in each parameter are reported in black font on a red (increased) or blue (decreased) background (color scales not shown). Asterisks (*) denote that the EG versus control eye difference for this parameter exceeds the PIPDmax for that parameter as determined by six bilateral normal animals.87 An additional analysis considers EG versus control eye comparisons that are confined to the inner-third, middle-third, and outer-third LC layers (not shown). (Bottom row) BD and PD frequency data are fitted with Gamma distribution to more robustly assess if there is a shape or scale change in the distribution of beam and pore diameters within the EG compared to the Control eye of each animal. Reproduced from Reynaud et al.87 under the CC BY-NC-ND 4.0 license.

Figure 7 depicts the range of animal-specific, Post-BMO Total Prelaminar Volume change within all 21 EG eyes. Laminar position change, anterior scleral canal opening expansion and ALI expansion and migration are plotted relative to it. These data together illustrate how EG vs control eye Post-BMO Total Prelaminar Volume Difference incorporates each of these phenomena, and in so doing serves as a surrogate of overall connective tissue deformation.

Figure 9 depicts the range of laminar thickness parameter alteration. It is clear that animal specific changes in laminar thickness were bimodal, being: 1. significantly thickened in 11 of the 15 EG eyes demonstrating 36% to 240% EG eye expansions in Post-BMO Total Prelaminar Volume (Animals 1 –15); 2. less thickened in animals demonstrating from 241 to 279% EG eye expansions in Post-BMO Total

Copyright © 2018. Kugler Publications. All rights reserved.

416

Prelaminar Volume; and 3. significantly thinned in two of the three animals demonstrating the greatest overall deformations. These data suggest that while the lamina was thickened in most eyes with minimal and moderate deformation, it was less thickened and then thinned in the most deformed eyes. It also suggests that the transition from (mostly) thickened to less thickened and then thinned in the 21 monkeys of this report appears to have occurred at or around overall deformations yielding EG eye Post-BMO Total Prelaminar Volume expansions of 240%. Significant anterior (inward migration of the ALI, Fig 9E) was present in the two EG eyes with the least global deformation as characterized by Post-BMO Total Prelaminar Volume Change. Progressively larger posterior migration of the ALI was detected in the 16 EG eyes demonstrating the largest global deformation. PLI migration was detected in 17 of 21 EG eyes, and was progressively outward, although this occurred in an early diminishing (Monkeys 1-6) and later increasing (Monkeys 7- 21) manner. Outward bowing of the peripapillary sclera, detected as significant increases in the parameter pp-scleral Position (Fig. 7), was present in 11 EG eyes, with a 12th demonstrating a significant decrease. Similar to scleral canal expansion, outward bowing of the pp-sclera was not progressive through the full range of overall deformation, achieving its maximum value in eyes with early levels of Post-BMO Total Prelaminar Volume expansion. These cross-sectional findings are important for two reasons. First, they suggest that a single volumetric parameter like Post-BMO Total Prelaminar Volume (Figs. 5 and 8) may, by itself or by its change over time, provide a measure that orders overall laminar/scleral connective tissue deformation and remodeling, and in so doing allows for its staging and phenotyping in glaucoma. Second, they identify the principal components of connective tissue alteration that allows for their respective mechanisms and links to RGC axonal insult to be the subject of future studies. We have previously proposed that laminar thickness change as well as ALI and PLI migration are separate manifestations of glaucomatous ONH connective tissue remodeling and/or mechanical failure.18,55 Previous

H. Yang et al.

finite element (FE) modeling88 has predicted that the lamina should thicken in response to elevated IOP, that its anterior insertion should migrate anteriorly, and that its posterior insertion should migrate posteriorly as part of this process. The fact that the two EG eyes with the least amount of overall deformation (Monkeys 1 and 2) demonstrate inward ALI migration, suggests that inward migration of the ALI represents an initial stage of connective tissue remodeling.88 These data also suggest, but do not prove, that as global ONH connective tissue deformation increases, inward ALI migration transitions to outward migration that is subsequently progressive. The longitudinal detection of ALI migration89 is therefore important for two reasons. First, using current OCT imaging, it may be linked to nerve fiber layer (NFL) hemorrhages,90 NFL defects,91 visual field progression,92 and the development of acquired optic disc pits.93 Second, it may confirm the relative timing of its direction (i.e., inward during initial deformation, outward as deformation progresses) suggested by our cross-sectional findings. Regarding PLI migration, we propose that outward PLI migration is a prominent component of laminar remodeling in response to chronic IOP elevation in the monkey eye. While it is possible that ALI and PLI migrations are completely independent, it is also possible that outward ALI migration contributes to the mechanisms driving outward PLI remodeling. In this regard, the suggestion in our data that outward migration of the PLI occurs in an initial phase that diminishes and is followed by a phase that progressively increases, may reflect a transition from ALI and PLI remodeling that stabilizes the insertions to PLI remodeling that is driven by outward migration of the ALI. 3.3. LC pores increase and beams both increase and decrease in early monkey EG85,87 Our method for quantifying laminar microarchitecture (LMA) has been described in previous publications,85,87,94 and is schematically depicted in Figure 10. EG vs control eye differences and percentage differences for beam diameter (BD), pore diameter (PD), Connective Tissue Volume Fraction (CTVF), Connective Tissue Volume (CTV), and Laminar Volume (LV) are generated for each animal. Animal-specific EG vs control eye differences are compared with the maximum value of the Physiologic

The connective tissue phenotype of glaucomatous cupping

417

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 11. LMA in early EG — Frequency and direction of animal-specific LMA parameter change by depth.87 The total number of animals demonstrating EG versus control eye increases (red) and decreases (blue) exceeding the PIPDmax for each parameter are reported. (Lower three rows) Similar data for the inner, middle, and outer LC layers are reported. Reproduced from Reynaud et al.87 under the CC BY-NC-ND 4.0 license.

Inter-eye Percent Difference (PIPD) within bilateral normal animals to determine significance. A gamma distribution function95 is used to fit the frequency data of the BD and PD voxels in each eye to generate distribution parameters which were used to compare overall EG vs control eye distribution differences. By distribution analysis, pores were on average 17% larger in the EG eyes, with this increase being consistent across all pore diameters. EG vs control eye differences in BD shape, scale, estimated mean, and estimated standard deviation did not achieve significance (all p > 0.05, paired t-test). Figure 11 graphically summarizes animal-specific EG vs control eye difference data for each LMA parameter both by full-thickness and laminar depth. EG eye BD was significantly larger than the control eye (14.1% and 16.5%, respectively) in two animals, and significantly smaller (10.4%–31.5%) in three animals, while PD was significantly larger (17.1%–37.6%) in six animals and decreased in none. In addition, CTVF was significantly smaller in one animal (–32.8%), while CTV was significantly larger in eight animals (20.7%–127.9%) and significantly smaller in one animal (–22.4%). LV was increased (15.4%–145.5%) in 10 of the 14 EG animals. 3.4. Implications of early LMA change in monkey EG LMA alterations in early monkey EG are important for several reasons. First, it has been shown that the LC is a site of axonal transport and flow blockade at all

levels of IOP in the normal and glaucomatous monkey eye.28,29,96,97 Second, the LC and pp-sclera are the major load-bearing connective tissue of the ONH, and the combination of their micro/macro-architecture and material properties determine their respective structural stiffness, macroscopic behavior, and the microscopic distribution of IOP-related stress and strain within their tissues.71,98,99 Each of these bioengineering phenomena likely generate primary and secondary effects on the connective tissues, contained blood vessels (and their autoregulation), and their constituent cells (activation, proliferation, migration, phagocytosis) that contribute to the mechanisms of axonal insult. Figure 12 depicts our hypotheses regarding the factors influencing EG eye-specific, LMA parameter change. We propose that these factors do so through their contributions to two principal determinants of ONH connective tissue homeostasis: 1. how much the ONH connective tissues deform in the setting of an acute or sub-acute change in the translaminar pressure difference (more specifically, the magnitude of macroscopic connective tissue deformation and associated microscopic tissue strain that is generated); and 2. how robust and/or protective is the cellular response elicited by a given amount of tissue strain. Animal age (or cellular senescence and connective tissue stiffness at all ages) and the magnitude of IOP insult

418

Copyright © 2018. Kugler Publications. All rights reserved.

may independently influence both the magnitude of deformation and the character of the connective tissue response (ranging from no response, to synthesis, to remodeling, to degradation, or some combination thereof). For a given ONH, the magnitude of deformation as well as the magnitude of connective tissue synthesis and remodeling govern the character of detected post-mortem EG vs control eye differences in LC microarchitecture. In the absence of any active connective tissue response, LC deformation alone should result in passive thinning of the LC beams and passive expansion of the pores. Once deformed, mechanoreceptors within LC beam fibroblasts and astrocytes should drive connective tissue synthesis and remodeling. From a beam that was acutely thinned due to deformation, if beam synthesis leads to a return to pre-deformation beam diameter, there will be no detected EG vs control eye BD difference — yet the number of connective tissue voxels will have increased (as seen in our data by increases in CTV). Beyond synthesis alone, where there is connective tissue remodeling and recruitment, there may be increases or decreases in the number of detected connective tissue voxels. Finally, where connective tissue synthesis and remodeling are not adequate, mechanical failure and connective tissue degradation may ensue, leading to a reduction in detected connective tissue voxels. Where beams have disappeared, pore enlargement that is not due to passive pore expansion may be detected. 3.5. Laminar insertion migration in early monkey EG appears to include remodeling of the retrolaminar orbital septa20 One aspect of the increase in laminar thickness as well as the profound increases in LV and CTV, without detectible increases in BD reported in Section 3.3. above, appears to be the addition of new laminar beams.20 Downs, Roberts and colleagues20 hypothesized that recruitment of the longitudinally oriented retrolaminar optic nerve septa into more transversely oriented structures may occur.20 Laminar segmentations from both eyes of three early EG animals underwent a post-hoc analysis in the Downs laboratory to estimate the number of laminar beams aligned in the plane of the LC of each eye. When comparing the number of laminar beam intercepts within the EG vs control eye of each animal, the mean

H. Yang et al.

number of laminar beams through the thickness of the LC was greater (46%, 18%, and 17%, respectively in the three EG eyes). While these data support the hypothesis that prelaminar or retrolaminar septa are ‘recruited’ or ‘remodeled into’ transverse, load-bearing, lamina-like beams, this method could not determine the location of the ‘new’ beams (i.e., if they were ‘added’ to the anterior or posterior surface of the pre-laser LC). 3.6. Implications of laminar insertion migration and retrolaminar septal recruitment Previous modeling studies by Grytz et al.88 predicted the lamina should add new beams both anteriorly and posteriorly as part of its early remodeling response. The strong 3-D histomorphometric evidence for outward (posterior) migration of both the ALI and PLI in early EG suggests that, if recruitment of the prelaminar glial column connective tissues occurs, these new beams are themselves either quickly remodeled away or undergo mechanical failure and dissolution. While both laminar insertion migration18 and mean intercept length analyses20 support retrolaminar septal recruitment, they do not prove that it is the sole form of laminar beam remodeling. Interestingly, Hayreh and co-workers reported retrolaminar fibrosis in the monkey model of EG.100 This observation is compatible with retrolaminar septal recruitment, although Hayreh made no comment about the orientation of beams or their insertion into the pia, and the animals in his study were at a more advanced stage of glaucomatous damage. It is reasonable to believe that the presence of retrolaminar septal recruitment and remodeling would increase the homeostatic demands on the retrolaminar astrocytes, microglia, and oligodendrocytes, and in so doing, contribute to early RGC axon injury. In two recent papers, collaborative work from the Marsh-Armstrong and Ellisman laboratories30,101 has shown that myelin transition zone astrocytes phagocytose myelin and RGC axonal mitochondria within the myelin transition zone (immediately behind the cellular lamina of the mouse eye) as part of the support they provide to the RGC axons. We have shown proteomic102 and immunohistochemistry (IHC) data (Fig. 13)103 that suggest expression of myelin-related proteins is decreased within the retrolaminar optic nerve in early monkey EG. We are actively studying the contribution of myelin

The connective tissue phenotype of glaucomatous cupping

419

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 12. Post-mortem EG vs control eye differences in LMA reflect both passive connective tissue deformation (vertical axis) and active connective tissue synthesis, remodeling, and mechanical failure (horizontal axis).87 For a given ONH, the magnitude of deformation (increasing up) and the magnitude of connective tissue synthesis and remodeling (increasing to the right) govern the character of detected post-mortem EG versus control eye differences in LC microarchitecture. Animal age (as a surrogate for stiff vs compliant tissues, and/or senescent vs robust cells at any age) and the magnitude of IOP insult (both bottom left and upper right) independently influence both the magnitude of deformation and the character of the connective tissue response. IOP: intraocular pressure; PD: pore diameter; BD: beam diameter; CTV: connective tissue volume; LV: LC volume; ECM: extracellular matrix; NC: no (detectable) change. Reproduced from Reynaud et al.87 under the CC BY-NC-ND 4.0 license.

Fig.13. ONH connective tissue deformation and remodeling is accompanied by decreased retrolaminar myelin basic protein (MBP) immunohistochemistry (IHC) signal (right) early in the optic neuropathy of monkey EG. (Left) 3-D histomorphometric section images from the same four early-to-end stage glaucoma monkeys83 depicted in Figure 5, are used here to depict the extent of connective tissue deformation and remodeling throughout early-to-end-stage monkey EG. In early EG, the lamina thickens in part because of new connective tissue synthesis,87 but also because retrolaminar orbital septa are ‘remodeled’ into ‘new’ posterior laminar beams in a process called ‘retrolaminar septal recruitment’.20 It is thus in the outer lamina and retrolaminar myelin transition zone that the cell biology of connective tissue remodeling and myelin remodeling should overlap. (Middle and right) Polarized (above) and red fluorescent IHC images of the same section (below) for MBP demonstrate decreased EG eye retrolaminar optic nerve signal density (lower right) vs its control eye in a monkey with 1.7% post-mortem EG eye axon loss. Red lines: BMO reference plane. Green lines: BMO in the polarized and red light image of the same section. Green arrows: LC. A total of eight myelin-related proteins demonstrate lower EG eye expression within the proteomics data. Retrolaminar EG eye decreased expression of three myelin-related proteins has been confirmed by quantitative IHC.

420

H. Yang et al.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 14. Differences in ONH connective tissue structural stiffness and/or remodeling may underlie ‘deep’ (left) and ‘shallow’ (right) forms of glaucomatous cupping in monkeys and humans. OCT ONH B-scans from the same location (green, lower left) from the EG eye of a young (left) and old (right) monkey when the eye was normal (upper), at the second confirmation of CSLT detection of ONH surface change in the young eye (lower left), and at the (later) pre-sacrifice data set in the old eye (lower right). All images were obtained after 30 minutes of manometer controlled IOP (10 mm Hg). In both eyes, while prelaminar neural tissue thickness alterations are present, laminar deformation is also apparent as an increase in the magnitude of space between the BMO reference plane (red line) and the anterior LC surface (gold dots). Laminar deformation in the old eye is far less than in the young eye, and this profound difference in laminar deformation occurred in the setting of a cumulative IOP insult that was approximately five times greater in the old eye. Reproduced from Yang et al.107 with permission from the Association for Research in Vision and Ophthalmology.

Fig. 15. Box plots representing distributions (median, interquartile range, and extremes) of EG (red) and control eye (blue) acute compliance at EG onset for all OCT neural (A) and connective tissue (B) parameters.108 See Section 3.7 for details. (A) The scale extends from –75 to 25 μm across all neural tissue parameters and from –250 to 50 μm across all (B) connective tissue parameters. EG eyes that fall outside the range of control eye parameters are shown as filled red circles; whereas EG eyes that are within the range of control eye parameters are shown as empty red circles (some circles overlap and appear as one). Eye-specific hypercompliance in EG eyes occurred in MRW (3 of 15 eyes), prelaminar tissue thickness (PLTT) (2 of 15 eyes), ALCSD-BM (8 of 15 eyes), ALCSD-BMO (9 of 15 eyes), and BMOD-BM (4 of 15 eyes). An eye-specific decrease in compliance in EG eyes was seen in MRW (two eyes), RNFLT (two eyes), ALCSD-BM (two eyes), and BMOD-BM (one eye). Reproduced from Ivers et al.108 under the CC BY-NC-ND 4.0 license.

Copyright © 2018. Kugler Publications. All rights reserved.

The connective tissue phenotype of glaucomatous cupping

421

homeostasis to the mechanisms of axonal injury in early monkey EG.

and anterior ischemic optic neuropathy (AION),106 which are discussed in Section 4.

3.7. Longitudinal detection of laminar deformation by OCT precedes retinal nerve fiber alteration in early monkey EG104 If ONH connective tissue deformation and remodeling is a defining pathophysiology of glaucomatous damage to the visual system, can we use longitudinal OCT imaging to detect it, and if so, when is it detectable relative to OCT-detected RNFL thickness (RNFLT) change? We previously reported the presence of OCT-detected deep ONH change at the time of confocal scanning laser tomography (CSLT) ONH surface change within the pre-sacrifice OCT data sets of nine rhesus macaque monkeys with chronic, laser-induced, unilateral IOP elevations.105 In a follow-up study, both eyes from four young and four old monkeys were tested three times at baseline, and then every two weeks following laser-induced, chronic unilateral IOP elevation until CSLT-detected ONH surface change was detected and confirmed on two subsequent occasions, at which point each animal was sacrificed.104 For both event- and trend-based analyses, onsets were achieved earliest and most frequently within the ONH neural and connective tissues using OCT and at the ONH surface using CSLT. OCT and Scanning laser polarimetry measures of RNFLT and multi-focal electroretinogram (mf-ERG) measures of visual function demonstrated similar onset rates, but occurred later than OCT ONH and CSLT surface change and in fewer eyes. Thus, the conversion from experimental ocular hypertension to glaucomatous damage to the monkey visual system within the EG eyes of these eight animals was detected earliest, most frequently, and with the greatest specificity within the ONH neural and deep connective tissues using OCT. These data contribute to the growing body of evidence that suggests that the ONH is a primary site of early insult to the visual system in glaucoma.27,55 In addition, they confirm that early glaucomatous damage to the monkey ONH includes both neural and connective tissue components.22,84 This finding is important because it identifies OCT-detectable ONH connective tissue endpoints for other monkey experimental optic neuropathy models, including chronic experimental CSFp lowering,41 endothelin,44 optic nerve transection,44

3.8. Age effects on OCT-detected laminar deformation in early monkey EG107 Deep and shallow forms of human glaucomatous cupping occur at all ages and IOP levels, but are classically seen in young and elderly eyes, respectively. (Fig. 14) We have proposed that the ONH connective tissues ‘harden’ with age and that, on average, aged eyes should demonstrate a shallower form of cupping (i.e., a shallower ‘phenotype’) as a result. Eye-specific differences in structural stiffness and/or remodeling, regardless of age, should contribute to the glaucomatous phenotype expressed by an individual eye (Fig. 14).54 In a follow-up study on the four young and four old animals studied in Section 3.5.,107 we analyzed the same longitudinal OCT data sets to test the hypothesis that OCT-detected ONH structural change was greater in the four young as compared with the four old monkey EG eyes at similar post-laser time intervals, similar levels of post-laser cumulative IOP insult, and at the onset of CSLT ONH surface change. In these four young and four old animals, the magnitude of OCT ONH parameter change was greater in the young compared to the old eyes both at the point of CSLT-detected ONH surface change and also when measured as continuous variables relative to post-laser time (in days) and post-laser cumulative IOP insult (in mmHg x days). These data support the concept that age-related differences in ONH connective tissue structural stiffness and/or remodeling may contribute to age-related differences in the appearance of early glaucomatous cupping in a given eye. 3.9. Longitudinal OCT detection of laminar hypercompliance in early monkey EG108 We have previously used simultaneous videography,109,110 CSLT ONH surface imaging,111 post-mortem histology,25,52 and 3-D HMRN19,112 to study ONH compliance in response to acute IOP elevation in monkey control and EG eyes. These studies indirectly suggested laminar and pp-scleral hypercompliance were present at the onset of monkey EG; however, each study was either not specific to the LC,109-111 or was post-mortem, and therefore could not separate ‘fixed deformation’ from ‘acute compliance’ within each individual study eye.19,25

Copyright © 2018. Kugler Publications. All rights reserved.

422

In a recent study, we used in-vivo OCT imaging to compare the EG vs fellow control eye ONH morphology change following acute IOP elevation from 10 to 30 mmHg in both eyes of 15 monkeys at the onset of unilateral EG (EG onset).108 IOP was chronically elevated in one eye of each animal using a laser. EG onset was identified using CSLT. OCT ONH imaging (40 radial B-scans) was performed at 10 mmHg prior to (pre) and following (post) laser. At EG onset, OCT scans were obtained at IOPs of 10 and 30 mmHg. OCT landmarks within both the 10 mmHg IOP and 30 mmHg IOP OCT data sets were delineated to quantify IOP 10/30 differences (compliance) for the following OCT parameters: ALCSD-BMO, ALCSD relative to peripheral BM (ALCSD-BM), and BMO depth relative to peripheral BM (BMOD-BM). The effect of elevating IOP from 10 to 30 mmHg was greater in EG vs control eyes for ALCSD-BMO (–46 ± 45 μm vs. –8 ± 13 μm, P = 0.0042) and ALCSD-BM (–92 ± 64 μm vs –42 ± 22 μm, P = 0.0075) within linear mixed effects models. EG eye-specific ALCSD-BMO and ALCSD-BM compliance exceeded the range of control eye compliance in 9 and 8 of the 15 EG eyes, respectively. Figure 15 reports similar distribution data for each neural and connective tissue parameter. Figure 18 schematically depicts EG eye acute compliance that exceeds control eye acute compliance in the study animal demonstrating the greatest amount of EG eye acute compliance. In this study, OCT compliance testing detected tissue deformation, not structural stiffness. Using in-vivo OCT ONH imaging to detect ONH connective tissue hypercompliance at the onset of monkey EG is important for two reasons. First, it is a likely manifestation of underlying ONH connective tissue remodeling, failed remodeling, or mechanical failure,83 suggesting it may be a biomarker for the presence of these processes, and therefore, a means of identifying underlying mechanisms and treatment interventions in future studies. Second, if present and detectable in human ocular hypertensive patients, it may be evidence of an early connective tissue response to the level of mechanical stress and strain they are experiencing, which precedes and/ or predicts subsequent RGC injury and loss. In this context, it might represent a structural precursor not only to functional loss, but also to clinically-significant structural involvement of the neural tissues.

H. Yang et al.

3.10. Hypercompliance and stiffening of the peripapillary and posterior sclera in early monkey EG by material property testing99,113 Downs and co-workers described early alterations in the biomechanical properties of the pp-sclera in early monkey EG using uniaxial testing and linear viscoelastic theory.77 That study demonstrated a significant increase in the equilibrium modulus of the pp-sclera from glaucomatous monkey eyes, but no changes were seen in the time-dependent viscoelastic parameters. Girard, working in Downs’ laboratory, developed an ex-vivo method to experimentally measure the 3-D deformation pattern and thickness of the posterior sclera and used it to study eyes of four young and four old bilaterally normal monkeys following IOP elevation from 5 to 45 mm Hg.99,114 Their results showed that the posterior and pp-sclera in old monkeys was significantly stiffer than that from young monkeys, and is therefore subject to higher stress but lower strain at all levels of IOP. Girard and Downs113 then used the same techniques99,114,115 to characterize peripapillary and posterior scleral biomechanics in both eyes of eight adult monkeys in which one eye had been exposed to chronic, laser-induced IOP elevations of modest to substantial magnitude and duration. They found that for all EG and control eyes, the posterior sclera exhibited inhomogeneous, anisotropic, non-linear biomechanical behavior. Changes caused by chronic IOP elevation in the EG eyes were complex and eye-specific. They concluded that stiffening of the sclera follows exposure to moderate levels of chronic experimental IOP elevation in the majority of monkey eyes. However, scleral hypercompliance may precede stiffening or be a unique response to minimal levels of chronic experimental IOP elevation in some monkey eyes. We have separately shown that posterior (outward) bowing of the pp-sclera is a principal component of ONH cupping in the monkey EG model by 3-D histomorphometry (Fig. 7). We have additionally demonstrated that bowing occurs early in the neuropathy within longitudinal post-laser OCT imaging (Section 3.7.) and is eventually accompanied by OCT-detected laminar and pp-scleral hypercompliance, as measured following acute, manometer-controlled IOP elevations from 10 to 30 mmHg (Section 3.9.). Taken together, the data summarized herein strongly support the importance

Copyright © 2018. Kugler Publications. All rights reserved.

The connective tissue phenotype of glaucomatous cupping

423

Fig. 16. EG eye acute compliance (left) far exceeds control eye acute compliance (right) in the animal that demonstrates the greatest EG eye acute compliance.108 Delineated structures within IOP 10 (A,F) and IOP 30 mmHg (B, G) OCT data sets of the EG (left) and control (right) eyes of Animal 15 in the above study. Insets in these panels are en-face views of the delineated BMO and ALCS points of each data set. In (C) and (H), the IOP 10 and IOP 30 OCT data sets have been overlaid by anchoring them to their shared BMO reference plane, shown in red. In (D) and (I), the same IOP 10 and IOP 30 OCT data sets have been overlaid by anchoring them to their shared BM-based reference plane, shown in blue. Note that posterior deformation of the IOP 30 ALCS (yellow dots) is present relative to the IOP 10 ALCS (off-white dots in C), and this deformation is larger in (D) because it also includes posterior deformation of BM relative to its reference plane (blue line). No adjustments to z-axis magnification have been made to these images. Magnified views of (D) and (I) are shown in (E) and (J), absent the internal limiting membrane (ILM, green) so as to make the laminar and pp-scleral deformation components more apparent. The structures shown are the ILM, (green), BM (orange), BMO (red points), and ALCS (yellow points). To differentiate the structures in the overlaid images, the colors at 10 mmHg have been washed out. The EG eye of this animal demonstrates the largest magnitude of EG vs control eye difference in ALCSD-BM acute compliance, which was the measure used to rank the animals 1-15 (–136.6 μm). It also demonstrated the largest magnitude of EG vs control eye difference in BMOD-BM (–44.8 μm), and ALCSD-BMO (–137.6 μm). It therefore demonstrates the greatest magnitude of ONH laminar and pp-scleral connective tissue hypercompliance among the 15 EG eyes. Reproduced from Ivers et al.108 under the CC BY-NC-ND 4.0 license.

424

of the pp-sclera in the optic neuropathy of glaucoma in the monkey and human eye.

Copyright © 2018. Kugler Publications. All rights reserved.

4. Phenotyping the optic neuropathy of glaucoma in the monkey and human eye should include the ONH connective tissues Monkey models for unilateral AION,106,116 optic nerve transection,44,117,118 and chronic optic nerve endothelin exposure,44,119-121 as well as bilateral optic neuropathy following primary CSFp lowering,41 have been described. Of these, the neuropathies in the AION and optic nerve transection models both demonstrate mild (transection) to profound (AION) disc swelling followed by diffuse pallor without evident ‘cupping’. In a longitudinal OCT study in five unilaterally transected monkeys, we report anterior rather than posterior laminar deformation within weekly, OCT data sets acquired through the first 60 days post-transection (Fig. 17).44 However, thinning of the RNFL and prelaminar rim tissue was profound, strongly supporting the concept that ‘prelaminar’ or ‘shallow’ forms of cupping can be present in non-glaucomatous optic neuropathies, due to prelaminar and rim tissue thinning that is not accompanied by laminar deformation and remodeling. In the implanted endothelin pump model of unilateral optic nerve vasoconstriction, after preliminary studies in rabbits,122,123 optic nerve blood flow reduction in monkeys was characterized121 and localized optic nerve axon loss in the setting of diffuse RNFL loss with shallow cupping was reported in a subset of 12 monkeys.119 Chauhan then reported optic nerve axon and RGC loss, but infrequent (1 of 21 eyes) ONH topographic change, in the rat endothelin optic neuropathy model.42 In a later study in five rhesus macaques unilaterally implanted with endothelin pumps and followed for 1.5 years,46 no significant changes in ONH morphology or ONH blood flow velocity were detected by CSLT and laser Doppler flowmetry, respectively. In that study, optic nerve axon counts were not significantly decreased in the endothelin treated eyes. Yang and co-authors recently reported diffuse RNFL and optic nerve rim thinning in two of four monkeys following primary surgical CSFp lowering.41 A third monkey demonstrated a single nerve fiber hemorrhage

H. Yang et al.

but no other change. While quantitative assessment was not reported, no qualitative evidence of laminar deformation was present within the published OCT images. Subsequent unpublished quantification has confirmed that there was no OCT-detected laminar deformation within the four studied animals (personal communication, Ningli Wang). While the appearance of this neuropathy is not glaucomatous by the criteria suggested above, the model is important because it demonstrates that primary CSFp lowering at normal levels of IOP is a risk factor for RGC axon loss in a subset of monkey eyes. It therefore also suggests that in a given eye, a relative increase in the translaminar pressure gradient (by whatever cause) may be a risk factor for RGC axon loss at all levels of IOP. However, the fact that primary CSFp lowering in these eyes did not result in laminar deformation and remodeling is also important. It supports the notion that scleral tensile effects on the lamina even at normal levels of IOP, likely exceed the direct effects of the increased translaminar pressure difference on the lamina that results from CSFp lowering. As noted above, there are no experimental models of a glaucomatous optic neuropathy that do not require IOP elevation (i.e., normal-tension glaucoma models) in the monkey or any other species. Those that have so far been suggested have either presented no characterization of the ONH phenotype,43,45 or have been shown to possess an ONH phenotype that is non-glaucomatous.41,46 Creating a normal-tension glaucoma model remains an important research target for our field because it will provide insight into how a primary, non-IOP-related insult, such as inflammation124,125 or autoimmunity,126 can influence the physiology of the ONH tissues in such a way that the connective tissues become susceptible to deformation and remodeling at normal levels of IOPrelated stress and strain. The data summarized in this report emphasize the importance of ONH connective tissue deformation and remodeling to the phenotype of glaucoma in the monkey eye. The models of primary CSFp lowering and optic nerve transection, as well as clinical experience with peripheral retinal photocoagulation in humans, tell us that primary insult to the RGC soma and axons outside of the ONH (retinal photocoagulation and optic nerve transection) or within it (CSFp) leads to a pale optic nerve that is non-glaucomatous in appearance and behaviour.

Copyright © 2018. Kugler Publications. All rights reserved.

The connective tissue phenotype of glaucomatous cupping

425

Fig. 17. Representative baseline (left) and pre-euthanasia (right) radial B-scans from the ONT (upper) and control eyes (lower) of five unilateral ONT monkeys.44 Scanning laser ophthalmoscopy image (left) showing radial B-scan location in each eye (green line). Within each baseline and pre-euthanasia radial B-scan, the following landmarks are delineated: ILM (green line); BMO reference plane (red line); and the ALCS (yellow dots). ONT-eye RNFLT (white arrows) is markedly thinned within the pre-euthanasia compared to the baseline B-scans, while control eye RNFLT remains unchanged in all animals. ONT-eye ALCS position relative to the BMO reference plane remains unchanged in M1 and M2 (and moves anteriorly in M3, M4, and M5), while laminar position remains unchanged in all control eyes. Reproduced from Ing et al.44 under the CC BY-NC-ND 4.0 license.

426

5. Acknowledgements and disclosures The text and figures of this chapter have been taken directly from our recently published review article,50 which contains portions of the figures from publications in which Dr. Burgoyne is the senior author.44,83,85,87,102 For figures, this is stated clearly in the legend. For text, the original manuscript is cited. The work reported herein has been supported in part by US Public Health Service grants R01EY011610 (Claude F. Burgoyne) and R01EY021281 (Claude F. Burgoyne) from the National Eye Institute, National Institutes of Health, Bethesda,

References

Copyright © 2018. Kugler Publications. All rights reserved.

1.

Janssen P, Naskar R, Moore S, Thanos S, Thiel HJ. Evidence for glaucoma-induced horizontal cell alterations in the human retina. Ger J Ophthalmol. 1996;5(6):378-385. 2. Nork TM, Ver Hoeve JN, Poulsen GL, et al. Swelling and loss of photoreceptors in chronic human and experimental glaucomas. Arch Ophthalmol. 2000;118(2):235-245. 3. Kendell KR., Quigley HA, Kerrigan LA, Pease ME, Quigley EN. Primary open-angle glaucoma is not associated with photoreceptor loss. Invest Ophthalmol Vis Sci. 1995;36(1):200-205. 4. Panda S, Jonas JB. Decreased photoreceptor count in human eyes with secondary angle-closure glaucoma. Invest Ophthalmol Vis Sci.1992;33(8):2532-2536. 5. Wygnanski T, Desatnik H, Quigley HA, Glovinsky Y. Comparison of ganglion cell loss and cone loss in experimental glaucoma. Am J Ophthalmol.1995;120(2):184-189. 6. Quigley HA. Ganglion cell death in glaucoma: pathology recapitulates ontogeny. Aust N Z J Ophthalmol. 1995;23(2):85-91. 7. Quigley HA, McKinnon SJ, Zack DJ, et al. Retrograde axonal transport of BDNF in retinal ganglion cells is blocked by acute IOP elevation in rats. Invest Ophthalmol Vis Sci.200;41(11):34603466. 8. Weber, AJ, Kaufman PL, Hubbard WC. Morphology of single ganglion cells in the glaucomatous primate retina. Invest. Ophthalmol. Vis. Sci. 1998;39(12):2304-2320. 9. Quigley HA, Nickells RW, Kerrigan LA, Pease ME, Thibault DJ, Zack DJ. Retinal ganglion cell death in experimental glaucoma and after axotomy occurs by apoptosis. Invest Ophthalmol Vis Sci. 1995;36(5):774-786. 10. Garcia-Valenzuela E, Shareef S, Walsh J, Sharma SC. Programmed cell death of retinal ganglion cells during experimental glaucoma. Exp Eye Res. 1995;61(1):33-44. 11. Asai T, Katsumori N, Mizokami K. [Retinal ganglion cell damage in human glaucoma. 2. Studies on damage pattern]. Nihon Ganka Gakkai Zasshi. 1987;91(12):1204-1213.

H. Yang et al.

MD, USA; a grant from the American Health Assistance Foundation, Rockville, MD, USA (Claude F. Burgoyne); a grant from The Whitaker Foundation, Arlington, VA, USA (Claude F. Burgoyne); a grant from Research to Prevent Blindness, Inc. New York, NY, USA (Claude F. Burgoyne); The Legacy Good Samaritan Foundation, Portland, OR, USA; and the Sears Trust for Biomedical Research, Mexico, MO, USA. Finally the authors would like to thank Joanne Couchman for her dedicated assistance in editing and submitting this manuscript.

12. Crish SD, Sappington RM, Inman DM, Horn PJ, Calkins DJ. (). Distal axonopathy with structural persistence in glaucomatous neurodegeneration. Proc Natl Acad Sci U S A. 2010;107(11):51965201. 13. Crish SD, Dapper JD, MacNamee SE, et al. Failure of axonal transport induces a spatially coincident increase in astrocyte BDNF prior to synapse loss in a central target. Neuroscience. 2013;229:55-70. 14. Crish SD, Calkins DJ. Central visual pathways in glaucoma: evidence for distal mechanisms of neuronal self-repair. J Neuroophthalmol. 2015;35 Suppl 1:S29-37. 15. Yucel YH, Zhang Q, Gupta N, Kaufman PL Weinreb, R. N. (2000). Loss of neurons in magnocellular and parvocellular layers of the lateral geniculate nucleus in glaucoma. Arch Ophthalmol 118(3):378-384. 16. Yucel, YH, Zhang Q, Weinreb RN, Kaufman PL, Gupta N. Atrophy of relay neurons in magno- and parvocellular layers in the lateral geniculate nucleus in experimental glaucoma. Invest Ophthalmol Vis Sci. 2001;42(13):3216-3222. 17. Yucel YH, Zhang Q, Weinreb RN, Kaufman PL, Gupta N. Effects of retinal ganglion cell loss on magno-, parvo-, koniocellular pathways in the lateral geniculate nucleus and visual cortex in glaucoma. Prog Retin Eye Res. 2003;22(4):465-481. 18. Yang H, Williams G, Downs JC, et al. Posterior (outward) migration of the lamina cribrosa and early cupping in monkey experimental glaucoma. Invest Ophthalmol Vis Sci. 2011;52(10):71097121. 19. Yang H, Thompson H, Roberts MD, Sigal IA, Downs JC, Burgoyne CF. Deformation of the early glaucomatous monkey optic nerve head connective tissue after acute IOP elevation in 3-D histomorphometric reconstructions. Invest Ophthalmol Vis Sci. 2011;52(1):345-363. 20. Roberts MD, Grau V, Grimm J, et al. Remodeling of the connective tissue microarchitecture of the lamina cribrosa in early experimental glaucoma. Invest Ophthalmol Vis Sci. 2009;50(2):681-690.

Copyright © 2018. Kugler Publications. All rights reserved.

The connective tissue phenotype of glaucomatous cupping 21. Yang H, Downs JC, Girkin C, et al. 3-D histomorphometry of the normal and early glaucomatous monkey optic nerve head: lamina cribrosa and peripapillary scleral position and thickness. Invest Ophthalmol Vis Sci. 2007;48(10):4597-4607. 22. Yang H, Downs JC, Bellezza A, Thompson H, Burgoyne CF. 3-D histomorphometry of the normal and early glaucomatous monkey optic nerve head: prelaminar neural tissues and cupping. Invest Ophthalmol Vis Sci. 2007;48(11):5068-5084. 23. Downs JC, Yang H, Girkin C, et al. Three-dimensional histomorphometry of the normal and early glaucomatous monkey optic nerve head: neural canal and subarachnoid space architecture. Invest Ophthalmol Vis Sci. 2007;48(7):3195-3208. 24. Burgoyne CF, Downs JC, Bellezza AJ, Hart RT. Three-dimensional reconstruction of normal and early glaucoma monkey optic nerve head connective tissues. Invest Ophthalmol Vis Sci. 2004;45(12):4388-4399. 25. Bellezza AJ, Rintalan CJ, Thompson HW, Downs JC, Hart RT, Burgoyne CF. Deformation of the lamina cribrosa and anterior scleral canal wall in early experimental glaucoma. Invest Ophthalmol Vis Sci. 2003;44(2):623-637. 26. Quigley HA, Green WR. The histology of human glaucoma cupping and optic nerve damage: clinicopathologic correlation in 21 eyes. Ophthalmology.1979;86(10):1803-1830. 27. Quigley HA, Addicks EM, Green WR, Maumenee AE. Optic nerve damage in human glaucoma. II. The site of injury and susceptibility to damage. Arch Ophthalmol. 1981;99(4):635-649. 28. Minckler DS, Bunt AH, Johanson GW. Orthograde and retrograde axoplasmic transport during acute ocular hypertension in the monkey. Invest Ophthalmol Vis Sci. 1977;16(5):426-441. 29. Gaasterland D, Tanishima T, Kuwabara T. Axoplasmic flow during chronic experimental glaucoma. 1. Light and electron microscopic studies of the monkey optic nervehead during development of glaucomatous cupping. Invest Ophthalmol Vis Sci. 1978;17(9):838-846. 30. Nguyen JV, Soto I, Kim K, et al. Myelination transition zone astrocytes are constitutively phagocytic and have synuclein dependent reactivity in glaucoma. Proc Natl Acad Sci U S A. 2011;108(3): 1176-1181. 31. Soto I, Pease ME, Son JL, Shi X, Quigley HA, Marsh-Armstrong N. Retinal ganglion cell loss in a rat ocular hypertension model is sectorial and involves early optic nerve axon loss. Invest Ophthalmol Vis Sci. 2011;52(1):434-441. 32. Filippopoulos T, Danias J, Chen B, Podos SM, Mittag TW. Topographic and morphologic analyses of retinal ganglion cell loss in old DBA/2NNia mice. Invest Ophthalmol Vis Sci. 2006;47(5):1968-1974. 33. Schlamp CL, Li Y, Dietz JA, Janssen KT, Nickells RW. Progressive ganglion cell loss and optic nerve degeneration in DBA/2J mice is variable and asymmetric. BMC Neurosci 2006;7:66. 34. Johansson JO. Inhibition of retrograde axoplasmic transport in rat optic nerve by increased IOP in vitro. Invest Ophthalmol Vis Sci. 1983;24(12):1552-1558. 35. Howell GR, Libby RT, Jakobs TC, et al. Axons of retinal ganglion cells are insulted in the optic nerve early in DBA/2J glaucoma. J Cell Biol. 2007;179(7):1523-1537.

427 36. Jakobs, TC, Libby RT, Ben Y, John SW, Masland RH. Retinal ganglion cell degeneration is topological but not cell type specific in DBA/2J mice. J Cell Biol. 2005;171(2):313-325. 37. Johnson EC, Jia L, Cepurna WO, Doser TA, Morrison JC. Global changes in optic nerve head gene expression after exposure to elevated intraocular pressure in a rat glaucoma model. Invest Ophthalmol Vis Sci 2007;48(7):3161-3177. 38. Danias J, Lee KC, Zamora MF, et al. Quantitative analysis of retinal ganglion cell (RGC) loss in aging DBA/2NNia glaucomatous mice: comparison with RGC loss in aging C57/BL6 mice. Invest Ophthalmol Vis Sci. 2003;44(12):5151-5162. 39. Johnson EC, Deppmeier LM, Wentzien SK, Hsu I, Morrison JC. Chronology of optic nerve head and retinal responses to elevated intraocular pressure. Invest Ophthalmol Vis Sci. 2000;41(2):431-442. 40. Johnson EC, Morrison JC, Farrell S, Deppmeier L, Moore CG, McGinty MR. The effect of chronically elevated intraocular pressure on the rat optic nerve head extracellular matrix. Exp Eye Res. 1996;62(6): 663-674. 41. Yang D, Fu J, Hou R, et al. Optic neuropathy induced by experimentally reduced cerebrospinal fluid pressure in monkeys. Invest Ophthalmol Vis Sci. 2014;55(5):3067-3073. 42. Chauhan BC, LeVatte TL, Jollimore CA, et al. Model of endothelin-1-induced chronic optic neuropathy in rat. Invest Ophthalmol Vis Sci. 2004;45(1):144-152. 43. Wax MB, Tezel G, Yang J, et al. Induced autoimmunity to heat shock proteins elicits glaucomatous loss of retinal ganglion cell neurons via activated T-cell-derived fas-ligand. J Neurosci. 2008;28(46):12085-12096. 44. Ing E, Ivers KM, Yang H, et al. Cupping in the monkey optic nerve transection model consists of prelaminar tissue thinning in the absence of posterior laminar deformation. Invest Ophthalmol Vis Sci. 2016;57(6):2598-2611. 45. Joachim SC, Reinehr S, Kuehn S, et al. Immune response against ocular tissues after immunization with optic nerve antigens in a model of autoimmune glaucoma. Mol Vis. 2013;19:1804-1814. 46. Brooks DE, Kallberg ME, Cannon RL, et al. Functional and structural analysis of the visual system in the rhesus monkey model of optic nerve head ischemia. Invest Ophthalmol Vis Sci. 2004;45(6): 1830-1840. 47. Burgoyne CF. The non-human primate experimental glaucoma model. Exp Eye Res. 2015;141: 57-73. 48. Yang H, Reynaud J, Lockwood, H., Williams, G., Hardin, C., Reyes, L., Gardiner, S. K. & Burgoyne CF (Accepted for publication Nov 2016 Forthcoming 2017).3D Histomorphometric Reconstruction and Quantification of the Optic Nerve Head Connective Tissues. In Methods in Glaucoma Research(Ed T. Jacobs). New York, NY: Springer. 49. Burgoyne, C. The morphological difference between glaucoma and other optic neuropathies. J Neuroophthalmol. 2015;35 Suppl 1:S8-S21. 50. Yang H, Reynaud J, Lockwood H, et al. The connective tissue phenotype of glaucomatous cupping in the monkey eye Clinical and research implications. Prog Ret Eye Res. 2017;59:152.

Copyright © 2018. Kugler Publications. All rights reserved.

428 51. Bellezza AJ, Hart RT, Burgoyne CF. The optic nerve head as a biomechanical structure: initial finite element modeling. Invest Ophthalmol Vis Sci. 2000;41(10): 2991-3000. 52. Bellezza AJ, Rintalan CJ, Thompson HW, Downs JC, Hart RT, Burgoyne CF. Anterior scleral canal geometry in pressurised (IOP 10) and non-pressurised (IOP 0) normal monkey eyes. Br J Ophthalmol. 2003;87(10):1284-1290. 53. Burgoyne CF, Downs JC, Bellezza AJ, Suh JK, Hart RT. The optic nerve head as a biomechanical structure: a new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage. Prog Retin Eye Res. 2005;24(1):39-73. 54. Burgoyne CF, Downs JC. Premise and prediction-how optic nerve head biomechanics underlies the susceptibility and clinical behavior of the aged optic nerve head. J Glaucoma. 2008;17(4):318-328. 55. Burgoyne CF. A biomechanical paradigm for axonal insult within the optic nerve head in aging and glaucoma. Exp Eye Res. 2011;93(2):120-132. 56. Langham M. The temporal relation between intraocular pressure and loss of vision in chronic simple glaucoma. Glaucoma. 1980;2(4):427-435. 57. Anderson DR, Hoyt WF, Hogan MJ. The fine structure of the astroglia in the human optic nerve and optic nerve head. Trans Am Ophthalmol Soc. 1967;65:275-305. 58. Hogan JJ, Alvarado JA, Weddell JE. Histology of the Human Eye. Philadelphia: WB Saunders Co;1971. 59. Stewart PS, Jensen OE, Foss AJ. A theoretical model to allow prediction of the CSF pressure from observations of the retinal venous pulse. Invest Ophthalmol Vis Sci. 2014;55(10):63196323. 60. Wang X, Rumpel H, Lim W, et al. Finite element analysis predicts large optic nerve head strains during horizontal eye movements. Invest Ophthalmol Vis Sci. 2016;57(6):2452-2462. 61. Girard MJ, Beotra MR, Chin KS, et al. In vivo 3-dimensional strain mapping of the optic nerve head following intraocular pressure lowering by trabeculectomy. Ophthalmology. 2016;123(6):1190-200. 62. Zhang L, Albon J, Jones H, et al. Collagen microstructural factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2015;56(3):2031-2042. 63. Downs JC Optic nerve head biomechanics in aging and disease. Exp Eye Res. 2015;133: 19-29. 64. Sigal IA, Grimm JL, Schuman JS, Kagemann L, Ishikawa H, Wollstein G. A method to estimate biomechanics and mechanical properties of optic nerve head tissues from parameters measurable using optical coherence tomography. IEEE Trans Med Imaging. 2014;33(6):1381-1389. 65. Sigal IA, Grimm JL. A few good responses: which mechanical effects of IOP on the ONH to study? Invest Ophthalmol Vis Sci. 2012;53(7):4270-4278. 66. Sigal IA, Bilonick RA, Kagemann L, et al. The optic nerve head as a robust biomechanical system. Invest Ophthalmol Vis Sci. 2012;53(6):2658-2667.

H. Yang et al. 67. Grytz R, Girkin CA, Libertiaux V, Downs JC. Perspectives on biomechanical growth and remodeling mechanisms in glaucoma. Mech Res Commun. 2012;42:92-106. 68. Clark AF. The cell and molecular biology of glaucoma: biomechanical factors in glaucoma. Invest Ophthalmol Vis Sci. 2012;53(5):2473-2475. 69. Girard MJ, Dahlmann-Noor A, Rayapureddi S, et al. Quantitative mapping of scleral fiber orientation in normal rat eyes. Invest Ophthalmol Vis Sci. 2011;52(13):9684-9693. 70. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Modeling individual-specific human optic nerve head biomechanics. Part I: IOP-induced deformations and influence of geometry. Biomech Model Mechanobiol. 2009:8(2):85-98. 71. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Modeling individual-specific human optic nerve head biomechanics. Part II: influence of material properties. Biomech Model Mechanobiol. 2009:8(2):99-109. 72. Sigal IA, Ethier CR. Biomechanics of the optic nerve head. Exp Eye Res. 2009;88(4):799-807. 73. Girard MJ, Strouthidis NG, Desjardins A, Mari JM, Ethier CR. In vivo optic nerve head biomechanics: performance testing of a three-dimensional tracking algorithm. J R Soc Interface. 2013;10(87):20130459. 74. Lei Y, Rajabi S, Pedrigi RM, Overby DR, Read AT, Ethier CR. In vitro models for glaucoma research: effects of hydrostatic pressure. Invest Ophthalmol Vis Sci. 2011;52(9):6329-6339. 75. Eilaghi, A, Flanagan JG, Simmons CA, Ethier CR. Effects of scleral stiffness properties on optic nerve head biomechanics. Ann Biomed Eng. 2010;38(4):1586-1592. 76. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Reconstruction of human optic nerve heads for finite element modeling. Technol Health Care. 2005;13(4):313-329. 77. Downs JC, Suh J.K, Thomas KA, Bellezza AJ, Hart RT, Burgoyne CF. Viscoelastic material properties of the peripapillary sclera in normal and early-glaucoma monkey eyes. Invest Ophthalmol Vis Sci. 2005;46(2):540-546. 78. Kalvin NH, Hamasaki DI, Gass JD. Experimental glaucoma in monkeys. I. Relationship between intraocular pressure and cupping of the optic disc and cavernous atrophy of the optic nerve. Arch Ophthalmol. 1966;76(1):82-93. 79. Quigley HA, Addicks EM. Chronic experimental glaucoma in primates. II. Effect of extended intraocular pressure elevation on optic nerve head and axonal transport. Invest Ophthalmol Vis Sci. 1980;19(2):137-152. 80. Furuyoshi N, Furuyoshi M, May CA, Hayreh SS, Alm A, Lutjen-Drecoll E. Vascular and glial changes in the retrolaminar optic nerve in glaucomatous monkey eyes. Ophthalmologica. 2000;214(1): 24-32. 81. Jonas J.B, Hayreh SS, Yong T. Thickness of the lamina cribrosa and peripapillary sclera in Rhesus monkeys with nonglaucomatous or glaucomatous optic neuropathy. Acta Ophthalmol. 2011;89(5):e423-427. 82. Hernandez MR. The optic nerve head in glaucoma: role of astrocytes in tissue remodeling. Prog Retin Eye Res. 2000;19(3):297-321.

Copyright © 2018. Kugler Publications. All rights reserved.

The connective tissue phenotype of glaucomatous cupping 83. Yang H, Ren R. Lockwood H, et al. The connective tissue components of optic nerve head cupping in monkey experimental glaucoma Part 1: Global change. Invest Ophthalmol Vis Sci. 2015;56(13):7661-7678. 84. Yang H, Downs JC, Burgoyne CF. Physiologic intereye differences in monkey optic nerve head architecture and their relation to changes in early experimental glaucoma. Invest Ophthalmol Vis Sci. 2009;50(1):224-234. 85. Lockwood H, Reynaud J, Gardiner S, et al. Lamina cribrosa microarchitecture in normal monkey eyes part 1: methods and initial results. Invest Ophthalmol Vis Sci. 2015;56(3):16181637. 86. Pazos M, Yang H, Gardiner SK, et al. Expansions of the neurovascular scleral canal and contained optic nerve occur early in the hypertonic saline rat experimental glaucoma model. Exp Eye Res. 2016;145:173-186. 87. Reynaud J, Lockwood H, Gardiner SK, Williams G, Yang H, Burgoyne CF. Lamina cribrosa microarchitecture in early monkey experimental glaucoma: Global change. Invest Ophthalmol Vis Sci. 2016;57(7):3451-3469. 88. Grytz R, Sigal IA, Ruberti JW, Meschke G,. Downs JC. Lamina cribrosa thickening in early glaucoma predicted by a microstructure motivated growth and remodeling approach. Mech Mater. 2012;44:99-109. 89. Lee KM, Kim TW, Weinreb RN, Lee EJ, Girard MJ, Mari, JM. Anterior lamina cribrosa insertion in primary open-angle glaucoma patients and healthy subjects. PLoS One. 2014;9(12):e114935. 90. Lee EJ, Kim TW, Kim M, Girard MJ, Mari JM, Weinreb RN. Recent structural alteration of the peripheral lamina cribrosa near the location of disc hemorrhage in glaucoma. Invest Ophthalmol Vis Sci. 2014;55(4):2805-2815. 91. Tatham AJ, Miki A, Weinreb RN, Zangwill LM,Medeiros FA. Defects of the lamina cribrosa in eyes with localized retinal nerve fiber layer loss. Ophthalmology. 2013;121(1):110-118. 92. Faridi OS, Park SC, Kabadi R, et al. Effect of focal lamina cribrosa defect on glaucomatous visual field progression. Ophthalmology. 2014;121(8):1524-1530. 93. You JY, Park SC, Su D, Teng CC, Liebmann JM, Ritch R. Focal lamina cribrosa defects associated with glaucomatous rim thinning and acquired pits. JAMA Ophthalmol. 2013;131(3):314320. 94. Grau ., Downs JC, Burgoyne CF. Segmentation of trabeculated structures using an anisotropic Markov random field: application to the study of the optic nerve head in glaucoma. IEEE Trans Med Imaging. 2006;25(3):245-255. 95. Carolynne AK. Chapter III: Two Parameter Gamma Distribution. In Gamma and Related Distributions, 6-27 (Ed. AK Carolynne). Norderstedt, Germany: Books on Demand;2014. 96. Anderson DR, Hendrickson A. Effect of intraocular pressure on rapid axoplasmic transport in monkey optic nerve. Invest Ophthalmol. 1974;13(10):771-783. 97. Quigley HA, Guy J, Anderson DR. Blockade of rapid axonal transport. Effect of intraocular pressure elevation in primate optic nerve. Arch Ophthalmol. 1979;97(3):525-531.

429 98. Roberts MD, Liang Y, Sigal IA, et al. Correlation between local stress and strain and lamina cribrosa connective tissue volume fraction in normal monkey eyes. Invest Ophthalmol Vis Sci. 2010;51(1):295-307. 99. Girard MJ, Suh JK, Bottlang M, Burgoyne CF, Downs JC. Scleral biomechanics in the aging monkey eye. Invest Ophthalmol Vis Sci. 2009;50(11):5226-5237. 100. Hayreh SS, Pe’er J, Zimmerman MB. Morphologic changes in chronic high-pressure experimental glaucoma in rhesus monkeys. J Glaucoma. 1999;8(1):56-71. 101. Davis CH, Kim KY, Bushong EA, et al. Transcellular degradation of axonal mitochondria. Proc Natl Acad Sci U S A. 2014;111(26):9633-9638. 102. Burgoyne CF, Stowell C, Jang G, et al. (2014). Non-Human Primate (NHP) Optic Nerve Head (ONH) Proteomic Change In Early Experimental Glaucoma (EEG). In ARVO Meeting Abstracts, Vol. 55. 103. Stowell, C., Jang, G., Reynaud J, Gardiner, S., Zhang, L., Crabb, J. S., Willard, B., Crabb, J. W. & Burgoyne CF (2014).Myelin-Related Proteins Are Decreased In The Immediate Retrolaminar Optic Nerve (ON) In Non-Human Primates (NHP) In Early Experimental Glaucoma (EEG). In ARVO Meeting Abstracts, Vol. 55. 104. He L, Yang H, Gardiner SK, et al. Longitudinal detection of optic nerve head changes by spectral domain optical coherence tomography in early experimental glaucoma. Invest Ophthalmol Vis Sci. 2014;55(1):574-586. 105. Strouthidis NG, Fortune B, Yang H, Sigal IA, Burgoyne CF. Longitudinal change detected by spectral domain optical coherence tomography in the optic nerve head and peripapillary retina in experimental glaucoma. Invest Ophthalmol Vis Sci. 2011;52(3):1206-1219. 106. Miller NR, Johnson MA, Nolan T, Guo Y, Bernstein AM, Bernstein S.L. Sustained neuroprotection from a single intravitreal injection of PGJ(2) in a nonhuman primate model of nonarteritic anterior ischemic optic neuropathy. Invest Ophthalmol Vis Sci. 2014;55(11):7047-7056. 107. Yang H, He L, Gardiner SK, et al. Age-related differences in longitudinal structural change by spectral-domain optical coherence tomography in early experimental glaucoma. Invest Ophthalmol Vis Sci. 2014;55(10):6409-6420. 108. Ivers KM, Yang H, Gardiner SK, et al. In vivo detection of laminar and peripapillary scleral hypercompliance in early monkey experimental glaucoma. Invest Ophthalmol Vis Sci. 2016;57(9):OCT388-403. 109. Burgoyne CF, Quigley HA, Thompson HW, Vitale S, Varma R. Early changes in optic disc compliance and surface position in experimental glaucoma. Ophthalmology. 1995;102(12):1800-1809. 110. Burgoyne CF, Quigley HA, Thompson HW, Vitale S, Varma R. Measurement of optic disc compliance by digitized image analysis in the normal monkey eye. Ophthalmology. 1995;102(12):1790-1799. 111. Heickell AG, Bellezza AJ, Thompson HW, Burgoyne CF. Optic disc surface compliance testing using confocal scanning laser tomography in the normal monkey eye. J Glaucoma. 2001;10(5):369-382.

430

Copyright © 2018. Kugler Publications. All rights reserved.

112. Yang H, Downs JC, Sigal IA, Roberts MD, Thompson H, Burgoyne CF. Deformation of the normal monkey optic nerve head connective tissue after acute IOP elevation within 3-D histomorphometric reconstructions. Invest Ophthalmol Vis Sci. 2009;50(12):5785-5799. 113. Girard MJ, Suh JK, Bottlang M, Burgoyne CF, Downs JC. Biomechanical changes in the sclera of monkey eyes exposed to chronic IOP elevations. Invest Ophthalmol Vis Sci. 2011;52(8):5656-5669. 114. Girard MJ, Downs JC, Bottlang M, Burgoyne CF, Suh JK. Peripapillary and posterior scleral mechanics--part II: experimental and inverse finite element characterization. J Biomech Eng. 2009;131(5):051012. 115. Girard MJ, Downs JC, Burgoyne CF, Suh JK. Peripapillary and posterior scleral mechanics--part I: development of an anisotropic hyperelastic constitutive model. J Biomech Eng. 2009;131(5):051011. 116. Chen CS, Johnson MA, Flower RA, Slater BJ, Miller NR, Bernstein SL. A primate model of nonarteritic anterior ischemic optic neuropathy. Invest Ophthalmol Vis Sci. 2008;49(7):2985-2992. 117. Quigley HA, Anderson DR. The histologic basis of optic disk pallor in experimental optic atrophy. Am J Ophthalmol. 1977;83(5):709-717. 118. Morrison JC, Dorman-Pease ME, Dunkelberger GR, Quigley HA. Optic nerve head extracellular matrix in primary optic atrophy and experimental glaucoma. Arch Ophthalmol. 1990;108(7): 1020-1024. 119. Cioffi GA, Wang L, Fortune B, et al. Chronic ischemia induces regional axonal damage in experimental primate optic neuropathy. Arch Ophthalmol. 2004;122(10):1517-1525. 120. Orgul S, Cioffi GA, Bacon DR, Van Buskirk EM. An endothelin-1-induced model of chronic optic nerve ischemia in rhesus monkeys. J Glaucoma. 1996;5(2):135-138. 121. Cioffi GA, Sullivan P. The effect of chronic ischemia on the primate optic nerve. Eur J Ophthalmol. 1999;9 Suppl 1:S34-36. 122. Orgul S, Cioffi GA, Wilson DJ, Bacon DR, Van Buskirk EM. An endothelin-1 induced model of optic nerve ischemia in the rabbit. Invest Ophthalmol Vis Sci. 1996;37(9):1860-1869.

H. Yang et al. 123. Cioffi GA, Orgul S, Onda E, Bacon DR, Van Buskirk EM. An in vivo model of chronic optic nerve ischemia: the dose-dependent effects of endothelin-1 on the optic nerve microvasculature. Curr Eye Res. 1995;14(12):1147-1153. 124. Tezel G, Wax MB. (2004). The immune system and glaucoma. Curr Opin Ophthalmol. 2004;15(2):80-84. 125. Tezel G, Yang X, Luo C, Cai J, Powell DW. An astrocyte-specific proteomic approach to inflammatory responses in experimental rat glaucoma. Invest Ophthalmol Vis Sci. 2012;53(7):42204233. 126. Grus FH, Joachim SC, Wuenschig D, Rieck J, Pfeiffer N. Autoimmunity and glaucoma. J Glaucoma. 2008;17(1):79-84. 127. Anderson DR, Hoyt WF. Ultrastructure of intraorbital portion of human and monkey optic nerve. Arch Ophthalmol. 1969;82(4):506-530. 128. 128.Cioffi GA, Van Buskirk EM. Vasculature of the anterior optic nerve and peripapillary choroid. In: The Glaucomas, Vol. 1, 177-197 (Eds R. Ritch, M. B. Shields and T. Krupin). St. Louis: Mosby;1996. 129. Quigley HA. Overview and introduction to session on connective tissue of the optic nerve in glaucoma. Chapter 2. In: Optic Nerve in Glaucoma, 15-36 (Ed S. M. Drance, Anderson, D.R.). Amsterdam/New York: Kugler Publications;1995. 130. Quigley HA, Brown AE, Morrison JD, Drance SM. The size and shape of the optic disc in normal human eyes. Arch Ophthalmol. 1990;108(1):51-57. 131. Morrison JC, L’Hernault NL, Jerdan JA, Quigley HA. Ultrastructural location of extracellular matrix components in the optic nerve head. Arch Ophthalmol. 1989;107(1):123-129. 132. Downs JC, Roberts MD, Burgoyne CF. Mechanical Strain and Restructuring of the Optic Nerve Head. In Glaucoma, Vol. 1(Eds: T. Shaarawy, M. B. Sherwood, R. A. Hitchings and J. G. Crowston). London: Saunders;2009.

29. Cellular mechanisms of lamina cribrosa remodeling in glaucoma Reinold K. Goetz, Deborah Wallace, Tabitha Goetz, Colm O’Brien Department of Ophthalmology, School of Medicine & Mater Misericordiae University Hospital, University College Dublin, Dublin, Ireland

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction The human lamina cribrosa (LC) is a specialized region of the optic nerve composed of approximately ten fenestrated, connective tissue sheets stacked together.1 These sheets consist of a core of elastin fibers and collagen type III, and are coated with collagen type IV and laminin.2 The structure of the sheets themselves is made of numerous laminar beams that overlap and branch to form pores that support the un-myelinated, retinal ganglion cell axons as they exit the eye through the optic nerve head (ONH).1 Normal laminar beams have a core of elastin, collagen types I, III, and VI, and glycosaminoglycans. Both elastin and collagen contribute to the resilience of this region, as elastin resists tissue deformation to mild stress and collagen plays a role in load bearing.3 Collagen types I and III are major structural components of the extracellular matrix, while type IV is a component of basement membranes, and type V and VI connect the collagen to surrounding tissues.4-6 The LC pores range in diameter from 10 to 100 μm and are larger in the superior and inferior regions compared to the nasal and temporal regions. The larger pore size is in keeping with the greater number of ganglion cell axons that pass through those regions. Less robust connective tissue support may underlie the increased susceptibility to early glaucomatous damage in the vertical polar regions of the LC.7 In glaucoma, a number of important changes occur in the LC. The pores become narrowed, elongated, and slit-like, and the collagen layers lining the pores appear

irregular.8,9 The elastin fibers of the laminar beams that are normally straight and tightly packed become curvilinear and disrupted.3 Posterior deformation of the LC results in compression, shearing, and collapse of the connective tissue sheets, and the normal thickness of the LC is reduced from 450 to 200 μm as it becomes stiff and fibrotic.10 Furthermore, axoplasmic flow, which is essential to normal axon function and integrity, becomes blocked, leading to axonal dysfunction and the degeneration of the retinal ganglion cells.11 Specific factors contribute to this neurodegeneration at the ONH, including elevated intraocular pressure (IOP) driven mechanical stretch,12 reduced ocular vascular perfusion pressure (hypoxia, ischemia),13 the actions of the biologically active cytokine-transforming growth factor beta (TGF-β),14 cerebrospinal fluid (CSF) pressure,15 and age.16 Multiple prospective, randomized, multi-center studies have shown IOP to be the most consistent and significant risk factor in the pathogenesis of glaucoma, and it is currently the main target for treatment.17,18 Downs et al. proposed that the biomechanical, vascular, and cellular influences on the LC are intrinsically intertwined, as mechanical strain and the changes to structural components of the LC affect the blood supply to the retinal ganglion cells. Conversely, insufficiencies in the blood supply may make the structure more vulnerable to the mechanical stress caused by raised IOP. The susceptibility of the ONH to glaucomatous damage is therefore dependent on the unique eye-specific combination of these factors.19

Correspondence: Reinold. K. Goetz, Department of Ophthalmology, School of Medicine & Mater Misericordiae University Hospital, University College Dublin, Eccles St, Dublin 7, Ireland. E-mail: [email protected] Biomechanics of the Eye, pp. 431-442 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

R.K. Goetz et al.

432

Copyright © 2018. Kugler Publications. All rights reserved.

2. Glaucoma: a fibrotic disease Inflammation, wound formation, and fibrosis are essential mechanisms that allow damaged tissues to repair, removing dead and damaged cells to ensure tissue integrity is maintained. When the process of fibrosis becomes exaggerated and persistent, however, destruction and scarring of tissue can lead to disease. Fibrosis can result in tissue destruction in numerous conditions, including diseases of the liver, kidney, heart, and lung. Increasingly, research has shown that the pathophysiology of glaucoma involves activation of pro-fibrotic pathways.20 In fibrosis, injured structural cells release inflammatory mediators to stimulate an antifibrinolytic coagulation cascade. Increased production of matrix metalloproteinases (MMPs) causes disruption of basement membranes to allow inflammatory cells to target the site of injury. Secreted chemokines and cytokines cause recruitment of other inflammatory cells to the damaged tissue, which in turn also secrete profibrotic cytokines such as Interleukin 13, platelet-derived growth factor, and TGF-β.21 These cytokines cause fibroblasts to differentiate into myofibroblasts. The myofibroblast cell is responsible for fibrotic contractions and it has a chief role in the excessive accumulation and deposition of extracellular matrix (ECM) that underlie tissue remodeling.22 The force generated by myofibroblasts depends on expression of alphasmooth muscle actin (α-SMA) in intracellular stress fibers.23 These cells can arise from a wide variety of pre-cursor cell types and myofibroblast differentiation is mainly regulated through TGF-β, although several chemokines, cytokines, and ECM components have also been implicated in this process (Fig. 1).22,24 There are two main pathways that bestow a pro-survival phenotype for myofibroblasts: focal adhesion kinase (FAK), which prevents the myofibroblast from going into apoptosis, and phosphatidylinositol 3-kinase (PI3k)-AKT signaling, which can be activated by TGF-β and Endothelin 1.25,26 Early mechanical changes in damaged tissues caused by collagen crosslinking via lysyl oxidase (LOX) enzymes may also be the trigger for myofibroblast persistence. As the ECM is remodeled by the myofibroblasts, the tissue becomes stiffer and this environment then promotes the cells to become even more contractile, creating a

Fig. 1. Schematic of the LC cell undergoing transformation to a myofibroblast via multiple mechanisms.

feed-forward cycle.27 It is now thought that this fibrotic cascade is an important underlying pathology in glaucomatous optic neuropathy.

3. The glial cells of the LC Anderson1 and Hernandez28 identified two distinct glial cell types within the LC: the LC cell and the ONH astrocyte. The collection of macromolecules synthesized by these cells constitutes the specialized ECM of the LC. The ECM is an intricate network and its major components include elastin, collagens, proteoglycans, and cell binding glycoproteins.29 The composition of the ECM gives the LC its resilience and compliance, and allows it to maintain its structural integrity despite variations in IOP.17 The remodeling, distortion, and increased synthesis of this ECM are implicated in the pathogenesis of glaucoma.30 The ECM of the human LC is distinct from that of the sclera; in normal eyes, it is a compliant tissue.2,31 The reactive astrocytes and the LC cell actively contribute to the progressive remodeling of the ECM in glaucoma, resulting in a loss of collagen fibers, and thickening and proliferation of basement membranes lining the cribriform sheets, eventually leading to an excavated LC.31,32 In glaucoma, the normal dense collagen matrix becomes granular, and loose basement membranes and bundles of microfibrils are found within the ECM.2 The possible mechanisms for this cellular dysfunction include oxidative stress, mitochondrial dysfunction, aberrant calcium homeostasis, autophagy, and epigenetic factors.

Cellular mechanisms of lamina cribrosa remodeling in glaucoma

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 2. Primary LC cell cultures from ONH explants of human donors. Image courtesy: Professor Abbot F. Clarke, Department of Cell Biology and Genetics University of North Texas and Health Science Centre at Fort Worth, Texas, USA.

3.1. Reactive astrocytes The ONH astrocyte provides cellular support to the retinal ganglion axons and contributes to the synthesis of the ECM.33 There are two identified types of ONH astrocytes: type 1A and 1B. Type 1B expresses neural cell adhesion molecule (NCAM) in addition to the glial fibrillary acid protein (GFAP) that is expressed by both types.34 ONH astrocytes line basement membranes along the cribriform sheets and surround the central retinal vessels, forming the barrier between the neural elements of the LC and connective tissue. These cells aid in preserving the integrity of neural tissue following injury or disease.33 In glaucoma, persistent activation of these astrocytes alters homeostatic functions within the LC, such as cell-cell communication, migration, growth factor pathway activation, and responses to oxidative stress.35 Raised IOP also causes proliferation of the ONH astrocytes.36 Reactive astrocytes are characterized by hyperplasia and hypertrophy.37 In response to injury, the ONH astrocytes shift from being quiescent to reactive, migrate into the LC pores, and increase the synthesis of new ECM macromolecules such as tenascin, laminin, and chondroitin sulphate proteoglycans that contribute to the formation of a glial scar.32 MMPs are key regulators of the ECM,38 and several MMPs as well as tissue inhibitors of MMPs (TIMPs) are present in ONH astrocytes.36 Although this new ECM isolates the injured neural tissue from the remaining axons, the process also inhibits axonal growth.

433

Fig. 3. Characterization of LC cells. Lanes 1 and 2 are normal donors, 3 and 4 are glaucomatous donors, lane 5 is optic nerve cDNA, and lane 6 is a negative control (water). GFAP, α-SMA, and binding adapter molecule 1 (Iba1) expression is demonstrated by polymerase chain reaction (PCR). As shown, optic nerve cDNA is positive for all the above genes, whereas LC cells from donors show no expression of GFAP or Iba1.81

Astrocytes upregulate elastin as well as heat-shock protein-27; In glaucoma, elastin may be upregulated up to four-fold in a disorganized state compared to the typical tubular elastic fibers that are normally present.39,40 Additionally, Liu et al. have demonstrated that the ONH astrocyte releases the neurotoxic mediator NO synthase-2 in response to mechanical strain, and may therefore directly induce axonal death in the glaucomatous ONH.41 When exposed to elevated hydrostatic pressures for several hours, the intracellular enzyme activity of adenylyl cyclase in the ONH astrocyte is increased. This may in turn facilitate the reorganization of the actin cytoskeleton of these cells, resulting in the typical actin stress fibers that run across the cytoplasm to become redistributed to the periphery. The cells then become more rounded with shorter processes, and this may be a protective mechanism against prolonged, elevated hydrostatic pressure.42 3.2. The LC cell The LC cells identified within and between the cribriform sheets are morphologically broad, flat, polygonal, star-shaped cells with abundant perinuclear granules, as well as intra-cytoplasmic granules (Fig. 2). Rosario Hernandez first described this distinct group of cells in 1988. The LC cells are distinguished from ONH astrocytes by the absence of immunofluorescent staining for glial fibrillary acidic protein (GFAP) both in vivo and in vitro (Fig. 3). The cytoplasm of the lamina cribrosa cell has abundant organelles, a well-developed Golgi apparatus, oval or round shaped mitochon-

R.K. Goetz et al.

Copyright © 2018. Kugler Publications. All rights reserved.

434

dria, and an active rough endoplasmic reticulum (RER) with membranes filled with electron-dense material and free ribosomes.28 This specialized population of cells is now thought to originate from the myofibroblast.43 As previously mentioned, myofibroblasts are a differentiated form of fibroblast that synthesize and deposit ECM and express α-SMA, giving them contractile potential. The myofibroblast plays an important role in physiological wound healing by re-establishing mechanical tissue organization, but can also cause pathological remodeling after tissue injury. It has been suggested that myofibroblasts are responsible for fibrotic conditions such as Dupytren’s contracture, renal and pulmonary fibrosis, and hepatic cirrhosis.44 During normal wound healing, myofibroblasts produce ECM components, such as collagen types I and III, that allow the contraction of granulation tissue. This disappears when epithelialization has been completed through apoptosis of the myofibroblasts and vascular cells.22 In pathological states, myofibroblasts persist in tissues, as the resolution phase of wound healing does not occur, and fibrosis results from deposition of excess ECM. For remodeling of this newly deposited ECM to be completed, the balance of proteolytic enzymes such as MMPs and their inhibitors, TIMPs, is crucial.44 Hinz et al. have identified three local events that are needed to generate myofibroblasts. The first event is the accumulation of the main myofibroblast inducer, transforming growth factor beta (TGF-β1). The second requirement is the presence of specialized ECM proteins including collagens, elastins, and proteoglycans that are upregulated by TGF-β1. The final required condition is high extracellular stress arising from new ECM.22 Reactive oxygen species (ROS) generated in mitochondria or by NADPH oxidases are also essential for TGF-β-mediated myofibroblast differentiation.45 LC cells have fibrogenic potential, as they express collagen I, II, α-SMA, elastin, and fibronectin. Kirwan et al. have used high throughput gene expression analysis to identify the upregulated as well as downregulated ECM/ fibrosis genes in glaucomatous LC cells. Upregulated genes include collagen type I, III, connective tissue growth factor, thrombospondin 1, and periostin.46 Periostin is a 90-kDAa disulfide-linked matricellular protein with expression in cells of mesenchymal origin, and binds to collagen type I to promote fibrillogene-

sis/elastic modulus/stiffness.47 Downregulated genes include those for MMP 1.46 The LC cell also upregulates the expression of genes that are known to be increased in glaucomatous ONH tissue such as collagens IV, VI, TGF-β1, MMP-2, and VEGF, as well as novel ECM genes such as the proteoglycans biglycan and versican, EMMPRIN (an ECM metalloproteinase inducer) and bone morphogenetic protein-7 (BMP-7), all of which function to either maintain or regulate the ECM.48

4. TGF-β TGF-β is a superfamily of multifunctional, pro-fibrotic, pro-inflammatory cytokines released in response to tissue injury. TGF-β can promote ECM synthesis and deposition by upregulating the transcription of collagen, fibronectin, proteoglycans, and integrins, as well as by suppression of MMP release. Remodeling of the ECM includes changes in fibrillar collagens, basement membrane components, and degradation of elastin fibers.49,50 Takeo et al. demonstrated increased TGF-β1 and TGF-β2 staining in the ONH of glaucomatous monkeys. The staining was particularly intense in the region of the LC.51 Pena et al. also demonstrated increased TGF-β2 staining in glaucomatous human ONH.52 Furthermore, pathologically high levels of TGF-β have also been found in the anterior chamber of patients with glaucoma compared to normal controls.53 TGF-β is thought to have a key role in the alteration of the ECM of the LC as well as the ECM of the trabecular meshwork, leading to an elevation in the IOP and consequent pathological neurodegeneration.54 Additionally, raised IOP is thought to further induce expression of TGF-β, contributing to the chronic neurodegeneration of the optic nerve in a feed-forward cycle. Several studies suggest that ONH astrocytes and LC cells respond to elevated IOP by increasing TGF-β2 synthesis, indicating that these cells may be an in-vivo source of TGF-β.55 TGF-β2 acts through the SMAD signaling pathway to synthesize and deposit ECM proteins that drive fibrosis.49 The activities of TGF-β1 and -β2 are modulated by the blocking effects of BMP-4 and BMP-7, and by the BMP antagonist gremlin.14 TGF-β1 stimulates the production of ROS by impairing mitochondrial function and inducing NADPH oxidases (NOXs), mainly NOX4. An increase in NOX4

Cellular mechanisms of lamina cribrosa remodeling in glaucoma

expression has been detected in other fibrotic diseases such as idiopathic pulmonary fibrosis.49 NOXs are a group of heme-containing transmembrane proteins that mediate the fibrogenic effects of TGF-β1 such as fibroblast activation, epithelial and endothelial cell apoptosis, epithelial–mesenchymal transition (EMT), and the expression of pro-fibrotic genes.14 TGF-β also suppresses antioxidant systems, such as the synthesis of glutathione (GSH), leading to oxidative stress or redox imbalance that, in turn, further activate TGF-β1 and promote fibrosis.45 Collagen types V and VI, elastin, and biglycan, all of which contribute to the remodeling of the ECM, are TGF-β1 responsive.56 Immunohistochemical studies of the glaucomatous ONH show increased collagen types I, IV, VI, elastin, chondroitin sulphate, dermatan sulphate proteoglycan, and increased deposition of TGF-β1.48,57 In optic nerve sections of glaucomatous eyes, collagen VI, which extends into nerve bundles, is upregulated up to 16-fold, filling spaces previously occupied by axons.56 Fukuchi et al. studied collagen distribution in the ONH of monkeys with argon laser-induced glaucoma, and found increased immunostaining for collagen V in the laminar beams of the LC as well as aso an increase in the total glycosaminoglycan content.58 There is also an increase in the collagen crosslink pentosidene (an advanced glycation end product), with reduced fibronectin and a four-fold increase in biglycan, which is associated with the upregulation of TGF-β.56

Copyright © 2018. Kugler Publications. All rights reserved.

5. Endothelin 1 Endothelin 1 is another mediator of ECM regulation.59 It is a 21-amino acid vasoactive peptide that acts as a pro-fibrotic factor, increasing the deposition of collagen in numerous cell types and tissues, and thereby initiating and maintaining fibrosis, as demonstrated in cardiac myocytes, smooth muscle cells, and fibroblasts.60-63 Elevated levels of Endothelin 1 have also been found in the aqueous humor of primary open-angle glaucoma patients, and it has therefore been implicated in glaucoma pathophysiology.64 Endothelin 1 increases the mRNA and protein levels of collagen type IαI and collagen type VIαI in LC cells.59 In numerous tissues, an increase in collagen type I is associated with a reduction in compliance and loss of normal structure

435

due to fibrosis.65 An increase in collagen type VI is considered an early marker of fibrosis; collagen type VI also further increases the rate of formation of collagen type I fibrils.66,67 As stated earlier, TIMPs are enzymes that inhibit MMPs responsible for collagen degradation. Endothelin 1 not only enhances collagen synthesis, but also increases the activity of TIMPs, therefore reducing collagen degradation.68,69 The effects of Endothelin 1 are mediated through seven transmembrane G-protein coupled receptors, Endothelin receptor A (ETA) and Endothelin receptor B (ETB).70 In glaucoma, the human ONH demonstrates an upregulation of ETB receptors.71 Furthermore, LC cells express both ETA and ETB receptors, and with prolonged exposure to Endothelin 1 there is a dose-dependent increase in intracellular calcium as well as NO release.72 Endothelin 1 increases ONH astrocyte proliferation through activation of the ETA/B receptors. In culture, exposure of ONH astrocytes to Endothelin 1 can result in up to a 30% increase in cells over 96 hours.73 In animal studies, intravitreal administration of Endothelin 1 results in blockade of axonal transport, activation of the ONH astrocytes, and apoptosis of retinal ganglion cells, producing an optic neuropathy.74,75 Anterograde axonal transport is essential for ganglion cell survival, and with the administration of intravitreal Endothelin 1 there is a pronounced reduction in the mitochondrial subcomponent of anterograde axonal transport.74 Of note, hypoxia promotes the expression of Endothelin 1 through hypoxia-inducible factor-1 (HIF-1).76,77 Endothelin 1 therefore contributes to the fibrosis seen in glaucoma at the LC through a variety of mechanisms: increasing collagen synthesis, decreasing collagen degradation, increasing intra-cellular calcium and NO release, blocking anterograde axonal transport, and activating ONH astrocytes.

6. LC cell mechano-transduction and calcium homeostasis Mechano-transduction refers to the mechanisms by which a cell responds to mechanical strain and converts the response to a chemical signal.78 The mechanisms by which mechanical forces are sensed and transduced in ocular cells are incompletely understood. Mecha-

R.K. Goetz et al.

436

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. Confirmation that LC cells have increased maxi K+ channel activity when stretched.79

no-transducers include stretch-activated channels as well as voltage-gated ion channels. Whole-cell patch clamping with electrophysiological analysis of specific ion channels involved in response to hypotonic cell membrane stretch was used to characterize maxi K+ channels on the LC cell membrane. These channels are large conductance K+ channels known to open in response to mechanical stretch and allow movement of cations across the cell membrane in a variety of cell types (skeletal muscle, myometrium, renal tubular epithelium, and endothelial cells). These channels couple the efflux of potassium with the movement of calcium ions across the cell membrane to the cytosol. The maxi K+ channels were identified and confirmed as being present and active in the LC cell using the K+ channel inhibitors tetraethylammonium (TEA), barium chloride, and iberiotoxin (a specific maxi K+- inhibitor)(Fig. 4).79 Calcium is an intracellular messenger required for the normal functioning of cells. It plays a vital role in regulating cell excitability, metabolism, cytoskeletal integrity, and synaptic function. Mechano-transduction dysfunction with consequent disruption of Ca2+ homeostasis has been shown to occur in LC cells from glaucomatous human donor eyes.80 Intracellular Ca2+, as well as the activity of maxi K+ channels, increases following hypotonic shock (stretch) of LC cells; these increases are more pronounced in LC cells from human glaucoma eyes than in those from normal eyes.79,81 Consequently, an intracellular accumulation of Ca2+ occurs that can trigger multiple signaling cascades. Calcium overload stimulates mitochondrial permeability transition pore opening, thus causing mitochondrial release of additional calcium

stores and ROS into the cytosol.82 This contributes to further mitochondrial dysfunction as ROS depolarize the organelle’s membrane and thereby decrease the mitochondria’s ability to buffer Ca2+, leading to even further disruption of calcium homeostasis.83 Mitochondrial dysfunction is the most important source of endogenous ROS, which can also directly damage proteins and nucleic acids. In normal LC cells, increased ROS can alter the expression of important Ca2+ extrusion systems and damage plasma membrane proteins such as plasma membrane Ca2+ ATPase (PMCA) and the Na+-Ca2+ exchanger. PMCAs are transport proteins that remove Ca2+ from the cell, and there is a 40% decrease in PMCA1 in LC cells from glaucomatous donors. Sarco/ endoplasmic reticulum Ca2+ ATPase (SERCA) pumps are also an integral part of the cellular Ca2+ homeostasis and transfer Ca2+ from the cytosol to the sarcoplasmic/ endoplasmic reticulum, replenishing depleted Ca2+ stores. SERCA pump dysfunction with increased levels of SERCA2 and SERCA3 proteins has been detected in LC cells from glaucomatous donor eyes.82,83 All these mechanisms serve to promote and maintain abnormal calcium levels in the cell. Quill et al. demonstrated that hypotonic stretch causes a sustained increase in Ca2+, with a subsequent increase in the expression of ECM genes such as TGF-β1, chondroitin sulfate proteoglycan 2 (CSPG2), and collagen 6A3 (COL6A3). Furthermore, the study demonstrated that the increase of these matrix genes in response to strain was reduced once the LC cell was pre-treated with the L-Type Ca2+ channel blocker verapamil, where 15% strain for 24 hours with verapamil showed a significant reduction in the transcriptional expression of all three genes compared with 15% strain alone.84,85 This provides evidence that Ca2+ channel blockers may modulate ECM remodeling.

7. Lipofuscin accumulation Lipofuscin is an auto-fluorescent, non-degradable macromolecule that accumulates with age.86 Auto-phagocytosed, compromised mitochondria constitute an important source of lipofuscin and, as stated earlier, mitochondria are the most important endogenous source of ROS, so when the ROS production overwhelms the cells antioxidant defences, lipofuscin formation is

Cellular mechanisms of lamina cribrosa remodeling in glaucoma

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 5. Quantification of lipofuscin-like lysosomes in each of ten randomly selected perinuclear fields at magnifications of 7450 X and/ or 22300 X were recorded LC cells from normal and glaucomatous donor eyes. These were more numerous in LC cells from glaucoma donor eyes compared to those from normal donor eyes (4.1 × 10,000 per h.p.f. ± 1.9 vs 2.0 × 10,000 per h.p.f. ± 1.3, p = 0.002, n = 3).86

stimulated.87 Lipofuscin can alter autophagy, i.e., the lysosomal degradation of the cell’s own constituents. Accumulation of cellular lipofuscin disrupts the normal function of autophagolysosomes, as newly produced lysosomal enzymes are unsuccessfully aimed towards degrading the lysosomes containing lipofuscin, which is non-degradable. The capacity of the lysosomal degradative system therefore becomes compromised, and the cell becomes incapable of removing either oxidative damaged structures or the defective mitochondria whose ROS production promotes such damage.86 Mitochondrial recycling is consequently limited due to this process. Optic nerves of patients with glaucoma have been shown to contain higher concentrations of lipofuscin compared to normal controls, and it has been suggested that this might play a role in encouraging glaucomatous optic neuropathy.88 McElnea et al. have shown that lipofuscin accumulation is increased and localized to the LC cells from donors with glaucoma, which highlights the importance of mitochondrial dysfunction and oxidative stress in glaucoma pathophysiology (Fig. 5).86

8. Autophagy Autophagy plays an important role in cellular homeostasis, but its complex role in retinal ganglion cell

437

neurodegeneration in glaucoma remains controversial. Evidence shows that autophagy promotes both retinal ganglion cell survival and death.89 In response to raised IOP, autophagy originally activates in the dendrites of retinal ganglion cells to promote protection, but it is subsequently activated in the cytoplasm and promotes cell death. This phenomenon is related to intracellular oxidative stress. Defects in autophagy have been identified in many age-related and neurodegenerative diseases.90 Elevated levels of cellular markers of autophagy are found in glaucomatous LC cells. Coughlin et al. found increased levels of mitochondria and auto-phagosomes in the optic nerves of DBA/2J mice. DBA/2J mice have inherited, age-related progressive glaucoma and develop severe optic nerve damage by the age of 12 months.91 Autophagy protein-5 (ATG5) is required for completion of the auto-phagolysosome and ATG5 levels are considered indicative of cellular autophagy activity. Increased levels of ATG5 mRNA have been found in the LC cells of glaucomatous donor eyes. These cells synthesize new auto-phagolysosomes in response to the accumulation of lipofuscin. It has also been demonstrated that the LC3-II protein level that is associated with auto-phagosome membranes is significantly upregulated after transection of the optic nerve, implying that activation of autophagy occurs in optic nerve damage.89 This suggests that there is an attempt to maintain cellular homesostasis by removing damaged mitochondria (mitophagy) by synthesising new auto-phagolysosomes in LC cells from glaucomatous donor eyes. However, there is incomplete turnover, and a subsequent build-up of intralysosomal waste, which becomes lipofuscin. In this way, a vicious cycle of imperfect autophagy, lipofuscin formation, mitochondrial dysfunction, and oxidative stress is completed.

9. The LC and aging Aging is associated with an increase in collagen type I, III, IV, and V in the LC sheets and, as mentioned previously, an increased level of collagen type I is associated with loss of normal tissue structure and function.65,92 There is also an increase in total collagen content in the LC with increasing age, as well as decreased collagen type III relative to collagen type I.6,93 Notably, collagen type

R.K. Goetz et al.

Copyright © 2018. Kugler Publications. All rights reserved.

438

III is associated with extensible and flexible tissues, so the relative decrease in this type of collagen implies a reduction in LC elasticity.6 Studies have shown that the LC increases in thickness with age, which correlates with the evidence of increased collagen deposition.94 An increase in laminar beam thickness has also been noted with increasing age, and this may result in changes in LC compliance.93,94 The increased thickness of the LC may also decrease the diffusion of nutrients from the lamina capillaries to the optic nerve axons.94 It is thought that the highly extensible elastin components of the LC allow it to distend in response to changes in IOP; however, as the IOP rises, the collagenous components, which are relatively inextensible, prevent further deformation.93 With an increase in collagen type I and total collagen content, the ageing LC is effectively a stiffer structure. Albon et al. measured the reversibility of the LC following pressure-induced deformation. They found that in the LC of older subjects, reversibility was decreased, and thus there was susceptibility to permanent deformation.93 After the age of 40-50 years, the mechanical compliance of the LC appeared to be markedly decreased. This in turn could affect how the ganglion cell axons are damaged by increased IOP, as they are structurally related to the LC sheets. If there is reduced compliance due to increased collagen in the older LC, it is likely that the ganglion cell axons may become more damaged during compression in the rigid LC compared to a compliant, younger LC; this may explain the reversibility of optic disc cupping in children with elevated IOP.6,93 There is also an age-related increase in pentosidine at the LC. Pentosidine is a pentose that forms from crosslinking between lysine and arginine residues in collagen.95 In collagen-rich tissues such as arteries, joints, and lungs, an increase in pentosidine has been associated with age-related stiffness.96 This increase in LC pentosidine therefore implies an increase in rigidity and stiffness of the LC.6 Evidence suggests that increased substrate stiffness can subsequently stimulate the formation of myofibroblasts. LC cells plated on stiff substrates have shown increased cell size as well as increased F-actin and α-SMA expression, which confirms a conversion to the fibrotic phenotype.97 With these biochemical changes, the mechanical integrity of the aging LC is affected, which may explain the susceptibility of elderly eyes to glaucoma.93

10. Epigenetics and the LC Epigenetics is defined as the study of heritable changes in gene function caused by mechanisms other than changes in the underlying DNA sequence.98 Factors such as oxidative stress, ageing/cell senescence, obesity/BMI, and diet are known to alter epigenetic patterning. In renal and pulmonary fibrosis, epigenetic mechanisms have been shown to upregulate pro-fibrotic factors, and studies suggest that this may also hold true in glaucoma, where epigenetics may contribute to the upregulation of ROS.99 Epigenetic alterations are seen in a number of other diseases such as Huntington’s, Alzheimer’s, autoimmune diseases, and a number of cancers. Research has already been directed towards epigenetic treatments which are now currently available and in clinical use, e.g., HDAC inhibitors in lymphoma.100-102 Mechanisms that regulate gene expression include DNA methylation, histone modifications, and microRNAs. Histones are proteins that are wrapped around DNA. When the DNA is tightly wrapped, transcription is repressed; when it is more loosely wrapped, transcription is more active. DNA methylation involves the addition of a methyl group to the fifth carbon of the cytosine base in the DNA sequence. This most commonly occurs in the dinucleotide CpG and plays a role in gene repression; CpG sites in promoters are typically unmethylated when genes are expressed. Histone acetylation and deacetylation occur when acetyl groups are added to or removed from the lysine tails of the histone proteins, and are associated with transctiptional activation and repression, respectively.103 Global DNA methylation has been shown to be significantly increased in LC cells from glaucomatous donor eyes and is accompanied by increased expression of DNA methyltransferases (DNMTs) 1 and 3A. DNMTs are the enzymes that regulate DNA methylation.104 In kidney fibrosis, DNMT1 promotes the hypermethylation of RASAL1, which is a gene that codes an inhibitor of Ras oncogene, resulting in persistent fibroblast activation.105 Due to the existence of epigenetic modulators such as methylation inhibitors, this could prove to be a potential target for future therapeutic options in glaucoma.

Cellular mechanisms of lamina cribrosa remodeling in glaucoma

References 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

Copyright © 2018. Kugler Publications. All rights reserved.

14.

15. 16.

17.

Anderson DR. Ultrastructure of human and monkey lamina cribrosa and optic nerve head. Arch Ophthalmol. 1969;82:800814. Hernandez MR, Luo XX, Igoe F, Neufeld AH. Extracellular matrix of the human lamina cribrosa. Am J Ophthalmol. 1987;104:567576. Quigley HA, Brown A, Dorman-Pease ME. Alterations in elastin of the optic nerve head in human and experimental glaucoma. Br J Ophthalmol. 1991;75:552-557. Modesti A, Kalebic T, Scarpa S, et al. Type V collagen in human amnion is a 12 nm fibrillar component of the pericellular interstitium. Eur J Cell Biol. 1984;35:246-255. Keene DR, Engvall E, Glanville RW. Ultrastructure of type VI collagen in human skin and cartilage suggests an anchoring function for this filamentous network. J Cell Biol. 1988;107:1995-2006. Albon J, Karwatowski WS, Avery N, Easty DL, Duance VC. Changes in the collagenous matrix of the aging human lamina cribrosa. Br J Ophthalmol. 1995;79:368-375. Quigley HA, Addicks EM. Regional differences in the structure of the lamina cribrosa and their relation to glaucomatous optic nerve damage. Arch Ophthalmol. 1981;99:137-143. Quigley HA, Addicks EM, Green WR, Maumenee AE. Optic nerve damage in human glaucoma. II. The site of injury and susceptibility to damage. Arch Ophthalmol. 1981;99:635-649. Miller KM, Quigley HA. The clinical appearance of the lamina cribrosa as a function of the extent of glaucomatous optic nerve damage. Ophthalmology. 1988;95:135-138. Jonas JB, Berenshtein E, Holbach L. Anatomic relationship between lamina cribrosa, intraocular space, and cerebrospinal fluid space. Invest Ophthalmol Vis Sci. 2003;44:5189-5195. Quigley H, Anderson DR. The dynamics and location of axonal transport blockade by acute intraocular pressure elevation in primate optic nerve. Invest Ophthalmol. 1976;15:606-616. Guo L, Moss SE, Alexander RA, Ali RR, Fitzke FW, Cordeiro MF. Retinal ganglion cell apoptosis in glaucoma is related to intraocular pressure and IOP-induced effects on extracellular matrix. Invest Ophthalmol Vis Sci. 2005;46:175-182. Cioffi GA. Ischemic model of optic nerve injury. Trans Am Ophthalmol Soc. 2005;103:592-613. Fuchshofer R, Tamm ER. The role of TGF-β in the pathogenesis of primary open-angle glaucoma. Cell Tissue Res. 2012;347:279290. Jonas JB. Role of cerebrospinal fluid pressure in the pathogenesis of glaucoma. Acta Ophthalmol. 2011;89:505-514. Hernandez MR, Luo XX, Andrzejewska W, Neufeld AH. Age-related changes in the extracellular matrix of the human optic nerve head. Am J Ophthalmol. 1989;107:476-484. Burgoyne CF, Downs JC, Bellezza AJ, Suh JK, Hart RT. The optic nerve head as a biomechanical structure: a new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage. Prog Retin Eye Res. 2005;24:39-73.

439 18. The Advanced Glaucoma Intervention Study (AGIS): 7. The relationship between control of intraocular pressure and visual field deterioration. The AGIS Investigators. Am J Ophthalmol. 2000;130:429-440. 19. Downs JC, Roberts MD, Sigal IA. Glaucomatous cupping of the lamina cribrosa: a review of the evidence for active progressive remodeling as a mechanism. Exp Eye Res. 2011;93:133-140. 20. Zhavoronkov A, Kanherkar RR, Izumchenko E, et al. Pro-fibrotic pathway activation in trabecular meshwork and lamina cribrosa is the main driving force of glaucoma. Cell Cycle. 2016;15:1643-1652. 21. Wynn TA. Cellular and molecular mechanisms of fibrosis. J Pathol. 2008;214:199-210. 22. Hinz B, Phan SH, Thannickal VJ, Galli A, Bochaton-Piallat ML, Gabbiani G. The myofibroblast: one function, multiple origins. Am J Pathol. 2007;170:1807-1816. 23. Tomasek JJ, Gabbiani G, Hinz B, Chaponnier C, Brown RA. Myofibroblasts and mechano-regulation of connective tissue remodelling. Nat Rev Mol Cell Biol. 2002;3:349-363. 24. Wipff PJ, Hinz B. Integrins and the activation of latent transforming growth factor beta1 - an intimate relationship. Eur J Cell Biol. 2008;87:601-615. 25. Horowitz JC, Rogers DS, Sharma V, et al. Combinatorial activation of FAK and AKT by transforming growth factor-beta1 confers an anoikis-resistant phenotype to myofibroblasts. Cell Signal. 2007;19:761-771. 26. Kulasekaran P, Scavone CA, Rogers DS, Arenberg DA, Thannickal VJ, Horowitz JC. Endothelin-1 and transforming growth factor-beta1 independently induce fibroblast resistance to apoptosis via AKT activation. Am J Respir Cell Mol Biol. 2009;41:484-493. 27. Georges PC, Hui JJ, Gombos Z, et al. Increased stiffness of the rat liver precedes matrix deposition: implications for fibrosis. Am J Physiol Gastrointest Liver Physiol. 2007;293:G1147-54. 28. Hernandez MR, Igoe F, Neufeld AH. Cell culture of the human lamina cribrosa. Invest Ophthalmol Vis Sci. 1988;29:78-89. 29. Yue B. Biology of the extracellular matrix: an overview. J Glaucoma. 2014;23:S20-3. 30. Hernandez MR, Ye H. Glaucoma: changes in extracellular matrix in the optic nerve head. Ann Med. 1993;25:309-315. 31. Hernandez MR. Ultrastructural immunocytochemical analysis of elastin in the human lamina cribrosa. Changes in elastic fibers in primary open-angle glaucoma. Invest Ophthalmol Vis Sci. 1992;33:2891-2903. 32. Hernandez MR, Andrzejewska WM, Neufeld AH. Changes in the extracellular matrix of the human optic nerve head in primary open-angle glaucoma. Am J Ophthalmol. 1990;109:180-188. 33. Hernandez MR. The optic nerve head in glaucoma: role of astrocytes in tissue remodeling. Prog Retin Eye Res. 2000;19:297-321. 34. Ye H, Hernandez MR. Heterogeneity of astrocytes in human optic nerve head. J Comp Neurol. 1995;362:441-452. 35. Hernandez MR, Miao H, Lukas T. Astrocytes in glaucomatous optic neuropathy. Prog Brain Res. 2008;173:353-373. 36. Johnson EC, Morrison JC. Friend or foe? Resolving the impact of glial responses in glaucoma. J Glaucoma. 2009;18:341-353.

Copyright © 2018. Kugler Publications. All rights reserved.

440 37. Ridet JL, Malhotra SK, Privat A, Gage FH. Reactive astrocytes: cellular and molecular cues to biological function. Trends Neurosci. 1997;20:570-577. 38. Manso AM, Elsherif L, Kang SM, Ross RS. Integrins, membrane-type matrix metalloproteinases and ADAMs: potential implications for cardiac remodeling. Cardiovasc Res. 2006;69:574-584. 39. Salvador-Silva M, Ricard CS, Agapova OA, Yang P, Hernandez MR. Expression of small heat shock proteins and intermediate filaments in the human optic nerve head astrocytes exposed to elevated hydrostatic pressure in vitro. J Neurosci Res. 2001;66:59-73. 40. Hernandez MR, Pena JD, Selvidge JA, Salvador-Silva M, Yang P. Hydrostatic pressure stimulates synthesis of elastin in cultured optic nerve head astrocytes. Glia. 2000;32:122-136. 41. Liu B, Neufeld AH. Expression of nitric oxide synthase-2 (NOS-2) in reactive astrocytes of the human glaucomatous optic nerve head. Glia. 2000;30:178-186. 42. Wax MB, Tezel G, Kobayashi S, Hernandez MR. Responses of different cell lines from ocular tissues to elevated hydrostatic pressure. Br J Ophthalmol. 2000;84:423-428. 43. Micallef L, Vedrenne N, Billet F, Coulomb B, Darby IA, Desmoulière A. The myofibroblast, multiple origins for major roles in normal and pathological tissue repair. Fibrogenesis Tissue Repair. 2012;5:S5. 44. Gabbiani G. The myofibroblast in wound healing and fibrocontractive diseases. J Pathol. 2003;200:500-503. 45. Liu RM, Desai LP. Reciprocal regulation of TGF-β and reactive oxygen species: A perverse cycle for fibrosis. Redox Biol. 2015;6:565-577. 46. Kirwan RP, Wordinger RJ, Clark AF, O’Brien CJ. Differential global and extra-cellular matrix focused gene expression patterns between normal and glaucomatous human lamina cribrosa cells. Mol Vis. 2009;15:76-88. 47. Hamilton DW. Functional role of periostin in development and wound repair: implications for connective tissue disease. J Cell Commun Signal. 2008;2:9-17. 48. Kirwan RP, Fenerty CH, Crean J, Wordinger RJ, Clark AF, O’Brien CJ. Influence of cyclical mechanical strain on extracellular matrix gene expression in human lamina cribrosa cells in vitro. Mol Vis. 2005;11:798-810. 49. Zode GS, Sethi A, Brun-Zinkernagel AM, Chang IF, Clark AF, Wordinger RJ. Transforming growth factor-β2 increases extracellular matrix proteins in optic nerve head cells via activation of the Smad signaling pathway. Mol Vis. 2011;17:1745-1758. 50. Lu P, Takai K, Weaver VM, Werb Z. Extracellular matrix degradation and remodeling in development and disease. Cold Spring Harb Perspect Biol. 2011;3. 51. Fukuchi T, Ueda J, Hanyu T, Abe H, Sawaguchi S. Distribution and expression of transforming growth factor-beta and platelet-derived growth factor in the normal and glaucomatous monkey optic nerve heads. Jpn J Ophthalmol. 2001;45:592-599. 52. Pena JD, Taylor AW, Ricard CS, Vidal I, Hernandez MR. Transforming growth factor beta isoforms in human optic nerve heads. Br J Ophthalmol. 1999;83:209-218.

R.K. Goetz et al. 53. Prendes MA, Harris A, Wirostko BM, Gerber AL, Siesky B. The role of transforming growth factor β in glaucoma and the therapeutic implications. Br J Ophthalmol. 2013;97:680-686. 54. Fuchshofer R. The pathogenic role of transforming growth factor-β2 in glaucomatous damage to the optic nerve head. Exp Eye Res. 2011;93:165-169. 55. Kirwan RP, Crean JK, Fenerty CH, Clark AF, O’Brien CJ. Effect of cyclical mechanical stretch and exogenous transforming growth factor-beta1 on matrix metalloproteinase-2 activity in lamina cribrosa cells from the human optic nerve head. J Glaucoma. 2004;13:327-334. 56. Kirwan RP, Leonard MO, Murphy M, Clark AF, O’Brien CJ. Transforming growth factor-beta-regulated gene transcription and protein expression in human GFAP-negative lamina cribrosa cells. Glia. 2005;52:309-324. 57. Knepper PA, Goossens W, Hvizd M, Palmberg PF. Glycosaminoglycans of the human trabecular meshwork in primary open-angle glaucoma. Invest Ophthalmol Vis Sci. 1996;37:1360-1367. 58. Sawaguchi S, Yue BY, Fukuchi T, et al. Collagen fibrillar network in the optic nerve head of normal monkey eyes and monkey eyes with laser-induced glaucoma--a scanning electron microscopic study. Curr Eye Res. 1999;18:143-149. 59. Rao VR, Krishnamoorthy RR, Yorio T. Endothelin-1 mediated regulation of extracellular matrix collagens in cells of human lamina cribrosa. Exp Eye Res. 2008;86:886-894. 60. Eng FJ, Friedman SL. Fibrogenesis I. New insights into hepatic stellate cell activation: the simple becomes complex. Am J Physiol Gastrointest Liver Physiol. 2000;279:G7-G11. 61. Eddy AA. Molecular basis of renal fibrosis. Pediatr Nephrol. 2000;15:290-301. 62. Wakatsuki T, Schlessinger J, Elson EL. The biochemical response of the heart to hypertension and exercise. Trends Biochem Sci. 2004;29:609-617. 63. Tsukada S, Parsons CJ, Rippe RA. Mechanisms of liver fibrosis. Clin Chim Acta. 2006;364:33-60. 64. Noske W, Hensen J, Wiederholt M. Endothelin-like immunoreactivity in aqueous humor of patients with primary open-angle glaucoma and cataract. Graefes Arch Clin Exp Ophthalmol. 1997;235:551-552. 65. Varga J, Brenner DA, Phan SH. Fibrosis research: Methods and Protocols. Totowa, NJ: Humana Press, 2005. 66. Specks U, Nerlich A, Colby TV, Wiest I, Timpl R. Increased expression of type VI collagen in lung fibrosis. Am J Respir Crit Care Med. 1995;151:1956-1964. 67. Harumiya S, Gibson MA, Koshihara Y. Antisense suppression of collagen VI synthesis results in reduced expression of collagen I in normal human osteoblast-like cells. Biosci Biotechnol Biochem. 2002;66:2743-2747. 68. Thirunavukkarasu C, Yang Y, Subbotin VM, Harvey SA, Fung J, Gandhi CR. Endothelin receptor antagonist TAK-044 arrests and reverses the development of carbon tetrachloride induced cirrhosis in rats. Gut. 2004;53:1010-1019. 69. He S, Prasanna G, Yorio T. Endothelin-1-mediated signaling in the expression of matrix metalloproteinases and tissue inhibi-

Cellular mechanisms of lamina cribrosa remodeling in glaucoma

70.

71.

72.

73.

74.

75. 76.

77.

78.

79.

80.

81.

Copyright © 2018. Kugler Publications. All rights reserved.

82.

83.

84.

85.

tors of metalloproteinases in astrocytes. Invest Ophthalmol Vis Sci. 2007;48:3737-3745. Takagi Y, Ninomiya H, Sakamoto A, Miwa S, Masaki T. Structural basis of G protein specificity of human endothelin receptors. A study with endothelinA/B chimeras. J Biol Chem. 1995;270:10072-10078. Prasanna G, Hulet C, Desai D, et al. Effect of elevated intraocular pressure on endothelin-1 in a rat model of glaucoma. Pharmacol Res. 2005;51:41-50. Rao VR, Krishnamoorthy RR, Yorio T. Endothelin-1, endothelin A and B receptor expression and their pharmacological properties in GFAP negative human lamina cribrosa cells. Exp Eye Res. 2007;84:1115-1124. Prasanna G, Krishnamoorthy R, Clark AF, Wordinger RJ, Yorio T. Human optic nerve head astrocytes as a target for endothelin-1. Invest Ophthalmol Vis Sci. 2002;43:2704-2713. Stokely ME, Brady ST, Yorio T. Effects of endothelin-1 on components of anterograde axonal transport in optic nerve. Invest Ophthalmol Vis Sci. 2002;43:3223-3230. Prasanna G, Krishnamoorthy R, Yorio T. Endothelin, astrocytes and glaucoma. Exp Eye Res. 2011;93:170-177. Yamashita K, Discher DJ, Hu J, Bishopric NH, Webster KA. Molecular regulation of the endothelin-1 gene by hypoxia. Contributions of hypoxia-inducible factor-1, activator protein-1, GATA-2, AND p300/CBP. J Biol Chem. 2001;276:12645-12653. Tezel G, Wax MB. Hypoxia-inducible factor 1alpha in the glaucomatous retina and optic nerve head. Arch Ophthalmol. 2004;122:1348-1356. McCain ML, Parker KK. Mechanotransduction: the role of mechanical stress, myocyte shape, and cytoskeletal architecture on cardiac function. Pflugers Arch. 2011;462:89-104. Irnaten M, Barry RC, Quill B, Clark AF, Harvey BJ, O’Brien CJ. Activation of stretch-activated channels and maxi-K+ channels by membrane stress of human lamina cribrosa cells. Invest Ophthalmol Vis Sci. 2009;50:194-202. Tezel G, Wax MB. Increased production of tumor necrosis factor-alpha by glial cells exposed to simulated ischemia or elevated hydrostatic pressure induces apoptosis in cocultured retinal ganglion cells. J Neurosci. 2000;20:8693-8700. Irnaten M, Barry RC, Wallace DM, et al. Elevated maxi-K(+) ion channel current in glaucomatous lamina cribrosa cells. Exp Eye Res. 2013;115:224-229. Osborne NN. Mitochondria: Their role in ganglion cell death and survival in primary open angle glaucoma. Exp Eye Res. 2010;90:750-757. McElnea EM, Quill B, Docherty NG, et al. Oxidative stress, mitochondrial dysfunction and calcium overload in human lamina cribrosa cells from glaucoma donors. Mol Vis. 2011;17:11821191. Quill B, Docherty NG, Clark AF, O’Brien CJ. The effect of graded cyclic stretching on extracellular matrix-related gene expression profiles in cultured primary human lamina cribrosa cells. Invest Ophthalmol Vis Sci. 2011;52:1908-1915. Quill B, Irnaten M, Docherty NG, et al. Calcium channel blockade reduces mechanical strain-induced extracellular

441 matrix gene response in lamina cribrosa cells. Br J Ophthalmol. 2015;99:1009-1014. 86. McElnea EM, Hughes E, McGoldrick A, et al. Lipofuscin accumulation and autophagy in glaucomatous human lamina cribrosa cells. BMC Ophthalmol. 2014;14:153. 87. Cadenas E, Davies KJ. Mitochondrial free radical generation, oxidative stress, and aging. Free Radic Biol Med. 2000;29:222230. 88. Fernandez de Castro JP, Mullins RF, Manea AM, Hernandez J, Wallen T, Kuehn MH. Lipofuscin in human glaucomatous optic nerves. Exp Eye Res. 2013;111:61-66. 89. Rodríguez-Muela N, Germain F, Mariño G, Fitze PS, Boya P. Autophagy promotes survival of retinal ganglion cells after optic nerve axotomy in mice. Cell Death Differ. 2012;19:162-169. 90. Lin WJ, Kuang HY. Oxidative stress induces autophagy in response to multiple noxious stimuli in retinal ganglion cells. Autophagy. 2014;10:1692-1701. 91. Coughlin L, Morrison RS, Horner PJ, Inman DM. Mitochondrial morphology differences and mitophagy deficit in murine glaucomatous optic nerve. Invest Ophthalmol Vis Sci. 2015;56:14371446. 92. Morrison JC, Jerdan JA, Dorman ME, Quigley HA. Structural proteins of the neonatal and adult lamina cribrosa. Arch Ophthalmol. 1989;107:1220-1224. 93. Albon J, Purslow PP, Karwatowski WS, Easty DL. Age related compliance of the lamina cribrosa in human eyes. Br J Ophthalmol. 2000;84:318-323. 94. Kotecha A, Izadi S, Jeffery G. Age-related changes in the thickness of the human lamina cribrosa. Br J Ophthalmol. 2006;90:1531-1534. 95. Sell DR, Monnier VM. Structure elucidation of a senescence cross-link from human extracellular matrix. Implication of pentoses in the aging process. J Biol Chem. 1989;264:2159721602. 96. Sell DR, Monnier VM. End-stage renal disease and diabetes catalyze the formation of a pentose-derived crosslink from aging human collagen. J Clin Invest. 1990;85:380-384. 97. Liu B, Kilpatrick J, Wallace DM, O’Brien CJ, Jarvis S. Altered Elasticity of Normal and Glaucoma Lamina Cribrosa (NLC and GLC) Cells in Response to Biophysical Stimuli. Invest Ophthalmol Vis Sci. 2015;56:4824. 98. McDonnell F, O’Brien C, Wallace D. The role of epigenetics in the fibrotic processes associated with glaucoma. J Ophthalmol. 2014;2014:750459. 99. Wiggs JL. The cell and molecular biology of complex forms of glaucoma: updates on genetic, environmental, and epigenetic risk factors. Invest Ophthalmol Vis Sci. 2012;53:2467-2469. 100. Kanwal R, Gupta S. Epigenetic modifications in cancer. Clin Genet. 2012;81:303-311. 101. Qureshi IA, Mehler MF. Advances in epigenetics and epigenomics for neurodegenerative diseases. Curr Neurol Neurosci Rep. 2011;11:464-473. 102. Chuang DM, Leng Y, Marinova Z, Kim HJ, Chiu CT. Multiple roles of HDAC inhibition in neurodegenerative conditions. Trends Neurosci. 2009;32:591-601.

442

Copyright © 2018. Kugler Publications. All rights reserved.

103. Yao HW, Li J. Epigenetic modifications in fibrotic diseases: implications for pathogenesis and pharmacological targets. J Pharmacol Exp Ther. 2015;352:2-13. 104. McDonnell FS, McNally SA, Clark AF, O’Brien CJ, Wallace DM. Increased global DNA methylation and decreased TGFβ1 promoter methylation in glaucomatous lamina cribrosa cells. J Glaucoma. 2016;25:e834-e842.

R.K. Goetz et al. 105. Bechtel W, McGoohan S, Zeisberg EM, et al. Methylation determines fibroblast activation and fibrogenesis in the kidney. Nat Med. 2010;16:544-550.

30. Optic nerve head biomechanics in health, aging, and disease J. Crawford Downs1 Department of Ophthalmology, University of Alabama at Birmingham School of Medicine Birmingham, AL, USA

1

1. Introduction Misconception This non-technical chapter is focused upon educating the reader on optic nerve head (ONH) biomechanics in both aging and disease along two main themes: what is known about how mechanical forces and the resulting deformations are distributed in the posterior pole and ONH biomechanics, and what is known about how the living system responds to those deformations (mechanobiology). We focus on how the ONH responds to IOP elevations as a structural system, insofar as the acute mechanical response of the lamina cribrosa (LC) is confounded with the responses of the peripapillary sclera, prelaminar neural tissues, and retrolaminar optic nerve. We discuss the biomechanical basis for IOP-driven changes in connective tissues, blood flow, and cellular responses. We use glaucoma as the primary framework to present the important aspects of ONH biomechanics in aging and disease, as ONH biomechanics, aging, and the posterior pole extracellular matrix (ECM) are thought to be centrally involved in glaucoma susceptibility, onset, and progression.

Copyright © 2018. Kugler Publications. All rights reserved.

2. The ONH as a biomechanical structure Glaucoma is primarily a disease of aging1,2 and is one of the leading causes of blindness in the developed world.3 ONH biomechanics and the posterior pole ECM are also thought to be centrally involved in glaucoma susceptibility, as well as disease onset and progression.4 Hence, we will use glaucoma as the primary framework to

Laplace’s Law for Thin-walled Pressure Vessels has historically been used to estimate stress in the eye wall, but this Law assumes that the vessel has uniform isotropic material properties, perfectly spherical shape, and uniform wall thickness. The eye doesn’t conform to these assumptions, as it’s not spherical, has an ocular coat thickness that varies by a factor of two, and exhibits inhomogeneous, anisotropic material properties. Hence, Laplace’s Law shouldn’t be used to estimate biomechanical stress in the eye.

present the important aspects of ONH biomechanics in health, aging, and disease in this review. The ONH is of particular interest from a biomechanical perspective because it is a weak spot within an otherwise strong corneoscleral envelope. Overwhelming evidence suggests that the LC is the principal site of retinal ganglion cell (RGC) axonal insult in glaucoma.5,6 Glaucoma is often associated with a characteristic pattern of focal visual field damage that is not present in other optic neuropathies, which often manifests as a distinct arcuate scotoma that respects the horizontal raphae.7 The ONH is the only location where the axons are packed in such a way that a focal lesion could create this characteristic visual field defect, which also suggests that the ONH is the site of glaucoma damage. In this

Correspondence: J. Crawford Downs, PhD, Professor, Department of Ophthalmology, University of Alabama at Birmingham School of Medicine, 1670 University Blvd., VH 390A, Birmingham, AL 35294, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 443-464 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

444

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 1. The ONH is a 3-D structure comprised of multiple interactive tissue systems that exist on different scales. This complexity has been a formidable deterrent to characterizing its mechanical environment. This figure shows a high-resolution 3-D reconstruction of the LC from a human donor eye. The fluorescent histologic reconstruction was created using a custom, automated, microtome-based episcopic fluorescent image capture device that images the embedded ONH tissue block face after each thin section is cut away, thereby capturing the LC structure in an image volume at 1.5 x 1.5 x 1.5 micrometer voxel resolution. Regional differences in laminar density and beam orientation are evident. Callouts show the laminar microstructure (top); the typical mechanical strain in the laminar microstructure in response to an IOP elevation from 10 to 45 mmHg as estimated by a computational model (middle); and the F-actin (red) and αSMA (green) in activated fibroblastic cells that engender LC remodeling after cyclic strain is applied (bottom). Figure reproduced with permission from Downs and Girkin.138

sense, glaucomatous optic neuropathy may be viewed as an axonopathy, where damage to the visual pathway is driven by insult to RGC axons as they exit the eye at the ONH.5,6 Hence, neither neuroprotection of the RGC soma or neuroregeneration of the RGC axons is likely to be effective in preventing, slowing, or reversing vision loss in glaucoma unless the pathologic environment in the ONH is also simultaneously addressed. As such, glaucoma prevention and treatment is a three-legged stool in which the health of the RGC soma, its axon, and the axonal pathway to the brain must be simultaneously supported and maintained to prevent vision loss. The mechanisms of RGC axonal insult at the ONH insult are poorly understood, but we present a framework of IOP-driven ONH biomechanics as a central mechanism in the pathophysiology of glaucoma in this chapter. The LC provides structural and functional support to the RGC axons as they pass from the relatively

J. Crawford Downs

high-pressure environment in the eye to a low-pressure region in the retrobulbar cerebrospinal space.4,8 To protect the RGCs in this unique anatomic region, the LC in higher primates has developed into a complex structure composed of a 3-D network of flexible beams of connective tissue (Fig. 1). The ONH is nourished by the short posterior ciliary arteries, which penetrate the immediate peripapillary sclera to feed capillaries contained within the laminar beams.9 This intra-scleral and intra-laminar vasculature is unique in that it is encased in load-bearing connective tissue, either within the scleral wall adjacent to the LC, or within the laminar beams themselves. While there may be other primary or secondary factors in the retina and brain that contribute to RGC axonal damage and loss, the preponderance of evidence suggests that the laminar region of the ONH is a principal site of insult. The LC is a fenestrated, 3-D network of load-bearing trabeculae, many of which contain capillaries, that provides structural and nutrient support to the RGC axons as they leave the eye on their path to the brain. From a biomechanical perspective, the LC is a weak spot in an otherwise robust pressure vessel, the corneoscleral envelope. This arises from the fact that the LC is only approximately one-third the thickness of the sclera at the scleral canal, and its load-bearing connective tissue components comprise only approximately 40% of the tissue volume in the laminar region of the ONH. Thus, the LC must accommodate the conflicting tasks of providing structural support to the ONH by withstanding IOP-related mechanical strain, or local deformation, while also allowing the axons an open pathway to leave the eye. The 3-D LC trabecular structure also contains the vascular capillaries that nourish the axons and cells in the laminar region, so resisting high mechanical strains that may reduce vessel lumen size and blood flow is paramount as well (Figs. 1 and 2). Consideration of the anatomy of the LC and peripapillary sclera alone suggests that the classic ‘mechanical’ and ‘vascular’ mechanisms of glaucomatous injury are inseparably intertwined (Fig. 2).10 To incorporate these concepts into an overarching conceptual framework, we and others have proposed that the ONH is a biomechanical structure in which IOPrelated stress (force/cross-sectional area) and strain (local relative deformation of the tissues) are central determinants of both the physiology and pathophysi-

Copyright © 2018. Kugler Publications. All rights reserved.

Optic nerve head biomechanics in health, aging, and disease

445

Fig. 2. IOP-related stress and strain are a constant presence within the ONH at all levels of IOP. IOP and cerebrospinal fluid pressure act mechanically on the tissues of the eye, producing deformations, strain and stress within the tissues. These deformations depend on the eye-specific geometry and material properties of the individual eye. In a biomechanical paradigm, the stress and strain will alter the blood flow (primarily), and the delivery of nutrients (secondarily) through chronic alterations in connective tissue stiffness and diffusion properties. IOP-related stress and strain also induce connective tissue damage directly (laminar beam yield), or indirectly (cell mediated remodeling), which drives a connective tissue remodeling process that alters the tissues’ geometry and mechanical response to loading. This feeds back directly onto the mechanical effects of IOP. Adapted from Sigal et al.10

ology of the ONH tissues and their blood supply at all levels of IOP (Fig 2).8,10-12 IOP perturbations induce not only alterations to the load-bearing ECM of the LC and the peripapillary sclera, but also activate the resident cells of these tissues and damage the RGC axons in the ONH.13 Age-related changes to the cells and ECM also significantly affect the ONH biomechanical

environment, so aging is an important pillar of the biomechanical framework.14 The prevalence of glaucoma is much higher in persons of African heritage compared to persons of European descent.3,15 Recent studies have shown significant racial differences in scleral collagen architecture16 as well as in scleral stiffness with age17,18 and race,19,20 which indicates that both aging and racial

446

J. Crawford Downs

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. High- and low-frequency IOP fluctuation in the NHP. (Top) Screen capture of approximately 7 seconds of the continuous IOP tracing from an unrestrained awake primate showing baseline mean IOP of ~8-13 mmHg and IOP fluctuations up to 12 mmHg associated with blinks and saccadic eye movements. IOP fluctuations can be much larger and of longer duration, especially when the animal squints or is agitated or stressed. (Bottom) Plot of the 10-minute time-window average of 24 hours of continuous IOP showing low-frequency IOP fluctuation from a single NHP. The color of the plot points and lines indicate how much data were removed from each 10-minute window after post-hoc digital filtering of signal dropout and noise. Green indicates that 100% of the continuous IOP data were used in the 10-minute average IOP plotted in each point, and yellow indicates that 50% were eliminated due to signal dropout or noise. Note the fluctuations in IOP are substantial even when the high-frequency transient IOP fluctuations seen in the top plot are averaged out. Adapted from Downs et al.21

differences in ocular biomechanics may play a role in glaucoma susceptibility. Although clinical IOP-lowering remains the only proven method of preventing the onset and progression of glaucoma, the role of IOP in the development and progression of the disease is not well understood. This largely arises from the clinical observation that significant numbers of patients with normal IOPs develop glaucoma (e.g., normal- or low-tension glaucoma), while other individuals with elevated IOP show no signs of the disease. This could mean that IOP (or some factor driven by IOP) is a primary causative factor in glaucoma, and IOP vulnerability varies between individuals. Another possibility is that clinical characterization of mean IOP using infrequent snapshot measurements fails to capture exposure to injurious IOP fluctuations that are partly driving the

disease in these normotensive glaucoma patients, which makes the IOP-glaucoma relationship murky. Please refer to the chapter on IOP in this book for a thorough presentation of the role of IOP in ocular homeostasis and potential disease pathology. Recent data indicate that IOP fluctuates as much as 5 mmHg day-to-day and hour-to-hour, and 15 to 40 mmHg second-to-second when measured continuously via telemetry in unrestrained, awake non-human primates (NHP) (Fig. 3).21 Very little is known about IOP fluctuations in humans and how the eye responds to these fluctuations, but IOP levels at all timescales have the potential to injure the RGC axons in the ONH.22,23 Interestingly, recent work has shown that the sclera,17,18,24 LC,25 and cornea26 stiffen significantly with age. One might assume this to be protective against axon damage, as stiffer connective tissues resist

Copyright © 2018. Kugler Publications. All rights reserved.

Optic nerve head biomechanics in health, aging, and disease

mechanical deformation better than more compliant tissues. However, stiffening of the corneoscleral shell also induces larger transient IOP fluctuations related to blinks, saccades, and vascular filling, in that the eye is less able to elastically expand to absorb IOP impulse (a measure of the mechanical insult delivered by transient IOP fluctuations). Hence, it may be that in the process of age-related connective tissue stiffening, the eye has remodeled to a state wherein the ONH is subjected to much larger transient IOP fluctuations. It is important to note however, that the magnitude of mechanical strain fluctuations in the tissues is likely to be much more important in terms of ONH and peripapillary scleral homeostasis than mean IOP and/or its transient fluctuations. Whether it is mean IOP and/or IOP fluctuations that drive glaucomatous pathogenesis, there is a wide spectrum of individual susceptibility to IOP-related glaucomatous vision loss, and the biomechanical effects of IOP on the tissues of the ONH likely play a central role in the development and progression of the disease at all IOPs. The individual susceptibility of a particular patient’s ONH to IOP insult is likely a function of the biomechanical response of the constituent tissues and the resulting mechanical, ischemic and cellular events driven by that response. Hence, eyes with a particular combination of tissue geometry and material properties may be susceptible to damage at normal IOP, while others may have a combination of ONH tissue geometry and material properties that can withstand even high levels of IOP. Age-related changes in the ONH and peripapillary sclera alone may change the biomechanical environment of the ONH sufficiently that RGC axonal damage results, even in the absence of chronically elevated IOP. Recent studies have also suggested that vascular deficiencies,27,28 as well as age-related loss of metabolic efficiency29,30 are also likely to contribute to the increased risk of glaucoma in the elderly. In this chapter, we focus on ocular biomechanics along two main themes: what is known about how mechanical forces and the resulting deformations are distributed in the posterior pole and ONH (biomechanics) and what is known about how the living system responds to those deformations (mechanobiology) in both aging and disease.

447

3. Mechanical environment of the ONH and peripapillary sclera 3.1. Basic engineering concepts The following are fundamental terms and concepts from engineering mechanics31 that may not be familiar to clinicians and non-engineering scientists. Stress is a measure of the load applied to, transmitted through, or carried by a material or tissue. Stress can be defined as the amount of force applied to a tissue divided by the cross-sectional area over which it acts (e.g., pressure is a stress and can be expressed in pounds per square inch or psi). It is important to note that stress is a mathematical quantity that can be calculated, but cannot be directly measured, felt, or observed. Strain is a measure of the local deformation in a material or tissue induced by an applied stress. It is important to recognize that strain, unlike stress, may be observed and measured experimentally. The localized relative displacement described by the strain provides a measurable indicator of the level of micro-deformation (stretch, compression, or shearing) experienced by the tissue. Local strain is known to induce cellular mechanotransduction,32 and strain in collagen fibrils has been shown to passively protect the fibrils from enzymatic degradation by matrix metalloproteases.33 Both these strain-driven mechanisms likely play important roles in connective tissue remodeling. The material properties of a tissue describe its ability to resist deformation under applied load, and therefore relate stress to strain (i.e., load to deformation). Material properties can be thought of as the stiffness or compliance of a particular tissue or material that is intrinsic to the material itself. Hence, a stiff tissue such as the sclera can have high stress, but low strain, while an equal volume of compliant tissue like the retina might have high strain even at low levels of stress. The material properties of a tissue are characterized by the stiffness, morphology, and interactions of its constituents (e.g., elastin, collagen fibrils, proteoglycans, and cells). Biological tissues are living matter; their material properties are not constant, but change over the lifespan due to aging, remodeling, wound healing, and disease. Another very useful concept in biomechanics is structural stiffness, which incorporates both the material properties and geometry of a complex load-bearing

448

J. Crawford Downs

Fig. 4. Complexities in the posterior pole biomechanical response. The image on the left shows the strain distribution in a macroscale model of the connective tissues of the posterior pole of the eye. Note that thickness variations in the sclera give rise to a non-uniform distribution of strain within the scleral shell, and that the strains are lower in the sclera than in the more compliant LC. The middle image shows a detail of the strain field within the macroscale representation of the LC. While this portion of the model has been assigned regional material properties related to the amount and orientation of the laminar beams (based on 3-D reconstruction data such as that in Fig. 5), the continuum description represents a bulk homogenization of the specific microarchitecture in each element. The right image shows the distribution of mechanical strain at the microscale in the laminar beam microarchitecture, demonstrating that strains concentrate focally in individual beams and around individual pores.

Copyright © 2018. Kugler Publications. All rights reserved.

structure into a composite measure of the structure’s resistance to deformation. In the posterior pole, both the geometry and material properties of the sclera and LC contribute to structural stiffness, and hence determine the deformation of the ONH and peripapillary sclera when exposed to IOP. As such, individual ONH biomechanics is governed by the geometry (size and shape of the scleral canal, scleral thickness, regional laminar density, and laminar beam orientation) and the material properties (stiffness) of the LC and sclera. Hence, two eyes exposed to identical IOPs may exhibit very different strain fields due to differences in their structural stiffness. 3.2. Overview of the mechanical environment of the ONH and peripapillary sclera The biomechanics of the ONH and peripapillary sclera are very complex (Fig. 4). IOP-related stress generates strain patterns in the ONH and peripapillary sclera that are not only dependent on local connective tissue geometries (Figs. 1 and 4) and material properties, but are also influenced by complex dynamic loading conditions (Fig. 3). The important factors governing

the ONH’s response to IOP include the alignment and density of collagen fibrils in each tissue (stiffness and anisotropy),34-36 the regional density and thickness of the tissue,37-39 the rate of change in IOP (via tissue viscoelasticity),21 and the level of IOP-related strain at the time of altered loading (via tissue non-linearity).36 In broad terms, the ONH connective tissues should be stiffer when there is already considerable strain present (elevated steady-state IOP) and/or if the IOP load is applied quickly (transient IOP fluctuations). Conversely, the ONH should be more compliant in response to slow changes in IOP and/or at low baseline levels of strain. In addition, studies have shown that mechanical strain is higher in regions of the ONH where laminar density is lower (Fig. 5).38 It is important to note that the ONH responds to IOP elevations as a structural system, so the acute mechanical response of the LC is confounded with the responses of the peripapillary sclera, prelaminar neural tissues, and retrolaminar optic nerve. The LC lies underneath the prelaminar neural tissues, and the structural responses of these two tissues to acute IOP elevations are quite different; hence, laminar

Copyright © 2018. Kugler Publications. All rights reserved.

Optic nerve head biomechanics in health, aging, and disease

449

Fig. 5. Regional differences in laminar microarchitecture in a normal eye, and the predicted relationship between regional laminar density and strain. Characterization of the laminar microarchitecture (left) utilizes the element boundaries of a continuum finite mesh to partition the LC connective tissue into 45 sub-regions. (Right) The connective tissue volume fraction (CTVF) for each region is expressed as a percentage and mapped to a grayscale value in the background. The arrows indicate the predominant orientation of the laminar beams in each region, with higher values (color-coded) indicating regions in which the beams are more highly oriented. Note that in the peripheral regions of the lamina, the beams are tethered radially into the scleral canal wall. (Bottom) FE model simulations in both eyes of four NHPs show that strains are highest in areas where the laminar density is lowest, and strains are lowest in areas where laminar density is highest. 38 The symbols represent strains in each of the elements, colored by eye and animal, and the lines represent the non-linear fit to those data.

deformation cannot be directly measured from imaging the surface topography of the ONH.40 It is important to keep in mind that cerebrospinal fluid pressure (CSFP) works in concert with IOP to determine the translaminar pressure gradient (a biomechanical stress; Fig. 2) that must be borne by the lamina cribrosa.41 While IOP loads the entire corneoscleral shell and ONH, CSFP only acts on the retrolam-

inar optic nerve and LC. Emerging evidence suggests a link between glaucoma and low CSFP in patients, further bolstering the evidence that laminar biomechanics plays a central role in glaucoma.42-45 A recent groundbreaking study showed glaucomatous ONH changes in NHPs subjected to experimental lowering of cerebrospinal pressure via lumbar shunt, without any perturbation in IOP.46 Although axon loss and ONH

Copyright © 2018. Kugler Publications. All rights reserved.

450

changes only occurred in half the primates subjected to CSFP lowering, this study definitively shows that an increase in the translaminar pressure difference, either by increasing IOP or decreasing CSFP, can induce an optic neuropathy.46 A very thorough treatment of both IOP and IOP fluctuations, and the biomechanical effects of the translaminar pressure difference (IOP-CSFP) are found in other chapters in this book. Intuitively, it may seem that for a given acute increase in IOP, the LC should deform posteriorly. Recent histologic and in-vivo optical coherence tomography (OCT) imaging studies have shown that the LC does not consistently deform posteriorly when IOP increases.40,47,48 In some eyes, the lamina moves anteriorly with respect to Bruch’s membrane opening after acute IOP elevation.40,47,48 Thus, our current understanding of the aggregate response of the ONH to acute IOP elevation is that expansion of the scleral canal pulls the lamina taut within the plane of the sclera to a variable degree, making it more resistant to posterior deformation out of that plane.10,49,50 Sigal and colleagues investigated the interplay between scleral canal expansion and laminar deformation using computational models, and found this relationship to be complex, although the majority of modeled ‘eyes’ with stiff sclerae exhibited posterior laminar deformation, and vice versa.49 It is important to note that the apparent lack of anterior-to-posterior laminar deformation with acute IOP elevation does not mean that the lamina is not strained. In this scenario, the expansion of the canal stretches the LC within the plane of the sclera, generating substantial tensile strain within the laminar beams. It remains unclear as to which mode(s) of strain, either bending when the lamina deforms posteriorly in the canal or tensile strain when the lamina is pulled taut and anteriorly in the canal, are most injurious to axons in the ONH.51 A recent cross-sectional clinical study in glaucoma patients showed that visual field damage was worse in those in which the lamina deformed anteriorly when IOP was raised acutely,52 indicating that excessive scleral canal expansion (and hence, tensile strain) may be more deleterious to axons in the laminar region. The cells that maintain the ocular connective tissues are biologically active, and the ONH and sclera are in a constant state of remodeling. Grytz and colleagues have proposed the notion that the cells are constantly expressing factors conducive to ECM degradation

J. Crawford Downs

Fig. 6. Regional changes in maximum principal strain with age and race. Overall regional mean maximum principal strain in the peripapillary region significantly decreases with age (P < 0.001) in European (ED, red thick curves) and African (AD, blue thick curves) descent groups; mid-peripheral strain did not exhibit a significant change with age in the ED group (red dashed), while this change was statistically significant in the AD group (blue dashed). Interestingly, the estimated average strain in the peripapillary sclera in the two groups is very similar at younger ages, but the average strain becomes significantly lower in the AD group at older ages due to the significantly higher rate of age-related stiffening in the AD group (P < 0.001). The thick lines denote the mean statistical estimate for each region and race. Each regression plot shows the 95% CI of the curve representing the maximum principal strain variation with age for each region (shaded region). In other words, the shaded regions show the 95% probability bound for the regression curve of the population. Figure reproduced with permission from Fazio et al.19

and synthesis in an effort to maintain a homeostatic mechanical environment.53,54 ONH cells express the pro-fibrotic growth factors TGFb2, CTGF, and gremlin, which have been shown to increase ECM production.5560 Interestingly, both TGFb2 and gremlin are elevated in the glaucomatous ONH. As such, the geometry and material properties of the sclera and LC change in response to both physiologic (age) and pathologic (IOPrelated damage) factors. These processes are driven in part by the natural aging processes that induce collagen crosslinking,61-63 and vascular64 and cellular29,30 changes. The eye is also exposed to ever changing loading conditions because IOP is extremely dynamic, with short-term and long-term fluctuations ranging from blinks and eye rubs to circadian rhythms (Fig. 3).21 Liu and colleagues have recently shown that stiffening even small areas of the ocular coat leads to increased transient IOP fluctuations associated with controlled microvolumetric fluid injections in porcine and human eyes.65,66 Also, transient IOP elevation amplitude with volume change has been shown to be positively correlated with scleral stiffness.67 Hence, IOP dynamics,

Optic nerve head biomechanics in health, aging, and disease

451

Fig. 7. The influence of scleral mechanics on ONH mechanics. IOP induces large scleral canal expansions in eyes with compliant sclerae (left) that pulls the contained lamina taut despite the direct posterior force of IOP on the laminar surface. Conversely, a stiff sclera allows relatively little canal expansion with IOP elevation (right) and less stretching of the contained lamina, thus allowing the lamina to be displaced posteriorly by the direct action of IOP on its anterior surface. Adapted from Sigal et al.10

Copyright © 2018. Kugler Publications. All rights reserved.

and resulting dynamic mechanical stress and strain, also change with aging and racial heritage because the corneoscleral shell is less able to elastically deform to absorb energy as it stiffens with age17,18 and African heritage (Fig. 6),19,20 resulting in larger transient IOP fluctuations in the elderly and persons of African heritage, even when steady-state IOP remains unchanged. 3.3. The contribution of the sclera to ONH biomechanics The results described above, as well as the closed form analyses and computational models described in the next section suggest that the sclera plays an important role in ONH biomechanics. The peripapillary sclera provides the mechanical boundary conditions for the ONH. By this we mean that the peripapillary sclera is the tissue through which load and deformation are transmitted to the ONH, and that the structural stiffness of the peripapillary sclera, therefore, influences how the lamina deforms (Fig. 7). This can be understood from the discussion above, in which a compliant sclera allows the scleral canal to expand following an acute IOP elevation, pulling the lamina taut within the canal and thereby increasing laminar resistance to posterior deformation. In contrast, a rigid sclera allows less IOP-driven expansion of the scleral canal or none at all, forcing the structural stiffness of the lamina alone to bear the IOP-related stress. Hence, characterization of both components of scleral structural stiffness (geometry and material properties) is essential to

understanding the effects of IOP on the ONH. 3.3.1 Scleral geometry Maps of the thickness variation for the posterior pole of human68,69 eyes show extreme spatial variation in scleral thickness, with very thin regions near the equator (as low as 300 µm in humans). The peripapillary sclera is notably thicker (1000 µm in humans), and the biomechanics of the peripapillary sclera has been shown to directly influence ONH biomechanics in computational simulations,49,70,71 while the more peripheral sclera has little effect on ONH biomechanics.70 Interestingly, this thick ring of peripapillary sclera is absent in the nasal quadrant of NHP eyes due to the oblique nasal insertion of the optic nerve through the scleral canal.72 Such variations in peripapillary scleral thickness, whether they occur naturally or in pathologic conditions such as myopia, certainly influence biomechanics and may be important in assessing individual susceptibility to glaucomatous damage. 3.3.2. Characterization of scleral material properties Uniaxial testing of scleral strips has been used to estimate scleral material properties in various species. However, uniaxial testing of scleral strips is limited in its ability to describe the non-linear and anisotropic responses of the sclera, which led to the development of new approaches to measure scleral strain in 3-D under inflation. Girard and Fazio have used a customized scleral shell pressurization apparatus,

452

J. Crawford Downs

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 8. A possible link between age-related changes in scleral stiffness and age-related loss of axons in normal eyes? Maps showing the rate of change in neural retinal rim area measurement with age in normal human eyes75 and the age-related change in underlying peripapillary scleral structural stiffness (note negative coefficients indicate increased scleral compliance with age and positive coefficients indicate increased stiffness with age).18 While these results are independent and there has not been a causative link established between these phenomena, one might speculate that the age-related changes in scleral stiffness contribute to the pattern of age-related axon loss in normal eyes.

precise IOP control, and laser-based electronic speckle pattern interferometry to measure the IOP-induced 3-D deformation of the entire posterior scleral shell in NHPs73 and humans.39 Their results show that the posterior sclera is highly non-linear (it gets stiffer as IOP increases) and anisotropic (the underlying collagen fibril distribution is non-uniform and changes throughout the scleral shell, which affects directional stiffness).73 In addition, Fazio has measured the regional strains in the posterior human eye, and found that peripapillary strains are highest in the temporal and inferior quadrants, and are in general higher than those further away from the ONH.39 Two groups have used inflation testing to show that human scleral strain significantly decreases with age, i.e., the sclera exhibits significant age-related stiffening,17-20 and another study showed a similar result in scleral strips.24 A computational study using inverse modeling to fit scleral material properties to experimental inflation data has shown that this age-related stiffening is likely due to a higher shear stiffness and a lower level of stretch at which the collagen fibrils uncrimp and stiffen.20 The sclera is also stiffer in human donor eyes with glaucoma,17 and studies in the NHP have shown that the scleral shell stiffens in response to chronic IOP exposure, although the response was eye-specific.74 Many studies have shown peripapillary scleral bio-

mechanics to be an important determinant of the ONH biomechanical environment, but there is little evidence that peripapillary scleral strain is directly related to axonal homeostasis in the ONH. As mentioned above, a recent cross-sectional clinical study in glaucoma patients associated visual field damage with anterior laminar deformation in response to acute IOP elevation,52 indicating that a more compliant peripapillary sclera that is prone to scleral canal expansion may be more injurious to axons. Recent studies have shown that the stiffness of the immediate peripapillary sclera changes significantly with age, but that the response varies with location.18 The resulting maps of the coefficients of scleral stiffness change with age in normal eyes18 match well with maps of neural rim area measurement change with age published for normal human eyes (Fig. 8).75 While this may be entirely coincidental, it does provide some support for the notion that age-related changes in scleral stiffness may impact normal age-related loss of axons in adjacent regions of the ONH. Previous results have suggested that glaucomatous damage of the ONH is related to aging, but mean IOP does not generally increase with age in most populations. However, we know the ocular coats stiffen with both age17,18 and African ancestry,19,20 as well as with exposure to chronically elevated IOP in a NHP model of

Copyright © 2018. Kugler Publications. All rights reserved.

Optic nerve head biomechanics in health, aging, and disease

glaucoma74 and in glaucomatous human donor eyes.17 Data also show that transient IOP fluctuations are larger in eyes with stiffer ocular coats,14 which suggests that IOP (and ocular perfusion pressure (OPP)) fluctuations will be larger in the elderly, persons of African heritage, and patients with a history of elevated IOP. The structural stiffness of the ocular coat is a factor in modulating the amplitude of transient IOP fluctuations.4,5 The ocular coat of the eye acts as an elastic shock absorber that serves to decrease the amplitude IOP fluctuations due to ocular perturbations such as blinks, saccades, and systolic vascular filling (OPA). Hence, when the ocular coat is stiff, IOP fluctuation magnitude will be greater due to the eye’s inability to elastically expand and absorb the perturbation. Recurring insults on the eye can be caused by internal forces (ocular pulse due to systolic filling and capillary filling), or external forces (blinks and saccades).15,24,25 Based on this, greater ocular stiffening of the corneoscleral shell and ONH will result in greater IOP fluctuations, potentially resulting in increased IOP-induced injury.34,48 Also, greater IOP fluctuation can occur at normal IOP mean levels in stiffer eyes or the IOP fluctuation can be lower at higher IOPs in compliant eyes. Prior research has also suggested that mechanical stress and strain in the LC and peripapillary sclera could lead to ONH damage in some eyes, even at statistically normal IOP levels.50–52 This could explain why some patients develop glaucoma at statistically normal mean IOP while other patients with high IOP do not show clinical signs of glaucoma progression.53,54 Prior studies have suggested that the sclera is stiffer in human eyes with glaucoma, and it has been shown that the sclera stiffens with chronically elevated IOP in the NHP model, suggesting a cellular response to connective tissue strain that alters the mechanical behavior of the scleral tissue.7,48 Ocular rigidity has also been shown to be higher in clinical glaucoma patients compared to healthy controls.55 The characterization and findings of how IOP and OPP fluctuations relate to biomechanical changes in ocular coat stiffness may have important clinical ramifications, in that modulation of ocular coat stiffness and/or blockade of IOP-induced remodeling may reduce injurious IOP and OPP fluctuations. The characterization of IOP and OPP fluctuations in comparison to mean IOP and OPP would yield a better understanding of risk of disease onset and progression, and may lead to new clinical diagnostics

453

and treatments for glaucoma. Recent work has shown that horizontal eye movements induce large deformations and mechanical strains in the ONH in vivo. While the authors suggest that these strains could lead to ONH damage in certain eyes, these eye movements are common to all people and not all people develop glaucoma, so it is not clear what eye-specific qualities would lead to axonal loss from otherwise common eye movements. The same can be said of transient IOP fluctuations, which are also common to all eyes. 3.4. Estimating stress and strain in the ONH and peripapillary sclera Attempts to mathematically model the mechanical environment of the ONH generally fall into two broad categories: closed-form solutions and numerical simulations. In closed-form solutions, engineering principles are used to derive equations that can be analyzed to understand the effects of selected biological parameters. However, closed-form solutions are of limited utility because they cannot capture the complexity of the ONH and peripapillary scleral tissues (e.g., the non-uniform and asymmetric geometry and material properties). To overcome the inherent limitations of closed-form solutions, researchers have turned to numerical simulation methods to study more complex biological systems. One of the most powerful of these is finite element (FE) analysis, in which complex load-bearing structures are broken into small, regularly shaped elements (Fig. 4). Stress and strain within each element are calculated and then superposed to predict the mechanical response of the entire structure. The power of FE analysis lies in its ability to model structures with highly complex geometries using material properties with varying levels of complexity, as warranted (e.g., inhomogeneous, anisotropic, non-linear, or viscoelastic material descriptions). The three inputs necessary for FE models are the 3-D geometry of the tissue structure to be modeled, the material properties of the different tissues in the model, and appropriate loading and boundary conditions. These requirements have spurred the development of methodologies to isolate and describe the 3-D geometry of the ONH and peripapillary sclera, and experimentally characterize their constituent material properties (Fig. 5).

Copyright © 2018. Kugler Publications. All rights reserved.

454

3.4.1. Parametric and eye-specific simulations of ONH biomechanics Parametric modeling involves computing stress and strain in average, idealized geometries that do not conform to any individual’s particular anatomy. Within these models, parameters such as peripapillary scleral thickness and laminar stiffness can be varied independently to gauge that parameter’s effects on ONH biomechanics as a whole.71 To address the limitations of idealized geometric and simplified material property descriptions inherent in parametric FE models, individual-specific FE models can be created from the reconstructed geometries of particular eyes.38,51 At present, individual-specific modeling is based on high-resolution 3-D reconstructions of NHP and human cadaver eyes (Fig. 1), with a long-term goal to build models based on clinical imaging of living eyes so as to use them in the assignment of target IOP in clinical management of glaucoma. This is especially important given that the 3-D geometry of the scleral canal and peripapillary sclera largely determine the stress and strain transmitted to the contained ONH. Anatomically accurate 3-D models are necessary to capture the biomechanics of anisotropic scleral material properties (varying collagen fibril orientation), scleral canals that are non-circular and have varying optic nerve insertion angles (i.e., the optic nerve inserts from the nasal side resulting in a thinner peripapillary sclera in that quadrant), and regional variations in laminar density and trabeculae orientation. When modeling an ONH with anatomic fidelity, the tissue geometries can be constructed either by serial histologic methods or 3-D imaging, and material properties are generally determined through direct mechanical testing. Unfortunately, imaging of the entire lamina in vivo is not yet possible at the resolutions required for modeling, and no technology exists for experimental biomechanical testing of laminar beams. As a result, FE models that include the full laminar and peripapillary scleral structure are typically constructed from eyes that are perfusion- or immersion-fixed at a selected IOP, and then undergo ex-vivo 3-D reconstruction of their connective tissues. OCT imaging has recently emerged in the laboratory setting and has shown promise as a means to determine the biomechanical response of the laminar macro- and microstructure in regions of the eye where the laminar

J. Crawford Downs

structure is not obscured by overlying tissue or blood vessels.76,77 Several studies have used digital volume correlation to calculate the deformations in ONH tissues in vivo by comparing OCT images from patients before and after acute IOP elevation,78 horizontal eye movements,79 or after surgical IOP reduction.80 These studies are similarly limited to tissues visible to OCT imaging, but are powerful since they can estimate mechanical deformation and strains in all visible tissues of the ONH, including the prelaminar neural tissues that are often disregarded in FE models constructed from ex-vivo reconstructions. In addition, FE models often rely on estimates of tissue deformations to calculate stress and strain, while these direct image-based methods calculate strains directly from the in-vivo deformations themselves. There are, however, limitations to these approaches to assessing ONH and laminar biomechanics in vivo, the most important of which are the errors inherent in matching ONH morphology in separate image volumes that have limited resolution, voxel size calculation errors,81 and the inability to quantify strains in the full extent of the lamina due to light penetration barriers.82 Burgoyne and colleagues developed a histologic technique to reconstruct the 3-D trabeculated structure of the LC from individual NHP eyes that were perfusion-fixed at varying levels of IOP.83 The resulting 3-D data sets form the geometries of individual-specific FE models of the ONH at the macro- and microscale. Roberts and coworkers have developed macroscale continuum FE models of the posterior pole and ONH connective tissues from individual NHP eyes (Figs. 4 and 5).38 In these models, the laminar microarchitecture is modeled using a continuum approach, with anisotropic material properties assigned to each FE in the ONH based on the connective tissue volume fraction and the predominant beam orientation of the contained laminar microarchitecture (Fig. 5). Regional differences in connective tissue volume fraction and predominant orientation are translated into similar distributions in local oriented stiffness so that regions of higher and lower porosity reflect greater and lesser compliance, respectively. The inclusion of regional laminar material properties (connective tissue volume fraction and beam orientation) into FE models has a pronounced effect on the ONH’s response to IOP (Fig. 5). This indicates that the regional variations in laminar geometry and

Optic nerve head biomechanics in health, aging, and disease

Copyright © 2018. Kugler Publications. All rights reserved.

structural stiffness must be represented in models to fully capture the biomechanical behavior of the ONH. Furthermore, these results show that regional laminar density is significantly associated with regional stress and strain, with areas of high laminar density showing less strain and regions of low laminar density exhibiting high strains (Fig. 5).38 3.4.2. Biomechanics of the laminar microstructure We have also used the 3-D reconstruction and continuum modeling approaches to characterize and explore laminar beam biomechanics.84 This microscale modeling approach utilizes a substructuring technique based on parent macroscale FE models to calculate the IOP-related stress and strain fields in laminar beams (Fig. 4).84 This technique reveals a complexity of IOPrelated strains and stresses within the LC microarchitecture that is not available through macroscale FE modeling. There have been several important results from this work. First, stress and strain in the laminar microarchitecture are likely higher than predicted by macroscale models of the ONH. Second, even at normal levels of IOP, the micro-FE models predict that while the majority of laminar beams are within physiologic strain ranges, there are individual laminar beams with levels of IOP-related strain that are likely pathologic. Third, mean strain within the laminar beams of different NHPs varies greatly, and is generally dependent on the 3-D geometry of ONH connective tissues in each eye.38 This approach holds the possibility of testing hypotheses about failure mechanisms and cellular responses at the level of the laminar beams. As previously mentioned, recent adaptive opticsbased studies have enabled limited structural and biomechanical characterization of the laminar microstructure in vivo.76,85,86 These techniques have limited field of view, and can only quantify the laminar structure in regions that are not obscured by the retinal vasculature, Bruch’s membrane, or thick prelaminar neural tissues.82,87 Other ex-vivo imaging techniques, such as polarization microscopy,88 second harmonic image generation (SHG) microscopy,89-93 small-angle light scattering (SALS),93,94 and phase-contrast micro-computerized tomography (CT)95 allow for characterization of laminar and scleral morphology and biomechanics in excised eyes. Specifically, collagen microstructure has been found to be altered with aging.96

455

4. Remodeling of the ONH with age and disease 4.1. Aging The ONH connective tissues are exposed to substantial levels of IOP-related stress and strain at normal levels of IOP (Fig. 4). Physiologic levels of stress and strain experienced over a lifetime induce a broad spectrum of changes in both the connective tissues and vasculature that are central to normal aging. Thus, the restructuring and remodeling of glaucomatous damage (described in the following sections) should be understood to occur in the setting of the physiologic restructuring and remodeling inherent in normal aging. Age-related alterations of the laminar ECM have been reported to include increased collagen deposition, thickening of astrocyte basement membranes,97,98 and increased rigidity.99 Further, a recent SHG and SALS imaging study found that collagen fibers were more aligned in the peripapillary sclera of eyes from older human donors compared to young donors.93 Age-related changes in the scleral and laminar ECM significantly reshapes the biomechanical environment of the ONH.18,93,99 However, aging not only stiffens the connective tissues;100 it should also diminish nutrient diffusion from the laminar capillaries through the laminar ECM, across the astrocyte basement membranes, and into the adjacent axons. Thus, in addition to the effects of age-related changes in ONH biomechanics, axonal nutrition in the aged eye may be further impaired as a result of diminished nutrient diffusion from the laminar capillaries to the center of the axon bundles. Glaucoma is primarily a disease of aging,1,2 and recent work has shown that the sclera and LC stiffen significantly with age.17,18,24,99 One might assume this to be protective against mechanical strain, in that stiffer connective tissues resist mechanical strain better than more compliant tissues. It is important to note, however, that this stiffening also induces larger transient IOP fluctuations related to blinks, saccades, and vascular filling, in that the eye is less able to elastically expand to absorb IOP energy. Hence, it may be that the process of age-related connective tissue stiffening has remodeled the eye to a state that is actually more susceptible to transient IOP fluctuations. A recent study in human cadaver eyes has shown that the peripapillary sclera stiffens significant-

456

ly with age in donors of European descent, but stiffens much more rapidly with age and over a larger area of the posterior scleral shell in donors of African heritage (Fig. 6).19 Transient IOP fluctuations should therefore be higher in the elderly, and even higher in persons of African descent, which may contribute to the increased glaucoma prevalence in these at-risk populations. Recent work in an experimental mouse model of glaucoma supports this view, in that a stiffer sclera was associated with increased ganglion cell loss.101-103 Also, Vande Geest and coworkers observed that the local orientation of the collagen fibrils changes through the thickness of the sclera, and was found to be different between donors of African heritage vs European heritage, although no significant changes were seen with age.16

Copyright © 2018. Kugler Publications. All rights reserved.

4.2. IOP-driven alterations of the ONH in glaucoma We have proposed a comprehensive framework within which to understand the biomechanically driven remodeling of the LC that results in glaucomatous ONH cupping (Fig. 2).104 Pathophysiologic stress and strain induce pathologic changes in cell synthesis and tissue microarchitecture that exceed the effects of aging and underlie the two governing pathophysiologies in glaucoma: 1. growth and/or remodeling of the load-bearing connective tissues of the ONH; and 2. progressive damage to the adjacent axons through multiple pathways (Fig. 2). 4.3. Glaucomatous changes in ONH morphology and LC microarchitecture There are several recent studies that investigated the change in ONH morphology after surgical IOP lowering or in response to acute IOP elevation. These studies assess the reversal of LC cupping, and/or assess the mechanical compliance of the ONH in vivo. In one recent longitudinal study of 34 Korean glaucoma patients, LC depth was assessed before surgical IOP reduction from a preoperative average of 24 mmHg to 11 mmHg, and 6 months and 2.5 years post-surgery. LC depth was reduced significantly at both follow-up visits, which indicates that LC cupping was reversed after IOP lowering, and that reversal was largely sustained over time. The rate of postoperative RNFL thinning was significantly slower in those patients in

J. Crawford Downs

whom IOP did not rise and LC depth retained its more anterior post-surgical position at the 2.5 year follow-up visit.105 Another longitudinal study showed that the rate of RNFL thinning was significantly associated with greater LC depth measured at presentation in a cohort of 110 Korean glaucoma patients.106 Interestingly, these studies do not elucidate the morphological changes in the LC in progressive glaucoma, but do indicate that glaucomatous axon loss is associated with posterior LC position in the scleral canal at native IOP. Tun and colleagues studied the mechanical response of the ONH to acute IOP elevation of ~20 mmHg via ophthalmodynamometry, and found that LC depth was not significantly increased in normal, glaucoma, or ocular hypertensive eyes upon IOP elevation; the 3-D shape of the LC did change significantly however, which indicates that the mechanical response of the LC is very complex and full 3-D analysis may be necessary to fully capture ONH morphological change with IOP change and/or disease.107 To this end, Girard and colleagues used an OCT volumetric image mapping approach108 to calculate the mechanical strain relief in the visible portions of the prelaminar and laminar tissues following surgical IOP reduction. Not surprisingly, tissue strain relief after IOP-lowering was significant but very variable between patients, suggesting eye-specific responses, but was not associated with the magnitude of IOP lowering; the eyes with the highest strain relief, i.e., the largest local morphological change after IOP-lowering, exhibited the highest visual field loss.80 This is supported by recent evidence in NHPs with induced experimental glaucoma that has shown that the sclera and LC can become more compliant at the onset of ONH surface topography change,109 although no further analysis was done to associate increased compliance with axon or visual field loss in these animals. In-vivo OCT imaging has also revealed that the LC is not a uniform fenestrated structure, but can exhibit focal defects including holes, pits, scleral disinsertions, and other features.110 This is important from a structural and biomechanical standpoint, as local laminar strain is correlated to local laminar density.38 Focal laminar defects have recently been associated with disk hemorrhages111-113 and RNFL defects114 in glaucoma patients, which suggests that focal damage or remodeling of the LC trabeculae may underlie many of the focal RNFL defects and resulting visual

Copyright © 2018. Kugler Publications. All rights reserved.

Optic nerve head biomechanics in health, aging, and disease

field scotomas in glaucoma. Global changes in the laminar microarchitecture have also been reported in recent NHP studies, including LC pore enlargement, and increased laminar region volume and laminar connective tissue volume in glaucoma eyes compared to their fellow control eyes.115 Hence, while focal defects are detectable clinically in human glaucoma, post-mortem studies of NHP glaucoma eyes using high resolution 3-D reconstructions of the LC reveal widespread remodeling of the laminar trabeculae as well. Early glaucomatous damage has not been rigorously studied in humans because human cadaver eyes with well-characterized early damage are rare. In NHPs, following moderate experimental IOP elevations, we have described the following changes in ONH and peripapillary scleral connective tissue architecture and material properties at the onset of confocal scanning laser tomography-detected ONH surface change (clinical cupping): 1. enlargement and elongation of the neural canal;116 2. posterior deformation and thickening of the LC;117 3. outward migration of the posterior lamina insertion point118 and significant but less pronounced outward migration of the anterior lamina insertion point; 118 and 4. alterations in the elastic and viscoelastic material properties of the peripapillary sclera.74,119 The increase in laminar thickness in these early glaucoma NHP eyes is likely due to connective tissue remodeling and new connective tissue synthesis. Quantification of the amount of connective tissue within 3-D reconstructions of the lamina showed an increase in connective tissue volume of 44% to 82% in early glaucoma compared to their contralateral control eyes, which is at least partially driven by the recruitment of retrolaminar septa into the load-bearing 3-D laminar structure.37 These data strongly support the notion that connective tissue remodeling and new connective tissue synthesis are very active in this early stage of the neuropathy. Furthermore, the work of Yang, Burgoyne, and co-workers has shown that the LC migrates posteriorly in the neural canal during glaucomatous progression, and that process starts early in the disease.118 Laminar depth was significantly larger in

457

glaucoma patients with younger age, higher untreated IOP, and lower RNFL thickness as measured with OCT in a recent cross-sectional study.120 In a recent comprehensive review, we proposed a framework that supports biomechanics-driven progressive laminar remodeling and migration as the central mechanism underlying the change in LC morphology from normal to the cupped and excavated shape typical of glaucoma.104 In-vivo OCT imaging studies in which the laminar position was measured relative to Bruch’s membrane opening at baseline and after acute IOP elevation in NHPs with experimental glaucoma have revealed changes in the structural stiffness of the LC that occur in early glaucoma. Preliminary results indicate that the LC deforms significantly more posteriorly in response to an acute IOP elevation from 10 to 30 mmHg in most glaucoma eyes compared to their contralateral normal controls, and that laminar compliance is significantly related to the peak IOP measured after chronic IOP elevation was induced. This suggests that IOP-driven remodeling is altering laminar structural stiffness as glaucoma progresses. Modeling studies in NHP early glaucoma have supported this hypothesis, and predict that even though the LC adds a significant volume of connective tissue through remodeling very early in the disease, the laminar connective tissue is weakened considerably during that process, resulting in a more substantial lamina that is still structurally more compliant than its contralateral control eye.121 These results lend credibility to the notion that the remodeling cascade in the laminar ECM begins with a reorganization process that weakens the tissues very early in the disease process, which is followed by a consolidation and stiffening process. It has been proposed that ONH astrocytes and LC cells play a central role in mediating the laminar ECM remodeling response and the resulting axonal insult.60,122-126 Cell activity associated with ECM remodeling has been observed in response to glaucoma in humans and exposure to chronically elevated IOP in animal models. Agapova and colleagues showed that matrix metalloproteases (MMPs) are elevated in the LC of NHPs with experimental glaucoma, but not those with optic nerve transection.127 These compounds are known to break down the ECM, allowing cells to migrate and rebuild the matrix.122 Recent numerical growth and remodeling simulations

458

Copyright © 2018. Kugler Publications. All rights reserved.

have given us additional confidence in the hypothesis that local biomechanics is driving ONH remodeling in glaucoma. Grytz and colleagues performed a FE simulation study based on a homeostatic control mechanisms that predicted that the LC has to thicken by about 40% to maintain optimal load-bearing conditions at the collagen fibril level for a chronic IOP elevation from 15 to 25 mmHg.54 Their study also suggested that the thickening of the LC is mainly due to the recruitment of pre- and retrolaminar tissue into the LC, which agrees with previous experimental studies.37 Their results also suggest that the lamina is biologically optimized to withstand IOP and constantly remodels to maintain strain within a homeostatic range. Axoplasmic transport blockade in the ONH has been associated with acute128,129 and chronic IOP elevations,130 indicating that IOP and its mechanical effects on the load-bearing tissues, vasculature,131,132 and/or cells directly affects axonal homeostasis. Studies of alterations in blood flow in early glaucoma are only just beginning. Recent studies by Wang and coworkers have shown that basal blood flow in the ONH is significantly decreased in early experimental glaucoma in NHPs.133 They also reported changes in the time course of blood flow autoregulation,134 which indicate that chronic alterations in blood flow accompany the alteration in connective tissue architecture and material properties described above. Together, these studies paint a complex picture of glaucomatous pathogenesis that involves simultaneous alterations in the connective tissues, cells, and vasculature. The unifying theme that ties these mechanisms together is the involvement of ONH biomechanics in the disease cascade. 4.3.1. The biomechanical mechanisms underlying collagen growth and remodeling The previously discussed numerical simulations were designed to estimate the stress and strain environment in the ONH for a given material or collagen architecture. Recent advances in numerical remodeling allow us gain insight into the origin of these anisotropic collagen structures in the eye. In these studies, stress or strain is not merely a predicted variable but is also used to predict the collagen fibril architecture (anisotropy) based on a remodeling rule. Biomechanically induced remodeling of tissue anisotropy was estimated by

J. Crawford Downs

allowing collagen fibers to be adaptively reoriented towards optimal load-bearing conditions based on the IOP-related tissue stress. This numerical approach was used to predict the physiological collagen fiber architecture in the peripapillary sclera and LC.36 The numerical results suggest that the anisotropic collagen fibril architecture in the peripapillary sclera and LC evolved to establish optimal load-bearing conditions in the connective tissues. Furthermore, the numerical remodeling simulation provides insight into the significant effects of these underlying collagen fiber orientations on the IOP-related deformation of the ONH. The simulations show that the circumpapillary ring of collagen fibers protects the ONH from large scleral canal expansions, and as such, shields the LC and neural canal tissues from high tensile stresses. In contrast, the radial alignment of fibers in the periphery of the LC seems to reinforce the LC against posterior deformations and high transversal shear stresses. 4.3.2. Experimental assessment of collagen remodeling Experimental studies have shown that collagen fibril synthesis, degeneration, and remodeling in soft tissues is modulated by mechanical stress and strain.33,135 Furthermore, recent findings suggest that growth and remodeling mechanisms occur in soft tissues to establish and maintain optimal load-bearing conditions, and these optimal conditions seem to be defined at the collagen fibril level.33,135 Based on these findings, Grytz and colleagues developed a numerical growth and remodeling method and applied it to the ONH.54 This study predicted that the formation of a LC in human eyes is necessary to establish optimal load-bearing conditions at the collagen fibril level. The simulation also suggests that smaller eyes, such as those in rodents, might not need a collagenous LC due to their small scleral canal, for which a cellular ‘lamina’ is sufficient.136 Taken together, these results support the hypothesis that elevated IOP, and presumably mechanical insult to the cells and/or reduced blood flow in the laminar region, underlie the significant ECM remodeling observed in glaucomatous eyes. Interestingly, these mechanisms are driven by exposure to IOP, a biomechanical insult, and are not simply a secondary effect of axonal damage and death. A recent in-vitro imaging study of human donor eyes study found that laminar collagen fiber

Optic nerve head biomechanics in health, aging, and disease

alignment was higher in the infero-temporal quadrant of glaucoma eyes compared to healthy controls, which is interesting since this region is often damaged early in glaucoma. What is unclear from this study, however, is whether the differences noted precede glaucoma (a risk factor) or were due to remodeling that occurred after the ONH was injured in the disease process. 4.4. Clinical implications

Copyright © 2018. Kugler Publications. All rights reserved.

4.4.1. How might we assess biomechanical risk to the ONH clinically? There are currently no science-based tools to predict at what level of IOP an individual ONH will be damaged. Eventually, knowing the relationship between IOP, IOP fluctuations, mechanical strain- or stress-driven remodeling, ONH blood flow, and astrocyte and axonal homeostasis will drive the clinical assessment of safe-target IOP, although the technologies to assess these factors have yet to materialize. Once developed, clinical characterization of the actual IOP insult through continuous, telemetric IOP monitoring will eventually allow us to understand the biomechanical loads in the eye, a critical component to understanding the forces driving glaucoma pathophysiology. In-vivo imaging is rapidly advancing, and will soon have the ability to image and quantify laminar microarchitecture, and therefore, regional laminar density could serve as a

459

biomarker for areas that are under increased strain relative to neighboring regions (Fig. 5).38,85,91,137 38 Also, there is increasing evidence that the lamina remodels very early in glaucoma,37,118 and that the biomechanical behavior of the LC is also altered in this process.121 Also, blood flow autoregulation changes are associated with early disease,27 and clinical detection is on the horizon. Once clinically detectable, early stabilization and perhaps reversal of these pathophysiologic changes will become new patient-specific endpoints to determine a safe target IOP.

Acknowledgements This chapter was based in large part on the following two reviews, which were written and published by the author: Downs, JC. Optic nerve head biomechanics in aging and disease. Exp Eye Res. 2015;133:19-29. PMID: 25819451 Downs JC, Girkin CA. Lamina cribrosa in glaucoma. Curr Opin Ophthalmol. 2017;28(2):113-119. PMID: 27898470 Much of the work presented herein was funded by US National Institutes of Health Grant R01 EY-018926, Research to Prevent Blindness (NY, USA), and the EyeSight Foundation of Alabama (AL, USA).

460

J. Crawford Downs

References 1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

Copyright © 2018. Kugler Publications. All rights reserved.

12.

13.

14.

15.

Gordon MO, Beiser JA, Brandt JD, et al. The Ocular Hypertension Treatment Study: baseline factors that predict the onset of primary open-angle glaucoma. Arch Ophthalmol. 2002;120(6):714-720; discussion 829-730. Leske M, Heijl A, Hussein M. Factors for glaucoma progression and the effect of treatment: the early manifest glaucoma trial. Arch Ophthalmol. 2003:121(1):48-56. Quigley HA, Broman AT. The number of people with glaucoma worldwide in 2010 and 2020. Br J Ophthalmol. 2006;90(3):262267. Zeimer RC, Ogura Y. The relation between glaucomatous damage and optic nerve head mechanical compliance. Arch Ophthalmol. 1989;107(8):1232-1234. Nickells RW, Howell GR, Soto I, John SW. Under pressure: cellular and molecular responses during glaucoma, a common neurodegeneration with axonopathy. Annu Rev Neurosci. 2012;35:153-179. Howell GR, Soto I, Libby RT, John SW. Intrinsic axonal degeneration pathways are critical for glaucomatous damage. Exp Neurol. 2013;246:54-61. Levin LA. Relevance of the site of injury of glaucoma to neuroprotective strategies. Surv Ophthalmol. 2001;45 Suppl 3:S243249; discussion S273-246. Downs JC, Roberts MD, Burgoyne CF. Mechanical environment of the optic nerve head in glaucoma. Optom Vis Sci. 2008;85(6):425-435. Cioffi GA, Van Buskirk EM. Vasculature of the anterior optic nerve and peripapillary choroid. In: Ritch R, Shields MB, Krupin T, eds. The Glaucomas. Mosby, St. Louis: Basic Sciences;1996:177-197. Sigal IA, Roberts MD, Girard MJA, Burgoyne CF, Downs JC. Chapter 20: Biomechanical Changes of the Optic Disc. In: Levin LA, Albert DM, eds. Ocular Disease: Mechanisms and Management. 1st Edition ed. London: Elsevier; 2010:153-164. Burgoyne CF, Downs JC, Bellezza AJ, Suh JK, Hart RT. The optic nerve head as a biomechanical structure: a new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage. Prog Retin Eye Res. 2005;24(1):39-73. Campbell IC, Coudrillier B, Ross Ethier C. Biomechanics of the posterior eye: a critical role in health and disease. J Biomech Eng. 2014;136(2):021005. Burgoyne CF. A biomechanical paradigm for axonal insult within the optic nerve head in aging and glaucoma. Exp Eye Res. 2011;93(2):120-132. Burgoyne CF, Downs JC. Premise and prediction-how optic nerve head biomechanics underlies the susceptibility and clinical behavior of the aged optic nerve head. J Glaucoma. 2008;17(4):318-328. Rudnicka AR, Mt-Isa S, Owen CG, Cook DG, Ashby D. Variations in primary open-angle glaucoma prevalence by age, gender, and race: a Bayesian meta-analysis. Invest Ophthalmol Vis Sci. 2006;47(10):4254-4261.

16. Yan D, McPheeters S, Johnson G, Utzinger U, Vande Geest JP. Microstructural differences in the human posterior sclera as a function of age and race. Invest Ophthalmol Vis Sci. 2011;52(2):821-829. 17. Coudrillier B, Tian J, Alexander S, Myers KM, Quigley HA, Nguyen TD. Biomechanics of the human posterior sclera: age- and glaucoma-related changes measured using inflation testing. Invest Ophthalmol Vis Sci. 2012;53(4):1714-1728. 18. Fazio MA, Grytz R, Morris JS, et al. Age-related changes in human peripapillary scleral strain. Biomech Model Mechanobiol. 2014;13(3):551-563. 19. Fazio MA, Grytz R, Morris JS, Bruno L, Girkin CA, Downs JC. Human scleral structural stiffness increases more rapidly with age in donors of African descent compared to donors of European descent. Invest Ophthalmol Vis Sci. 2014;55(11):71897198. 20. Grytz R, Fazio MA, Libertiaux V, et al. Age- and race-related differences in human scleral material properties. Invest Ophthalmol Vis Sci. 2014;55(12):8163-8172. 21. Downs JC, Burgoyne CF, Seigfreid WP, Reynaud JF, Strouthidis NG, Sallee V. 24-hour IOP telemetry in the nonhuman primate: implant system performance and initial characterization of IOP at multiple timescales. Invest Ophthalmol Vis Sci. 2011;52(10):7365-7375. 22. Resta V, Novelli E, Vozzi G, et al. Acute retinal ganglion cell injury caused by intraocular pressure spikes is mediated by endogenous extracellular ATP. Eur J Neurosci. 2007;25(9):2741-2754. 23. Cullen DK, LaPlaca MC. Neuronal response to high rate shear deformation depends on heterogeneity of the local strain field. J Neurotrauma. 2006;23(9):1304-1319. 24. Geraghty B, Jones SW, Rama P, Akhtar R, Elsheikh A. Age-related variations in the biomechanical properties of human sclera. J Mech Behav Biomed Mater. 2012;16:181-191. 25. Albon J, Purslow PP, Karwatowski WS, Easty DL. Age related compliance of the lamina cribrosa in human eyes. Br J Ophthalmol. 2000;84(3):318-323. 26. Knox Cartwright NE, Tyrer JR, Marshall J. Age-related differences in the elasticity of the human cornea. Invest Ophthalmol Vis Sci. 2011;52(7):4324-4329. 27. Wang L, Cull G, Burgoyne CF, Thompson S, Fortune B. Longitudinal alterations in the dynamic autoregulation of optic nerve head blood flow revealed in experimental glaucoma. Invest Ophthalmol Vis Sci. 2014;55(6):3509-3516. 28. Flammer J, Konieczka K, Bruno RM, Virdis A, Flammer AJ, Taddei S. The eye and the heart. Eur Heart J. 2013;34(17):12701278. 29. Kong YX, van Bergen N, Bui BV, et al. Impact of aging and diet restriction on retinal function during and after acute intraocular pressure injury. Neurobiol Aging. 2012;33(6):1126 e11151125. 30. Chrysostomou V, Trounce IA, Crowston JG. Mechanisms of retinal ganglion cell injury in aging and glaucoma. Ophthalmic Res. 2010;44(3):173-178. 31. Timoshenko SJ. Theory of Elasticity. New York:McGraw-Hill;1970.

Copyright © 2018. Kugler Publications. All rights reserved.

Optic nerve head biomechanics in health, aging, and disease 32. Morrison JC. Integrins in the optic nerve head: potential roles in glaucomatous optic neuropathy (an American Ophthalmological Society thesis). Trans Am Ophthalmol Soc. 2006;104:453477. 33. Flynn BP, Bhole AP, Saeidi N, Liles M, Dimarzio CA, Ruberti JW. Mechanical strain stabilizes reconstituted collagen fibrils against enzymatic degradation by mammalian collagenase matrix metalloproteinase 8 (MMP-8). PLoS One. 2010;5(8):e12337. 34. Pijanka JK, Coudrillier B, Ziegler K, et al. Quantitative mapping of collagen fiber orientation in non-glaucoma and glaucoma posterior human sclerae. Invest Ophthalmol Vis Sci. 2012;53(9):5258-5270. 35. Coudrillier B, Boote C, Quigley HA, Nguyen TD. Scleral anisotropy and its effects on the mechanical response of the optic nerve head. Biomech Model Mechanobiol. 2013;12(5):941-963. 36. Grytz R, Fazio MA, Girard MJ, et al. Material properties of the posterior human sclera. J Mech Behav Biomed Mater. 2014;29:602-617. 37. Roberts MD, Grau V, Grimm J, et al. Remodeling of the connective tissue microarchitecture of the lamina cribrosa in early experimental glaucoma. Invest Ophthalmol Vis Sci. 2009;50(2):681-690. 38. Roberts MD, Liang Y, Sigal IA, et al. Correlation between local stress and strain and lamina cribrosa connective tissue volume fraction in normal monkey eyes. Invest Ophthalmol Vis Sci. 2010;51(1):295-307. 39. Fazio MA, Grytz R, Bruno L, et al. Regional variations in mechanical strain in the posterior human sclera. Invest Ophthalmol Vis Sci. 2012;53(9):5326-5333. 40. Agoumi Y, Sharpe GP, Hutchison DM, Nicolela MT, Artes PH, Chauhan BC. Laminar and prelaminar tissue displacement during intraocular pressure elevation in glaucoma patients and healthy controls. Ophthalmology. 2011;118(1):52-59. 41. Morgan WH, Chauhan BC, Yu DY, Cringle SJ, Alder VA, House PH. Optic disc movement with variations in intraocular and cerebrospinal fluid pressure. Invest Ophthalmol Vis Sci. 2002;43(10):3236-3242. 42. Berdahl JP, Allingham RR, Johnson DH. Cerebrospinal fluid pressure is decreased in primary open-angle glaucoma. Ophthalmology. 2008;115(5):763-768. 43. Berdahl JP, Ethier CR, Allingham RR. Cerebrospinal fluid pressure and glaucomatous optic disc cupping. Graefes Arch Clin Exp Ophthalmol. 2009;247(9):1289-1290; author reply 1291-1284. 44. Berdahl JP, Allingham RR. Intracranial pressure and glaucoma. Curr Opin Ophthalmol. 2010;21(2):106-111. 45. Fleischman D, Berdahl JP, Zaydlarova J, Stinnett S, Fautsch MP, Allingham RR. Cerebrospinal fluid pressure decreases with older age. PLoS One. 2012;7(12):e52664. 46. Yang D, Fu J, Hou R, et al. Optic neuropathy induced by experimentally reduced cerebrospinal fluid pressure in monkeys. Invest Ophthalmol Vis Sci. 2014;55(5):3067-3073. 47. Yang H, Downs JC, Sigal IA, Roberts MD, Thompson H, Burgoyne CF. Deformation of the normal monkey optic nerve head

461

48.

49.

50.

51.

52.

53.

54.

55.

56.

57.

58.

59.

60.

connective tissue after acute IOP elevation within 3-D histomorphometric reconstructions. Invest Ophthalmol Vis Sci. 2009;50(12):5785-5799. Strouthidis NG, Fortune B, Yang H, Sigal IA, Burgoyne CF. Effect of acute intraocular pressure elevation on the monkey optic nerve head as detected by spectral domain optical coherence tomography. Invest Ophthalmol Vis Sci. 2011;52(13):94319437. Sigal IA, Yang H, Roberts MD, Burgoyne CF, Downs JC. IOP-induced lamina cribrosa displacement and scleral canal expansion: an analysis of factor interactions using parameterized eye-specific models. Invest Ophthalmol Vis Sci. 2011;52(3):1896-1907. Sigal IA, Yang H, Roberts MD, et al. IOP-induced lamina cribrosa deformation and scleral canal expansion: independent or related? Invest Ophthalmol Vis Sci. 2011;52(12):9023-9032. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Predicted extension, compression and shearing of optic nerve head tissues. Exp Eye Res. 2007;85(3):312-322. Tun TA, Atalay E, Baskaran M, et al. Association of Functional Loss With the Biomechanical Response of the Optic Nerve Head to Acute Transient Intraocular Pressure Elevations. JAMA Ophthalmol. 2018;136(2):184-192. Grytz R, Girkin CA, Libertiaux V, Downs JC. Perspectives on biomechanical growth and remodeling mechanisms in glaucoma. Mech Res Commun. 2012;42:92-106. Grytz R, Sigal IA, Ruberti JW, Meschke G, Downs JC. Lamina cribrosa thickening in early glaucoma predicted by a microstructure motivated growth and remodeling approach. Mech Mater. 2012;44:99-109. Wordinger RJ, Agarwal R, Talati M, Fuller J, Lambert W, Clark AF. Expression of bone morphogenetic proteins (BMP), BMP receptors, and BMP associated proteins in human trabecular meshwork and optic nerve head cells and tissues. Mol Vis. 2002;8:241-250. Zode GS, Clark AF, Wordinger RJ. Bone morphogenetic protein 4 inhibits TGF-beta2 stimulation of extracellular matrix proteins in optic nerve head cells: role of gremlin in ECM modulation. Glia. 2009;57(7):755-766. Zode GS, Sethi A, Brun-Zinkernagel AM, Chang IF, Clark AF, Wordinger RJ. Transforming growth factor-beta2 increases extracellular matrix proteins in optic nerve head cells via activation of the Smad signaling pathway. Mol Vis. 2011;17:17451758. Fuchshofer R. The pathogenic role of transforming growth factor-beta2 in glaucomatous damage to the optic nerve head. Exp Eye Res. 2011;93(2):165-169. Wallace DM, Clark AF, Lipson KE, Andrews D, Crean JK, O’Brien CJ. Anti-connective tissue growth factor antibody treatment reduces extracellular matrix production in trabecular meshwork and lamina cribrosa cells. Invest Ophthalmol Vis Sci. 2013;54(13):7836-7848. Wallace DM, Murphy-Ullrich JE, Downs JC, O’Brien CJ. The role of matricellular proteins in glaucoma. Matrix Biol. 2014;37:174182.

Copyright © 2018. Kugler Publications. All rights reserved.

462 61. Birch HL, Bailey JV, Bailey AJ, Goodship AE. Age-related changes to the molecular and cellular components of equine flexor tendons. Equine Vet J. 1999;31(5):391-396. 62. Sady C, Khosrof S, Nagaraj R. Advanced Maillard reaction and crosslinking of corneal collagen in diabetes. Biochem Biophys Res Commun. 1995;214(3):793-797. 63. Vasan S, Foiles P, Founds H. Therapeutic potential of breakers of advanced glycation end product-protein crosslinks. Arch Biochem Biophys. 2003;419(1):89-96. 64. Sawabe M. Vascular aging: from molecular mechanism to clinical significance. Geriatr Gerontol Int. 2010;10 Suppl 1:S213220. 65. Liu J, He X. Corneal stiffness affects IOP elevation during rapid volume change in the eye. Invest Ophthalmol Vis Sci. 2009;50(5):2224-2229. 66. Clayson K, Pan X, Pavlatos E, et al. Corneoscleral stiffening increases IOP spike magnitudes during rapid microvolumetric change in the eye. Exp Eye Res. 2017;165:29-34. 67. Morris HJ, Tang J, Cruz Perez B, et al. Correlation between biomechanical responses of posterior sclera and IOP elevations during micro intraocular volume change. Invest Ophthalmol Vis Sci. 2013;54(12):7215-7222. 68. Olsen TW, Aaberg SY, Geroski DH, Edelhauser HF. Human sclera: thickness and surface area. Am J Ophthalmol. 1998;125(2):237241. 69. Norman RE, Flanagan JG, Rausch SM, et al. Dimensions of the human sclera: thickness measurement and regional changes with axial length. Exp Eye Res. 2010;90(2):277-284. 70. Norman RE, Flanagan JG, Sigal IA, Rausch SM, Tertinegg I, Ethier CR. Finite element modeling of the human sclera: influence on optic nerve head biomechanics and connections with glaucoma. Exp Eye Res. 2011;93(1):4-12. 71. Sigal IA, Flanagan JG, Ethier CR. Factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2005;46(11):4189-4199. 72. Downs JC, Blidner RA, Bellezza AJ, Thompson HW, Hart RT, Burgoyne CF. Peripapillary scleral thickness in perfusion-fixed normal monkey eyes. Invest Ophthalmol Vis Sci. 2002;43(7):2229-2235. 73. Girard M, Downs JC, Burgoyne CF, Bottlang M, Suh J-KF. Anisotropic and nonlinear mechanical behavior of monkey posterior sclera under intraocular pressure. Invest Ophthalmol Vis Sci. 2007;48(13):3304 74. Girard MJ, Suh JK, Bottlang M, Burgoyne CF, Downs JC. Biomechanical changes in the sclera of monkey eyes exposed to chronic IOP elevations. Invest Ophthalmol Vis Sci. 2011;52(8):5656-5669. 75. See JL, Nicolela MT, Chauhan BC. Rates of neuroretinal rim and peripapillary atrophy area change: a comparative study of glaucoma patients and normal controls. Ophthalmology. 2009;116(5):840-847. 76. Wang B, Nevins JE, Nadler Z, et al. In vivo lamina cribrosa micro-architecture in healthy and glaucomatous eyes as assessed by optical coherence tomography. Invest Ophthalmol Vis Sci. 2013;54(13):8270-8274.

J. Crawford Downs 77. Wang B, Nevins JE, Nadler Z, et al. Reproducibility of in-vivo OCT measured three-dimensional human lamina cribrosa microarchitecture. PLoS One. 2014;9(4):e95526. 78. Beotra MR, Wang X, Tun TA, et al. In vivo three-dimensional lamina cribrosa strains in healthy, ocular hypertensive, and glaucoma eyes following acute intraocular pressure elevation. Invest Ophthalmol Vis Sci. 2018;59(1):260-272. 79. Wang X, Beotra MR, Tun TA, et al. In vivo 3-dimensional strain mapping confirms large optic nerve head deformations following horizontal eye movements. Invest Ophthalmol Vis Sci. 2016;57(13):5825-5833. 80. Girard MJ, Beotra MR, Chin KS, et al. In vivo 3-dimensional strain mapping of the optic nerve head following intraocular pressure lowering by trabeculectomy. Ophthalmology. 2016;123(6):1190-1200. 81. Sigal IA, Schuman JS, Ishikawa H, Kagemann L, Wollstein G. A problem of proportions in OCT-based morphometry and a proposed solution. Invest Ophthalmol Vis Sci. 2016;57(2):484485. 82. Girard MJ, Tun TA, Husain R, et al. Lamina cribrosa visibility using optical coherence tomography: comparison of devices and effects of image enhancement techniques. Invest Ophthalmol Vis Sci. 2015;56(2):865-874. 83. Burgoyne CF, Downs JC, Bellezza AJ, Hart RT. Three-dimensional reconstruction of normal and early glaucoma monkey optic nerve head connective tissues. Invest Ophthalmol Vis Sci. 2004;45(12):4388-4399. 84. Downs JC, Roberts MD, Burgoyne CF, Hart RT. Multiscale finite element modeling of the lamina cribrosa microarchitecture in the eye. Conference proceedings: Annual International Conference of the IEEE Engineering in Medicine and Biology Society IEEE Engineering in Medicine and Biology Society Conference. 2009;2009:4277-4280. 85. Nadler Z, Wang B, Schuman JS, et al. In vivo three-dimensional characterization of the healthy human lamina cribrosa with adaptive optics spectral-domain optical coherence tomography. Invest Ophthalmol Vis Sci. 2014;55(10):6459-6466. 86. Wang B, Tran H, Smith MA, et al. In-vivo effects of intraocular and intracranial pressures on the lamina cribrosa microstructure. PLoS One. 2017;12(11):e0188302. 87. Lucy KA, Wang B, Schuman JS, et al. Thick prelaminar tissue decreases lamina cribrosa visibility. Invest Ophthalmol Vis Sci. 2017;58(3):1751-1757. 88. Jan NJ, Lathrop K, Sigal IA. Collagen architecture of the posterior pole: high-resolution wide field of view visualization and analysis using polarized light microscopy. Invest Ophthalmol Vis Sci. 2017;58(2):735-744. 89. Agopov M, Lomb L, La Schiazza O, Bille JF. Second harmonic generation imaging of the pig lamina cribrosa using a scanning laser ophthalmoscope-based microscope. Lasers in medical science. 2009;24(5):787-792. 90. Brown DJ, Morishige N, Neekhra A, Minckler DS, Jester JV. Application of second harmonic imaging microscopy to assess structural changes in optic nerve head structure ex vivo. J Biomed Opt. 2007;12(2):024029.

Copyright © 2018. Kugler Publications. All rights reserved.

Optic nerve head biomechanics in health, aging, and disease 91. Sigal IA, Grimm JL, Jan NJ, Reid K, Minckler DS, Brown DJ. Eye-specific IOP-induced displacements and deformations of human lamina cribrosa. Invest Ophthalmol Vis Sci. 2014;55(1):1-15. 92. Winkler M, Jester B, Nien-Shy C, et al. High resolution three-dimensional reconstruction of the collagenous matrix of the human optic nerve head. Brain Res Bull. 2010;81(2-3):339-348. 93. Jones HJ, Girard MJ, White N, et al. Quantitative analysis of three-dimensional fibrillar collagen microstructure within the normal, aged and glaucomatous human optic nerve head. J R Soc Interface. 2015;12(106). 94. Zhang L, Albon J, Jones H, et al. Collagen microstructural factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2015;56(3):2031-2042. 95. Coudrillier B, Geraldes DM, Vo NT, et al. Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa. IEEE Trans Med Imaging. 2016;35(4):988-999. 96. Danford FL, Yan D, Dreier RA, Cahir TM, Girkin CA, Vande Geest JP. Differences in the region- and depth-dependent microstructural organization in normal versus glaucomatous human posterior sclerae. Invest Ophthalmol Vis Sci. 2013;54(13):79227932. 97. Morrison JC, Dorman-Pease ME, Dunkelberger GR, Quigley HA. Optic nerve head extracellular matrix in primary optic atrophy and experimental glaucoma. Arch Ophthalmol. 1990;108(7):1020-1024. 98. Morrison JC, Jerdan JA, Dorman ME, Quigley HA. Structural proteins of the neonatal and adult lamina cribrosa. Arch Ophthalmol. 1989;107(8):1220-1224. 99. Albon J, Karwatowski WS, Avery N, Easty DL, Duance VC. Changes in the collagenous matrix of the aging human lamina cribrosa. Br J Ophthalmol. 1995;79(4):368-375. 100. Bailey AJ, Paul RG, Knott L. Mechanisms of maturation and ageing of collagen. Mech Ageing Dev. 1998;106(1-2):1-56. 101. Nguyen C, Cone FE, Nguyen TD, et al. Studies of scleral biomechanical behavior related to susceptibility for retinal ganglion cell loss in experimental mouse glaucoma. Invest Ophthalmol Vis Sci. 2013;54(3):1767-1780. 102. Pease ME, Oglesby EN, Cone-Kimball E, et al. Scleral permeability varies by mouse strain and is decreased by chronic experimental glaucoma. Invest Ophthalmol Vis Sci. 2014;55(4):25642573. 103. Steinhart MR, Cone-Kimball E, Nguyen C, et al. Susceptibility to glaucoma damage related to age and connective tissue mutations in mice. Exp Eye Res. 2014;119:54-60. 104. Downs JC, Roberts MD, Sigal IA. Glaucomatous cupping of the lamina cribrosa: a review of the evidence for active progressive remodeling as a mechanism. Exp Eye Res. 2011;93(2):133-140. 105. Lee EJ, Kim TW. Lamina Cribrosa Reversal after trabeculectomy and the rate of progressive retinal nerve fiber layer thinning. Ophthalmology. 2015;122(11):2234-2242. 106. Lee EJ, Kim TW, Kim M, Kim H. Influence of lamina cribrosa thickness and depth on the rate of progressive retinal nerve fiber layer thinning. Ophthalmology. 2015;122(4):721-729.

463 107. Tun TA, Thakku SG, Png O, et al. Shape changes of the anterior lamina cribrosa in normal, ocular hypertensive, and glaucomatous eyes following acute intraocular pressure elevation. Invest Ophthalmol Vis Sci. 2016;57(11):4869-4877. 108. Girard MJ, Strouthidis NG, Desjardins A, Mari JM, Ethier CR. In vivo optic nerve head biomechanics: performance testing of a three-dimensional tracking algorithm. J R Soc Interface. 2013;10(87):20130459. 109. Ivers KM, Yang H, Gardiner SK, et al. In vivo detection of laminar and peripapillary scleral hypercompliance in early monkey experimental glaucoma. Invest Ophthalmol Vis Sci. 2016;57(9):OCT388-403. 110. Park SC, Hsu AT, Su D, et al. Factors associated with focal lamina cribrosa defects in glaucoma. Invest Ophthalmol Vis Sci. 2013;54(13):8401-8407. 111. Lee EJ, Kim TW, Kim M, Girard MJ, Mari JM, Weinreb RN. Recent structural alteration of the peripheral lamina cribrosa near the location of disc hemorrhage in glaucoma. Invest Ophthalmol Vis Sci. 2014;55(4):2805-2815. 112. Kim YK, Park KH. Lamina cribrosa defects in eyes with glaucomatous disc haemorrhage. Acta ophthalmologica. 2016;94(6):e468-473. 113. Sharpe GP, Danthurebandara VM, Vianna JR, et al. Optic disc hemorrhages and laminar disinsertions in glaucoma. Ophthalmology. 2016;123(9):1949-1956. 114. Kim YK, Jeoung JW, Park KH. Effect of Focal Lamina cribrosa defect on disc hemorrhage area in glaucoma. Invest Ophthalmol Vis Sci. 2016;57(3):899-907. 115. Reynaud J, Lockwood H, Gardiner SK, Williams G, Yang H, Burgoyne CF. Lamina cribrosa microarchitecture in monkey early experimental glaucoma: global change. Invest Ophthalmol Vis Sci. 2016;57(7):3451-3469. 116. Downs JC, Yang H, Girkin C, et al. Three-dimensional histomorphometry of the normal and early glaucomatous monkey optic nerve head: neural canal and subarachnoid space architecture. Invest Ophthalmol Vis Sci. 2007;48(7):3195-3208. 117. Yang H, Downs JC, Girkin C, et al. 3-D histomorphometry of the normal and early glaucomatous monkey optic nerve head: lamina cribrosa and peripapillary scleral position and thickness. Invest Ophthalmol Vis Sci. 2007;48(10):4597-4607. 118. Yang H, Williams G, Downs JC, et al. Posterior (outward) migration of the lamina cribrosa and early cupping in monkey experimental glaucoma. Invest Ophthalmol Vis Sci. 2011;52(10):71097121. 119. Downs JC, Suh JK, Thomas KA, Bellezza AJ, Burgoyne CF, Hart RT. Viscoelastic characterization of peripapillary sclera: material properties by quadrant in rabbit and monkey eyes. J Biomech Eng. 2003;125(1):124-131. 120. Jung KI, Jung Y, Park KT, Park CK. Factors affecting plastic lamina cribrosa displacement in glaucoma patients. Invest Ophthalmol Vis Sci. 2014;55(12):7709-7715. 121. Roberts MD, Sigal IA, Liang Y, Burgoyne CF, Downs JC. Changes in the biomechanical response of the optic nerve head in early experimental glaucoma. Invest Ophthalmol Vis Sci. 2010;51(11):5675-5684.

464

Copyright © 2018. Kugler Publications. All rights reserved.

122. Hernandez MR. The optic nerve head in glaucoma: role of astrocytes in tissue remodeling. Prog Retin Eye Res. 2000;19(3):297321. 123. Hernandez MR, Luo XX, Andrzejewska W, Neufeld AH. Age-related changes in the extracellular matrix of the human optic nerve head. Am J Ophthalmol. 1989;107(5):476-484. 124. Hernandez MR, Ye H. Glaucoma: changes in extracellular matrix in the optic nerve head. Ann Med. 1993;25(4):309-315. 125. Kirwan RP, Fenerty CH, Crean J, Wordinger RJ, Clark AF, O’Brien CJ. Influence of cyclical mechanical strain on extracellular matrix gene expression in human lamina cribrosa cells in vitro. Mol Vis. 2005;11:798-810. 126. Balaratnasingam C, Morgan WH, Bass L, et al. Elevated pressure induced astrocyte damage in the optic nerve. Brain Res. 2008;1244:142-154. 127. Agapova OA, Kaufman PL, Lucarelli MJ, Gabelt BT, Hernandez MR. Differential expression of matrix metalloproteinases in monkey eyes with experimental glaucoma or optic nerve transection. Brain Res. 2003;967(1-2):132-143. 128. Quigley H, Anderson DR. The dynamics and location of axonal transport blockade by acute intraocular pressure elevation in primate optic nerve. Invest Ophthalmol. 1976;15(8):606-616. 129. Quigley HA, Anderson DR. Distribution of axonal transport blockade by acute intraocular pressure elevation in the primate optic nerve head. Invest Ophthalmol Vis Sci. 1977;16(7):640644. 130. Quigley HA, Addicks EM. Chronic experimental glaucoma in primates. II. Effect of extended intraocular pressure elevation on optic nerve head and axonal transport. Invest Ophthalmol Vis Sci. 1980;19(2):137-152.

J. Crawford Downs 131. Geijer C, Bill A. Effects of raised intraocular pressure on retinal, prelaminar, laminar, and retrolaminar optic nerve blood flow in monkeys. Invest Ophthalmol Vis Sci. 1979;18(10):1030-1042. 132. Radius RL. Optic nerve fast axonal transport abnormalities in primates. Occurrence after short posterior ciliary artery occlusion. Arch Ophthalmol. 1980;98(11):2018-2022. 133. Wang L, Cull GA, Piper C, Burgoyne CF, Fortune B. Anterior and posterior optic nerve head blood flow in nonhuman primate experimental glaucoma model measured by laser speckle imaging technique and microsphere method. Invest Ophthalmol Vis Sci. 2012;53(13):8303-8309. 134. Cull G, Burgoyne CF, Fortune B, Wang L. Longitudinal hemodynamic changes within the optic nerve head in experimental glaucoma. Invest Ophthalmol Vis Sci. 2013;54(6):4271-4277. 135. Foolen J, van Donkelaar CC, Soekhradj-Soechit S, Ito K. European Society of Biomechanics S.M. Perren Award 2010: an adaptation mechanism for fibrous tissue to sustained shortening. J Biomech. 2010;43(16):3168-3176. 136. Sun D, Lye-Barthel M, Masland RH, Jakobs TC. The morphology and spatial arrangement of astrocytes in the optic nerve head of the mouse. J Comp Neurol. 2009;516(1):1-19. 137. Sredar N, Ivers KM, Queener HM, Zouridakis G, Porter J. 3D modeling to characterize lamina cribrosa surface and pore geometries using in vivo images from normal and glaucomatous eyes. Biomed Opt Express. 2013;4(7):1153-1165. 138. Downs JC, Girkin CA. Lamina cribrosa in glaucoma. Curr Opin Ophthalmol. 2017;28(2):113-119.

31. Cerebrospinal fluid pressure and the translaminar pressure gradient in optic nerve head biomechanics Julia Raykin1, Brian C. Samuels2, Andrew J. Feola1, C. Ross Ethier1,3 Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, Atlanta, GA, USA; 2Department of Ophthalmology, University of Alabama at Birmingham, Birmingham, AL, USA; 3 George W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA 1

Copyright © 2018. Kugler Publications. All rights reserved.

1. Introduction Clinically, a pathophysiologic imbalance between intraocular (IOP) and cerebrospinal fluid pressure (CSFp) across the optic nerve head (ONH) appears to play a critical role in several ophthalmic pathologies. Most familiar is increased IOP being a major risk factor for primary open-angle glaucoma. Here, we instead focus on the role of cerebrospinal fluid pressure (CSFp), whose alterations are implicated in several additional ophthalmic conditions. For example, there is now good evidence (see below) that low-tension glaucoma is associated with decreased CSFp.1–4 Further, elevated CSFp has long been known to result in papilledema, a hallmark of idiopathic intracranial hypertension (pseudotumor cerebri).5 Finally, it is also thought that an increase in CSFp plays a role in the ophthalmic changes associated with Visual Impairment/Intracranial Pressure (VIIP) syndrome experienced by astronauts who spend extended periods of time in microgravity.6,7 The ONH is of particular interest because it is the primary site of glaucomatous damage;8 moreover, it has been shown to have the highest levels of stresses and strains in the posterior eye wall.9 Therefore, this region is thought to play a role in other ophthalmic pathologies. The lamina cribrosa (LC), a porous network of collagen and elastin beams through which the retinal ganglion cell (RGC) axons pass as they exit the eye, is the

major structural component of the ONH. It separates two ocular regions at different pressures: the globe contents experience IOP, and the ONH and retrolaminar optic nerve, where the pressure varies with CSFp. The pressure within the optic nerve immediately behind the LC is known as the retrolaminar tissue pressure (RLTP). It is related to, but not identical to, retrobulbar subarachnoid CSFp. We shall return to this point, but for simplicity, we will at present approximate RLTP by CSFp. It is well accepted that glaucomatous damage to RGC axons is initiated at the level of the LC.10–12 Further, it is known that cells of the ONH are mechanosensitive.13–19 It is therefore natural to consider how the LC (and surrounding ONH tissues) respond to the pressures acting on the ONH from a biomechanics perspective. Historically, there has been debate as to the cause of axonal damage in glaucoma, with hypotheses including pressure-linked mechanical injury or vascular compromise. As Priestly Smith recognized as far back as the 1870s, glaucoma pathophysiology is likely a combination of both mechanical and vascular insults in the eye. In 2005, Burgoyne and colleagues proposed a unifying biomechanical theory that has gained broad acceptance. It posits that the ONH can be viewed as a biomechanical structure, and that IOP-related stresses and strains play critical roles in the pathophysiologic changes seen in ONH tissue and blood supply.20 By extension, given that the CSF fills the optic nerve sheath

Correspondence: C. Ross Ethier, Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology and Emory University, 315 Ferst Dr. NW, Atlanta, GA 30332, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 465-478 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

466

J. Raykin et al.

to its insertion at the posterior aspect of the globe, this theory allows for the notion that changes in CSFp may also create pathologic mechanical stresses and strains at the level of the ONH. Thus, changes in CSFp may also lead to axonal damage. In fact, several clinical, experimental, and computational studies support the hypothesis that pathologic levels of CSFp may be associated with optic neuropathy.

Copyright © 2018. Kugler Publications. All rights reserved.

2. What is the translaminar pressure gradient? We define the translaminar pressure difference (TLPD) as IOP minus retrobulbar subarachnoid CSFp. This is related to, but not the same as, the translaminar pressure gradient, which is equal to the translaminar pressure difference divided by the anterior-posterior thickness of the LC. Regrettably, there is some confusion about nomenclature in the literature, and the terms ‘translaminar pressure difference’ and ‘translaminar pressure gradient’ are sometimes used interchangeably. This is conceptually incorrect and practically misleading for several reasons: 1. LC thickness varies from person to person, and is specifically known to be significantly less in glaucoma patients.21 Thus, the same translaminar pressure difference can lead to very different translaminar pressure gradients, depending on LC thickness. 2. The translaminar pressure gradient is the more biomechanically relevant measure when considering LC deformation in response to changes in IOP or CSFp. This is because LC deformation will depend both on intrinsic material properties of the LC and on geometric features, including scleral canal opening size and LC thickness. The latter quantity is accounted for in the translaminar pressure gradient, but not in the TLPD. Unfortunately, it is very challenging, if not impossible, to measure LC thickness reliably in the clinic, and therefore we are usually forced to consider only the TLPD in clinical studies. Important data regarding the relationship between the TLPD and the translaminar pressure gradient have been provided by Morgan and colleagues,22 who directly controlled IOP and CSFp in

Fig. 1. The relationship between the translaminar pressure difference (horizontal axis) and translaminar pressure gradient (vertical axis) as measured in dogs using a servo-nulling micropipette system. Dashed lines show 95% confidence interval for the linear regression (solid line). The inset (upper left) shows a schematic of how the measurements were carried out: a micropipette was advanced from the vitreous through the ONH tissues, recording pressures as a function of position as IOP and CSFp were controlled. Data replotted and inset from Morgan et al.22

dogs by cannulation, and measured pressures within the LC using a micropipette servo-null system. It was observed that there was a reasonable correlation between the translaminar pressure difference and gradient (Fig. 1); however, this correlation would likely be reduced in glaucomatous vs normal human eyes due to the LC thinning in glaucoma patients described above. It is also important to understand that CSFp is not the only pressure that acts in the retrobulbar space. In addition to blood pressures in the central retinal vasculature, the tissue pressure within the retrolaminar optic nerve is related to, but is not necessarily the same as, CSFp. Again, Morgan and colleagues22 have provided important quantification of this relationship (Fig. 2). In dogs, CSFp and retrolaminar tissue pressure (RLTP) track one another closely so long as CSFp is greater than ~4 mmHg. However, these pressures become decoupled when CSFp drops below this value, which occurs during upright posture in humans.23 Morgan and colleagues suggested that the plateaus seen in Figure 2 represent the situation when the retrobulbar subarachnoid space collapses, so that tissue pressures in the optic nerve are essentially determined by periorbital tissue pressure. In summary, one can consider that IOP and CSFp give

Cerebrospinal fluid pressure and the translaminar pressure gradient in optic nerve head biomechanics

Fig. 2. Relationship between retrobulbar pressures and CSFp in dogs, as measured by micropipette. A good correlation can be seen when CSFp is larger than ~4 mmHg, but retrobulbar pressures become decoupled from CSFp at low CSFp values. ONSASp = optic nerve subarachnoid space pressure.22

rise to the forces shown schematically in Figure 3, where RLTP is closely related to CSFp, acting in the retrobulbar subarachnoid space at CSFp levels > 4 mmHg. When considering Figure 3, it should also be noted that IOP acts directly to displace the lamina posteriorly, and also indirectly to increase scleral tension on the LC, which in turn pulls the LC taut,24 as discussed elsewhere in this volume. Misconception 1: CSFp/IOP Balance

Copyright © 2018. Kugler Publications. All rights reserved.

There is a common misconception that CSFp can totally counterbalance IOP at the ONH when IOP = CSFp; this is not the case, as IOP acts on the entire ocular coat and can cause laminar strain through scleral canal expansion even when IOP and CSFp are in perfect balance. Finally, it is worth noting that the CSFp within the retrobulbar subarachnoid space is usually taken to be equal to CSFp, possibly with a suitable hydrostatic offset. However, this may not necessarily hold true. Evidence of this disconnect is apparent at low CSFp values (Fig. 2), where there is likely collapse of the retrobulbar subarachnoid space. Another potentially clinically important situation arises in so-called ‘optic nerve compartment syndrome’, a poorly understood condition where there is evidence of incomplete com-

467

Fig. 3. Schematic overview of how pressures lead to loading on ONH tissues. The effects of blood pressure acting within the central retinal vessels is not shown. IOP: intraocular pressure; CSFp: cerebrospinal fluid pressure; RLTP: retrolaminar tissue pressure. Underlying scanning electron micrograph taken from Albon et al.25

munication between the retrobulbar subarachnoid space and the intracranial subarachnoid space.26 The full clinical extent and impact of this syndrome is unclear. In the absence of other information, we will adopt the common approach in the literature and continue to take CSFp as a surrogate for retrobulbar subarachnoid space pressure. Since it is not clinically possible to measure the retrolaminar tissue pressure, and despite the above complexities, TLPD values are usually approximated as the difference between IOP and CSFp. Under physiologic conditions, the TLPD is estimated to be 3.7 mmHg in the supine position27 in humans. Larger TLPD due to elevations in IOP or reductions in CSFp result in an increased posterior force on the LC, usually — although not always — leading to posterior deformation of the LC.28,29

3. CSFp measurement In view of the above, we see that determination of TLPD requires knowledge of both IOP and CSFp. There are well-established clinical methods for non-invasive determination of IOP,30 and although such measurements can be subject to certain errors, we will not

Copyright © 2018. Kugler Publications. All rights reserved.

468

concern ourselves with these issues here. More clinically challenging is the non-invasive determination of CSFp. Several invasive methods exist, including placement of a ventricular catheter/pressure transducer after craniotomy31 and determination of the opening pressure during lumbar puncture with the patient in the lateral decubitus position.32 However, these approaches are unsuitable for routine screening. Several technologies and approaches have been considered to develop non-invasive or minimally invasive techniques for CSFp determination. For example, mathematical formulas have been proposed that estimate CSFp based on factors such as age, BMI, etc.; however, a recent study indicates that the accuracy of such formulas is poor.33 Thus, there has been great interest in the development of non-invasive or minimally-invasive techniques for CSFp measurement. A wide variety of non-invasive approaches have been suggested and tested. A partial list of such methods includes: 1. detecting movement of the tympanic membrane;34 2. detecting changes in otoacoustic emission spectra;35 3. two-depth Doppler to compare arterial pulsations in the intra- and extra-cranial segments of the ophthalmic artery as orbital pressure is changed;36 4. measurement of optic nerve sheath diameter by ultrasound or MRI;37 and 5. monitoring retinal vein pulsations as IOP is changed.38–42 Unfortunately, these non-invasive technologies have yet to be widely adopted clinically.43–45 In addition to cost and complexity, there are several reasons for this. First, some of these methods can assess changes in CSFp over time, but do not give an absolute CSFp reading, which is required in certain clinical situations. Second, and more notably, these techniques tend to have poor accuracy and resolution, which are both clinically significant. For example, the mean CSFp difference between normal-tension glaucoma patients and controls is modest (~2.7 mmHg),2 and so any non-invasive approach would ideally achieve or exceed this level of accuracy and resolution. This is difficult for non-invasive methods, since they all rely indirectly or directly on population-averaged assumptions about

J. Raykin et al.

the biomechanical properties of the tissues being interrogated, which can vary significantly from patient to patient.46 Much effort continues to be expended in this area, and newer technologies may eventually provide clinically useful approaches. In the interim, however, invasive approaches remain the ‘gold standard’ for CSFp determination.

4. Clinical aspects of lowered CSFp and glaucoma The concept of reduced CSFp contributing to RGC loss dates back many years. Yablonski et al. studied the effect of reduced CSFp on ONH morphology in cats in the late 1970s. This work showed that reducing CSFp resulted in structural changes within the ONH that were consistent with either pre-glaucomatous injury or early experimental glaucoma depending on the duration of CSFp reduction.47,48 These data do not appear to have gained much traction at the time, as there is little available evidence in the literature of additional studies in this area. However, nearly 30 years after Yablonski’s work, interest in the role of the TLPD on glaucoma pathogenesis has been renewed, as we now describe. Low-tension or normal-tension glaucoma is characterized by an open iridocorneal angle, glaucomatous appearance of the optic disk, visual field changes consistent with the observed optic nerve damage, and consistent IOP measurements below 21 mmHg. A vascular etiology has often been suggested as the cause of normal-tension glaucoma due to its increased prevalence in patients with Raynaud’s phenomenon, migraine headaches, and systemic hypotension. However, in 2008 and 2009, Berdahl and colleagues revived interest in the reduced-CSFp/elevated TLPD hypothesis of low/normal-tension glaucoma in a series of retrospective studies.2,49 Patients with a diagnosis of open-angle glaucoma, normal-tension glaucoma, or ocular hypertension that had undergone lumbar puncture for reasons not related to their ocular disease were compared to matched controls. The IOP for each group was compared to the lumbar opening pressure obtained in the lateral decubitus position, and the TLPD was calculated. The studies showed that patients with both primary open-angle glaucoma and normal-tension glaucoma had significantly lower CSFp

Cerebrospinal fluid pressure and the translaminar pressure gradient in optic nerve head biomechanics

469

5. Clinical aspects of elevated CSFp and optic neuropathy

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. TLPPD in control subjects and glaucoma patients. (a) Intracranial pressure in primary open-angle glaucoma (POAG) patients and normal-tension glaucoma (NTG) patients is significantly lower than their matched controls. (b) Additionally, the calculated TLPD (IOP-CSFp) is significantly higher than in controls. ICP: intracranial pressure; OHT: ocular hypertension.2

compared to control subjects. Thus, both groups also had a greater calculated TLPD than controls (Fig. 4). Subsequent prospective studies have confirmed these findings.3,4 In addition, a recent case report shows evidence suggesting that a patient with normal-tension glaucoma had progression of her disease after undergoing ventriculoperitoneal shunt placement to reduce CSFp.50 Together, these clinical data provide strong evidence for reduced CSFp contributing to a glaucomatous optic neuropathy; further, this data is consistent with the hypothesis that alterations of the biomechanical environment within the ONH play a critical role in this neuropathy.

While continued research in the area of normal-tension glaucoma will provide additional clarity on the role of reduced CSFp, it is well established that elevated CSFp causes optic nerve pathology. Increased CSFp was first recognized as the cause for papilledema in the 1850s, but the exact etiology of the optic disc swelling took much longer to identify. After decades of research in this area, Hayreh concluded that the cause of optic nerve edema is primarily a mechanical insult initiated by an increase in CSFp in the brain that is transmitted down the optic nerve sheath. This causes increased tissue pressure in the nerve proper, which results in axoplasmic stasis. Swelling of the axons in the ONH is then followed by prelaminar disc edema.5 Although there are multiple causes for increased CSFp, we will limit our discussion to two clinical presentations: idiopathic intracranial hypertension (IIH, or pseudotumor cerebri), and astronauts that experience VIIP syndrome. Interestingly, while there clinical similarities, the demographics of these two patient populations are quite different. IIH is typically seen in overweight females of child-bearing age, while VIIP syndrome has only been identified thus far in middle-aged men.7,51 Headaches are one of the most common complaints in patients subsequently diagnosed with IIH. However, patients have also been noted to seek medical attention for transient visual obscurations, visual disturbances, and pulsatile tinnitus or other pulsatile intracranial noises.51,52 On physical examination, patients often exhibit papilledema, cranial nerve VI palsy, chorioretinal folds, and visual field defects. In subjects with visual field disturbances, the most common defects are thought to be an enlarged blind spot and/or arcuate defects consistent with nerve bundle-type defects.53 While the enlarged blind spot is consistent with the papilledema, one would anticipate that the arcuate bundle type defects are more consistent with a biomechanics-induced injury in the ONH similar to that seen with glaucoma. Mechanical stresses and strains on the ONH likely play a larger role in the pathogenesis of IIH than has been historically recognized. Magnetic resonance imaging (MRI) supports the notion of increased

Copyright © 2018. Kugler Publications. All rights reserved.

470

J. Raykin et al.

Fig. 5. Intracranial hypertension results in two types of biomechanical strain/deformation: (a) anterior deformation of the LC and peripapillary sclera (1) and swelling of the ONH (2). (b) Internal expansive compression and tensile stress at the base of the ONH may cause peripapillary wrinkles. (c) Horizontal folds are likely caused by tensile strain that generates secondary orthogonal compression in the papillomacular bundle. The radial retinal folds may be explained by axisymmetric compression at the scleral flange or by symmetrical expansion of the ONH.90

Fig. 6. ONH images of an astronaut diagnosed with VIIP syndrome. The pre-flight images (top) were normal bilaterally. However, post-flight (bottom) images show significant Frisen Grade 3 edema in the right eye (OD) and more modest Frisen Grade 1 edema in the left eye (OS). ONH swelling in the astronauts experiencing VIIP is very similar to the papilledema seen in patients with idiopathic intracranial hypertension, including a pattern of early nasal edema that spreads superiorly and inferiorly as the condition worsens.6

mechanical loading on the ONH, as evidenced by posterior pole scleral flattening, perioptic retrobulbar optic nerve sheath distention, protrusion of the prelaminar optic nerve tissue into the vitreous space, and tortuosity of the orbital optic nerve.52 In addition, studies from the Idiopathic Intracranial Hypertension Treatment Trial group shows convincing evidence that the chorio­retinal folding seen on exam is also likely due to altered mechanical loading on the ONH (Fig. 5). There is ample data supporting the role of increased CSFp on creating optic nerve pathology in IIH patients. However, the idea that increased CSFp may lead to a previously unrecognized type of optic neuropathy in astronauts is relatively new. Since the 1960s, data has been gathered and analyzed to study the physiologic and psychologic effects of space flight on human beings.55–57 Entrance into microgravity results in the loss of the terrestrial hydrostatic pressure gradient, which results in an estimated cephalad fluid shift of 1-3 liters.58,59 Astronauts adapt to their new environment through a cascade of physiologic changes involving nearly every organ system. These include alterations of the cardiovascular system, reduction in bone density, muscle atrophy, psychological stress,

and circadian dysregulation, among others. For most US astronauts traveling on space shuttle missions through the 1990s, the typical microgravity exposure was about 14 days. However, the opening of the International Space Station in 2000 allowed mission duration to increase significantly. While changes in visual acuity had been reported with shorter duration space flights, this increased temporal exposure to microgravity resulted in the recognition of a new pathophysiologic phenomenon, classically termed VIIP Syndrome. VIIP Syndrome is a constellation of ophthalmic changes that results in alterations in visual function, engorgement and folding of the choroid, posterior globe flattening, kinking and distention of the optic nerve sheath, and ONH edema.6,7 In the first cohort of systematically studied long-duration spaceflight astronauts (mean age of 50.2 ± 4.2 years), 9 of the 47 astronauts experienced alterations in visual function and 12 out of 47 had persistent anatomic changes upon returning to Earth. In some cases, the manifest changes have lasted years. Interestingly, all cases thus far have been in male astronauts; however, it is unknown whether this is indicative of a hitherto unknown risk factor or simply selection bias based on the ratio of

Cerebrospinal fluid pressure and the translaminar pressure gradient in optic nerve head biomechanics

male-to-female astronauts. While the actual cause of the anatomic and physiologic changes associated with VIIP syndrome is still not fully understood, evidence points toward increased CSFp as playing a role given some of the clinical similarities to IIH. The loss of the normal gravity-induced hydrostatic pressure gradient and resultant cephalad fluid shift is theorized to precipitate an increase in CSFp in microgravity. While CSFp has not been directly recorded in microgravity, several key findings support this notion. First, four of the seven astronauts initially diagnosed with VIIP syndrome underwent lumbar punctures post-flight after the ophthalmic pathology was noted. An opening pressure range of 21 to 28.5 cm H20 was noted in these individuals, some up to 19 months post-flight in some astronauts.7 While there is some disagreement on the accepted normal range, it has been suggested that this level of CSFp is likely indicative of CSFp elevation in microgravity. In addition, five of the seven astronauts were noted to have optic disc edema ranging from Frisen grade 1-3 in at least one eye (Fig. 6). The optic nerve pathology is consistent with that seen in idiopathic intracranial hypertension.60–62 Finally, post-flight ultrasonography revealed optic nerve sheath distention, and MRI showed posterior globe flattening, optic nerve kinking, and optic nerve tortuosity. These findings are again consistent with imaging from patients with known elevated CSFp.54,63 Until non-invasive techniques for determining CSFp become more accurate or the use of an in-vivo chronic CSFp monitor is approved for astronauts on long-duration missions, the question as to whether or not CSFp increases in microgravity will remain unresolved.

Copyright © 2018. Kugler Publications. All rights reserved.

6. Animal models to study the effects of CSFp on ONH biomechanics The clinical and experimental studies described above all suggest that CSFp has an impact on ONH deformation and consequent axonal pathology. There is a significant need for further investigations in this area. While several studies have looked at the effects of IOP on LC deformation in vivo and in vitro,70–72 only a limited number of studies have directly investigated the impact of CSFp on ONH biomechanics. Since it is currently not possible to non-invasive-

471

ly monitor CSFp clinically, several animal models have been developed to study the effects of CSFp on the ONH and optic neuropathies. As described above, Yablonski and coworkers studied the effects of chronically decreased CSFp in a cat model. In this study, the CSFp was decreased and the IOP in one eye was decreased, while the contralateral eye was unaltered. Glaucomatous-like optic neuropathy was observed in the unaltered eye, while the eye with lowered IOP remained normal.47,48 Next, Yang et al.64 demonstrated that a long-term reduction in CSFp, via a lumbar-peritoneal shunt, led to a glaucoma-like optic neuropathy in some primates at normal IOP, although others were not affected. Further, Zhang et al.67 showed that short-term decreases in CSFp and increases in IOP led to impeded orthograde axoplasmic flow and retrograde axonal transport in the RGC axons in rats. Taken together, these studies suggest that changes in the TLPD can induce glaucoma-like changes and coincident axonal loss. Few studies have attempted to investigate the effects of increased CSFp on optic neuropathies. However, one such study demonstrated that elevated CSFp in mice results in optic nerve axonal loss that could be similar to IIH or VIIP.66 To elucidate the mechanical causes of axonal damage in response to CSFp alterations, several studies have looked at CSFp-induced ONH deformation in animal models. Morgan et al.67 investigated the effects of independently varying IOP and CSFp on ONH deformation in a canine model using confocal scanning laser tomography. Significant posterior displacement of the ONH surface was observed in response to elevations in IOP, while an elevation in CSFp resulted in anterior displacement. This study was the first to show that changes in the TLPD result directly in deformation of the ONH surface. However, as these studies were limited to ONH surface tomography, no data were presented on deformation of the subsurface structures of the ONH, including the LC or retrolaminar neural tissue. Tran et al.68 directly examined the effects of acute changes in CSFp and IOP on LC displacement in a primate model using optical coherence tomography imaging. This study demonstrated that IOP and CSFp altered strain in the LC, and reported strains exceeding 20%. While this study was only done in one animal and these results cannot yet be generalized due to possible inter-individual differences, these results are consistent with

472

J. Raykin et al.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 7. The mean (left column) and peak (95th percentile; right column) principal strains in the LC (top panel) and retrolaminar neural tissue (bottom panel), measured in ex-vivo porcine eyes. As CSFp increased, peak and mean tissue strains increased, especially in the retrolaminar neural tissue, where very large values were observed, representing radial compression and axial stretching of the optic nerve. Error bars: standard deviation.67

the study performed by Morgan et al.,67 suggesting that there is a significant effect of CSFp on ONH and LC displacement. Finally, we mention the recent work of Feola et al.69 While not an animal model in the usual sense, these authors imaged enucleated porcine eyes in which the IOP and retrobulbar subarachnoid space pressures were controlled by cannulation. By using phase-­ contrast micro-computerized tomography imaging techniques, it was possible to detect the small motions of connective tissues in the ONH, including the LC, as ‘CSFp’ was changed experimentally. The results were qualitatively consistent with numerical models (see below): Elevating CSFp from 4 mmHg to 30 mmHg had a significant impact on the biomechanical strain distributions within the LC, and more prominently, within the retro-laminar neural tissue (Fig. 7). Further, this work was qualitatively consistent with previous studies that examined the effects of acute CSFp elevations on ONH deformation. This provides direct experimental evidence that changes in CSFp directly affect ONH tissue strains.

7. Computational modeling and experimental studies of the effects of CSFp on ONH biomechanics Since IOP and CSFp act on different regions of the LC (Fig. 3), considering only TLPD as the ‘driving load’ greatly oversimplifies ONH biomechanics. Many other factors, such as ocular geometry and the material properties of ocular tissues, play an important role in the complex interaction between IOP, CSFp, and ONH deformation. Indeed, Tran et al.68 demonstrated that the effects of IOP and CSFp on LC deformation do not strictly balance each other, i.e., a given increase in IOP is not cancelled out by the same increase in CSFp. This discrepancy likely arises from the fact that IOP affects both the ONH and scleral shell, while CSFp counteracts IOP only at the ONH. This highlights the complexity of ONH biomechanics and reinforces the need to study the biomechanical properties of the individual ONH tissue components and the relevant loadings to form an integrated understanding of ONH biomechanics. Gaining insight into such a complex system with limited physical access poses several significant exper-

Cerebrospinal fluid pressure and the translaminar pressure gradient in optic nerve head biomechanics

473

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 8. The geometric model of the posterior eye and extended optic nerve used by Feola et al.77 for finite element modeling.

imental challenges. Due to these challenges, computer modeling of the posterior eye is often used to help answer basic mechanical questions and gain insight into complex biological systems. For example, finite element modeling and other types of numerical simulation have long been used to investigate the influence of ocular geometry, tissue material properties, and inter-individual differences on ONH deformation.9,73–75 The results from these models have been used to motivate further experimental studies and identify important targets for clinical diagnosis. Originally proposed by Bellezza et al.73 to study ONH biomechanics, finite element modeling has been adopted by multiple groups to investigate the effects of elevated IOP on the ONH with particular interest in the LC.9,24,73,74,76 The finite element approach is particularly powerful because it allows for the consideration of multiple tissue components with complex geometries and biomechanical properties, as well studies of how the ONH responds to a variety of loading conditions. Unfortunately, few studies to date have incorporated the effects of CSFp into finite element models of the ONH. Feola et al.77 used finite element analysis to investigate the effects of inter-individual variations of tissue material properties and pressures on the deformation of the ONH. This study examined the influence of various CSFp conditions on the strains in the prelaminar neural tissue, LC, and retrolaminar optic nerve. Expanding on previous geometric and finite element models of the posterior eye and ONH

Fig. 9. Computed peak strains in the ONH from finite element model simulations. The solid lines represent the peak tension (positive) and compressive (negative) strains under three CSFp conditions (e.g., upright posture, supine posture, and elevated CSFp). The corresponding dashed lines represent the 95% confidence bounds of these distributions. The shaded region highlights the range of strains predicted to occur under normal CSFp levels (upright and supine conditions). ICP: intracranial pressure.77

developed by Sigal et al.9,24 of the posterior eye and ONH, a geometric model that included the pia mater, dura mater, and optic nerve extending 10 mm posterior to the globe was developed (Fig. 8). This model included the posterior sclera, peripapillary sclera, and the annular scleral ring that surrounds the scleral canal. These tissues were modeled as a mixture composite material that included a ground substance (Neo-

Copyright © 2018. Kugler Publications. All rights reserved.

474

Hookean) with embedded collagen fibers with various degrees of alignment following a von Mises distribution. The pia mater and dura mater were modeled with the same constitutive relationship, while the remaining tissues were idealized as linear-elastic. Then, utilizing Latin hypercube sampling to simulate inter-individual variations in material properties and pressure, the researchers investigated the effects of upright, supine, and elevated CSFp conditions on peak strains in each tissue region. Interestingly, within each CSFp condition, there was a range of peak strains experienced in the prelaminar neural tissue, LC, and retrolaminar optic nerve (Fig. 9). This may indicate that there is a degree of inter-individual variation of typical strains associated with normal CSFp ranges (upright and supine positions). However, there was a notable increase in the strains in the retrolaminar optic nerve as CSFp increased, with up to 47% of simulated individuals having a peak strain in the retrolaminar optic nerve greater than that predicted to occur under upright and supine conditions. In addition, elevating CSFp increased the strains in the retrolaminar optic nerve. IOP, CSFp, optic nerve stiffness, and LC stiffness had the largest impact on the peak strains in the ONH. This study illustrates that CSFp and inter-individual variations in pressures and tissue material properties impact the loading environment of the ONH. Additional simulations by Hua et al.78 examined the influence of variations in material properties and ocular geometry on CSFp-induced deformations of the ONH. This study used a similar baseline geometric model, assuming linearly elastic material properties as Feola et al.77 and Sigal et al.9 This study also found that CSFp elevation increased strains within the retrolaminar optic nerve and decreased strains within the LC. In agreement with the simulations by Feola et al.,77 sensitivity analysis revealed that retrolaminar optic nerve deformation was mainly influenced by optic nerve and pia mater stiffness. In addition, scleral canal size had a large impact on deformation within the retrolaminar optic nerve. They also concluded that LC strain was influenced by two geometric parameters (e.g., scleral thickness and scleral canal size) and LC stiffness, which corroborates the work by Sigal et al.9 Overall, these finite element studies illustrate that CSFp impacts the strains within the ONH and has a profound impact on strains within the retrolaminar nerve. Thus,

J. Raykin et al.

Fig. 10. Simplified models in which the LC was treated as a thin plate or membrane with various boundary conditions. These free body diagrams illustrate the applied pressures (IOP and retrolaminar pressure), with or without an in-plane tension (N) and various boundary conditions (clamped or simple supported).80

these studies suggest that CSFp may be an important factor for ocular diseases that merits additional investigation. More traditional mathematical approaches have also been used to study the mechanics of the posterior eye. Here, we focus on models that include a retrolaminar pressure, or CSFp, but to-date have not specifically examined the influence of CSFp on the LC or ONH. These models are briefly described to highlight their importance and potential use for studying the effects of CSFp on ONH deformation. These models are commonly used to investigate the effect of mechanical loading on LC deformation. For instance, a model developed by Dongqi and Zeqin79 focused on the effects of IOP on laminar deformation, but was also developed to account for a retrolaminar pressure to oppose IOP. The overall load on the LC was defined as the TLPD. In this study, the geometry of the LC was simplified to a thin plate to allow insight into LC deformations in response to changes in pressure. This early formulation demonstrated that the TLPD may influence the displacement of the LC, and that LC thickness and LC radius play a role in LC deformation. Others utilized a similar simplified system to examine LC deformation at various IOPs, boundary conditions, and lateral tensions. While these models are generalizations, they can help us better understand how the sclera and LC interact, the influence of in-plane LC tension, and the effect of various constitutive relation-

Cerebrospinal fluid pressure and the translaminar pressure gradient in optic nerve head biomechanics

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 11. A model of the LC within the ONH. Here the LC was modeled as a poroelastic material containing collagen, neural tissue, and blood vessels. Blood vessels were modeled as permeable, parallel cylindrical tubes throughout the LC thickness. The LC was also subjected to three mechanical loads: IOP acting on the anterior surface; RLTp acting on the posterior surface; and an in-plane scleral tension/rotation.81

ships. One such study examined six different idealized conditions of the LC geometry (Fig. 10). These models included a retrolaminar pressure, but were limited to a simple function that directly related the retrolaminar pressure to IOP. Specifically, the retrolaminar pressure was defined as 0.5∙IOP for IOP < 20 mmHg and equal to 10 mmHg for IOPs above 20 mmHg.79,80 In addition, a 3-D finite element model of the eye and LC was developed to identify which boundary conditions and model assumptions best represented the finite element case. In these models, the LC displaced the most at its center; however, modeling the LC as fixed with in-line tension mirrored the finite element simulations. The authors concluded that this mathematical model would be best for future simulations and sensitivity studies. Thus, these studies provide a framework to examine the influence of various retrolaminar pressures utilizing numerical modeling. More sophisticated models of the ONH model the LC as a poroelastic structure that is subjected to IOP, retrolaminar pressure, and in-plane tension from the sclera (Fig. 11).81 In this study, Causin et al. modeled the LC as a 2-D composite material consisting of connective tissue (collagen, elastin, and extracellular matrix), neural tissue, and blood vessels. In these simulations, the retrolaminar pressure was fixed at 7 mmHg as the IOP was elevated from 15 to 35 mmHg. This study suggests that scleral tension and rotation drastically increase the stress and displacement of the LC; however, they

475

did not directly examine the impact of independently varying the retrolaminar pressure. These modeling approaches provide early evidence that CSFp and retrolaminar pressure play an important role in the deformation of the ONH and that they should be accounted for in future simulations. Notably, the profound deformation predicted to occur in the retrolaminar neural tissue due to CSFp elevation illustrates the importance of considering CSFp in understanding ONH biomechanics. In addition, these studies provide some insight into the structural or material properties of several tissues in the posterior eye (e.g., sclera, LC, pia mater, and optic nerve) that may have the largest impact in determining how CSFp impacts ONH tissue deformations. More generally, they underscore the critical importance of computational modeling as a tool to probe complex systems and help identify key areas for future investigations.

8. Conclusions There is strong clinical, experimental, and computational evidence that changes in CSFp (both increases and decreases) can affect ONH biomechanics and contribute to optic nerve pathologies. Further, current information supports the notion that altered biomechanical loading on the ONH plays a role in the pathogenesis of glaucoma, IIH, and VIIP. However, there remains much that is poorly understood about how CSFp influences ONH biomechanics. Future computational models should incorporate improved treatment of factors such as: 1. the biomechanical influence of the choroid;82,83 2. more accurate biomechanical properties of the sclera;84,85 3. optic nerve sheath tension;86–88 and 4. residual stresses89 in the eye. It is also worth noting that CSFp is not constant and varies during changes in posture, which could therefore have a significant effect on ONH deformation and should also be incorporated into these models. Such improved in-silico approaches, coupled with ex-vivo studies of tissue biomechanics and animal models, will improve the understanding of optic neuropathies and inform the development of new clinical diagnoses and interventions.

J. Raykin et al.

476

References 1.

2.

3.

4.

5. 6.

7.

8. 9.

10.

11. 12.

Copyright © 2018. Kugler Publications. All rights reserved.

13.

14.

15.

16.

Berdahl JP, Allingham RR, Johnson DH. Cerebrospinal fluid pressure is decreased in primary open-angle glaucoma. Ophthalmology. 2008;115(5):763–768. Berdahl JP, Fautsch MP, Stinnett SS, Allingham RR. Intracranial pressure in primary open angle glaucoma, normal tension glaucoma, and ocular hypertension: a case-control study. Invest Ophthalmol Vis Sci. 2008;49(12):5412–5418. Ren R, Jonas JB, Tian G, et al. Cerebrospinal fluid pressure in glaucoma: a prospective study. Ophthalmology. 2010;117(2):259–266. Ren R, Zhang X, Wang N, Li B, Tian G, Jonas JB. Cerebrospinal fluid pressure in ocular hypertension. Acta Ophthalmol. 2011;89(2):e142–8. Hayreh SS. Pathogenesis of optic disc edema in raised intracranial pressure. Prog Retin Eye Res. 2016;50:108–144. Mader TH, Gibson CR, Pass AF, et al. Optic disc edema, globe flattening, choroidal folds, and hyperopic shifts observed in astronauts after long-duration space flight. Ophthalmology. 2011;118(10):2058–2069. Alexander DJ V, Gibson CR V, Hamilton DR, Lee SM, Mader TH, Otto C, et al. Evidence Report: Risk of spaceflight-induced intracranial hypertension and vision alterations. Houston, Texas: National Aeronautics and Space Administration; 2012. Quigley HA. Optic Nerve Damage in Human Glaucoma. Arch Ophthalmol. 1982;100(1):135. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Finite element modeling of optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2004;45(12):4378–4387. Levin LA. Relevance of the site of injury of glaucoma to neuroprotective strategies. Surv Ophthalmol. 2001;45 Suppl 3:S243– 9; discussion S273. Quigley HA. Glaucoma: macrocosm to microcosm the Friedenwald lecture. Invest Ophthalmol Vis Sci. 2005;46(8):2662–2670. Crawford Downs J, Roberts MD, Sigal IA. Glaucomatous cupping of the lamina cribrosa: a review of the evidence for active progressive remodeling as a mechanism. Exp Eye Res. 2011;93(2):133–140. Tehrani S, Davis L, Cepurna WO, et al. Astrocyte structural and molecular response to elevated intraocular pressure occurs rapidly and precedes axonal tubulin rearrangement within the optic nerve head in a rat model. PLoS ONE. 2016;11(11):e0167364. Lim JC, Lu W, Beckel JM, Mitchell CH. Neuronal release of cytokine IL-3 triggered by mechanosensitive autostimulation of the P2X7 receptor Is neuroprotective. Front Cell Neurosci. 2016;10:270. Stowell C, Burgoyne CF, Tamm ER, Ethier CR, Lasker/IRRF Initiative on Astrocytes and Glaucomatous Neurodegeneration Participants. Biomechanical aspects of axonal damage in glaucoma: A brief review. Exp Eye Res. 2017;157:13-19. Choi HJ, Sun D, Jakobs TC. Astrocytes in the optic nerve head express putative mechanosensitive channels. Mol Vis. 2015;21:749–766.

17. Quill B, Docherty NG, Clark AF, O’Brien CJ. The effect of graded cyclic stretching on extracellular matrix-related gene expression profiles in cultured primary human lamina cribrosa cells. Invest Ophthalmol Vis Sci. 2011;52(3):1908–1915. 18. Lu W, Albalawi F, Beckel JM, Lim JC, Laties AM, Mitchell CH. The P2X7 receptor links mechanical strain to cytokine IL-6 upregulation and release in neurons and astrocytes. J Neurochem. 2017;141(3):436-448 19. Rogers RS, Dharsee M, Ackloo S, Sivak JM, Flanagan JG. Proteomics analyses of human optic nerve head astrocytes following biomechanical strain. Mol Cell Proteomics. 2012;11(2):M111.012302. 20. Burgoyne CF, Downs JC, Bellezza AJ, Suh J-KF, Hart RT. The optic nerve head as a biomechanical structure: a new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage. Prog Retin Eye Res. 2005;24(1):39–73. 21. Jonas JB, Berenshtein E, Holbach L. Anatomic relationship between lamina cribrosa, intraocular space, and cerebrospinal fluid space. Invest Ophthalmol Vis Sci. 2003;44(12):5189–5195. 22. Morgan WH, Yu DY, Alder V a., et al. The correlation between cerebrospinal fluid pressure and retrolaminar tissue pressure. Invest Ophthalmol Vis Sci.1998;39(8):1419-28 23. Chapman PH, Cosman ER, Arnold MA. The relationship between ventricular fluid pressure and body position in normal subjects and subjects with shunts: a telemetric study. Neurosurgery. 1990;26(2):181–189. 24. Sigal IA, Flanagan JG, Ethier CR. Factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2005;46(11):4189–4199. 25. Albon J, Farrant S, Akhtar S, et al. Connective tissue structure of the tree shrew optic nerve and associated ageing changes. Invest Ophthalmol Vis Sci. 2007;48(5):2134–2144. 26. Killer HE, Jaggi GP, Miller NR. Optic nerve compartment syndrome. Acta Ophthalmol (Copenh). 2011;89(5):e472–e472. 27. Morgan WH, Yu DY, Balaratnasingam C. The role of cerebrospinal fluid pressure in glaucoma pathophysiology: the dark side of the optic disc. J Glaucoma. 2008;17(5):408–413. 28. Burgoyne CF. A biomechanical paradigm for axonal insult within the optic nerve head in aging and glaucoma. Exp Eye Res. 2011;93(2):120–132. 29. Downs JC, Roberts MD, Burgoyne CF. Mechanical environment of the optic nerve head in glaucoma. Optom Vis Sci. 2008;85(6):425–435. 30. Gloster J. Tonometry and Tonography [Internet]. Boston: Little, Brown & Company; 1965. Available from: https://www.amazon. com/Tonometry-Tonography-John-Gloster/dp/B000JF4H2S 31. Zhong J, Dujovny M, Park HK, Perez E, Perlin AR, Diaz FG. Advances in CSFp monitoring techniques. Neurol Res. 2003;25(4):339–350. 32. Lee SCM, Lueck CJ. Cerebrospinal fluid pressure in adults. J Neuroophthalmol. 2014;34(3):278–283. 33. Fleischman D, Bicket AK, Stinnett SS, et al. Analysis of cerebrospinal fluid pressure estimation using formulae derived from clinical data. Invest Ophthalmol Vis Sci. 2016;57(13):5625–5630.

Copyright © 2018. Kugler Publications. All rights reserved.

Cerebrospinal fluid pressure and the translaminar pressure gradient in optic nerve head biomechanics 34. Kast R. A new method for noninvasive measurement of shortterm cerebrospinal fluid pressure changes in humans. J Neurol. 1985;232(4):260–261. 35. Williams MA, Malm J, Eklund A, Horton NJ, Voss SE. Distortion product otoacoustic emissions and intracranial pressure during CSF infusion testing. Aerospace medicine and human performance. 2016;87(10):844–851. 36. Koskinen L-OD, Malm J, Zakelis R, Bartusis L, Ragauskas A, Eklund A. Can intracranial pressure be measured non-invasively bedside using a two-depth Doppler-technique? J Clin Monit Comput. 2017;31(2):459–467. 37. Dubourg J, Javouhey E, Geeraerts T, Messerer M, Kassai B. Ultrasonography of optic nerve sheath diameter for detection of raised intracranial pressure: a systematic review and meta-analysis. Intensive Care Med. 2011;37(7):1059–1068. 38. Levine DN. Spontaneous pulsation of the retinal veins. Microvasc Res. 1998;56(3):154–165. 39. Jacks AS, Miller NR. Spontaneous retinal venous pulsation: aetiology and significance. J Neurol Neurosurg Psychiatr. 2003;74(1):7–9. 40. Golzan SM, Kim MO, Seddighi AS, Avolio A, Graham SL. Non-invasive estimation of cerebrospinal fluid pressure waveforms by means of retinal venous pulsatility and central aortic blood pressure. Ann Biomed Eng. 2012;40(9):1940–1948. 41. Stockslager MA, Samuels BC, Allingham RR, et al. System for rapid, precise modulation of intraocular pressure, toward minimally-invasive in vivo measurement of intracranial pressure. PLoS ONE. 2016;11(1):e0147020. 42. Morgan WH. Pressure gradients across the optic disk. PhD Thesis, University of Western Australia. 1999. 43. Raboel PH, Bartek J, Andresen M, Bellander BM, Romner B. Intracranial pressure monitoring: invasive versus non-invasive methods-A review. Crit Care Res Pract. 2012;2012:950393. 44. Kristiansson H, Nissborg E, Bartek J, Andresen M, Reinstrup P, Romner B. Measuring elevated intracranial pressure through noninvasive methods: a review of the literature. J Neurosurg Anesthesiol. 2013;25(4):372–385. 45. Robba C, Bacigaluppi S, Cardim D, Donnelly J, Bertuccio A, Czosnyka M. Non-invasive assessment of intracranial pressure. Acta Neurol Scand. 2016;134(1):4–21. 46. De Moraes CGV, Prata TS, Liebmann J, Ritch R. Modalities of tonometry and their accuracy with respect to corneal thickness and irregularities. J Optom. 2008;1(2):43–49. 47. Yablonski ME, Krupin T, Becker B. Decreased intracranial pressure and optic disc cupping in the cat. Paper presented at ARVO Annual Meeting. Invest Ophthalmol Vis Sci. 1978 April 30 – May 5. Sarasota, FL. Abstract number 6. 48. Yablonski ME, Ritch R, Pokorny KS. Effect of decreased intracranial pressure on optic disc. Paper presented at ARVO Annual Meeting. Invest Ophthalmol Vis Sci. 1979 April 30 – May 4. Sarasota, FL. Abstract number 8. 49. Berdahl JP, Ethier CR, Allingham RR. Cerebrospinal fluid pressure and glaucomatous optic disc cupping. Graefes Arch Clin Exp Ophthalmol. 2009;247(9):1289–90; author reply 1291.

477

50. Chen BH, Drucker MD, Louis KM, Richards DW. Progression of normal-tension glaucoma after ventriculoperitoneal shunt to decrease cerebrospinal fluid pressure. J Glaucoma. 2016;25(1):e50–2. 51. Wall M, George D. Idiopathic intracranial hypertension. A prospective study of 50 patients. Brain. 1991;114(Pt 1A):155–180. 52. Wall M. Idiopathic intracranial hypertension. Neurol Clin. 2010;28(3):593–617. 53. Keltner JL, Johnson CA, Cello KE, Wall M, NORDIC Idiopathic Intracranial Hypertension Study Group. Baseline visual field findings in the Idiopathic Intracranial Hypertension Treatment Trial (IIHTT). Invest Ophthalmol Vis Sci. 2014;55(5):3200–3207. 54. Brodsky MC, Vaphiades M. Magnetic resonance imaging in pseudotumor cerebri. Ophthalmology. 1998;105(9):1686–1693. 55. Williams D, Kuipers A, Mukai C, Thirsk R. Acclimation during space flight: effects on human physiology. CMAJ. 2009;180(13):1317–1323. 56. Williams DR. The biomedical challenges of space flight. Annu Rev Med. 2003;54:245–256. 57. Hawkey A. The physical price of a ticket into space. J Br Interplanet Soc. 2003;56(5-6):152–159. 58. Montgomery LD. Body volume changes during simulated weightlessness: an overview. Aviat Space Environ Med. 1987;58(9 Pt 2):A80–5. 59. Moore TP, Thornton WE. Space shuttle inflight and postflight fluid shifts measured by leg volume changes. Aviat Space Environ Med. 1987;58(9 Pt 2):A91–6. 60. Frisén L. Swelling of the optic nerve head: a staging scheme. J Neurol Neurosurg Psychiatr. 1982;45(1):13–18. 61. Echegaray S, Zamora G, Yu H, Luo W, Soliz P, Kardon R. Automated analysis of optic nerve images for detection and staging of papilledema. Invest Ophthalmol Vis Sci. 2011;52(10):7470–7478. 62. Scott CJ, Kardon RH, Lee AG, Frisén L, Wall M. Diagnosis and grading of papilledema in patients with raised intracranial pressure using optical coherence tomography vs clinical expert assessment using a clinical staging scale. Arch Ophthalmol. 2010;128(6):705–711. 63. Maralani PJ, Hassanlou M, Torres C, et al. Accuracy of brain imaging in the diagnosis of idiopathic intracranial hypertension. Clin Radiol. 2012;67(7):656–663. 64. Yang D, Fu J, Hou R, et al. Optic neuropathy induced by experimentally reduced cerebrospinal fluid pressure in monkeys. Invest Ophthalmol Vis Sci. 2014;55(5):3067–3073. 65. Zhang Z, Liu D, Jonas JB, et al. Axonal transport in the rat optic nerve following short-term reduction in cerebrospinal fluid pressure or elevation in intraocular pressure. Invest Ophthalmol Vis Sci. 2015;56(8):4257–4266. 66. Nusbaum DM, Wu SM, Frankfort BJ. Elevated intracranial pressure causes optic nerve and retinal ganglion cell degeneration in mice. Exp Eye Res. 2015;136:38–44. 67. Morgan WH, Chauhan BC, Yu D-Y, Cringle SJ, Alder VA, House PH. Optic disc movement with variations in intraocular and cerebrospinal fluid pressure | IOVS | ARVO Journals. Invest Ophthalmol Vis Sci [Internet]. 2002 Oct 1; Available from: http:// iovs.arvojournals.org/article.aspx?articleid=2122964

478

Copyright © 2018. Kugler Publications. All rights reserved.

68. Tran H, Grimm J, Wang B, Smith MA, et al. Mapping in-vivo optic nerve head strains caused by intraocular and intracranial pressures. In: Larin KV, Sampson DD, editors. Optical Elastography and Tissue Biomechanics IV. SPIE; 2017. p. 100670B. 69. AJ. Feola, B Coudrillier, J Mulvihill, et al. Deformation of the lamina cribrosa and optic nerve due to changes in cerebrospinal fluid pressure. Invest Ophthalmol Vis Sci. 2017;58(4):20702078. 70. Midgett DE, Pease ME, Jefferys JL, et al. The pressure-induced deformation response of the human lamina cribrosa: analysis of regional variations. Acta Biomater. 2017;53:123-139. 71. Coudrillier B, Geraldes D, Vo N, et al. Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa. IEEE Trans Med Imaging. 2015 Nov 30. doi: 10.1109/ TMI.2015.2504440. 72. Ivers KM, Yang H, Gardiner SK, et al. In vivo detection of laminar and peripapillary scleral hypercompliance in early monkey experimental glaucoma. Invest Ophthalmol Vis Sci. 2016;57(9):OCT388–403. 73. Bellezza AJ, Hart RT, Burgoyne CF. The optic nerve head as a biomechanical structure: initial finite element modeling. Invest Ophthalmol Vis Sci. 2000;41(10):2991–3000. 74. Sigal IA, Bilonick RA, Kagemann L, et al. The optic nerve head as a robust biomechanical system. Invest Ophthalmol Vis Sci. 2012;53(6):2658–2667. 75. Voorhees AP, Grimm JL, Bilonick RA, et al. What is a typical optic nerve head? Exp Eye Res. 2016;149:40–47. 76. Grytz R, Meschke G, Jonas JB. The collagen fibril architecture in the lamina cribrosa and peripapillary sclera predicted by a computational remodeling approach. Biomech Model Mechanobiol. 2011;10(3):371–382. 77. Feola AJ, Myers JG, Raykin J, et al. Finite element modeling of factors influencing optic nerve head deformation due to intracranial pressure. Invest Ophthalmol Vis Sci. 2016;57(4):1901– 1911. 78. Hua Y, Tong J, Ghate D, Kedar S, Gu L. Intracranial pressure influences the behavior of optic nerve head. J Biomech Eng. 2016;139(3). 79. Dongqi H, Zeqin R. A biomathematical model for pressure-dependent lamina cribrosa behavior. J Biomech. 1999;32(6):579– 584.

J. Raykin et al. 80. Newson T, El-Sheikh A. Mathematical modeling of the biomechanics of the lamina cribrosa under elevated intraocular pressures. J Biomech Eng. 2006;128(4):496–504. 81. Causin P, Guidoboni G, Harris A, Prada D, Sacco R, Terragni S. A poroelastic model for the perfusion of the lamina cribrosa in the optic nerve head. Math Biosci. 2014;257:33–41. 82. Rhodes LA, Huisingh C, Johnstone J, et al. Peripapillary choroidal thickness variation with age and race in normal eyes. Invest Ophthalmol Vis Sci. 2015;56(3):1872–1879. 83. Ayyalasomayajula A, Park RI, Simon BR, Vande Geest JP. A porohyperelastic finite element model of the eye: the influence of stiffness and permeability on intraocular pressure and optic nerve head biomechanics. Comput Methods Biomech Biomed Engin. 2016;19(6):591–602. 84. Eilaghi A, Flanagan JG, Simmons CA, Ethier CR. Effects of scleral stiffness properties on optic nerve head biomechanics. Ann Biomed Eng. 2010;38(4):1586–1592. 85. Fazio MA, Grytz R, Bruno L, et al. Regional variations in mechanical strain in the posterior human sclera. Invest Ophthalmol Vis Sci. 2012;53(9):5326–5333. 86. Wang X, Beotra MR, Tun TA, et al. In vivo 3-dimensional strain mapping confirms large optic nerve head deformations following horizontal eye movements. Invest Ophthalmol Vis Sci. 2016;57(13):5825–5833. 87. Raykin J, Forte TE, Wang R, et al. Characterization of the mechanical behavior of the optic nerve sheath and its role in spaceflight-induced ophthalmic changes. Biomech Model Mechanobiol. 2017;16(1):33-43. 88. Demer JL. Optic nerve sheath as a novel mechanical load on the globe in ocular duction. Invest Ophthalmol Vis Sci. 2016;57(4):1826–1838. 89. Wang R, Raykin J, Gleason RL, Ethier CR. Residual deformations in ocular tissues. J R Soc Interface. 2015;12(105). 90. Sibony PA, Kupersmith MJ, Feldon SE, Wang J-K, Garvin M, OCT Substudy Group for the NORDIC Idiopathic Intracranial Hypertension Treatment Trial. Retinal and choroidal folds in papilledema. Invest Ophthalmol Vis Sci. 2015;56(10):5670–5680.

32. Parametric analysis to identify biomechanical risk factors: taking control of population diversity and experiment variability Andrew P. Voorhees1, Yi Hua1, Ian A. Sigal1,2 Department of Ophthalmology, University of Pittsburgh, Pittsburgh, PA, USA; 2Department of Bioengineering, University of Pittsburgh, Pittsburgh, PA, USA

1

Introduction

Copyright © 2018. Kugler Publications. All rights reserved.

In this chapter we will discuss the use of parametric modeling, with a particular focus on optic nerve head (ONH) biomechanics. We will begin with a brief introduction to parametric modeling and its utility for ocular biomechanics in general. We will then review parametric modeling studies of the ONH and conclude with a discussion on current knowledge gaps and potential future directions. 1.1. What is parameterization? Simply put, parameterization is the act of describing a complex system with a set of characteristics, the parameters. As humans, we parameterize the world around us every day to help us recognize patterns. We parameterize light into red, blue, and green. We parameterize sound by its pitch, volume, and timbre. In medicine, we describe a person by their height, weight, gender, and age, and we even use these factors to determine their risk for disease. Given the vastness of human diversity, there is no manageable set of factors that can completely describe a single person. The goal, instead, is to identify the set of parameters that are most useful in describing a person and their risk for developing a particular disease. While a model helps us understand the response of a system to a given set of inputs, parametric modeling allows us to vary those inputs and draw broader

conclusions on the relationship between the inputs and the system response. This is well exemplified by Laplace’s Law, one of the simplest parametric models in ocular biomechanics: Intraocular  Pressure · Globe Radius

      ​​    ​ cleral Tension​ = ​​  _________________________ S ​(2 · Wall Thickness)​ (1) Immediately, we can understand that the scleral tension will be higher in eyes with a large radius or a thin wall. Deriving this relationship requires making assumptions about the eye, including that it is a thin-walled sphere with constant radius and thickness, and uniform material properties. Of course, the eye is not this simple, yet predictions from Laplace’s law are still useful in many situations.1 Laplace’s law is useful because it allows us to understand how the stress on the sclera depends in part on three simple parameters. 1.2. Why do we need parametric models? In ocular biomechanics, we face tremendous variability and uncertainty. There is inter-individual variation in the anatomy and material properties of the tissues. The dimensions and mechanical properties vary from person to person, with age and disease, and obtaining precise measurements of those properties is challenging. No experimental techniques are free from error and uncertainty. Even if there were a feasible method for determining, without uncertainty, the

Correspondence: Ian A. Sigal, PhD, Ocular Biomechanics Laboratory, Department of Ophthalmology, University of Pittsburgh School of Medicine, 203 Lothrop Street, Rm 930, Pittsburgh, PA 15213, USA. E-mail: [email protected] Biomechanics of the Eye, pp. 479-495 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

480

Copyright © 2018. Kugler Publications. All rights reserved.

geometry and material properties, these parameters are dynamic, changing with temperature, hydration, age, and disease.2-6 Parametric modeling allows us to incorporate this variability and uncertainty into the models, so that we can understand their effects and reach more general and robust conclusions. Parametric modeling is therefore an indispensable technique in ocular biomechanics. A common misconception in modeling is that building a model with average parameters will produce an average biomechanical response. It turns out that this is not the case. Parametric studies have shown that models built from population averages can have atypical responses.7,8 While patient-specific or specimen-specific modeling avoids this ‘average model trap’ to some extent, the problem remains, since it is not clear how to extend findings from a set of specimen-specific models to a wide population. Further, specimen-specific models are typically specific on only some characteristics, and risk falling into the ‘average model trap’ for the rest. 1.3. What can we learn from parametric models? The power of parametric modeling to help understand the effects of variability and uncertainty can be leveraged for many uses. Parametric modeling is the basis for sensitivity analyses, which can be used to identify the factors that most influence the biomechanical response of the eye. Knowing which factors are important allows us to direct our research towards areas with the highest potential impact. An example of this is the focus of research on scleral stiffness. Several parametric modeling studies have shown that the stiffness of the sclera is the most important biomechanical determinant of intraocular pressure (IOP)-induced deformation in the lamina ­cribrosa.9-12 While these initial studies all assumed simple isotropic and linear material properties, the findings encouraged researchers to obtain refined, non-linear and anisotropic measurements of scleral stiffness.13-15 Parametric models employing these detailed measurements are now being used to further dissect the effects of scleral stiffness on lamina deformation,16,17 following the classic iterative approach of model > experiment > model again > experiment again. Parametric modeling is useful to identify potential biomarkers for disease susceptibility, provide insight

A.P. Voorhees, Y. Hua and I.A. Sigal

into the mechanisms of disease, and inform treatment strategies. Based on the aforementioned findings on the influence of scleral stiffness, work has gone towards establishing scleral stiffness as a clinical indicator of glaucoma susceptibility. Several studies have experimentally measured scleral stiffness across different age and racial groups,3-5,18 and increased scleral stiffness has been found in both the elderly and people of African descent, groups known to be at higher risk for developing glaucoma than those that are younger or are of European descent. Research has also been started to test scleral stiffening as potential treatment for glaucoma.19,20 Parametric modeling can also be used to simplify the analysis of the complex biomechanical structure of the eye with many potentially interacting input factors. Parametric models that consider the interaction between the input parameters help us understand how different components and features of the eye act together to determine the stability and robustness of the eye. An example is the relationship between scleral stiffness and scleral thickness, both of which contribute to the structural stiffness of the scleral shell. The interest in understanding eye biomechanics with high detail has brought about an increasing complexity of constitutive models and mechanical testing configurations. This, in turn, has also increased the need for parametric modeling to aid in experimental studies. Inverse finite element modeling allows for the determination of material properties from experimental measurements of deformation and force. Iteratively solving models for different combinations of material properties and comparing the results to the experimental measurements can identify the best fitting properties.13-15,21

2. Parametric models of the posterior segment Mechanical models are traditionally divided into two groups: analytical models, which have closed-form solutions, and numerical models, for which solutions are obtained through computational means. Analytical models are the simplest models and are parametric by definition. In mechanics, they are frequently used to relate basic geometric parameters,

Parametric Modeling

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 1. An example of a generic parameterized optic nerve head. Adapted from Voorhees et al.17 2016. Reprinted with permission from Elsevier.

such as radius of curvature and thickness, and material properties, such as Young’s modulus, to the stresses and strains engendered by loading. Laplace’s law in Equation (1) is a simple analytical model of the eye. A major challenge of modeling is to capture all of the important biomechanical features of the eye while still being solvable. This is difficult for analytical models, which must have a closed-form solution, and hence, are limited in complexity. Numerical models, while still simplified, can consider more complex geometries and material properties than analytical models. Hence, the vast majority of ocular biomechanics models created over the last two decades have been numerical models. Numerical models can be further subdivided into two classes, generic models and specimen-specific models. Generic models are based on parametric idealizations of the eye. The concept is similar to the way in which Laplace’s law idealizes the eye as a sphere with a given radius and thickness that can be varied. Typically, numerical models use many more parameters than analytical models to describe the geometry. An example of a generic ONH geometry we have used in our parametric modeling studies is shown in Figure 1. Specimen-specific models are intended to represent a specific eye or ONH, and are not necessarily parametric. Thus, specimen-specific models are usually regarded as being less idealized than generic models or analytical models. In actuality, the specimen-specif-

481

ic modeling process still requires many assumptions and approximations about the geometry and material properties of the eye. Similar to both analytical and generic models, one of the major challenges in specimen-specific modeling is to ensure that these simplifications do not brush over the key biomechanical details. The limited availability of experimental data also dictates that many models are only partially specimen-specific. For example, researchers may choose to build models with specimen-specific geometries and generic material properties or build models with specimen-specific material properties and generic geometries. Since both the geometry and material properties are important, models that neglect one to focus on the other need to be interpreted carefully. Parametric analysis of specimens-specific models can be utilized to help understand the implications associated with the assumptions and the limits of the models. Beyond its use for interpreting the effects of model assumptions, parametric analysis has another important use in interpreting the results of specimen-specific models. The lack of parameters in specimen-specific models can make it difficult to compare one model to another and draw conclusions that can be extended to a larger population. The parameterization of specimen-specific models after they have been created and solved allows for these comparisons to be made in a rigorous manner. As an example, for a set of specimen-specific models of the ONH, the cup-to-disk ratio in each model could be measured and a statistical analysis could be conducted to determine if the ratio was significantly correlated with increased deformation in the lamina. While specimen-specific models are often thought of as an alternative to parametric modeling, we assert that they are most useful when used in conjunction with parametric modeling and analysis. Below we provide an overview of parametric analytical and numerical biomechanical modeling studies of the posterior pole following a format similar to our previous review.22 2.1. Analytical models The earliest models of the eye were analytical models, since the solutions are elegant and can be calculated without the need for computers. As discussed above, Laplace’s law is the most widely used analytical model

482

A.P. Voorhees, Y. Hua and I.A. Sigal

of the eye, and a thorough discussion of its use and misuse can be found in a recent review from Chung et al.1 Laplace’s law, can be generalized to ellipsoidal models using the following formulation: T1 T2 _ ​​   ​ + _  ​R  ​ = P​ (2) R 1 2

Here, R1 and T1 are the radii of curvature of an arbitrary hoop of an ellipsoidal shell and the tension in the direction perpendicular to that hoop, while R2 and T2 are the radius of curvature and tension orthogonal to R1 and T1, respectively. Readers interested in closed-form solutions for the stresses at an arbitrary point in a thin-walled ellipsoid may be interested in the work of Krauss23 and Regen.24,25 One of the foundations of ocular biomechanics is the concept ocular rigidity introduced by Friedenwald:26 log​ P ​ ‒ log​ P ​

( 2) ( 1) ​K =  ​__________   ​​ (3)   V  ‒ V  

Copyright © 2018. Kugler Publications. All rights reserved.

2

1

Here, K is the ocular rigidity, a measure of the resistance of the eye to an increase in volume. P1 and V1 are the initial pressure and volume of the eye, while P2 and V2 are the pressure and volume after the addition of a small amount of fluid. Simply put, the Friedenwald equation is an elegant non-linear relationship between IOP and the fluid volume in the eye. Although ocular rigidity is a simple measure of the lumped stiffness of the entire eye, it has been foundational in the creation of analytical models to study the relationship between ocular deformation and tonometry. Early versions of these models were developed by Friedenwald himself.26 In 1965 McEwen and St. Helen extended the work of Friedenwald, developing an analytical solution for the stress and strain in the eye based on infinitesimal strain theory.27 Greene incorporated an exponential stiffness into his relationship between stress, strain, volume, and pressure.28 While the models discussed above represent the deformation of the globe as a whole, they may not be useful for specific regions, such as the ONH. Hence, several groups have worked to develop analytical models specific to the lamina cribrosa. Dongqi and Zeqin in 199929 and Edwards and Good in 200130 both developed analytical models of the lamina. Both groups used the Kármán equation, which describes the bending of a thin plate as the basis of their model.

Fig. 2. An analytical model of the lamina cribrosa proposed by Sander et al.31 (a) Lamina pores were modeled as octagonal unit cells. (b) Macroscale stress was applied to the unit cell; (c) stress in the lamina cribrosa beams and deformation of the pores was determined. (d) The unit cell strains were found to be larger for more elliptical canals (solid lines) as compared to circular canals (dashed lines). Strains were also dependent on the ratio of the scleral stiffness to the lamina beam stiffness and the porosity of the lamina. Adapted from Sander et al.31 Reprinted with permission from ASME.

These models demonstrated that increasing lamina thickness reduced the deformation of the lamina through increased structural rigidity, and that an increase in the radius of the lamina increased the deformation of the lamina. Sander et al. developed a porous model of the lamina (Fig. 2).31 In this model, they parameterized the ratio of connective tissue to neural tissue. The model allowed them to examine the stresses and strains at both the microstructure level and the macroscale level. They reported the results for individual parametric variations in lamina cribrosa thickness, scleral thickness, lamina cribrosa porosity, and scleral canal eccentricity. In a sensitivity analysis, they varied each individual parameter by 10%, finding that scleral stiffness and thickness were the two largest

Parametric Modeling

483

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 3. Parametric sensitivity analysis of ONH geometric and material properties. (Left) The sensitivity of 29 output parameters to 21 input parameters was calculated through independent parametric variation. The area of a particular color denotes its relative influence on a particular outcome. (Right) The total influence across all 29 outcome measures is shown. Total influence was calculated using a wide input factor range (Full), a halved range and a small range with little variation (Minimal). Scleral modulus was the most influential factor on ONH mechanics.12 Reprinted with permission from the Association for Research in Vision and Ophthalmology.

determinants of both macroscopic and microscopic stress within the lamina. Analytical models have also been used to study the mechanics of retinal detatchment.32,33 Bottega et al. created an energy-based quasi-static model of retinal delamination for retinas with and without tears.33 Their model predicted that a tear in the retina could impede detachment progression by lowering the structural stiffness of the retina. They studied how variations in the mechanical properties and geometry of the eye affected the rate of delamination, and found that increasing the vitreous stiffness, or the stiffness of the vitreous fibrils at the vitreous-retinal interface, does not necessarily slow retinal detachment. 2.2. Generic numerical models Generic numerical models are typically developed from idealized, population-based dimensions and material

properties, making it possible to produce models with different magnitudes for particular parameters of interest. For example, it is possible to produce two models that are identical except for the thickness of the sclera. While this approach of varying one parameter at a time allows the effects of that parameter to be isolated, it can also be misleading as it neglects the potential interactions between parameters. More comprehensive parametric analyses can be done in which multiple parameters are varied simultaneously, allowing for the consideration of factor interactions. In this section, we will examine the development and use of parametric analysis for generic numerical models of the posterior pole. An example of early generic numerical modeling is the work of Bellezza and coworkers, who studied the effects of the scleral canal size and shape as well as scleral thickness on the biomechanical response of the

Copyright © 2018. Kugler Publications. All rights reserved.

484

ONH.34 They found that, for a given level of IOP, a thinner sclera with a larger and more elliptical canal induced higher stresses within the load-bearing connective tissues of the ONH. Expanding on this early work, we developed a more realistic generic model that incorporated pre- and post-laminar neural tissues, as well as the central retinal vessel and the pia mater.35 Based on a simple parametric analysis, we concluded that mean laminar strain was more sensitive to scleral compliance than to laminar compliance, and was only weakly dependent on the compliance of the neural tissues and pia mater. Our model also predicted that the properties of the central retinal vessel had little effect on the biomechanics of the ONH. To determine which anatomic and biomechanical factors most influenced the biomechanical response of the ONH to acute changes in IOP, we parameterized the generic model into 21 factors representing ONH tissue anatomy and material properties.12 The biomechanical response of the ONH tissues was quantified through a set of 29 outcome measures, including peak and mean stress and strain within each tissue, and measures of geometric changes in ONH tissues, such as the cup-to-disc ratio (Fig. 3). We identified the five most important determinants of ONH biomechanics (in rank order) as: the compliance of the sclera, the size of the eye, IOP, the compliance of the lamina cribrosa, and the thickness of the sclera. This study was the first to highlight the importance of scleral stiffness on ONH stress and deformation using computational methods. This study, however, was performed with the simple, but limited, method of varying one parameter at a time. We then extended this work by varying the geometric and material parameters simultaneously.10 By varying multiple parameters at once in a systematic way, it was possible to determine the strength of the interactions between the parameters, that is, how one parameter influences another. This inter-relationship between factor influences is a fundamental concept in sensitivity analysis. When factors interact, it may be misleading to interpret the effects on a factor independently, as this effect depends on the other factor. An example is represented by the concept of structural, or effective, stiffness, where the mechanical response of the sclera depends on both its thickness and its material properties (Fig. 4). Independently increasing either the stiffness or thickness of the sclera leads to reduced

A.P. Voorhees, Y. Hua and I.A. Sigal

Fig. 4. The effect on prelaminar neural tissue strains of interactions between scleral stiffness and scleral thickness. Increased scleral compliance increased neural tissue strain, while increasing scleral thickness reduced this strain. The reduction in strain due to increased thickness was smaller when the sclera was stiff. Adapted from Sigal.10 Reprinted with permission from the Association for Research in Vision and Ophthalmology.

deformations being transmitted to the ONH. However, if the sclera is quite stiff, then changing its thickness has relatively little effect on ONH biomechanics and vice versa. In this way, we can see that individual eyes can have parameter sensitivities that can vary greatly from the global sensitivity of the population, i.e., an individual with a thick sclera will be much less sensitive to a change in scleral stiffness than the average individual. There are many geometric and material factors, as well as various biomechanical responses, to consider when studying ocular biomechanics. This presents many challenges. The most natural is that it may require a tremendous number of models. However, just as problematic is that it can be difficult to track and report the influences of many factors, including their interactions, in many responses. A solution is to take advantage of the fact that many responses are correlated with each other. This allows the use of dimensionality reduction techniques, i.e., principal component analysis, used to identify a subset of responses that capture all the key effects. We demonstrated this in a study in which we tested 4,646 generic models of the ONH representing a wide range of tissue anatomy and mechanical properties.36 The effects of IOP were quantified through a set of 25 responses including stress, strain, and geometric deformation of the lamina

Copyright © 2018. Kugler Publications. All rights reserved.

Parametric Modeling

485

Fig. 5. The ‘average model trap’: typical ONHs do not necessarily have typical biomechanical responses. (Left) ONHs with at least one atypical characteristic tend to have lamina cribrosa displacements (x-axis) and scleral canal expansions (y-axis) near the center of the distribution of responses. Responses are colored by the number of atypical ONH characteristics (1-5); the black outline represents the smallest area containing 95% of all responses. (Right) ONHs with all typical characteristics frequently have atypical responses. Occasionally, the responses can be highly atypical, as indicated in the figure. ONHs with typical responses have been masked. Adapted from Voorhees et al.7 Reprinted with permission from Elsevier.

Fig. 6. A generic model of the posterior globe with varying scleral fiber alignment. Circumferentially oriented scleral collagen reduced canal expansion, but increased globe elongation and lamina cribrosa cupping. A meridional arrangement of collagen increased canal expansion, but limited globe elongation.15 Reprinted with permission from ASME.

cribrosa and peripapillary sclera. We found that four independent principal components were responsible for 96% of the response variance. Another approach to deal with the complexity of multiple interacting factors affecting many responses is to use an interactive applet. In a separate study we produced an applet based on a large population of generic models that combines the ease-of-use and speed of analytical models with the flexibility and power of finite element models.37 The applet utilized a response surface methodology in which the responses of a large population of parametric models were captured with high-order multivariable polynomial function. This allowed for responses to be calculated rapidly for any combination of geometric or material properties, not just the cases explicitly solved using finite element analysis. The applet was simple enough for use by basic researchers and clinicians to gain a preliminary understanding of how anatomy and tissue stiffness affect biomechanics. The use of applets that capture the essential aspects of a biomechanical system, while at the same time being easy to use, is a powerful application of parametric methods. As an extension, we also developed another applet that allows for rapid estimates of ONH biomechanics and tissue properties based solely on parameters measurable in vivo using optical coherence tomography.38 It is widely believed that models with popula-

tion-averaged anatomies and material properties will lead to biomechanical outcomes typical of the entire population. Following this assumption, the factors in ONH models have been traditionally determined by the median values within the range of reported experimental measurements. In complex non-linear models with factor interactions, such as the eye, this assumption is often not true.39 This is what we had described above as the ‘average model trap’. We explored this issue using parametric modeling of 100,000 generic models of the ONH.7 We classified the characteristics and responses of the models as typical or atypical using a percentile-based threshold. We found that most ONHs with atypical characteristics actually had completely typical responses (Fig. 5). Further, many ONHs with completely typical characteristics had atypical responses. We found this to be the case even in a highly simplified linear isotropic model. This work highlights the importance of population-based parametric modeling in understanding complex biomechanical systems, and suggests that identifying risk based on the proximity to the population median may not be a sound strategy. Several groups have used parametric modeling approaches to study the posterior pole. Girard et al. developed a generic model to investigate the effects of scleral collagen fiber alignment on scleral and ONH mechanics.14,15 The influence of the fiber concentra-

Copyright © 2018. Kugler Publications. All rights reserved.

486

tion factor, a parameter used to control collagen fiber alignment along a preferred fiber orientation, was also evaluated. Results showed that a circumferential fiber organization in the sclera reduced scleral canal expansion, whereas the opposite was observed with a meridional fiber organization (Fig. 6). Perez et al. developed a generic model of the corneoscleral shell to simulate the viscoelastic responses of the eye during micro-volumetric changes.40 The viscoelastic properties of the cornea and the sclera, including the instantaneous modulus, equilibrium modulus, and relaxation time constants were parameterized to examine their effects on IOP elevations at different rates of volumetric change. Results showed that all viscoelastic properties influenced the profile of the dynamic IOP due to volumetric changes, and the relative significance of a specific parameter was highly dependent on the rate of change. From this, they concluded that it is necessary to better characterize the viscoelastic properties of ocular tissues. Recently, efforts have focused on understanding not just the role of IOP, but also other fluid pressures, particularly intracranial pressure (ICP), on the ONH. Feola et al. created a generic model of the ONH to simulate how elevated ICP and inter-individual differences affect tissue deformations within the ONH.41-43 Latin hypercube sampling was used to parameterize a range of pressures and ONH tissue mechanical properties. Results showed that IOP, ICP, and optic nerve and lamina cribrosa moduli had the strongest influence on the strains within the ONH. However, variations in ONH anatomy were not considered in this work. In another study by Hua et al., both geometry and mechanical properties of the ONH were parameterized based on an orthogonal experimental design.42 It was found that the sensitivity of ONH responses to various factors was region-specific. In the lamina, the strain was most strongly dependent on the scleral thickness, lamina modulus, and scleral canal size, whereas in the post-laminar neural tissue, the strain was more sensitive to the scleral canal size, neural tissue modulus, and pia mater modulus (Fig. 7). Ayyalasomayajula et al. developed a porohyperelastic model of the ONH to discern the effects of interstitial and intracellular fluid pressure on the biomechanical response to IOP.44 A generic model of the human eye was constructed and the fluid permeabilities of the retina-Bruch’s-choroid complex, sclera, uveoscleral

A.P. Voorhees, Y. Hua and I.A. Sigal

Fig. 7. Effects of intracranial pressure (ICP). (A) The model of Feola et al. shows that stretch and compression in the ONH depend on intracranial pressure. (B) The model of Hua et al. predicts that increased ICP increases the displacement of the posterior pia, but has little influence on the displacement of the pia near the sclera. Adapted from Feola et al.41 and Hua et al.42 Reprinted with permission from the Association for Research in Vision and Ophthalmology and ASME, respectively.

pathway, and trabecular meshwork were parameterized. IOP, translaminar pressure gradient, and strains in the lamina were considered as computational outputs. As tissue permeability increased, both IOP and translaminar pressure gradient decreased, resulting in decreased strains in the lamina. Parametric modeling approaches have also been used to study the effects of ocular trauma on the posterior pole. Gray and colleagues created a finite volume model to study the effects of paintball impacts that identified several injury modes including globe rupture, optic nerve avulsion, lens displacement, and retinal detachment.45 Through parametric analysis they determined that impact speed was the primary determinant of globe rupture and that impact location was the primary determinant of optic nerve severing. Surprisingly, they found no major differences due to variations in paintball properties.

Parametric Modeling

Given the fact that blunt eye trauma typically occurs with projectiles traveling at high speeds, it is necessary to incorporate viscoelastic material properties into models of the eye and surrounding fatty tissues. In a 2011 study, Rossi and colleagues developed a model for BB impact (a small spherical projectile typically fired by an air pistol or rifle) impact that included viscoelastic material properties for the vitreous and aqueous.46 They followed up this work with a model for TNT blast injury that also included the effects of viscoelastic orbital fats.47 Through parametric analysis they were able to study the effects of blast magnitude and incident angle on tissue pressures, strain rates, and retina and ONH insult. Variations in blast wave angle were found to have strong effects on eye pressures.

Copyright © 2018. Kugler Publications. All rights reserved.

2.3. Specimen-specific models Specimen-specific models can be based on the geometry and anatomy of an individual eye, the material properties of an individual eye, or both. Models built from specimen-specific geometries are intended to capture the intricate features of a specimen. Generic models, by nature, often miss these details. In this section, we will discuss three key parametric modeling techniques for the analysis of specimen-specific models: 1. factor influence and sensitivity analysis to test the effects of model properties and assumptions; 2. inverse modeling for determining material properties; and 3. the use of post-hoc parametric analysis techniques to investigate model-to-model population variability. 2.3.1. Factor influence analysis We have developed several models of human posterior poles with specimen-specific geometries to explore the complex deformations of the ONH due to elevated IOP.9,11,48-50 In a 2009 study, we created a set of ten models with specimen-specific geometries.11,49 The material properties used in these models were not specimen-specific, thus we conducted a parametric sensitivity analysis to determine the relative influence of tissue stiffness on our results.11 The material properties of seven tissues in the model were varied independently to determine the relative influence of the parameter on the strains in the lamina cribrosa. The

487

sensitivity analysis revealed that scleral stiffness was the most important material parameter in determining the biomechanical insult to the lamina, matching the findings from generic models. We also found only minor differences between individual eyes, suggesting that geometry had only modest effects on the strains within the ONH, with the caveat that the demographic variability within this dataset was rather low. Eight of the ten eyes were paired sets, all donors were male, and all donors were from a similar age group, 70 years or older.49 In comparing the results of our eye-specific models to our generic models, we found that both generic models and specimen-specific models predicted similar levels of strain. The asymmetry of the specimen-specific models did allow for asymmetric deformations and displacements that were not predicted by the generic models. In a 2010 study, Roberts et al. created specimen-specific models from a set of monkey eyes in which one eye from each animal had undergone photocoagulation of the trabecular meshwork to generate elevated IOP and an early glaucoma phenotype.51 Their models were hybrid, with a specimen-specific lamina cribrosa embedded in a realistic, but not specimen-specific, scleral shell. To better understand the potential role of glaucomatous remodeling, they varied the stiffness of the lamina in their models. They found that increased stiffness of the lamina resulted in a lamina that bulged anteriorly rather than posteriorly under increased IOP. The anterior bulging phenomenon was more pronounced in the early glaucoma eyes for two of the three pairs included. In another 2010 study, Roberts et al. used a similar monkey specimen-specific approach to correlate local laminar connective tissue volume fraction to local stress and strain in the lamina.52 They found that, generally, the areas of low connective tissue density experienced greater strains and lower stresses, and conversely, the regions of high connective tissue density experienced low strains and high stresses. They also conducted parametric studies to determine the influence of lamina cribrosa stiffness (Fig. 8). Hybrid geometries combining specimen-specific corneoscleral shells and generic ONH’s have also been developed by Norman et al.53 One of the main goals of this study was to determine the effects of globe shape and size on ONH biomechanics. Out of all the geometric factors studied, peripapillary scleral thickness was

488

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 8. A parametric analysis detailing the effects of lamina cribrosa stiffness on laminar strains. Two models with specimen-specific geometries, connective tissue fractions, and preferred fiber orientations were modeled. Strain maps are shown for the two models with three different levels of tissue stiffness. As the stiffness increased, the maximum strains in the lamina were reduced. 52 Reprinted with permission from the Association for Research in Vision and Ophthalmology

the largest determinant of ONH biomechanics, with decreased thickness resulting in increased maximum strains in the lamina cribrosa and increased scleral canal expansion. Specimen-specific models are limited in that, by definition, they only represent variation through the differences in the actual eyes included in the data set. While this may be less of a problem if the data set was constructed from a large set representative of the population of interest, this is usually not the case due to the challenges and effort required to reconstruct the models. In addition, the models are often based on donor tissues, which severely restricts access to some populations. While parameterizing material properties in specimen-specific models is relatively straightforward, the geometry is much more complicated. To get around this problem, we developed a method for

A.P. Voorhees, Y. Hua and I.A. Sigal

parameterizing and varying the geometry of specimen-specific models using ‘morphing’ techniques.48 Geometric morphing is a powerful technique that has been successfully used to study how shape variations alter the biomechanical responses of a structure to loading.54 This approach allowed us to study the biomechanical sensitivity of an individual eye to its geometric and anatomical dimensions. Examples of parameters that have been studied with this approach include scleral canal size, scleral thickness, and lamina cribrosa curvature. In a 2011 paper, we used this geometric morphing technique to study the influence of geometric variation on ONH biomechanics using monkey specimen-specific models.53 Our study used a two-level, full factorial experimental design in which seven geometric or tissue stiffness parameters were varied and the individual eye was included as a categorical variable. This study design allowed us to quantify factor interactions. We found that lamina cribrosa deformation was highly sensitive to the position and stiffness of the lamina, whereas scleral canal expansion was sensitive primarily to scleral thickness and modulus. We also found that lamina cribrosa deformation was sensitive to factor interactions, including interactions between canal size and lamina position, canal size and lamina modulus, lamina thickness and lamina position, and lamina position and lamina modulus. The expansion of the scleral canal was less sensitive to factor interactions. More recently, efforts have been made to understand the effects of collagen fiber microarchitecture within the lamina cribrosa on the stretch of this tissue due to IOP. Zhang et al. created planar models of human ONHs, including collagen anisotropy as determined by small-angle light scattering.whi Although the direction of anisotropy was specimen-specific, the material properties were generic and non-linear, and the resolution of the experimental data was too low to capture the trabecular structure of the lamina cribrosa itself. They conducted a parametric sensitivity analysis to determine the effects of the tissue stiffness and degree of fiber alignment. Somewhat surprisingly, they found that increased lamina cribrosa fiber anisotropy actually increased laminar strains. Less surprisingly, they found that the strains within the lamina were highly dependent upon the material properties of both the lamina and sclera, which is consistent with other

Parametric Modeling

489

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 9. Three models of the lamina cribrosa built from micro-computerized tomography (CT) that incorporate varying amounts of specimen-specific data in the material properties. 55 (a) The micro-CT data from which the models were built. (b-d) The first principal strains in models that include: (b) both connective tissue density and fiber direction; (c) neither connective tissue density nor fiber direction; and (d) only connective tissue density. In the models that consider the connective tissue density, the strain field was more heterogeneous and peak strains occurred near the periphery of the lamina. When fiber direction was considered, the peak strains were reduced. 54 Reprinted with permission from the Royal Society.

Fig. 10. A microstructure-aware model that considers the lamina pores and neural tissues independently from the connective tissues.17 (Left) Strains in the neural tissue pores under an IOP of 30 mmHg were large and varied from one pore to another. (Right) The material properties of the connective tissue were varied. The distribution of strain within the neural tissues of the lamina decreased when connective tissue stiffness increased. Increasing the non-linearity of the tissue decreased the range of neural tissue strains, but did not have a major effect on the median. The red line is the volume weighted median, blue box ranges from 25-75th percentiles, whiskers denote the 5th and 95th percentiles, and cyan lines indicate the average macroscale stretch of the lamina region.

models. Campbell et al. created a finite element model with a generic geometry but non-linear and anisotropic material properties based on specimen-specific measurements of connective tissue volume fraction and collagen beam orientation obtained from a μCT scan of a porcine eye (Fig. 9).55 They compared their full model

to a model of a homogenous isotropic lamina and an inhomogeneous isotropic lamina. They found that the structure of the lamina cribrosa homogenizes the strain field within the lamina and that the anisotropy of the collagen beams had little influence on the lamina strains.

Copyright © 2018. Kugler Publications. All rights reserved.

490

Neither of these recent microstructure-aware lamina cribrosa models explicitly distinguished between the stiff collagenous connective tissue and the highly compliant neural tissues which are affected in glaucoma, instead modeling the lamina as a mixture of the two materials. To study the influence of lamina cribrosa microstructure on neural tissue strains, we developed specimen-specific, non-linear anisotropic models of lamina microstructure based on high-resolution polarized light microscopy.17,56-59 We found that IOP-induced strains in the neural tissues at the level of the lamina cribrosa were much larger than the macroscale strain of the lamina (Fig. 10). We performed a parametric analysis in which we varied the material properties of both the connective tissues and the neural tissue, finding that increasing connective tissue stiffness reduced the peak neural tissue strain.58 Specimen-specific modeling has not been limited to the study of the ONH response to IOP. In a 2006 paper, Cirovic et al. created a simplified eye-specific model that included the whole globe as well the optic nerve, orbit, and surrounding muscles based on magnetic resonance imaging (MRI).60 They used this model to study blunt impact resulting from an eye poke. They conducted parametric variations examining the effects of impact velocity, depth, and location. It was found that an off-center finger impact caused significant translation of the globe and led to high stress concentrations at the optic nerve which could lead to optic nerve avulsion. Wang et al. recently published a study using models based on patient-specific geometries of the eye and optic nerve as imaged by MRI to predict the strains in the ONH and optic nerve due to horizontal eye movements.61 In this study, they found that the strains in the tissues of the ONH induced by a 13° rotation of the eye were greater than the strains induced by a 35 mmHg increase in IOP. They conducted a two-level, full-factorial parametric sensitivity analysis to study the effects of lamina, sclera, pia mater, and dura mater stiffness. Their analysis revealed that increased dura mater stiffness reduced strains in the retrolaminar tissues, while a stiff sclera reduced the strains in the prelaminar tissues and lamina. Increasing the stiffness of the optic nerve sheath (pia and dura mater stiffness) increased the predicted strains in the lamina and prelaminar tissues due to horizontal eye rotation.

A.P. Voorhees, Y. Hua and I.A. Sigal

2.3.2 Inverse modeling One of the major challenges facing the biomechanics community is obtaining accurate measurements of non-linear, inhomogeneous, and anisotropic material properties. Inverse finite element modeling has become a powerful tool for obtaining these measurements from experimental testing that mimics the conditions in the eye.3,4,13,14 Coudrillier et al. developed a model with human specimen-specific scleral geometry, including specimen-specific details of sclera collagen anisotropy derived from wide angle x-ray scattering data, but with a generic lamina.13 The non-linear material stiffness used in this study was also specimen-specific and determined through inverse modeling. This model implemented a distributed fiber-based constitutive equation that allowed them to study the influence of collagen fiber alignment and anisotropy through an elegant parametric variation. They found that increasing fiber anisotropy in the peripapillary sclera resulted in a decrease in lamina cribrosa strains and scleral canal expansion, but also resulted in a posterior deformation of the lamina cribrosa. Grytz and colleagues also used an inverse modeling approach to measure scleral stiffness.4 Unlike the models used by Coudrillier et al., the preferred fiber orientation was determined through inverse modeling rather than through experimental measurement. The non-linear and anisotropic measurements were determined by fitting models to surface displacement data obtained from an ex-vivo inflation test of human eyes from donors of various ages and races. They reported that the collagen fibril crimp angle decreased and scleral shear modulus increased significantly with age in donors of European descent, and that these changes were significantly greater in donors of African descent compared to European donors. 2.3.3. Post-hoc parametric analysis Post-hoc parametric analysis of specimen-specific models can offer tremendous insight into the potential causes and risk factors of disease. In this analysis, researchers use the natural variability within the set of models to conduct a sensitivity analysis rather than introducing it into their models. Perhaps the simplest example is the use of age to parameterize a set of specimen-specific models. Coudrillier et al. and Grytz et al. both used their inverse models to study the effects of age on scleral stiffness,3,4 both concluding that scleral

Parametric Modeling

stiffness increased with age. Coudrillier et al. also examined the interaction of age with diabetes in their study, and found that scleral stiffness did not increase with age in patients with diabetes.3 Grytz et al. investigated the effects of aging on scleral stiffness in eyes from donors of European and Africandescent,4 determining that scleral stiffness increased more rapidly in eyes of donors of African descent. In fact, they determined that scleral stiffness of 50-year-old donors of African descent was similar to the scleral stiffness of 80-year-old donors of European descent. In another study, Coudrillier used inverse modeling to explore the differences in scleral mechanical properties from donor eyes of patients with and without glaucoma.62 Their models predicted that the material properties of the peripapillary sclera of glaucomatous eyes was more homogenous than that of healthy eyes. Interestingly, we are not aware of any inverse modeling studies that examine the differences in scleral mechanics between male and female eyes. Post-hoc analysis techniques are not limited to studying the effects of demographic variables. It is possible to make geometric measurements of a set of specimen-specific models and use that data as the basis for a sensitivity analysis. Using our microstructure-specific models of the lamina, we demonstrated that the shape and size of the pores contribute to a pore’s sensitivity to elevated IOP.63 By identifying pore shapes likely to undergo high IOP-induced deformation, it may be possible to determine a patient’s susceptibility to glaucoma from in-vivo imaging. A limitation of post-hoc analysis is that it can require a large number of models to produce statistically robust results.

Copyright © 2018. Kugler Publications. All rights reserved.

3. Future directions The last decade has seen tremendous improvements in imaging technology that allow for enhanced visualization and characterization of the collagenous microarchitecture of the eye. These advances include synchrotron micro-computerized tomography,55,64 adaptive optics optical coherence tomography,65 polarized light microscopy,56,57 magic angle MRI,66 and second harmonic image generation.67,68 The high-resolution data provided by these techniques will help determine how the microstructural properties of the posterior pole, and specifically of the lamina cribrosa,

491

affect the biomechanical response to elevated IOP, ICP, and ocular trauma. Current efforts include the development of specimen-specific models that capture the heterogeneity of the lamina cribrosa, including both the distinct mechanics of the retinal ganglion cell axons and the connective tissue.17 As new data becomes available, it is important that modeling techniques and constitutive formulations keep pace. Although recent studies in the field have included fiber anisotropy measurements taken directly from experimental data,3,13,16 the material models employed are still exponential or power law curves fit to mesoscale deformations. Constitutive models formulated from the underlying microstructural and biochemical properties, such as collagen crimp, which can be measured through polarized light ­microscopy,69-71 or the degree of collagen cross-linking, could help us identify new biomechanical risk factors for disease and injury. While collagen is known to be the major load-bearing material in the body, constitutive formulations that include the contributions of elastic fibers and proteoglycans, molecules that are known to influence the elastic and compressive properties of the eye,72,73 will help us understand the underlying mechanisms of disease. Furthermore, as the ocular biomechanics community moves toward developing microscale and multiscale models, it will be important to consider the influence of intracellular fibers such as actin and microtubules. A new generation of parametric models will help elucidate the relationship between mechanical strain and the disruption of axoplasmic transport and continue to guide our experimental research. To understand glaucoma pathogenesis, it is imperative to determine the complex interaction between glial cells, retinal ganglion cell axons, connective tissue, capillary hemodynamics, and mechanical strain within the lamina cribrosa. While models that capture the static behavior of this system will improve our understanding of the disease, it is also necessary to understand the dynamic interactions. Work has gone into developing strain-driven growth and remodeling,74,75 but this work has been limited to highly simplified generic geometries. Detailed parametric studies examining the influence of the growth and remodeling parameters on the biomechanical response of the ONH, and how these depend on the geometry and material properties of a specimen, have

492

Copyright © 2018. Kugler Publications. All rights reserved.

not been performed. Moving forward, it will also be important to develop growth and remodeling models that are capable of considering experimental mechanobiological measurements of protease expression, intracellular fiber remodeling, and cell membrane mechanics. Advances in these areas have been made for generic soft tissues76,77 and cardiac remodeling,78,79 and their adoption by the ocular biomechanics community should provide information on the genomic and proteomic factors that influence the development and progression of glaucoma. While the field of computational ocular biomechanics has made steady progress, clinical translation is still an unmet goal. The adoption of optical coherence tomography has provided a new paradigm for tracking the disease; however, clinicians still do not have the tools to predict glaucoma progression until permanent visual field loss has begun. Structural and biochemical biomarkers of disease progression need to be established so that clinicians can plan an effective course of treatment for each patient. Parametric modeling is a means of identifying these microstructural biomarkers, but validation is pending and translation will require the education of the clinical community. While modelers may be disposed towards adding computational complexity to their models, clinical translation requires the development of user-friendly models that can provide immediate clinical answers. We have worked to develop tools and models capable of predicting the stresses and deformations of the ONH based on clinical optical coherence tomography measurements.38 These tools were only made possible by an extensive parametric analysis. Although these

A.P. Voorhees, Y. Hua and I.A. Sigal

models were generic, linear, and isotropic, the same approach can be used to develop tools that consider more complex geometries and material properties. Eventually, it may be possible to create multi-scale models that consider both biochemical and structural dynamics into the clinic to help physicians develop individualized dosing and treatment protocols. Modeling can be an important clinical tool, but it is up to the ocular biomechanics community to demonstrate the power and utility to the clinical community.

4. Conclusion Parametric modeling is a powerful tool for understanding ocular biomechanics. As we have discussed, it has allowed identifying structural and material factors that may increase or decrease the sensitivity of an eye to elevations of IOP or trauma. Parametric modeling has inspired the development of new therapeutic treatments such as scleral stiffening,19,20 and has even been used to optimize the design of surgical implants.80 As imaging techniques and computational power improves, parametric modeling will remain essential to identify biomechanical risk factors for disease and treatment strategies to optimize patient care.

Acknowledgments This work has been supported in part by US National Institutes of Health grants R01-EY023966, R01-EY025011, P30-EY008098, and T32-EY017271 (Bethesda, MD, USA), as well as the Eye and Ear Foundation (Pittsburgh, PA, USA).

Parametric Modeling

References 1.

2.

3. 4.

5.

6.

7. 8.

9.

10.

11.

12.

Copyright © 2018. Kugler Publications. All rights reserved.

13.

14.

15.

16.

Chung CW, Girard MJ, Jan NJ, Sigal IA. Use and misuse of Laplace’s Law in ophthalmology. Invest Ophthalmol Vis Sci. 2016;57:236-245. Palko JR, Morris HJ, Pan X, et al. Influence of age on ocular biomechanical properties in a canine glaucoma model with ADAMTS10 mutation. PLoS One. 2016;11:e0156466. Coudrillier B, Pijanka JK, Jefferys J, et al. Effects of age and diabetes on scleral stiffness. J Biomech Eng. 2015;137(7). Grytz R, Fazio MA, Libertiaux V, et al. Age- and race-related differences in human scleral material properties. Invest Ophthalmol Vis Sci. 2014;55:8163-8172. Fazio MA, Grytz R, Morris JS, Bruno L, Girkin CA, Downs JC. Human scleral structural stiffness increases more rapidly with age in donors of African descent compared to donors of European descent. Invest Ophthalmol Vis Sci. 2014;55:71897198. Stylianopoulos T, Aksan A, Barocas VH. A structural, kinetic model of soft tissue thermomechanics. Biophys J. 2008;94:717725. Voorhees AP, Grimm JL, Bilonick RA, et al. What is a typical optic nerve head? Exp Eye Res. 2016;149:40-47. Cook DD, Robertson DJ. The generic modeling fallacy: Average biomechanical models often produce non-average results! J Biomech. 2016;49:3609-3615. Sigal IA, Yang H, Roberts MD, Burgoyne CF, Crawford Downs J. IOP-induced lamina cribrosa displacement and scleral canal expansion: An analysis of factor interactions using parameterized eye-specific models. Invest Ophthalmol Vis Sci. 2011;52:18961907. Sigal IA. Interactions between geometry and mechanical properties on the optic nerve head. Invest Ophthalmol Vis Sci. 2009;50:2785-2795. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Modeling individual-specific human optic nerve head biomechanics. Part II: Influence of material properties. Biomech Model Mechanobiol. 2009;8:99-109. Sigal IA, Flanagan JG, Ethier CR. Factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2005;46:41894199. Coudrillier B, Boote C, Quigley Ha, Nguyen TD. Scleral anisotropy and its effects on the mechanical response of the optic nerve head. Biomech Model Mechanobiol. 2013;12:941-963. Girard MJa, Downs JC, Bottlang M, Burgoyne CF, Suh J-KF. Peripapillary and posterior scleral mechanics-Part II: experimental and inverse finite element characterization. J Biomech Eng. 2009;131:051012. Girard MJa, Downs JC, Burgoyne CF, Suh J-KF. Peripapillary and posterior scleral mechanics--part I: development of an anisotropic hyperelastic constitutive model. J Biomech Eng. 2009;131:051011. Zhang L, Albon J, Jones H, et al. Collagen microstructural factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2015;56:2031-2042.

493 17. Voorhees AP, Jan N-J, Flanagan JG, Sivak JM, Sigal IA. A microstructure based model of lamina cribrosa mechanical insult under IOP. Invest Ophthalmol Vis Sci. 2016;57(12). 18. Geraghty B, Jones SW, Rama P, Akhtar R, Elsheikh A. Age-related variations in the biomechanical properties of human sclera. J Mech Behav Biomed Mater. 2012;16:181-191. 19. Coudrillier B, Campbell IC, Read AT, et al. Effects of peripapillary scleral stiffening on the deformation of the lamina cribrosa. Invest Ophthalmol Vis Sci. 2016;57:2666-2677. 20. Kimball EC, Nguyen C, Steinhart MR, et al. Experimental scleral cross-linking increases glaucoma damage in a mouse model. Exp Eye Res. 2014;128:129-140. 21. Whitford C, Joda A, Jones S, Bao F, Rama P, Elsheikh A. Ex vivo testing of intact eye globes under inflation conditions to determine regional variation of mechanical stiffness. Eye Vis (Lond). 2016;3:21. 22. Sigal IA, Ethier CR. Biomechanics of the optic nerve head. Exp Eye Res. 2009;88(4)799-807. 23. Kraus H. Thin Elastic Shells: An Introduction to the Theoretical Foundations and the Analysis of their Static and Dynamic Behavior. New York: Wiley; 1967. 24. Prange HD. Laplace’s law and the alveolus: a misconception of anatomy and a misapplication of physics. Adv Physiol Educ. 2003;27:34-40. 25. Regen DM. Tensions and stresses of ellipsoidal chambers. Ann Biomed Eng. 1996;24:400-417. 26. Friedenwald JS. Contribution to the theory and practice of tonometry. Am J Ophthalmol. 1937;20:985-1024. 27. McEwen WK, St Helen R. Rheology of the human sclera. Unifying formulation of ocular rigidity. Ophthalmologica. 1965;150:321346. 28. Greene PR. Closed-form ametropic pressure-volume and ocular rigidity solutions. Am J Optom Physiol Opt. 1985;62:870-878. 29. Dongqi H, Zeqin R. A biomathematical model for pressure-dependent lamina cribrosa behavior. J Biomech. 1999;32:579-584. 30. Edwards ME, Good TA. Use of a mathematical model to estimate stress and strain during elevated pressure induced lamina cribrosa deformation. Curr Eye Res. 2001;23:215-225. 31. Sander EA, Downs JC, Hart RT, Burgoyne CF, Nauman EA. A cellular solid model of the lamina cribrosa: mechanical dependence on morphology. J Biomech Eng. 2006;128:879-889. 32. Lakawicz JM, Bottega WJ, Prenner JL, Fine HF. An analysis of the mechanical behaviour of a detaching retina. Math Med Biol. 2015;32:137-161. 33. Bottega WJ, Bishay PL, Prenner JL, Fine HF. On the mechanics of a detaching retina. Math Med Biol. 2013;30:287-310. 34. Bellezza AJ, Hart RT, Burgoyne CF. The optic nerve head as a biomechanical structure: Initial finite element modeling. Invest Ophthalmol Vis Sci. 2000;41:2991-3000. 35. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Finite element modeling of optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2004;45:4378-4387. 36. Sigal IA, Grimm JL. A few good responses: Which mechanical effects of IOP on the ONH to study? Invest Ophthalmol Vis Sci. 2012;53:4270-4278.

Copyright © 2018. Kugler Publications. All rights reserved.

494 37. Sigal IA. An applet to estimate the IOP-induced stress and strain within the optic nerve head. Invest Ophthalmol Vis Sci. 2011;52:5497-5506. 38. Sigal IA, Grimm JL, Schuman JS, Kagemann L, Ishikawa H, Wollstein G. A method to estimate biomechanics and mechanical properties of optic nerve head tissues from parameters measurable using optical coherence tomography. IEEE Trans Med Imaging. 2014;33:1381-1389. 39. Sigal IA, Bilonick RA, Kagemann L, et al. The optic nerve head as a robust biomechanical system. Invest Ophthalmol Vis Sci. 2012;53:2658-2667. 40. Perez BC, Morris HJ, Hart RT, Liu J. Finite element modeling of the viscoelastic responses of the eye during microvolumetric changes. J Biomech Eng. 2013;6:29-37. 41. Feola AJ, Myers JG, Raykin J, et al. Finite element modeling of factors influencing optic nerve head deformation due to intracranial pressure. Invest Ophthalmol Vis Sci. 2016;57:1901-1911. 42. Hua Y, Tong J, Ghate D, Kedar S, Gu L. Intracranial pressure influences the behavior of optic nerve head. J Biomech Eng. 2017;139(3). 43. Hua Y, Voorhees AP, Sigal IA. Cerebrospinal fluid pressure: revisiting factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2018;59(1):154-165. 44. Ayyalasomayajula A, Park RI, Simon BR, Vande Geest JP. A porohyperelastic finite element model of the eye: the influence of stiffness and permeability on intraocular pressure and optic nerve head biomechanics. Computer methods in biomechanics and biomedical engineering 2016;19:591-602. 45. Gray W, Sponsel WE, Scribbick FW, et al. Numerical modeling of paintball impact ocular trauma: Identification of progressive injury mechanisms. Invest Ophthalmol Vis Sci. 2011;52:75067513. 46. Rossi T, Boccassini B, Esposito L, et al. The pathogenesis of retinal damage in blunt eye trauma: Finite element modeling. Invest Ophthalmol Vis Sci. 2011;52:3994-4002. 47. Rossi T, Boccassini B, Esposito L, et al. Primary blast injury to the eye and orbit: Finite element modeling. Invest Ophthalmol Vis Sci. 2012;53:8057-8066. 48. Sigal IA, Yang H, Roberts MD, Downs JC. Morphing methods to parameterize specimen-specific finite element model geometries. J Biomech. 2010;43:254-262. 49. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Modeling individual-specific human optic nerve head biomechanics. Part I: IOP-induced deformations and influence of geometry. Biomech Model Mechanobiol. 2009;8:85-98. 50. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Predicted extension, compression and shearing of optic nerve head tissues. Exp Eye Res. 2007;85:312-322. 51. Roberts MD, Sigal Ia, Liang Y, Burgoyne CF, Crawford Downs J. Changes in the biomechanical response of the optic nerve head in early experimental glaucoma. Invest Ophthalmol Vis Sci. 2010;51:5675-5684. 52. Roberts MD, Liang Y, Sigal Ia, et al. Correlation between local stress and strain and lamina cribrosa connective tissue volume fraction in normal monkey eyes. Invest Ophthalmol Vis Sci. 2010;51:295-307.

A.P. Voorhees, Y. Hua and I.A. Sigal 53. Norman RE, Flanagan JG, Sigal Ia, Rausch SMK, Tertinegg I, Ethier CR. Finite element modeling of the human sclera: Influence on optic nerve head biomechanics and connections with glaucoma. Exp Eye Res. 2011;93:4-12. 54. Rivera G, Stayton CT. Effects of asymmetry on the strength of the chelonian shell: A comparison of three species. J Morphol. 2013;274:901-908. 55. Campbell IC, Coudrillier B, Mensah J, Abel RL, Ethier CR. Automated segmentation of the lamina cribrosa using Frangi’s filter: a novel approach for rapid identification of tissue volume fraction and beam orientation in a trabeculated structure in the eye. J R Soc Interface. 2015;12(104):20141009. 56. Jan N-J, Lathrop KL, Sigal IA. Collagen architecture of the posterior pole; high-resolution, wide-field-of-view visualization and analysis using polarized light microscopy. Invest Ophthalmol Vis Sci. 2017;58(2):735-744. 57. Jan N-J, Grimm JL, Tran H, et al. Polarization microscopy for characterizing fiber orientation of ocular tissues. Biomed Opt Express. 2015;6:4705-4718. 58. Voorhees AP, Jan NJ, Sigal IA. Effects of collagen microstructure and material properties on the deformation of the neural tissues of the lamina cribrosa. Acta Biomater. 2017;58:278-290. 59. Voorhees AP, Jan NJ, Austin ME, et al. Lamina cribrosa pore shape and size as predictors of neural tissue mechanical insult. Invest Ophthalmol Vis Sci. 2017;58(12):5336-5346. 60. Cirovic S, Bhola RM, Hose DR, et al. Computer modelling study of the mechanism of optic nerve injury in blunt trauma. Br J Ophthalmol. 2006;90:778-783. 61. Wang X, Rumpel H, Lim WE, et al. Finite element analysis predicts large optic nerve head strains during horizontal eye movements. Invest Ophthalmol Vis Sci. 2016;57:2452-2462. 62. Coudrillier B, Pijanka JK, Jefferys JL, et al. Glaucoma-related changes in the mechanical properties and collagen micro-architecture of the human sclera. PLoS One. 2015;10:e0131396. 63. Voorhees AP, N-J Jan, ME Austin, et al. Lamina cribrosa pore shape and size as predictors of neural tissue mechanical insult. Invest Ophthalmol Vis Sci. 2017;58(12):5336-5346. 64. Coudrillier B, Geraldes DM, Vo NT, et al. Phase-contrast micro-computed tomography measurements of the intraocular pressure-induced deformation of the porcine lamina cribrosa. IEEE Trans Med Imaging. 2016;35:988-999. 65. Nadler Z, Wang B, Schuman JS, et al. In vivo three-dimensional characterization of the healthy human lamina cribrosa with adaptive optics spectral-domain optical coherence tomography. Invest Ophthalmol Vis Sci. 2014;55:6459-6466. 66. Ho LC, Sigal IA, Jan NJ, et al. Magic angle-enhanced MRI of fibrous microstructures in sclera and cornea with and without intraocular pressure loading. Invest Ophthalmol Vis Sci. 2014;55:5662-5672. 67. Sigal IA, Grimm JL, Jan NJ, Reid K, Minckler DS, Brown DJ. Eye-specific IOP-induced displacements and deformations of human lamina cribrosa. Invest Ophthalmol Vis Sci. 2014;55:1-15. 68. Jones HJ, Girard MJ, White N, et al. Quantitative analysis of three-dimensional fibrillar collagen microstructure within the normal, aged and glaucomatous human optic nerve head. J R Soc Interface. 2015;12(106).

Parametric Modeling

Copyright © 2018. Kugler Publications. All rights reserved.

69. Jan N-J, Iasella M, Lester M, et al. Novel method reveals heterogeneous micro-scale response of sclera collagen bundles to homogeneous macro-scale stretch. Invest Ophthalmol Vis Sci. 2016;57:3566-3566. 70. Sigal IA, Jan N-J, Moed S, et al. A microstructural basis for nonlinear effects of IOP on the lamina cribrosa and sclera. Invest Ophthalmol Vis Sci. 2015;56:4821-4821. 71. Jan NJ, Gomez C, Moed S, et al. Microstructural crimp of the lamina cribrosa and peripapillary sclera collagen fibers. Invest Ophthalmol Vis Sci. 2017;58(9):3378-3388. 72. Quigley EN, Quigley HA, Pease ME, Kerrigan LA. Quantitative studies of elastin in the optic nerve heads of persons with primary open-angle glaucoma. Ophthalmology. 1996;103:16801685. 73. Murienne BJ, Jefferys JL, Quigley HA, Nguyen TD. The effects of glycosaminoglycan degradation on the mechanical behavior of the posterior porcine sclera. Acta Biomater. 2015;12:195-206. 74. Grytz R, Sigal IA, Ruberti JW, Meschke G, Downs JC. Lamina cribrosa thickening in early glaucoma predicted by a microstructure motivated growth and remodeling approach. Mech Mater. 2012;44:99-109.

495 75. Grytz R, Meschke G, Jonas JB. The collagen fibril architecture in the lamina cribrosa and peripapillary sclera predicted by a computational remodeling approach. Biomech Model Mechanobiol. 2011;10:371-382. 76. Tonge TK, Ruberti JW, Nguyen TD. Micromechanical modeling study of mechanical inhibition of enzymatic degradation of collagen tissues. Biophys J. 2015;109:2689-2700. 77. Obbink-Huizer C, Foolen J, Oomens CW, et al. Computational and experimental investigation of local stress fiber orientation in uniaxially and biaxially constrained microtissues. Biomech Model Mechanobiol. 2014;13:1053-1063. 78. Rouillard AD, Holmes JW. Coupled agent-based and finite-element models for predicting scar structure following myocardial infarction. Prog Biophys Mol Biol. 2014;115:235-243. 79. Zeigler AC, Richardson WJ, Holmes JW, Saucerman JJ. Computational modeling of cardiac fibroblasts and fibrosis. J Mol Cell Cardiol. 2016;93:73-83. 80. Lanchares E, del Buey MA, Cristóbal JA, Calvo B, Ascaso FJ, Malvè M. Computational simulation of scleral buckling surgery for rhegmatogenous retinal detachment: on the effect of the band size on the myopization. J Ophthalmol. 2016;2016:3578617.

Copyright © 2018. Kugler Publications. All rights reserved.

33. In-vivo characterization of optic nerve head biomechanics for improved glaucoma management Xiaofei Wang1, Meghna R. Beotra1, Liang Zhang1, Michaël J.A. Girard1,2 Ophthalmic Engineering & Innovation Laboratory, Department of Biomedical Engineering, Faculty of Engineering, National University of Singapore, Singapore; 2Singapore Eye Research Institute, Singapore National Eye Centre, Singapore 1

1. The biomechanical theory of glaucoma and its relevance to clinical practice

Copyright © 2018. Kugler Publications. All rights reserved.

1.1. Glaucoma is caused by axonal damage within the lamina cribrosa The central event in glaucoma is slow and irreversible damage of retinal ganglion cell (RGC) axons. RGCs carry visual information from the retina to the brain. When damaged, they undergo programmed cell death (apoptosis) resulting in vision loss. The main site of RGC damage occurs within the lamina cribrosa (LC),1 a connective tissue structure of the optic nerve head (ONH) located at the back of the eye. 1.2. IOP is a major risk factor for glaucoma We know that increased intraocular pressure (IOP) is associated with increased prevalence2 and incidence3 of glaucoma. In fact, reduction of IOP, either pharmacologically (e.g., eye drops) or surgically, is the only currently available and effective treatment proven to slow the progression of vision loss in glaucoma.4 However, IOP-lowering therapy is not always successful, as progressive damage to the RGC axons persists approximately 50% of the time.5 In addition, some patients with elevated IOP never develop glaucoma (a condition called ocular hypertension, OHT). Finally, glaucoma occurs nearly as often in patients with normal levels of IOP (normal-tension glaucoma, NTG) as in those with elevated levels6 (high-tension glaucoma, HTG), and

does so without distinct aetiology.7 In brief, our current understanding of glaucoma is insufficient: we know that IOP is important, but clearly, risk factors other than IOP must play important roles in the development and progression of this disease.3 1.3. Biomechanics could explain glaucoma The biomechanical theory of glaucoma8 suggests a mechanism that explains the conflicting observations related to IOP and glaucoma risks. It hypothesizes that IOP (at any level) deforms the ONH tissues, particularly the LC (see model illustrations in Fig. 1a and b), and that these deformations drive RGC injury and death. This theory is supported by substantial circumstantial evidence,9-11 and can explain differing sensitivities to IOP. Thus, the central idea of the biomechanical theory is that strains (i.e., deformations) and biomechanical properties of the ONH tissues might be superior to gold-standard parameters (e.g., IOP) in predicting visual field progression. 1.4. The story is not yet complete: IOP is not the only load deforming the ONH The cerebrospinal fluid pressure (CSFP – the pressure of the fluid bathing the brain and the spinal cord) opposes IOP at the level of the ONH. Chronically elevated CSFP has been shown to significantly deform the ONH, resulting in anterior deformations and bending of ONH connective tissues (LC and peripapillary sclera), which causes loss of vision that is associated with ‘swelling’

Correspondence: Dr Michaël J.A. Girard, Ophthalmic Engineering & Innovation Laboratory, Department of Biomedical Engineering, National University of Singapore, Engineering Block 4, #04-8, 4 Engineering Drive 3, Singapore, 117583. E-mail: [email protected] Biomechanics of the Eye, pp. 497-511 Edited by: C.J. Roberts, W.J. Dupps and J.C. Downs © 2018 Kugler Publications, Amsterdam, The Netherlands

498

X. Wang et al.

resonance imaging (MRI),20 all converge to the single fact that horizontal eye movements considerably deform the ONH tissues (through the ‘strong’ optic nerve traction imposed on the ONH; see model illustration in Fig. 1d), and that these deformations can be as large (or significantly larger) than those induced by a substantial IOP elevation.16,18 Because optic nerve traction appears to have a strong impact on the ONH tissues, and can even alter the axial length of the eye,21 it may have a critical importance in glaucoma, but this currently remains unexplored as a contributing factor.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 1. Summary of loading scenarios that deform the LC utilizing computational modeling. (A) Baseline ONH geometry in primary gaze position. (B) An increase IOP can result in stretching and posterior deformation of the LC. (C) An increase in CSFP can result in anterior deformation of the LC. (D) A change in gaze position can distort the LC through the pulling action of the optic nerve sheath (dura mater). Note: All illustrations provided in this figure were simulated using computational models in which various loads were applied to a baseline idealized ONH geometry. Such models help us understand the biophysics of the eye (i.e., the effect of each load on ONH deformations) but may not exactly represent true in-vivo LC deformations, as subjects exhibit more complex ONH morphologies, biomechanical properties, and loading environments.

of ONH tissues (see model illustration in Fig. 1c).12 Elevated CSFP can result in RGC injury and irreversible visual field loss that is similar to that seen in glaucoma; it has sometimes been referred to as ‘the reverse of glaucoma’. Recent research has suggested that an abnormal IOP, CSFP, or the pressure gradient between the two across the LC, may result in vision loss.13 In fact, low CSFP has been documented in NTG patients.14 A better understanding of how CSFP deforms the ONH tissues acutely in vivo (Fig. 1c), in conjunction with IOP, could enhance our understanding of glaucoma development and pathogenesis. 1.5. Optic nerve traction: a third load deforming the ONH Recently, eye movements have been suggested to play a role in the development and progression of optic neuropathies such as glaucoma. Specifically, studies that employed optical coherence tomography (OCT),1517 finite element (FE) modeling,18,19 and magnetic

1.6. Relevance to clinical practice Over the past decade, the biomechanical theory of glaucoma has gained significant ground in ophthalmology. Considerable efforts, through the development of novel engineering technologies, are currently underway to assess the biomechanical environment of the ONH in healthy and glaucoma subjects.22 Developing such technologies represents great challenges that will be discussed in further detail below. If it were true that an abnormal biomechanical environment drives glaucoma, it would encourage research to use biomechanics as a glaucoma biomarker to prognosticate treatment. For instance, we could consider more aggressive treatments in the eyes that are deemed biomechanically susceptible. ONH biomechanics could also become a strong diagnostic marker to predict those at higher risk of developing glaucoma. This would be especially useful for OHT subjects. Biomechanics may also yield explanations for why NTG subjects develop glaucoma at normal levels of IOP, and may even lead the way to new therapeutic approaches to alter ONH biomechanics in vivo.23 The goal of this chapter is to discuss how to bridge the gap between the clinical and biomechanical worlds for the benefit of glaucoma patients.

2. Biomechanical biomarkers for glaucoma and challenges associated with their in-vivo measurements 2.1. Modulating in-vivo loads is a necessary first step for characterizing ONH biomechanics in patients To fully assess the biomechanical behavior of the ONH in vivo, one would need to alter one of the three known loads acting on the ONH (IOP, CSFP, or optic

In-vivo characterization of optic nerve head biomechanics for improved glaucoma management

nerve traction) while continuously monitoring the ONH tissues and measuring their resulting local deformations. Only then can the stiffness (or biomechanical properties) of ONH tissues – roughly speaking, the ratio of load changes to deformations – be estimated. It is important to realize that these ‘in-vivo biomechanical tests’ need to be performed within a safe physiological range in order to avoid further progression of visual field loss. Furthermore, and as for any controlled mechanical test, only one load should be altered at a time while all others should remain constant, which represents a significant clinical challenge.

Copyright © 2018. Kugler Publications. All rights reserved.

2.2. How to modulate IOP in vivo? IOP is not a fixed value in vivo, but rather exhibits fluctuations associated with the cardiac cycle. The amplitude of such fluctuations is small (2-4 mmHg in normal patients) and is referred to as the ocular pulse amplitude.24 Detecting ONH deformations due to naturally occurring fluctuations in IOP would be a powerful means of characterizing ONH biomechanics without artificial IOP manipulation. Furthermore, by using the ocular pulse as a natural dynamic load, the time-dependent properties (i.e., viscoelastic properties) of the ONH could be extracted, which would be difficult by increasing the IOP statically. Other means of modulating IOP in vivo, include, but are not limited to: ophthalmodynamometry, pharmacological (eye drops) and surgical (trabeculectomy) treatments, and the water drinking test.25 It is important to emphasize that IOP remains the only modifiable and measurable load that can deform the ONH tissues in vivo, and has remained a parameter of choice in most biomechanical studies. 2.3. How to modulate CSFP in vivo? Similar to IOP, CSFP exhibits fluctuations on the order of 4 mmHg with the cardiac cycle,26 and such fluctuations could potentially be used as biomechanical loading. Other means of manipulating CSFP in vivo include changes in body posture (from sitting to supine position),27 or use of the Valsalva maneuver,28 but such techniques inevitably result in a simultaneous change in IOP.29,30 The biggest limiting factor in modulating CSFP is that it cannot be measured non-invasively in vivo other than with surrogates that are not well validated.

499

2.4. How to modulate optic nerve traction in vivo? Requesting subjects to move their eyes horizontally from a primary gaze position can increase the magnitude of the optic nerve traction force. While we have estimated the optic nerve traction force to be 150 mN in adduction and 90 mN in abduction (13°) using computational modeling,31 traction force cannot yet be measured in vivo. Further, it is plausible that eye movements will also result in simultaneous changes in IOP and CSFP, but this has yet to be proven. 2.5. ONH strain/deformation as a potential glaucoma biomarker Strain — the engineering metric for local deformation — is believed to be the most important quantity that could correlate with visual field loss and progression. A prominent hypothesis suggests that ONH strains (induced by IOP, CSFP, or optic nerve traction) damage the RGCs either directly23 or indirectly through a mechanical disruption of axonal transport in RGCs, thus depriving RGCs from essential trophic ­factors.32-34 An alternative hypothesis suggests that ONH strains can alter the hemodynamics within the ONH, which will in turn reduce the diffusion of nutrients to astrocytes and/or induce ischemia, thus resulting in RGC death. To date, ONH strains can be estimated using imaging modalities such as OCT. However, OCT is only capable of imaging the anterior portion of the LC and sclera,35 which limits its ability to fully capture the biomechanical environment of the ONH in vivo. 2.6 ONH biomechanical properties as potential glaucoma biomarkers Since the ONH is the main site of glaucoma damage, it is plausible that ONH biomechanical behavior is a biomarker of susceptibility to glaucoma development and progression. Indeed, there is great interest in understanding variations in biomechanical properties between healthy and glaucoma patients in vivo, as those may directly reflect connective tissue remodeling known to exist in glaucoma.36,37 A preliminary study by Tun et al.38 has shown that ONH biomechanical behavior is associated with glaucoma severity in primary open-angle glaucoma. Assuming that changes in loading conditions in the ONH can be controlled and measured, and that resulting ONH deformations can be quantified, one can envision developing techniques to

500

X. Wang et al.

Fig. 2. Steps to track displacement of a single tissue point: (1) an ROI is created in the undeformed OCT volume; (2) the ROI undergoes a combination of affine transformations (translation, rotation, shear, and stretch); (3) a displacement vector can be extracted when the deformed ROI best matches a co-localized ROI in the deformed volume. Adapted from Girard et al.55

Copyright © 2018. Kugler Publications. All rights reserved.

estimate the patient-specific biomechanical properties of ONH tissues. This step can be performed using inverse computational techniques, as discussed in more detail below. Assessing ONH biomechanical properties in vivo is a challenge, since ONH tissues exhibit complex behaviors such as non-linearity (stiffer with stretch), viscoelasticity (stiffer if loaded more rapidly), heterogeneity (stiffer in certain locations), and anisotropy (stiffer along reinforced directions due to the presence of collagen fibers). It seems unlikely that a single in-vivo biomechanical test will be able to capture all these properties simultaneously, and within their full range. For instance, most ex-vivo biomechanical tests dealing with ocular tissues can vary IOP from 5 to 50 mmHg or higher to derive non-linear tissue properties for that IOP range.39,40 However, modulating IOP across such a wide range in vivo may ultimately put patients at risks of hypotony, ischemia, or further IOP-driven ONH damage.

3. Measuring ONH deformations in patients 3.1. First ‘clinical estimates’ of ONH deformations Recent advances in medical imaging have made it possible to image the deep ONH structures using OCT41 — a fast, high-resolution, and non-invasive 3-D imaging modality. With the global adoption of OCT in clinical practice, multiple research groups have inves-

tigated changes in ONH morphology (either chronic or with acute IOP elevations) as potential surrogates for ONH deformations, with a special emphasis on the LC. Agoumi and coworkers were the first to use OCT to investigate LC displacements in glaucoma patients following changes in IOP through ophthalmodynamometry, but they found that LC movements were very variable among patients following an acute IOP elevation of ~12 mmHg.42 Further studies in both monkeys and humans reported changes in LC depth either with IOP increases,43,44 or with IOP lowering following trabeculectomy.45-50 LC depth is typically measured as the average or maximum distance between the plane of Bruch’s membrane opening and the anterior LC surface, and can be defined either in 2-D (from a single B-Scan) or in 3-D (from a raster scan).51 However, LC depth (or its change) relative to Bruch’s membrane opening is a poor surrogate for LC deformations, as it is influenced by concurrent deformations of the choroid, sclera, and other peripapillary tissues. For instance, following an acute elevation of IOP, an eye exhibiting a decrease in choroidal thickness (but no LC deformations) would also exhibit a decrease in LC depth. In addition, the LC could exhibit significant deformations (high compressive strain, or stretch along a direction parallel to the plane of Bruch’s membrane opening) that would yield no changes in LC depth. Other studies have measured a reduction in LC curvature following trabeculectomy in

In-vivo characterization of optic nerve head biomechanics for improved glaucoma management

Copyright © 2018. Kugler Publications. All rights reserved.

glaucoma subjects, 52 and changes in LC global shape index following acute IOP elevations in normal, ocular hypertensive, and glaucoma subjects. 53 The LC global shape index54 is a single number that characterizes the geometrical shape of the anterior LC surface as a whole (as can be derived from OCT), and that does not depend on a reference plane (as opposed to LC depth). Using such an index, Tun et al.53 found that the LC of glaucoma eyes was more posteriorly curved than that of normal subjects. In addition, the LC global shape index became significantly smaller (indicating cupping) following an acute IOP elevation to ~38 mmHg in normal and glaucoma subjects, but not in OHT subjects. This may suggest that the connective tissues of OHT subjects are able to withstand a larger mechanical load, but further validation is required. 3.2. Engineering tools to measure ONH strains: static IOP and CSFP loading The aforementioned studies (on LC depth, curvature, and shape) are limited because none of them have been able to map in-vivo 3-D displacements and strains (the engineering definition for deformation) that could indicate local compression, shear, or stretch of the axons passing through the LC. Such information is of critical value if we wish to understand how local ONH deformations could lead to RGC damage and apoptosis. To this end, Girard et al.55 have developed a 3-D tracking algorithm that can track displacements and strains of the ONH following a change in IOP. This algorithm requires two OCT volumes of the ONH: one is captured before a change in IOP, and is referred to as the ‘undeformed’ volume; the other is captured after a change in IOP and is referred to as the ‘deformed’ volume. Briefly, the tracking algorithm defines regions of interest (ROIs or group of voxels [3D pixels]) in the undeformed OCT volume, subjecting them to mechanical transformations (rigid translation, rigid rotation, stretch/compression and shear) until they best match their co-localized ROIs in the deformed OCT volume (Fig. 2). The output is a 3-D displacement field from which tensile, compressive, and effective (average) strain components can be derived and mapped. Using such a technique, Girard et al.56 have reported in-vivo local displacement/strain mapping of ONH tissues following IOP lowering by trabeculectomy in glaucoma subjects. Specifically, they found that:

501

1. local IOP-induced -3D displacements and strains could be measured in vivo; 2. the LC displaced posteriorly, anteriorly, or not at all following IOP lowering, suggesting strong biomechanical variability in the LC across subjects; 3. trabeculectomy significantly relieved strains in the ONH tissues (on average 8.6%) which may be of benefit to RGCs (Fig. 3); 4. the largest IOP decrease did not always correlate with the largest strain relief, reinforcing the concept of large biomechanical variability across subjects; and 5. there was an association between local retinal sensitivity and local LC strain relief (Fig. 4), suggesting a potential link between local LC deformations and visual field damage. This last point is important as IOP-induced LC strains have the potential to: • disrupt axoplasmic flow; • alter blood flow;57 • increase RGC apoptosis; • activate astrocytes, glia, and LC cells.23 Accordingly, it may seem logical that a direct spatial correlation between LC deformations and visual field loss should exist. Beotra et al.58 used the same 3-D tracking algorithm and mapped LC strains in healthy, glaucoma, and OHT subjects in which IOP was elevated acutely to approximately 35 mmHg, then 45 mmHg, using ophthalmodynamometry. They found clear strain differences across groups (Fig. 5) and that the average LC strain in OHT subjects (3.96%) was significantly lower than that measured in healthy subjects (6.81%; P < 0.05). This also suggests that OHT subjects may have stiffer than normal connective tissues, although this may be related to higher CSFP, as previously reported in those subjects.59 Similar tracking algorithms have been applied to map ONH strains in vivo in non-human primates. Fazio and coworkers60 continuously mapped 2-D strains following an acute IOP elevation from 10 to 30 mmHg and observed large neural tissue strains in the rim area of the disc — a region that is potentially highly susceptible to damage. Sigal and colleagues found that acute elevations in both CSFP (5-40 mmHg) and IOP (5-50 mmHg) resulted in complex deformation patterns in the LC, and concluded that the translaminar pressure difference (IOP – CSFP) was too simplistic to correlate with resulting LC deformations.61

Copyright © 2018. Kugler Publications. All rights reserved.

502

X. Wang et al.

Fig. 3. Color maps of tensile (1st principal), compressive (3rd principal), and effective (averaged) strain relief superimposed on clipped ONH geometries (in normal controls in which IOP was not altered and primary open-angle glaucoma subjects that underwent trabeculectomy). Note that ONH tissues in the normal controls exhibited little strain (mostly blue in all cases) as opposed to the glaucoma eyes. All left eyes were flipped to a right-eye configuration. N: normal; Nas: nasal; POAG: primary open-angle glaucoma; Temp: temporal. Adapted from Girard et al.56

In-vivo characterization of optic nerve head biomechanics for improved glaucoma management

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 4. Association between median retinal sensitivity and median LC strain relief (effective). Median LC strain relief was calculated for each of six sectors of the LC (according to the regionalization scheme of Garway-Heath) and for each of eight patients who underwent trabeculectomy and then plotted against corresponding median retinal sensitivity. dB: decibels. Adapted from Girard et al.56

503

3.3. Engineering tools to measure ONH strains: static optic nerve traction loading Using the same 3-D tracking algorithm described in section 3.2, Wang et al. were able to measure LC strains in healthy eyes induced by changes in gaze positions and compared them with those induced by a large IOP increase.16 Specifically, each ONH was imaged using OCT at baseline (twice, control case; Fig. 6a), in different gaze positions (adduction and abduction of 20°; Fig. 6b-c), and following an acute IOP elevation of approximately 20 mmHg from baseline (via ophthalmodynamometry). Wang et al. found that, for all 16 healthy eyes, horizontal eye movements could generate significant ONH strains. Gaze-induced LC strains were comparable to those induced by IOP (Fig. 6d). Interestingly, some eyes were more susceptible to gaze changes while others were more susceptible to IOP elevation (see Fig. 6e showing LC strain maps for two subjects and all loading scenarios). Two other independent studies15,17 also found large relative displacements of peripapillary tissues induced by gaze changes in 2-D OCT images, further confirming the hypothesis that eye movements can generate large ONH deformations.

Fig. 5. (a) Box plot of median LC effective strains across diagnostic groups (healthy, high-tension primary open-angle glaucoma (POAG), primary angle-closure glaucoma [PACG], ocular hypertension [OHT]) following acute IOP elevations. Asterisks indicate statistical significance (p < 0.05). (b) Representative color maps of acute IOP-induced effective strain superimposed on the LC geometry for healthy, POAG, PACG and OHT subjects. Note that for each subject, one en-face view and one mid-coronal view of the LC are shown.

Copyright © 2018. Kugler Publications. All rights reserved.

504

X. Wang et al.

Fig. 6. (a) Standard OCT acquisition in ‘baseline eye position’ illustrated using an MRI image of a healthy subject; (b) OCT acquisition in abduction together with a counterclockwise head rotation of 20° from the baseline head position in (a); (c) OCT acquisition in adduction together with a clockwise head rotation of 20° from the baseline head position in (a). Note that head rotations in these MRI images were larger than 20° and were used for illustration purposes only. L: left; R: right. (d) Box plots of mean LC effective strains for all 16 healthy eyes and for all loading scenarios (control, adduction, abduction, and IOP increase of 20 mmHg). (e) Color maps (cropped) of LC effective (averaged) strains for one eye of two subjects for all loading scenarios (control, adduction, abduction, and IOP increase). Adapted from Wang et al.16

In-vivo characterization of optic nerve head biomechanics for improved glaucoma management

3.4. Engineering tools to measure LC displacements: dynamic IOP loading Dragostinoff et al. have demonstrated that ONH displacements (induced by the ocular pulse) can be measured in vivo in patients with an OCT technology called time-domain low-coherence interferometry at an extremely high resolution of 50 nm.62 This technique allows for the analysis of amplitudes, time courses, and phase differences of fundus pulsations at preselected axial and transversal positions of the ONH. However, time-domain low-coherence interferometry is limited in the sense that it can only measure displacements along the axial direction (and not in 3-D) and that it is not yet applicable clinically because of the rather long measurement time. Another imaging modality, known as phase-sensitive Fourier Domain OCT,63 has shown great promise as it can measure relative movements of ONH tissue structures during the cardiac cycle. Because these techniques allow for continuous measurements of ONH tissue displacements induced by the ocular pulse, they may be used to extract the viscoelastic (i.e., time-dependent) properties of ONH tissues. Furthermore, it should be emphasized that imaging modalities that rely on a natural loading, such as the ocular pulse, and that do not require any artificial manipulations in IOP or CSFP may find priority for translation as part of a biomechanical clinical test, as this would avoid any eye manipulation in patients.

Copyright © 2018. Kugler Publications. All rights reserved.

4. Measuring ONH biomechanical properties in patients Ex-vivo studies have shown that the biomechanical properties of ONH connective tissues change with age,40,64 race,65,66 and glaucoma severity.40,67 In-vivo measurements of these properties could therefore potentially serve as strong biomarkers to detect the earliest stage of glaucoma damage and help us profile patients that are at risk of developing disease pathology. At present, in-vivo measurements of ONH biomechanical properties are, in principle, achievable through inverse methods, as described below. 4.1. Inverse FE method The FE method is a tool regularly used by engineers to investigate complex, 3-D structures such as aircraft

505

wings and engines. It is increasingly being used in different areas of medical research.39,68 A FE model of the ONH can predict ONH deformations (initially unknown), given known information about 3-D ONH geometry, tissue biomechanical properties, and boundary/loading conditions. The FE method can also be run in an inverse mode (also referred to as the inverse finite element method or IFEM), where this time the biomechanical properties are unknown, but all other parameters are known, including the loads acting on the ONH tissue (see section 2), the resulting ONH deformations (see section 3), and the geometry of the ONH (as can be derived from OCT). The principle of IFEM is relatively simple and consists in running thousands of FE models (each with a different set of biomechanical properties) until one model predicts ONH deformations that best match those observed clinically. The biomechanical properties for that best-matched model will be assumed to be those for the ONH of the studied patient. IFEM has been widely used as a research tool to extract the biomechanical properties of ocular tissues using ex-vivo experimental data from inflation tests of human and animal eye globes.39,40,66,69,70 While Qian et al. were able to extract the in-vivo biomechanical properties of the retina and choroid in cat eyes using IFEM,71 no studies have quantified the in-vivo biomechanical properties of other ONH tissues such as the LC and peripapillary sclera. This may be because IFEM poses a major challenge: it is extremely computationally expensive and may require hours (if not days) of computational time for a single ONH, which clearly limits its clinical impact. 4.2. Virtual fields method The virtual fields method (VFM) is a more recent and more elegant technique based on the principle of virtual work. VFM can extract the biomechanical properties of tissues given the same inputs required for IFEM, but with drastically superior computational speed. It has, for instance, been used to identify the stiffness of human aortic tissues in vitro.72,73 More recently, Zhang et al.74 have applied VFM to in-vivo deformation data of the ONH (obtained with OCT, 3-D tracking, and ophthalmodynamometry; see Section 3). They found that VFM: 1. was insensitive to rigid body motion (e.g., subject’s head/eye movement);

506

X. Wang et al.

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 7. (a) Flowchart for the implementation of the VFM to extract the biomechanical properties of human ONH tissues. (b) Digital reconstruction of the prelaminar tissues and LC from the OCT volume of the ONH of one healthy subject. (c) Relative position between the isolated region of interest needed for calculation of biomechanical properties with VFM (shown in blue) and the segmented ONH geometry (retina/prelaminar tissues shown in yellow, LC shown in orange). (d) Mesh used in the VFM. Adapted from Zhang et al.74

2. provided estimates of LC biomechanical properties even though the LC was only partially visible (as is common in OCT); 3. only required knowledge of IOP changes (as can be obtained clinically) but not CSFP changes; 4. was 2 orders of magnitude faster than IFEM; 5. was found to extract LC stiffness with a 0.227% error through numerical verification; and 6. was able to extract an elastic modulus of 189.1 kPa for the LC, and an elastic modulus of 100.3 kPa for the prelaminar tissues in a first tested patient (within the range of ex-vivo values)75-78 (Fig. 7). While VFM requires further ex-vivo and in-vivo validation, it may have great potential in identifying patient-specific ONH biomechanical properties in the clinic.

5. Mapping the connective tissue microstructure of ONH tissues in vivo

4.3. Prefitting method Sigal and colleagues have developed an elegant prefitting method that can be used to estimate the ONH stress/strain levels (induced by IOP) and biomechanical properties of a patient given inputs from OCT imaging.79 For this technique, numerous FE models representing a wide range of eye and ONH characteristics need to

Collagen fiber orientation has been demonstrated to be a key determinant of ONH biomechanics and can significantly influence ONH deformations induced by IOP, CSFP, or optic nerve traction. In humans, collagen fibers typically follow a ring pattern in the peripapillary sclera (highly anisotropic) and a radial arrangement in the LC, although LC anisotropy is not as strong as in the peri-

be built and run, which when combined with statistical models can allow for predictions of non-measurable parameters. This method has some advantages, as it allows quick calculations of stress/strain levels and stiffness of ONH tissues using measurable parameters such as eye size, IOP, scleral canal size, or LC displacement. However, it should be used with caution, as its current implementation is limited to linear, homogeneous, and isotropic material properties as well as simplified ONH geometries. Such a method would likely require further validation with in-vivo data to provide reliable estimates of the output variables.

In-vivo characterization of optic nerve head biomechanics for improved glaucoma management

507

Copyright © 2018. Kugler Publications. All rights reserved.

Fig. 8. (a) Fundus image of the rat ONH. (b) Collagen fiber orientations (color map) in the peripapillary sclera, approximately 160 μm posterior to the retinal pigment epithelium. Color scale: -90° to 90°. S, T, I, N: superior, temporal, inferior, nasal. (c) Preferred collagen fiber orientations in the peripapillary sclera showing a ring pattern. Adapted from Baumann et al.84

papillary sclera.80,81 Such an arrangement is believed to shield the ONH from mechanical insult by limiting scleral canal expansion with IOP and tethering the LC into the canal wall.81 Interestingly, key differences in collagen fiber organization have been reported between normal and glaucoma eyes,82,83 suggesting that a disrupted collagen fiber organization (e.g., malformed scleral ring) could potentially lead to the development and progression of glaucoma. A note of caution is that that these studies were cross-sectional, so it is unknown whether the change in collagen fiber orientation in the glaucoma eyes was a result of glaucomatous collagen remodeling or a precursor to disease. Hence, further investigation is necessary. Nevertheless, quantitatively mapping collagen fiber organization in vivo in human subjects may prove critical to improve glaucoma diagnosis and management. Recently, polarization-sensitive OCT has been used to evaluate the volumetric microstructural tissue organization in rat peripapillary sclera in vivo. This was done by taking advantage of the birefringence caused by collagen fibers.84 In that study, a peripapillary scleral fiber ring was observed (Fig. 8), which was validated against conventional histology and found consistent with other ex-vivo studies.85 Translating polarization-sensitive OCT to the clinic could be considered in the near future; however, challenges such as light-penetration limits and poor birefringence measurements in the deepest ONH tissues remain.

6. In-vivo ONH biomechanics: future prospects In-vivo ONH biomechanics is still in its infancy, and the most pressing concern is to further demonstrate

and validate that the biomechanical properties of ONH tissues are indeed measurable in vivo. Improvements in OCT hardware, including adaptive optics,86 swept source,87 multi-wavelength, phase-sensitive technology,63 micro-imaging,88 and image processing techniques such as adaptive compensation,89,90 are likely to push the quality and availability of in-vivo biomechanical measurements to the next level. Other imaging approaches such as Brillouin microscopy91 and shear-wave elastography92 may show promise if they can be successfully applied to the ONH, but they also exhibit serious limitations, since the reported elastic moduli typically differ from direct measures by several orders of magnitude. Computational algorithms such as 3-D tracking, IFEM, VFM, and prefitting will need to be further validated and optimized for speed (e.g., using Graphics Processing Unit programming) if we ever want to see them available in clinical practice. Furthermore, we are just beginning to scratch the surface in our understanding of the loads acting on the ONH in vivo. It was only recently discovered that optic nerve traction generates large ONH strains during eye movements, and other loads such as orbital fat pressure,93 the tension transmitted by the ciliary muscle,94 and vascular pulsations from the central retinal trunk, may prove important in glaucoma pathogenesis. Although these forces are present in all eyes, all eyes do not develop glaucoma, so some additional measures of susceptibility are needed. Translating ONH biomechanics to the clinic will first require several longitudinal studies in large cohorts, driven by strong collaborations between engineers and clinicians. One will have to assess whether strain or stiffness (and for which mechanical range) is a better predictor of visual field progression and a better biomarker for early glaucoma. Also, it is plausible, if not very likely, that we

508

will discover multiple forms of biomechanical insults in glaucoma (e.g., NTG patients may suffer abnormal loadings acting on the ONH that are not IOP-related). Only then may we consider adding ONH biomechanical testing as part of the battery of clinical tools available

References

Copyright © 2018. Kugler Publications. All rights reserved.

1.

Quigley HA, Addicks EM, Green WR, Maumenee AE. Optic nerve damage in human glaucoma. II. The site of injury and susceptibility to damage. Arch Ophthalmol. 1981;99:635-649. 2. Sommer A, Tielsch JM, Katz J, et al. Relationship between intraocular pressure and primary open angle glaucoma among white and black Americans. The Baltimore Eye Survey. Arch Ophthalmol. 1991;109:1090-1095. 3. Leske MC, Wu SY, Hennis A, Honkanen R, Nemesure B. Risk factors for incident open-angle glaucoma: the Barbados Eye Studies. Ophthalmology. 2008;115:85-93. 4. Heijl A, Leske MC, Bengtsson B, Hyman L, Bengtsson B, Hussein M. Reduction of intraocular pressure and glaucoma progression: results from the Early Manifest Glaucoma Trial. Arch Ophthalmol. 2002;120:1268-1279. 5. Leske MC, Heijl A, Hussein M, Bengtsson B, Hyman L, Komaroff E. Factors for glaucoma progression and the effect of treatment: the early manifest glaucoma trial. Arch Ophthalmol. 2003;121:48-56. 6. Quigley HA. Glaucoma: macrocosm to microcosm the Friedenwald lecture. Invest Ophthalmol Vis Sci. 2005;46:2662-2670. 7. Leske MC. Open-angle glaucoma -- an epidemiologic overview. Ophthalmic Epidemiol. 2007;14:166-172. 8. Burgoyne CF, Downs JC, Bellezza AJ, Suh JK, Hart RT. The optic nerve head as a biomechanical structure: a new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage. Prog Retin Eye Res. 2005;24:39-73. 9. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Predicted extension, compression and shearing of optic nerve head tissues. Exp Eye Res 2007;85:312-322. 10. Kirwan RP, Crean JK, Fenerty CH, Clark AF, O’Brien CJ. Effect of cyclical mechanical stretch and exogenous transforming growth factor-beta 1 on matrix metalloproteinase-2 activity in lamina cribrosa cells from the human optic nerve head. J Glaucoma. 2004;13:327-334. 11. Quigley HA, Addicks EM. Regional differences in the structure of the lamina cribrosa and their relation to glaucomatous optic nerve damage. Arch Ophthalmol-Chic. 1981;99:137. 12. Kupersmith MJ, Sibony P, Mandel G, Durbin M, Kardon RH. Optical coherence tomography of the swollen optic nerve head: deformation of the peripapillary retinal pigment epithelium layer in papilledema. Invest Ophthalmol Vis Sci. 2011;52:6558-6564.

X. Wang et al.

in glaucoma practice. Finally, future personalized treatments for glaucoma patients involving modulating ONH biomechanical properties could become a reality in the not-too-distant future.

13. Wang N, Xie X, Yang D, et al. Orbital cerebrospinal fluid space in glaucoma: the Beijing intracranial and intraocular pressure (iCOP) study. Ophthalmology. 2012;119:2065-2073 e2061. 14. Berdahl JP, Fautsch MP, Stinnett SS, Allingham RR. Intracranial pressure in primary open angle glaucoma, normal tension glaucoma, and ocular hypertension: a case-control study. Invest Ophthalmol Vis Sci. 2008;49:5412-5418. 15. Sibony PA. Gaze evoked deformations of the peripapillary retina in papilledema and ischemic optic neuropathy. Invest Ophthalmol Vis Sci. 2016;57:4979-4987. 16. Wang X, Beotra MR, Tun TA, et al. In vivo 3-dimensional strain mapping confirms large optic nerve head deformations following horizontal eye movements. Invest Ophthalmol Vis Sci. 2016;57:5825-5833. 17. Chang MY, Shin A, Park J, et al. Deformation of optic nerve head and peripapillary tissues by horizontal duction. A J Ophthalmol. 2017;174:85-94. 18. Wang X, Rumpel H, Lim WEH, et al. Finite element analysis predicts large optic nerve head strains during horizontal eye movements. Invest Ophthalmol Vis Sci. 2016;57:2452-2462. 19. Wang X, Rumpel H, Lim WEH, et al. Author Response: Peripapillary suprachoroidal cavitation, parapapillary gamma zone and optic disc rotation due to the biomechanics of the optic nerve dura mater. Invest Ophthalmol Vis Sci. 2016;57:43744375. 20. Demer JL. Optic nerve sheath as a novel mechanical load on the globe in ocular duction. Invest Ophthalmol Vis Sci. 2016;57:1826-1838. 21. Ghosh A, Collins MJ, Read SA, Davis BA. Axial length changes with shifts of gaze direction in myopes and emmetropes. Invest Ophthalmol Vis Sci. 2012;53:6465-6471. 22. Girard MJ, Dupps WJ, Baskaran M, et al. Translating ocular biomechanics into clinical practice: current state and future prospects. Curr Eye Res. 2015;40:1-18. 23. Strouthidis NG, Girard MJ. Altering the way the optic nerve head responds to intraocular pressure-a potential approach to glaucoma therapy. Curr Opin Pharmacol. 2013;13:83-89. 24. Hoffmann EM, Grus FH, Pfeiffer N. Intraocular pressure and ocular pulse amplitude using dynamic contour tonometry and contact lens tonometry. BMC Ophthalmol. 2004;4:4. 25. Danesh-Meyer HV, Papchenko T, Tan Y-W, Gamble GD. Medically controlled glaucoma patients show greater increase in intraocular pressure than surgically controlled patients with the water drinking test. Ophthalmology. 2008;115:1566-1570.

Copyright © 2018. Kugler Publications. All rights reserved.

In-vivo characterization of optic nerve head biomechanics for improved glaucoma management 26. Morgan WH, Lind CRP, Kain S, Fatehee N, Bala A, Yu D-Y. Retinal vein pulsation is in phase with intracranial pressure and not intraocular pressure. Invest Ophthalmol Vis Sci. 2012;53:46764681. 27. Andresen M, Hadi A, Petersen LG, Juhler M. Effect of postural changes on ICP in healthy and ill subjects. Acta Neurochirurgica. 2014;157:109-113. 28. Kim YW, Girard MJ, Mari JM, Jeoung JW. Anterior displacement of lamina cribrosa during valsalva maneuver in young healthy eyes. PLoS One. 2016;11:e0159663. 29. Prata TS, De Moraes CGV, Kanadani FN, Ritch R, Paranhos Jr A. Posture-induced intraocular pressure changes: considerations regarding body position in glaucoma patients. Surv Ophthalmol. 2010;55:445-453. 30. Zhang Z, Wang X, Jonas JB, et al. Valsalva manoeuver, intra-ocular pressure, cerebrospinal fluid pressure, optic disc topography: Beijing intracranial and intra-ocular pressure study. Acta Ophthalmol. 2014;92:e475-e480. 31. Wang X, Fisher LK, Milea D, Jonas JB, Girard MJ. Predictions of optic nerve traction forces and peripapillary tissue stresses following horizontal eye movements.Invest Ophthalmol Vis Sci. 2017;58(4):2044-2053. 32. Fechtner RD, Weinreb RN. Mechanisms of optic nerve damage in primary open angle glaucoma. Surv Ophthalmol. 1994;39:23-42. 33. Burgoyne CF, Downs JC, Bellezza AJ, Suh J-KF, Hart RT. The optic nerve head as a biomechanical structure: a new paradigm for understanding the role of IOP-related stress and strain in the pathophysiology of glaucomatous optic nerve head damage. Prog Retin Eye Res. 2005;24:39-73. 34. Quigley HA, McKinnon SJ, Zack DJ, et al. Retrograde axonal transport of BDNF in retinal ganglion cells is blocked by acute IOP elevation in rats. Invest Ophthalmol Vis Sci. 2000;41:3460-3466. 35. Girard MJ, Tun TA, Husain R, et al. Lamina cribrosa visibility using optical coherence tomography: comparison of devices and effects of image enhancement techniques. Invest Ophthalmol Vis Sci. 2015;56:865-874. 36. Crawford Downs J, Roberts MD, Sigal IA. Glaucomatous cupping of the lamina cribrosa: a review of the evidence for active progressive remodeling as a mechanism. Exp Eye Res. 2011;93:133-140. 37. Roberts MD, Grau V, Grimm J, et al. Remodeling of the connective tissue microarchitecture of the lamina cribrosa in early experimental glaucoma. Invest Ophthalmol Vis Sci. 2009;50:681-690. 38. Tun TA, Atalay E, Baskaran M, et al. Association of functional loss with the biomechanical response of the optic nerve head to acute transient intraocular pressure elevations. JAMA Ophthalmol. 2018;136(2):184-192. 39. Girard MJA, Downs JC, Bottlang M, Burgoyne CF, Suh JKF. Peripapillary and posterior scleral mechanics-part ii: experimental and inverse finite element characterization. J Biomech Eng T Asme. 2009;131. 40. Coudrillier B, Tian J, Alexander S, Myers KM, Quigley HA, Nguyen TD. Biomechanics of the human posterior sclera: age- and glaucoma-related changes measured using inflation testing. Invest Ophthalmol Vis Sci. 2012;53:1714-1728.

509

41. Sigal IA, Wang B, Strouthidis NG, Akagi T, Girard MJ. Recent advances in OCT imaging of the lamina cribrosa. Br J Ophthalmol. 2014;98(Suppl 2):ii34-39. 42. Agoumi Y, Sharpe GP, Hutchison DM, Nicolela MT, Artes PH, Chauhan BC. Laminar and prelaminar tissue displacement during intraocular pressure elevation in glaucoma patients and healthy controls. Ophthalmology. 2011;118:52-59. 43. Strouthidis NG, Fortune B, Yang H, Sigal IA, Burgoyne CF. Effect of acute intraocular pressure elevation on the monkey optic nerve head as detected by spectral domain optical coherence tomography. Invest Ophthalmol Vis Sci. 2011;52:9431-9437. 44. Fazio MA, Johnstone JK, Smith B, Wang L, Girkin CA. Displacement of the lamina cribrosa in response to acute intraocular pressure elevation in normal individuals of african and european descent. Invest Ophthalmol Vis Sci. 2016;57:3331-3339. 45. Lee EJ, Kim TW, Weinreb RN. Reversal of lamina cribrosa displacement and thickness after trabeculectomy in glaucoma. Ophthalmology. 2012;119:1359-1366. 46. Reis AS, O’Leary N, Stanfield MJ, Shuba LM, Nicolela MT, Chauhan BC. Laminar displacement and prelaminar tissue thickness change after glaucoma surgery imaged with optical coherence tomography. Invest Ophthalmol Vis Sci. 2012;53:5819-5826. 47. Strouthidis NG, Fortune B, Yang H, Sigal IA, Burgoyne CF. Longitudinal change detected by spectral domain optical coherence tomography in the optic nerve head and peripapillary retina in experimental glaucoma. Invest Ophthalmol Vis Sci. 2012;52:1206-1219. 48. Wu Z, Xu G, Weinreb RN, Yu M, Leung CK. Optic nerve head deformation in glaucoma: a prospective analysis of optic nerve head surface and lamina cribrosa surface displacement. Ophthalmology. 2015;122(7):1317-29. 49. Lee EJ, Kim TW, Weinreb RN, Kim H. Reversal of lamina cribrosa displacement after intraocular pressure reduction in open-angle glaucoma. Ophthalmology. 2013;120:553-559. 50. Park HY, Shin HY, Jung KI, Park CK. Changes in the lamina and prelamina after intraocular pressure reduction in patients with primary open-angle glaucoma and acute primary angle-closure. Invest Ophthalmol Vis Sci. 2014;55:233-239. 51. Seo JH, Kim TW, Weinreb RN. Lamina cribrosa depth in healthy eyes. Invest Ophthalmol Vis Sci 2014;55:1241-1251. 52. Lee SH, Yu DA, Kim TW, Lee EJ, Girard MJ, Mari JM. Reduction of the lamina cribrosa curvature after trabeculectomy in glaucoma. Invest Ophthalmol Vis Sci. 2016;57:5006-5014. 53. Tun TA, Thakku SG, Png O, et al. Shape changes of the anterior lamina cribrosa in normal, ocular hypertensive, and glaucoma eyes following acute intraocular pressure elevation. Invest Ophthalmol Vis Sci. 2016; 57(11):4869-4877. 54. Thakku SG, Tham YC, Baskaran M, et al. A global shape index to characterize anterior lamina cribrosa morphology and its determinants in healthy indian eyes. Invest Ophthalmol Vis Sci. 2015;56:3604-3614. 55. Girard MJ, Strouthidis NG, Desjardins A, Mari JM, Ethier CR. In vivo optic nerve head biomechanics: performance testing of a three-dimensional tracking algorithm. J R Soc Interface. 2013;10:20130459.

X. Wang et al.

Copyright © 2018. Kugler Publications. All rights reserved.

510 56. Girard MJA, Beotra MR, Chin KS, et al. In vivo 3-dimensional strain mapping of the optic nerve head following intraocular pressure lowering by trabeculectomy. Ophthalmology. 2016;123:1190-1200. 57. Chuangsuwanich T, Birgersson KE, Thiery A, Thakku SG, Leo HL, Girard MJ. Factors influencing lamina cribrosa microcapillary hemodynamics and oxygen concentrations. Invest Ophthalmol Vis Sci. 2016;57:6167-6179. 58. Beotra M, Wang X, Tun TA, et al. In vivo 3-dimensional strain mapping of the lamina cribrosa in healthy, ocular hypertensive and glaucoma eyes following acute intraocular pressure elevation. Invest Ophthalmol Vis Sci. 2018;59(1):260-272. 59. Ren R, Zhang X, Wang N, Li B, Tian G, Jonas JB. Cerebrospinal fluid pressure in ocular hypertension. Acta Ophthalmol. 2011;89:e142-148. 60. Fazio MA, Turner D, Girkin CA, Downs JC, Bruno L. Real-time in vivo 2-d deformations of the optic nerve head using OCT imaging. Invest Ophthalmol Vis Sci. 2016;57(12). 61. Sigal IA, Judisch A, Tran H, et al. High-resolution mapping of in-vivo stretch and compression of the lamina cribrosa in response to acute changes in intraocular and/or intracranial pressures. Invest Ophthalmol Vis Sci. 2016;57. 62. Dragostinoff N, Werkmeister RM, Klaizer J, Groschl M, Schmetterer L. Time course and topographic distribution of ocular fundus pulsation measured by low-coherence tissue interferometry. J Biomed Opt. 2013;18:121502. 63. O’Hara KE, Schmoll T, Vass C, Leitgeb RA. Measuring pulse-induced natural relative motions within human ocular tissue in vivo using phase-sensitive optical coherence tomography. J Biomed Opt. 2013;18:121506. 64. Girard MJA, Suh JKF, Bottlang M, Burgoyne CF, Downs JC. Scleral biomechanics in the aging monkey eye. Invest Ophthalmol Vis Sci. 2009;50:5226-5237. 65. Fazio MA, Grytz R, Morris JS, Bruno L, Girkin CA, Downs JC. Human scleral structural stiffness increases more rapidly with age in donors of African descent compared to donors of European descent. Invest Ophthalmol Vis Sci. 2014;55:71897198. 66. Grytz R, Fazio MA, Libertiaux V, et al. Age- and race-related differences in human scleral material properties. Invest Ophthalmol Vis Sci. 2014;55:8163-8172. 67. Girard MJA, Suh JKF, Bottlang M, Burgoyne CF, Downs JC. Biomechanical changes in the sclera of monkey eyes exposed to chronic IOP elevations. Invest Ophthalmol Vis Sci. 2011;52:5656-5669. 68. Wang X, Neely AJ, McIlwaine GG, Lueck CJ. Multi-scale analysis of optic chiasmal compression by finite element modelling. J Biomech. 2014;47:2292-2299. 69. Grytz R, Fazio MA, Girard MJ, et al. Material properties of the posterior human sclera. J Mech Behav Biomed Mater. 2014;29:602-617. 70. Coudrillier B, Boote C, Quigley HA, Nguyen TD. Scleral anisotropy and its effects on the mechanical response of the optic nerve head. Biomech Model Mechanobiol. 2013;12:941-963. 71. Qian X, Zhang K, Liu Z. A method to determine the mechani-

72.

73.

74.

75.

76. 77.

78.

79.

80.

81.

82.

83.

84.

85.

86.

cal properties of the retina based on an experiment in vivo. Biomed Mater Eng. 2015;26(Suppl 1):S287-297. Kim J-H, Avril S, Duprey A, Favre J-P. Experimental characterization of rupture in human aortic aneurysms using a full-field measurement technique. Biomech Model Mechan. 2012;11:841-853. Avril S, Badel P, Duprey A. Anisotropic and hyperelastic identification of in vitro human arteries from full-field optical measurements. J Biomech. 2010;43:2978-2985. Zhang L, Thakku SG, Beotra MR, et al. Verification of a virtual fields method to extract the mechanical properties of human optic nerve head tissues in vivo. Biomech Model Mechanobiol. 2017;16(3):871-87. Chen KN, Weiland JD. Mechanical properties of orbital fat and its encapsulating connective tissue. J Biomech Eng T Asme. 2011;133(6):064505. Chen K, Weiland JD. Mechanical characteristics of the porcine retina in low temperatures. Retina. 2012;32:844-847. Chen K, Rowley AP, Weiland JD, Humayun MS. Elastic properties of human posterior eye. J Biomed Mater Res A. 2014;102:20012007. Sigal IA, Flanagan JG, Tertinegg I, Ethier CR. Modeling individual-specific human optic nerve head biomechanics. Part II: influence of material properties. Biomech Model Mechanobiol. 2009;8:99-109. Sigal IA, Grimm JL, Schuman JS, Kagemann L, Ishikawa H, Wollstein G. A method to estimate biomechanics and mechanical properties of optic nerve head tissues from parameters measurable using optical coherence tomography. IEEE Trans Med Imaging. 2014;33:1381-1389. Jones HJ, Girard MJ, White N, et al. Quantitative analysis of three-dimensional fibrillar collagen microstructure within the normal, aged and glaucomatous human optic nerve head. J R Soc Interface. 2015;12(106). Zhang L, Albon J, Jones H, et al. Collagen microstructural factors influencing optic nerve head biomechanics. Invest Ophthalmol Vis Sci. 2015;56:2031-2042. Pijanka JK, Coudrillier B, Ziegler K, et al. Quantitative mapping of collagen fiber orientation in non-glaucoma and glaucoma posterior human sclerae. Invest Ophthalmol Vis Sci. 2012;53:5258-5270. Coudrillier B, Pijanka JK, Jefferys JL, et al. Glaucoma-related changes in the mechanical properties and collagen micro-architecture of the human sclera. PLoS One. 2015;10:e0131396. Baumann B, Rauscher S, Glösmann M, et al. Peripapillary rat sclera investigated in vivo with polarization-sensitive optical coherence tomography. Invest Ophthalmol Vis Sci. 2014;55:7686-7696. Girard MJA, Dahlmann-Noor A, Rayapureddi S, et al. Quantitative mapping of scleral fiber orientation in normal rat eyes. Invest Ophthalmol Vis Sci. 2011;52:9684-9693. Nadler Z, Wang B, Wollstein G, et al. Automated lamina cribrosa microstructural segmentation in optical coherence tomography scans of healthy and glaucomatous eyes. Biomed Opt Express. 2013;4:2596-2608.

In-vivo characterization of optic nerve head biomechanics for improved glaucoma management

Copyright © 2018. Kugler Publications. All rights reserved.

87. Wang B, Nevins JE, Nadler Z, et al. In vivo lamina cribrosa micro-architecture in healthy and glaucomatous eyes as assessed by optical coherence tomography. Invest Ophthalmol Vis Sci. 2013;54:8270-8274. 88. Ang M, Konstantopoulos A, Goh G, et al. Evaluation of a micro-optical coherence tomography for the corneal endothelium in an animal model. Sci Rep. 2016;6:29769. 89. Girard MJ, Strouthidis NG, Ethier CR, Mari JM. Shadow removal and contrast enhancement in optical coherence tomography images of the human optic nerve head. Invest Ophthalmol Vis Sci. 2011;52:7738-7748. 90. Mari JM, Strouthidis NG, Park SC, Girard MJA. Enhancement of lamina cribrosa visibility in optical coherence tomography images using adaptive compensation. Invest Ophthalmol Vis Sci. 2013;54:2238-2247.

511

91. Scarcelli G, Pineda R, Yun SH. Brillouin optical microscopy for corneal biomechanics. Invest Ophthalmol Vis Sci. 2012;53:185190. 92. Dikici AS, Mihmanli I, Kilic F, et al. In vivo evaluation of the biomechanical properties of optic nerve and peripapillary structures by ultrasonic shear wave elastography in glaucoma. Iran J Radiol. 2016;13:e36849. 93. Riemann CD, Foster JA, Kosmorsky GS. Direct orbital manometry in patients with thyroid-associated orbitopathy. Ophthalmology. 1999;106:1296-1302. 94. Croft MA, Lütjen-Drecoll E, Kaufman PL. Age-related posterior ciliary muscle restriction – A link between trabecular meshwork and optic nerve head pathophysiology. Exp Eye Res. 2017;158:187-189.

Copyright © 2018. Kugler Publications. All rights reserved.

Index A Accommodation 295-298, 300-302, 307-315, 326, 332, 386, 388 Acoustic 33-38, 121, 140, 141, 159-162, 224, 225, 299, 308, 325 Acoustic radiation force elasticity microscope (ARFEM) 34-40 Advanced glycation endproducts (AGES) 123, 220, 300, 307, 311, 384, 385, 387, 391, 396, 417, 421, 490 Aging 123, 220, 296, 297, 300, 302, 307, 311, 313, 339, 349, 355, 375, 405, 406, 443, 445, 447, 450-452, 455, 456, 459, 491 Air puff (See also Ocular Response Analyzer and Corvis ST) 169, 173-176, 178-182, 203, 205, 211 Analytical model 338, 481 Angle-closure glaucoma (See also glaucoma) 282, 285, 287, 378, 503 Anisotropy (See also Material Properties) 4, 31, 51, 81, 82, 84, 85, 87, 89, 104, 120, 132, 134, 312, 363-375, 448, 458, 488-491, 500, 506 Anterior chamber angle 282-285 Aqueous humor 63, 64, 67, 68, 73, 134, 281-285, 297, 323, 325, 333, 338, 347, 348, 351, 353, 355, 356, 379 Astrocyte 405, 406, 455, 459 reactive 432, 433 Autophagy 432, 437 Axial length 179, 220, 285, 370, 383-387, 391-396, 498

Copyright © 2018. Kugler Publications. All rights reserved.

B Biomechanical assessment 140, 148, 170, 182, 200, 203, 213 Body position 351, 353, 354 Boundary conditions 18, 70, 93, 96, 134, 141, 451, 453, 474, 475 Brillouin microscopy 31, 33, 40, 118, 140, 159, 162-167, 213, 224, 225, 270, 308 C Calcium 432, 435, 436 Calcium intracelular 435-436 Central corneal thickness (CCT) 75, 76, 135, 175-180, 182, 200, 201, 211, 357, 377 Cerebrospinal fluid pressure (CSFP) 405, 406, 421, 424, 449, 450, 465-475, 497-499, 501, 505, 506 Cohesive tensile strength 263, 264 Collagen 4-7, 11, 15-20, 22-25, 31-33, 38-41, 45-56, 63-71, 75-77, 81-89, 91, 94, 96, 108, 111, 117, 147, 148, 153, 161, 163, 164, 166, 171, 182, 199, 217-222, 224-227, 233, 234, 236, 238, 241, 247, 248, 250, 253, 262, 263, 268, 271, 281, 295, 310, 311, 323, 324, 326, 348, 349, 352, 363-375, 389, 390-397, 445, 447, 448, 450, 452, 454-456, 458, 465, 474, 475, 485, 486, 488-491, 500, 506, 507 anisotropy 4, 31, 81-89, 363-375, 448, 488-491, 500, 506 crosslinking 7, 17, 18, 24, 31, 33, 51, 91, 94, 96, 147, 153, 163, 171, 182, 199, 217-222, 233, 234, 236, 238, 241, 242, 394, 397, 450 crimp (or crimping) 5, 16, 348, 352, 363, 389, 390, 392, 393, 394, 396, 397, 452, 490, 491 fibrils 5-7, 9-11, 15-25, 31, 45-50, 52, 55-56, 63-73 447, 448, 452, 456, heterogeneity 364-365, microstructure 40, 41, 363, 455 remodeling 458, 507, sliding 23, 393, 395-397

Copyright © 2018. Kugler Publications. All rights reserved.

514

swelling interaction 63-78 turnover 25, 395, types 15-25, 63-78, 81, 311 Computational model 24, 248, 251 Confocal microscopy 10, 24, 238, 239 Continuum mechanics 65, 67, 87, 324 Convection 332, 333, 348 Conventional outflow (See also outflow) 351, 355, 356 Cornea 3-11, 15-22, 24, 25, 31-41, 49-52, 54, 56, 63, 64, 67, 69, 73, 75-78, 81-85, 87-89, 91-97, 103, 108-111, 113, 117-121, 123, 128, Corneal biomechanics 3, 31, 41, 63, 114, 147, 152, 153, 156, 169, 173, 180-182, 199, 211, 264, 266, 267, 273 Corneal curvature 5, 8, 9, 76, 138, 152, 178, 182, 246, 247, 249, 251, 254, 285 Corneal endothelium 73, 222, 237 Corneal hydration 8-10, 63, 64 stroma 63-78 Corneal Hysteresis 170, 200, 251 Corneal layers 128, 163, 219 Corneal microstructure 89, 245 Corneal stiffness 121, 128, 134, 141, 148, 224, 225, 233, 236, 240, 242, 246, 249, 380 Corneoscleral shell 355, 357, 358, 378, 380, 447, 449, 451, 453, 486 dynamic response 377-381 Corvis ST 169, 173, 174, 175, 176, 178, 179, 180, 181, 182, 203, 205, 211 Corvis Biomechanical Index (CBI) 178, 179, 211 Creep 8, 9, 17, 309, 326, 380, 393-397 Creep rate 393, 394 Crimp 5, 16, 348, 363, 389, 392, 394, 490, 491 Crosslinking Accelerated 237, 240-241 Athens Protocol 239-240 Customized 123 Cytotoxic threshold 233 Demarcation line 237-238 Dresden protocol 233, 235-241 Enzymatic 218-219 Irradiation dose 236 Kmax 237 Non-enzymatic 219, 241 Oxygen concentration 234-235 Photochemical reaction 221-222, 234, 237 Pulsed 237-238 Reactive oxygen species 221, 234-235, 241 Riboflavin 237, 257 Diffusion 239 Transepithelial 239 UV-light 234-242, 257 Crosslinks 24, 166, 217-220, 222, 224, 234, 235, 239, 311, 391, 393, 394, 396, 397 Crystalline lens 31, 140, 141, 227, 313

Index

515

Cyclic softening 394, 396, 397

Copyright © 2018. Kugler Publications. All rights reserved.

D Damped natural frequency (DNF) 123 Decorin 18, 63, 390, 391, 393 Deflection amplitude 175, 176 Defocus 384, 385, 387-389, 396 peripheral 387, 389 Deformation amplitude 121, 140, 148, 174-176, 178-181, 201, 205 Differential interference contrast (DIC) 46, 47, 55, 95, 364, 365 Diffusion 104, 222, 227, 234, 235, 237, 239, 240, 332, 333, 335, 348, 408, 455, 499 Digital image correlation 95, 108, 364 Displacement 8, 33-38, 46, 48, 49, 55, 56, 67, 70-72, 87, 93-97, 104, 108-111, 113, 114, 118-121, 123, 128, 140, 148-156, 203, 249, 253, 285, 300, 313, 327, 378, 447, 471, 472, 474, 475, 486, 490, 501, 506 Drug delivery 332, 333 Durotaxis 51, 52 Dynamic excitation 119 Ectasia 11, 22, 91, 114, 117, 147, 156, 164-166, 180-182, 199, 200, 203, 205, 211, 213, 233, 236, 237, 240, 246, 248, 254, 258, 268, 270 E Elastic anisotropy (See also Anistropy) 132-134 Elastic fibers 18-20, 67, 491 Elastic modulus (See also Young’s Modulus of Elasticity) 4-6, 10, 18, 32-34, 36, 38, 39, 94, 114, 118, 119, 121-123, 125, 128, 129, 132-135, 138-141, 147, 160-164, 166, 170, 187-193, 189, 241, 247-249, 252-257, 287, 296-299, 325, 326, 337, 434, 481, 506 Elastic wave propagation 123, 128, 137, 138, 140 Elastic waves 119, 121 Elasticity 3-6, 10, 22, 31-35, 38-41, 51, 56, 68, 71, 118-120, 123, 128, 134, 135, 138-141, 163, 166, 170, 173, 263, 298, 302, 307-312, 314, 325, 330, 352, 356 Elastogram 113, 119, 138, 140 Elastography (see also Optical Coherence Elastography and Ultrasound elastography) Emmetropia 76, 383, 384-386, 396 Emmetropization 383-389, 392-397 Endothelin 421, 424 Epigenetics 438 Episcleral venous pressure 351, 378 Epithelium 21, 78, 82, 117, 128, 138, 164, 222, 223, 227, 239, 240, 248, 282, 287, 296, 332, 334-336, 338, 389, 394 Equilibrium modulus 287, 380, 422, 486 Extracellular matrix (ECM) 45-54, 56, 81, 217, 219, 443, 445, 450, 455, 457, 458 F Femtosecond laser 11, 34, 35, 37, 75, 181, 240, 250, 261, 310 Fibroblast 46, 48, 50-52, 405, 406 Fibroblast growth factor (FGF) 52, 54 Finite element analysis (FEA) 245, 246, 251, 267, 268, 270

516

Finite element method (FEM) 52, 87, 104, 114, 121, 134, 135, 137, 258 Inverse 363, 365-368, 505-507 Fluid-structure interface (FSI) 137 Focal plane 348, 383-388, 394-397 Formaldehyde releasers (FARS) 220, 221 Fourier domain mode-locked (FDML) 138, 139 Fourier fast transform (FFT) 88, 128 G Glaucoma 282, 285, 287, 378, 503 cellular response 417, 443, 453, 455 cupping 357, 405-425 non-human primate model 405-425, 501 ONH phenotype 424 pathogenesis 431-432, 447, 458, 468, 475, 491, 498, 507, Glial fibrillary acid protein (GFAP) 433 Glycosaminoglycan (GAG) 7, 18, 40, 63-68, 71, 72, 77 Glycosylation 220

Copyright © 2018. Kugler Publications. All rights reserved.

H Heterogeneity (See also collagen) collagen 364-365 Heterogeneity (See also material properties) material properties 7, 22, 123, 364-365, 491, 500, Hooke’s law 3, 34, 94, 119 Hyperelasticity 81, 352 Hyperopia 75, 233, 258, 388 Hyperopic defocus 387 Hysteresis 121, 132, 134, 170, 178, 180, 181, 200, 201, 251 Idiopathic intracranial hypertension (IIH) 465, 469-471 Imaging 33, 35, 37, 38, 40, 46-48, 51, 54-56, 93-97, 103-108, 111, 114, 118, 119, 123, 128, 135, 138-141, 148-150, 152, 159, 160, 165, 166, 173, 203, 217, 218, 225, 227, 254, 287, 299, 308, 325, 333, 356, 363, 364, 367, 369, 416, 421, 422, 449, 450, 454-459, 469, 471, 472, 490-492, 498-500, 505-507 I Incompressibility 87, 88, 89, 284, 285 Incompressible material 88 Infectious Keratitis 233, 240-242 Inflation testing 91, 92, 147, 224, 225, 254, 299, 452 Inhomogeneous 87, 117, 326, 372, 422, 453, 489, 490 Instantaneous modulus 287, 380, 381, 486 Intraocular pressure (IOP) 63, 76-78, 109, 110, 119-121, 128, 132, 134, 138, 139, 147, 148, 170, 174-180, 182, 200, 203, 226, 246, 248, 253, 256, 262, 268, 347-349, 351-358, 363-366, 372, 373, 375, 377-381, 405, 406, 408, 410, 416, 417, 421, 422, 424, 443-459, 465-468, 471-475, 480, 482, 484, 486, 487, 488, 490-492, 497-503, 505-508 dynamic 381, 486, 505, fluctuation 347, 349, 351-358 transient fluctuations 355-356

Index

517

Inverse concave radius 174-176 Inverse finite element method (See also Finite Element Method) 363, 505 Inverse modeling 452, 487, 490, 491 Iontophoresis 223, 239 Iris 281-288, 307, 348 biomechanics 281-288 configuration 282, 284-285 Isotropic (see also Material Properties) 4, 20, 36, 51, 87, 88, 93, 119, 134, 161, 246-248, 257, 296, 298, 337, 374, 480, 485, 489, 492, 506

Copyright © 2018. Kugler Publications. All rights reserved.

K Keratoconus 3, 9, 20-24, 31, 50, 51, 89, 128, 156, 164-166, 169, 173, 176, 177, 180, 199, 203, 217, 233, 251, 253, 258, 267, 348, 349 keratectasia 199, 218, 233, 239, 240 Keratocytes 19, 45, 46, 48, 49, 51, 52, 54, 56, 65, 67 Keratoplasty 24, 25, 50, 87, 166, 251 Kinetics of CXL (See also crosslinking) 234 L Lamellae 7, 8, 10, 11, 15, 16, 18-20, 22, 23, 25, 31, 32, 40, 45, 56, 63, 67, 71, 75, 82, 88, 89, 108, 217, 225, 262, 263, 264, 265, 267, 271, 273, 348, 389, 390, 391, 393, 395, 397 Lamina cribrosa 97, 347-349, 354, 357, 363, 375, 405, 443, 449, 459, 465, 480, 482, 484, 486-491, 497 aging 437-438 biomechanics 449, 454, insertion 432-438, 457, 501 microarchitecture 407-412, 414, 418, 457 microstructure 416, 418-419, 448-449, 454-457, 459 remodeling 444, 455 cell 416, 457 Laplace’s law 93-95, 479, 481, 482 Laser 10, 11, 25, 34, 35, 37, 39, 46, 49, 64, 75, 93, 95, 97, 104, 107, 117, 121, 138, 139, 141, 147, 148, 150, 157, 165-167, 180, 181, 199, 218, 219, 223, 233, 240, 246, 248, 250, 261, 262, 264, 267, 271, 282, 283, 299, 310, 365, 367, 370, 418, 421, 422, 424, 452, 457, 471 Laser Assisted In Situ Keratomileusis (LASIK), (See also Refractive Surgery) 11, 25, 49, 64, 75-77, 117, 147, 166, 180-182, 199, 200, 211, 218, 233, 237, 246-251, 262-268, 270-273 Lens 31, 34, 105, 111, 113, 118, 119, 140, 141, 176, 220-223, 226, 227, 242, 281, 282, 284, 285, 288, 295-302, 307-315, 323, 326, 330-332, 334, 335, 348, 383-389, 396, 486 Lens biomechanics 308 Lens capsule biomechanics 311 Light scattering 45, 159, 299, 364, 455, 488 Line-field low-coherence holography (LF-LCH) 138 Lipofuscin 436, 437 Lumican 63 M Material properties 4, 81, 87, 92-95, 104, 118, 159, 181, 248, 249, 253, 256, 267, 285, 347-349, 352, 357, 358, 393, 417, 447, 448, 450-454, 457, 458, 466, 472-475, 479-481, 483-485, 487-492, 506

518

Anisotropic 4,6, 51, 81-89, 91, 94, 117, 132, 147, 155, 247, 250-251, 286-287, 348, 363-375, 422, 443, 451-454, 458, 480, 489-490, 506 Isotropic 7, 22, 123, 364-365, 491, 500, heterogeneity 4, 20, 36, 51, 85, 87-88, 93, 119, 134, 161, 246-248, 257, 296, 298, 337, 374, 443, 480, 485, 489, 492, 506, M-B mode 123, 138, 141 Mechanical anisotropy (See also anisotropy) 51, 81, 89, 120,132, 134, 363-365, 368, 375 Mechanical characteristics 82 Mechanical testing 5, 123, 128, 134, 140, 363, 365, 380, 454, 480 Mesh 51, 328 Microfibrils 16, 19, 85, 326 Micro-scale spatial resolution 141 Microstructure 4, 6, 39-41, 81, 82, 86, 89, 104, 245, 315, 363, 365, 372, 454, 455, 482, 490, 491, 506 anisotropic 81-89 M-mode 123, 138, 141 Monkey 405, 406, 408, 410-412, 416-418, 421, 422, 424, 487, 488 Murine 123, 140 Myofibroblast 48, 53, 54, 56 Myopia 9, 75, 76, 89, 181, 220, 233, 239-242, 249, 258, 331, 347-349, 363, 377, 383-385, 387-389, 391-397, 451 Myopic defocus 385, 387, 396

Copyright © 2018. Kugler Publications. All rights reserved.

N Nanotopography 54 Neo-Hookean law 89 Non-contact tonometer 170, 182, 199 Non-destructive 118, 148 Non-human primate 301, 311, 367 non-linear continuum mechanics (NLCM) 87 Non-linear elasticity 5, 6 Numerical model 89, 300, 338 numerical simulation 84, 86, 87, 453, 473 O Ocular coat 348, 352, 354, 355, 378, 380, 450, 453 Ocular physiology 355 Ocular pulse amplitude (OPA) 351, 354-357, 453 Ocular Response Analyzer (ORA)  169, 173-176, 178-182, 203, 205, 211 Ocular rigidity 352, 355, 453, 482 Optic nerve head (ONH) 355-357, 364-368, 370-375, 405, 406, 408, 410-412, 416-418, 421, 422, 424, 443-459, 465, 466, 468-475, 479, 481, 482, 484-488, 490-492, 497-501, 503, 505-508 biomechanics 443-459, 471-473, 475, 479, 484-488, 498-499, 506-507 morphology 422, 424, 454, 456, 468, 500 remodeling 349, 405-426, 458-459, 487, 491-492, 499, 507 Optic nerve traction 498, 499, 503, 506, 507 Optical coherence elastography (OCE) 110, 111, 118-121, 123, 128, 132, 134, 135, 137-141 Optical coherence tomography (OCT) 31, 33, 35, 103-108, 111, 114, 118-121, 123, 128, 138-141, 238, 405, 410, 416, 421, 422, 424, 450, 454, 456-501, 503, 505-507

Index

519

Optomechanic 246, 298, 301 Osmotic pressure 63, 64, 67-74, 76, 77, 335 Outflow 282, 283, 338, 347, 351, 352, 355, 356, 377, 378, 381 conventional 347, 351, 355-356 unconventional 347, 356 Oxygen 220-224, 234, 235, 237-240, 242, 254, 324, 339, 347, 348, 351

Copyright © 2018. Kugler Publications. All rights reserved.

P Parameterization 411, 479, 481 Parametric model 454, 479-481, 485-487, 491, 492 Peripapillary sclera 217, 348, 357, 365-368, 370-375, 377, 380, 406, 416, 443-445, 447, 448, 451-455, 457, 458, 473, 485, 490, 491, 497, 505-507 Phase velocities 128, 134, 135 Phase-sensitive OCE (PHS-OCE) (See also Optical Coherence Tomography) 121, 140, 141 Photochemical 221, 222, 234, 235, 237, 238, 241, 242 Photorefractive keratectomy (PRK), (See also Refractive Surgery) 49, 56, 180, 181, 240, 246-248, 264-267, 270, 271, 273 Platelet derived growth factor (PDGF) 49, 51, 52, 54 Porcine 38, 110, 118, 120, 121, 128, 132, 134, 138, 139, 141, 153, 155, 163, 164, 166, 224, 225, 227, 233, 235, 236, 283, 285, 287, 298, 299, 301, 313, 325, 364, 380, 450, 472, 489 Posterior pole 336, 347, 375, 389, 391, 443, 447, 448, 451, 454, 470, 481, 483, 485, 486, 491 Prefitting method 506 Presbyopia 140, 141, 295, 298, 300-302, 307-311, 315 Principal strain 270, 365, 368 Proteoglycan 18, 40, 48, 63, 81, 217, 222, 391, 393 R Rabbit 5, 10, 49, 51, 56, 75-77, 110, 113, 120, 123, 128, 135, 137, 140, 141, 224-226, 235, 236, 241, 242, 261, 299, 333, 335, 336 Radial keratotomy (RK), (See also Refractive Surgery) 246, 247 Rayleigh-lamb frequency equation 134 Reactive Oxygen Species (ROS), (See also crosslinking) 234, 237, 241 Refractive error 245, 246, 254, 328, 331, 383, 384, 386, 397 Refractive index 159-161, 264, 297, 301, 307, 308, 310 Refractive surgery 9, 50, 56, 114, 147, 148, 165, 169, 180-182, 199, 218, 245, 246, 248, 258, 261, 264, 267, 273 Radial keratotomy (RK) 246, 247 Photorefractive keratectomy (PRK) 49, 56, 180, 181, 240, 246-248, 264-267, 270, 271, 273 Laser Assisted In Situ Keratomileusis (LASIK) 11, 25, 49, 64, 75-77, 117, 147, 166, 180-182, 199, 200, 211, 218, 233, 237, 246-251, 262-268, 270-273 Refractive surgery Small Incision Lenticule Extraction (SMILE) 11, 147, 181, 182, 240, 250, 262-268, 270-273 Relaxation rate 123 Relaxation time constants 486 Remodeling 45-48, 348, 349, 355, 365, 372, 375, 383, 385, 386, 388-397, 405, 406, 410, 416, 418, 421, 422, 424, 447, 450, 453, 455-459, 487, 491, 492, 499, 507 collagen 458, 507, lamina cribrosa 416, 457 sclera 348, 349, 365, 372, 375, 383-397, 406, 410, 416,  422, 424, 447, 450, 453, 455- 458,  491,  507

520

Copyright © 2018. Kugler Publications. All rights reserved.

Residual stromal thickness 264, 267 Resonant frequencies 121, 330 Retina 31, 107, 118, 222, 223, 226, 227, 281, 323, 324, 326, 330-333, 335-339, 348, 356, 383, 384, 387, 388, 389, 394, 406, 444, 447, 483, 486, 487, 497, 505 Retinal detachment 324, 335, 337, 384, 483, 486 Retinal ganglion cell 348, 356, 372, 375, 405, 443, 465, 491, 497 Retinal tear 335, 338 Retrolaminar septal recruitment 418 Retrolaminar tissue pressure 347, 465, 466, 467 Rheology 324, 325, 330, 339 vitreous 324-325 Rho 47, 48-50, 56 Rho kinase (ROCK) 47-52 Riboflavin (See crosslinking) 24, 96, 135, 154, 182, 218, 221-224, 226, 227, 233-242, 257 Rose-bengal/green light (RGX), (See also crosslinking) 135, 137 S Schlemm’s canal 334, 356 Sclera 16, 20, 40, 81, 84, 85, 89, 97, 217, 220, 223, 241, 328, 332, 334, 337, 338, 347-349, 357, 363-375, 377, 380, 388-397, 406, 408, 410, 412, 416, 417, 422, 424, 443-448, 450-458, 473-475, 479, 480, 483-485, 486, 488, 490, 491, 497, 499, 500, 505-507 biomechanics 357, 363-375, 392-394, 396-397, 422, 452, collagen microstructure 363 composition 389, 391-393, 396 growth 391, 394-397 microstructure 81, 86, 89, 348, 363, 365, 372 remodeling 348, 349, 365, 372, 375, 383-397, 406, 410, 416,  422, 424, 447, 450, 453, 455- 458,  491,  507 stiffness 81, 348,  357, 364, 365, 368, 369, 379, 380, 392, 393, 397, 408, 417, 422, 445, 447, 448, 450-455, 457, 474, 480, 483-485, 488, 490, 491, 499, 506, 507 structure 16, 19, 40,  81, 84, 85, 348, 349, 357, 367, 368, 371, 389-392, 395, 443, 444, 448, 453-457, 475, 480, 488,  497 Second harmonic generation (SHG) 31, 32, 40, 54, 56, 370, 372, 375, 455 Sensitivity analysis 248, 252, 474, 482, 484, 487, 488, 490, 491 Shear modulus 4, 7, 32, 33, 161-164, 252, 298, 299, 301, 490 Shear-strain 7, 97, 151, 161, 162 Shear-stress 3, 92, 94, 161, 324, 331, 338, 356, 458 Simple squamous endothelium 117 Small Incision Lenticule Extraction (SMILE), (See also refractive surgery) 11, 147, 181, 182, 240, 250, 262-268, 270-273 Spatial heterogeneity (See also heterogeneity) 123 Spatial resolution 31, 46, 95, 97, 117-119, 138, 140, 141, 150, 159, 327 Specimen-specific model 480, 481, 487, 488, 490, 491 Speckle interferometry 149, 365, 367 Spectral analysis 128, 139, 141, 167 Spherical cap 93-95 Stiffness 7, 32, 34, 45, 46, 50-54, 81, 82, 88, 89, 104, 108, 111, 118, 121, 123, 128, 132, 134, 135, 140, 141, 148, 152, 173, 178, 211, 217, 218, 220, 224-226, 233, 236, 240-242, 246, 248, 249, 253, 257, 263, 267, 268, 284, 285, 287,

Index

521

297-300, 307-312, 315, 348, 352, 354-358, 364, 365, 368, 369, 379, 380, 392, 393, 397, 408, 417, 421, 422, 445, 447, 448, 450-455, 457, 474, 480, 482-485, 487, 488, 490, 491, 499, 505-507 Strain 3-8, 10, 33-35, 38, 51, 81, 87-89, 91-96, 97, 104, 110, 111, 118, 119, 138, 151, 152, 160-164, 170, 224, 225, 245, 251, 263, 267, 268, 270, 299, 300, 311, 324-326, 348, 349, 352, 357, 363, 365, 367, 368, 392, 397, 405-408, 417, 422, 424, 444, 447, 448, 450-456, 458, 459, 471, 472, 474, 482, 484, 486, 487, 489, 490, 491, 499-501, 503, 506, 507 Strain energy function 87, 88 Stress-relaxation 8, 235 Stress-strain 4, 5, 33, 81, 91-95, 161, 163, 164, 170, 224, 225, 299, 311 Stroma 4, 7, 8, 10, 15, 19, 20, 22, 24, 25, 31, 32, 39, 45, 46, 51, 54, 56, 63-67, 69-78, 82-84, 96, 107, 108, 111, 113, 117, 128, 163, 181, 218, 222-224, 226, 227, 234, 236-240, 242, 254, 256, 257, 262-267, 271-273, 281, 284, 285, 287, 288 Structural stiffness 355, 357, 358, 408, 417, 421, 422, 447, 448, 451, 453, 455, 457, 480, 483 Surface displacement 490 Swelling pressure 7, 8, 40, 64, 66, 69, 70, 391 Swept source laser 138, 141 Synchrotron 83, 84, 491 T Tangential tensile strength 263 Tensegrity 45 Tensional homeostasis 51, 52, 217 Thin plate 134, 474, 482 Trabecular meshwork 282, 351, 356, 486, 487 Tractional force 46, 47 Transforming growth factor-beta (TGF-β) 431, 432, 434-436 Translaminar pressure gradient (also called Translaminar pressure difference) 424, 449, 465, 466, 486 Transparency 7, 15, 17, 18, 45, 49, 63, 64, 66, 71, 77, 107, 117, 118, 141, 221, 262, 296 Trauma 15, 486, 487, 491, 492 Tree shrew 384-386, 389, 392, 394, 396 Type I collagen matrix (See also collagen) 48, 49

Copyright © 2018. Kugler Publications. All rights reserved.

U Ultrasound elastography (See also elastography) 96, 104, 108, 118, 140 Ultraviolet (UV) light (See also crosslinking) 221-223, 226, 234 Uncertainty 21, 252, 479, 480 Uniaxial strip testing (See also mechanical testing) 91 UV-induced collagen crosslinking (See also crosslinking) 117 V VHF digital ultrasound 272, 273 Virtual fields method 505 Viscoelastic properties 10, 162, 328, 364, 380, 486, 499 Viscoelasticity 8, 18, 81, 123, 140, 308, 311, 312, 315, 330, 334, 352, 448, 500 Viscosity 128, 134, 135, 160, 170, 323, 325, 331 Visual stimulus 384, 386-389, 396 Vitreoretinal traction 330, 336-338 Vitreous dynamics 327, 328, 331 Vitreous humor 282, 297, 300, 323-325, 327, 328, 330-336, 338, 339, 348, 363

522

Vitreous motion 326-328, 330, 331, 339 Von-Mises stress (See also stress) 250, 267, 268 W Wave velocity 33, 121, 123, 128, 132, 141, 225 Wide-angle x-ray scattering (WAXS) 6, 83-85, 364, 367-369, 371-375 X X-ray diffraction 16, 83, 117, 253 X-ray scattering 6, 18-20, 22-24, 31, 40, 65, 69, 82-84, 86, 89, 364, 490

Copyright © 2018. Kugler Publications. All rights reserved.

Y Young’s modulus of elasticity (See also elastic modulus) 4-6, 10, 18, 32-34, 36, 38, 39, 94, 114, 118, 119, 121-123, 125, 128, 129, 132-135, 138-141, 147, 160-164, 166, 170, 187-193, 189, 241, 247-249, 252-257, 287, 296-299, 325, 326, 337, 434, 481, 506

Copyright © 2018. Kugler Publications. All rights reserved.

ISBN 978-90-6299-250-8

9 789062 992508