Bone Quantitative Ultrasound: New Horizons (Advances in Experimental Medicine and Biology, 1364) 3030919781, 9783030919788

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Advances in Experimental Medicine and Biology 1364

Pascal Laugier Quentin Grimal   Editors

Bone Quantitative Ultrasound New Horizons

Advances in Experimental Medicine and Biology Volume 1364 Series Editors Wim E. Crusio, Institut de Neurosciences Cognitives et Intégratives d’Aquitaine, CNRS and University of Bordeaux, Pessac Cedex, France Haidong Dong, Departments of Urology and Immunology, Mayo Clinic, Rochester, MN, USA Heinfried H. Radeke, Institute of Pharmacology & Toxicology, Clinic of the Goethe University Frankfurt Main, Frankfurt am Main, Hessen, Germany Nima Rezaei, Research Center for Immunodeficiencies, Children’s Medical Center, Tehran University of Medical Sciences, Tehran, Iran Ortrud Steinlein, Institute of Human Genetics, LMU University Hospital, Munich, Germany Junjie Xiao, Cardiac Regeneration and Ageing Lab, Institute of Cardiovascular Science, School of Life Science, Shanghai University, Shanghai, China

Advances in Experimental Medicine and Biology provides a platform for scientific contributions in the main disciplines of the biomedicine and the life sciences. This series publishes thematic volumes on contemporary research in the areas of microbiology, immunology, neurosciences, biochemistry, biomedical engineering, genetics, physiology, and cancer research. Covering emerging topics and techniques in basic and clinical science, it brings together clinicians and researchers from various fields. Advances in Experimental Medicine and Biology has been publishing exceptional works in the field for over 40 years, and is indexed in SCOPUS, Medline (PubMed), Journal Citation Reports/Science Edition, Science Citation Index Expanded (SciSearch, Web of Science), EMBASE, BIOSIS, Reaxys, EMBiology, the Chemical Abstracts Service (CAS), and Pathway Studio. 2020 Impact Factor: 2.622

Pascal Laugier • Quentin Grimal Editors

Bone Quantitative Ultrasound New Horizons

Editors Pascal Laugier Sorbonne Université, INSERM, CNRS, Laboratoire d’Imagerie Biomédicale, Paris, France

Quentin Grimal Sorbonne Université, INSERM, CNRS, Laboratoire d’Imagerie Biomédicale, Paris, France

ISSN 0065-2598 ISSN 2214-8019 (electronic) Advances in Experimental Medicine and Biology ISBN 978-3-030-91978-8 ISBN 978-3-030-91979-5 (eBook) https://doi.org/10.1007/978-3-030-91979-5 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Foreword

Let’s assume you are a physicist or engineer who would be given the following task: Develop a diagnostic method to comprehensively assess the mechanical properties of bone. You have to choose the modality that has the best prospects of accomplishing the task. You have access to unlimited resources, and time is not an issue (in other words, this is a researcher’s wonderland). So, what would you do – specifically, which modality would you choose? I would go for ultrasound. I believe probing bone with a mechanical wave is the natural choice for evaluation of mechanical properties. This is not a new insight; in fact, it was one key consideration to enter this research field three decades ago. I agree that other modalities may yield valuable insights into bone properties as well, but I am convinced that taking the direct route via analysis of acoustical wave interaction with bone is the preferred way. Many ingenious ideas have been developed and a lot of progress has been achieved in this time, but even more work and ingenuity will be necessary to achieve the goal. Ultrasound analysis is extremely complex, so many different sound waves can propagate, and disentangling them to obtain accurate information on bone properties remains largely unresolved. Different groups have followed different strategies, ranging from empirical approaches to the high road of modeling the complex pattern of wave propagation. Research on ultrasound is a lot like taming the beast: as soon as something is accomplished, other hurdles pop up. Being aware of this, the next step I would take if I were entrusted with this task: I would study this book very carefully. The book offers a comprehensive overview and a lot of detail, essential for bone ultrasound researchers. Technology development for bone ultrasound as it is now being pursued perhaps started with work on cortical bone in the 1970s by H.S. Yoon and L.J. Katz and cancellous bone in the late 1980s by C.M. Langton et al. To the best of my knowledge this is only the third book on quantitative ultrasound (QUS) of bone, the first one published in 1999 by C.F. Njeh et al., wrapping up the first roller coaster decade of QUS applications in osteoporosis and a second one published in 2011 by P. Laugier and G. Haïat with much more v

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in-depth focus of modeling and theoretical background of bone assessment by QUS methods. It is fascinating and reassuring to see so many ultrasound researchers who advanced the field in the last two decades contributing to this book. The current book on the one hand presents reviews of the approaches taken to date, but more importantly, it presents exciting avenues for future developments. The focus is on ultrasound technology, but a wide range of clinical applications are also covered.

Lessons from the Past Some lessons from the past may have relevance also for future developments. First, technology and clinical needs must match. A technology with broad claims may discredit itself if the claims are not substantiated in due time. Technology needs to be validated, a substantial challenge specifically for measurements in vivo since many skeletal properties and non-skeletal confounders affect the ultrasound measures. So carefully ex vivo experiments ranging from specimens of simple geometry to limit structural impact to realistic whole bone measurements represent the basis, ideally complemented by theoretical prediction or simulation of the outcome (as thoroughly pursued since about 2000 for the study of sound propagation in cortical bone in the research group of the editors). Some techniques such as phalangeal ultrasound or ultrasound critical angle reflectometry did not pass the test of time, perhaps not because of intrinsic technological deficiencies but because of a mismatch of technical and clinical claims. Calcaneal QUS did succeed in accomplishing one specific clinical aim, i.e., predicting osteoporotic fracture risk, but since it was not included in studies on osteoporosis therapy, it missed the claim to permit identification of patients in whom osteoporosis drugs would work. Standardization is another important step, and consensus among researchers should be sought. Certification of operators adds credibility. Without consensus on standardized evaluation procedures, jointly formulated by technical experts and clinicians, ill-founded marketing claims, e.g., on correlations or sensitivity and specificity, can create a lot of confusion. Vague claims should be avoided since they are another source of confusion, and are close to impossible to prove and easy to attack. Ultrasound as THE technique to measure bone QUALITY was such a claim, and still today, we witness misleading marketing claims along those lines. Bone quality is an illdefined term and in reality has so many facets that it is impossible to meet the expectations. Having said this, the main and unique contribution of ultrasound will indeed be in the non-invasive ionizing-radiation-free assessment of bone properties beyond bone mass. These include (i) tissue mineral density; (ii) microstructure, specifically trabecular separation and cortical porosity; and (iii) mechanical properties, specifically, stiffness, strength, and toughness. So, the field needs to seek validation of specific claims, solid associations of ultrasound parameters with specific bone quality factors.

Foreword

Foreword

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Prospects for the Future We currently see great interest in rare skeletal disorders. Several of them, e.g., osteogenesis imperfecta as the most prominent one, feature altered material properties (and, perhaps as a consequence of this, altered microstructure). Other than bone indentation techniques (that yields only a local measurement and is not entirely non-invasive), currently there is no approach suited for clinical investigations of material properties in vivo. In my view, ultrasound is the modality that has the best potential to fill this gap. And this would be clinically important, beyond rare bone diseases. It is already foreseeable that increased knowledge about (measurement of) altered material properties will feed back to the highly prevalent skeletal disorders including osteoporosis. The accepted notion that osteoporosis reflects loss of bone mass but that the bone that is left has normal bone quality should be refined. Enhanced bone turnover, e.g., around menopause, will lead to undermineralization, at least temporarily. Early-onset osteoporosis has genetic causes and implications on mechanical properties, and should be an interesting target of assessment with well-standardized ultrasound methods. Personally, I am quite convinced that osteoporosis (even what we today subsume under primary osteoporosis) is not a monolithic disorder but comes in different flavors. If ultrasound will allow to differentiate underlying processes, it will also have a role in the assessment of many secondary osteoporoses and other skeletal disorders: diabetes and renal disorders, two applications with very high clinical relevance. This would help in the development of personalized therapies. Speaking about therapy: monitoring treatment effects with ultrasound may be of interest as well – if bone-anabolic agents have different effects on periosteal bone apposition, why not try to measure this with ultrasound? To finish up, let’s revisit the beginning of this preface. I sketched out a task: Develop a diagnostic method to comprehensively assess the mechanical properties of bone. What makes me optimistic that this task can be accomplished with QUS approaches? First, ultrasound physics provide the information sought after. Second, quantification, i.e., parametrization of ultrasound signals, has provided insights in the past and will be the basis for disentangling the complexity of ultrasound interaction with bone. In the 1990s, when QUS for the assessment of osteoporosis was all the rage, parametrization of ultrasound signal patterns definitely was not mainstream, at least not for medical applications, and still today it remains a challenge. However, in particular, for a technique that commonly is considered to be subjective and operator dependent, quantification is most relevant. Third, the combination of different types of transducers to augment the quantification of sound wave parameters by improved localization via ultrasound imaging should become feasible. Reproducible VOI placement could help improve accuracy but even more so precision, relevant for monitoring applications. Studying the impact of treatment on bone material properties may become feasible. Problems related to sound transmission through overlaying soft tissue have hampered some ultrasound approaches. However, a related topic may provide unique opportunities for expanded ultrasound assessment: I am referring to a fourth

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Foreword

frontier, parametric QUS-based assessment of muscle properties, perhaps using ultrasound computed tomography (USCT) approaches. Quantification of muscular competence, including size plus visceral adipose tissue composition and distribution (a topic researched by the editor about 35 years ago), would complement skeletal competence by adding factors related to risk of falling. Similarly, ultrasound could potentially permit a comprehensive assessment of musculoskeletal disorders. These are all exciting perspectives for expanded clinical and basic research applications. But perhaps the greatest technological advance could be expected by (fifth) breaking the complexity barriers of ultrasound signal analysis by artificial intelligence methods. Above, I mentioned the different strategies ranging from empirical measurements to complex modeling. AI methods should allow to combine these approaches. Just brute force recording of signals and associating them with mechanical or microstructural properties may help to some extent. Associating wave propagation patterns derived from theoretical modeling with wave patterns observed may improve understanding and enable analysis of wave patterns that are too complex for the human mind to disentangle. First steps into this promising direction are already presented in the book. In summary, I do encourage bright young researchers to enter this field and continue the quest for comprehensive noninvasive assessment of bone properties by means of QUS approaches. In about 10 years from now, it will be interesting to watch out for a fourth book on musculoskeletal QUS to study the exiting developments ahead of us. Kiel, Germany

Claus-C. Glüer

Contents

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quentin Grimal and Pascal Laugier

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Part I Ultrasound Methods for Skeletal Status Clinical Assessment 2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture Risk: An Update . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Didier Hans, Antoine Métrailler, Elena Gonzalez Rodriguez, Olivier Lamy, and Enisa Shevroja

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Clinical Devices for Bone Assessment . . . . . . . . . . . . . . . . . . . . . Kay Raum and Pascal Laugier

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Axial Transmission: Techniques, Devices and Clinical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nicolas Bochud and Pascal Laugier

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Signal Processing Techniques Applied to Axial Transmission Ultrasound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tho N. H. T. Tran, Kailiang Xu, Lawrence H. Le, and Dean Ta

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6 Ultrasonic Assessment of Cancellous Bone Based on the Two-Wave Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . Katsunori Mizuno, Yoshiki Nagatani, and Isao Mano

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Pulse-Echo Measurements of Bone Tissues. Techniques and Clinical Results at the Spine and Femur . . . . . . . . . . . . . . . Delia Ciardo, Paola Pisani, Francesco Conversano, and Sergio Casciaro

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8 Scattering in Cancellous Bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . Keith Wear

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9 Ultrasound Scattering in Cortical Bone . . . . . . . . . . . . . . . . . . . Yasamin Karbalaeisadegh and Marie Muller

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10 Single-Sided Ultrasound Imaging of the Bone Cortex: Anatomy, Tissue Characterization and Blood Flow . . . . . . . . . Guillaume Renaud and Sébastien Salles

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Contents

Ultrasound Computed Tomography . . . . . . . . . . . . . . . . . . . . . . Philippe Lasaygues, Luis Espinosa, Simon Bernard, Philippe Petit, and Régine Guillermin

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Part II Ex Vivo Measurement of Bone Material Properties: New Methods and Data 12

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Measurement of Cortical Bone Elasticity Tensor with Resonant Ultrasound Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . Simon Bernard, Xiran Cai, and Quentin Grimal

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Documenting the Anisotropic Stiffness of Hard Tissues with Resonant Ultrasound Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . Xiran Cai, Simon Bernard, and Quentin Grimal

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14 Assessing the Elasticity of Child Cortical Bone . . . . . . . . . . . . Cécile Baron, Hélène Follet, Martine Pithioux, Cédric Payan, and Philippe Lasaygues 15

Piezoelectric and Opto-Acoustic Material Properties of Bone . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Atsushi Hosokawa and Mami Matsukawa

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Part III Emerging Applications of Bone Quantitative Ultrasound 3D Ultrasound Imaging of the Spine . . . . . . . . . . . . . . . . . . . . . . Yong Ping Zheng and Timothy Tin Yan Lee

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17 Ultrasonic Evaluation of the Bone-Implant Interface . . . . . . . Yoann Hériveaux, Vu-Hieu Nguyen, and Guillaume Haïat

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18 Adaptive Ultrasound Focusing Through the Cranial Bone for Non-invasive Treatment of Brain Disorders . . . . . . . Thomas Bancel, Thomas Tiennot, and Jean-François Aubry

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Guided Waves in the Skull . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Héctor Estrada and Daniel Razansky

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Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1

Introduction Quentin Grimal and Pascal Laugier

Diagnostic ultrasound imaging has gained wide acceptance for a broad range of clinical uses. In many cases, ultrasonography is the first-line imaging modality selected for its ease of access and absence of ionizing radiation. Over the last decades, ultrasonography has considerably evolved and is currently contributing to important improvements in patient diagnosis and treatment. Modern ultrasound imaging can provide soft tissue anatomical (shape, size . . . ) and functional information (tissue movements, blood flow) in 3D and 4D, characterization and distinction among tissues (echostructure) and quantification of tissue properties (microstructure, tissue stiffness). Soft tissue quantitative ultrasound (QUS) refers to methods specifically developed to assess quantitative variables reflecting tissue physical properties, usually by analyzing the raw radiofrequency signals and/or its spectral characteristics. Bone QUS methods were introduced in the 1970s to assess bone loss in the context of osteoporosis, a disease characterized by a decreased bone mass and a deteriorated bone microstructure, resulting in reduced bone strength, Q. Grimal () · P. Laugier Sorbonne Université, INSERM, CNRS, Laboratoire d’Imagerie Biomédicale, Paris, France e-mail: [email protected]; [email protected]

elevated bone fragility and increased fracture risk. At that time, the demand for measurement of skeletal status to identify subjects who could be exposed to an increased risk of fracture was rapidly increasing. Safe, easy-to-use, radiationfree, and portable QUS techniques were rapidly developed and were thought to be particularly indicated to assess bone status and to complement X-ray based densitometry techniques. Bone QUS has been a vivid research field. Many significant achievements in new ultrasound technologies to measure bone and models to elucidate the interaction and the propagation of ultrasonic waves in complex bone structures were reported. A first book entitled Bone QUS (https://www. springer.com/fr/book/9789400700161) has been published in 2011. In almost ten years from 2011 to 2021, significant progress and growth in quantitative ultrasound techniques could be seen. From the development of new procedures and techniques to new devices and new applications, QUS is continuing to increase our knowledge about bone elastic properties and contribute a major impact to clinical diagnosis. We feel that it is timely to bring together in one book the most recent research. This book Bone quantitative ultrasound: new horizons reflects the current status of the research and is intended to be a complement to the first book, rather than a second edition, in the sense

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 P. Laugier, Q. Grimal (eds.), Bone Quantitative Ultrasound, Advances in Experimental Medicine and Biology 1364, https://doi.org/10.1007/978-3-030-91979-5_1

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that basic notions already presented in the first book will not be repeated here. The physics of ultrasound propagation in bone (a hard tissue) substantially differs from the propagation in soft tissues. It involves shear waves coupled to longitudinal waves, guided waves, strong scattering effects, strong attenuation and velocity dispersion. This complex physics has hampered a fast development of bone QUS but the engineer can also take advantage of this rich physics to design specific methods to probe bone properties. For instance, guided waves carry important diagnostic information on cortical thickness, porosity and elastic properties; shear waves may provide complementary information to longitudinal waves on material properties; poroelasticity is a rich framework to interpret ultrasound propagation in trabecular bone and extract microstructural parameters; frequency-dependent backscattering is successfully used to probe microstructural features of trabecular and cortical bone. In this book, many examples of the use of this rich physics to measure bone properties are presented, together with pragmatic approaches relying on empirical correlations between osteoporosis biomarkers and ultrasound quantities. Bone QUS has progressed taking advantage of improvements in transducer technology, electronics, availability of ultrasound open platforms and increase in computer power. B-mode cortical bone imaging, measurement of bone vascularization, bone tomography coupled to full waveform inversion open up new horizons for the bone QUS research field. Machine learning is increasingly being used to process raw radio-frequency signals for the quantification of bone properties and for classification of patients. Also, during the last decade, new devices appeared on the market and new approaches to quantify microstructure have been further developed. Finally, a large amount of data documenting the mechanical and acoustical properties of bone, a keystone to the development of bone QUS, have recently been made available. The bone QUS research community brings together individuals from various backgrounds, i.e., acoustics, medical imaging, biomechanics, biomedical engineering, applied mathematics, bone biology and clinical sciences. This book

Q. Grimal and P. Laugier

is intended for the researchers, graduate or undergraduate students, engineers and clinicians from these backgrounds. It presents the most recent experimental results, theoretical concepts and technologies developed so far, together with recent clinical results. The book chapters are organized in three parts as detailed below. Part I is devoted to ultrasound methods developed for the diagnosis of osteoporosis. It collects chapters describing methods to assess cortical and trabecular bone status and their clinical applications. Chapters 2 and 3 present the generic measurement methods implemented in currently available bone clinical ultrasound devices. They describe the state-of-the art devices, their practical use and clinical performance, and the current clinical consensus. Chapters 4 and 5 deal with ultrasound guided waves in cortical bone. This topic represents a significantly growing area in the past decade and it has sparkled intense research in both instrumentation and signal processing. Instrumentation and signal processing techniques are presented in detail altogether with the most recent clinical results as example. These chapters also describe in details the models that are used to solve the direct problem and strategies that are currently developed to solve the inverse problem. Chapter 6 presents the most recent results together with the most recent clinical findings exploiting the two-wave phenomenon predicted by Biot theory of poroelastic media. Chapters 7, 8, and 9 present general principles for measuring ultrasound scattering and cover recent progress in understanding and measuring scattering from cancellous and cortical bone. The goal of these chapters is to give the reader an extensive view of the scattering interaction mechanisms as an aid to understand the QUS potential and the types of variables that can be determined by QUS scattering in order to characterize bone microstructure. Metrics can be calculated from the radio frequency signals measured in pulse echo mode, which demonstrate empirical correlation with bone mineral density. These metrics serve as a basis for the in vivo evaluation of osteoporosis at the hip and spine (Chap. 7) or at the calcaneus (Chap. 8). A new approach to characterize cortical bone microstructure (poros-

1 Introduction

ity, pore size) based on ultrasound scattering is presented in Chap. 9. To conclude Part I, Chaps. 10 and 11 cover cutting-edge researches still at an early development stage but presenting an exciting potential for clinical applications. Chapter 10 unveils recent advances in real-time quantitative imaging of cortical bone and measurement of cortical blood vascularization. Chapter 11 describes quantitative ultrasound tomography of cortical bone. These imaging techniques exploit experimental and signal processing approaches inspired from the methods well-known from seismologists to image Earth. Chapters 12, 13, 14, and 15 of Part II focus on bone material properties, such as elasticity and piezoelasticity. Resonant ultrasound spectroscopy (RUS), a method recently introduced in the bone field to measure the anisotropic stiffness tensor of cortical bone with the aim to become a standard measurement device in the lab, is presented in details in Chap. 12. Chapters 13 and 14 summarize the most recent results of elasticity measured with RUS or the time of flight technique from hundreds of bone specimens harvested from several skeletal sites of adults and children. These data provide and unprecedented collection of anisotropic elasticity and speed of sound values of hard tissues that are of fundamental interest for bone biomechanics and bone QUS. Interesting piezoelectric and opto-acoustic properties of bone are discussed in Chap. 15 together with details of the measurement techniques.

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Although the issue of osteoporosis and biomechanics are still the main motivation for developing bone QUS and occupies a central place in the book, thus reflecting the status of the research in the past 10 years, we wanted to broaden the horizon with Chaps. 16, 17, 18, and 19 of Part III by including new exciting topics which receive some attention as clinical tools. Chapter 16 presents three-dimensional ultrasound imaging of the spine allowing large-scale screening to diagnose scoliosis. Chapter 17 describes recent developments of quantitative ultrasound methods to investigate implant anchorage with a focus on dental implants. Acoustic properties of the skull are increasingly being investigated in the context of brain imaging and therapy. One methodology to efficiently focus ultrasound in the brain accounting for skull properties is presented in Chap. 18. The physics of ultrasound guided waves in the skull and the opportunities of using these for imaging and therapy are discussed in Chap. 19. Hopefully, the light shed on these techniques which are still unfamiliar in the bone field will be enriching and, together with the knowledge accumulated in bone QUS in the past 25 years, may help to produce constructive and ongoing interactions among all fields. We believe that the book (together with the previous one) will provide a comprehensive overview of the methods and principles used in bone quantitative ultrasound and will be an invaluable resource for all novice or experienced researchers in the field.

Part I Ultrasound Methods for Skeletal Status Clinical Assessment

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Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture Risk: An Update Didier Hans, Antoine Métrailler, Elena Gonzalez Rodriguez, Olivier Lamy, and Enisa Shevroja

Abstract

Quantitative ultrasound (QUS) presents a low cost and readily available alternative to DXA measurements of bone mineral density (BMD) for osteoporotic fracture risk assessment. It is performed in a variety of skeletal sites, among which the most widely investigated and clinically used are first the calcaneus and then the radius. Nevertheless, there is still uncertainty in the incorporation of QUS in the clinical management of osteoporosis as the level of clinical validation differs substantially upon the QUS models available. In fact, results from a given QUS device can unlikely be extrapolated to another one, given the technological differences between QUS devices. The use of QUS in clinical routine to identify individuals at low or high risk of fracture could be considered primarily when central DXA is not easily available. In this later case, it is recommended that QUS bone parameters are used in combination with established clinical D. Hans () · A. Métrailler · E. Gonzalez Rodriguez · O. Lamy · E. Shevroja Interdisciplinary Center of Bone Diseases, Bone and Joint Department, Lausanne University Hospital (CHUV) and Lausanne University, Lausanne, Switzerland e-mail: [email protected]; [email protected]; [email protected]; [email protected]; [email protected]; [email protected]

risk factors for fracture. Currently, standalone QUS is not recommended for treatment initiation decision making or follow-up. As WHO classification of osteoporosis thresholds cannot apply to QUS, thresholds specific for given QUS devices and parameters need to be determined and cross-validated widely to have a well-defined and certain use of QUS in osteoporosis clinical workflow. Despite the acknowledged current clinical limitations for QUS to be used more widely in daily routine, substantial progresses have been made and new results are promising. Keywords

Quantitative ultrasound · BUA · SOS · Osteoporosis · Fracture

2.1

Osteoporosis: The Clinical Problem

2.1.1

The Skeleton and Bone Tissue

Bone is a highly specialized connective tissue, containing cells, fibers and ground substance. Differently than other forms of connective tissue, the extracellular components of bone are mineralized, giving it strength and toughness, but also elasticity. This makes bone fulfill its role as

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 P. Laugier, Q. Grimal (eds.), Bone Quantitative Ultrasound, Advances in Experimental Medicine and Biology 1364, https://doi.org/10.1007/978-3-030-91979-5_2

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the mechanical support of the body. Typically, in adult humans, 206 bones altogether create the skeleton, which in interaction with muscles, enable our ability to move. Without bones, our bodies would be a jellyfish-like mass unable to sit or stand upright. In addition, bones provide protection to the inner organs and bone marrow; and play fundamental functions in metabolic pathways associated with mineral homeostasis, where bones represent calcium and phosphate reserves (Moreira et al., 2000; Su et al., 2019). According to their shapes and sizes, bones can be classified in four principal types: long bones (e.g., humerus, femur, radius), short bones (metacarpal and phalanx), flat bones (skull and ribs), and irregular bones (vertebrae) (Currey, 1984). Anatomically, there are two types of bone tissue: cortical and trabecular (Hadjidakis & Androulakis, 2006). Although they are identical in their chemical composition, cortical and trabecular bones differ both microscopically and macroscopically. The cortical bone, differently named compact bone, appears as a solid continuous mass in which spaces can be seen only with a microscope. The trabecular bone, differently named cancellous bone, appears as a spongy structure, having a mass four times lower than cortical bone. There is no sharp boundary between the cortical and trabecular types of bone. Although smaller in size, the metabolic turnover rate in trabecular bone is eight times higher than in cortical bone. The combination of both cortical and trabecular bone tissues grants the hollow structure of bone, which provides a light-but-strong frame for the body (Hadjidakis & Androulakis, 2006). Despite its solid and inert appearance, bone is a vital and dynamic organ, constantly undergoing adaptation processes. From childhood throughout adulthood, the skeleton passes through the phases of growth, modeling and remodeling. During these phases, the skeleton can change size or shape, or renew its structures (Eriksen et al., 1994). Growth occurs during childhood and early adulthood. It consists of the skeleton growth in length and bones expansion in diameter. The peak

D. Hans et al.

bone mass is typically reached during the second or third decade of life. Thereafter, a gradual bone loss begins. During the bone loss process, bones worsen in both contexts, qualitative and quantitative (Riggs & Melton, 1986).

2.1.2

Defining Osteoporosis

In 1830’s, Jean Lobstein observed that there are holes in every bone, but in individuals of a certain age and suffering from certain diseases, these holes were bigger. He referred to bones with bigger holes as porous. Osteoporosis, porous bone, was the term used to describe aged human bone with increased porosity. In 1984, the National Institute of Health (NIH) defined osteoporosis as a disease characterized by low bone mass and microarchitectural deterioration of bone tissue, leading to enhanced bone fragility and a consequent increase in fracture risk (Consensus conference: Osteoporosis, 1984). Based on its etiology, osteoporosis can be primary or secondary. Primary or age-related osteoporosis is the most common type (Mirza & Canalis, 2015). Typically, women lose bone mass more rapidly than men and this bone loss is more obvious post-menopause due to the estrogen deficiency. Hence, this type of osteoporosis is also known as postmenopausal osteoporosis. Sex hormones deficiency due to the advancing age is the main cause of postmenopausal osteoporosis (Lawrence Riggs et al., 2002). Yet, factors such as genetics and nutrition also affect the pace of bone loss during the advanced age. Secondary osteoporosis happens when an underlying disease (genetic: cystic fibrosis; endocrine: diabetes, hypogonadism, hyperthyroidism, hyperparathyroidism, Cushing disease; autoimmune: rheumatoid arthritis; etc.), lifestyle behavior (smoking, alcohol abuse, sedentary life) and/or drugs use (glucocorticoids, hypogonadism-inducing agents etc.) causes the excessive bone loss. This type of osteoporosis is mainly present in younger adults and the majority of men with osteoporosis. Moreover,

2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture…

up to one third of postmenopausal women with osteoporosis have underlying health conditions that might further contribute to their bone loss. Ten years after the NIH definition, in 1994, the World Health Organization (WHO) introduced for the first time the use of the T-score concept for the bone mass classification suggesting an operational definition for osteoporosis (Kanis, 1994).

2.1.3

The Hallmark of Osteoporosis: Fracture

Osteoporotic or fragility fracture is a fracture occurring due to falls from a standing height in response to mechanical forces that would not normally result in fracture (Cummings & Melton, 2002; Warriner et al., 2011). Hip, spine, humerus and forearm are the most common types of fragility fractures, also referred to as major osteoporotic fractures (Klop et al., 2016). The lifetime risk for having a fracture that will come to clinical attention is 40%, equivalent to the risk for cardiovascular disease. After the age of 50 years, one in two women and one in four men are expected to experience a major osteoporotic fracture in their remaining lifetime (Schuit et al., 2004; Kanis et al., 2000). In women over the age of 45 years, osteoporosis accounts for more days spent in hospital than diseases such as diabetes, myocardial infarction and breast cancer (Kanis et al., 2019). Moreover, a prior fracture is associated with an 86% increased risk of a subsequent fracture (Kanis et al., 2004). Fractures are associated with high morbidity and mortality; and are often a precursor of disability, loss of independence, and premature death among the elderly (Kanis et al., 2004). Worldwide, nine million fragility fractures occur annually. This number is expected to increase due to the populations’ aging (Binkley et al., 2017). In America and Europe, fractures account for more disability-adjusted life years (DALYs, a measure for disease burden) lost than hypertension, breast or prostate cancer (Johnell & Kanis, 2006).

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In the European Union (EU), it is estimated that the number of osteoporotic individuals in 2025 will rise with 23% as compared to 2010 and reach 33.9 million individuals. 4.5 million fractures are expected to happen annually in 2025, corresponding to an increase of 28% as compared to 2010. In 2010, 1.2 million quality-adjusted life years (QALYs) were lost due to fractures; in 2025, it is expected to reach 1.4 million. In the EU, in 2010, the cost of osteoporosis, including pharmacological intervention, was estimated at A C37 billion – out of which: 66% represented costs of treating incident fractures, 5% pharmacological prevention and 29% long-term fracture care. In high income countries, osteoporotic fractures account for more hospital bed days than myocardial infarction, breast cancer or prostate cancer (Hernlund et al., 2013). Fracture is evidently a highly traumatic experience, which comes at great health, social and economic burden. It is a major challenge for the public health and necessitates particular research focus. As independency is one of the major factors defining the healthy ageing of the population, preventing the loss of independency by preventing fractures is of great importance.

2.1.4

Osteoporosis Diagnosis and Treatment

The overall management and prevention of osteoporosis requires an accurate clinical assessment of bone health and fracture risk. Dual-energy Xray absorptiometry (DXA) scan is the current gold standard technique to assess the general bone density related condition by measures performed at the Anteroposterior (AP) spine, proximal hip (femoral neck and total hip) and 1/3 radius (Dimai, 2017; Schuit et al., 2004). Additional skeletal sites can also be assessed for bone related information, vertebral fracture assessment or body composition. The DXA-derived parameter most used in fracture prediction and further decision-making in osteoporosis management, is bone mineral density (BMD) at the indicated

10

regions of interest. One standard deviation (SD) decrease of BMD is associated with a two-fold increase in the risk for fracture, making BMD one of the strongest predictors of fragility fractures (Dawson-Hughes et al., 2008). According to WHO criteria, an individual would be diagnosed as osteoporotic if their BMD value measured by DXA is 2.5 SD lower than the BMD value of a person of the same sex and race at the age of peak bone mass (20–30 years old). Further, individuals with BMD values between 1.0 and 2.5 SD below the peak bone mass values, are classified as osteopenic, an additional operational category for bone loss quantification (Kanis, 1994). In most instances, the lowest BMD value of these sites is considered. Efforts have also been made towards the quantification of the fracture risk as based on factors known to be associated with increased risk for fragility fractures. FRAX is the most widely used fracture risk quantification algorithm (Kanis et al., 2017). FRAX calculates the 10year probability of having a major osteoporotic fracture or a spine fracture based on clinically assessable risk factors such as: age, sex, weight, height, diabetes mellitus, history of fracture, parental fracture, smoking, alcohol intake, glucocorticoids use, rheumatoid arthritis, and/or BMD and TBS (Trabecular Bone Score, a parameter of bone structure). Once the fracture risk is identified, prevention steps are taken on a certain ‘hierarchical’ level: general lifestyle advices; adequate calcium and/or vitamin D supplementation intake in addition to a healthy lifestyle; and/or pharmacological therapy. Based on the mechanism of function, there are two types of anti-osteoporotic pharmacological therapies: antiresorptive agents (such as bisphosphonates, estrogen agonists/antagonists, estrogens, calcitonin and denosumab) which reduce bone resorption; and anabolic agents (such as teriparatide, abaloparatide) which stimulate bone formation. More recently, romosozumab has been approved for its bone forming effects (Tu et al., 2018).

D. Hans et al.

2.2

Quantitative Ultrasound: The Principles and the Method

2.2.1

The Basics

Ultrasonics is a branch of acoustics dealing with frequencies beyond the audible limit. Inaudible acoustic waves were firstly investigated in the nineteenth century (Faulkner, 2000). One of the most interesting methods to detect highfrequency acoustic waves was the sensitive flame, first observed by LeConte in 1857. He observed that the flame exhibited pulsations in height that were exactly synchronous with the audible music. The sensitive flame became a standard laboratory tool for detecting inaudible acoustic waves until the advent of electro-acoustic means, discovered by the Curie brothers in 1880. Medical applications of ultrasound for diagnosis purpose originated in Austria in 1937 with Dussik, who developed a technique to detect intracranial tumors by sending an ultrasonic beam across the head and mapping the variations in ultrasonic attenuation. The nature of ultrasonic waves is not different from that of sound waves. Ultrasound is classified as a sound wave possessing high frequency (Faulkner, 2000). Quantitative ultrasound (QUS) was first used for osteoporosis and fracture risk estimation in 1984 (Langton et al., 1984). QUS applied to bone uses sound waves at approximately 0.2– 2 megahertz (MHz). The physical and mechanical properties of bone progressively alter the shape, intensity and speed of propagating ultrasonic waves (Hans & Baim, 2017). QUS can be used in transmission mode (measure of modifications of US waves when passing through the bone) or reflection mode (measure of modifications of emitted US waves reflected by the bone). It allows evaluating parameters of bone quality, including elasticity, microarchitecture and strength. The two main parameters measured by QUS in transmission are ultrasound attenuation and the speed of sound. Ultrasound attenuation

2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture…

(Broadband Ultrasound Attenuation (BUA)) is defined as the slope at which attenuation increases with frequency, generally between 0.2 MHz and 0.6 MHz; and is measured in decibels per megahertz, dB/MHz. Ultrasonic velocity (Speed of Sound (SOS)) is measured in meters per second, m/s. BUA and SOS can also be combined to provide additional parameters such as the stiffness index (SI = (0.67 * BUA + 0.28 * SOS) - 420), present in the QUS devices manufactured by GE Healthcare or quantitative ultrasound index (QUI = (0.67 * BUA + 0.28 * SOS)), present in the QUS devices manufactured by Hologic. More recently, a new pulse echo-based technique has been developed, Radiofrequency Echographic Multi Spectrometry (REMS) which uses the analysis of backscattered radiofrequency signals (RF) measured at the spine or femoral neck to estimate BMD (Hans & Baim, 2017). The topic of REMS technique and its clinical application is also covered in detail in Chap. 7 of this book.

2.2.2

QUS Devices

The different QUS technologies are presented in detail in Chap. 3 of this book. Only a brief overview of the different classes of devices is given here. QUS devices can be classified based on the site where they measure bone properties, the manufacturer or the type of the US transmission. QUS classification according to the US transmission includes also the site where each US transmission type can be applied. There are four types of US transmissions: trabecular transverse transmission, cortical transverse transmission, cortical axial transmission, and pulse-echo measuring devices.

2.2.2.1 Trabecular Transverse Transmission Trabecular transverse transmission enables the ultrasound waves to travel through trabecular bone. In this type of transmission, two transducers (a transmitting and a receiving one) are positioned at each side of the measured bone. The QUS devices using trabecular transverse transmission

11

have water-based or direct-contact (dry) systems. In the latter systems, the coupling medium is an oil-based gel. These devices use focused or unfocussed transducers to acquire a set of parameters (typically BUA and SOS, plus a combination of the two such as SI or QUI) that might also include the formation of a parametric ultrasound image. QUS devices using trabecular sound transmission are best used to measure the calcaneus bone in the heel; they are the most widely used type of QUS devices. In addition, they have the largest body of empirical evidence and the majority of them are FDA-approved (Cheng et al., 1999; Njeh et al., 2000).

2.2.2.2 Cortical Transverse Transmission Cortical transverse transmission enables the ultrasound waves to travel through cortical bone, again by using two transducers at each side of the measured bone (Hans et al., 1999a). Currently, QUS contact devices for phalanges and for the distal radius are the sole type of devices in this category. In overall, there is insufficient empirical evidence to support the wide clinical use of these devices. None of them has yet been approved by the FDA in the United States, and only few have been tested for clinical use in Europe. Given their current limited consideration in the clinical context, the phalanges QUS devices will not be discussed further in this chapter. The technical aspects and clinical performance of the distal radius QUS device, currently used exclusively in Japan, are covered in Chap. 6 and thus are not addressed here. 2.2.2.3 Cortical Axial Transmission Cortical axial transmission consists of ultrasound guided waves traveling primarily along cortical bone. The transmitting and receiving transducers are placed along the measured bone. The most commonly used sites by QUS devices using cortical axial transmission are the phalanges, radius, and tibia (Hans et al., 1999a, b). Several axial transmission technologies have been described in recent years, but few have received approval for a clinical use. More details about these technologies can be found in Chap. 4. Currently,

12

few FDA-approved QUS devices are available for clinical use beyond heel QUS, all of them within the multi-skeletal site Sunlight Omnisense series (BeamMed Ltd., Tel-Aviv, Israel) yielding a measure of axial SOS. Recently, a novel axial transmission Finnishmade device has been introduced into the market: the Oscare device for low ultrasound frequency (at about 200 kHz) axial SOS measurements at the radius. The early results of the investigation of these devices are promising. Nevertheless, the overall level of evidence supporting the use of either of them is lower as compared to heel QUS devices; and only one of these devices reported findings supporting its fracture prediction ability (Karjalainen et al., 2016; Moilanen et al., 2013).

2.2.2.4 Pulse-Echo Measuring Devices (i) Radiofrequency Echographic Multi Spectrometry (REMS) (see also Chap. 7 in this book): EchoStation® (Echolight Spa, Lecce, Italy) is a dedicated device developed to integrate analysis of US images and native raw unfiltered RF backscattered US signals, acquired during an echographic scan of lumbar vertebrae (Conversano et al., 2015) or femoral neck (Casciaro et al., 2016). As it uses the pulse-echo measurement method, only one convex transducer of 3.5 MHz (as used for abdominal and gynecological examinations) is needed for the measures. It is a rapid method, taking 3 min maximum per site for acquisition and data processing. Developers describe it as a simple and easy-tolearn acquisition procedure. Whether an adapter module could be added to a standard point-of-care US device has not been stated. Despite the very limited clinical data, the device has been FDAapproved for the measurement of BMD, T-score and Z-score, and for monitoring bone changes in the clinical routine, a concept that has never been studied by QUS to date as the idea was not to replace BMD measurement but to complement it. (ii) The Bindex point-of-care pulse-echo device measures the cortical bone thickness of the tibia and the Density Index, a parameter that estimates the bone density of the hip.

D. Hans et al.

2.2.3

QUS Advantages over DXA

DXA is the gold standard and the most widely used method to assess BMD. The ease of use, high precision and low radiation exposure of the patient are the DXA features that made it popular. However, there are several limitations to the BMD measurements performed by DXA. First, the presence of osteophytes, aortic calcifications, degenerative hypertrophy of the facet joints, and intervertebral disk space narrowing in degenerative disk disease in the posteroanterior lumbar spine DXA scans, may overestimate the measured lumbar spine BMD. Second, DXA is not universally available due to its relatively high cost and certain reimbursement issues (Hans & Baim, 2017). Ultrasound-based techniques are very attractive due to the absence of ionizing radiation and their ability to obtain real-time measurement employing mobile equipment at a significantly lower cost than is incurred with other medical imaging modalities. Also, ultrasound at the power levels currently employed in medical diagnostic applications is considered to be very safe (Hans & Baim, 2017). QUS introduced a number of new diagnostic parameters that seem to be different from what is measured with BMD. The two QUS principal variables that have been applied clinically are SOS and BUA, both related not only to BMD but also to trabeculae orientation, the proportion of trabecular and cortical bone, the composition of organic and inorganic components, bone elasticity damage and fatigue (Hans & Baim, 2017). Evidence shows that heel QUS is as effective as axial DXA at predicting osteoporosis-related fractures in elderly women. However, measurements with different QUS devices introduce high heterogeneity leading to erroneous interpretations of results and difficulties in results interpretation. QUS devices differ technologically from each other (Zagórski et al., 2021). Thus, direct comparisons of different QUS devices present significant bias and are therefore not advised. The overall advantage of QUS over DXA supports its use as a bone health assessment method

2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture…

that could more easily be available worldwide, and as such could be incorporated in clinical routine as a screening approach, particularly in situations where DXA is of limited access (Hans & Baim, 2017).

2.3

QUS Use in Osteoporosis Fracture Risk Prediction

Given the advantages of QUS as a method to assess bone health, it was important to study its actual clinical application and further positioning in clinical routine. Several studies of original, review or meta-analyses settings demonstrated that heel QUS parameters are strong predictors of osteoporotic fractures, suggesting QUS as a valuable tool for fracture prediction especially in situations of limited access to DXA. A resume of the studies that have analyzed the validity of QUS to predict the risk of having a fracture (hip, spine or any), grouped by the QUS site, is shown in Table 2.1 and the predicted risks in Fig. 2.1.

2.3.1

QUS Heel Devices (Trabecular Transverse Transmission)

Heel or calcaneus QUS has shown to be moderately correlated with spine and/or hip BMD as measured by DXA. There is a growing body of evidence showing that QUS measures independently correlate with fracture risk. It is generally accepted that calcaneus QUS can be used for osteoporosis screening and fracture risk evaluation, especially when DXA is not easily accessible. In general, QUS heel devices are the most clinically applicable ones at current, with some devices – like the GE-Lunar Achilles and the Hologic Sahara – having more evidence on their clinical utility than the others. International Society of Clinical Densitometry (ISCD) official recommendations for osteoporosis management state that validated heel QUS devices predict fractures in postmenopausal women and men older than 65 years, independently of spine/hip BM .(Njeh et al., 2000). Discordant results between heel QUS and central DXA are not

13

infrequent, but not necessarily an indication of methodological error. ISCD further recommends that heel QUS can be used in conjunction with clinical risk factors to identify individuals at very low risk of fracture, excluding therefore the need for further diagnostic evaluations (Karjalainen et al., 2016). Besides fracture prediction, the decisionmaking for anti-osteoporotic treatment initiation is another crucial moment in the overall osteoporosis management. Currently, this decisionmaking is based on the BMD values as provided by central DXA. As mentioned above, DXA availability worldwide is considerably limited. In these situations and places, anti-osteoporotic treatment could potentially be initiated as based on the fracture probability assessed by heel QUS and clinical risk factors. To note, the thresholds are device and parameter specific. As of today, there is insufficient evidence to use heel QUS for the monitoring of anti-osteoporotic treatment therapy (Njeh et al., 2000). A limitation of heel QUS performance is that patients need to take off shoes and socks, which may decrease their compliance to cooperate, especially when outdoors or in winter. Also, it brings sanitary concerns which might result in infection in case of wrong use or if the device is not disinfected appropriately. Finally, QUS measurement is very much sensitive to the foot/room/coupling agent temperature. The utility of heel QUS in fracture risk prediction has been investigated in cross-sectional and prospective studies (Alenfeld et al., 1998; Augat et al., 1998; Barkmann et al., 2000; Casciaro et al., 2016; Cepollaro et al., 1997; Clowes et al., 2005; Conversano et al., 2015; Karjalainen et al., 2016; Moilanen et al., 2013; Marín et al., 2006; Moayyeri et al., 2012; D. C. Bauer et al., 1995; Damilakis et al., 2003, 2004; Donaldson et al., 1999; Drozdzowska & Pluskiewicz, 2002; Drozdzowska et al., 2003; Durosier et al., 2006; Ekman et al., 2001, 2002; Esmaeilzadeh et al., 2016; Frediani et al., 2006; Frost et al., 1999, 2000, 2001, 2002; Gerdhem et al., 2002; Glüer et al., 1996; Glüer et al., 2004; Gnudi et al., 1998; Gnudi & Ripamonti, 2004; Gonnelli et al., 1995, 2005; Greenspan et al., 1997, 2001; Guglielmi

USA

Italy

USA

USA

UK

Netherland Elderly men cohort

Italy

Heaney 1995

Mele 1997

Bauer 1997

Huang 1998

Thompson 1998

Pluijm 1999

Gnudi 2000

Cohort

GP registry cohort

Communitybased cohort

Communitybased cohort

Cohort

Cohort

Country

Study type

First author, y of publication

254/0

578/132

3180/0

560/0

6189/0

211/0

130/0

2.0

3.2 2.0

2.7

2.6

2.8

5.47

52.0 ± 11.5 75.8 ± 4.7

73.7 ± 4.9

60.8 ± 6.7

82.8 ± 5.9

58.0 ± 7.6

Followup (years)

64.9 ± 10.0

N (wom- Age en/men) (mean ± SD)

Distal radius Patella

Heel

Heel

Heel

Heel

Phalanx

Patella

QUS site

Table 2.1 Studies on QUS parameters association with fracture risk prediction

1.9 [1.3–2.9] 1.3 [0.9–1.8] 2.3 [1.4–3.7] 1.6 [1.2–2.1]

Any clinical MOF NonVF HF Any clinical NonVF

NonVF

Signet

Signet

McCue CUBA

Achilles

Any clinical

1.89 [1.27–2.88] 1.72 [1.30–2.31] 1.4 [1.1–1.6]

3.89 [1.53–9.90]

1.6 [1.1–2.3] 1.3 [1.0–1.6] 3.69 [1.18–11.49]

Age, age at menop, we, he, treatment

1.6 [1.0–2.5] 2.2 [1.4–3.4] 1.1 [0.9–1.5] Age, sex

1.3 [1.1–1.5] 1.5 [1.3–1.8] Age

Age

Age

Age

2.0 [1.5–2.7] 1.50 [1.05–2.16]

SI/QUI

Age, clinic

1.5 [1.1–1.7]

SOS/ AD-SOS 2.11 [1.14–3.91]

Adjusted for

1.3 [0.9–2.0]

BUA

Fracture risk prediction End point RR/SD (spine, hip, all) [95% CI]

OsteoVF Technology Prototype 1 DBM Sonic NonVF 1200 Walker NonVF Sonix UBA 575 HF Walker VF Sonix UBA 575 NonVF

QUS device

14 D. Hans et al.

UK

USA

Australia

Finland

France

UK

EU

UK

Japan

McGrother 2002

Miller 2002

Devine 2004

Huopio 2004

Hans 2004

Khaw 2004

Glüer 2004

Stewart 2005

Fujiwara 2005

Communitybased cohort

Communitybased cohort

Cohort

Communitybased cohort GP registry cohort

Communitybased cohort

Communitybased cohort

GP registry cohort

GP registry cohort

3.0

1.0

3.0

2.6

3.5

1.9

77.9 ± 6.1

64 ± 5

75.1 ± 2.7

59.6 ± 3

80.5 ± 3.7

8339/648562.4 ± 9.1

9.7

5.0

47.8 ± 1.4

3024/100467.5 ± 8.9

775/0

–

–

1885/0

5898/0

422/0

1499/0

7562/0

1289/0

Heel

Heel

Heel

Heel

Heel

Heel

Heel

Heel

Heel

VF

Any clinical

Achilles

WF

HF

NonVF

1.60 [1.17–2.03] 1.57 [1.30–1.84]

2.50 [2.13–2.87] 1.44 [1.19–1.69]

1.54 [1.39–1.69]

3.11 [2.62–3.61] 1.71 [1.42–2.00]

1.80 [1.62–1.98]

(continued)

Age, sex, we, he

Age, we, he, smoking, history of fracture Age

Center

Age, we, HRT, Ca intake, history of fracture Unadjusted

2.25 [1.51–3.34] 1.53 [1.37–1.70]

1.49 [1.30–1.70]

1.76 [1.16–2.66] 1.95 [1.67–2.27]

1.72 [1.22–2.45]

1.38 [1.14–1.66]

Age, we, he, menop status

1.49 [1.30–1.70]

1.63 [1.34–1.99]

1.84 [1.22–2.79] 1.77 [1.52–2.06]

1.80 [1.27–2.56]

1.39 [1.15–1.67]

Age, history of fracture

Age

1.37 [1.21–1.55] 1.53 [1.19–1.96]

1.95 [1.50–2.52]

1.53 [1.01–2.33] 1.86 [1.61–2.15]

Any osteop HF

1.43 [1.01–2.04]

1.60 [1.31–1.94] 1.31 [0.84–2.04] 1.29 [1.07–1.56]

1.1 [0.77–1.58]

Any clinical

Any clinical

Walker Any clinical Sonix UBA 575 MOF

Achilles+

McCue CUBA

Achilles

Achilles

Achilles

HF

Walker HF Sonix UBA 575 Sahara Any clinical

2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture… 15

Germany

Brazil

SwitzerlandCommunitybased cohort

Glüer 2005

Pinheiro 2006

Krieg 2006

Outpatient clinic cohort

Díez-Pérez 2007

Spain

Elderly men cohort

Sambrook 2007 Australia

Outpatient clinic cohort Communitybased cohort

Country

Study type

First author, y of publication

Table 2.1 (continued)

5.0

2.9

2.0

2.8

75.6 ± 6.6

75.2 ± 3.1

1532/473 85.7 ± 7.1

72.3 ± 5.4

5146/0

7062/0

208/0

87/0

2.0

Followup (years)

64.3 ± 7.8

N (wom- Age en/men) (mean ± SD)

Heel

Heel

Phalanx

Heel

Heel

Heel

QUS site

HF HF

Sahara DBM Sonic 1200 McCue CUBA Mark II Sahara NonVF

Any clinical

HF

Any clinical

VF

1.33 [1.17–1.51]

1.48 [1.10–1.97]a

2.2 [1.7–3.0]

2.4 [1.8–3.1]

BUA 2.13 [1.04–4.34]

Fracture risk prediction End point RR/SD (spine, hip, all) [95% CI]

Achilles+

Achilles+

Achilles

QUS device

SI/QUI 2.83 [1.26–6.34] 2.23 [1.30–3.83]

Age

1.20 [1.08–1.34]

1.31 [1.15–1.49]

2.3 [1.8–3.2] 2.4 [1.8–3.1] 1.2 [0.9–1.5]

Age, previous falls, family history of fracture, personal history of fracture, Ca intake

Unadjusted

Age, we, he, BMI, history of fracture, smoking, comorbidities, physical activity, treatment 2.3 [1.7–3.1] 2.6 [1.9–3.4] Age, BMI, centre

SOS/ AD-SOS 2.58 [1.17–5.68]

Adjusted for

16 D. Hans et al.

Olszynski 2013 Canada

Kwok 2012

HK

Cohort

Cohort

FranceCommunitySwitzerlandbased cohort UK GP registry cohort

Hans 2008

Moayyer 2009

SwitzerlandCommunitybased cohort

Hollaender 2008

Communitybased cohort

USA

Bauer 2007

4.2

3.4

3.2

10.3

6.5 5.0

76.6 ± 6.6

69.9 ± 3.1

12,958/0 77.6 ± 4.3

69.5 ± 3.0

72.4 ± 5 66.1 ± 11.5

2633/0

0/1921

752/703

432/0

0/5607

Phalanx

Tibia

Distal radius

Heel

Heel

Heel

Phalanx

Heel

Heel

NonVF

Any clinical

NonVF

Any clinical

HF

BeamMed Any clinical Omnisense Multisite Quantitative Ultrasound NonVF

Sahara

McCue CUBA

1.23 [1.03–1.47]

2.04 [1.55–2.69]

2.3 [1.3–3.8]

1.56 [1.13–2.16] 2.0 [1.5–2.8] 1.9 [1.2–3.0]

HF HF VF

1.6 [1.4–1.8]

NonVF

Sahara VF DBM Sonic VF BP Achilles+ HF

Achilles+

Sahara

1.85 [1.56–2.17] 2.00 [1.39–2.86] 1.65 [1.41–1.92] 1.67 [1.41–1.96]

1.06 [0.95–1.18] 1.83 [1.56–2.17]

1.32 [1.10–1.59]

2.1 [1.3–3.3]b

(continued)

Age, BMI, history of fracture, smoking, alcohol intake, BMD Age, history of fracture Unadjusted

Age

1.40 [1.01–1.95] 2.2 [1.6–3.1] 2.3 [1.4–3.8] Age

2.9 [1.6–5.5] 2.8 [1.5–5.0] 1.1 [0.7–1.7]

1.21 [0.95–1.56] 2.2 [1.6–3.2] 2.4 [1.4–4.1]

1.6 [1.4–1.9] 1.6 [1.4–1.9] Age, clinic

2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture… 17

Study type

Cohort

Country

Olszynski 2013 Canada

First author, y of publication

Table 2.1 (continued)

0/1108

63.3 ± 12.9

N (wom- Age en/men) (mean ± SD)

5.0

Followup (years)

Phalanx

Tibia

Distal radius

QUS site

HF

NonVF

Any clinical

HF

Any clinical

HF

NonVF

Any clinical

HF

BUA

Fracture risk prediction End point RR/SD (spine, hip, all) [95% CI]

BeamMed Any clinical Omnisense Multisite Quantitative Ultrasound NonVF

QUS device

1.06 [0.69–1.63] 1.37 [0.57–3.33] 1.37 [0.93–2.04] 1.35 [0.90–2.00] 1.03 [0.47–2.27] 1.26 [0.86–1.82]

SOS/ AD-SOS 2.00 [1.41–2.86] 1.52 [1.30–1.79] 1.54 [1.30–1.82] 2.30 [1.59–3.33] 1.12 [0.74–1.69]

SI/QUI

Unadjusted

Adjusted for

18 D. Hans et al.

Individual 46,124 level meta-analysis

70.0 ± NA 4.7

Heel

–

HF

MOF

1.45 [1.40–1.51]

1.25 [0.85–1.82] 1.47 [0.74–2.94] 1.42 [1.36–1.47] Age, time since baseline

1.69 1.60 [1.56–1.82] [1.48–1.72] VF 1.40 1.45 [1.26–1.55] [1.30–1.63] DFF 1.44 1.41 [1.34–1.54] [1.31–1.51] HuF 1.45 1.40 [1.31–1.59] [1.27–1.54] RF 1.24 1.18 [1.12–1.37] [1.07–1.30] PF 1.52 1.37 [1.30–1.78] [1.17–1.59] VF vertebral fracture, HF hip fracture, WF wrist fracture, MOF major osteoporotic fracture, DFF distal forearm fracture, HuF humerus fracture, RF rib fracture, PF pelvis fracture, we weight, he height, Ca calcium, BMD bone mineral density, BMI body mass index, menop menopause, BUA broadband ultrasound attenuation, SOS speed of sound, AD-SOS amplitude-dependent speed of sound, SI stiffness index, QUI quantitative ultrasound index, RR relative risk, SD standard deviation a BUA tertile ]39.7–58.9[; b SI as a categorical variable ]59.1–77.6[ The majority of studies reported SOS or SI, for those that reported AD-SOS or QUI, the RR/SD [95% CI] is in italic

McCloskey 2015

HF

NonVF

2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture… 19

20

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Fig. 2.1 Studies that observed the risk of having a fracture (hip, spine or any) as predicted by QUS devices, grouped by the QUS site. Footnote: SOS speed of sound, RR relative risk, SD standard deviation

et al., 2003; Hadji et al., 2000; Hamanaka et al., 1999; Hans et al., 2002, 2003; Hartl et al., 2002; He et al., 2000; Hernández et al., 2004; Hollevoet et al., 2004; Ingle & Eastell, 2002; Karlsson et al., 2001; Knapp et al., 2001, 2002; Krieg et al., 2003; Kung et al., 1999; López-Rodríguez et al., 2003; Maggi et al., 2006; Marshall et al., 1996; Matsushita et al., 2000; Mészáros et al., 2007; Mikhail et al., 1999; Mulleman et al., 2002; Muraki et al., 2002; Nguyen et al., 2004; Njeh et al., 2000; Ohishi et al., 2000; Peretz et al., 1999; Pinheiro et al., 2003; Pluskiewicz & Drozdzowska, 1999; Ross et al., 1995; Roux et al., 2001; Sakata et al., 1997; Schneider et al., 2004; Schott et al., 1995; Shuhart et al., 2019; Stegman et al., 1995; Stewart et al., 1995; Travers-Gustafson et al.,

1995; Turner et al., 1995; Varenna et al., 2005; Welch et al., 2004; Weiss et al., 2000; Wüster et al., 2000; Zagórski et al., 2021). The strongest evidence to date is on the heel QUS prediction ability for hip and spinal fractures. Given the heterogeneity between the QUS devices, comparing the results of individual studies is difficult and further statistical standardization of the data to reduce inter-center differences in QUS measurement variables is recommended (Paggiosi et al., 2012). Combining the results of different studies comprising tens of thousands of individuals, it was found that the increase in relative risk for fracture per each SD decrease in SI, measured by heel QUS, was roughly 1.6–2.0 for the hip and spine fractures; and approximately 1.3–1.5 for all

2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture…

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fractures combined. This suggests that heel QUS predictive ability for fracture is similar to DXA (Durosier et al., 2006). To note, its performance in fracture risk prediction has only been tested in some ethnicities (Bauer, 1988; Bauer & Deyo, 1987). There is ample empirical evidence that the heel QUS SI, as assessed by some but not all QUS devices, is predictive of hip fracture risk in Caucasian and Asian women older than 55 years, and of any fracture risk in Caucasian women over 55 years. Less robust findings show as well that SI assessed with the GE-Lunar device, predicts hip fracture risk in Caucasian and Asian men over age 70; vertebral fracture risk in Caucasian and Asian women over age 55; and any fracture risk in Asian women and Caucasian or Asian men >70 (Krieg et al., 2008). There is no data available on African ethnicity population. Two recent reviews and meta-analyses performed by Moayyeri et al. (2012) and McCloskey et al. (2015) provide the largest and most robust empirical evidence on the fracture predic-

tion ability of heel QUS. Moayyeri et al. conducted an inverse-variance random-effects metaanalysis of 21 prospective studies, comprising 55,164 women and 13,742 men altogether. Each study had heel QUS performed at baseline and incident fracture assessment at the end of followup. The total follow-up of the included studies was 279,124 person-years. The random effects of these studies for both heel QUS parameters, BUA and SOS, are shown in Fig. 2.2. In brief, the findings of this meta-analysis suggested that the four heel QUS parameters studied (BUA, SOS, SI and QUI) were predictive of fracture risk. The relative risk (RR (95% CI)) for hip fracture was 1.69 (1.43–2.00) per each SD decrease in BUA; 1.96 (1.64–2.34) per each SD decrease in SOS; 2.26 (1.71–2.99) per each SD decrease in SI; and 1.99 (1.49–2.67) per each SD decrease in QUI. In addition, in the meta-analysis adjusted for hip DXA, a significant association of BUA with fracture risk (relative risk per standard deviation decrease RR/SD (95% CI) 1.34 (1.22–1.49) was seen. Moayyeri et al. make certain key statements

Fig. 2.2 Random effects meta-analysis for studies with BUA and SOS for prediction of any clinical fracture, hip fracture and vertebral fracture. (Reproduced from Moayy-

eri et al., with permission) Footnote: BUA broadband ultrasound attenuation, SOS speed of sound

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in their work: (i) QUS of the heel using validated devices predicts risk of different types of fractures in elderly men and women; (ii) All four approved QUS measured parameters investigated by the included studies, BUA, SOS, SI and QUI, can be used for fracture risk assessment; (iii) Validated devices from different manufacturers can predict fracture risk with a similar performance, (iv) There was a trend of higher performance of SI and QUI in fracture risk prediction compared to BUA and SOS, but without reaching statistical significance; (v) In overall, the current evidence is mainly on Caucasian postmenopausal women and Caucasian men over the age of 65. Prospective studies in ethnicities other than Caucasian are needed; (vi) The QUS fracture risk prediction ability is similar in both women and men. McCloskey et al. performed an individuallevel meta-analysis of nine prospective studies, comprising altogether 46,124 individuals. The study population was from Asia, Europe and North America, thus multi-ethnic. 3018 incident fractures occurred during the studies’ followup period. The gradient of risk (GR (95% CI)) for any type of fractures was similar for BUA 1.45 (1.40–1.51) and SOS 1.42 (1.36–1.47). For hip fracture, the GR was 1.69 (1.56–1.82) and 1.60 (1.48–1.72) for BUA and SOS, respectively (Table 2.1). Notably, the GR was significantly higher for both fracture outcomes at lower baseline values of BUA and SOS (p < 0.001). The fracture risk predictive value of QUS was similar for women and men and for all ages (p > 0.20). The predictive value of both BUA and SOS for osteoporotic fracture risk decreased significantly over time (p = 0.018 and p = 0.010, respectively). For instance, the GR of BUA for any type of fracture, adjusted for age, was 1.51 (1.42–1.61) 1 year after baseline, and 1.36 (1.27–1.46) 5 years after baseline. The results from McCloskey et al. confirmed that QUS is an independent predictor of fracture for men and women, and its predictive ability is particularly higher in individuals with lower values of QUS parameters. Based on current evidence, heel QUS parameters are significant predictors of fractures occurring secondary to osteoporosis, and of hip fractures in particular. The predictive ability is similar

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to that of other axial or peripheral measures of bone strength. Nevertheless, femoral neck BMD remains the best hip fracture predictor among the parameters provided by bone assessment tools. Moreover, the fracture predictive value of heel QUS is greater at lower values of the parameters and decreases slowly over time. To date, the incorporation of QUS parameters within fracture risk prediction quantification tools is not applied yet. However, efforts to integrate QUS parameters within a tool for fracture risk calculation have been introduced by the EPISEM cohort (Hans et al., 2008). In this study, they combined major clinical risk factors with validated QUS parameters into a probabilistic model to calculate both 5- and 10-year probabilities of osteoporotic fractures and of hip fractures specifically. Their analysis comprised 12,958 elderly women from the EPISEM cohort. The fracture clinical risk factors used in the multivariate modes were: age, body mass index (BMI), prior history of fracture, results of the chair test, a fall within the preceding 12 months, current tobacco smoking, diabetes mellitus, and the heel SI as measured by QUS. This combination of clinical risk factors and heel QUS was found to be good at predicting fracture risk at different ages, and its predictive ability was superior to either clinical risk factors or heel QUS SI alone. The average GR for hip fracture was 2.10 per one SD decrease of SI in the models comprising both clinical risk factors and QUS heel, 1.52 of SI alone, and 1.52 of clinical risk factors alone. The authors further demonstrated the ability of the model combining heel QUS SI as expressed in a Z-score and fracture clinical risk factors to predict the 10-year probability of hip fractures (Fig. 2.3), which would allow its incorporation to an existing tool as FRAX. This model remained predictive even when fall-related factors and the chair test were excluded. This approach demonstrates how a complex model can be converted into a practically useable tool in routine clinical practice. Nevertheless, on the pathway towards the development of a similar clinically useful tool, several challenges have to be addressed. The risk prediction tool will have to be validated in several variable cohorts. Cohort

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Fig. 2.3 Example of 10-year probabilities of hip fracture for subjects with four clinical risk factors (CRF) and different QUS Z-score

studies will likely have a different set of risk factors, and the relative weight of common risk factors will also likely differ. Ten-year probability estimates might be too long, as it has been shown that the ability of heel QUS to predict fractures decreases over time. The ultimate clinical use of heel QUS parameters to assess the fracture risk will have to be based and further validated in currently widely used approaches such as FRAX (Kanis et al., 2017) or Garvan (Chan et al., 2012).

2.3.2

QUS Radius Devices (Cortical Axial Transmission)

QUS radius parameters are the most studied after heel QUS parameters. Nonetheless, in general, they show poorer fracture prediction ability and fracture discrimination ability as compared to heel. A recent systematic review and meta-analysis conducted by Fu et al. (2021) included 13 studies (using a single technology –

Beammed Omnisense) that had observed the fracture discriminative ability of radius QUS. The review comprised 16,681 individuals, among which, 5892 were men and 10,789 were women; and 1296 fracture cases in total. One SD decrease in radial SOS contributed to an increased risk of total and hip fracture of 32% (RR (95% CI) 1.32 (1.04–1.67)) and 66% (RR (95% CI) 1.66 (1.10–2.51)), respectively, in women. In the general population, men and women, these risks were increased by 21% and 55%, respectively. The association between QUS radial SOS and fracture risk was even stronger in postmenopausal women, indicating that radius QUS has greater potential as an effective tool for fracture risk evaluation in women. Biver et al. explored low-frequency velocity (LFV), a parameter derived from radius OsCare Sono® device in 271 community-dwelling postmenopausal women and men from the Geneva Retirees Cohort (Biver et al., 2019). They saw that in models adjusted for age and sex, LFV was

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significantly associated with prevalent fractures and the odds ratio (OR (95% CI)) per SD decrease in LFV was 1.50 (1.05, 2.14), p = 0.024. This study showed that LFV had a discrimination performance comparable to that of femoral neck or distal radius BMD in their specific population. Conceptually similarly to the effort in the EPISEM cohort (Hans et al., 2008), Subasinghe et al. (2019) evaluated the possibility of replacing DXA BMD input with radius QUS axial SOS in calculating fracture risk by FRAX. Their study included 339 postmenopausal women. They compared the 10-year probabilities of major osteoporotic fracture and hip fracture for models including clinical risk factors, clinical risk factors and BMD, and clinical risk factors and radius QUS T-score. Their work concluded that the model without BMD had 79.2% sensitivity, 80.1% specificity, 68.8% positive predictive value (PPV) and 87.4% negative predictive value (NPV). The model with the QUS radius T-score had 78.4% sensitivity, 70% specificity, 59.8% PPV and 85% NPV. The ROC AUC curves of both were higher than 0.80. Their findings suggest that adding QUS parameters to the clinical risk factors for FRAX calculations, does not present added value in fracture prediction. However, the study sample size was small and further investigations on the matter should be taken to adequately address the use of QUS parameter in FRAX instead of BMD. To note, as for QUS heel devices, the underlying technology of the QUS radius devices differ substantially between manufacturers despite measuring the same skeletal site. Therefore, clinical results obtained on one device may not be forcedly applicable to other technologically different ones.

2.3.3

QUS Other Devices

Other measurements sites of QUS devices are finger phalanges, tibia, and less common femur, posterior processes of the spine and ulna.

The finger phalanges measurement site is the distal metaphysis of the first phalanx of the last four fingers. The metaphysis consists of both cortical and trabecular bone. Age-related losses of both bone tissues increase the overall bone fragility importantly (Njeh et al., 1999). Midtibia has a long, straight and smooth surface. The overlying soft tissue is very thin minimizing the errors of SOS (Njeh et al., 1999). Tibia has therefore been a chosen site for QUS devices. Tibia consists of cortical bone, which forms 80% of the skeleton and thus is a crucial factor in the overall bone fragility. Oral et al. compared the performance of heel, radius, tibia and phalanx QUS parameters at identifying individuals with osteoporosis as defined by the BMD T-score (Oral et al., 2019). They saw that in women (n = 131) the ROC AUC was 0.712–0.764 for heel QUS parameters, 0.661– 0.673 for radius QUS parameters, 0.586 for tibia SOS, and 0.526 for phalanx SOS. The AUC of QUS heel and radius were statistically significant. Similar results were obtained for men (n = 109), but in men only the AUCs of QUS heel parameters were statistically significant. The largest study to date aiming at assessing the ability of a non-heel QUS device to predict fractures, was performed in the Canadian Multicenter Osteoporosis Study (Olszynski et al., 2013). They aimed at assessing the ability of a non-heel QUS device to predict fractures over 5 years of follow-up. In total, 1108 men and 2633 women were assessed with QUS at the tibia, radius and phalanx with the axial transmission QUS device (Beammed). Over the duration of follow-up, 204 fractures were documented. In women, 1 SD decrease in SOS measure was associated with an increase of fracture risk by 83% when measured at the radius (Hazard Ratio - HR = 1.83 (1.56–2.17)), by 65% when measured at the tibia (HR = 1.65 (1.41– 1.92)) and by 52% when measured at the phalanx (HR = 1.52 (1.30–1.79)). For hip fracture, 1 SD decrease in SOS measure was associated with an increase of fracture risk by 100% when measured

2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture…

at the radius (HR = 2.00 (1.39–2.86)) and tibia (HR = 2.00 (1.41–2.86)), and 130% when measured at the phalanx (HR = 2.30 (1.59–3.33)). For non-vertebral fractures, the HR/SD decrease was 1.85 (1.56–2.17), 1.67 (1.41–1.96) and 1.54 (1.30–1.82) for radius, tibia and phalanx SOS, respectively. In non-adjusted models, radius SOS performed better than the tibia or phalanx SOS. After adjusting for other known variables, including most of the clinical risk factors incorporated into the FRAX model and femoral neck BMD, there was an overall attenuation of the predictive ability of the QUS measures. Nevertheless, radial and tibial SOS did not lose their predictive power for hip fractures after multivariate adjusting. This study concluded that QUS at the radius and tibia, but not the phalanx, is a valid and independent of BMD and fractures clinical risk factors tool for fracture risk assessment. In general, the latter has been a consistent finding across all the main studies comparing the fracture predictive power of QUS at different skeletal sites. Although radius and tibia stand superior to phalanx, their fracture predictive power is inferior to that of heel QUS. Pulse-echo radiofrequency signals measured at the lumbar spine proximal femur allow the derivation of different bone indexes, from which two have been studied in the clinical setting, namely the Osteoporotic Score and the Fracture score given by the REMS technology (Chap. 7 gives a detailed description of this pulse-echo technique). The Osteoporotic Score (OS) allows the calculation of equivalent sitespecific BMD values from XA Hologic® devices (Hologic, Waltham, MA, USA) and their Tscores and Z-scores based on the NHANES database (Casciaro et al., 2016; Conversano et al., 2015). The calculated BMD values displayed high osteoporosis diagnostic agreement when compared with standard DXA measures in a population of 1914 postmenopausal women 51 to 70 years (over 88.2% at both sites, κ > 0.794, p < 0.001). The main drawback of this effort was that reference data were only available for

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post-menopausal Caucasian women 50–60 years for lumbar spine, and 60–70 years for femoral neck; thus, limiting the generalization of the results. Further, a case-control sub-study (175 fractured and 350 non-fractured participants) of an observational prospective cohort of Caucasian post-menopausal women showed that both OSderived and DXA-derived lumbar spine Tscores were able to discriminate patients with incident fragility fractures (AUC = 0.66 vs. 0.61 respectively, p = 0.0002) (Adami et al., 2020). The Fragility Score (FS) obtained with REMS method has been derived by comparing acquired data from a case-control study of 102 postmenopausal fractured and not fractured women, (Pisani et al., 2017) and was correlated with FRAX® assessment and DXA lumbar BMD in a second case-control study of 84 post-menopausal women (Greco et al., 2017). In overall, the reported study remained small, limited and dependent, thus their findings should be interpreted with caution. Finally, Cortet et al. studied REMS performance in osteoporosis diagnosis as compared to DXA in a large European multicenter study comprising 4307 Caucasian women 30–90 years old (Cortet et al., 2021). Interestingly, their findings suggest for a high performance of REMS in osteoporosis identification, referred to as ‘excellent performance’ in their manuscript, with both sensitivity and specificity values surprisingly higher than 90%; and a higher association of REMS than DXA T-scores with prevalent fractures. Moreover, the ESCEO experts’ consensus meeting of 2019 highlighted the REMS as the first clinically available method that can measure lumbar and femoral BMD with no exposure to ionization radiation and with high accuracy (Diez-Perez et al., 2019). However, this statement was surprisingly strong given the limited evidence provided by only few published studies. Evidence on the novel pulse-echo Bindex QUS device is also limited. Schousboe et al. studied the osteoporosis presence discriminative ability

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of Bindex in 555 postmenopausal women (Schousboe et al., 2017). They saw that using the measured parameter, a follow-up DXA would be avoided in approximately 70% of the individuals. Similarly, Karjalainen et al. saw in 1091 postmenopausal women that 68% of them would be excluded from additional DXA measurements (Karjalainen et al., 2018). Both studies suggest the potential of Bindex as initial screening tests for osteoporosis.

2.3.4

QUS Incorporation into the Clinical Routine of Osteoporosis Management

The international Society of Clinical Densitometry (ISCD) gives precise recommendations for the use of non-central bone assessment methods such as QUS (Shuhart et al., 2019): (i) bone density measurements from different devices cannot be directly compared; (ii) different devices should be independently validated for fracture risk prediction by prospective trials, or by demonstration of equivalence to a clinically validated device; (iii) T-scores from measurement other than DXA at the femur neck, total femur, lumbar spine, or onethird (33%) radius cannot be used according to the WHO diagnostic classification because those T-scores are not equivalent to T-scores derived by DXA; (iv) device-specific education and training should be provided to the operators and interpreters prior to clinical use; (v) quality control procedures should be performed regularly. Current evidence suggests the clinical use of heel QUS as the only validated skeletal site for osteoporosis management. Heel QUS is also the sole site that ISCD recommendations recognize to be used in clinical practice, which we summarize here. Heel QUS positions itself as an attractive prescreening tool for osteoporosis, serving as a potential alternative to DXA. Prescreening will have as an objective a case-finding approach, which consists in distinguishing individuals at high or

low risk for a given state (fracture), who would therefore require no further investigation due to their accurately defined fracture status. In individuals at intermediate risk, fracture status would remain equivocal, thus further evaluation would be required. At present, the use of heel QUS for the case-finding approach for osteoporosis fractures is fairly supported by empirical evidence particularly among Caucasian and Asian postmenopausal women. The evidence on the utility of QUS cortical bone-based devices, men and ethnicities other than Caucasian and Asian, in osteoporosis or fracture case-finding strategy is poorer. Results of REMS studies seem promising, but more studies are needed to validate them. Combining both QUS and clinical risk factors for fractures could identify patients at very low risk who require no further evaluation, as well as those at very high risk for whom treatment initiation could be started without further evaluation. This strategy shows promise at minimizing the unnecessary overuse of clinical means. Any patient in the intermediate rank of risk would be referred for additional testing, such as DXA acquisition (Fig. 2.4). Importantly, the use of QUS parameters in clinical routine, either as a pre-screening or stratification tool, must be based on elaborated devicespecific cutoffs validated in the population(s) where they are intended to be used. QUS is currently not recommended for the monitoring of response to therapy as most common treatments for osteoporosis result in small changes in the appendicular skeleton. The confidence at which QUS can be used in the treatment follow-up context is defined by two main limitations: the high variability of QUS measurements causing a poor index of individuality, and the lack of clinical trials showing that individuals selected as high risk by QUS have a lower fracture risk after treatment. In addition, the precision and stability of the different QUS machines measures – crucial parameters for treatment effect followup – are not, once standardized, sufficient or as good as those of DXA.

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Fig. 2.4 Case finding strategy based on fracture probability, as assessed by both QUS and CRFs. Footnote: CRF clinical risk factors, QUS quantitative ultrasound,

DXA dual energy X-ray densitometry, TBS trabecular bone score, FRAX 10-year fracture risk probability

2.4

the existing evidence and impedes its widespread acceptance for use in clinical practice. However, the clinical utility of heel QUS devices in particular has been disentangled and its clinical use considerably established. Radius QUS is inferior to heel in this hierarchy, and leaves behind other sites such as tibia, phalanx etc. In general, QUS is recommended to be used for the identification of individuals at low risk of fracture or high risk of fracture. In both these categories, the use of QUS would avoid the further use of alternative clinical means to assess fracture risk, such as DXA. Also, QUS is considered safe to be used in this context in areas

Conclusions

The promising contribution of QUS in the osteoporosis field is relatively inhomogeneous upon the QUS devices. In general terms, QUS, when combined with clinical risk factors, is considered as an acceptable alternative approach to DXA to estimate fracture risk and/or as a case finding strategy. Compared to DXA, it has lower costs, no radiation exposure, easier use and procedure performance, and wider availability. The variability of the QUS devices regarding their sites and manufacturers induces variability in their measurements as well. This heterogeneity is mirrored in

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and situations where DXA is unavailable. QUS parameters are strongly encouraged to be used in combination with clinical risk factors for fracture for the identification of subjects at low or high risk of fracture. Current state of evidence on QUS suffers from the lack of device and parameter specific thresholds. Such thresholds should be developed and cross-validated to ease the practical use of QUS parameters and their contribution to the treatment initiation decision-making. Further investigations of the QUS parameters behavior in men, ethnicities other than Caucasian and Asian, and sites other than heel should be encouraged.

Compliance with Ethical Standards All authors have no conflict of interest to declare.

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2 Quantitative Ultrasound (QUS) in the Management of Osteoporosis and Assessment of Fracture… ables in the identification of osteoporosis in women and men. Turkish Journal of Physical Medicine & Rehabilitation, 65(3), 203–215. https://doi.org/10.5606/ tftrd.2019.1894 Paggiosi, M. A., Barkmann, R., Glüer, C. C., Roux, C., Reid, D. M., Felsenberg, D., et al. (2012). A European multicenter comparison of quantitative ultrasound measurement variables: The OPUS study. Osteoporosis International, 23(12), 2815–2828. https://doi.org/ 10.1007/s00198-012-1912-2 Peretz, A., De Maertelaer, V., Moris, M., Wouters, M., & Bergmann, P. (1999). Evaluation of quantitative ultrasound and dual X-ray absorptiometry measurements in women with and without fractures. Journal of Clinical Densitometry, 2(2), 127–133. https://doi.org/10.1385/ jcd:2:2:127 Pinheiro, M. M., Castro, C. H., Frisoli, A., Jr., & Szejnfeld, V. L. (2003). Discriminatory ability of quantitative ultrasound measurements is similar to dual-energy Xray absorptiometry in a Brazilian women population with osteoporotic fracture. Calcified Tissue International, 73(6), 555–564. https://doi.org/10.1007/s00223002-1096-4 Pisani, P., Greco, A., Conversano, F., Renna, M. D., Casciaro, E., Quarta, L., et al. (2017). A quantitative ultrasound approach to estimate bone fragility: A first comparison with dual X-ray absorptiometry. Measurement, 101, 243–249. https://doi.org/10.1016/ j.measurement.2016.07.033 Pluskiewicz, W., & Drozdzowska, B. (1999). Ultrasound measurements at the calcaneus in men: Differences between healthy and fractured persons and the influence of age and anthropometric features on ultrasound parameters. Osteoporosis International, 10(1), 47–51. https://doi.org/10.1007/s001980050193 Riggs, B. L., Khosla, S., & Melton, L. J., III. (2002). Sex steroids and the construction and conservation of the adult skeleton. Endocrine Reviews, 23(3), 279–302. https://doi.org/10.1210/edrv.23.3.0465 Riggs, B. L., & Melton, L. J., 3rd. (1986). Involutional osteoporosis. The New England Journal of Medicine, 314(26), 1676–1686. https://doi.org/ 10.1056/nejm198606263142605 Ross, P., Huang, C., Davis, J., Imose, K., Yates, J., Vogel, J., et al. (1995). Predicting vertebral deformity using bone densitometry at various skeletal sites and calcaneus ultrasound. Bone, 16(3), 325–332. https://doi.org/ 10.1016/8756-3282(94)00045-x Roux, C., Roberjot, V., Porcher, R., Kolta, S., Dougados, M., & Laugier, P. (2001). Ultrasonic backscatter and transmission parameters at the os calcis in postmenopausal osteoporosis. Journal of Bone and Mineral Research, 16(7), 1353–1362. https://doi.org/10.1359/ jbmr.2001.16.7.1353 Sakata, S., Kushida, K., Yamazaki, K., & Inoue, T. (1997). Ultrasound bone densitometry of os calcis in elderly Japanese women with hip fracture. Calcified Tissue International, 60(1), 2–7. https://doi.org/10.1007/ s002239900176

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Schneider, J., Bundschuh, B., Späth, C., Landkammer, C., Müller, H., Sommer, U., et al. (2004). Discrimination of patients with and without vertebral fractures as measured by ultrasound and DXA osteodensitometry. Calcified Tissue International, 74(3), 246–254. https:// doi.org/10.1007/s00223-002-2137-8 Schott, A. M., Weill-Engerer, S., Hans, D., Duboeuf, F., Delmas, P. D., & Meunier, P. J. (1995). Ultrasound discriminates patients with hip fracture equally well as dual energy X-ray absorptiometry and independently of bone mineral density. Journal of Bone and Mineral Research, 10(2), 243–249. https://doi.org/10.1002/ jbmr.5650100210 Schousboe, J. T., Riekkinen, O., & Karjalainen, J. (2017). Prediction of hip osteoporosis by DXA using a novel pulse-echo ultrasound device. Osteoporosis International, 28(1), 85–93. https://doi.org/10.1007/s00198016-3722-4 Schuit, S. C., van der Klift, M., Weel, A. E., de Laet, C. E., Burger, H., Seeman, E., et al. (2004). Fracture incidence and association with bone mineral density in elderly men and women: The Rotterdam Study. Bone, 34(1), 195–202. https://doi.org/10.1016/j.bone.2003.10.001 Shuhart, C. R., Yeap, S. S., Anderson, P. A., Jankowski, L. G., Lewiecki, E. M., Morse, L. R., et al. (2019). Executive summary of the 2019 ISCD position development conference on monitoring treatment, DXA crosscalibration and least significant change, spinal cord injury, peri-prosthetic and orthopedic bone health, transgender medicine, and pediatrics. Journal of Clinical Densitometry, 22(4), 453–471. https://doi.org/10.1016/ j.jocd.2019.07.001 Stegman, M. R., Heaney, R. P., & Recker, R. R. (1995). Comparison of speed of sound ultrasound with single photon absorptiometry for determining fracture odds ratios. Journal of Bone and Mineral Research, 10(3), 346–352. https://doi.org/10.1002/jbmr.5650100303 Stewart, A., Felsenberg, D., Kalidis, L., & Reid, D. M. (1995). Vertebral fractures in men and women: How discriminative are bone mass measurements? The British Journal of Radiology, 68(810), 614–620. https:/ /doi.org/10.1259/0007-1285-68-810-614 Su, N., Yang, J., Xie, Y., Du, X., Chen, H., Zhou, H., et al. (2019). Bone function, dysfunction and its role in diseases including critical illness. International Journal of Biological Sciences, 15(4), 776–787. https://doi.org/ 10.7150/ijbs.27063 Subasinghe, H., Lekamwasam, S., Ball, P., Morrissey, H., & Morrissey, E. I. (2019). Performance of Sri Lankan FRAX algorithm without bone mineral density and with quantitative ultrasound data input. The Ceylon Medical Journal, 64(1), 17–24. https://doi.org/10.4038/ cmj.v64i1.8836 Travers-Gustafson, D., Stegman, M. R., Heaney, R. P., & Recker, R. R. (1995). Ultrasound, densitometry, and extraskeletal appendicular fracture risk factors: A crosssectional report on the Saunders County Bone Quality Study. Calcified Tissue International, 57(4), 267–271. https://doi.org/10.1007/bf00298881

34 Tu, K. N., Lie, J. D., Wan, C. K. V., Cameron, M., Austel, A. G., Nguyen, J. K., et al. (2018). Osteoporosis: A review of treatment options. P t, 43(2), 92–104. Turner, C. H., Peacock, M., Timmerman, L., Neal, J. M., & Johnson, C. C., Jr. (1995). Calcaneal ultrasonic measurements discriminate hip fracture independently of bone mass. Osteoporosis International, 5(2), 130– 135. https://doi.org/10.1007/bf01623314 Varenna, M., Sinigaglia, L., Adami, S., Giannini, S., Isaia, G., Maggi, S., et al. (2005). Association of quantitative heel ultrasound with history of osteoporotic fractures in elderly men: The ESOPO study. Osteoporosis International, 16(12), 1749–1754. https://doi.org/10.1007/ s00198-005-1914-4 Warriner, A. H., Patkar, N. M., Yun, H., & Delzell, E. (2011). Minor, major, low-trauma, and high-trauma fractures: What are the subsequent fracture risks and how do they vary? Current Osteoporosis Reports, 9(3), 122. https://doi.org/10.1007/s11914-011-0064-1 Weiss, M., Ben-Shlomo, A., Hagag, P., & Ish-Shalom, S. (2000). Discrimination of proximal hip fracture by quantitative ultrasound measurement at the radius. Osteoporosis International, 11(5), 411–416. https:// doi.org/10.1007/s001980070108

D. Hans et al. Welch, A., Camus, J., Dalzell, N., Oakes, S., Reeve, J., & Khaw, K. T. (2004). Broadband ultrasound attenuation (BUA) of the heel bone and its correlates in men and women in the EPIC-Norfolk cohort: A cross-sectional population-based study. Osteoporosis International, 15(3), 217–225. https://doi.org/10.1007/ s00198-003-1410-7 Wüster, C., Albanese, C., De Aloysio, D., Duboeuf, F., Gambacciani, M., Gonnelli, S., et al. (2000). Phalangeal osteosonogrammetry study: Age-related changes, diagnostic sensitivity, and discrimination power. The Phalangeal Osteosonogrammetry Study Group. Journal of Bone and Mineral Research, 15(8), 1603–1614. https:/ /doi.org/10.1359/jbmr.2000.15.8.1603 Zagórski, P., Tabor, E., Martela, K., Adamczyk, P., Glinkowski, W., & Pluskiewicz, W. (2021). Does quantitative ultrasound at the calcaneus predict an osteoporosis diagnosis in postmenopausal women from the Silesia Osteo Active Study? Ultrasound in Medicine & Biology, 47(3), 527–534. https://doi.org/10.1016/ j.ultrasmedbio.2020.11.025

3

Clinical Devices for Bone Assessment Kay Raum and Pascal Laugier

Abstract

Although it has been over 30 years since the first recorded use of quantitative ultrasound (QUS) technology to predict bone strength, the field has not yet reached its maturity. Among several QUS technologies available to measure cortical or cancellous bone sites, at least some of them have demonstrated potential to predict fracture risk with an equivalent efficiency compared to X-ray densitometry techniques, and the advantages of being non-ionizing, inexpensive, portable, highly acceptable to patients and repeatable. In this Chapter, we review instrumental developments that have led to in vivo applications of bone QUS, emphasizing the developments occurred in the decade 2010–2020. While several proposals have been made for practical clinical use, there are various critical issues that still need to be addressed, such as quality control and standardization. On the other K. Raum () Charité—Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin, Humboldt-Universität zu Berlin, CC04 Center for Biomedicine, Berlin, Germany e-mail: [email protected] P. Laugier Sorbonne Université, INSERM, CNRS, Laboratoire d’Imagerie Biomédicale, Paris, France e-mail: [email protected]

side, although still at an early stage of development, recent QUS approaches to assess bone quality factors seem promising. These include guided waves to assess mechanical and structural properties of long cortical bones or new QUS technologies adapted to measure the major fracture sites (hip and spine). New data acquisition and signal processing procedures are prone to reveal bone properties beyond bone mineral quantity and to provide a more accurate assessment of bone strength. Keywords

Attenuation · Axial transmission · Cortical bone · Trabecular bone · Speed of sound · Transverse transmission

3.1

Introduction

The current established standard method for the in-vivo assessment of bone strength and of its clinical counterpart, the risk of fracture, is based on the measurement of bone mineral density (BMD) by means of dual-energy Xray absorptiometry (DXA) (Miller et al., 2002). While BMD is an important predictor of bone strength (Bouxsein et al., 1999), additional

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 P. Laugier, Q. Grimal (eds.), Bone Quantitative Ultrasound, Advances in Experimental Medicine and Biology 1364, https://doi.org/10.1007/978-3-030-91979-5_3

35

36

factors are required to explain individual strength more accurately. These include tissue-intrinsic structural and viscoelastic material properties. Because ultrasound wave propagation is governed by the structural and material properties of the propagation medium, a diversity of innovative technological developments targeting the in-vivo characterization of bone strength has been implemented in medical devices (Table 3.1). The first clinical application of ultrasound waves to bone, using propagation in cortical bone, was described in the late 1950s for monitoring fracture healing at the tibia (Siegel et al., 1958). The technique did not have a great success. It was revived 30 years later by Alexej Tatarinov and colleagues to assess bone conditions during bed rest studies conducted to simulate long exposure to weightlessness. These studies published in Russian have gone unnoticed in the West but marked the beginning of axial transmission techniques dedicated to the measurement of guided waves in cortical bone. Investigations on the field are still going on as detailed later in this Chapter and also in Chaps. 4 and 5 of this book. The introduction of quantitative ultrasound (QUS) methods in the field of osteoporosis followed the study published in 1984 by Langton et al. (1984), a seminal work that strongly influenced later developments, demonstrating that the slope of the frequency-dependent attenuation at the calcaneus could discriminate osteoporotic from non-osteoporotic patients. This led to the opening of a new research and development area known as bone QUS. Many advances have been achieved during the last 30 years and a variety of technologies have been introduced to assess in vivo the skeletal status by providing measurements of ultrasonic parameters of cancellous bone or cortical bone at multiple anatomical sites, e.g., calcaneus, fingers phalanges, radius, tibia, proximal femur, and spine (Fig. 3.1). Theoretical and numerical studies emerged, and several different techniques were tested with more or less success. These include backscattering,

K. Raum and P. Laugier

propagation in poroelastic media, guided waves, and pulse-echo imaging. By coupling model to experimental data, these approaches have the power to derive bone biomarkers that reflect structural and material properties. Research is continuing in most of these areas. The absence of exposure to ionizing radiation, the portability and the modest cost of the machines are appealing factors of QUS devices. The main clinical field of application is fracture risk prediction for osteoporosis (see Chap. 2), although many other pathological bone conditions may benefit from ultrasound measurements, e.g., monitoring of fracture healing (Nicholson et al., 2020), monitoring of implant osseointegration (see Chap. 17), assessment of spinal deformities (Lam et al., 2011; Wong et al., 2019) (see Chap. 16), as a treatment monitoring tool for the management of rare bone diseases in children (Raimann et al., 2020), assessment of skeletal status in neonates and infants (Liu et al., 2020; Mao et al., 2019), and for the screening of adolescents and young adults (Jafri et al., 2020). As described in Chap. 2, the clinical validation for fracture risk prediction and the acceptance among clinicians is however not identical for all devices (Njeh et al., 2000). Until now, only heel QUS measures are proven to predict hip fractures and all osteoporotic fractures with similar relative risk as other central X-ray based bone density measurements (Gluer et al., 2004; Krieg et al., 2008; Marin et al., 2006; Moayyeri et al., 2009) (see Chap. 2). This Chapter describes the different clinical devices that have been developed for the in-vivo assessment of skeletal status in the context of the clinical management of osteoporosis. They can be classified according to the targeted tissue type (trabecular vs. cortical bone), measurement type (axial vs. transverse transmission, pulse-echo), and the type of interaction of the acoustic waves with the bone tissue (bulk compression/shear wave propagation, guided wave propagation, single vs. multi-path propagation, specular reflection vs. scattering). Depending on the type of measurement, different acoustic fre-

AD-SOS, BTT, UBPS

Finger phalanx Radius

LD-100 Radius

BUA, SOS, BQI

Calcaneus

Ultrascan

SOS, TI, OSI

Calcaneus

Attenuation, Radius Thickness, CT.Th, Trabecular Prop, Elasticity NTDCW, NTDDW,

BUA

Calcaneus

OYO Electric Co., Ltd. Kyoto, Japan CyberLogic, Inc., New York, NY, USA

BUA, SOS

Calcaneus

BUA, QUI

BUA, SOS

Calcaneus

BUA, SOS, SI

Calcaneus

Calcaneus

Hologic

Measurement parameter

Measurement site

Diagnostic Medical Systems, Montpellier, France DTU Meditech, Hawthorn, CA, USA CUBA McCue Ultrasonics, Winchester, UK AOS-100 Hitachi Medical Systems, Singapore Sonost Osteosys Corp., Seoul, Korea Cortical transverse transmission (Ct.TT) DBM Sonic Bone Profiler IGEA, Carpi, Italy

UBIS

Sahara

Device Vendor Trabecular transverse transmission (Tr.TT) Achilles GE Lunar, Madison, WI, USA

Stein et al. (2013) (continued)

Gluer et al. (2004), Gonnelli et al. (2005), Sakata et al. (2004) and Savino et al. (2013) Breban et al. (2010)

Njeh et al. (2000) and Tsuda-Futami et al. (1999) Jafri et al. (2020)

Chan et al. (2013)

Dobnig et al. (2007), Gluer et al. (2004), Gonnelli et al. (2005), Njeh et al. (2000) and Ramteke et al. (2017) Delshad et al. (2020), Gluer et al. (2004), He et al. (2000), Miller et al. (2002), Olmos et al. (2020) and To and Wong (2011) Gluer et al. (2004) and Sasagawa et al., 2011) Gluer et al. (2004)

References

Table 3.1 Overview of clinical bone QUS devices covered in this Chapter and respective vendors, measurement sites, and measurement parameters. The last columns provide references, from which information was compiled

3 Clinical Devices for Bone Assessment 37

SOS

SOS Ct.ThUS Ct.PoUS

Distal radiusTibiaProximal phalanx

Distal radiusTibia Distal radiusTibia

Femoral neckLumbar spine

Ct.ThAPP DI

SOS

Tibia

Distal radiusProximal tibiaDistal tibia

Measurement parameter

Measurement site

Behrens et al. (2016), Karjalainen et al. (2008), Karjalainen et al. (2012), Lewiecki (2020), Nazari-Farsani et al. (2020), Schousboe et al. (2017) and van den Berg et al. (2020)

Minonzio et al. (2019) and Schneider et al. (2019)

Moilanen et al. (2013)

Dobnig et al. (2007), Roggen et al. (2015) and Shenoy et al. (2017)

Foldes et al. (1995)

References

BMDUS Adami et al. (2020), Casciaro et al. (2016), T-score Di Paola et al. (2019) and Diez-Perez et al. Z-score (2019) FS AD-SOS Amplitude-Dependent Speed of Sound, BMDUS Ultrasound derived BMD value, BTT Bone Transmission Time, BUA Broadband Ultrasound Attenuation, BQI Bone Quality index, CT.Th Cortical Thickness (the subscripts US and APP denote real ultrasound based thickness and apparent thickness), FS Fragility Score, NTD Net Time Delay (the subscripts CW and DW denote circumferential and direct waves, respectively), DI Density Index, OSI Osteo-Sono-assessment Index, SOS Speed Of Sound, SI Stiffness Index, QUI Quantitative Ultrasound Index, UBPS Ultrasound Bone Profile Score, TI Transmission Index

Trabeculae pulse-echo (Tr.PE) Echo Echolight Spa, Lecce, Italy

Cortical pulse-echo (Ct.PE) BI Bone Index Finland Ltd, Kuopio, Finland

Device Vendor Cortical axial transmission (Ct.AT) Soundscan Myriad, Myriad Ultrasound Systems Ltd., Israel Omnisense Sunlight ultrasound Technologies Ltd., Rehovot, Israel Sono Oscare Medical Oy, Vantaa, Finland BDAT Azalée, Paris, France

Table 3.1 (continued)

38 K. Raum and P. Laugier

3 Clinical Devices for Bone Assessment

39

important clinical bone QUS devices (Table 3.1) are classified and presented according to their measurement principle, i.e., • • • • •

Trabecular transverse transmission (Tr.TT) Cortical transverse transmission (Ct.TT) Cortical axial transmission (Ct.AT) Cortical pulse-echo (Ct.PE) Trabecular pulse-echo (Tr.PE)

Some devices introduced in the Chapter are also described in detail in other Chapters of this book. A short description of the basic principles will be given here and we refer our readers to the corresponding Chapters for a comprehensive technical and performance description of these devices. Recent techniques, such as pulseecho imaging (Chaps. 9 and 10) and tomography (Chap. 11) not implemented yet in clinical devices, are not covered by the present Chapter, but the readership will find more information in the corresponding Chapters of this book.

3.2

Fig. 3.1 Overview of different measurement locations of clinical QUS devices (Adapted from Servier Medical Art by Servier under a Creative Commons Attribution 3.0 Unported License). See Table 3.1 for the explanation of the abbreviations and a summary of the clinical devices used at the indicated anatomical measurement sites

quency ranges and transmitter/receiver arrangements are used, and a plethora of acoustical, structural, elastic, and surrogate properties are derived. While most clinical bone QUS devices aim at deriving a BMD surrogate parameter based on empirically derived correlations with the DXAbased BMD reference, some recent devices provide quantitative structural bone biomarkers, e.g., cortical thickness and porosity, which are known to be related to bone strength (Iori et al., 2020) and fracture risk (Bala et al., 2014; Bjornerem et al., 2013). In the present Chapter, the most

Trabecular Transverse Transmission (Tr.TT)

The transverse transmission technique uses transmitter and receiver placed on opposite sides of the skeletal site to be measured. Systems with singleelement focused transducer pairs coupled to a mechanical scanning device as well as array systems have been developed. While the calcaneus (heel bone) is the preferred skeletal site, the method has also been applied at the proximal femur at the hip (Barkmann et al., 2008, 2010). Principles of measurements have been detailed in (Chappard et al., 1997; Laugier et al., 1997) and are only briefly recalled here for the sake of completeness. Assuming that the system response and the propagation are linear, the propagation characteristics such as attenuation and velocity are obtained using the well-known substitution technique, i.e., the signal transmitted through the skeletal site in response to a broadband ultrasonic excitation is compared to the signal transmitted through a reference medium such as water of known attenuation. The frequency-dependent

40

K. Raum and P. Laugier

attenuation is obtained from the spectral analysis of the two signals Aref (f) and A(f), typically using a Fast Fourier Transform algorithm.

3.2.1

Broadband Ultrasound Attenuation (BUA)

The apparent frequency-dependent attenuation, i.e., the signal loss, is defined on a logarithmic scale as follows:  ref  A (f ) α(f ˆ ) l = ln (3.1) |A(f )| where α(f ˆ ) is the measured apparent attenuation coefficient. In the frequency range used to make in-vivo measurements of the human calcaneus, the ultrasonic attenuation varies quasilinearly with frequency (Chaffai et al., 2000; Wear, 2001). Therefore, the slope of a linear regression fit to α(f ˆ ) · l in the frequency range of approximately 0.2–0.6 MHz yields the BUA value. The extraction of an unbiased attenuation slope from the empirically determined signal loss in Eq. 3.1 assumes that (i) the effect of diffraction is small and can be neglected (Droin et al., 1998; Xu and Kaufman, 1993), (ii) transmission losses are independent of frequency (the effect of interface losses on the attenuation curve is a simple vertical offset which does not affect the slope estimate) (Strelitzki and Evans, 1998) and (iii) phase cancellation effects are negligible, which is the case if the sample thickness and speed of sound across the ultrasonic beam profile are uniform. Overlapping of fast and slow waves (see Chap. 6) may also cause phase cancellation (Anderson et al., 2008; Bauer et al., 2008) but is usually not a concern for in vivo measurements, at least at the heel. The measurements yield the total loss through the intervening tissues in the beam, i.e., bone and surrounding soft tissues. The effect of the latter is generally neglected (Laugier, 2008). Not many devices do provide an estimate of the bone thickness. Therefore, the slope of the frequency-dependent attenuation (BUA) rather than the slope of the attenuation coefficient (i.e., BUA normalized by thickness) is measured.

The Hitachi AOS-100 does not perform a spectral analysis to measure BUA. Instead, the signal is analyzed in the time-domain and the “Transmission Index” TI, defined as the full-width-halfmaximum of the first positive peak of the received waveform is measured instead (Tsuda-Futami et al., 1999).

3.2.2

Speed of Sound

Two principal approaches have been used to measure SOS. The first one assumes that c is frequency-independent and uses simple timedomain methods, i.e., c is simply calculated from the difference of two time-of-flight (TOF) measurements, whereas for the first and second measurements the signal is transmitted through the reference material alone and through the reference material and the heel, respectively: L reference material : T OF ref = cref reference material and sample : T OF = L−l + cl cref l difference signal : T OF = cl − cref

c=

1 cref

1 + T lOF

(3.2)

(3.3)

If measurements are taken using probes in direct contact to the skin equation Eq. 3.3 reduces to:

c=

l T OF

(3.4)

Various criteria are used to estimate TOF, for example the first arrival point, the first zerocrossing point, or a fixed threshold on the rising front of the received electrical signal. However, frequency-dependent attenuation and velocity dispersion are acknowledged sources of bias when measuring velocity in the time domain (Droin et al., 1998; Nicholson et al., 1996; Strelitzki et al., 1996; Wear, 2000).

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41

Because there is no consensus on a standardized protocol for velocity determinations in bone, the comparison or pooling of measurements obtained from different devices is particularly difficult. Wear has suggested a numerical method to compute corrections for previously acquired SOS, to improve standardization in bone sonometry and to overcome discrepancies in SOS estimates due to transit-time marker location (Wear, 2008), but such a method has not been implemented yet in practice. As discussed for BUA, the thickness l of the skeletal site must be known, and the impact of soft tissue must be neglected. In the second approach, a frequencydependent c(f ) is estimated from the phase ϕ(f ) of the complex ratio of the spectra: 

 A(f ) ϕ(f ) = atan Aref (f )   1 1 = 2πlf − cref c(f )

(3.5)

After unwrapping the measured phase ϕ(f ), the phase velocity can be calculated as follows: c(f )

1 1 cref

−

ϕu (f ) 2π f l

(3.6)

where ϕu (f ) is the unwrapped phase.

3.2.3

Bone Stiffness and Quality Surrogates

The trabecular transverse transmission technique does not provide any direct measurement of stiffness, strength, or tissue quality. However, various surrogate parameters have been established (see Table 3.1.). The Lunar Achilles series provide a “Stiffness Index” SI, which is derived from normalized BUA and SOS values (Hans et al., 1994): SI = (nBUA + nSOS) /2, nBUA = (BUA-50) /75 × 100% nSOS = (SOS-1380) /180 × 100%.

(3.7)

Similarly, the Hologic Sahara provides the “Quantitative Ultrasound Index” QUI: QUI = 0.41 × (SOS + BUA) –571.

(3.8)

SI and QUI values agree fairly well (R = 0.83, p < 0.01) (Alenfeld et al., 2002), but QUI values were found on average 2.4% higher than SI values, and the difference was more pronounced for higher ultrasound values (Ingle et al., 2001). The Hitachi AOS-100 combines SOS with the attenuation surrogate TI to an “Osteo SonoAssessment Index” OSI as follows (TsudaFutami et al., 1999): OSI = TI × SOS2 .

(3.9)

These system-specific differences prevented a broader use of these parameters in clinical practice.

3.3

Cortical Transverse Transmission

The transducer configuration for cortical transverse transmission devices is similar to that of trabecular transverse transmission devices, but they have been introduced to measure the propagation of sound waves through both the cortical shell and medullary cavity. The DBM Sonic Bone Profiler measures the amplitude-dependent speed of sound (Ad-SOS) at the distal metaphysis of the first phalanx of fingers I–IV. The instrument is equipped with two 12-mm diameter, 1.25-MHz plane transducers mounted on an electronic caliper that measures the distance between the probes. The probes are positioned on the mediolateral surfaces of the distal metaphysis of the phalanx using the phalanx condyle as reference point. Coupling is achieved with a standard ultrasound gel. The probe positioning is slightly varied until the optimum signal (defined in terms of number of peaks and the amplitude of the peaks, following manufacturer recommendations) is recorded, then Ad-SOS is measured.

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K. Raum and P. Laugier

Fig. 3.2 Numerical sound propagation simulation (Bossy et al., 2002) through a human phalanx. A plane wave is transmitted from an unfocused transducer (a). Three distinct sound propagation pathways can be observed (b). Some waves bypass the bone and propagate through soft

tissue only (SW). Other waves either pass directly through cortical bone and the medullary cavity (DW) or are guided as circumferential waves (CW) within the cortical bone shell. Due to different propagation path lengths, the two circumferential waves reach the receiver at different travel times (c)

Fig. 3.3 The UltraScan 650 ultrasound bone assessment device (a) Numerical sound propagation simulation (Bossy et al., 2002) through a human radius showing three propagation paths. i.e., SW: soft tissue only; CW: cir-

cumferential wave; DW: direct wave (b) The 64-element receiver array allows a distinct analysis of the travel times of the SW, DW and CW signals. (a) and (b) were taken and adapted from Stein et al. (2013) with permission

Time-Of-Flight (TOF) is defined as the time between the emitted pulse and the first part of the signal that is above a predetermined amplitude threshold. The velocity measured with this technique is amplitude related and has been termed amplitude-dependent speed of sound (Ad-SOS). With this configuration, the fast waves (FW) are circumferential waves guided through the cortical shell (Fig. 3.2). In osteoporotic bones the attenuation is considerably higher than in normal bones and the amplitude of the first peak is too small to trigger the read-out electronics. The detection of the second peak is associated with an apparent longer travel time of flight. However, the exact propagation path length is unknown. Therefore, using the finger thickness rather than the exact path length results in an apparent speed of sound rather than in an accurate velocity estimate.

More recent systems apply the transverse transmission approach at the distal radius at the forearm. The Cyberlogic Ultrascan (Fig. 3.3) consists of a rectangular single-element 3.5MHz source transducer and a 1 × 4.8 cm 64element receiver array (Stein et al., 2013). The radius is positioned at 1/3 location in the device. Similar to the phalanx configuration, three different sound propagation pathways can be distinguished. One “Direct Wave” (DW) travels through cortical bone and the medullary cavity. The “Circumferential Wave” (CW) is guided through the cortical shell. At the peripheral ends of the emitter-receiver pair, waves travelling through soft tissue only (SW) can be observed. The advantage of the array-receiver configuration is that the distinct travel times can be analyzed more easily. The device measures two ultrasound

3 Clinical Devices for Bone Assessment

43

Fig. 3.4 Numerical sound propagation simulations (Bossy et al., 2002) of a focused wave through a human radius at three different time point showing the development of slow and fast waves (a–c), which

are recorded be the receiver (d). The travel-times and amplitudes of these waves are used to estimate apparent cancellous bone properties. The radius image was taken from Kazakia et al. (2013) with permission

net time delay (NTD) parameters: NTDDW and NTDCW define the difference between the transit times of waves traveling the DW and CW paths, respectively, and the travel time of the SW path. It has been shown in vitro that the cortical cross-sectional area CSA can be estimated by a non-linear combination of NTDDW and NTDCW (R = 0.95) (Le Floch et al., 2008):

estimate structural and elastic parameters from both, cortical and trabecular bone compartments. Theory and clinical applications of the twowave phenomenon are described in detail in Chap. 6. Briefly, the system measures at the ultradistal radius region (see Fig. 6.16), at which the cortical shell is thin and the medullary cavity is filled with a dense trabecular network (Fig. 6.14). The device uses two coaxially and confocally aligned 1-MHz transducers (Fig. 3.4), which are mechanically scanned. Data are captured both, in transmission and pulse-echo modes. A coarse scan in transmission mode provides maps of apparent attenuation and sound velocity, which are used to select the scan region for the measurement of a direct wave through the radius (Fig. 6.17). Several bone properties are estimated from the combination of transmission and reflection measurements following the model described in Chap. 6. These include thickness of cortical bone (mm) (Mano et al., 2015), bone mass (bone mineral density (mg/cm3 )) and bone volume fraction BV/TV (%) of cancellous bone, and elastic constant of cancellous bone (GPa) (Otani, 2005). It should be noted that the estimations of these properties require the a priori knowledge of multiple properties. The estimation of cortical thickness is based on the analysis of time delays of outer and inner cortical boundaries measured in pulse-echo mode and conversion to thickness using the assumption of a constant

CSA = a × NTDCW × NTDDW –b × NTDDW 2 + c.

(3.10)

A similar equation has been derived empirically in a clinical study on 60 adult subjects of both gender, age range between 22 and 84 years, to predict BMD values assessed at the same radius location (R = 0.93) (Stein et al., 2013): BMDUS = 0.19 × (NTDCW × NTDDW )1/2 + 0.28. (3.11) The LD-100 device (OYO Electrics, Kyoto, Japan, see Chap. 6, Fig. 6.13) is a hybrid technology, which combines transverse transmission measurements through cortical and trabecular bone compartments with pulse-echo measurements in cortical bone. It also uses a more sophisticated theoretical framework to

44

K. Raum and P. Laugier

Fig. 3.5 Principle of cortical axial transmission (a), reprinted from Foldes et al. (1995) with permission. The measurements can be performed at tibia (b) and radius

bones, adapted and reprinted from Schneider et al. (2019) with permission

compression wave velocity in the radial direction of cprad = 3300 m/s in cortical tissue:

transducer arrangement for a cortical axial transmission measurement is shown in Fig. 3.5. The SoundScan system was the first device introduced to measure the longitudinal transmission of an acoustic 250-kHz pulse along the cortical layer of the mid-tibia (Foldes et al., 1995). The probe is placed parallel to the longitudinal axis of the bone (Fig. 3.5a). The transducers are coupled to the skin through standard ultrasound gel. The transit time of a pulse along a defined 50-mm distance is measured. The probe is moved back and forth across the tibial surface and velocity readings are continuously recorded. The resultant velocity is an average of the five highest percent readings during the scan. With the Omnisense, multi-site axial transmission was introduced commercially as the direct successor to tibial axial transmission. The device offers a family of small hand-held probes designed to measure various skeletal sites under different soft tissue thickness conditions. The smallest probes can be used to measure skeletal sites where the layer of covering soft tissue is the thinnest such as the finger phalanxes, while the larger probes are dedicated for skeletal sites covered by a thicker layer of soft tissue such as the distal one-third radius. Still some patients cannot be measured due to thick soft tissue (Weiss et al., 2000). The main advantage of a multi-site device is the possibility of measuring skeletal sites which may be more relevant for fracture risk prediction than the tibia. While the basic measurement

Ct.T h =

cprad · t 2

.

(3.12)

A priori knowledge of propagation speeds, attenuation constants, densities and acoustic impedances of water, soft tissue and cortical bone are required for the estimations of the other parameters. However, as these properties are not known and can vary considerably, the properties reported by the device must be considered as “apparent” bone properties (Breban et al., 2010). However, reasonable correlations with cortical thickness (r = 0.88) and cancellous bone density (r = 0.76) derived from high-resolution Xray tomography have been obtained (see Figs. 16.18 and 16.19) and the system has been used successfully in different clinical studies (Sect. 16.3.2).

3.4

Cortical Axial Transmission

The principle of axial wave propagation differs considerably from conventional throughtransmission and pulse-echo measurements (for a detailed description, see Chap. 4). These devices are designed to measure the propagation velocity of ultrasonic waves axially transmitted along cortical bone in long bones. The common

3 Clinical Devices for Bone Assessment

45

Fig. 3.6 Principle of bi-directional axial ultrasound transmission. The ultrasound transducer consists of two emitter arrays and one receiver array separated by gel filled gap regions (dimensions are given in mm). The numerical sound propagation simulation shows an ultrasound pulse emitted at element 3 of emitter array 1, which propagates through skin and soft tissue into the bone. One part of

the wave is transmitted into the medullary canal and other parts propagate as compressional and dispersive guided waves in the axial bone direction through the cortical shell. These waves leak acoustic waves back into the soft tissue which are detected by the central receiver array. (Reprinted from (Raimann et al., 2020) with permission)

principle is identical for all cortical axial transmission devices, the technical configurations and data analyses are quite different. The probe of the Omnisense device contains four 1.25-MHz transducers, i.e., a transducer pair and a receiver pair. The four ultrasonic transducers are used for an estimation of the velocity in the soft tissue between transducer and bone and to compensate changes in the tissue thickness along the bone. Moreover, to increase the amplitude of the transmitted and received signals, the transducers are mounted at an angle close to the critical angle relative to the surface of the probe. Both factors severely impact on the trueness of the “speed of sound” (SOS) measurement through bone. Although the exact algorithm used by the manufacturer remains undisclosed, one may reasonably assume that several ultrasonic recordings are performed by combining direct transmission or reflection between different transmitters and receivers, so that several acoustic pathways involving soft tissue path portions of the same length and variable bone path length may be analyzed. Thus, processing different signal propagation times yields the signal propagation velocity of the first arriving signal νFAS . Depending on the thickness-to-wavelength ratio, different waves may be involved in the fastest part of the detected signal. Thereby, the reported SOS value may correspond to the velocity

of a bulk compression wave, a guided wave or a mixture of both (Raum et al., 2005). The Sono device makes use of the excitation and analysis of a fundamental flexural guided wave (FFGW), which is equivalent to the lowest antisymmetric Lamb mode (i.e., A0) for a plate (Moilanen et al., 2013). With the bi-directional axial transmission (BDAT) device an ultrasonic pulse is transmitted along the bone surface in two opposite directions from two sources placed at both ends of a distinct group of receivers (Fig. 3.6) (Bossy et al., 2004). A simple combination of the time delays derived from waves propagating in opposite directions efficiently corrects automatically for variable soft tissue thickness. In addition to the estimation of the first arriving signal the array configuration allows the full dispersion analysis of multiple dispersive waves by means of a 2-D spatio-temporal Fourier transform and dedicated signal processing (Minonzio et al., 2010). Different probes have been developed to ensure a suitable thickness-to-wavelength range for measurements with 1-MHz waves at the onethird distal radius (Minonzio et al., 2019; Vallet et al., 2016) and with 500-kHz waves at tibia bones (Schneider et al., 2019). In contrast to other bone QUS axial transmission devices, this method provides, under the assumptions that cortical bone behaves like a free wave-guiding isotropic plate

46

K. Raum and P. Laugier

Fig. 3.7 Principle of pulse-echo measurement of the apparent cortical thickness (a) A single-element focused transducer emits a wave and receives signals reflected from the periosteal and endosteal cortical bone interfaces.

Pulse-echo signal and Hilbert-transformed envelope signal measured by the same transducer (b) The time delay t between these two reflections is converted to a thickness valued using the assumption of a constant sound velocity in the radial bone direction

and the tissue stiffness of the cortical bone is constant, real measurements of cortical porosity (Ct.Po) and cortical thickness (Ct.Th). Other cortical axial transmission devices have been introduced but not yet commercialized, e.g., the dual frequency axial transmission (Tatarinov et al., 2014) and a low-frequency axial transmission (Vogl et al., 2019). The reader is referred to Chaps. 4 and 5 for a comprehensive introduction to the principles, signal processing and models implemented in this category of devices.

cortical bone interfaces, two reflections can be observed (Fig. 3.7a). The method relies on the assumptions that the specular reflections from periosteal and endosteal cortical bone interfaces are stronger than signals backscattered from cortical pores and that they are well separated in time, i.e., the time lag t between these two echoes can be measured using conventional peak detection algorithms applied to the envelope signal (Karjalainen et al., 2008) (see Fig. 3.7b). With the further assumption of a known and invariant radial sound velocity of cprad = 3565 m/s, the apparent cortical thickness Ct.Th is derived via Eq. 3.12. This value was obtained invivo by comparison with site-matched peripheral computed tomography (pQCT, in-plane pixel size: 500 μm × 500 μm) on 20 young and healthy volunteers (12 males, age (mean ± SD) 35.0 ± 12.7 years; 8 females, age (mean ± SD) 42.1 ± 14.3 years) (Karjalainen et al., 2008). It should be noted that the center frequency of the probe used in that study was 2.25 MHz and that different cprad values obtained at different measurement sites (proximal tibia: 3447 m/s; distal tibia: 3551 m/s; distal radius: 3634 m/s) were averaged. Accuracy and precision for the thickness estimation using the average value were reported to be 6.6% and 0.29 mm. This is in agreement with the reported error of 6% for Ct.Th by using use of a predefined, constant value for radial SOS (Eneh et al., 2016).

3.5

Cortical Pulse-Echo

Pulse-echo measurements using single-element transducers have been introduced by Karjalainen et al. (Karjalainen et al., 2012) and are now implemented in the Bindex device. This method provides estimates of the apparent cortical thickness Ct.Th measured at different anatomical sites, i.e., at proximal and distal tibia and at the distal radius. Moreover, a density index (DI) is calculated by a combination of age, weight, and multi-site apparent Ct.Th estimations. The device consists of a single-element focused transducer including a buffer-rod to send short ultrasound pulses through skin and soft tissue to the bone. If the beam inclination is approximately normal to the outer (periosteal) and inner (endosteal)

3 Clinical Devices for Bone Assessment

It was shown that the apparent cortical thickness measured at distal radius and distal tibia correlates with BMD (r  0.71, p < 0.001, 0.30 < R2 < 0.55) (Behrens et al., 2016). Thereby, a density index (DI) was introduced in an in-vivo study on 30 elderly women (age: 74.4 ± 2.9 years) with and without hip fractures (Karjalainen et al., 2012). By means of multivariate linear regression using age, weight, and apparent Ct.Th measured at distal and proximal tibia a significant model with BMD measured at the neck (r = 0.86) was obtained. While these early proof-of-concept studies have used transducers with a center frequency of 2.25 MHz, the commercialized devices have a nominal center frequency of 3 MHz (Karjalainen et al., 2016, 2018; Schousboe et al., 2017).

3.6

Trabecular Pulse-Echo

In analogy to transmission measurements, trabecular bone can be probed in pulseecho configuration. The implementation of radiofrequency echographic multi spectrometry (REMS) in a clinical device and the fundamentals of scattering in cancellous bone are covered in Chaps. 7 and 8, respectively. Briefly, the Echolight system uses conventional B-mode 128element array technology including a 3.5 MHz convex transducer array (Casciaro et al., 2016) and sophisticated image processing and machinelearning based algorithms for automatically selecting the appropriate region of interest and for computing quantitative indices. Measurements are performed at the spine (through the abdomen) or at the femoral neck. An “Osteoporosis Score” OS is derived by comparison of the mean power spectrum measured in a patient with age-, sex-, BMI- and site-matched spectral models of pathologic and healthy conditions, which were derived empirically by comparison with DXA-based BMD values (Casciaro et al., 2016). Similarly, the “Fragility Score” is obtained by comparing an analogous spectral similarity to subjects that reported a recent fragility fracture with respect to control subjects without fracture history (see Chap. 7 for further details). Although

47

the methods are not ground on a physical backscatter model, reasonable predictions of BMD have been obtained in postmenopausal women (R = 0.87) (Casciaro et al., 2016).

3.7

What Has Been Achieved and What Is Still Missing in Bone QUS?

Years 1990–2000 have been the decade of the QUS golden age with heel transverse transmission measuring BUA and SOS. A few heel devices such as the Achilles (GE Healthcare) and the Sahara (Hologic) were validated through large scale prospective studies including tens of thousands of patients. However, despite good clinical performances and a general clinical consensus that they were useful for fracture risk assessment and case-finding, particularly in regions of the world where access to DXA is uneasy (see Chap. 2), these approaches have generally declined and receded in the background. The low added value and the lack of standardization compared to DXA as well as the missing therapeutic trials with QUS-based inclusion of patients have been major obstacles to the broader establishment of heel transverse transmission in clinical routine. Currently, DXA remains the main modality used for the clinical management of osteoporotic patients and in addition to heel ultrasound a variety of other QUS modalities have been established, which provide bone density surrogate markers (e.g., BMDUS Density Index, T- and Zscores) derived from empirical correlations with BMD. Meanwhile, with the development of highresolution peripheral computed tomography a focus has been placed on the key role played by cortical bone in bone strength and on the importance of assessing cortical bone for a better clinical management of osteoporotic patients (Zebaze et al., 2010). This has revitalized the research effort on cortical bone quantitative ultrasound and years 2010–2020 have seen a major surge in the development and clinical application of technologies for the assessment of cortical bone, including developments of axial transmission, scattering, pulse-echo techniques and imaging methods. Al-

48

though most of the modern QUS approaches have been developed for the application at peripheral skeletal sites for practical reasons, e.g., ease of access and minimal influence of soft tissue, these measurement sites have now been confirmed to be highly relevant for the identification people at high risk for fragility fractures at the spine and other skeletal sites. For example, decreased cortical thickness and the prevalence of large BMU’s at the tibia have been shown ex-vivo to be quantifiable ‘fingerprints’ of structural deterioration at the femoral neck (Iori et al., 2020) and reduced proximal femur bone strength (Iori et al., 2019). While some of the recent technologies (e.g., BI and LD-100) assess an “apparent thickness”, a model-based measurement cortical thickness and cortical porosity Ct.Po has been achieved for the first time with the BDAT system by means of multimode waveguide dispersion analysis in axial transmission measurements. The method considers variations of porosity as a major source of variations of cortical bone elasticity, sound velocity and compression strength in postmenopausal women (Granke et al., 2011; Granke et al., 2016; Peralta et al., 2021). Results of a first validation study in postmenopausal women confirmed a comparable fracture discrimination performance of the BDAT variables as BMD for both vertebral and peripheral fractures (see Chap. 4). However, axial transmission measurements do not provide direct image-guidance and are restricted to patients with low BMI (Minonzio et al., 2019). In contrast to other bone QUS devices, Echolight has introduced the first bone QUS system based on a conventional medical ultrasound pulse-echo imaging platform. Moreover, they target with their approach the two major fracture sites, i.e., hip and spine (see Chap. 7). As ultrasound scanners are the by far most frequently applied imaging devices in clinical routine, the approach has great potential to reach a widespread application if it can be integrated into existing or future scanners from various vendors. The measurements are conducted through thick layers of soft tissue. However, as the REMS technology provides only ultrasoundbased BMD surrogate parameters and empirical associations with the occurrence of fragility

K. Raum and P. Laugier

fractures, the technology may provide a nonionizing diagnostic alternative to the DXA measurement but cannot surpass the limitations of BMD for the identification of people with increased fracture risk despite non-osteoporotic BMD values. Other promising technologies with a potential to complement or even surpass current radiative gold standards are still under development. These methods benefit from the increasing availability of sophisticated open programmable ultrasound platforms with multichannel data acquisition hardware. With these systems, the Delay-And-Sum (DAS) beamforming integrated into the hardware of conventional medical ultrasound scanners to reconstruct images from the ultrasound backscattered signals can be overcome. Thereby, the strong distortions of acoustic waves caused by refraction, scattering and diffusion at bone-soft tissue boundaries and intracortical pores can be incorporated in the image reconstruction. One promising recent research direction combines pulse-echo imaging using conventional medical ultrasound array imaging technology with refraction corrected multifocal image reconstruction (Nguyen Minh et al., 2020). The algorithm provides local estimations of both cortical thickness and sound velocity. Another sophisticated inversion method was inspired from seismic image reconstruction to image the internal structure (i.e., the endosteal cortical bone interface) of long bones (Renaud et al., 2018). This reconstruction algorithm also provides local estimations of Ct.Th and anisotropic sound velocity, and can even assess intraosseous blood perfusion (see Chap. 10). The diversity by which ultrasound interactions with cortical bone are explored are still expanding. For example, multiple scattering and sound diffusion models hold the possibility to assess cortical bone properties, such as pore size and density (Karbalaeisadegh et al., 2019) from backscattered waves (see Chap. 9). Very recently, Iori et al. (Iori et al., 2021) have proposed a cortical bone backscatter model, from which, for the first time, the cortical pore size distribution in the range between 20 and 120 μm could be retrieved (Iori et al., 2021).

3 Clinical Devices for Bone Assessment

It should be noted that this pore size range is not resolvable by any other medical imaging modality but covers the transition from normal to pathologically increased pore dimensions. In the ex-vivo study, pore structure, particularly the parameters describing prevalence of large pores could be predicted with high accuracy (adj. R2 ≥ 0.54). The combination of cortical thickness and backscatter parameters measured at the tibia were highly associated with stiffness and ultimate force of the proximal femur (adj. R2 ≥ 0.54). When combined with cortical thickness, 78% of the variation of the ultimate force at the proximal femur could be explained. So far, these novel cortical bone imaging methods have been developed and validated in-silico, ex-vivo on a few healthy volunteers, or in small pilot studies. In a first pilot study on 55 postmenopausal women with low BMD (Armbrecht et al., 2021), cortical pore size distribution and frequency-dependent attenuation assessed from cortical bone backscatter measurements demonstrated superior discrimination performance for fragility fractures (area under the receiver operating characteristic curve [AUC]: 0.69 ≤ AUC ≤ 0.75) compared with DXA (0.54 ≤ AUC ≤ 0.55). Their potential for the diagnosis of osteoporosis and fracture risk prediction has yet to be demonstrated in clinical studies.

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4

Axial Transmission: Techniques, Devices and Clinical Results Nicolas Bochud and Pascal Laugier

Abstract

Recent progress in quantitative ultrasound have sparked increasing interest towards the measurement of long cortical bones (e.g., radius or tibia), because their ability to sustain loading and resist fractures is known to be related to their mechanical properties at different length scales. In particular, applying guided waves for the assessment of cortical bone is inspired by widely used techniques developed earlier in the field of nondestructive testing and evaluation of different waveguide structures. This approach is based on the experimental evidence that the cortex of long bones can act as a natural waveguide for ultrasound, despite its irregular geometry, attenuation, and heterogeneous material properties. Because guided waves could yield the characterization of several bone properties (e.g., cortical thickness, anisotropic stiffness or porosity) at the mesoscopic level by fitting the dispersion characteristics of a waveguide model to the measured dispersion N. Bochud () Univ Paris Est Creteil, Univ Gustave Eiffel, CNRS, UMR 8208, MSME, Créteil, France P. Laugier Sorbonne Université, INSERM, CNRS, Laboratoire d’Imagerie Biomédicale, Paris, France e-mail: [email protected]

curves (i.e., solving an inverse problem), this method has a strong clinical potential as a tool for bone status assessment. This chapter revisits the roadmap that allowed the so-called bidirectional axial transmission technique to progress from a pure laboratory concept to a diagnostic tool of clinical interest over the second decade of the twenty-first century and discusses the current clinical challenges associated with cortical bone characterization by ultrasound guided waves. Keywords

Quantitative ultrasound · Cortical bone · Axial transmission · Guided waves · Inverse problem · Bone quality

4.1

Introduction

Our skeleton is comprised of two types of bone tissue: cortical bone is a compact tissue that forms the outer shell (i.e., the cortex) of our bones, accounting for about 80% of the total weight of the skeleton (Zebaze et al., 2010); in contrast, trabecular bone is a lightweight, highly porous material located within the inner regions of bones. While bone alteration in osteoporosis has essentially been associated with trabecular bone loss

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 P. Laugier, Q. Grimal (eds.), Bone Quantitative Ultrasound, Advances in Experimental Medicine and Biology 1364, https://doi.org/10.1007/978-3-030-91979-5_4

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for several decades (Parfitt, 2002), around 2010 the focus has been shifted towards cortical bone, which has been recognized to play a pivotal role in bone strength as well, in particular at fracture sites such as the proximal femur (Holzer et al., 2009) and the distal radius (Augat et al., 1996). During aging, an imbalance of the bone turnover events leads to an increased porosity and thinning of the cortical shell, alterations which have been related to increased fracture risk in postmenopausal osteoporotic women (Kral et al., 2017). In particular, cortical bone porosity has been increasingly acknowledged as a fracture risk factor in the 2010s (Ahmed et al., 2015; Bala et al., 2015b; Zebaze et al., 2016). The current “gold-standard” method for diagnosing osteoporosis is a two-dimensional (2-D) projection technique called dual-energy X-ray absorptiometry (DXA), which provides a measure of the areal bone mineral density (aBMD) as well as its adimensional counterpart (i.e., T-score). Areal BMD is mainly measured in trabecular fracture sites, i.e., lumbar spine and hip (Kanis et al., 2001), and this imperfectly reflects the actual structure of the skeleton (80% of which being cortical) and the epidemiology of osteoporosis (80% of fractures being cortical). Indeed, more than half of individuals having low-trauma fractures remain under-diagnosed according to the osteoporotic threshold defined by the World Health Organization (T-score = −2.5) (Geusens et al., 2011). Besides its lack of sensitivity (Briot et al., 2013; Siris et al., 2004), DXA suffers from further drawbacks including high equipment costs and limited portability, as well as exposure to ionizing radiation. Diagnosis in terms of risk assessment should thus include an accurate evaluation of cortical bone to improve the identification of individuals at high risk of fracture and treatment monitoring. Because of its projection technique, DXA is unable to provide reliable quantitative information on cortical bone. Furthermore, the measurement of aBMD alone does not capture alterations of bone quality factors, such as

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structural and material properties. Cortical bone at peripheral skeletal sites such as the leg or forearm can be assessed non-invasively by highresolution peripheral quantitative computed tomography (HR-pQCT). This technique provides full three-dimensional (3-D) information and has experienced recent developments regarding the assessment of cortical porosity (Nishiyama et al., 2010; Sundh et al., 2017; Zebaze et al., 2013). However, like conventional CT devices this modality is prone to cost issues and ionizing radiations, and its use is currently limited to clinical research facilities only. Moreover, HRpQCT provides insufficient spatial resolution (of the order of 100 μm) to accurately evaluate the intracortical porosity-related bone loss. Reference point indentation has also been proposed to probe the mechanical behavior of cortical bone, specifically the bone matrix (DiezPerez et al., 2010; Mellibovsky et al., 2015), but it remains invasive and only provides a local measurement of the bone tissue under the assumption of mechanical isotropy. Motivated by the need to overcome these limitations and to provide a non-invasive, portable, and affordable diagnostic modality for the management of osteoporosis, quantitative ultrasound (QUS) techniques have been developed since the 1990s (Gräsel et al., 2017; Karjalainen et al., 2016; Mishima et al., 2015; Stein et al., 2013). QUS is thought as a particularly relevant means to probe bone quality, because it relies on the use of mechanical waves, which possess intrinsic sensitivity to the effective mechanical properties contributing to the overall bone strength. The use of QUS for the management of osteoporosis, along with the different types of clinical QUS devices developed since the 2000s, are discussed in Chaps. 2 and 3, respectively. The focus of the present chapter is on a particular category of QUS techniques, referred to as axial transmission (AT), specifically developed to measure guided waves propagating along the main axis of long bones and to provide intrinsic cortical bone quality markers, such as corti-

4 Axial Transmission: Techniques, Devices and Clinical Results

cal thickness and intracortical porosity (a quantity reflected in material properties), which carry information beyond BMD (Grimal & Laugier, 2019). Before addressing the technical and scientific challenges associated with this sophisticated technique, next section briefly recalls its historical evolution.

4.2

Background

Applying AT for the assessment of cortical bone is inspired by widely used techniques developed earlier in the field of nondestructive testing and evaluation of different waveguide structures, such as plates and tubes (Chimenti, 1997; Rogers, 1995). Hence, it is based on the experimental evidence that the cortex of long bones can act as a natural waveguide for ultrasound, despite attenuation, irregular geometry and heterogeneous material properties (Jansons et al., 1984; Lefebvre et al., 2002; Nicholson et al., 2002). This technique relies on the simple idea that an ultrasound wave transmitted by a source into the cortex of a long bone (e.g., the radius or the tibia) through the overlying soft tissue can generate vibrations that continuously interact with the bone cortex boundaries and propagate over a distance up to several centimeters being guided by the cortical shell (Wear et al., 2018). As they propagate, these guided waves leak energy out from the waveguide to the adjacent soft tissue surrounding the bone. The leaked energy can be detected using surface sensors placed on the skin, typically a few centimeters away from the source. Strengths of AT are that it only requires unilateral access to the bone and has the ability to evaluate multiple waveguide properties over a relatively large region and cross-section of the bone, even within a single measurement sequence. Guided waves are dispersive and the relation between the wavenumber (k) and frequency (f ), specific to each guided mode, is determined by the structural and material properties of the waveguide. Alterations in cortical thickness, porosity and elastic properties observed with aging, osteoporosis or in response to treatments, are thus expected to modify the dispersion characteristics

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of guided waves. Thereby, the choice of the excitation frequency and the measured guided modes govern the mechanical properties that can be retrieved. Following this principle, a variety of AT techniques has been reported in the literature, exploring several possible modes of signal recording and processing. First investigations of cortical bone using the AT technique date back to the 1950s, where the first clinical application concerned fracture healing monitoring (Siegel et al., 1958). In the mid1970s until the late 1980s, researchers from Eastern European countries, in particular at the Riga Technical University, played an exploratory role in determining the speeds of surface and flexural waves at the mid tibia using low frequency (around 100 kHz) for evaluating patients in the context of immobilization atrophy (Dzene et al., 1981). That period also coincided with the idea of using guided waves to monitor the accelerated demineralization of cosmonauts’ skeleton exposed to microgravity for a long period during spaceflights (Tatarinov et al., 1990). Following these investigations, the first industrial AT bone ultrasonometer was developed in former USSR in the 1980s. More recently, the burden of osteoporosis in the aging population and the limited diagnostic capabilities of available X-ray techniques have triggered the development of further AT techniques. At least two devices, tested in clinical studies in the mid and late 1990s (Barkmann et al., 2000; Foldes et al., 1995; Weiss et al., 2000), have appeared on the market. For the AT approaches developed in the early 2000s, a single transmitter and single receiver configuration was implemented, in which the speed-of-sound was simply derived from the measurement of the separation distance and the time-of-flight (TOF) between the two transducers. Such TOF approach has generally been associated with the measurement of the first arriving signal (FAS) in bone, which is defined as the first component of the signal that emerges from noise. Different criteria can be used to evaluate the TOF, and their impact on the velocity of the FAS has been studied in Bossy et al. (2002). To improve the evaluation of the FAS velocity, spatio-temporal signals can also be recorded at

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different receiver positions along the waveguide. In that case, the velocity is determined from the TOF measurement at each receiver position, achieved either by mechanically moving the receiver (Nicholson et al., 2002) or by using a linear transducer array (Bossy et al., 2004a). Under the assumption that the bone cortex can be assimilated with a planar waveguide, the FAS can be considered as a transient mode, consistent either with a lateral longitudinal wave (which propagates at the longitudinal bulk wave velocity) when the ratio of the cortical thickness to the acoustic wavelength is much greater than unity, or with the lowest symmetric Lamb mode (i.e., S0 ) for a plate otherwise (Talmant et al., 2011). The FAS is thus essentially a weakly dispersive guided wave, affected by the boundaries of the cortex, whose velocity has been shown to provide relevant information on microstructural and mechanical properties according to the used acoustic wavelength (Bossy et al., 2004a; Moilanen et al., 2004; Raum et al., 2005; Talmant et al., 2011). Although a comprehensive theoretical basis defining the FAS characteristics has been provided using numerical simulations (Bossy et al., 2004b), its velocity cannot be predicted analytically and inferring waveguide characteristics from it thus remains elusive. Clinically, the FAS velocity has exhibited only a limited sensitivity to DXA-defined osteoporosis (Knapp et al., 2004; Krestan et al., 2004). Nevertheless, it has demonstrated a certain ability in discriminating fracture cases from controls for postmenopausal women in numerous clinical studies (Hans et al., 1999; Knapp et al., 2001; Määttä et al., 2014; Moilanen et al., 2013; Olszynski et al., 2013; Talmant et al., 2009); although, compared with DXA, the performance of the FAS velocity was not shown to be superior for fracture prediction. Other parts of the recorded signal than the FAS have been exploited. In particular, a slower but more energetic waveform has been identified and interpreted as the fundamental flexural guided wave (FFGW), which is equivalent to the lowest antisymmetric Lamb mode (i.e., A0 ) for a plate (Nicholson et al., 2002). The

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dispersion characteristics of that mode, that is to say its frequency-related velocity variations, were shown to be sensitive either to bending stiffness, BMD (Stüssi & Fäh, 1988), pathological changes in the endosteal region (Talmant et al., 2011), or cortical thickness according to the applied frequency-thickness ratio regime (Moilanen et al., 2006). Thereby, the FFGW was thoroughly investigated by Petro Moilanen and colleagues at the University of Jyväskyla (Finland) (Moilanen, 2008). In particular, they showed that the measured phase velocity of the FFGW allowed for an accurate estimation of cortical thickness, which has been shown to be related to fracture risk (Moilanen et al., 2007a). Following these findings, an ex vivo study conducted at the radius showed a significant correlation between the velocity of the FFGW and cortical thickness (Muller et al., 2005). However, when investigated in vivo at the tibia, this correlation was weaker (Kilappa et al., 2011; Moilanen et al., 2003). This lower performance was shown to be likely due to interferences with soft tissue, in which ultrasound propagate at phase velocities (∼1500 m s−1 ) similar to that of the A0 -mode in cortical bone (Moilanen et al., 2008). Researchers at Artann Laboratories (New Jersey, USA) developed a dual-frequency AT device, which combines measurements at low and high frequencies (i.e., 100-kHz and 1-MHz). In this way, switching the center frequency of the transmitted acoustic pulse allows modifying the ratio of the acoustic wavelength to the cortical thickness, and so the signal recorded at different frequencies provides a possible means of distinguishing the contributions of structural and material properties (Tatarinov et al., 2005). Indeed, while the velocity of the received waveform at 1MHz is mainly determined by dispersion characteristics related to the longitudinal bulk wave (i.e., mass density and stiffness), the measurement of a lower order guided mode at 100-kHz strongly depends on the cortical thickness. Clinical results suggested that such dual-frequency AT device can distinguish early changes induced by osteoporosis more clearly than single-frequency AT techniques (Egorov et al., 2014; Sarvazyan et al., 2009).

4 Axial Transmission: Techniques, Devices and Clinical Results

The rub is that these studies were mostly limited to the analysis of a single waveform, being either the FAS or the FFGW. However, an infinite number of guided modes can exist in a finite waveguide. Multiple modes contain more information but are also more difficult to extract and interpret, since each mode interferes with every other mode and distinguishing dispersion curves in the recorded signals can be challenging. From 2010 to 2020, the team led by JeanGabriel Minonzio and Pascal Laugier at Sorbonne University in Paris (France) developed the socalled bidirectional axial transmission (BDAT) technique towards this goal. In short, BDAT uses a one-dimensional (1-D) linear transducer array adapted to clinical measurements to record guided modes that propagate in two opposite directions from two emitting arrays placed on each side of a central receiving array. Combining measurements from these two opposite directions automatically compensates for the bias resulting from the overlying soft tissues on the measured broadband spatiotemporal signals. Once the measured dispersion curves are obtained from dedicated signal processing (Minonzio et al., 2011, 2010; Moreau et al., 2014a), the waveguide characteristics can then be retrieved through a robust inversion method (Bochud et al., 2016, 2017; Foiret et al., 2014), which, to some extent, exhibits similarities to problems encountered in the nondestructive testing community. This approach allowed for the concurrent identification of cortical thickness and material properties, and has been validated ex vivo and in vivo in proofof-principle tests (Minonzio et al., 2018b, 2019; Schneider et al., 2019a,b). Altogether, the results obtained using this sophisticated technique have represented a positive turning point for QUS cortical bone assessment. Since then, the development of multimode AT techniques has experienced an important popularity worldwide, e.g., in Switzerland (team led by William R. Taylor at ETH Zürich (Vogl et al., 2017, 2016)), Canada (teams led by Lawrence H. Le at University of Alberta, Edmonton (Tran et al., 2018, 2019) and Pierre Belanger at the École de Technologie Supérieure, Montréal (Abid et al.,

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2017; Pereira et al., 2019)), China (team led by Dean Ta at Fudan University, Shanghai (Li et al., 2019b, 2020)), and Japan (Bustamante et al., 2019; Chiba et al., 2020; Ishimoto et al., 2019). This chapter aims at revisiting several key contributions achieved by the French researchers over the second decade of the twenty-first century, which allowed the BDAT technique to progress from the state of a pure laboratory concept to a clinically relevant tool for fracture risk assessment. It is organized as follows: A first part (Sect. 4.3) recalls the main methodological steps that are necessary to recover cortical bone quality markers from multimode guided wave measurements. Although the proposed methods focus on the BDAT technique, a critical assessment is also provided in the light of the recent open literature. A second part (Sect. 4.4) is then dedicated to the presentation of the most significant results achieved using BDAT, including the inverse characterization of multimode guided waves (Sect. 4.4.1), the analysis of the impact of soft tissue on the estimated waveguide properties (Sect. 4.4.2), the ex vivo validation of cortical bone quality markers (Sect. 4.4.3), and recent clinical findings (Sect. 4.4.4). These main achievements and the current challenges are finally discussed in Sects. 4.5 and 4.6, respectively.

4.3

Methods

In what follows, we introduce (1) the ultrasonic measuring device used to record broadband spatio-temporal signals, (2) the dedicated signal processing developed to extract experimental dispersion curves, (3) the waveguide model that is used to capture the effective mechanical behavior of cortical bone at the mesostructural scale, and (4) the objective function and model parameters optimization routine involved in the inverse procedure used to identify multiple cortical bone properties from the comparison between measured and modeled guided modes. It should be noted that basic concepts on elastic guided waves are not recalled here, but the interested reader may refer to classical textbooks for further

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details thereon (Achenbach, 2012; Royer & Dieulesaint, 1999). An introduction to guided waves in cortical bone can be found in Talmant et al. (2011).

The developed BDAT prototype device (Azalée, Paris, France) consists of the three custom-made components depicted in Fig. 4.1a, which include an ultrasonic probe (Vermon, Tours, France), a driving electronics (Althaïs, Tours, France) and a human machine interface (BleuSolid, Paris, France). The original probe is a compact linear transducer array adapted to clinical forearm measure-

ments at the one-third distal radius, which is composed of one array of 24 receivers (N R ) surrounded by two arrays of 5 emitters (2×N E ) each (Fig. 4.1b). The array pitch is 0.8 mm, and the dimensions of each rectangular-shaped element are 0.8×8 mm2 . A distance of 8 mm separates the receiving array from each emitting array. The probe is placed directly in contact with the patients’ forearm and ultrasonic gel is used for coupling. These three arrays of piezocomposite elements were specifically designed to launch and detect elastic guided waves propagating in two opposite directions, allowing thus correction of the bias on the guided modes wavenumbers induced by the inclination angle between the probe and the bone, which can result from the presence of uneven overlying soft tissues (Moreau et al., 2014a). The

Fig. 4.1 Overview of the ultrasonic measuring device: (a) Illustration of the BDAT prototype placed at the lateral one-third distal radius; (b) Schematic view of the 1-MHz probe, which consists of a 24 elements receiving array surrounded by two arrays of 5 emitters each; (c) Recorded radio-frequency signals corresponding to all

possible pairs of emitter/receiver elements; and (d) Measured dispersion curves obtained after applying a dedicated signal processing (see Sect. 4.3.2). Figure reproduced and adapted from Bochud et al. (2017), with permission according to the terms of the Creative Commons CC BY license

4.3.1

Ultrasonic Measuring Device

4 Axial Transmission: Techniques, Devices and Clinical Results

electronic device is used to transmit, record, and digitize the radio-frequency signals. It allows for the successive excitation of each emitter with a wideband pulse (central frequency of 1-MHz) of −6 dB power spectrum spanning a frequency range from 0.4 to 1.6 MHz. For each propagation direction, a set of N E × N R radio-frequency signals corresponding to all possible pairs of emitter/receiver elements can be obtained (Fig. 4.1c). The human machine interface was developed to display the dispersion spectrum of guided waves in quasi-real time (at a frame rate up to 4 Hz) and allows guiding the operator in finding the optimal probe positioning with respect to the main bone axis during a measurement sequence. Later findings suggesting that cortical bone parameters measured at the tibia are strong predictors of hip fractures (Kroker et al., 2017; Sundh et al., 2017) motivated the development of a second probe adapted to clinical measurements at the proximal third of the tibia. In this way, the probe characteristics were slightly modified to ensure a nearly constant frequencythickness product across human anatomical sites (Schneider et al., 2019a), as the cortical thickness at the diaphysis of the tibia typically exhibits a larger range (i.e., 2–6 mm) than that at the one-third distal radius (i.e., 1– 4 mm) (Karjalainen et al., 2008). Therefore, the central frequency was reduced from 1-MHz to 500-kHz (−6 dB frequency bandwidth from 300 to 700 kHz), whereas the probe dimensions and the pitch were slightly increased accordingly. The leftover hardware characteristics remained unchanged. Apart from using these specifically designed probes, it is worth mentioning that such guided wave measurements could, in principle, also be achieved with standard linear phased-array transducers used for routine clinical ultrasound imaging purposes (Renaud et al., 2018).

4.3.2

Dedicated Signal Processing: Features Extraction

In order to extract the measured dispersion curves, the recorded radio-frequency signals

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are transformed to the frequency-wavenumber (f − k) space using a singular value decomposition (SVD) enhanced 2-D spatio-temporal Fourier transform. This procedure, which is straightforwardly applied following the signal processing steps comprehensively described in Minonzio et al. (2011, 2010), aims at improving the wavenumbers resolution with respect to the primarily developed method for converting propagating multimode signals into the Fourier space (Alleyne & Cawley, 1991). In short, (1) for each propagation direction, the N E × N R radio-frequency signals are Fourier transformed with respect to time and stored in a response matrix; (2) at each frequency, a SVD is applied to that response matrix; (3) enhancement of the signal-to-noise ratio is then achieved by retaining only the singular vectors, denoted by U n , associated with the highest singular values, the lowest singular values being associated with noise; (4) the projection of a variable testing vector etest onto the singular vector basis leads to the so-called Norm function (Minonzio et al., 2010), defined as Norm(f, k) = ||etest (k)||2U n (f ) ,

(4.1)

whose maxima correspond to the wavenumbers of the guided modes. The testing vector etest is an attenuated spatial plane wave with a complex wavenumber (Minonzio et al., 2011). This testing vector spans all the waves measurable within the device bandwidth, and each pixel (f , k) of the Norm function thus reflects the presence rate of a guided mode into a 0 − 1 scale. Next steps consists in (5) applying the bidirectional correction to the measurements by considering the data acquired from the two emitting arrays (Moreau et al., 2014a); (6) extracting the measured dispersion curves, i.e., the maxima of the corrected Norm function, using a dilation operator (Vallet et al., 2016); (7) removing outliers by applying statistical denoising over multiple measurement sequences successively recorded without moving the probe; and (8) gathering together the denoised data obtained on each direction, thus yielding a single set of dispersion curves for each measured sample or subject (see for instance

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Fig. 4.1d, which displays the dispersion curves obtained on a bilayer phantom). Note that the extraction of dispersion characteristics from multimode guided wave measurements has sparked increasing discussion in the literature. Particular emphasis has been given to the enhancement of the wavenumber resolution, leading to the implementation of several techniques, including among others the high-resolution and dispersive Radon transform (Tran et al., 2014; Xu et al., 2018), the sparse SVD (Xu et al., 2016a) or an adaptive beamforming approach (Okumura et al., 2018), which all were consistently compared in Xu et al. (2016b). Overall, this topic has been thoroughly investigated by Dean Ta, Lawrence H. Le and colleagues, and Chap. 5 in this book is entirely dedicated to signal processing techniques applied to axial transmission. Besides the extraction of multiple guided modes, at least two further features can be assessed based on BDAT measurements, i.e., the velocity of the lowest order antisymmetric guided mode, vA0 , and the velocity of the first arriving signal, vFAS . First, the phase velocity of the A0 -mode can be calculated in the frequencydomain based on the SVD-enhanced 2-D spatiotemporal Fourier transform described above. The main processing steps to this goal are as follows: (1) the Norm function is converted from the frequency-wavenumber (f − k) into the frequency-phase velocity (f − cp ) domain using cp (f ) = 2πf/k; (2) the A0 -mode is then windowed using fixed frequency (0.5–0.8 MHz) and phase velocity (1400–1900 m s−1 ) ranges; (3) within this window, the amplitudes of the Norm function are averaged over frequency, thus yielding a single-peaked function whose maximum is defined as the unidirectional velocity vA0 ; and (4) for each measurement sequence, the harmonic mean of the two velocities resulting from the BDAT measurements is calculated to correct for the inclination angle between the probe and the bone surface. This process is illustrated in Fig. 4.2. It should be noted that, in contrast to earlier studies that identified vA0 by extracting the corresponding waveforms directly in the time-domain (Moilanen et al., 2007a; Tatarinov et al., 2011), the method proposed here

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allows isolating the A0 -mode in the frequencyphase velocity domain. This approach is believed to be more accurate, since it reduces possible interferences with other signal contributions that are difficult to filter out in the time-domain. Second, the TOF can be determined for each emitter-receiver distance using the first extremum of the time-domain signal. The speed-of-sound is then derived from the inverse slope of a linear fit through these time points plotted against the known emitter-receiver distances. This procedure is applied to each of the five emitters and for both directions to account for small inclination angles between the probe and the bone surface. Since large probe inclination angles were shown to increase the relative measurement error of vFAS (Bossy et al., 2004a), BDAT measurements for which the absolute difference between the velocities derived from the two opposite directions exceeded 50 m s−1 are eliminated (Talmant et al., 2009).

4.3.3

Waveguide Modeling

The BDAT technique was developed with the aim of recovering cortical bone properties from the comparison of experimental dispersion curves with a proper waveguide model. At the macroscale, the cortical shell of human long bones is an anisotropic, absorbing and heterogeneous material, whose geometry is a rather irregular hollow structure filled with marrow and surrounded by soft tissue in vivo. The choice of the waveguide model used to retrieve cortical bone properties from in vivo measurements is a key step of this process. Given the complexity of the cortical bone waveguide, this choice should result from a tradeoff between the complexity of the model (i.e., number of model parameters) and the accuracy of the estimated properties (i.e., stability of the inverse problem solution in terms of convergence, existence and uniqueness). The purpose of the anisotropic waveguide model introduced in Sect. 4.3.3.1 is to represent a simplified but sufficient inverse model to fit experimental data and provide a robust inference of multiple

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Fig. 4.2 Procedure for calculating the unidirectional phase velocity of the A0 -mode: (a) SVD-enhanced 2-D Fourier transform (Norm function) of the N E × N R radiofrequency signals corresponding to all possible pairs of emitter/receiver elements in the frequency-wavenumber (f − k) domain; (b) Norm function converted into the frequency-phase velocity (f − cp ) domain, where the black rectangle represents the fixed window used to extract

the A0 -mode; (c) the amplitudes of the Norm function are averaged over frequency in that range, thus yielding a single-peaked function; and (d) the maximum of that function delivers the retained phase velocity vA0 . Figure reproduced and adapted from the supplementary material provided in Schneider et al. (2019a), with permission according to the terms of the Creative Commons Attribution 4.0 International License

waveguide characteristics. The question of whether the waveguide model must include the effects of bone curvature and irregular geometry, soft tissue coating and marrow filling, or some other additional factors as well, such as, e.g., the absorption or heterogeneity, is briefly addressed in the light of the literature in Sect. 4.3.3.2.

wavelengths of guided waves, ranging from around 1 to 10 mm, are much larger than the typical size of the heterogeneities (osteons, pores). Ultrasound waves are thus sensitive to the effective elastic properties of cortical bone, which can be considered as a homogeneous propagation medium at the mesoscopic scale (Baron et al., 2007). Second, the cortex is generally not uniform and is subject to local cortical thickness variation along the main axis of the bone. Notwithstanding, given the rather limited length of the receivers array of the BDAT prototype probes (from about 20 to 30 mm for the radius and the tibia, respectively), a uniform cortical

4.3.3.1 Inverse Waveguide Model The cortex of long bones is modeled here as a 2-D transverse isotropic homogeneous free plate waveguide. Several observations guided the choice of this model. First, in the frequency bandwidth of interest (around 1-MHz), the

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thickness in the measurement region of interest can be assumed (Moreau et al., 2014b). Third, given the characteristics of the probes (i.e., the elements width is much larger than the pitch), bone curvature can be neglected as guided waves mostly propagate in the axial direction. The rather tubular bone shape can thus be locally approximated by a plate (Minonzio et al., 2015). Fourth, although the soft tissue coating still probably plays a minor impact on the guided modes, choosing a more complicated model is not likely to improve the inverse problem solution in the considered frequency bandwidth (Bochud et al., 2017). The effective mechanical behavior of such a 2-D waveguide model is governed by means of four independent stiffness coefficients cij in Voigt notation (i.e., c11 , c13 , c33 and c55 ), the mass density ρ, and the thickness h, where x1 x2 represents the plane of mechanical isotropy (see Fig. 4.3a). The dispersion equations are generally written as a function of bulk wave velocities and stiffness ratios only, without the need for specifying the mass density ρ that is implicitly embedded in the velocities (Foiret et al., 2014; Rhee et al., 2007),   c13 c33 ⊥ FA,S f, k; VL , VT , , , h = 0 , (4.2) c11 c11 where subscripts A and S stand for the antisymmetric and symmetric modes, respectively. The compression and shear bulk wave velocities in the transverse plane of the plate are denoted by √ √ VL⊥ = c11 /ρ and VT = c55 /ρ, respectively. The anisotropic stiffness ratio can be related to the

Fig. 4.3 Modeling hypotheses: (a) The cortex of long bones can be modeled as a 2-D transverse isotropic homogeneous free plate waveguide; and (b) the effective stiffness tensor C can be reasonably well predicted from

compression bulk wave velocities as, c33 = c11





VL VL⊥

2 ,

(4.3)

√  where VL = c33 /ρ is the compression bulk wave velocity in the axial direction. To further reduce the amount of model parameters, it has been shown that the effective stiffness tensor C can be reasonably well predicted from a single microstructural parameter (Granke et al., 2011), i.e., the cortical porosity p, which represents the average fraction of pores volume within the total cortical bone volume. In this regard, an asymptotic homogenization model was proposed by Parnell and Grimal (2009), in which cortical bone is represented as a two-phase composite material made of a homogeneous transverse isotropic matrix pervaded by infinite water-filled cylindrical-shaped pores that are periodically distributed on a hexagonal lattice (see Fig. 4.3b). Given the elastic properties (stiffness tensor Cm ) and mass density (ρ m ) of the bone matrix, the properties of the fluid within the pores (Cf , ρ f ), and the volume fraction of pores (p), this homogenization model allows for the computation of the effective stiffness tensor C (Parnell et al., 2012). Such representation leads to transversely isotropic elasticity at the mesoscale. In most studies achieved by the French team (see Sect. 4.4), the effective stiffness was computed following this asymptotic homogenization approach, by assuming that the bone matrix is spatially homogeneous and uniform among in-

the cortical porosity p using asymptotic homogenization. Figure reproduced and adapted from Granke et al. (2011), with the permission of Elsevier

4 Axial Transmission: Techniques, Devices and Clinical Results

dividuals. The stiffness tensor Cm and the mass density ρ m of the bone matrix were thus assumed to be known and set according to values measured at the femur of aged female donors (Granke et al., m m m 2011): c11 = 26.8 GPa, c33 = 35.1 GPa, c44 = m m 7.3 GPa, c66 = 5.8 GPa, c13 = 15.3 GPa, thus m m m c12 = c11 − 2c66 = 15.2 GPa, and ρ m = −3 1.91 g.cm . The stiffness tensor Cf was set based on typical properties for water (i.e., a nearly incompressible medium with a bulk modulus of K = 2 GPa and a Poisson’s ratio of ν = 0.49), whose mass density is equal to ρ f = 1 g.cm−3 . Therefore, one particular porosity value p allows determining the full set of effective stiffness coefficients, whereas the effective mass density is defined as ρ = ρ m (1 − p) + ρ f p. The bulk wave velocities and stiffness ratios of Eq. (4.2) can directly be derived from these values. Note that the model parametrization in terms of porosity p does not modify the dispersion equations but can simply be regarded as a sampling of the complete elasticity domain spanned by the stiffness coefficients cij (Bochud et al., 2016). Therefore, the dispersion equations can now be written as FA,S (f, k; p, h) = 0 .

(4.4)

Solving the dispersion equations for propagation in the meridian plane using partial wave theory (Li and Thompson, 1990), along with a rootfinding algorithm (e.g., Newton-Raphson), pro-

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vides the set of all possible (f , k)-pairs that form the so-called Lamb modes. Figure 4.4 depicts the influence of the thickness h and porosity p on the Lamb modes for typical values of cortical thickness (1 and 2 mm) and porosity (5 and 15%). The number of modes scales with thickness, whereas an increase in porosity is associated with an increase in wavenumber k (or a decrease in phase velocity cp (f ) = 2πf/k).

4.3.3.2 Overview of Advanced Waveguide Models The anisotropic plate model introduced in Sect. 4.3.3.1 represents a reasonable starting point for developing more accurate models. To tackle the impact of soft tissue on the top of bone, a natural extension of the plate model consisted in the introduction of a fluidsolid bilayer waveguide model (see Fig. 4.5a), which was developed following the works of Yapura and Kinra. Their initial model considered the solid subsystem of the bilayer as isotropic (Yapura & Kinra, 1995), but it was subsequently extended to account for an orthotropic solid subsystem (Yapura & Kinra, 1997). An intermediate case was considered here, in which the solid subsystem was considered as transversely isotropic and non-absorbing. It is noteworthy that the mechanical behavior at the fluid-solid interface may differ from that between soft tissue and cortical bone in vivo, in that fluid does not sustain shear stresses whereas

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2

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1 0

0 0

0.5

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Fig. 4.4 Examples of Lamb modes calculated using a 2D transverse isotropic free plate waveguide model with

0

0.5

1

1.5

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homogenized elastic properties (Eq. (4.4)), for porosities p equal to 5% (black lines) and 15% (gray lines): (a) h = 1 mm and (b) h = 2 mm

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Fig. 4.5 (a) Modeling hypothesis: The impact of the soft tissue layer on the top of bone can be accounted for by using a fluid-solid bilayer waveguide model. (b) Example of the plate (continuous black lines) and bilayer (dotted

gray lines) modes calculated using Eq. (4.5) with h = 1.8 mm, κf = 0.83, τ = 1.25, and γ = 0.54 (Bochud et al., 2017). The mass density ρs and stiffness coefficients cij were taken from Bossy et al. (2004b)

soft tissue does. Nevertheless, this difference is not believed to induce a too large deviation while modeling the guided modes of the considered bilayer waveguide, as shear waves are likely to be attenuated in the considered ultrasound frequency regime (Moilanen et al., 2006). A fluid-solid bilayer system introduces further constraints to the particle motion at the interface (compared with free boundaries), so that the energy of the guided waves leaks from the solid to the fluid in the form of leaky waves (Chen et al., 2013). When these waves encounter boundaries between different media, they are reflected back to the top boundary of the overlying fluid and transmitted to the solid substrate. Consequently, the guided waves do not propagate in the fluid or solid layer independently (as suggested in Chen et al. (2012)), but in the whole bilayer structure. This coupling is known to affect the dispersion characteristics of the guided modes, so that the dispersion equation for such fluid-transversely isotropic solid bilayer waveguide now reads as

plate model described in the former section, the density of the solid layer ρs must now be explicitly incorporated into the dispersion equation. An example of the plate and bilayer modes is depicted in Fig. 4.5b. It should be noted that the notation of antisymmetric (An ) and symmetric (Sn ) modes is valid for uncoated waveguides only. Here, since the guided modes obtained using a bilayer model are no longer classical Lamb modes due to the asymmetry of the waveguide, the ordinal subscripts notation (n) introduced in Yapura and Kinra (1995) has been adopted to label the bilayer modes. As can be observed, the bilayer model leads to additional modes and modifies the trajectory of the modes obtained using a plate model (i.e., coupling between the coating and substrate), particularly in the regions of the f − k plane where the modes reach their cut-off frequencies (k = 0 rad.mm−1 ) or asymptotic behavior (small wavelengths λ = 2π/k). Overall, the development of more accurate models has received significant attention from researchers involved in the bone QUS community, including among so many others researchers from the Université Paris-Est Créteil (France) and the University of Ioannina (Greece). More advanced modeling efforts have focused on the incorporation of the following characteristics of cortical long bone, which generally concerned (1) its geometry (e.g., tubular shape (Moilanen

  c13 c33 F f, k; κf , τ, γ , ρs , VL⊥ , VT , , ,h = 0, c11 c11

(4.5) where κf = cf /VT , τ = hf / h, and γ = ρf /ρs . Subscripts s and f denote the model parameters belonging to the solid substrate and the fluid coating, respectively. Note that, in contrast to the

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et al., 2007a; Ta et al., 2009) and irregular crosssection (Pereira et al., 2017)), (2) its material properties (e.g., anisotropy, poroelasticity, viscoelasticity and absorption (Naili et al., 2010; Nguyen & Naili, 2013; Rosi et al., 2016)), (3) its multilayer nature (e.g., presence of soft tissue (Chen et al., 2012; Moilanen et al., 2008), bone marrow (Baron & Naili, 2010) or both of them (Lee et al., 2014; Nguyen et al., 2017; Thakare et al., 2017; Tran et al., 2013)), and (4) its heterogeneity (e.g., gradient of elastic properties (Baron, 2012; Haïat et al., 2009; Vavva et al., 2009), strain gradient elasticity (Papacharalampopoulos et al., 2011), probabilistic or random elastic properties (Abdoulatuf et al., 2017; Desceliers et al., 2012)). Furthermore, when it is warranted to accurately describe more realistic geometrical features (e.g., irregular shape, rough boundaries) or heterogeneous distribution of material properties, it is possible to resort to numerical methods (e.g., finite difference time domain method) for modeling guided waves propagating in bone directly by incorporating high resolution images into the simulation field (Bossy et al., 2004b; Kaufman et al., 2008; Moilanen et al., 2007b; Saeki et al., 2020). An exact physical model must obviously take the influence of these cortical bone characteristics into account. Nevertheless, a too complex model involving many physical parameters would make the inverse identification of cortical bone quality markers more challenging. It should be noted that, to date, only the anisotropic free plate model has been clinically evaluated (Minonzio et al., 2019).

4.3.4

Inverse Problem Based on Multimode Guided Waves

Although guided waves analysis in the bone QUS field is not as mature as in the nondestructive testing community yet, waveguide characteristics, such as thickness, anisotropic stiffness or porosity, could theoretically be deduced from guided wave measurements by fitting a waveguide model to the experimental data. Such model-based approach requires solving a multiparametric inverse problem, which consists in adjusting the model

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parameters until modeled and measured guided modes are matched. One of the most commonly applied approaches for retrieving such waveguide characteristics is to pose the inverse problem in an optimization form. In the bone community, only a few studies have reported inverse problem based on the measurement of multimode guided waves. Among these, estimates of the Young’s moduli of ex vivo ox bone samples were obtained by fitting an isotropic plate model (assuming known cortical thickness) to the measured phase velocities of three Lamb modes (identified as A0 , S0 and A1 ) using a least-mean-squares algorithm (Lefebvre et al., 2002). In a related study, the thickness of bovine tibiae was identified by manually fitting an isotropic hollow tube model filled with viscous liquid (assuming known material properties) to the measured phase velocities of the three first cylindrical modes (Ta et al., 2009). A pioneering proposal provided a concurrent identification of the cortical thickness and bulk wave velocities from measurements on five ex vivo human radius specimens by minimizing the square differences between the experimental and calculated frequencies using a least-squares optimization criterion together with a gradient-based method (Foiret et al., 2014). However, a prior heuristic assignment of the theoretical modes to each experimental trajectory was needed to ensure a proper convergence towards the optimal inverse solution. Nevertheless, this prior assignment is generally far from trivial, particularly in the case of in vivo measurements, where noise and soft tissue modes may corrupt the experimental trajectories. Inverse problems based on guided waves are, however, well accepted and widely used in the field of nondestructive testing, including different applications such as the quality control of thin bonds and the characterization of composite materials. Among the works dealing with multimode guided waves, a number of studies were dedicated to the estimation of the elastic properties of anisotropic waveguides (Datta et al., 1999; Fei et al., 2003; Gsell & Dual, 2004; Veres & Sayir, 2004; Dahmen et al., 2010). Nonetheless, only a limited number of researchers addressed the concurrent estimation of both structural and

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material properties (Deán et al., 2008; Karim et al., 1990; Yeh & Yang, 2011; Bochud et al., 2018; Yan et al., 2014), and most of the proposed approaches were applied to laboratory-controlled measurements on isotropic plates, or even on simulated data. Guided modes measured on cortical bone are, however, particularly complicated to deal with. Indeed, for relatively short receiver arrays (recall Sect. 4.3.1), modal superposition cannot be avoided in regions of the f − k plane where the modes are close to each other, especially higher order modes (Maraschini et al., 2010). Furthermore, the experimental data are usually incomplete and noisy, in that some modes show up as piecewise trajectories because some frequency regions are not properly excited or are contaminated by the presence of additional guided modes due to the overlying soft tissue (Chen et al., 2012; Tran et al., 2013). Altogether, these ambiguities prevent a clear identification of the theoretical guided modes corresponding to the experimental data. Thereby typical approaches based on curve fitting, in which mode numbering prior to the inversion is required, are not feasible here, and a method in which the mode-order is kept blind is clearly needed.

4.3.4.1 General Framework: A Genetic Algorithm-Based Identification The difference between measured and modeled guided modes is generally the most important

Fig. 4.6 Illustration of the inherent ambiguity for identifying waveguide characteristics when dealing with incom-

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part of the objective function, in which the inversion process can be expressed as a curve fitting problem (i.e., Euclidean distance in a least-square sense). Nevertheless, it is not necessarily trivial to a priori identify which Lamb mode each data point of the experimental dispersion curves belongs to, especially when dealing with an important thickness range, like those clinically reported at the radius and tibia. For instance, several modes in Fig. 4.6a (e.g., S0 and A1 ) could be confused with other modes in Fig. 4.6b (e.g., A1 and S2 ), thus giving rise to a misleading identification of the waveguide characteristics. To overcome such ambiguity, an additional model parameter can be introduced to account for the pairing of the Lamb modes with the incomplete and noisy experimental data. This model parameter, denoted by M, is a sparse pairing vector that represents the combination (i.e., existence) of Lamb modes that are necessary to explain the experimental data. In this way, the mode-order is kept blind and there is no need to manually identify the modes before solving the inverse problem. The sparsity of this pairing vector is consistent with the experimental evidences that (1) some modes are not excited (due to insufficient outof-plane displacement or high attenuation (Foiret et al., 2014)) or (2) pairwise higher order modes (i.e., an antisymmetric mode Ai and its symmetric counterpart Si , with i > 0) nearly overlap (e.g., A2 and S2 cannot be easily distinguished around 1-MHz in Fig. 4.6b). An example of the

plete guided modes: Waveguide models calculated from Eq. (4.4) using (a) h = 1.5 mm; p = 8% and (b) h = 3.2 mm; p = 5%

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Fig. 4.7 Illustration of the impact of the pairing vector M on the theoretical guided modes for h = 2 mm and p = 10%. Modes that are missing in the pairing vector are displayed as dashed gray lines: (a) A2 and A3 ; and (b) S0 , S1 , and A3

impact of the pairing vector M on the theoretical guided modes is displayed in Fig. 4.7. As can be observed, for a same set of structural and material properties, this model parameter allows testing several combinations of modes to cope with the expected incomplete experimental data. Based on these considerations, the objective function F (θ) consists in maximizing the occupancy rate of the Lamb modes (Bochud et al., 2016). Hence, M exp 1 Nm , F (θ ) = N m=1 Nmth (θ) max

restricted to

in Nm exp Nm = 0 exp

(4.6)

if Nm > 0.1 · N¯ exp , otherwise (4.7) exp

where Nm and Nmth (θ ) denote the number of experimental and theoretical data of a mode m, exp respectively; N¯ exp is the mean value of Nm ; Nmin is the number of inliers of a mode m; and N is the total number of experimental data. In short, Eqs. (4.6)–(4.7) mean that experimental data can only form an experimental trajectory if a sufficiently large amount of them belong to a Lamb mode. Furthermore, an experimental data is considered as an inlier of a mode m if its Euclidean distance d to that mode satisfies the following condition

  d=

f − f (θ ) fmax

2

 +

k − k(θ ) kmax

2 ≤ d0 , (4.8)

where d0 is a dimensionless threshold corresponding to the normalized resolution in k (i.e., (π/L)/kmax , with L being the length of the receivers array) (Minonzio et al., 2010). This simple criterion concurrently allows determining if a data point belongs to the model (i.e., inlier or outlier) and, if yes, to which Lamb mode of the pairing vector M it belongs (i.e., inlier m). Therefore, the experimental data belonging to each individual Lamb mode are automatically sorted out by the inversion procedure to quantify the occupancy rate from Eq. (4.6). Formally, the optimal model parameters θˆ result from θˆ = arg max F (θ) , θ ∈Θ

(4.9)

where Θ denote the bounds of the model parameters θ, which are generally selected according to physiological observations. A custom-made genetic algorithm, comprehensively described in Bochud et al. (2016), is applied to maximize Eq. (4.9), owing to its capability in finding a near global solution in situations where the objective function is multidimensional and nonconvex. A genetic algorithm is a heuristic optimization technique based on the rules of natural selection

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and genetics, which simulates the mechanisms of survival competition. Unlike gradient-based optimization, a genetic algorithm does not update a single solution at a generic iteration on the basis of the modeling error and gradient values, but consists in selecting, among a population of individuals that represents a set of potential inverse problem solutions, the individual that yields the optimal solution (Marzani & De Marchi, 2013). It thus presents several advantages over gradientbased optimization techniques (Sun et al., 2014): (1) it is robust and conceptually simple; (2) it succeeds in finding a nearly global inverse problem solution without the need of an accurate initial guess for the model parameters θ; and (3) its search mechanisms possess an inherent parallelism that allows for a rapid sampling of the solution space. The number of generations, along with the probabilities associated with each genetic operator, are empirical values based on a trade-off between the inverse problem error and the computational cost, selected so that the convergence to a near global optimum is guaranteed (Fahim et al., 2013).

4.3.4.2 Specific Inverse Framework Towards Clinical Applications To make the BDAT technique clinically available, some simplifications were required to reduce the computing time and improve the robustness of the model parameters identification (Minonzio et al., 1 Proj(θ) = fmax − fmin

4.4



fmax

fmin

2018b). To this end, the identification of cortical bone quality markers, i.e., θ = [h p], has then been adapted through an approach that is an extension of the signal processing applied to extract the experimental guided mode wavenumbers from the maxima of the Norm function (recall Sect. 4.3.2). In this case, instead of spanning all measurable waves, the testing vectors are now restricted to the guided modes of the cortical bone waveguide model calculated from Eq. (4.4). A database of models was calculated for different model parameters θ along a multidimensional grid in steps. The cortical thickness ranged from 0.8 to 4.5 mm with steps of 0.1 mm and the cortical porosity from 1 to 25% with steps of 1%. The objective function is now defined as the projection of a tested model in the singular vector basis, where fmin and fmax correspond to the frequency bandwidth limits and M denotes the number of theoretical guided modes. This approach takes advantage of the sparsity of the f − k plane, i.e., for a considered model, only a finite number M of guided mode wavenumbers km (f, θ) are present at each frequency (Drémeau et al., 2017; Xu et al., 2016a; Zhao et al., 2017). Each pixel of the objective function reflects in a 0–1 scale the presence rate of the tested model in the measured signals. Thus, the optimal model parameters θˆ can be found by maximizing the objective function from Eq. (4.10).

M 2 1  test e (km (f, θ))U n (f ) df M m=1

Main Achievements

With the aim of enhancing fracture risk prediction by assessing cortical bone, the BDAT technique has experienced a number of significant advances from 2015 to 2020. These main achievements, whose description constitute the core of this section, are structured as follows: (1) the validation of a fully automated inverse characterization method that allows inferring multiple cortical bone properties

(4.10)

from multimode guided wave measurements (Sect. 4.4.1); (2) the investigation of the impact of soft tissue on the retrieved estimates, thoroughly discussed in the light of the complexity of the waveguide model to be used as an inverse model (Sect. 4.4.2); (3) the ex vivo assessment of cortical thickness and porosity at two different appendicular skeletal sites, i.e., the radius and tibia, and their site-matched validation using a state of the art technique (Sect. 4.4.3); and (4) the discussion of recent clinical findings (Sect. 4.4.4).

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As a first step towards the identification of multiple cortical bone properties in vivo, this subsection recalls and discusses the most significant results reported in Bochud et al. (2016). In that study, the authors presented a global search approach based on genetic algorithm (recall Sect. 4.3.4.1), which allowed for a concurrent identification of the structural and material properties of cortical bone samples, avoiding any prior knowledge on the experimental data. This was achieved by including an additional parameter in the waveguide model, by means of a pairing vector, which represents the combination of theoretical guided modes that are necessary to fit the experimental data. The proposed approach

was first validated on a series of laboratorycontrolled samples (e.g., isotropic plates, plane and tubular bone-mimicking phantoms) and then evaluated ex vivo on human radius specimens and in vivo on healthy subjects. All measurements were performed using the 1-MHz ultrasonic measuring device adapted to clinical forearm investigations (Sect. 4.3.1). To serve as an example, Fig. 4.8 depicts the optimal matching between the experimental data and the Lamb modes for some of the investigated samples. As can be observed, a remarkable agreement was found between the experimental data and the model for the academic waveguides (Fig. 4.8a–b). For these laboratorycontrolled samples, the relative error on the retrieved thickness and material properties was found to be within a few percent with respect to reference measurements. For the bone samples,

Fig. 4.8 Optimal matching between the experimental data (dots) and the Lamb modes (lines) for a representative selection of inverse problem solutions: (a) 2-mm thick copper plate, (b) 2.3-mm thick bone-mimicking plate, (c) 2.3-mm thick ex vixo human radius specimen; and (d) 2.9-

mm thick in vivo forearm. Modes that are missing in the optimal pairing vector M are displayed as dashed lines, whereas inliers and outliers are displayed as red and blue dots, respectively. Data were taken from Bochud et al. (2016)

4.4.1

Inverse Characterization of Multiple Cortical Bone Properties

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although the larger number of outliers reveal the lower signal-to-noise ratio and the possible presence of additional guided modes (in vivo), a reasonable agreement was found between the experimental data and the Lamb modes (Fig. 4.8c–d). The estimates of cortical thickness and porosity inferred ex vixo could be positively compared to reference values delivered by sitematched X-ray microcomputed tomography. The absolute difference on cortical porosity exceeded somewhat that of the thickness, and was expected to be due, in part, to the assumption of a universal matrix stiffness in the homogenization model (recall hypothesis 2 in Fig. 4.3). The cortical thickness estimates obtained in vivo were shown to be in good agreement with the reference HRpQCT values, whereas the porosity estimates could only be compared to values reported in the literature (Tjong et al., 2014), as there was no available technologies at that time to measure cortical porosity or anisotropic elasticity in vivo. Overall, correct structural and material properties could be identified through the proposed multiparametric inversion, even when high order modes were superimposed in the experimental data and when it was not trivial to a priori determine to which Lamb mode each data point of the experimental guided modes belongs to. The main contribution of the proposed approach was that the global search performed by the genetic algorithm, together with the formulation of an objective function in terms of occupancy rate, did not require any prior knowledge neither on the model parameters θ (e.g., initial guess as in gradientbased optimization) nor on the way to sort the experimental data according to a specific Lamb mode (i.e., the mode-order was kept blind through the introduction of a pairing vector). Therefore, the proposed approach outperformed earlier studies (Foiret et al., 2014; Minonzio et al., 2015) in that it accounted for all experimental data and was not restricted to a specific number of model parameters, for which applying an exhaustive sweeping routine might prove to be rather intractable from a computational viewpoint. As a limitation, it should be noted that the authors could not conclude on the correctness of the identified pairing vectors. This limitation could

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be circumvent by performing a sensitivity analysis on the excitability of the guided modes (Abid et al., 2017; Tran et al., 2018). Nonetheless, their results, which showed a good consistency between the inverted properties and the reference values, a posteriori justified using the pairing vector to reach their objective. As a further drawback, their approach was evaluated on a limited number of bone samples only, whose cortical thickness and porosity encompassed values that may likely differ from elderly or ill patients, in whom thinner cortex and higher porosity can be expected. The investigation of a larger number of subjects, in whom bone properties cover a broader range that might be associated with aging and pathologies, is further addressed in Sects. 4.4.3 and 4.4.4.

4.4.2

Impact of Soft Tissue on Cortical Bone Estimates

In order to gain confidence in the preliminary results obtained in Sect. 4.4.1 and to transfer these into a clinical context, a second challenge was to understand the impact of soft tissue on the retrieved waveguide characteristics. In particular, it was mandatory to clarify whether soft tissue must be incorporated in the waveguide modeling to infer reliable cortical bone properties in vivo. It is commonly acknowledged that the influence of the soft tissue layer on the top of bone is twofold: First, soft tissue nearly behaves like a fluid waveguide for ultrasound. It can thus give rise to additional guided modes, which may be mistaken with those propagating in cortical bone when their phase velocities overlap. A second effect arises from the coupling of the two waveguides (i.e., the soft tissue and the bone waveguide), potentially resulting in a repulsion of the guided modes in some regions of the dispersion curves due to the asymmetric nature of the bilayer waveguide. To date, the impact of overlying soft tissue has been analyzed in a few phantom studies only, whose main conclusions were that (1) the presence of soft tissue attenuates the measured time-domain signals, (2) the number of observed guided modes significantly rises when the

4 Axial Transmission: Techniques, Devices and Clinical Results

thickness of soft tissue increases, and (3) the presence of soft tissue slightly modifies the dispersion curves belonging to the solid (bone) waveguide in certain regions of the f − k plane only (recall for instance Fig. 4.5b). In particular, it has been shown that the development of more sophisticated models (Chen et al., 2012; Lee et al., 2014; Moilanen et al., 2008; Nguyen et al., 2017; Tran et al., 2013) could help elucidating the existence of additional or modified guided modes owing to the presence of soft tissue mimics. Although all these studies provided valuable insights for solving the forward problem using a priori known bone-mimicking properties, none of these quested the ability of these models to infer cortical bone properties for clinical purposes. It is indeed not clear whether such sophisticated models could be applied in vivo, where both the properties of cortical bone and soft tissue are unknown. Overall, no general consensus has been reached yet regarding the complexity of the inverse waveguide model to be used to recover reliable estimates of cortical bone properties in vivo. Therefore, here we recall and discuss the most significant results reported in Bochud et al. (2017), which hypothesized that the waveguide model introduced in Sect. 4.3.3.1 is accurate enough to retrieve the thickness and anisotropic stiffness of cortical bone, despite the presence of soft tissue and bone curvature. This hypothesis was first tested on laboratorycontrolled measurements performed on several assemblies of bone- and soft tissue mimicking phantoms and then on in vivo subjects using the 1-MHz ultrasonic measuring device. To further support this hypothesis, the retrieved estimates were subsequently inserted into the bilayer model (Sect. 4.3.3.2). To serve as an example, Fig. 4.9 depicts the matching between the experimental data and the guided modes for some of the investigated samples. The optimal matching resulting from the inverse problem solution using the free plate model is displayed in the left panels, whereas the forward problem solution using the bilayer model is displayed in the right panels. It should be noted that the latter has been calculated by using optimal input values issued from the former plus soft

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tissue properties either reported from the manufacturer (for the soft tissue mimics) or assessed by performing conventional 20-MHz pulse-echo measurements (for the subjects). As can be observed in the left panels, the optimal inverse problem solutions revealed that parts of the experimental data (red dots) can be identified as guided modes belonging to the solid subsystem (continuous lines), despite the presence of a rather thick soft tissue layer around 5 − 6 mm and eventually sample curvature. First, it should be noted that the outliers (blue dots) consisted of both additional modes at rather low phase velocities (i.e., nearly pure fluid modes) and modified modes due to repulsion effects between the fluid and solid subsystems (observable for instance at a frequency f = 1.4 − 1.6 MHz and wavenumber k = 1 − 2 rad.mm−1 in Fig. 4.9a–b). Second, the results interestingly suggested that the measurements performed on the coated tube and in vivo (Fig. 4.9b– c) were less affected by the presence of soft tissue than the coated plate (i.e., the relative percentages of inliers raised from around 30% to 55%). Therefore, this observation reinforces the hypothesis that, for the investigated frequency-thickness regime, BDAT measurements on a coated non-flat contact surface can be modeled using a free plate waveguide (Minonzio et al., 2015). Furthermore, there was overall a good agreement between the ultrasound-based estimates (i.e., thickness and bulk wave velocities) inferred using the free plate model and the reference values, thus further supporting the robustness of the genetic algorithmbased inverse procedure introduced earlier. On the other hand, the forward problem using the bilayer model (right plots) confirmed the correctness of the estimates, as it allowed predicting most of the experimental data considered as outliers in the left plots (see the significant rise in the relative percentages of inliers). The main contribution of this study was the elucidation of a potential source of confusion for the reader between the forward problem (i.e., prediction) and the inverse problem (i.e., inference), whose expected outcomes are different (Tarantola, 2005). Indeed, a waveguide model either aims (a) at supplying an as exact as possible physics-based model or (b) at representing a sim-

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Fig. 4.9 Matching between experimental data (dots) and guided modes (lines) for a representative selection of the investigated phantoms/subjects: (a) 1.25-mm thick bonemimicking plate coated with a soft tissue-mimicking layer of thickness equal to 6 mm, (b) 2.32-mm thick bonemimicking tube coated with a soft tissue-mimicking layer of thickness equal to 6 mm, and (c) in vivo subject, whose

cortex and soft tissue thickness amount to 3.30 and 5 mm, respectively. Left plots represent the optimal matching resulting from the inverse problem solutions using the free plate model (Eq. (4.2)), whereas right plots represent the forward problem solutions calculated with the bilayer model (Eq. (4.5)). Data were taken from Bochud et al. (2017)

plified but sufficiently accurate inverse model to provide a robust inference of one or several waveguide properties from the experimental data. Since a free plate model obviously predicts in

vivo measurements in a rather incomplete manner, one could intuitively expect that a more sophisticated model (recall Sect. 4.3.3.2) might be necessary to perform an accurate inversion of

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these data. However, the purpose of applying a free plate model is not to fit all the data, but to provide a means for extracting features from a simplified equivalent waveguide only, whose physical characteristics can be linked to the real characteristics of the medium. The presented results have shown that the dispersion curves measured on the bilayer phantoms and in vivo subjects exhibit regions of the f −k plane that contain (1) the fingerprints of the solid (bone) subsystem, (2) the fingerprints of the soft tissue subsystem, and (3) the coupling between the two subsystems. According to the employed frequency bandwidth and some other factors that are not properly understood yet, different AT techniques have shown disparate sensitivities to these different regions. Within the context of multimode guided waves, the reported BDAT measurements, which are performed over a rather important frequencythickness product range, mainly exhibit sensitivity to the solid subsystem (i.e., cortical bone), in which case the free plate model provided an appropriate inverse model. The high level of consistency between the inferred properties and the reference values a posteriori justified the proposed approach. In addition, although more sophisticated models, and bilayer models in particular, have been shown to be valuable predictive tools for differ-

ent material characterization applications (Mezil et al., 2014; Niklasson et al., 2000; Simonetti, 2004), the reported results suggest that they have a limited meaning for the inverse assessment of cortical bone properties in vivo. For instance, solving a multiparametric inverse problem involving a bilayer waveguide model is challenging for three reasons at least (Bochud et al., 2017): (1) unlike the free plate model (recall Eq. (4.2)), the fluid-solid bilayer model explicitly depends upon the mass density ρs of the solid waveguide, which is generally unknown for bone; (2) solving the identification procedure with nine model parameters (recall Eq. (4.5)) may lead to an illposed inverse problem (i.e., several local optima) and overfitting of the data (Chiachío et al., 2017); and (3) the bilayer model has a significantly larger computational cost than the free plate model and is prone to numerical instabilities (Honarvar et al., 2009). Overall, using even more sophisticated models is expected to further exacerbate these drawbacks. Despite everything, the proposed approach suffers from some constraints. It was indeed observed that it could fail for soft tissue thickness larger than 10 mm, thus leading to an ill-posed problem associated with several local optima. To highlight this statement, Fig. 4.10 represents 3-D slices of the normalized objective function F (θ)

Fig. 4.10 3-D slices of the normalized objective function F (θ) along three model parameters, i.e., h, VT and c33 /c11 , with optimal values for the remaining three parameters (c13 /c11 , VL⊥ and M). This example corresponds to a 1.25-mm thick bone-mimicking plate coated with (a) a 2-mm soft tissue-mimicking layer and (b) an 8-mm soft

tissue-mimicking layer. The circle and triangle represent the global and a local optima associated with the values of the objective function, F1 (θ ) and F2 (θ ), respectively. Figure reproduced and adapted from Bochud et al. (2017), with permission according to the terms of the Creative Commons CC BY license

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along three model parameters, i.e., h, VT and c33 /c11 , whereas the remaining three (c13 /c11 , VL⊥ and M) were fixed to their optimal values. The circle at the intersection of the slices corresponds to the global optima (i.e., F1 (θ) = 1). As can be observed, the relative amplitude between the global and local optima tends to decrease with increasing coating thickness (i.e., F2 (θ)). Nevertheless, this potential source of failure was here essentially due to the decreasing quality of the measurements for thick soft tissue coatings, rather than a misidentification of the inverse procedure or a limitation of the free plate model. Indeed, earlier studies already reported the difficulty of measuring guided waves on subjects associated with a high body mass index (Moilanen et al., 2008; Talmant et al., 2009).

4.4.3

Ex Vivo Validation of Cortical Bone Quality Markers

Recovering waveguide characteristics, such as cortical thickness and porosity (hereinafter denoted by Ct.Th and Ct.Po), could provide reliable information about skeletal status and future fracture risk. Before evaluating the performance of such cortical bone quality markers in vivo, it is mandatory to validate these ex vivo. A first validation study for assessing cortical thickness and porosity has been comprehensively described in Minonzio et al. (2018b), in which 31 radii and 15 tibiae harvested from human cadavers underwent 1-MHz BDAT measurements (recall Sect. 4.3.1). Seventeen donors were females and fourteen were males (age 50–98 years, mean 78.9 ± 11.9 years). Automatic parameters identification was achieved through the solution of an inverse problem, in which the dispersion curves were predicted with the free plate model introduced in Sect. 4.3.2. Ultrasound-based estimates were then compared with site-matched micro-computed tomography (μ-CT) images of the bone specimens (imaged at 9 μm voxel size), which served as the gold standard to test their accuracy. Pearson’s correlation analysis was used to compare ultrasound estimates with reference

values. As can be observed in Fig. 4.11a, a strong correlation was found between Ct.ThμCT and Ct.ThUS (R 2 = 0.89; root mean square error, RMSE = 0.3 mm). In addition, the Bland and Altman plot revealed virtually no systematic difference (d = 0.06 mm) between both methods. For the cortical porosity, a significant but moderate correlation (R 2 = 0.63, RMSE = 1.8%) and virtually no systematic difference (d = 0.1%) were found between both methods (Fig. 4.11b). Overall, the reported inverse procedure was successful for 40 bone specimens (27 radii and 13 tibiae) out of the 46 that were measured with BDAT. The excellent accuracy of the cortical thickness estimates, which were retrieved using the free plate model, showed that the proposed method is robust even when the waveguide model used for solving the inverse problem does not exactly match the complexity of the cortex (e.g., geometric irregularities or presence of heterogeneities). In contrast, despite the general good agreement for cortical porosity, results showed that the interval corresponding to the limits of agreement was important (about 7.5%), which, compared to the dynamics of the variability of cortical porosity (about 15%), was significant, thus indicating that both methods, i.e., BDAT and μ-CT, are not interchangeable. For homogeneous and regular bone specimens, the measurement sequences were shown to be stable and reproducible, and thus the two-parameter identification procedure (recall Eq. (4.10)) delivered unambiguous and reliable inverse problem solutions. Nonetheless, when the bone waveguide significantly deviates from the homogeneous plate model, the identification of cortical characteristics can result in an ill-posed inverse problem associated with multiple local solutions or even no solution at all. Indeed, the notion of waveguide presupposes well-defined boundaries on which the propagating waves are reverberated, thus giving rise to the presence of guided modes. The disruption of the endosteal bone edge that can be observed in case of strongly deteriorated bones is likely to weaken such waveguide hypothesis. Another issue is the presence of large resorption cavities that

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Fig. 4.11 Estimated waveguide characteristics, i.e., cortical (a) thickness and (b) porosity, plotted against reference values obtained using site-matched μ-CT. Left panels represent the Pearson’s correlation analysis, whereas right

panels represent the Bland and Altman plots. Radius and tibia specimens are displayed as blue and red dots, respectively. Data were taken from Minonzio et al. (2018b)

has been described in strongly eroded bones of elderly cadavers. Strong wave scattering may arise from the interaction of ultrasound waves with these cavities and we suspect that the superposition of these scattered signals with the guided waveforms makes the signal analysis and modes identification particularly challenging. In the same vein, a gradient of porosity from the periosteal to the endosteal cortical bone edges could be observed in some specimens, and this heterogeneous pores’ distribution may be a further source of modes misidentification. Altogether, these factors explain, in parts, the moderate success in retrieving accurate cortical porosity estimates, as well as the six failure cases (i.e., 4 radii and 2 tibiae) typically associated with poor measurements. A possible solution to

address this issue would be either to conduct 3-D numerical simulations of the wave propagation based on real bone structures derived from high resolution images, or to incorporate a somewhat more complicated waveguide model in the identification process, at the cost of a more challenging multiparametric inverse problem analysis (recall Sect. 4.3.4.2). Another potential limitation concerns the model of elasticity used to obtain cortical porosity (recall Fig. 4.3b), which was based on the assumption of universal matrix elasticity. Using constant values of stiffness Cm and mass density ρ m means that the properties of the matrix are spatially homogeneous and uniform among individuals. Neglecting the matrix heterogeneity and diversity could introduce errors

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that may impact the model parameters estimation, especially that of cortical porosity. First, it should be noted that porosity estimates depend on the choice of the matrix properties used in the model. Available experimental values of Cm , measured at the femur of aged female donors (Granke et al., 2011), have been used here. Although it is commonly acknowledged that matrix properties do not vary to a large extent, small local differences may still exist across different skeletal sites. Therefore, other matrix properties could have been selected according to data available in the literature, either measured at other skeletal sites (Bernard et al., 2016; Cai et al., 2019b, 2020) or predicted from multiscale models (Morin & Hellmich, 2014; Vu & Nguyen-Sy, 2019). Second, because the proposed effective model does not account for inter-individual variability, small deviations that exist between individual matrix characteristics may explain some of the disagreement between the porosity estimates and their reference counterparts. A solution to circumvent the difficulty in selecting the proper matrix elasticity would be to solve the inversion procedure directly in terms of stiffness (recall Eq. (4.2)) as in (Bochud et al., 2017; Foiret et al., 2014). In a complementary study aiming as well at the ex vivo validation of cortical thickness and porosity estimates (Schneider et al., 2019a), guided waves were now measured on 19 human tibiae diaphysis using the specifically designed 500-

kHz BDAT probe. Thirteen donors were females and six were males (age 69–94 years, mean 83.7± 8.4 years). Several amendments have been introduced to tackle some of the limitations reported in the former study (Minonzio et al., 2018b). First, further ultrasound-based characteristics (i.e., vA0 and vFAS ) and site-matched reference parameter (i.e., volumetric bone mineral density, VBMD , derived from μ-CT) were included to broaden the analysis. Second, to account for a possible interindividual variability of the bone matrix elasticity, the analysis also incorporated information on the acoustic impedance, which was assessed by sitematched scanning acoustic microscopy (SAM). Third, to improve the data acquisition and the accuracy of the estimates, notably longer measurement sequences were acquired by slowly tilting the probe along the circumferential direction during the measurement cycle. Altogether, the statistical results showed that the ultrasound-based prediction of cortical thickness (R 2 = 0.57, RMSE = 0.4 mm) was weaker than for cortical porosity (R 2 = 0.83, RMSE = 2.2%). The moderate agreement for cortical thickness estimates was mainly explained by the heterogeneity of one specimen (considered hereinafter as an outlier), which had a strongly trabecularized cortex (see Fig. 4.12a). When removing this sample from the statistical analysis, the correlation between Ct.ThUS and Ct.ThμCT significantly improved to an R 2 = 0.92 and a RMSE = 0.2 mm. This ambiguity was believed

Fig. 4.12 Reference μ-CT images with 39 μm isotropic voxel size. Transverse cross-sections (left subplots) display the location of the BDAT measurements. Longitudinal sections (right subplots) were taken at the dashed line of the transverse cross-sections. The green area show the segmented cortex region used to calculate site-matched VBMD and Ct.ThμCT . (a) Specimen considered as an out-

lier owing to its strongly trabecularized cortex, for which cortical thickness estimated by BDAT significantly deviates from that evaluated using the reference technique; (b– c) Specimens for which the BDAT measurements fail. Figure reproduced and adapted from Schneider et al. (2019a), with permission according to the terms of the Creative Commons Attribution 4.0 International License

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to be due, in part, to the definition of the sitematched area used to calculate Ct.ThμCT , which results uncertain for highly trabecularized inner cortical bone regions. Indeed, a consensus on how to segment the cortical bone compartment has not been reached yet. For instance, the longitudinal section in Fig. 4.12a suggests that guided waves may also propagate in the trabecularized bone region (i.e., different interpretation of the waveguide thickness between BDAT (dashed red line) and μ-CT (green area)). Furthermore, the dependency of vFAS on VBMD was consistent with earlier reported results at the tibia using other AT devices working at different excitation frequencies (Kilappa et al., 2011; Moilanen et al., 2003; Sievänen et al., 2001). However, in contrast to earlier studies (Kilappa et al., 2011; Moilanen et al., 2003), no statistically significant correlation was found between vFAS and Ct.ThμCT . The dependency of vA0 on Ct.ThμCT and VBMD also confirmed earlier ex vivo findings at the radius using a lower frequency AT device (Muller et al., 2005). It should be noted that the variability of the matrix elasticity assessed by SAM did not improve the modelbased predictions of Ct.ThUS and Ct.PoUS , thus supporting the idea that variations in matrix stiffness have a minor impact on the effective stiffness compared to the variations in porosity (Cai et al., 2019a,b; Granke et al., 2011). Therefore, the increased agreement for cortical porosity estimates with respect to the former study is thought to be due essentially to the improved measurement protocol. The latter was indeed shown to ease settingup a proper criterion to automatically exclude poor measurements (i.e., noisy or incomplete dispersion curves), thus improving the accuracy of the inverse problem solutions. The main limitation of this study was the small number of investigated specimens (N = 19). Two samples were excluded due to large deviations across the ultrasound measurement cycles. The first failure case had a thin cortical thickness lower than 2 mm (Fig. 4.12b), for which the 500kHz probe is unlikely to excite a sufficient number of guided modes within the limited frequency bandwidth. The second failure case exhibited a

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very inhomogeneous cortex (Fig. 4.12c), which challenged the waveguide hypothesis.

4.4.4

Towards Clinical Applications

Testing in vivo the performance of the BDAT approach can be considered as the natural outcome of the ex vivo validation studies discussed in Sect. 4.4.3. To unlock this goal of clinical interest, two steps were necessary: (1) to assess to what extent cortical bone quality markers obtained from the BDAT measurements agree or correlate with site-matched reference values; and (2) to evaluate the ability of these quality markers for discriminating between fractured and nonfractured patients. The first step was addressed in a recent in vivo pilot study (Schneider et al., 2019b), which proposed to test the 500-kHz BDAT technique at the tibia of a small group of patients, with the aim of retrieving estimates of cortical thickness and porosity (i.e., Ct.ThUS and Ct.PoUS ), as well as ultrasound velocities (i.e., vFAS and vA0 ). These estimates were subsequently compared to reference values delivered by site-matched pQCT (i.e., Ct.ThpQCT and VBMD , the latter being used as a surrogate for cortical porosity) and distal HR-pQCT (i.e., four parameters of the cortical bone compartment plus the total volumetric bone mineral density). The measurement location and assessed parameters of each individual scanning technique are depicted in Fig. 4.13. The study cohort was compound of 20 patients including 8 women and 12 men (mean age: 51 ± 14 years). The proposed approach was successful for 15 out of the 20 patients. Five patients were excluded because of their thin cortex at the measurement site (Ct.ThpQCT < 2.5 mm), which limited the measurement of multiple guided modes within the selected frequency bandwidth. Excellent agreement was obtained between Ct.ThUS and site-matched Ct.ThpQCT (R2 = 0.90, RMSE = 0.19 mm), thus confirming earlier results obtained on a population of healthy subjects (Vallet et al., 2016). Moreover, although VBMD has been proved to be a strong predictor of cortical porosity (Ostertag et al., 2016), only a moderate cor-

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Fig. 4.13 (a) Overview of the parameters assessed from the in vivo pilot study: 500-kHz BDAT was performed site-matched with pQCT (voxel size, 0.5 mm) at the proximal third of the tibia (blue boxes); HR-pQCT (voxel size, 82 μm) was applied to the distal site of the same

limb (red boxes). (b) The transverse cross-section of the pQCT image shows the tangential position of the BDAT probe, which was placed at the anteromedial surface of the tibia. Figure reproduced and adapted from Schneider et al. (2019b), with the permission of Elsevier

relation between Ct.PoUS and site-matched VBMD was found (R 2 = 0.57). Several factors could explain this limited performance, especially the fact that the region of interest explored by BDAT and pQCT was not exactly site-matched (Schneider et al., 2019b). In addition, for the ultrasound velocities, moderate correlations were found between vFAS and VBMD (R 2 = 0.43), as well as between vA0 and Ct.ThpQCT (R 2 = 0.31), and VBMD (R 2 = 0.28). This could be expected since the velocities of guided waves depend both on structural and material properties. Compared with that of vFAS , the impact of vA0 has been much less studied in vivo. Nevertheless, the predictive capability of this velocity was in good agreement with the results reported in a clinical study that used a 200-kHz AT device at the tibia of pubertal girls (Moilanen et al., 2003). The overall agreement of the ultrasound-based estimates with pQCT was in contrast with the moderate success in comparing these with HR-pQCT, especially because the distal tibiae of only 8 patients was scanned with this technique, thus limiting the significance of the statistical analysis. The second step was addressed in a pilot crosssectional study (Minonzio et al., 2019), which

aimed at evaluating the ability of two QUS cortical parameters, Ct.ThUS and Ct.PoUS , estimated from measurements at the one-third distal radius using the 1-MHz BDAT device, to discriminate postmenopausal women with non-traumatic fractures from a control group. Central DXA measurements, performed at the femoral neck, total femur, and lumbar spine delivered reference aBMD values that serve as the gold standard for skeletal status assessment. Figure 4.14 presents an overview of the applied scanning techniques, the clinical history of the investigated patients, as well as the different steps used to perform the statistical analysis. This study reported for the first time on the concurrent in vivo estimates of two cortical bone quality markers, i.e., Ct.ThUS and Ct.PoUS , using a device based on the propagation of ultrasound guided waves, and their association with fractures. The main findings were that (1) Ct.PoUS was discriminant for all non-traumatic fractures combined and, in particular, for vertebral and wrist fractures, while Ct.ThUS was discriminant for hip fractures only; (2) a significant association was found between increased Ct.PoUS and vertebral and wrist fractures, while these frac-

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Fig. 4.14 Overview of the pilot cross-sectional study: (a) 1-MHz BDAT was performed at the one-third distal radius of 301 patients to identify cortical thickness and porosity (Ct.ThUS and Ct.PoUS ); (b) DXA reference measurements of the femoral neck (aBMD neck), total femur (aBMD femur), and L2 to L4 lumbar spine (aBMD spine)

were performed using two cross-calibrated systems of the same manufacturer (Hologic, Bedford, MA, USA); and (c) Clinical history of the investigated cohort. The remaining boxes display the statistical tools used to evaluate the performance of the BDAT approach

tures were not associated with any of the aBMD variables; (3) the association between increased Ct.PoUS and all non-traumatic fractures combined independently of aBMD neck; and (4) the association between decreased Ct.ThUS and hip fractures independently of aBMD femur. The two QUS parameters could not be identified for 49 patients, and the reported failure rate of around 20% was typically associated with subjects displaying a high body mass index (BMI), thus confirming earlier evidences based on the FAS velocity (Talmant et al., 2009; Weiss et al., 2000). A higher BMI generally entails a thicker soft tissue layer, which in turn implies a higher signal attenuation, unwanted additional guided modes, and difficulties in correctly aligning the

probe with the main bone axis. Thereby a correct identification of cortical bone quality markers in presence of thick soft tissue may be challenging and could require the use of more sophisticated waveguide models (recall Sect. 4.3.3.2) or dedicated signal processing. Besides, the general complexity of the bone cortex, in particular the disruption of the endosteal bone edge and the presence of large resorption cavities observed in case of strongly deteriorated bones, may further impact the generation, propagation and detection of guided waves. Notwithstanding, the failure rate reported here was not correlated with the fracture history of the patients. The results described in Minonzio et al. (2019) also revealed that Ct.ThUS and Ct.PoUS exhibited

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significant age-related dependence for females: concurrent to the increased porosity, the thickness at the radius was reduced with aging. These observations were consistent with previously reported data using HR-pQCT (Alvarenga et al., 2017; Bala et al., 2014; Nicks et al., 2012; Shanbhogue et al., 2016; Vilayphiou et al., 2016). Moreover, Ct.ThUS and Ct.PoUS were shown to be associated with fracture. Although there are no equivalent QUS studies to corroborate this, several studies that evaluated cortical microstructural parameters derived by HR-pQCT measurements at the ultradistal radius, demonstrated that alterations, such as low Ct.Th (Boutroy et al., 2016; Nishiyama et al., 2013; Sornay-Rendu et al., 2017, 2009; Wang et al., 2016; Zhu et al., 2016) or high Ct.Po (Bala et al., 2015a; Edwards et al., 2016), were associated with prevalent fracture. In a few studies, even after adjustment for aBMD, the association between Ct.Th and the existence of fractures remained significant (Boutroy et al., 2016; Sornay-Rendu et al., 2009). In contrast to these numerous works relying on HR-pQCT, only a few studies reported on the assessment of cortical thickness using QUS modalities, such as ultrasound transmission (Mishima et al., 2015) and pulse-echo ultrasonometry (Schousboe et al., 2017). Furthermore, the adjusted odd ratios (ORs) and areas under the ROC curve (AUCs) obtained from guided wave measurements were of comparable magnitude to those delivered by aBMD measurements. Altogether, these observations confirmed earlier results that reported alterations of cortical bone structure in subjects with fracture, which were associated with hip, vertebral, wrist or combination of fragility fractures. Despite these promising results, this study suffered from several limitations (Minonzio et al., 2019). A first drawback was the overall moderate number of patients, and particularly the small number of fractures in each group (recall Fig. 4.14c). Larger clinical trials are warranted to address the questions of whether (1) Ct.ThUS and Ct.PoUS can be used as site-specific fracture risk factors; (2) these parameters are risk indicators of fracture independent of aBMD, in

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particular for patients with normal aBMD (as determined by DXA), or (3) they offer additional discriminatory capacity over aBMD for a particular category of fractures. Second, the waveguide model used for the identification of cortical bone characteristics was parametrized in terms of thickness and porosity by assuming universal material properties of the tissue matrix, thus neglecting the inevitable inter-individual variability of bone tissue properties (Cai et al., 2020; Unal et al., 2018). Notwithstanding, this hypothesis led to reasonably accurate identification of Ct.ThUS and Ct.PoUS of human radius and tibia specimens ex vivo (Minonzio et al., 2018b; Schneider et al., 2019a), as discussed in Sect. 4.4.3. This model simplification could be circumvented by using a parametrization in terms of thickness and stiffness (i.e., four independent stiffness coefficients can account for the generally acknowledged transverse isotropy of cortical long bones measured axially). This strategy was satisfactorily adopted ex vivo on a few specimens (Foiret et al., 2014) and in vivo on a reduced number of healthy subjects (Bochud et al., 2017). However, solving such a multiparametric inverse problem could lead to an ill-posed identification (i.e., numerous local optima) and overfitting of the data in the case of strongly deteriorated bones potentially encountered in elderly populations. To make the BDAT technique clinically available, model simplifications were currently required to reduce computing time and improve the robustness of the parameters identification. A third limitation of BDAT concerns its non-negligible failure rate when the soft tissue thickness is important (i.e., typically associated with BMI larger than 28 kg m−2 ). Further research is needed to make this technology available to patients with large BMI. Towards this goal, current improvements are focusing on (1) the human machine interface, by incorporating quantitative information to deliver a real time feedback on the correctness of the probe alignment and (2) the development of more sophisticated waveguide models to account for the soft tissue, whose thickness could be determined by conventional pulse-echo imaging for instance.

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4.5

Summary and Outlook

The development of a robust and accurate technique for structural and material properties identification using guided waves rises several challenges for complex waveguides such as the cortex of long bones. This chapter summarized the determinant steps and key contributions that were necessary to make the BDAT technique available clinically. • Inverse identification of cortical bone quality markers: A fully automated inverse problem based on genetic algorithm optimization has been proposed to retrieve the thickness, anisotropic stiffness and porosity of different waveguide structures that are likely to mimic cortical long bones. A key factor of this approach was the introduction of an additional parameter in the waveguide model, which accounted for the pairing of the modeled guided modes with the measured ones. Unlike classical approaches used so far in the field, the mode-order was kept blind and there was no need to identify the modes prior to solving the inverse procedure. This model-based approach was validated on laboratory-controlled measurements performed on isotropic plates and bone-mimicking phantoms with known properties, as well as evaluated ex vivo on a few human specimens. The strength of this approach is that it is not restricted to any specific number of model parameters, for which applying an exhaustive sweeping routine might prove to be rather intractable from a computational viewpoint. • Impact of soft tissue on the identified properties: The complexity of the waveguide model used to retrieve in vivo cortical bone quality markers is a key issue in data processing. To address the question of whether or not the inverse waveguide model should incorporate the impact of soft tissue, the proposed model-based approach was also tested on coated bone-mimicking phantoms and healthy subjects using both a free plate and a bilayer waveguide models. Correct thickness and stiffness estimates could be retrieved

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using the free plate model, even for relatively thick soft tissue layers, thus suggesting that a simplified equivalent waveguide model could be accurate enough to tackle the complexity of in vivo measurements performed using BDAT in the reported frequency bandwidth. It should be noted, however, that these observations cannot necessarily be extended to other AT techniques working at different excitation frequencies. • Ex vivo validation of cortical thickness and porosity: An adapted inverse procedure was then applied to human radius and tibia specimens in two ex vivo proof-of-principle studies. The inferred cortical bone quality markers, i.e., cortical thickness and porosity, were validated by site-matched comparison with reference values obtained from X-ray microcomputed tomography. Overall, there was a good agreement between the ultrasound parameters and the reference values. Nevertheless, several factors were shown to impact the accuracy of the cortical porosity estimates, among which it is worth recalling the influence of the choice of the matrix properties used in the homogenized waveguide model. Despite everything, a strength of the BDAT approach is that the homogenized elastic properties at the millimeter length scale are partly determined by the microstructure. Therefore, in principle, the reported cortical porosity estimates reflect the porosity below the resolution limit of HRpQCT. • Clinical perspectives: The latter approach was finally applied to human radius and tibia specimens in two in vivo proof-of-principle studies. The first study investigated to what extent the cortical bone quality markers obtained from the BDAT measurements agreed or correlated with site-matched reference values delivered by state of the art imaging technologies. Excellent and moderate predictions were respectively obtained for cortical thickness and porosity, thus confirming the earlier results found ex vivo. The second study reported for the first time on the concurrent in vivo estimates of two cortical bone quality markers assessed by

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BDAT and their association with fracture. Nonetheless, BDAT measurements were done retrospectively after the fractures were sustained. The independent contribution of cortical bone quality markers as evaluated by BDAT to the risk of fracture has to be evaluated prospectively. Altogether, the reported results have shown that the BDAT approach led to excellent results for homogeneous and regular bones that can be reasonably approximated by an anisotropic free plate waveguide model. In such circumstances, guided wave measurements were shown to be stable and reproducible, so that multiple guided modes could be clearly identified, in which case the identification procedure delivered unambiguous and reliable inverse problem solutions. Notwithstanding, when the bone cortex significantly deviates from a homogeneous and regular structure, the identification of cortical bone quality markers could result in an illconditioned inverse problem associated with multiple local solutions or even no solution at all. The disruption of the endosteal bone edge, along with the presence of large resorption cavities, that could be observed in the case of strongly deteriorated bones in elderly are likely to weaken the underlying waveguide hypothesis. These factors explained, in part, the moderate success in retrieving accurate cortical bone characteristics for some of the investigated cases. Another issue was the relatively high failure rate of the method, especially in vivo, which was typically associated with subjects exhibiting a high body mass index. Overall, these considerations could conceivably represent significant sources of methodological improvements of current AT technologies. First, the signal recording and processing, and thus the measured guided modes, are governed by the choice of the excitation frequency and the investigated anatomical site. To avoid potential modes misidentification inherently related to broadband measurements, some researchers have proposed alternative approaches based on the use of mode-selective excitation (Bai et al., 2016; Moilanen et al., 2017) or mode conversion (Bustamante et al., 2019). Second, the departure from

a 2-D transverse isotropic free plate waveguide model that assumes a perfect alignment of the probe with the main bone axis has been shown to affect the accuracy of the retrieved cortical bone quality markers. Several sources of model sophistications have been discussed, including different geometric features and constitutive properties to account for the cortical bone complexity. These studies, however, only solved the forward problem without providing any hints on a possible inversion, i.e., on the ability to infer cortical bone properties for clinical purposes. To the best of our knowledge, only two models incorporating additional features have been used so far as inverse models in the literature. In a first proposal (Pereira et al., 2019), a bone-like geometry including two additional geometric features (i.e., outer diameter and a shape factor) was implemented using the semi-analytical finite-element method to perform the inverse characterization of five ex vivo radius specimens at low frequencies ( λ 0 if A ≤ λ, (5.5)

and α is a constant that must be greater than or equal to the maximum eigenvalue of WH W and the superscript H denotes Hermitian. The clever update hj reducing the computational time is given by

 1 H λ = SOFT hj + W (s − Whj ), α 2α (5.4)    1 + 1 + 4ξj2 ξj − 1 hj = rj + (rj − rj −1 ) with ξj +1 = . ξj +1 2

(5.6)

As a practical example, Fig. 5.2 displays the sparsity-constrained spectral decomposition of the UGW signals acquired from an ex-vivo ATU experiment on a bovine femur plate (Tran et al., 2021). The offset range covers the near, mid, and far transmitter-receiver distances. Timefrequency analysis transforms a one-dimensional

(1D) time series into a two-dimensional (2D) t-f map. Wavelet decomposition has recently been used to transform UGW signals into the energy density domain (Liu et al., 2019). While STFT considers a signal as a set of windowed sinusoids of various frequencies, wavelet transform (WT) repre-

Fig. 5.2 (a) Ultrasonic guided wave signals acquired at different offsets from an ex-vivo ATU experiment on a bovine femur bone plate. (b)–(h) The spectrograms mapped by the high-resolution spectral decomposition technique. The black solid and dashed lines superimposed

in the dispersion plots are the theoretical asymmetric and symmetric guided modes respectively, which were simulated using a free isotropic cortical plate of 5.8 mm thickness (Reproduced with modifications from Tran and He et al., Ultrasonic Imaging, 2021; accepted)

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Fig. 5.3 SWT scalogram of the experimental signal produced by an axial ultrasound measurement of a bovine tibial bone plate with a propagation distance of 70 mm. Three Lamb modes were identified by the theoretical dispersion curve matching. The bone model was a 4 mm thick isotropic plate (Reproduced from Liu et al., Ultrasonics, 2019;99:105948. https://doi.org/10.1016/j.ultras. 2019.105948, with the permission of Elsevier)

sents a signal using a function that is scaled and time-shifted. WT uses scalable size windows to achieve time-frequency scalogram computation. Liu et al. employed the synchrosqueezing wavelet transform (SWT) (Jiand & Suter, 2017) to obtain the high-resolution TFR of a bone-plate data set (Fig. 5.3).

5.2.2

Modal Filtering

Albeit the spectrogram provides useful information about pulse-broadening and dispersion of the propagating guided wave modes, signal interpretation is challenging when one encounters signals with intersecting signatures in timefrequency space. Mode conversion and overlap phenomena complicate the single-channel guided wave analysis. Separation of different modes arriving closely and overlapped in time becomes a significant task. In addition, certain wave modes’ propagation characteristics carry more information than the other modes about the underlying bone structure (Tran et al., 2018a). There have been numerous techniques developed and applied to the multi-component axiallytransmitted record for the purpose of extracting the signal of interest.

An STFT-based method called multiridgebased analysis was applied by Xu et al. (2010) to detect and separate t-f energy ridges from a multi-modal signal. First, STFT computes the t-f energy density spectrum of a bone data set. A crazy-climber algorithm is then used to extract the time-frequency ridges of their corresponding guided modes from the computed spectrogram. The corresponding waveform representatives of individual guided modes are subsequently reconstructed from the filtered t-f ridges. However, the drawback of this method is that manual user interaction is required for modal identification, which makes the technique less attractive. Song et al. (2011) implemented the joint approximate diagonalization of eigen-matrices algorithm (JADE) (Cardoso & Souloumiac, 1993) to separate the superimposed guided waves in long bones. After the separation, group velocity spectra of the extracted modes are computed by the adaptive Gaussian chirplet t-f (Yin et al., 2002) and the difference value methods. Even though JADE achieves fair time-frequency resolution and efficient computational cost, identifying the guided modes under noisy condition is still a challenging task with this technique and pretreatments are prerequisite to denoise the signals. Dispersion compensation method enabled the dispersive Lamb wave separation of multi-modal single-channel recording (Xu et al., 2012). The approach, nevertheless, was unable to separate UGW modes traveling at the same speed and requires a great deal of prior knowledge about the UGW data which is difficult to have access in clinical settings. Its performance was limited to application on the steel-plate experimental signals only. The modal selective excitation and detection can also be accomplished using wideband dispersion reversal (WDR) technique (Xu et al., 2014). Similar to the dispersion compensation method (Xu et al., 2012), WDR technique makes use of some a priori knowledge of the UGW dispersion characteristics to synthesize the corresponding dispersive reversal excitations, which is its limitation.

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Fig. 5.4 The filtered and reconstructed Lamb wave signals measured from a bovine tibia: (a) A1 mode, (b) S1 mode, (c) S2 mode, and (d) multi-mode (Reproduced from Liu et al., Ultrasonics, 2019;99:105948, https:// doi.org/10.1016/j.ultras. 2019.105948, with the permission of Elsevier)

Zhang et al. (2013) utilized joint spectrogram segmentation and ridge-extraction (JSSRE) method to perform guided wave mode filtering. First, a Gabor t-f transform calculates the spectrogram of the multi-modal signals. Sequentially a multi-class image segmentation algorithm, which includes an improved watershed transform and a region growing procedure, is used to locate the corresponding energy cluster of each UGW mode in the spectrogram. Finally, the temporal signals of individual modes are reconstructed from the respective extracted ridges by an inverse Gabor transform. Despite the performance of the algorithm was illustrated using only synthetic data sets with different SNR in Zhang et al.

(2013), the interaction-free JSSRE algorithm showed a great potential for bone data processing. The most recent work by Liu et al. (2019) investigated the feasibility of using SWT combined with image segmentation methods, e.g. watershed transform and region growing, for automatic modal filtering. A local maximum search is first performed in the time-frequency scalogram (Fig. 5.3). Then watershed transform (Meyer, 1994) and region growing segment the t-f spectrum into distinct energy trajectories of wave components. The wavefields of the separated modes can be restored from the TFR partitions by the inverse SWT (Jiand & Suter, 2017) (Figs. 5.4 and 5.5).

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Fig. 5.5 Separated time-frequency scalograms of the filtered experimental signals shown in Fig. 5.4: (a) A1 mode, (b) S1 mode, and (c) S2 mode (Reproduced from Liu et

5.3

Multiple Transmitter-Receiver Configuration

5.3.1

Dispersion Imaging and Filtering

As multi-channel ultrasonic axial-transmission data are intrinsically dispersive and multi-modal, dispersion imaging and filtering is important because the signal analysis is usually limited to the fundamental guided modes. To explore the dispersive properties of UGW, a set of recorded temporal-spatial signals measured in bone specimens can be transformed into frequency-wavenumber (f -k) domain using the classical two-dimensional Fourier transform (2D-FT) with a subsequent interpolation via cp = 2πf/k (Lefebvre et al., 2002; Tran et al., 2013a). The extracted dispersion trajectories of the guided modes usually have poor resolution in the transformed domain to discriminate closelyspaced guided wave dispersive energies. The resolving power associated with the Fourier transform is closely linked to the aperture and distribution of the receiving elements. In clinical measurements, the spatial aperture is limited by the accessibility of the skeletal site of interest, the regularity of the scanning surface, the length of the ultrasound probe, and the number of receiving channels. This limits the application of the 2DFT in bone tissue characterization (Moilanen, 2008). A group velocity filtering (GVF) was

al., Ultrasonics, 2019;99:105948, https://doi.org/10.1016/ j.ultras.2019.105948, with the permission of Elsevier)

attempted to improve the 2D-FT extraction of the fundamental flexural guided mode from quantitative ultrasound recordings (Moilanen et al., 2006). The GVF technique relies on the use of a Hanning time window to selectively envelope and isolate the late arrival contribution from the recorded signals. The so-called “selective 2D-FT” approach can not increase the 2DFT resolution and lacks of the capability to discriminate signals that are overlapping in time domain. Radon transform, originally introduced by the Austrian mathematician Johann Radon (1986), is an integral transform along linear trajectories. Inspired by the successful applications of the highresolution Radon transform (HRRT) in geophysical and seismic signal processing (Sacchi et al., 1995), the technique was applied to image dispersive guide wave energy in long cortical bones and to filter and reconstruct the UGW modes. The research efforts were reported for the first time in 2013 (Le et al., 2013; Nguyen et al., 2013a,b; Tran et al., 2013b,c) and 2014 (Nguyen et al., 2014; Tran et al., 2014a,b) respectively. The discrete linear Radon or time intercept-slowness (τ -p) transform considers the UGW fields as a superposition of plane waves defined by the ray parameters or slowness, p, and the arrival time at zero offset, τ . The ray parameter p is related to the material velocity and incident angle via Snell’s law (Fig. 5.6a). The transform is computed by stacking the signal amplitudes in t-x domain along straight lines t = τ + px with a range of slopes p and intercepts τ and then

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Fig. 5.6 (a) An illustration of the phase slowness and velocity concept. A plane wavefront travels obliquely into a medium at an incident angle i with respect to the horizontal surface. The wave ray, which is normal to the plane wavefront, propagates at the same incident angle i with the normal of the surface. When the wavefront travels a distance vt into the material with v being the material velocity, the point of intersection x1 where the wavefront meets the surface, travels to x2 through a distance cp t where cp is the phase velocity. By trigonometry, cp = 1/p. (b) The schematic diagram for forward and inverse linear Radon or τ -p transform.

The records are summed along linear trajectories with different slowness slopes p and time intercepts τ . Stacking along p1 goes through strong signal peaks yielding a strong energy focus in the transformed panel (black ellipse) while stacking along p2 encounters amplitudes of opposite polarities leading to less Radon energy (dark gray ellipse). Stacking along p3 results in trivial Radon energy due to very weak amplitudes of the signals (light gray ellipse). (Reproduced with modifications from Tran et al., J Acoust Soc Am, 2014;136:248–259, https://doi.org/10. 1121/1.4881929, with the permission of the Acoustical Society of America)

mapping them onto the τ -p plane (Fig. 5.6b). Wavefields traveling at different phase velocities and intercepting the time axis at different zerooffset arrival time are well separated in the τ p panel. The mapping is reversible, i.e. the τ -p

signals can be mapped back to the t-x domain. The slant-stack transformation algorithm is posed as a frequency-domain inverse problem with a Cauchy-norm sparseness constraint to enhance the focusing power of the Radon operator.

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Considering a series of ultrasonic time signals d(t, xn ) at different offsets x1 , x2 , …, xN , the time signals can be written as a superposition of Radon coefficients: d(t, xn ) =

Z

m(τ = t − pz xn , pz ),

n = 1, ..., N

equation system, which can be solved by the iterative re-weighted least-squares (IRLS) method (Sacchi et al., 1997). A pseudocode implementation of HRRT is provided in Algorithm 1. Detailed mathematical derivation of the method can be referred to Tran et al. (2014a,b).

z=1

(5.7) where the slowness p is sampled at p1 , p2 , ..., pZ . Taking the temporal Fourier transform of Eq. (5.7) yields: D(f, xn ) =

Z

M(f, pz )e−i2πfpz xn

(5.8)

procedure radon(d,x,p,μ,σ ,n) D(f, x) = fft(d(t, x)) for f = fmin , ..., fmax do L = exp(−i2πf xT p) M0 (f, :) = (LH L + μI)−1 LH D(f, :) for g = 1, ..., n do Qg−1,zz =

z=1

which in matrix notation becomes D = LM where L = exp (−i2πfpz xn ) is the Radon inverse operator and LH is the adjoint Radon forward operator. The adjoint Radon operator has a poor resolving power therefore does not provide adequate focusing in the dispersion panel (Tran et al., 2014a). To improve the dispersion imaging resolution, a regularized Radon solution is often sought by optimizing the cost function J = LM − D 2 +μQ(M) (Tran et al., 2014a,b): M = (LH L + μQ(M))−1 LH D

(5.9)

where μ is trade-off parameter. Q(M) is a diagonal weighting matrix with elements: Qzz =

Algorithm 1 Implementation of high-resolution Radon transform

1 (1 + Mz2 /σ 2 )

(5.10)

where σ 2 is the scale factor of the Cauchy distribution and Mz is the slowness-spectral scalar at pz . When replacing Q(M) with the identity matrix I, the Radon panel is a damped leastsquares solution. In order to achieve reliable spectral analysis, attention should be given to tradeoff parameter μ determination which may significantly influence the computing results. A preferred method to determine the optimal value of the trade-off parameter is the L-curve (Engl & Grever, 1994). Equation (5.9) provides a highresolution Radon solution and is a non-linear

1 (1 + (Mg−1 (f, z))2 /σ 2 )

Mg (f, :) = (LH L + μQg−1 )−1 LH D(f, :) end for(g) end for(f ) Return M = Mn end procedure

From the f -p Radon solution, the f -cp dispersion map is subsequently obtained via the relation cp = 1/p and preferably, linear interpolation. A τ -p panel can also be created by inverse Fourier transform. Figure 5.7 summarizes a flow chart of the Radon method to transform bone ATU signals back and forth between domains for dispersion imaging and filtering. HRRT offers a powerful tool to enhance the resolution of phase velocity dispersion curves especially when the data acquisition aperture is limited and uneven station sampling occurs in clinical measurements. The improvement in imaging resolution renders more discriminating power to separate UGW modes and provides an opportunity to isolate the wavefields/guided modes more precisely for further analysis. Figures 5.8, 5.9, and 5.10 showcase example applications of HRRT for use with bone ATU data sets. Singular value decomposition (SVD) has also been applied to analyze the energetic late-arrival UGW signals (Sasso et al., 2008) and to extract the dispersion trajectories of ex-vivo (Minonzio et al., 2010; Moreau et al., 2014; Schnei-

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Fig. 5.7 A flowchart of the Radon method to transform bone ATU signals into differing domains for dispersion imaging and filtering

Fig. 5.8 Synthetic dispersive signals with random noises and its phase velocity imaging: (a) noisy signals with 10 dB SNR, (b) 2D Fourier panel, (c) adjoint Radon panel, (d) damped least-squares Radon panel, and (e) high-resolution Radon panel. The true dispersion, which

is plotted by the white dashed  curve, is calculated using cp (f ) = cmin + (cmax − cmin )/ 1 + (f/fc )4 with cmin = 1000 m/s, cmax = 2200 m/s, and the critical frequency fc = 120 kHz (Tran et al., 2014a)

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Fig. 5.9 Dispersion imaging of an ex-vivo cylindrical bone data set. (a) The high-resolution phase-velocity map. The theoretically computed dispersion curves of the 6 identified guided modes are plotted in white. The theo-

retical dispersion is derived from a water-filled cylinder with 4.4 mm cortical shell thickness and 12.5 mm inner diameter. (b) The 3D τ -p plot shows the energy ridges

Fig. 5.10 τ -p filtering analysis of a simulated ATU data: (a) non-dispersive fast-traveling signals, (b) dispersive slowly-traveling signals, (c) superposition of two wavefields with the addition of 0 dB Gaussian noise, (d) the τ p panel, (e) the reconstructed wavefield of fast signals, (f)

the reconstructed wavefield of slow signals, (g) difference between [a] and [e], and (h) difference between [b] and [f]. The vertical line at p = 4 × 10−4 s/m in (d) differentiates the two energy clusters used for waveform reconstruction

der et al., 2019a) and in-vivo (Schneider et al., 2019b) human radius data. Xu et al. (2016a,b) developed a sparse-SVD (SSVD) algorithm to image the dispersion curves of ultrasonic wave signals guided by long cortical bones. Similar to the high-resolution Radon transform, the SSVD

method uses penalty constraints to enforce the solution sparsity. The implementation of SSVD algorithm is briefed as follows (Xu et al., 2016a): (1) 2D-FT projects D(R, E, t), a 3D data matrix measured by a multi-emitter (E) and multi-

5 Signal Processing Techniques Applied to Axial Transmission Ultrasound

receiver (R) transducer, to W(k, E, f ) in f k domain. The next steps are iterated for each frequency fz ∈ {f1 , f2 , ..., fZ }. (2) SVD decomposition to compute the singular vectors and singular values: [U, S, V] = SVD[W(k, E, fz )]

(5.11)

(3) Modifying UR by removing the insignificant singular vectors and enhancing the weak modes by normalizing the highest singular values. (4) Sparse-SVD procedure initialization with least-squares solution:

107

H −1 −1 −1 H ˜ n+1 = [(U−1 U n ) Un + μt Q] (Un ) (5.17)

˜ n+1 (k, E, fz ) = U ˜ n+1 SVH W

(5.18)

(7.2) Updating the Toeplitz matrix Q using ˜ n+1 (k, E, fz ). the updated W (7.3) Computing the 1 -norm (Eq. (5.19)) or Cauchy norm (Eq. (5.20)) cost function: H 2 ˜ ˜ −1 W Jn+1 = U n+1 n+1 (k, E, fz ) − SV F + ⎛ ⎞ Nk NE 2 2 ˜ n+1 (i, j, fz ) | ⎠ ⎝σ + |W μ i=1

j =1

(5.19) the regularization parameter μt H −1 = μtrace[(U−1 R ) UR ]

(5.12)

˜0 the singular vector U −1 H H −1 −1 = [(U−1 R ) UR + μt I ] (UR )

(5.13) ˜ 0 (k, E, fz) the 2D Fourier transformed data W ˜ 0 SVH =U

(5.14)

(5) Computing the Nk × Nk Toeplitz matrix Q ˜ 0 (k, E, fz ) where Nk is the size of using W the wavenumber axis. (6) The initial cost function to be minimized: J0 = μ  W(k, E, fz ) 2F

˜ and W: ˜ Updating the estimated U H −1 μt = μtrace[(U−1 n ) Un ]

i=1

(5.20) where σ is the Cauchy distribution’s scale factor. (7.4) Calculating the relative iteration convergence difference:

J = 2 | Jn+1 − Jn | /(Jn+1 + Jn ) (5.21)

(5.15)

where  · 2F represents the Frobenius norm of the matrix. (7) Reweighting iteration for the sparse minimization: While n < nmax and J > ξ (with nmax being the maximal number of iterations and ξ being the threshold of the relatively convergence difference of the cost function), (7.1)

H 2 ˜ ˜ −1 W Jn+1 = U n+1 n+1 (k, E, fz ) − SV F + ⎛ ⎞ NE Nk ˜ n+1 (i, j, fz ) |2 |W j =1 ⎠ μ ln ⎝1 + σ2

(5.16)

(7.5) Continue to the next iteration until the tolerance ξ of J is reached. (8) Updating the estimated norm function ˜ whose maxima correspond to the U wavenumbers of the guided modes. An ex-vivo experiment confirmed the high wavenumber resolution of the SSVD method (Fig. 5.11). Comparisons on simulated and experimental signals showed that HRRT and SSVD are complementary to cover a broad inspected frequency band (Xu et al., 2016b).

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Fig. 5.11 Sparse SVD dispersion curve imaging of a multi-modal UGW signals measured in an ex-vivo human radius with 2.5 mm-thick cortex: (a) SVD, (b) sparse SVD with 1 norm, (c) sparse SVD with Cauchy norm,

and (d) wavenumber resolution comparison at 0.5 MHz (Reproduced from Xu et al., IEEE Trans Ultrason Ferroelectr Freq Control, 2016;63:1514–1524, https://doi.org/ 10.1109/TUFFC.2016.2592688, with the permission of IEEE)

HRRT is suitable to analyze UGW at low frequency range while SSVD is robust at the higher end of the spectrum. Depending on the particular application, one chooses the appropriate technique. The linear Radon transform was recently modified to track along the wavenumber dispersion curves (Xu et al., 2018) (Fig. 5.12). The transform is similar to Eq. (5.7), where the exponential argument (i2πfpxn ) is replaced by (i2πkxn ) and k = k(f, y) is a function of frequency and a specific parameter of interest y, for instance, thickness, stiffness coefficient, or density. Generally speaking, the mathematical formulation and the subsequent implementation with regularization and IRLS solver are similar to the linear HRRT. Further details of the dispersive Radon transform (DRT) algorithm can be learned from Xu et al. (2018). Figure 5.13 depicts the spectral analysis of ATU-UGW signals measured from an ex-vivo human radius with 2.5 mm-thick cortex. Com-

pared to the 2D-FT, the SSVD method achieves a higher-resolution extraction of the dispersive energy trajectories, e.g. the weak S1 and S2 modes can be successfully identified. The DRT method can further be applied as an efficient way for mode identification, mode separation, and waveguide evaluation. As shown in Fig. 5.13d–f, the signals of the three fundamental modes S0, A1, and S2 are projected into the DRT domain. The cortical thickness estimates can be obtained from the coordinates of the three modes’ energy maxima. In addition, the wavefield of each Lamb mode can be reconstructed from the corresponding DRT distributions using the inverse DRT operator (Xu et al., 2018).

5.3.2

Dispersion Inversion

The ultimate goal of quantitative bone ultrasonography is to extract the bone parameters such as cortical thickness and mechanical properties

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Fig. 5.12 The f -k tiling patterns of different transforms: (a) 2D-FT, (b) linear Radon transform, and (c)–(d) dispersive Radon transform using the dispersion curves of the fundamental Lamb S0 mode (c) and A1 mode (d) with y being the material thickness (0.2 < y < 4 mm). The DRT f -k atoms closely follow the dispersion trajectories.

The dispersive trajectory of a certain wave mode can be tracked and projected to an energy cluster in the DRT domain (Reproduced from Xu et al., J Acoust Soc Am, 2018;143:2729–2743, https://doi.org/10.1121/1.5036726, with the permission of the Acoustical Society of America)

from UGW signals. Cortical bone thickness and mechanics contribute to the mechanical competence and fragility of the whole bone. Cortical bone property estimation provides meaningful ultrasonically-analyzed information about the bone health status relevant to osteoporosis/osteopenia. Therefore, simultaneous measurement of site-specific cortical thickness and mechanical properties may improve the clinical estimation of fracture risk and facilitates effective management of osteoporosis. Multiparametric dispersion-based inversion of axiallytransmitted ultrasonic records for cortical bone

characterization has been advancing in the last few years. Foiret et al. (2014) reported the first work on the inversion-based estimation of several cortical bone properties from UGW measurements in bone-mimicking phantoms and ex-vivo human radius bone samples. The Matlab built-in gradient method was employed to recover bone thickness and elastic characteristics with a few percent error. The method was subsequently applied to invivo data measurements from the forearm of 14 healthy subjects (Vallet et al., 2016). An exhaustive search in the frequency-wavenumber model

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Fig. 5.13 Spectral analysis of a set of axially-transmitted ultrasonic signals measured from an ex-vivo human radius with 2.5 mm-thick cortical bone: (a) the array signals, (b) the f -k mapping by 2D Fourier transform, (c) the f -k imaging by sparse SVD, and (d)–(f) the dispersive Radon representations of S0, A1, and S2 Lamb modes with y being the material thickness (1.5 < y < 3 mm). The cortical

thickness is estimated by the maximum of the DRT modal energy distributions. The temporal waveform of each wave mode can be reconstructed from its corresponding DRT representation by the inverse DRT operator (Reproduced from Xu et al., J Acoust Soc Am, 2018;143:2729–2743, https://doi.org/10.1121/1.5036726, with the permission of the Acoustical Society of America)

space with a range of cortical thickness from 0.5 mm to 4 mm was presented. The cortical thickness estimates were validated by comparison with the site-matched values derived from high-resolution peripheral quantitative computer tomography. A significant correlation has been found between the inverted and reference values (r 2 = 0.7, p < 0.05, RMSE = 0.21 mm). Bochud et al. (2016, 2017) proposed a genetic algorithm (GA) and the application of the genetic algorithm-based inversion on in-vivo data sets. The objective function is defined as the occupancy rate of the Lamb wave modes (Bochud et al., 2016):

restricted to 

F (θ) =

Mmax Nie 1 N i=1 Nit (θ )

(θ min < θ < θ max ) (5.22)

Nie =

Niin 0

if Nie > 0.1 · N¯ e otherwise

(5.23)

where θ is the model parameter vector θ = [h S M]. h, S, and M are the cortical waveguide thickness, the stiffness ratios, and the Lamb mode pairing vector respectively. θ min and θ max are the lower and upper bounds of the model parameters. Nie and Nit (θ ) denote the number of experimental and theoretical f -k data of a mode i. Mmax is the maximal number of modeled Lamb modes, N is the total number of experimental data, and Niin is the number of inliers of a mode i. Equations (5.22) and (5.23) basically mean that the experimental data points can only form a dispersion trajectory if a sufficient proportion of them belong to a guided mode. An experimental dispersion point

5 Signal Processing Techniques Applied to Axial Transmission Ultrasound

is considered as an inlier of a Lamb mode i if its Euclidean distance d to that mode’s f -k curve satisfies the following condition:

111

Figure 5.14 outlines the underlying steps of GA bone optimization technique. First, an initial population of Np potential solutions is ran-

domly generated. Each solution is evaluated by computing its corresponding objective function. The stopping criterion of the GA scheme is then checked. If the maximal number of generations is reached, the best solution is output as the final inverted solution. If the stopping criterion is not satisfied, a child population will be created by stochastically modifying the parents from the previous generation using genetic operators, e.g. tournament, crossover, mutation, and elitism, to inject genetic diversity into the new population. With the new generation’s candidates, the algorithm restarts from recomputing the objective function. The procedure continues until the stopping criterion is met. A nonlinear inversion framework, which combined semi-analytical finite-element (SAFE) forward modeling and grid-search optimization method, was developed and applied in bone

Fig. 5.14 Schematic overview of the steps involved in the model-based inverse problem solution by genetic algorithms (Reproduced from Bochud et al., Phys Med

Biol, 2016;61:6953–6974, https://doi.org/10.1088/00319155/61/19/6953, with the permission of the IOP Publishing)

  d=

f − f (θ ) fmax

2

 +

k − k(θ ) kmax

2 ≤ d0 (5.24)

with the user-defined threshold d0 = 0.025 corresponding to the normalized wavenumber resolution (Minonzio et al., 2010). The optimal model parameters are determined by maximizing the modal occupancy rate using the genetic algorithm: θˆ = arg max F (θ ) (5.25) θ min 50 years of age admitted to a hospital for first hip fracture were measured by LD-100 to investigate their differences in bone structural parameters, including bone density, in a region other than the proximal femur (Horii et al., 2017). There were 63 cases of femoral neck fracture (mean age, 78.2 years) and 37 cases of trochanteric fracture (mean age, 85.9 years). Mean values of cancellous bone density and elasticity of the distal radius were significantly higher for femoral neck fractures. A ROC curve analysis was performed to examine the degree of effect of each parameter for femoral neck and trochanteric fracture cases. AUC were 0.72 for age, and 0.61, 0.65, and 0.65 for cortical bone thickness, cancellous bone density, and cancellous bone elasticity, respectively. LD-100 parameters indicated that trochanteric fracture cases were more fragile than femoral neck fracture cases, even at the distal radius. There might be systemic differences between them, in addition to localized factors at the proximal femur.

6.3.2.3 Cohort Study LD-100 was used in the Japan Multi-Institutional Collaborative Cohort Study (J-MICC Study) (Wakai et al., 2011) Kyoto field, and achieved several research findings. 230 men in their 50s and 60s were measured by LD-100 to assess whether the combination

K. Mizuno et al.

of serologically determined Helicobacter pylori infection and atrophic gastritis is available as a biomarker for bone conditions (Mizuno et al., 2015). As a result, both Helicobacter pylori infection and atrophic gastritis significantly increased the risk of low cancellous bone density. Compared with anti-Helicobacter pylori antibody (−) and atrophic gastritis (−) subjects, antiHelicobacter pylori antibody (+) and atrophic gastritis (+) subjects were a significant highrisk group for low cancellous bone density. A serological diagnosis of Helicobacter pylori infection and atrophic gastritis, which is utilized for risk assessment of gastric cancer, was suggested to be useful for risk assessment of osteoporosis. 221 men and women (mean age: 55.1 + 7.0 years) were measured by LD-100 to evaluate the association between sleep, sympathetic nervous system activity, and bone mass (Kuriyama et al., 2017). As a result, short sleep was associated with the decline in cortical bone thickness due to the promotion of bone resorption and sympathetic nervous system hyperactivity in the middle-aged group. Leptin (substance with activities to increase energy expenditure and suppress appetite) levels and cortical bone thickness were found to be closely related, suggesting that cortical bone mass may be regulated via interaction with the leptin-sympathetic nervous system.

6.3.2.4 Relationship with Lifestyle-Related Disease Cortical bone thickness, cancellous bone density and cancellous bone elasticity at the distal radius were assessed in type 2 diabetes mellitus patients (n = 173) with LD-100 to clarify the risk factor for vertebral fractures (Mishima et al., 2015). In multivariate logistic regression analysis, the cancellous bone elasticity was independently and significantly associated with vertebral fractures in patients with high chronic kidney disease. In contrast, only cortical thickness was independently and significantly associated with vertebral fractures in the patients with low chronic kidney disease. Cortical bone thickness might be more important for the analysis of bone fragility in type 2 diabetes mellitus with renal dysfunction.

6 Ultrasonic Assessment of Cancellous Bone Based on the Two-Wave Phenomenon

Patients with type 2 diabetes mellitus show high prevalence of sarcopenia (low muscle mass). Cortical bone thickness and cancellous bone density at the distal radius were assessed in type 2 diabetes mellitus female patients (n = 122) and non-diabetes mellitus female controls (n = 704) using LD-100 to clarify the association of handgrip strength with cortical porosis, a major risk for fracture of diabetes mellitus (Nakamura et al., 2018). Type 2 diabetes mellitus patients over 40 years old showed significantly lower handgrip strength and cortical bone thickness, but not cancellous bone density, compared to nontype 2 diabetes mellitus counterparts (Fig. 6.19). Multivariate analysis revealed handgrip strength as an independent factor positively associated with cortical bone thickness, but not cancellous bone density, in type 2 diabetes mellitus patients. Reduced muscle strength associated with diabetes mellitus might be a major factor for cortical porosis development in diabetes mellitus patients. Cortical bone thickness and cancellous bone density of 182 type 2 diabetes mellitus patients were determined at the distal radius using LD-100 to examine their relationship with plasma leptin (Kurajoh et al., 2019). Plasma leptin, but not body mass index, was inversely correlated with cortical bone thickness, while body mass index, but not plasma leptin, was positively correlated with cancellous bone density. In multivariable regression analysis, plasma leptin was inversely associated with cortical bone thickness, but not with cancellous bone density. Furthermore, plasma leptin level retained a significant association with cor-

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tical bone thickness after further adjustment for body mass index and body mass index plus waistto-hip ratio. Hyperleptinemia resulting from obesity might contribute to cortical porosis in patients with type 2 diabetes mellitus.

6.3.2.5 Athlete 22 male athletes (age, 24.2 ± 4.3 years), 19 male controls (age, 27.4 ± 4.8 years), 21 female athletes (age, 25.0 ± 2.8 years) and 31 female controls (age, 27.8 ± 4.4 years) were measured using LD-100 (Breban et al., 2010). The different sports encountered were ball collective sports (football, rugby, handball, basketball or volleyball), judo and weightlifting. A significantly higher ultrasonic attenuation, cortical and radius thicknesses were found in the athletes compared to the controls in both sexes. Distinguishing athletes from non-athletes was feasible using LD-100. 45 kendo practicing females (mean age: 49.4 years old) and 110 no-regular-exercise females (mean age: 48.8 years old) were measured with LD-100 (Matsui et al., 2017). Kendo practicing females had significantly higher cancellous bone density and cortical bone thickness than no-regular-exercise females. All Kendo practicing female were right handed, although the left cancellous bone density and cortical bone thickness were significantly higher than those of the right. Kendo practitioners primarily use a bamboo sword with the left hand. Therefore, in Kendo, the left radius may have a high-impact loading compared with the right

Fig. 6.19 Age-stratified handgrip strength (a) and cortical bone thickness (b) and cancellous bone density (c). (Modified from (Nakamura et al., 2018))

138

Fig. 6.20 Measurement on high school students

radius. LD-100 has the potential to evaluate the effectiveness of training.

6.3.2.6 Young People The acquisition of high bone density at a young age is a strategy to prevent fractures and falls later in life. 1314 students (678 boys and 636 girls) between 12 and 18 years old in Japan were measured with LD-100 to investigate the increase in cortical bone thickness and cancellous bone density of young people (Fig. 6.20) (Ozaki et al., 2020). LD-100 was utilized safely as there was no exposure to radiation. Based on the results, cortical bone thickness in both sexes increased with age, but cancellous bone density increased only until the age of 17 years for boys and until the age of 15 years for girls (Figs. 6.21 and 6.22). Age, body mass index, exercise and body fat percentage were independent factors for the cortical bone thickness, while age, body mass index and body fat percentage were independent factors for the cancellous bone density. These results of this study may contribute to the acquisition of high bone density for children and adolescents. 6.3.2.7 Future Work Elasticity is a mechanical parameter related to mechanical strength which can be measured nondestructively and non-invasively. Presently, cancellous bone elasticity in vivo can be obtained only with LD-100. This parameter may be uti-

K. Mizuno et al.

lized to evaluate “bone quality” which is related to bone strength along with bone density. Additionally, LD-100 also provides estimates of cortical thickness which is directly related to bone strength. Therefore, LD-100 is expected to be used for clinical studies on some medications that are considered to cause deterioration of bone quality and thinning of cortical bone thickness separately. Since, radius is a non-load-bearing bone, it is possible to assess the skeletal status while neglecting the difference in weight or load-bearing. Also, the radius is easier to measure than the calcaneus because it does not require someone to take off his or her socks. Moreover, ultrasonic method can be used safely and repeatedly, therefore LD-100 can be operated for follow-up on bone growth progress of children, bone change of pregnant female or bone deterioration of longdistance female runners with three interrelated components (low energy availability, menstrual dysfunction, and low bone density). It may contribute to reduce the number of future osteoporosis patients.

6.4

Conclusion

In this chapter, the methods to derive useful information of cancellous bone by the two-wave phenomenon-based ultrasonic assessment was introduced. Cancellous bone has complex structure and several methods have been developed in order to derive valuable information from the received ultrasonic waveform. Experimental measurements allowed investigating the precise behavior of the fast wave and slow wave and determining their properties, including their amplitude, speed, and frequency characteristics. In addition, theoretical studies including Biot’s theory and other advanced mathematical techniques for the separation of fast and slow waves also support the understanding of the two-wave phenomenon. Numerical techniques directly provided many benefits for investigating wave propagation in cancellous bone. By using computer simulation techniques, the physical parameters, the geometry of the specimen and

6 Ultrasonic Assessment of Cancellous Bone Based on the Two-Wave Phenomenon

139

Fig. 6.21 Cortical bone thickness (mm) and cancellous bone density (mg/cm3 ) by age (boys). (Modified from (Ozaki et al., 2020))

Fig. 6.22 Cortical bone thickness (mm) and cancellous bone density (mg/cm3 ) by age (girls). (Modified from (Ozaki et al., 2020))

the measuring conditions can be easily controlled so that various conditions needed for designing clinical devices can be efficiently explored. Going forward, the evolving computational speed and capacity will enable us to solve challenging problems currently waiting to be undertaken. Finally, the results of the clinical assessment using a device based on the twowave phenomenon was introduced in this chapter. Assessing the bone growth processes in young people shown in this chapter is suggestive for future direction of the bone ultrasound studies.

Conflict of Interest Yoshiki Nagatani is an employee of Pixie Dust Technologies, Inc. Isao Mano is an employee of OYO Electric Co., Ltd.

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142 Mizuno, K., Nagatani, Y., Yamashita, K., et al. (2011a). Propagation of two longitudinal waves in a cancellous bone with the closed pore boundary. The Journal of the Acoustical Society of America, 130(2), EL122–EL127. Mizuno, K., Somiya, H., Kubo, T., et al. (2010). Influence of cancellous bone microstructure on two ultrasonic wave propagations in bovine femur: An in vitro study. The Journal of the Acoustical Society of America, 128(5), 3181–3189. Mizuno, K., Yamashita, K., Nagatani, Y., et al. (2011b). Effect of boundary condition on the two-wave propagation in cancellous bone. Japanese Journal of Applied Physics, 50(7S), 07HF19. Mizuno, S., Matsui, D., Watanabe, I., et al. (2015). Serologically determined gastric mucosal condition is a predictive factor for osteoporosis in Japanese men. Digestive Diseases and Sciences, 60(7), 2063–2069. Mézière, F., Juskova, P., Woittequand, J., et al. (2016). Experimental observation of ultrasound fast and slow waves through three-dimensional printed trabecular bone phantoms. The Journal of the Acoustical Society of America, 139(2), EL13–EL18. Mézière, F., Muller, M., Dobigny, B., et al. (2013). Simulations of ultrasound propagation in random arrangements of elliptic scatterers: Occurrence of two longitudinal waves. The Journal of the Acoustical Society of America, 133(2), 643–652. Nagatani, Y., Guipieri, S., Nguyen, V. H., et al. (2017). Three-dimensional simulation of quantitative ultrasound in cancellous bone using the echographic response of a metallic pin. Ultrasonic Imaging, 39(5), 295–312. Nagatani, Y., Imaizumi, H., Fukuda, T., et al. (2006). Applicability of finite-difference time-domain method to simulation of wave propagation in cancellous bone. Japanese Journal of Applied Physics, 45(9R), 7186. Nagatani, Y., Mizuno, K., & Matsukawa, M. (2014). Twowave behavior under various conditions of transition area from cancellous bone to cortical bone. Ultrasonics, 54(5), 1245–1250. Nagatani, Y., Mizuno, K., Saeki, T., et al. (2008). Numerical and experimental study on the wave attenuation in bone–FDTD simulation of ultrasound propagation in cancellous bone. Ultrasonics, 48(6–7), 607–612. Nagatani, Y., Nguyen, V., Naili, S., et al. (2015). The effect of viscoelastic absorption on the fast and slow wave modes in cancellous bone. In 2015 6th European Symposium on Ultrasonic Characterization of Bone, pp. 1–2. Nagatani, Y., Okumura, S., & Wu, S. (2018). Neural network based bone density estimation from the ultrasound waveforms inside cancellous bone derived by FDTD simulations. IEEE International Ultrasonics Symposium (IUS), 2018, 1–4. Nagatani, Y., Okumura, S., Wu, S., et al. (2020). Two-dimensional ultrasound imaging technique based on neural network using acoustic simulation. arXiv preprint arXiv 2004, 08775. Nagatani, Y., & Tachibana, R. O. (2014). Multichannel instantaneous frequency analysis of ultrasound propa-

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7

Pulse-Echo Measurements of Bone Tissues. Techniques and Clinical Results at the Spine and Femur Delia Ciardo, Paola Pisani, Francesco Conversano, and Sergio Casciaro

Abstract

The aim of this chapter is to review the available pulse-echo approaches for the quantitative evaluation of bone health status, with a specific application to the assessment of possible osteoporosis presence and to the fracture risk prediction. Along with a review of the main in-vivo imaging approaches for skeletal robustness evaluation and fracture risk assessment, further understanding into Radiofrequency Echographic Multi Spectrometry (REMS), an ultrasound-based method measuring clinically relevant bone districts (i.e. lumbar vertebrae and proximal femur), is provided, and the further potentialities of this technology are discussed. Currently, the bone mineral density (BMD) provided by dual X-ray absorptiometry (DXA) is considered an established indicator for osteoporosis status assessment and fracture risk prediction, however, in order to obtain

more accurate results, an additional step beyond BMD would be necessary, which means including data on bone quality for an improved evaluation of the disease and its consequences. REMS is a technology which allows both osteoporosis diagnosis, through the BMD estimation, and the prediction of fracture risk, through the computation of the Fragility Score; both measures are obtained by the automatic processing of unfiltered ultrasound signals acquired in correspondence of anatomical reference sites. Keywords

Osteoporosis diagnosis · Fracture risk assessment · Radiofrequency Echographic Multi Spectrometry (REMS) · Femoral neck · Lumbar spine

7.1

Novel Approaches for Echographic Evaluation of Osteoporosis on Proximal Hip and Lumbar Spine

7.1.1

Introduction

D. Ciardo National Research Council of Italy – Institute of Clinical Physiology, Lecce, Italy Echolight S.p.A. – R&D Department, Lecce, Italy e-mail: [email protected] P. Pisani · F. Conversano · S. Casciaro () National Research Council of Italy - Institute of Clinical Physiology, Lecce, Italy e-mail: [email protected]; [email protected]; [email protected]

Osteoporosis is a highly prevalent skeletal disease that appears as a decrease of bone mineral density

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 P. Laugier, Q. Grimal (eds.), Bone Quantitative Ultrasound, Advances in Experimental Medicine and Biology 1364, https://doi.org/10.1007/978-3-030-91979-5_7

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(BMD) and a degradation of the bone inner microarchitecture, implying a higher bone fragility and to an augmented fracture risk (Bernabei et al., 2014), with significant societal and medical costs. In 2010, 3.5 million new osteoporotic fractures were estimated in the European Union (Hernlund et al., 2013), resulting in a total cost of about A C40 billion for the National Healthcare Systems (Kanis et al., 2012); because of population aging, this figure may double by 2040 (Odén et al., 2015). Spine and femoral fractures are not only the most frequent and onerous osteoporotic fractures, but also they typically cause an important reduction in the patients’ quality of life because of important morbidity and mortality rates (Albanese et al., 2011; Ensrud et al., 2000; Cooper, 1997; Johnell & Kanis, 2006). In Europe, in 2010, 43.000 died for the consequences of a fragility fracture, with about 80% of the cases being represented by hip or vertebral fractures (Hernlund et al., 2013). According to recent global estimates, 200 million of women suffer from osteoporosis (Pisani et al., 2013; Kanis et al., 2007), with almost 40% of them being located in Europe, USA and Japan (WHO, 1994). Unfortunately, approximately 75% of these cases are undiagnosed due to of the absence of accurate diagnostic tools (Pisani et al., 2013). Moreover, the foreseen increment of osteoporosis prevalence worldwide further emphasizes the substantial lack of effectiveness of the methods currently used for diagnosing and managing the disease in clinical practice. In this context, innovative tools for more reliable diagnosis of osteoporosis and more accurate identification of frail patients are needed, promoting public health measures and reducing the consequences of the disease in every aspect. The World Health Organization (WHO) has defined osteoporosis as a decrease in lumbar or femoral BMD of 2.5 standard deviations (SDs) or more with respect to the mean of a reference population represented by young adults (Kanis et al., 1994; Genant et al., 1999). Currently, dualenergy X-ray absorptiometry (DXA) is referred to as the reference method for BMD assessment

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and osteoporosis diagnosis at the aforementioned skeletal sites (Baim & Leslie, 2012; Link, 2012; Schnitzer et al., 2012). Nonetheless, important intrinsic limitations have been identified for DXA technology, which hinder its employment for screening purposes (Casciaro et al., 2015). Furthermore, BMD estimates demonstrated a limited sensitivity as a means of identifying patients subject to osteoporotic fractures, with several fractures actually occurring in patients whose DXAmeasured BMD is in the range of osteopenia (WHO, 1994; Kanis et al., 2001; Wainwright et al., 2005; Adami et al., 2020), resulting the fact that osteoporosis is significantly underdiagnosed and undertreated (Curtis & Safford, 2012; van den Bergh et al., 2012). It is acknowledged that mechanical properties of bones derive from the combination of BMD and several structure quality factors (e.g., elastic properties, trabecular organization, etc.) not captured by standard DXA testing (Raum et al., 2014; Diez-Perez et al., 2019). One way to fill in this gap is represented by the implementation of fracture risk assessment tools, like FRAX® , Garvan, QFracture and many others (Marques et al., 2015), which provide the 10-year likelihood of fragility fractures using specific risk factors assessed through dedicated questionnaires, possibly integrated with femoral BMD and/or the Trabecular Bone Score (TBS), which is an additional parameter obtained from a dedicated grey scale analysis on spinal DXA images providing complementary information to conventional BMD (Martineau & Leslie, 2018). In the last years, other research efforts focused on the research and employment of quantitative ultrasound (QUS) methods for probing bone conditions (Schnitzer et al., 2012; Bréban et al., 2010; Nayak et al., 2006; Paggiosi et al., 2012; Pais et al., 2010; Trimpou et al., 2010) as, in principle, ultrasound (US) waves are naturally suitable for the assessment of the mechanical properties of human tissues, and US devices are typically associated with several advantages

7 Pulse-Echo Measurements of Bone Tissues. Techniques and Clinical Results at the Spine and Femur

(such as absence of radiation, low cost, small device size, wide accessibility) not applicable to DXA (Raum et al., 2014; Diez-Perez et al., 2019). As detailed in Chap. 2 of this book, QUS devices currently in the market can be used on appendicular sites only (e.g., wrist, tibia, phalanges, etc.) and are not applicable on central anatomical sites; several scientific studies investigating QUS performance with respect to DXA obtained contradictory results (Schnitzer et al., 2012; Bréban et al., 2010; Trimpou et al., 2010; Dane et al., 2008; El Maghraoui et al., 2009; Iida et al., 2010; Kwok et al., 2012; Liu et al., 2012; Moayyeri et al., 2012; Stewart et al., 2006). Consequently, QUS approaches may be considered valuable as a screening method, but clinical and therapeutic decisions still require a further DXA verification on central sites (Iida et al., 2010; Liu et al., 2012). In order to improve this situation, innovative US approaches directly applicable to femur and/or spine have been investigated (Barkmann et al., 2010; Karjalainen et al., 2012; Conversano et al.,

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2015). A schematic overview of the applicability of existing bone health assessment methods is pictured in Fig. 7.1.

7.1.2

Novel Radiofrequency Echographic Multi Spectrometry (REMS) Approach for Hip and Spine

Existing US methods for assessing peripheral skeletal sites are covered in Chaps. 2 and 3 of this book. A new US-based methodology, named Radiofrequency Echographic Multi Spectrometry (REMS) and capable of direct investigations on lumbar vertebrae and femoral neck, has been recently introduced (Conversano et al., 2015; Casciaro et al., 2016) and clinically validated (Di Paola et al., 2019; Adami et al., 2020; Cortet et al., 2021). The key concept behind REMS technique is that “raw” ultrasound signals, the so-called radiofrequency (RF) signals, contain useful infor-

Fig. 7.1 Applicability of existing methods for bone health evaluation

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Fig. 7.2 Employment of the described method to lumbar vertebrae and femoral neck: (a) echographic scan; (b) Spinal (top; lumbar vertebrae indicated by arrows) and

femoral (bottom, femoral profile indicated by arrows) image frames; (c) illustration of an ROI for the subsequent analysis of the RF signal

mation for characterizing the status of the considered bone, and this characterization can be quantified through advanced comparisons of spectral features obtained from raw US signals acquired from the patient with reference spectral models previously derived with the aim of characterizing the diseased or healthy conditions. Such an approach is combined with conventional echography: image frames are automatically processed by a segmentation algorithm which identifies the region of interest (ROI) within the investigated bone, to which diagnostic calculations are applied. Many RF signals, associated to the vertical lines of a given echographic image, are simultaneously acquired, providing the basis needed for the following statistical calculations in the frequency domain. While, in theory, the described methodology could be used for all the skeletal regions, the employment on lumbar vertebrae and femoral neck of the proposed methodology are pictured in Fig. 7.2. In order to quantitatively define the bone conditions for “osteoporosis” and “frailty” (i.e., “decreased BMD” and “predisposition to fracture”, respectively), two new, original indicators were proposed: the Osteoporosis Score (OS), measuring the analogies of the measured spectral characteristics with reference models derived from subjects having a low BMD, and the Fragility Score (FS), which similarly measures the analogies between the current patient spectra and those obtained from subjects who reported a recent fragility fracture.

Deeper insights into REMS are provided in Sect. 7.2 of this chapter. Section 7.3 presents the most recent clinical results obtained with REMS.

7.2

Insights into REMS Technology

7.2.1

Overview

REMS is an ultrasound-based approach for diagnosing osteoporosis at the reference anatomical sites. The underlying theory involves spectral measurements on the raw backscattered US pulses obtained from a dedicated ultrasound investigation of lumbar column and/or proximal femur. Through the subsequent signal processing, all the information related to the features of the insonified anatomical targets is retained, differently from what normally happens with ultrasound signal processing aimed at providing traditional echographic frames. The bone condition is evaluated by comparing acquired spectra with the corresponding models for the pathology under investigation, one for the diseased status and the other for the healthy one (Conversano et al., 2015; Casciaro et al., 2016). The acquired signals provide information on either bone quantity and bone quality. Results are therefore exploitable for bone fragility characterization and for predicting the likelihood of fractures. In practice, during a REMS scan, the transducer is positioned

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Fig. 7.3 REMS scan on femoral neck. The bone interface and the ROI are detected by the software

Fig. 7.4 REMS data (panel A) are processed in the frequency domain (sample spectra shown in panel B) and compared with spectral models of pathological and healthy conditions (panel C, shown in red and green, respectively)

trans-abdominally or on the patient hip, aiming to insonify the sought bone target. The clinician sets image depth and focus; then, the algorithm automatically identifies the target interfaces in the series of images and detects the ROIs for the subsequent calculations (Fig. 7.3). Through the spectral processing of each US signal, those associated to artifacts (e.g., osteophytes) are automatically excluded, because of the presence of “anomalous” characteristics in the frequency domain. The obtained spectrum related to the bone target under investigation is finally obtained from the selected data and is subsequently compared with anthropometrically-matched models stored into the pre-defined database of pathological or non-pathological bones (Fig. 7.4). In turn, this leads to a BMD quantification and a corresponding diagnostic cataloging. Firstly, the Osteoporosis Score (OS) is calculated, that is, the portion

of patient spectra cataloged as “osteoporotic” as a consequence of the spectral analyses (Conversano et al., 2015; Casciaro et al., 2016). Secondly, a BMD value is obtained from linear equations applied to the OS. Furthermore, additional parameters suitable for probing bone strength and related to bone quality can be obtained using the REMS approach. FS has been designed with the goal of providing an BMD-independent estimation of fracture risk. FS is a dimensionless indicator ranging from 0 to 100, derived from the comparison of the patient spectrum with reference models obtained from fractured and non-fractured patients. Preliminary validation studies have demonstrated not only the good performance of FS in detecting frail patients, but also its significant correlation with the probability of fracture calculated by FRAX® when femoral

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neck BMD is used as a FRAX® input (Caffarelli et al., 2018; Greco et al., 2017; Pisani et al., 2017).

7.2.1.1 Osteoporosis Score While OS and its application to lumbar spine is detailed in Conversano et al., 2015, the fundamentals of the adopted framework together with the most relevant results are briefly summarized herein and detailed in paragraph 7.2.2. Data were obtained with both technologies, DXA and REMS, from the lumbar spine of the enrolled patients, who were first subdivided in 5-year age range groups and, for each group, further divided between the reference database (for spectral model implementation) and the study population (for performance tests). US data belonging to the first group (database) were employed for the calculation of spectral models for “osteoporosis” and “non-osteoporosis”. After model calculation, data associated to the remaining patients underwent the processing procedures described in (Conversano et al., 2015). The statistical analysis showed a significant association between OS and DXA diagnostic classification (Conversano et al., 2015). BMD values obtained by REMS OS were strongly correlated with estimates obtained by DXA (r = 0.84, p < 0.001) and the diagnostic agreement between REMS and DXA was 91.1% (Cohen’s k = 0.859, p < 0.0001) (Conversano et al., 2015). The same methodology was applied on femoral neck in a different study (Chiriacò et al., 2014), which reported a diagnostic agreement of 81.3%, regardless of patient age or BMI. Important correlations were found between REMS-derived and DXA-based BMD (r up to 0.80, p < 0.01) proving the feasibility of the approach also on proximal femur (even on obese patients) and leading to refinements of the segmentation step of the algorithm for femoral application, which then helped reaching a diagnostic performance comparable to the spinal application (Casciaro et al., 2016). Given the complete absence of ionizing radiations, REMS approach might have a potential in reducing the burden of osteoporosis through early

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diagnosis in the young adults at the primary level of healthcare (Bernabei et al., 2014): indeed, an early identification of osteopenia can provide the motivation to undertake simple modifications of lifestyle and daily habits which, in turn, can slow or even stop the expected disease evolution.

7.2.1.2 Fragility Score As the clinical approach to osteoporosis began to evolve about 20 years ago, awareness arose about the fact that most of fragility fractures actually occurs in subjects with normal or osteopenic BMD (Kanis et al., 2001) and the scientific community gradually moved away his attention from a patient classification based on BMD thresholds (Kanis et al., 2002): in other words, the importance of indicators characterizing skeletal strength and quality independently of its density was progressively recognized. This provided an additional boost to the diffusion of QUS-based approaches, aiming at providing a more direct estimation of bone quality (El Maghraoui et al., 2009; Kwok et al., 2012; Liu et al., 2012; Barkmann et al., 2010; Karjalainen et al., 2012; Hartl et al., 2002). In this context, a first implementation of FS has been unveiled (Pisani et al., 2014; Greco et al., 2014); the indicator was designed to be derived from spinal scans and it was thought to quantify the general skeletal fragility. The preliminary validation of FS in a clinical setting demonstrated its ability in the identification of “frail” subjects and included 84 white women (40 with a previous osteoporotic fracture and 44 without any fracture) (Pisani et al., 2014). The results of this study documenting FS was able to significantly discriminate fractured patients from the controls, FS being lower in the latters; furthermore, FS was inversely correlated with DXA BMD values. ROC curves showed that FS and BMD had a similar discrimination ability, since the area under the curve (AUC) was the same (AUC = 0.77). Another work (Greco et al., 2014) studied the relationship between FS and FRAX® outcomes, when the latters included DXA-measured femoral neck BMD as an input, and concluded that FS values measured on spine were signifi-

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cantly correlated with FRAX® outputs (r up to 0.75, p < 0.001). These preliminary evaluations showed interesting features for FS, such as a discrimination ability very close to that of lumbar spine DXA BMD in the detection of subjects with past fragility fractures and a linear correlation with FRAX® output probabilities. Also considering the safety of US-derived FS, its introduction in clinical routine might be of help in timely recognizing people having an augmented predisposition to fragility fractures. Literature-available methodology descriptions and validation studies of OS and FS are detailed in 7.2.2. and 7.2.3, respectively.

7.2.2

Osteoporosis Score Calculation

Fundamentals of the method (construction of reference database, derivation of spectral models, reproducibility and performance evaluation in comparison with DXA) and main results related to the application of OS are briefly summarized herein. The following section thoroughly illustrates the related methodology applied to lumbar spine (paragraphs “Overview of the methodology”, “Construction of the reference database”, “Selection of Reference models”).

7.2.2.1 Overview of the Methodology The approach presented in Conversano et al., 2015 for lumbar vertebrae (below reported in detail), and similarly in Casciaro et al., 2016 for femoral neck, is based on an automatic identification of the bone interfaces and ROIs on US Bmode images followed by statistical comparisons between signal spectra backscattered from target bones and the models obtained, in a previous step, from age-, gender-, BMI-, and site-matched “osteoporotic” and “healthy” patients as detailed later. The analysis is composed by the following points: 1. Detection of vertebral bodies in the series of B-mode frames; 2. For each detected bone target and for each US scan line, automatic detection of the RF signal portion crossing the vertebral edge;

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3. Classification of the vertebral ROI volume as “osteoporotic” or “healthy” according to the grade of correlation between ROI spectral features and a matched couple of reference models (one “osteoporotic” and one “healthy” spectral model); 4. For each vertebral body, calculation of the OS value according to the portion of the target region that was classified as “osteoporotic” in point 3. (see also “Automatic Identification of Vertebrae and Calculation of Osteoporosis Score”); 5. Average of the values calculated for each single vertebra providing the final OS. The construction of the reference database as well as the selection of spectral models for “healthy” and “osteoporotic” patients has been described elsewhere; the interested reader is referred to Conversano et al. (2015) and references therein, where more detail about the segmentation algorithm can be found.

7.2.3

Fragility Score Calculation

The employed algorithm is similar to that described in Conversano et al., 2015, aimed at using an analogous method to obtain a different indicator (the OS, which was importantly related to the BMD provided by DXA) (Conversano et al., 2015). In this specific case, the goal was to quantify the amount of target bone regions having spectral characteristics with a correlation higher with a “frail” model rather than with a “non-frail” model.

7.2.3.1 Overview of the Adopted Method The adopted automatic algorithm processes RF signal portions associated to automatically identified ROIs within the vertebrae: similarly to the description of the OS calculation, for each RF signal crossing the target bone interface, the maximum of the signal envelope was detected and assumed as indicative of the echo of the target bone interface; the first subsequent point with amplitude less than 15% of the maximum was taken

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as the begin of a 200-point Hamming-windowed signal portion. This signal segment was zeropadded to 4096 points before FFT calculation and the obtained spectrum was employed for FS calculation. The algorithm compared the spectra obtained from the subject under investigation with spectral models of “frail” and “non-frail” vertebral targets previously derived from US scans on subjects who sustained a recent osteoporotic fracture (hence identified as patients whose bone structure is “frail”) and controls (catalogued as “nonfrail”).

7.2.3.2 Construction of the Reference Database The reference model database had been built analogously to what is described in Conversano et al., 2015, where the models to be calculated were the “osteoporotic” one and the “healthy” one. In this case, each model was obtained from an independent group of 50 patient datasets. Patients were included into the database by adopting the same of enrollment criteria of the study, which were integrated by the following further criterion: the recent occurrence of an osteoporotic fracture (for “frail” model derivation) or the lifetime absence of fracture history (for “non-frail” model derivation). The database size (100 subjects per age group, 50 “frail” and 50 “non-frail”) was determined by following well-consolidated methods (Hou et al., 2008; Engelke & Glüer, 2006), opportunely adapted to our specific case. Thus, the approach to derive a couple of spectral models for frail and non-frail patients followed the one used to derive osteoporotic and healthy spectral models referred to a generic 5-y age range. In particular, each RF segment was classified as “frail” or “non-frail” following the correlation degree between the corresponding spectrum and each age-matched model previously stored in a reference database: each RF segment was cataloged as “frail” if the Pearson coefficient between its spectrum and the opportune “frail” model was higher than the corresponding value with the related “non-frail” model, otherwise it was cataloged as “non-frail”. Then, the FS value of a given vertebra is calculated as the portion of the processed signal

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segments that were cataloged as “frail” and, for each considered patient, the FS is provided as the mean of the single vertebra FS values.

7.2.3.3 Calculation of the Fragility Score For a generic patient dataset considered, after the identification of the two anthropometricallymatched spectral models, the algorithm segmented the target bone surfaces within the series of acquired frames, just as described in our previous paper (Conversano et al., 2015). After the segmentation step, the algorithm proceeded to process the RF segments associated to the ROIs that had been automatically identified below the detected bone surfaces. The spectrum of each considered RF segment belonging to the ROIs was labeled as “frail” or “non-frail” based on its Pearson coefficient with each of the matched models (frail and non-frail). Then, the FS for the entire vertebral body was obtained as the percentage ratio of the spectra labeled as “frail” out of the spectra of the corresponding segmented ROI. The FS for the examined patient is then calculated averaging the FS values obtained for each vertebra.

7.3

Clinical Studies

7.3.1

Comparison Between REMS and DXA for Osteoporosis Diagnosis

The study published by Di Paola et al. (2019) was a multicenter transversal study on data obtained from adult women, aiming to assess variability (both intra- and inter-operator) and diagnostic performance of REMS with respect to DXA. In this work, 1914 Caucasian women (aged 51–70 y) were scanned with DXA at lumbar vertebrae (n = 1553) and/or proximal femur (n = 1637), and all of them underwent also REMS scans of the same skeletal sites. All the diagnostic measurements were verified by experts in order to identify possible inaccuracies: for DXA scans, potential pitfalls were detected in accordance

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with the ISCD guidelines (Shepherd et al., 2015); REMS mistakes, instead, were detected as inaccurate scan procedures with respect to manufacturer indications. In the lumbar group, the mentioned quality check resulted in the exclusion of 280 patients whose medical reports included REMS scan inaccuracies and 78 patients whose reports were affected by DXA errors, while further 296 DXA reports with recoverable errors were corrected and re-evaluated. For the femoral group, instead, the quality check resulted in 205 exclusions because of REMS inaccuracies, 59 exclusions because of DXA problems, and 217 erroneous and re-analysed DXA scans. The final dataset (n = 1195 for lumbar vertebrae, n = 1373 for femoral neck) has been used for the actual comparison. REMS results were in good agreement with DXA ones: the mean BMD difference (bias ±2SD) was −0.004 ± 0.088 g/cm2 for lumbar vertebrae and − 0.006 ± 0.076 g/cm2 for femoral neck. Regression analysis also demonstrated the significant correlation between the two technologies: for lumbar spine, slope = 0.95 and r = 0.94 (p-value 0.9) with absolute difference smaller than 3◦ for intra- and inter-operator measurements. Furthermore the ultrasound results obtained from both methods showed significant and excellent correlations and good agreement with X-ray Cobb angle.

16.2.3 Design and Procedures Adopted for the Production Version of Scolioscan Before conducting more follow-up and larger scale studies using the customized 3D ultrasound

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system, the interfaces of the hardware and software were improved with industrial and ergonomic designs and examination procedures were standardized for the production version of the Scolioscan system (Fig. 16.7). Once the scanning procedure was completed, the 3D ultrasound volume would undergo VPI formation to generate 9 different coronal image layers for curvature measurement which corresponds to different depth of the ultrasound volume as mentioned in previous sub-chapter. Overall, the scanning procedure would consume around 30 s and the VPI formation would take no more than 2 min. The total time for assessing the patient took around 10 min in average. Further specification of the instrumentation and experimental procedures were described in previous studies (Zheng et al., 2016; Lee et al., 2019a).

16.3

Related Studies Based on the Production Version of Scolioscan

16.3.1 Evaluation of Coronal Curvature of Spine on AIS Subjects A comprehensive study design was applied in the first study of this system to evaluate the reliability and validity of the 3D ultrasound system (Zheng et al., 2016). Patients with Cobb less than 50◦ , received X-ray assessment within three months, without metallic implants and BMI lower than 25.0 kg/m2 were recruited. Spinous process angle was the parameter used to represent coronal angles of the 3D ultrasound system. To investigate the reliability of the ultrasound angle, intraand inter-operator reliabilities of the ultrasound angles acquired from 20 patients with AIS (Age: 16.4 ± 2.7 years, 4 M and 16F) in terms of scanning and measurement were investigated. These patients received ultrasound scans twice by two operators. The most optimal coronal images selected from each of these scans were then measured by three raters manually and independently twice, hence total 24 sets of results were obtained for each subject. To validate the ultrasound results, correlation between ultrasound angles and radiographic Cobb acquired from total 49 patients

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Fig. 16.5 The diagram illustrates (a) planar and (b) nonplanar volume rendering technique using skin surface as reference for coronal ultrasound imaging; (c) The non-

planar layer with the most optimal depth was selected and (d) projected into a 2D plane after image enhancement

Fig. 16.6 The diagram illustrates the method of using (a) spinous processes shadow; and (b) transverse processes as landmarks for spinal curvature measurement. For the

latter method, coronal layers of different depths were used in early stage research for the visualization of transverse processes in different vertebrae region

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Fig. 16.7 The diagram showing the production version of scolioscan. (Image was acquired from the article: Zheng et al., 2016 (Fig. 1) in the reference list)

with AIS (Age: 15.8 ± 2.7 years, 15 M and 34F, Cobb angle: 27.6◦ ± 11.8◦ ) were investigated. Excellent intra-rater and intra-operator reliabilities (ICC ≥ 0.88) and excellent interrater and inter-operator reliabilities (ICC ≥ 0.87) were demonstrated. The RMS differences of the results within and between raters were clinically insignificant, i.e. less than 5◦ . In addition, moderate to strong correlations (R2 > 0.7) were demonstrated between the ultrasound and Cobb angles for both thoracic and lumbar regions (Fig. 16.8a, b). Furthermore, the RMS between Cobb and the corrected ultrasound angles, based on the regression equation was 4.7◦ . The findings of this study showed that ultrasound coronal angles provided by the 3D ultrasound system appeared to be promising for mass screening, curvature evaluation and monitoring for patients with AIS.

Although spinous processes and transverse processes were demonstrated to be reliable landmarks (Cheung et al., 2015b), no study was performed to investigate the appropriateness of both methods for evaluating spinal coronal deformity. Brink et al. thus conducted a study to investigate the reliability and validity of three different ultrasound angle measurements by recruiting 33 patients with AIS (Age: 13.8 ± 2.3 years, 3 M and 30F, Cobb range: 3◦ –90◦ ) who had underwent X-ray scan of the spine (Brink et al., 2018). The three ultrasound measurements, which were automatic spinous process angle (see details in Sect. 16.3.7) (Fig. 16.9a), manual spinous process angle (Fig. 16.9b) and manual transverse process angle (Fig. 16.9c), were compared with conventional radiographic Cobb (Fig. 16.9d). Two operators

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Fig. 16.8 The diagram illustrates the linear equation and correlation between (a) thoracic and (b) lumbar radiographic Cobb angles and ultrasound spinous process an-

gles respectively. (Images were acquired from the article: Zheng et al., 2016 (Figs. 7 and 8 respectively) in the reference list)

Fig. 16.9 The diagram illustrates the coronal measurements in terms of (a) automatic ultrasound spinous process angle; (b) manual ultrasound spinous process angle; (c) manual ultrasound transverse process angle; and (d) radiographic Cobb angle. Similar to spinous process angle,

transverse process angle was calculated between the two most tilted transverse process lines (red lines), where transverse process lines were manually drawn between the right and the left transverse processes of each vertebra

conducted scans and performed measurements twice on 10 of the subjects to evaluate the intraand inter-operator and raters reliabilities. The study ultimately showed that for all three angles, excellent reliabilities of different measurements either on the same scan (ICC ≥ 0.93) or

different scans (ICC ≥ 0.84) and excellent linear correlations with Cobb angle were achieved (R2 ≥0.97), and with no significant clinical differences between each measurements (p ≥ 0.388), which suggested that all proposed

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measurement methods could be used for 3D ultrasound coronal evaluation. Wong et al. (2019) further conducted an evident-based study by involving a much larger number of AIS subjects. Coronal ultrasound angle evaluations were conducted using the automatic spinous process angle method (Zhou et al., 2017) and traditional Cobb using EOS system for 952 idiopathic scoliosis patients (mean age: 16.7 ± 3.0 years; 231 M and 721 F; Cobb 28.7◦ ± 11.6◦ ). 1432 out of 1636 structural curves were detected by the ultrasound system and significant and good correlations were observed between spinous process and Cobb angle of these curves (p < 0.001) (Fig. 16.10). The other missing curves were mainly upper thoracic curves. All these detected curves were either upper (r = 0.873, apices T7-T12/L1 intervertebral disc) or lower spinal curves (r = 0.740, apices L1 or below) respectively. More than 60% of the predicted Cobb angles of the upper and lower spinal curves, which were computed using the linear correlation equation obtained between spinous process and Cobb angle, showed clinically insignificant differences with Cobb angle for patients who possessed small Cobb angles, i.e. Cobb 0.57). Furthermore, the two ultrasound angles showed good agreement using Bland-Altman plot with no significant difference (p ≥ 0.326) with Cobb’s angle after adjustment.

16.3.3 Assessment on Spinal Flexibility Since spinal flexibility is one of the essential parameters for clinical decision for patients with AIS, He et al. investigated spinal flexibility to predict the initial in-brace correction, which is the immediate change of the spinal deformity when a newly fabricated brace is worn by a patient for the first time, using Scolioscan. 35 patients with AIS (Cobb’s angle: 28◦ ± 7◦ ; age:

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Fig. 16.10 The scatter-plots between radiographic Cobb and ultrasound spinous process angles. E_Cobb Cobb angle measured manually on EOS, SPA spinous process

angle, UTC upper thoracic curve, USC upper spinal curve, LSC lower spinal curve

12 ± 2 years; Risser sign: 0 ± 2 in average) were recruited and underdone 3D ultrasound scanning in 5 positions, which were natural standing, supine, prone, lateral bending in seated and prone postures respectively (He et al., 2017). An example of corresponding coronal ultrasound images from a patient is shown in Fig. 16.12a–e. The average in-brace correction was found to be 41% while the average curvature correction were 40%, 42%, 127% and 143% during supine, prone, prone with lateral bending, and sitting with lateral

bending, respectively. Meanwhile, the correlation coefficients between initial in-brace correction and curve correction during the 4 postures were r = 0.66 (supine), r = 0.75 (prone), r = 0.03 (prone with lateral bending) and r = 0.04 (sitting with lateral bending). The results suggested that prone position could be the most effective posture for predicting the initial effect of brace treatment on patients with AIS.

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Fig. 16.11 The diagram on the left illustrates the sagittal ultrasound image showing (a) spinous processes and (b) laminae which exists in different layers. The diagram on the right illustrates the measurement of (c) sagittal

ultrasound spinous process angle; (d) sagittal ultrasound laminae angle; and (e) radiographic Cobb angle for evaluating thoracic kyphosis and lumbar lordosis respectively

Fig. 16.12 An example for coronal ultrasound images obtained from an AIS subject in (a) standing; (b) supine (c) prone; (d) sitting with lateral bending position; and (e) prone with lateral bending posture. The upper and lower blue lines indicates the upper and lower most tilted verte-

brae levels respectively. The numbers in yellow font indicates the value of the curvature during different postures, which negative value refers to the curve being modified to the opposite direction. (Images were acquired from the article: He et al., 2017 (Fig. 2) in the reference list)

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16.3.4 Changes in Spinal Curvature during Forward Bending Adam’s forward bending test is a common approach to identify postural asymmetry and is used for early detection of scoliosis for adolescent during school screening. However, as scoliosis is a 3D deformity, changes in the sagittal profile of spine during forward bending would also likely cause coupling effect on the coronal and transverse plane (Mac-Thiong et al., 2003; Hong et al., 2017). Yet the differences of coronal curvatures during upright and forward bending postures were not investigated due to the limitation of other conventional imaging modalities. Therefore, Jiang et al. utilized Scolioscan to investigate the changes of coronal curvatures between erect and forward bending postures (Jiang et al., 2018). Since maintaining stability and repeatability were major concerns for the ultrasound scanning procedure, the patients were required to receive scanning in a seated posture twice during both upright and forward bending postures. Before investigating the posture effect on spinous process angle, spinous process angles between standing and seated postures were first compared because upright posture was adopted for conventional Scolioscan evaluation. 72 patients with AIS (Age: 15.3 ± 1.9 years, 17 M & 55 F) were recruited and 21 of them (Age: 16.0 ± 1.4 years, 5 M & 16 F) were involved in the upright standing scanning session. The curvature angles between upright standing and seated postures were found to be highly and significantly correlated (r = 0.86, p < 0.001) and excellent repeatability of spinous process angle during seated and seated forward bending were acquired (ICC ≥ 0.84). It was found that the curvature changes before and after forward bending could be categorized into three main patterns. The ultrasound images acquired during seated and seated forward bending and Xray images in upright posture of the three types of patterns were obtained (Fig. 16.13a–c). The shape of type I and II curves remained unchanged after forward bending, yet significant angle reduction for type I curves was observed. Patients with type III curves were those who possessed double curves at first, which then turned into

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one single curve after forward bending, but the location of such single curve varies throughout the thoracic and lumbar regions. To conclude, this study demonstrated that 3D ultrasound was capable to monitor and evaluate the dynamical changes of coronal curvatures of patients with AIS during different postures.

16.3.5 Generation of Coronal Images Using Fast Projection Imaging Manual selection for the optimal ultrasound images and measurement on ultrasound images requires certain amount of experience and training for specialists in order to conduct promising evaluation. Reduction of time for images generation could also shorten the examination process. Further researches had been conducted to facilitate 3D ultrasound evaluation to become more time-efficient and user-friendly. Since the entire spine region is being scanned and it generally takes around 2000 B-mode images for the scan to cover the entire spine, the volume reconstruction procedure was relatively time-consuming. Thus later on, Jiang et al. (2019) applied a narrowband volume rendering method, which was first proposed by Gee et al. (2002), to reduce the time needed for generating the coronal images. This method is composed of three procedures: (1) Non-planar image reslicing; (2) Bilinear interpolation and; (3) Image enhancement. Comparing to the conventional approach, this alternative projection method demonstrated to provide coronal curvature data with high correlation and no significant difference, at the same time with just oneeighth of the conventional processing time, which was approximately 15 s.

16.3.6 Conducting Semi-automatic Measurement on Ultrasound Images Though conducting spinous process angle measurement on coronal ultrasound images was demonstrated to be repeatable with high ICC, certain practice and awareness were required for

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Fig. 16.13 The diagram illustrates three alternation patterns of spinal curvature during forward bending: (a) Type I: maintained two curves; (b) Type II: maintained one curve; and (c) Type III: transited from two curves to one

curve. The images shown from left to right for each type are ultrasound image under sitting posture; ultrasound image under sitting forward bending posture and radiograph image of the same subject respectively

the raters during measurement. In addition, the placement of the lines for computing spinous process angle could be debatable in some occasion, thus leading to angle discrepancies between results measured by the same rater over time. To tackle with this issue, a couple of studies have been conducted. A semi-automatic method was first introduced by Zhou et al. to evaluate the curvature based on the spinous process shadow from the ultrasound images (Zhou et al., 2016). Instead of drawing tangential lines, a number of

points (no less than 6 points) were first manually placed in the middle of the spinous process shadow of the ultrasound images to delineate the curvature using a customized software (Fig. 16.12a), followed by employing a sixth order polynomial curve fitting algorithm to obtain the curve profile. The coronal ultrasound angle was then defined by the maximum angle formed by the normals of two adjacent inflection points obtained from the curve profile. By recruiting 70 subjects with scoliosis (age: 15.9 ± 2.7 years;

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22 M and 48F), the results obtained from the semi-automatic method were demonstrated to be highly and significantly correlated to those of the manual method (r = 0.9; p < 0.001).

16.3.7 Conducting Automatic Measurement on Ultrasound Images Zhou and the related research team continued on exploring the possibility of full automatic measurement on evaluating coronal angle on ultrasound coronal images. Zhou and Zheng first explored the automatic measurement on 36 subjects (Age: 30.1 ± 14.5) with different spine curvatures, based on Otsu’s method (Otsu, 1979) to segment the spinous profile (Zhou & Zheng, 2015). This method categorized the spinous column profile by a one-dimension valley-like curve in each row. The pixel with the smallest intensity of each column, also called the valley bottom, was then identified. A 6th order polynomial curvature was then fitted to all the identified valley bottoms and used to calculate the spinal curvatures. Though the curvatures obtained were demonstrated to be highly and significantly correlated with those of the manual method (r = 0.92; p < 0.001), there were major drawbacks of using the Otsu method. Satisfactory segmentation of the spinous column profile from the ultrasound VPI image may not be successfully performed when no distinct valley point was present in the histogram of some of the rows owing to speckle noise and low contrast of the features or when the true valley bottom could not be detected. An extensive study was therefore carried out, in which a novel automatic approach was developed to estimate the spinal curve from the ultrasound images while at the same time minimizing the above two issues (Zhou et al., 2017). The novel approach consisted of four stages: (1) Phase congruency preprocessing, (2) Bony feature segmentation, (3) Identification of spinous column profile; and (4) Spine curve detection (Fig. 16.14). During the phase congruency process, all the symmetric and asymmetric features of the coronal ultrasound

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images were measured to favor the detection of the medial spinous process shadow and the lateral vertebrae features such as transverse processes and the ribs. The bony features were then isolated from the images using a newly developed twofold thresholding strategy. The spinous column profile was extracted from the features and was used to compute the spinal curvature using the same method as mentioned in the previous work using the Ostu method (Zhou & Zheng, 2015). The results obtained using the novel automatic approach showed high and significant correlation with the manual spinous process angle (r = 0.91; p < 0.001) and X-ray Cobb’s method (r = 0.83; p < 0.001). Though the twofold thresholding strategy used in the segmentation stage improved the ability of the automatic algorithm to detect the medial spinous process line, the presence of the lateral features such as the ribs would affect the segmentation accuracy. In addition, both ends of the spinous process shadow could be missed because the information of lateral features was generally insufficient in these regions. Furthermore, the previous automatic algorithm relied heavily on images rendering with proper symmetric bony features, thus it may fail when the quality of the coronal ultrasound images was not satisfactory. Since all the above issues could potentially affect the accuracy of the automatic measurement, Zhou et al. applied an advanced method for automatic detection using adaptive local phase features (Zhou et al., 2020). The major difference of the proposed approach compared to the previous ones was that histogram equalization was first applied to improve the contrast of the coronal ultrasound image, followed by the extraction of the spinous process shadow using an oriented phase congruency measure with adaptive log-Gabor wavelet, which made use of the geometric arrangement of the anatomic features and minimized the influence of the projection depth and bilateral features on spinous process shadow detection. In addition, the computation time of this method was shorter than the previous automatic ones, which only took about 5 s for each ultrasound image. The concept of the proposed algorithm was shown in Fig. 16.15a.

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Fig. 16.14 The diagram illustrates the flow of the algorithm for automatic spinal curvature evaluation

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Fig. 16.15 On the left is the (a) The flow diagram of using adaptive local phase features for automatic detection of the spinous process profile. The images on the right are an example of using the proposed adaptive local phase features for automatic detection of the spinous process profile on a coronal ultrasound image: (b) Enhancement coronal ultrasound image; (c) Image with phase congruency using log-Gabor with frequency parameter = 0.1; (d) The phase

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congruency using log-Gabor frequency parameter = 0:15; (e) Optimized segmentation of the spinous column profile; (f) Finalization of spine curve detection and spine curvature measurement. The red curve is the automatically estimated spine curve with sixth order polynomial and the numbers in the green and pink text represent tangent at the inflection points and the angle between two adjacent inflections respectively

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To conclude, this method is composed of image contrast enhancement (Fig. 16.15b), segmentation of spinous column profile (Fig. 16.15c–e) and spine curve detection (Fig. 16.15f). The ultrasound coronal angles obtained using the proposed method from 29 patients with scoliosis (age: 30.6 ± 14.7; 9 M and 20 F) were also demonstrated to have a high and significant linear correlation with those obtained by the manual method (r = 0.90, p < 0.001) and radiographic Cobb (r = 0.87, p < 0.001).

16.3.8 Performing Automatic Selection for Optimal Ultrasound Images for Evaluation 9 different layers of coronal ultrasound images which corresponds to different depths of the scanned 3D ultrasound volume were generated using Scolioscan, thus each image possesses different imaging definitions. A convolution learning-to-rank algorithm was developed to automatically select the optimal coronal images for measurement, which eventually reduce the time needed and avoid the subjectivity among users during image selection (Lyu et al., 2019). To achieve the goal, Lyu et al. considered the image selection process as a ranking problem and replacing RankNet, a pairwise learning-torank algorithm, with convolution neural network to improve the feature extracting ability from the ultrasound images. In short, the backbone of the proposed network was a 3-layer convolutional neural network. The first two layers were typical convolution, max-pooling groups; while a global average pooling layer was applied after the third convolution layer. Finally a fully-connected layer was used to compute the output score. The best ultrasound image layer was defined by an experienced operator who had been involved in evaluating and analyzing coronal ultrasound images of Scolioscan for more than five years and served as the gold standard in this study. The selection criteria were based on a clear observation of the medial spinous process shadow and other lateral features such as transverse

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processes and ribs. The preliminary results shows that the proposed convolutional RankNet method is more appropriate for optimal image selection than traditional one, as it achieves perfect accuracy while the latter only achieved 35%.

16.4

Extensive Studies Related to Other Ultrasound System on Human Subjects

There were a couple of studies using ultrasound system other than Scolioscan to conduct 3D evaluation of spine on human subjects with scoliosis throughout the past decade. Purnama et al. (2010) demonstrated the feasibility of utilizing a freehand 3D ultrasound system of the Institute of High Frequency Engineering, Ruhr-University Bochum (Bochum, Germany), which is composed of a conventional ultrasound machine (Siemens Sonoline Omnia), an optical tracking system (Polaris from NDI) and a computer system to generate a 3D ultrasound image from a subject with human spine. Li et al. (2012) investigated the effectiveness of orthotic treatment on patients with AIS using an Esaote Technos MPX ultrasound unit (Esaote China Ltd., China) with a 7.5 MHz linear transducer together with a 3D tracking system (Tom Tec 3D Sono-Scan Pro, Germany). The study proposed spinous process angle as a clinical parameter for ultrasound to estimate conventional radiographic Cobb angle in order to determine the optimal location of the pressure pad for bracing. The ultrasound-assisted group was found to have a significant larger immediate in-brace corrections (p < 0.005) than the control groups for both thoracic and lumbar curves, demonstrating that the proposed method was beneficial to 62% of the patients. Koo et al. (2014) utilized the spatial positions of the spinous process tips of dry bone specimens obtained by a customized ultrasound system to evaluate the performance of various curve fitting methods and angle metrics which tends to provide a better estimation for the scoliosis deformity. The study showed that the ultrasound angles achieved by locally weighted

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polynomial regression with smoothing parameter equals to 0.4 provided the best comparison with radiographic Cobb, test reliabilities, less digitization errors and accuracy of identifying end vertebrae and convexity direction. An ultrasound system composed of an Olympus TomoScan Focus LTTM Phased Array instrument (Olympus NDT Inc., Waltham, MA), which equipped with a 5-MHz 128-element transducer and a mini-wheel encoder, was used to investigate coronal deformation (Chen et al., 2013) and axial vertebral rotations (Chen et al., 2016). In addition, the TomoViewTM software (ver. 2.9 R6; Olympus NDT Inc.) was connected to the phased array equipment for data acquisition and to export data in the coronal, sagittal and transverse planes for further post-acquisition analysis. Coronal curvatures of 5 AIS subjects (Age: 13.6 ± 1.1 years; 1 M and 4 F; Cobb angle: 25◦ ± 8.6◦ ) and axial vertebral rotations of 13 female AIS subjects (Age: 13.7 ± 1.8 years; Cobb angle: 22◦ ± 8◦ ) were measured using the centre of laminae (CoL) of the vertebrae for ultrasound assessments. The ultrasound angles measured using the CoL method showed excellent reliabilities with no significant clinical differences with radiographic Cobb for coronal curvature assessment, while excellent reliabilities but poor agreement was observed for axial rotation evaluation. The CoL method was then validated using a SonixTABLET ultrasound system coupled with the SonixGPS and a C5– 2/60 GPS Convex transducer (Ultrasonix, BC, Canada) on 36 curves of 20 AIS patients (Age: 14.5 ± 1.7 years; 4 M and 16F, major Cobb: 10◦ – 45◦ ) with the aid of radiograph (Young et al., 2015). The ultrasound angles obtained showed high intra-rater reliability and high correlation with radiographic Cobb. Wang et al. (2015) further investigated the reliability and validity of the CoL methods in the clinical setting by comparing the results acquired from 16 females patients with AIS (Age: 15.4 ± 2.6 years; Cobb: 10◦ –80◦ ) to the corresponding MRI measurement in supine position. Similarly, the results showed high intra- and inter-rater reliability, no significant difference and good agreement with MRI Cobb for thirty curves

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of the curves. Trac et al. further investigated the vertebral axial rotation (AVR) and plane of maximum curvature (PMC) using the same ultrasound machine and CoL method on 101 children with AIS who possessed 157 curves with Cobb ≤50◦ (Age: 13.7 ± 1.7 years; 14 M and 87F), using Da Vinci measurements from the EOS system as control (Trac et al., 2019). The study showed that the intra- and interrater and operator reliabilities were excellent (ICC > 0.9) and the PMC and AVR between both modalities were comparable. In addition, PMC orientations between two modalities were observed to be strongly correlated (R2 = 0.88). In addition, the reliabilities and mean absolute differences of PMC and AVR acquired from 3D spinal images of 21 patients (Age: 10.8– 17.8 years; Cobb: 10◦ –45◦ ) using a novel semiautomatic 3D ultrasound reconstruction method were found to be high and within the clinical accepted tolerances, respectively (Vo et al., 2019). Ferràs-Tarragó et al. (2019) proposed a Cobb angle measurement method by utilizing a smartphone (Samsung S8 Smartphone device) and a conventional ultrasound device (Mindray DC-70 Exp. ultrasonographic device). The orientation of the ultrasound probe was manually rotated until the transverse processes of the upper and lower end vertebrae of a curve could be observed in a single B-mode image. The proposed idea was that by attaching the smartphone, with an applications installed that allows inclination measurement, onto the ultrasound probe, the corresponding inclinations of the upper and lower end vertebrae would then be acquired for curve evaluation. The ultrasound angles acquired in this study showed excellent reliabilities and very high agreement.

16.5

Conclusion

3D ultrasound has become more attractive in monitoring and evaluating spinal curvatures in different planes. The results obtained by Scolioscan from human spine phantoms and clinical studies demonstrated that the spinal curvatures were significantly correlated with

16 3D Ultrasound Imaging of the Spine

radiographic Cobb with no clinical difference, with excellent repeatability in terms of raters and operators. However, it should be noted that ultrasound should not be considered as a substitute of X-ray and it is understandable that discrepancies exist between the results of both modalities, the most critical reasons are: (1) Different structures are taken into account during measurement and; (2) Repeatability of the scanning postures. Generally, patients were required to receive ultrasound scanning in standing posture in order to achieve the best outcome when comparing the Cobb angle obtained from X-ray. It has been suggested that different shapes of transducers, orientation of the ultrasound probe and scanning frequencies should be used in viewing different components of spine to achieve the best visualization of the vertebrae structures (Chang et al., 2019). However, for spinal curvature evaluation, it is not practical to have the entire spine scanned with various transducers in different orientations during a single sweep. Integrating multiple sweeps could possibly be a solution, but motion artifact would become more significant and should also be taken into consideration. There are other limitations of the 3D ultrasound imaging for scoliosis assessment yet to be solved. For instance, patients with metallic implants and high BMI were generally excluded, as metallic implants would affect the spatial sensing accuracy of the ultrasound probe and high BMI would likely lead to poor image quality in the lumbar region. In future studies, methods other than electromagnetic devices such as optical sensor could be used for spatial orientation detection and lower frequency could be used during ultrasound scanning for patients with high BMI to tackle with the above issues. Nevertheless, several issues require further investigation related to 3D ultrasound evaluation on spine, such as for instance, the investigation of coupling effect between orthogonal spinal parameters, determining possible prognostic factor and conducting longterm monitoring for curve progression, application of flexible array transducer, automatic evaluation of 3D spinal parameters.

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3D ultrasound is relatively cheap, radiationfree and easily accessible. Since quite a number of clinicians refuse the usage of X-ray for spine evaluation due to space issue and its ionizing nature, 3D ultrasound could be their alternative choice. Another advantage of using 3D ultrasound for spine evaluation is that there is no restriction on the posture of the subjects being scanned, thus the ultrasonic results obtained in different postures could serve as a “bridge” for validating different imaging modalities which generally patients are restricted in certain posture. Furthermore, there are even ongoing developments to introduce portable prototype 3D ultrasound transducers to the field for spine evaluation, thus implementing 3D ultrasound mass screening in schools could be possible in the near future. Acknowledgements The authors would like to thank all the team members who have contributed to the development of 3D ultrasound imaging in our team, including Qinghua Huang, Guangquan Zhou, Weiwei Jiang, James Cheung, De Yang, Kelly Lai, Heidi Lau, Michael Li, Henry Wong, Joseph Hui, Yen Law, Takman Mak, Qiang Meng, Lyn Wong; The authors also appreciate all the supports of collaborators in the development and application of 3D ultrasound for scoliosis, as well the supports of staff in Telefield Medical Imaging Limited. Compliance with Ethical Standards Funding: The studies were supported by Hong Kong Research Grant Council Research Impact Fund (R5017– 18). Disclosure of Interests: Y.P. Zheng reported his role as a consultant to Telefield Medical Imaging Limited for the development of Scolioscan. He is also the inventor of a number of patents related to 3D ultrasound imaging for scoliosis, licensed to Telefield Medical Imaging Limited through Hong Kong Polytechnic University. Ethical approval: All procedures performed in studies involving human participants were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. Approval was granted by [Joint Chinese University of Hong Kong-New Territories East Cluster Clinical Research Ethics Committee (2015.463)]. Informed Consent: Informed consents for participation and publication were obtained from all individual participants included in the study.

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372 Thaler, M., Kaufmann, G., Steingruber, I., Mayr, E., Liebensteiner, M., & Bach, C. (2008). Radiographic versus ultrasound evaluation of the Risser grade in adolescent idiopathic scoliosis: A prospective study of 46 patients. European Spine Journal, 17(9), 1251–1255. https://doi.org/10.1007/s00586-008-0726-6 Trac, S., Zheng, R., Hill, D. L., & Lou, E. (2019). Intraand interrater reliability of Cobb angle measurements on the plane of maximum curvature using ultrasound imaging method. Spinal Deformity, 7(1), 18–26. https:/ /doi.org/10.1016/j.jspd.2018.06.015 Vo, Q. N., Le, L. H., & Lou, E. (2019). A semi-automatic 3D ultrasound reconstruction method to assess the true severity of adolescent idiopathic scoliosis. Medical & Biological Engineering & Computing, 57(10), 2115–2128. https://doi.org/10.1007/s11517-01902015-9 Wang, Q., Li, M., Lou, E. H., & Wong, M. S. (2015). Reliability and Validity Study of Clinical Ultrasound Imaging on Lateral Curvature of Adolescent Idiopathic Scoliosis. PLoS One, 10(8):e0135264 https://doi.org/ 10.1371/journal.pone.0135264 Wong, Y. S., Lai, K. K. L., Zheng, Y. P., Wong, L. L. N., Ng, B. K. W., Hung, A. L. H., et al. (2019). Is radiationfree ultrasound accurate for quantitative assessment of spinal deformity in idiopathic scoliosis (IS): A detailed analysis with EOS radiography on 952 patients. Ultrasound in Medicine & Biology, 45(11), 2866–2877. https://doi.org/10.1016/j.ultrasmedbio.2019.07.006 Yazici, M., Acaroglu, E. R., Alanay, A., Deviren, V., Cila, A., & Surat, A. (2001). Measurement of vertebral rotation in standing versus supine position in adolescent idiopathic scoliosis. Journal of Pediatric Orthopedics, 21(2), 252–256.

Y. P Zheng and T. T. Y. Lee Young, M., Hill, D. L., Zheng, R., & Edmond, L. E. (2015). Reliability and accuracy of ultrasound measurements with and without the aid of previous radiographs in adolescent idiopathic scoliosis (AIS). European Spine Journal, 24(7), 1427–1433. https://doi.org/ 10.1007/s00586-015-3855-8 Zheng, Y. P., Lee, T. T. Y., Lai, K. K. L., Yip, B. H. K., Zhou, G. Q., Jiang, W. W., et al. (2016). A reliability and validity study for Scolioscan: A radiation-free scoliosis assessment system using 3D ultrasound imaging. Scoliosis and Spinal Disorders, 11, 13. https://doi.org/ 10.1186/s13013-016-0074-y Zhou, G. Q., & Zheng, Y. P. (2015). Assessment of scoliosis using 3-D ultrasound volume projection imaging with automatic spine curvature detection. IEEE International Ultrasonics Symposium, 2015, 1–4. https:// doi.org/10.1109/ULTSYM.2015.0485 Zhou, G. Q., Jiang, W. W., Lai, K. L., & Zheng, Y. P. (2017). Automatic measurement of spine curvature on 3-D ultrasound volume projection image with phase features. IEEE Transactions on Medical Imaging, 36(6), 1250–1262. https://doi.org/10.1109/ TMI.2017.2674681 Zhou, G. Q., Jiang, W. W., Lai, K. L., Lam, T. P., Cheng, J. C. Y., & Zheng, Y. P. (2016). Semi-automatic measurement of scoliotic angle using a freehand 3-D ultrasound system Scolioscan. XIV Medicon on Medical and Biological Engineering and Computing, 57, 341–346. https://doi.org/10.1007/978-3-319-32703-7_67 Zhou, G. Q., Li, D. S., Zhou, P., Jiang, W. W., & Zheng, Y. P. (2020). Automating spine curvature measurement in volumetric ultrasound via adaptive phase features. Ultrasound in Medicine & Biology, 46(3), 828–841. https://doi.org/10.1016/j.ultrasmedbio.2019.11.012

Ultrasonic Evaluation of the Bone-Implant Interface

17

Yoann Hériveaux, Vu-Hieu Nguyen, and Guillaume Haïat

Abstract

While implant surgical interventions are now routinely performed, failures still occur and may have dramatic consequences. The clinical outcome depends on the evolution of the biomechanical properties of the bone-implant interface (BII). This chapter reviews studies investigating the use of quantitative ultrasound (QUS) techniques for the characterization of the BII. First, studies on controlled configurations evidenced the influence of healing processes and of the loading conditions on the ultrasonic response of the BII. The gap of acoustical properties at the BII increases (i) during healing and (ii) when stress at the BII increases, therefore inducing a decrease of the reflection coefficient at the BII. Second, an acoustical model of the BII is proposed to better understand the parameters Y. Hériveaux · G. Haïat () CNRS, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Créteil Cedex, France e-mail: [email protected]; [email protected] V.-H. Nguyen Université Paris-Est, Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Créteil Cedex, France e-mail: [email protected]

influencing the interaction between ultrasound and the BII. The reflection coefficient is shown to decrease when (i) the BII is better osseointegrated, (ii) the implant roughness decreases, (iii) the frequency of QUS decreases and (iv) the bone mass density increases. Finally, a 10 MHz device aiming at assessing dental implant stability was validated in vitro, in silico and in vivo. A comparison between QUS and resonance frequency analysis (RFA) techniques showed a better sensitivity of QUS to changes of the parameters related to the implant stability. Keywords

Quantitative ultrasound · Bone-implant interface · Implant stability · Osseointegration · Finite element · In vivo study

17.1

Introduction

Titanium implants are routinely used in many clinical procedures in various fields, such as orthopedic, maxillofacial or dental surgeries (Carlo, 2016). However, implant failures and surgical complications still occur and may have serious consequences. The phenomena leading to implant failures remain poorly understood because of the

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 P. Laugier, Q. Grimal (eds.), Bone Quantitative Ultrasound, Advances in Experimental Medicine and Biology 1364, https://doi.org/10.1007/978-3-030-91979-5_17

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complexity of bone tissue, which evolves constantly. Remodeling processes occurring at the bone-implant interface (BII) involve the coupling of biological, chemical and mechanical phenomena, which allow bone tissue to adapt its structure to the mechanical stress it undergoes. In particular, following surgical interventions of endosseous implants, bone tissue will progressively grow in intimate contact with the implant, which corresponds to a process referred to as osseointegration. Osseointegration phenomena play a major role in the clinical success of endosseous implant surgeries (Khan et al., 2012). The tissues surrounding an implant are initially non-mineralized (Moerman et al., 2016), and progressively transform into mineralized bone during normal osseointegration processes (Fraulob et al., 2020a; Le Cann et al., 2020). However, in cases of surgical failures, osseointegration phenomena do not occur in an appropriate manner, leading to the presence of fibrous tissue around the implant and to the implant aseptic loosening (Pilliar et al., 1986). The surgical success is mainly determined by the evolution of the implant biomechanical stability (Mathieu et al., 2014) which is directly related to the biomechanical properties of the BII (Mathieu et al., 2014; Franchi et al., 2007). Two kinds of implant stability should be considered: the primary stability and the secondary stability. Primary stability corresponds to the implant stability just after surgery. It should be sufficient to avoid excessive micromotion (Pilliar et al., 1986) at the BII, but an excessive loading of the BII could cause bone necrosis (Sotto-Maior et al., 2010) and therefore compromise the implant integration success. Secondary stability is defined as the implant stability after the healing period. The initial stability of the implant has then been reinforced by new bone formation and maturation due to the remodeling process. Various approaches have been suggested to assess implant stability. X-rays or Magnetic Resonance Imaging based techniques are not adapted due to artifacts related to the presence of metal

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(Shalabi et al., 2007; Gill and Shellock, 2012). Impacts methods have been developed in order to assess the primary stability of the acetabular cup implant (Michel et al., 2016a, b), of the femoral stem (Albini Lomami et al., 2020; Dubory et al., 2020) as well as of dental implant stability (Van Scotter and Wilson, 1991; Schulte et al., 1983). In the field of dental implantology, impact methods present a low reproducibility due to their sensitivity to handpiece angulation and striking height (Meredith et al., 1998). Resonance frequency analysis (RFA) (Meredith et al., 1996; Pastrav et al., 2009; Georgiou and Cunningham, 2001) is commonly used to investigate implant stability, especially for dental implants. However, the orientation and fixation of the transducers were found to have significant effects on the Implant Stability Quotient (ISQ) (Pattijn et al., 2007). Moreover, RFA measurements are related to the resonance frequency of the bone-implant system, which depends on properties of the entire host bone that vibrates when excited mechanically (Rittel et al., 2019). Therefore, the RFA is sensitive to the properties of tissues surrounding the implant at the organ scale, and cannot be used to directly assess the BII characteristics (Aparicio et al., 2006). On the contrary, the ultrasonic propagation within an endosseous implant directly depends on the boundary conditions given by the biomechanical properties of the BII. Therefore, the use of quantitative ultrasound (QUS), which was first suggested in (de Almeida et al., 2007), constitutes an attractive alternative to assess implant stability. Moreover, QUS methods are relatively cheap, non-invasive and non-ionizing (Mathieu et al., 2014), so that they are adapted to capture information on living tissues for clinical applications. While a few studies showed the potential of non-linear ultrasound techniques to retrieve information on implants stability (Rivière et al., 2010; 2012), the present chapter will focus on the analysis of the reflection of an ultrasonic wave at the BII, which currently constitutes one of the most promising use of QUS to determine implant stability (Bhaskar et al., 2018).

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This chapter reviews various works including in silico, in vitro and in vivo studies dealing with QUS approaches to characterize the BII. First, the standardized case of a planar BII is considered. In particular, the evolution of peri-implant bone properties during healing and its influence on the ultrasonic response of the BII are described. Second, a model describing the acoustical behavior of the BII is exposed in order to better understand the interaction between an ultrasonic wave and the BII. Third, a QUS device aiming at assessing dental implant stability is presented. This device is validated using cylindrical implants and dental implants, and its performances are compared to the ones of RFA.

tion (Vayron et al., 2012) to retrieve quantitative information on local bone properties around an implant, at the scale of several micrometers. Histology is the standard technique used to assess the degree of osseointegration of an implant (Vayron et al., 2014a; Nkenke et al., 2003; Scarano et al., 2006), and may be used to distinguish preexisting mature from newly formed bone tissue. However, histology does not provide quantitative information on the bone properties. Therefore, nanoindentation was used to measure the apparent Young’s modulus and the hardness of different materials at the microscopic scale (Zysset et al., 1999). Table 17.1 summarizes the biomechanical properties of newly formed bone tissue obtained by coupling these techniques in a rabbit model. Newly formed bone tissue has lower Young’s modulus, hardness and ultrasonic velocities compared to mature bone tissue, which is due to a lower mineral content. Moreover, coupling nanoindentation with micro Brillouin analysis allowed deriving the relative variation of mass density between newly formed and mature bone tissues. More recently, Fraulob et al. (2020a) combined micro Brillouin scattering and nanoindentation methods in order to assess the spatio-temporal dependence of the bone properties around the implant during healing in a rabbit model. A good agreement was found with results from Table 17.1. Furthermore, Fraulob et al. evidenced that bone had higher values of Young’s modulus and of ultrasound velocity in the vicinity of the implant than further away from the implant. This result may be explained by local stress fields around the implant, which is known to stimulate the process of osseointegration (Haïat et al., 2014).

17.2

QUS Evaluation of a Planar Bone-Implant Interface

17.2.1 Evolution of Bone Peri-Implant Properties During Healing Implant stability is directly related to the biomechanical properties of bone tissues located at a distance lower than around 200 μm from the implant surface (Huja et al., 1999; Luo et al., 1999). Therefore, different experimental approaches have been used to investigate the properties of newly formed bone at the scale of a few tens of micrometers around the implant. Interestingly, the local ultrasonic wave velocity of the bone tissue surrounding an implant may be determined using micro Brillouin scattering (Mathieu et al., 2011a). This technique consists in using the photo acoustic interaction between a laser beam and a sample and provides results with a resolution of a few micrometers. Estimating the wave velocity of bone tissue is of interest to determine the mismatch in acoustic impedance between the implant and the surrounding medium at the BII, which is determinant when using QUS to characterize the BII. The reader is referred to Chap. 15 (Matsukawa, Hosokawa et al.) for further information on that technique. Vayron et al. (2014a) combined micro Brillouin scattering with histology and nanoindenta-

17.2.2 Influence of Healing Time on the Ultrasonic Response of the BII The influence of healing time on the ultrasonic response of the BII was first evidenced by (Mathieu et al., 2012) in the case of coin-shaped implants

376 Table 17.1 Mean values and standard deviation of the apparent Young’s modulus and hardness measured by nanoindentation and of the ultrasound velocity measured

Y. Hériveaux et al. with micro Brillouin scattering in newly formed (NB) and mature (MB) bone tissue of New Zealand White Rabbits

7 weeks 13 weeks Healing time NB MB NB MB Young’s modulus (GPa) 15.85 (±1.55) 20.46 (±2.75) 17.82 (±2.10) 20.69 (±2.41) Hardness (GPa) 0.660 (±0.101) 0.696 (±0.150)a 0.668 (±0.074) 0.696 (±0.150)a −1 Ultrasound velocity (m.s ) 4966 (±145) 5305 (±36) 5030 (±80) 5360 (±10) Mass density 0.878 ρ 7w b ρ 7w b 0.978 ρ 13w b ρ 13w b Data from (Vayron et al. 2012, 2014a) a Values of hardness for mature bone were not differentiated for the samples with healing times of 7 and 13 weeks b Only a relative variation of the bone mass density was obtained. ρ 7w and ρ 13w correspond to the mass density of the samples with healing times of 7 and 13 weeks, respectively Fig. 17.1 Schematic representation of the quantitative ultrasound device. Arrows represent the possible translations following each direction

placed on rabbit tibiae, in cortical bone tissue. The QUS response of the BII was measured in vitro at 15 MHz after seven and 13 weeks of healing time. To do so, ultrasonic measurements were performed in a water container using the QUS device illustrated by Fig. 17.1. The ultrasonic probe was positioned so that the BII was perpendicular to the transducer axis. For each sample, QUS measurements were compared to the bone-implant contact ratio (BIC) measured by histomorphometry, and to the degree of mineralization of bone estimated by histological staining. A significant decrease of the amplitude of the echo of the BII as a function of healing time was obtained, which may be explained by (i) the increase of the BIC ratio from 27% to 69% when the healing time increased from 7 to 13 weeks, and (ii) the increase of mineralization of newly formed bone tissue, which modifies its Young’s modulus and its ultrasound velocity (see Table 17.1). This study demonstrated the sensitivity of QUS to osseointegration phenomena.

Fraulob et al. (2020b) further confirmed the correlation between the BIC and the ultrasonic response of the BII using the same device illustrated in Fig. 17.1. Moreover, this second study (Fraulob et al., 2020b) focused on the influence of the implant surface roughness on the ultrasonic response of the BII. Ultrasonic echoes with lower amplitude were obtained when considering implants with rougher surfaces, which may be explained by a higher degree of osseointegration.

17.2.3 Influence of Loading Conditions on the Ultrasonic Response of the BII The stress distribution around the implant during and after surgery is an important determinant for the surgical success. While a minimum level of stress is required to stimulate osseointegration (Buser et al., 2002), excessive stresses may degrade the consolidating BII (Sotto-Maior et al.,

17 Ultrasonic Evaluation of the Bone-Implant Interface

Fig. 17.2 Variation of the apparent reflection coefficient as a function of the stress applied to the BII for a trabecular bone sample. (Data from (Hériveaux et al., 2019a))

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σ < σ 2 , bone trabeculae are progressively pressed onto the implant, which leads to an increase of the BIC, so that the reflection coefficient at the BII decreases. However, when σ = σ 2 , the trabecular network of bone collapses, and its pores are progressively filled by the debris generated by the fracture of trabeculae. Finally, when σ > σ 2 , all the pores of the trabecular bone samples have been filled, so that the BIC is close to 100% and therefore does not increase anymore. Therefore, for σ > σ2 , compression has a lower influence on the ultrasonic response of the BII. The significant elasto-acoustic correlation obtained through this study enhances the feasibility to perform the elastography of the BII (Hériveaux et al., 2019a).

17.3 2010). Nevertheless, the loading conditions at the BII remain difficult to be assessed experimentally. Therefore, a recent study (Hériveaux et al., 2019a) investigated the sensitivity of QUS to the loading conditions of the BII. To do so, in (Hériveaux et al., 2019a), bovine trabecular bone samples were compressed onto coin-shaped implants. Simultaneously, the ultrasonic device illustrated in Fig. 17.1 was used to estimate the evolution of the amplitude of the ultrasonic echo reflected from the BII during compression. Figure 17.2 shows that the apparent reflection coefficient at the BII decreases as a function of the stress level, which proves the sensitivity of the QUS response of the BII to its loading conditions. It may be explained (i) by changes of bone material properties and (ii) by an increase of the BIC ratio when the bone trabeculae are compressed onto the implant. As shown in Fig. 17.2, the apparent reflection coefficient is less sensitive to the loading conditions of the BII after a given stress value σ 2 was reached. This observation may be explained by the mechanical behavior of trabecular bone, which may be modeled by a Neo-Hookean constitutive law, with σ 2 approximately corresponding to the fracture stress of the bone samples. When

Modeling the Acoustical Behavior of the BII

Parameters influencing the ultrasonic propagation at a rough BII are often difficult to precisely control, and may also vary simultaneously. Therefore, acoustical modeling is a useful tool in order to better understand how the ultrasonic wave interacts with the BII. Modeling the acoustical behavior of the BII is a complex problem because of (i) its multiscale nature, (ii) the multiphasic structure of the bone tissue surrounding the implant, (iii) the surface roughness of the implant and (iv) the time dependence of bone properties. Interestingly, several studies investigated the impact of the multiscale roughness of the implant on the ultrasonic propagation at the BII by describing the implant roughness at two different scales (Heriveaux et al., 2018, 2019b, 2020a, b). First, the geometry of an implant engenders a macroscopic roughness (e.g. the threading of dental implants). Second, implants have a microscopic roughness due to the surface treatments they undergo, for example sandblasting or acid etching (Strnad and Chirila, 2015). The present section will introduce models developed to investigate the interaction between an ultrasonic wave and a rough BII by considering macroscopic and microscopic roughness.

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17.3.1 Macroscopic Roughness 17.3.1.1 Description of the Model Heriveaux et al. (2018) developed a 2-D finite element model of time domain transient wave propagation in order to simulate the influence of the macroscopic roughness of the implant on the ultrasonic reflection at the BII. To do so, an irregular interface was introduced between two half-spaces, which represents an implant made of titanium alloy (Ti-6Al-4V) and cortical bone tissue, respectively. This model is illustrated by Fig. 17.3a. The implant roughness was described by a sinusoidal function of amplitude h and halfperiod L, which constitutes an approximation of dental implants threading. Moreover, due to the symmetry of the problem, a simplified model considering only a single half sine period of the roughness was introduced and is illustrated by Fig. 17.3b. A soft tissue layer was introduced between bone and the implant to describe non-mineralized fibrous tissue that surrounds non-osseointegrated implants (Heller and Heller, 1996). Osseointegration processes were simulated by progressively increasing the thickness W of the soft tissues at the interface. The acoustical source was modeled by imposing a uniform impulse pressure at the top of the implant surface.

Fig. 17.3 Schematic illustrations of (a) the geometrical configuration of the BII considered and (b) the model used in the numerical simulations. (Reprinted with permission from (Heriveaux et al., 2018). ©2018, Acoustic Society of America)

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The reflection coefficient in amplitude r of the BII was assessed using this model for different values of roughness amplitude h, soft tissue thickness W, central frequency of the ultrasonic wave fc and bone mechanical properties.

17.3.1.2 Influence of the Implant Roughness and of the Presence of Soft Tissues Figure 17.4 shows the variation of r as a function of the ratio W/h for different values of h and for a frequency fc = 10 MHz. The value of r increases as a function of W/h for all values of h, which is due to an increase of the gap of acoustical properties at the interface when the soft tissue thickness W increases. Moreover, except for the case h = 1 mm, r increases when the roughness amplitude h decreases. This may be related to the wavelength λTi of the ultrasonic wave propagating in Titanium alloy (around 580 μm) which is close to typical values of the implant roughness. Such a situation results in phase cancellation phenomena (Heriveaux et al., 2018). Figure 17.5 illustrates the variation of the acoustic field at the BII at different times for a BII with a standard roughness (h= 360 μm, Fig. 17.5a) and for a relatively rough BII (h= 1 mm, Fig. 17.5b), while all other parameters were fixed (fc = 10 MHz, L = 900 μm, W/h = 1). Two wave fronts may be distinguished in the case of

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Fig. 17.4 Variation of the reflection coefficient r for fc = 10 MHz and for different values of the roughness amplitude h as function of the ratio of the soft tissue

thickness W and of the roughness amplitude h. (Reprinted with permission from (Heriveaux et al., 2018). ©2018, Acoustic Society of America)

Fig. 17.5 Snapshots corresponding to the spatial variation of the logarithm of the absolute value of the velocity in the y direction at different times in the macroscopic case. The computations are performed for fc = 10 MHz with (a) h = 360 μm and L = 900 μm and (b) h = 1 mm

and L = 900 μm. For t = 1.45 μs (a), the two arrows indicate the wave fronts corresponding to the reflection of the ultrasonic wave on the top and on the bottom of the surface. (Reprinted with permission from (Heriveaux et al., 2018). ©2018, Acoustic Society of America)

the standard BII and are evidenced by arrows in Fig. 17.5a. The first wave front corresponds to the ultrasonic signal reflected on the top of the sinusoidal surface, while the second wave

front corresponds to the signal reflected on the bottom of the sinusoidal surface, which regions are both perpendicular to the direction of propagation of the wave. For lower roughness,

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constructive interference may occur between these two wave fronts, so that the value of r increases, as illustrated in Fig. 17.4. Figure 17.5b illustrates another interesting phenomenon that occurs for rougher BII, when the angle between the axis y and the normal of the BII is locally higher than 45◦ . In this configuration, reflected waves may propagate in the x direction, which engenders multiple scattering from the implant boundaries. Analyzing the reflected echo is therefore more complex, which explains the different ultrasonic response obtained for the highest roughness (h = 1 mm) in Fig. 17.4.

17.3.1.3 Influence of Bone Properties As evidenced in Sect. 17.2.1, the properties of peri-implant bone tissues evolve during healing. Therefore, the values of the P-wave velocity Cp , of the shear wave velocity Cs and of the mass density ρ of the bone tissue were modified by +/− 20% compared to their reference values in order to assess the effects of osseointegration on the ultrasonic response of the BII. The reflection coefficient r decreases when ρ and Cp increase, but weakly depends on Cs, which may be due to the fact that ultrasonic propagation occurs perpendicularly to the BII. r was found to be sensitive to bone properties only when W/h is lower than around 0.25, with a maximum variation of 12% when ρ or Cp increase by 20%. For values of W/h higher than 0.25, the low contact area between the bone and the implant may explain the weak influence of bone properties on r. 17.3.1.4 Influence of the Central Frequency of the Ultrasonic Wave The value of the central frequency of the ultrasonic wave was found to significantly influence phase cancellation phenomena. For high frequencies (i.e. for small wavelengths), the two wave fronts illustrated by Fig. 17.5a could be distinguished. However, for low frequencies, constructive interference occurs between these two wave fronts. As a result, the reflection coefficient r decreases as a function of fc .

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17.3.2 Microscopic Roughness 17.3.2.1 Profilometry-Measured Profiles In order to model the microscopic roughness of the implant, a second study (Heriveaux et al., 2019b) used a similar model as the one described in (Heriveaux et al., 2018), except that actual implant surface profiles were considered. To do so, profilometry measurements were performed on 21 coin-shaped implants that were either 3Dprinted or had their surfaces treated by laser. The profiles obtained were then introduced into the numerical model, as illustrated by Fig. 17.6, and will be referred as original profiles in what follows. 3D-printed implants had values of mean arithmetical roughness Ra comprised between 14.0 μm and 24.2 μm, while implants with laser modified surfaces had values of Ra comprised between 0.898 μm and 6.94 μm. Note that influence of other roughness parameters such as the maximum peak height Rp and the maximum

Fig. 17.6 Schematic illustration of the 2-D model used in numerical simulations for a profilometry-measured roughness profile. (Reprinted with permission from (Heriveaux et al., 2019b). ©2019, Acoustic Society of America)

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valley depth Rv were also investigated in this study. Figure 17.7 shows the variation of the reflection coefficient r as a function of the soft tissue thickness for fc = 10 MHz and for six implants with laser-modified surfaces and six 3D-printed implants. For both types of implants, r increases as a function of W, due to the associated increase of the gap of acoustical properties at the BII. Moreover, the increase in r occurs for smaller values of W when considering surfaces with lower roughness, because for a given value of W, there is more bone in contact with the implant when considering a higher roughness profile. However, Fig. 17.7 also illustrates some differences in the acoustical behavior of the BII depending whether the implants have a relatively low (implants with laser-modified surfaces) or high (3D-printed implants) surface

roughness. For implants with low roughness (see Fig. 17.7a), qualitatively similar results were obtained for all the profiles considered: r first increases as a function of W from around 0.54 to around 0.92, and then slightly decreases to tend towards 0.88. However, for implants with higher surface roughness (see Fig. 17.7b), the values of r obtained for W = 0 and for W = 200 μm are not the same for all the roughness profiles and increase as a function of Ra . This last result may be explained by scattering effects of the wave on the BII, which are more significant for rougher profiles. Note that these results are in qualitative agreement with experimental results from (Fraulob et al., 2020b) described in Sect. 17.2.2. Overall, Fig. 17.7 shows that for fc = 10 MHz, the reflection of the ultrasonic wave at the BII is sensitive to the properties of the soft tissues located at a distance smaller than 50 μm for implants with laser modified surfaces, and lower than 100 μm for 3D-printed implants.

Fig. 17.7 Variation of the reflection coefficient r of the bone-implant interface as a function of the soft tissue thickness W for fc = 10 MHz and for (a) six implants with laser-modified surfaces roughness profiles and (b)

six 3D-printed implants roughness profiles. (Reprinted with permission from (Heriveaux et al., 2019b). ©2019, Acoustic Society of America)

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17.3.2.2 Equivalence with the Sinusoidal Model In order to decrease calculation costs and to derive a better control on the roughness parameters, Heriveaux et al. (2019b) investigated to what extent actual implant roughness could be replaced by a sinusoidal profile. An optimization procedure was developed in order to find the equivalent sinusoidal profiles leading to ultrasonic responses that would best match the ones of each original profile. To do so, for each original profile, the reflection coefficient was assessed for 10 values of soft tissue thickness W. A cost function was then defined as the averaged difference between the reflection coefficient obtained with original and sinusoidal profiles for these 10 values of W. Figure 17.8 shows the ultrasonic response obtained for 3 original profiles and their equivalent sinusoidal profiles. A good agreement was found for each original profile, which validated the use of sinusoidal profiles to describe microscopic roughness. Therefore, the acoustical behavior of the BII could be determined using the model illustrated by Fig. 17.3 both for microscopic and macroscopic roughness. Using the sinusoidal model, the influence of bone properties and of the central frequency of the ultrasonic wave could be assessed at the microscopic scale. Similarly as for the macroscopic roughness, r varied by a maximum of 13% when the bone density ρ or its P-wave velocity Cp

increased by 20% (Heriveaux et al., 2018). Concerning the frequency, r was found to depend almost only on k·W, where k is the wavenumber in the titanium implant. r increases as a function of k·W when k·W < 1, but does not depend on k·W when k·W > 1. Overall, the results indicate a higher sensitivity of r to variations of W when fc increases.

Fig. 17.8 Variation of the reflection coefficient r as function of the soft tissue thickness W for roughness profiles of implants with (a) Ra = 1.52 μm, (b) Ra = 5.83 μm, (c) Ra = 18.2 μm and for their corresponding optimized

sinusoidal roughness profiles. (Reprinted with permission from (Heriveaux et al., 2019b). ©2019, Acoustic Society of America)

17.3.2.3 Analytical Modeling of the BII In the previous subsections, numerical approaches were proposed to model the interaction between an ultrasonic wave and the BII. However, analytical modeling would allow determining the constitutive law of the BII subjected to an ultrasonic wave. This law could then be used to replace the BII conditions in future finite element models of bone-implant systems, and therefore simplify numerical models and save computation time. To do so, Hériveaux et al. (2020b) considered that the BII could be replaced by two springs acting in parallel between the bone and the implant, as illustrated in Fig. 17.9. These two springs model (i) the contribution Kc due to the contact between the implant and the bone and (ii) the contribution Kst related to the presence of non-mineralized tissues at the BII, respectively. Several approximations have been made in order to determine the expressions of Kc and Kst . First, soft tissues regions of the BII (see Fig. 17.3) were assumed to behave like open cracks. Based on this hypothesis, Kc was assessed using the

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Fig. 17.10 Variation of the analytical total stiffness of the bone-implant interface K and of the stiffness constributions Kc and Kst corresponding to the bone-implant contact and to soft tissues, respectively, as a function of the ratio of

the soft tissue thickness W and of the roughness amplitude h for L = 50 μm and (a) h = 10 μm, (b) h = 20 μm, (c) h = 40 μm. (Data from (Hériveaux et al., 2020b))

Fig. 17.9 Spring model used to describe the BII. Kc and Kst represent the contributions of the contact between the bone and the implant and of soft tissues at the interface, respectively

work of (Lekesiz et al., 2013). However, note that this approximation may lose in validity for higher roughness values. Second, soft tissues have mechanical properties close to those of liquid, and were therefore assimilated to a thick liquid film present between the implant and bone. Based on this assumption, the work of (Dwyer-Joyce et al., 2011) was considered to assess the analytical expression of Kst . The total stiffness K of the interface was then defined as the sum of Kc and Kst . Figure 17.10 shows the evolution of K, Kc and Kst as a function of the ratio W/h for three values of implant roughness h. For low roughness (h = 10 μm), Kc is predominant over Kst , while for high roughness (h = 40 μm), Kst is predominant over Kc . This result may be explained by the fact that a higher roughness induces more contact between the bone and the implant. Moreover, K decreases suddenly when W = h for all roughness because for W > h, the implant is no longer in contact with bone, so that Kc = 0.

Based on the stiffness values of the BII, the reflection coefficient in the time domain could be determined using the work of (Tattersall, 1973). Figure 17.11 shows the evolution of the analytical and numerical reflection coefficients obtained for different implant roughness and different central frequencies of the ultrasonic wave. Analytical and numerical results are in good agreement, which validates the analytical model. However, some discrepancies between analytical and numerical results can be observed for higher roughness, which may be explained by a loss of validity of the open-cracks approximation. Similarly, analytical results are closer to numerical ones for lower frequencies, because of the larger associated wavelength. Finally, a steep increase of the reflection coefficient may be observed both analytically and numerically around W = h, which can be explained through the steep decrease of K that was evidenced for that special configuration (see Fig. 17.10).

17.3.3 Limitations of the Model The model described in Sect. 17.3 has several limitations. First, microscopic and macroscopic implant roughness have not been combined. Implants used in clinical practice have both macroscopic threading and microscopic surface roughness, resulting in an interaction of the phenomena considered for microscopic and macroscopic scales, which should be considered in future studies.

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Fig. 17.11 Variation of the reflection coefficient of the BII as a function of the ratio of the soft tissue thickness W and of the roughness amplitude h for different frequencies fc, for L = 50 μm and for (a) h = 10 μm, (b) h = 20 μm,

(c) h = 40 μm. Solid lines represent the analytical values of r whereas the symbols represent the numerical values. (Data from (Hériveaux et al., 2020b))

Second, only a normal incidence of the ultrasonic wave on the BII was considered, and future studies should account for oblique incidences. Third, the bone geometry around the implant surface was described by a bone level corresponding to the parameter W, while voids and cavities may be present in peri-implant bone tissue, which makes its geometry more complex. Fourth, strong assumptions were made on the bone materials properties, which were considered homogeneous, elastic and isotropic. In particular, the fact that bone is a strongly dispersive medium (Haiat and Naili, 2011; Haiat et al., 2008) was not taken into account in this model, and bone anisotropy (Haïat et al., 2009; Sansalone et al., 2012) was neglected. Fifth, the present results were obtained with a 2D model. However, (Hériveaux et al., 2020a) compared the results obtained with a 3D model to the ones previously described. For typical implant roughness, a good agreement was found between 2D and 3D results, which validates the 2D approach. Besides these limitations, Sect. 17.3 emphasizes the influence of the implant macroscopic and surface roughness as well as of osseointegration phenomena on the interaction between an ultrasonic wave of different frequencies and the BII. Three models of the BII have been proposed, considering original or sinusoidal implant roughness, and using numerical or analytical approaches, and an equivalence between the different models was obtained. The results lead to a better understand-

ing of the interaction between an ultrasonic wave and the BII, which could help to improve the QUS characterization techniques.

17.4

Development of a QUS Device to Assess Dental Implant Stability

17.4.1 Presentation of the QUS Device Assessing dental implant stability clinically is difficult (Haïat et al., 2009) because it is directly dependent on many parameters such as the geometry and surface properties of the implant, the patient bone quality and/or the surgical protocol. Furthermore, surgical procedures used in oral implantology are not standardized. For example, the literature reports duration between the implant insertion and loading in a range from 0 up to 6 months (Raghavendra et al., 2005). Accurate measurements of dental implant stability could therefore be useful to adapt the surgical strategy to each patient, in particular concerning the choice of the healing period. The use of ultrasonic techniques to assess dental implant stability was first suggested in (de Almeida et al., 2007), which studied the variations of the 1 MHz response of a screw inserted in aluminum. Following this preliminary study, dental implants have been used as an ultrasonic wave guide in order to assess their stability, using a QUS device that was validated in vitro (Math-

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Fig. 17.12 Ultrasonic device including the implant, the transducer and the dedicated electronics

ieu et al., 2011b; Vayron et al., 2013, 2014b, 2018a), in silico (Rittel et al., 2019; Vayron et al., 2014a, 2018b; Mathieu et al., 2011c) and in vivo (Vayron et al., 2014a, 2018b; Hériveaux et al., 2021). Figure 17.12 illustrates the principle of this QUS device. An ultrasonic transducer with a central frequency of 10 MHz is positioned in contact with the emerging surface of a dental implant inserted in bone. The ultrasonic probe is connected to an analyzer, and the radiofrequency (rf) signal from the analyzer is recorded with a sampling frequency equal to 100 MHz. The Hilbert’s envelope of the rf signals is then computed in order to derive an indicator I representing the average amplitude of the measured signal. Note that different definitions of I were considered depending on the studies, so that quantitative comparisons of the values of I were not possible. The inner structure of the rf signals was also more extensively investigated through multifractal analysis (Scala et al., 2018). When the implant is surrounded by fluids (soft tissues, blood, water or air), the gap of acoustical impedance at the BII is higher than when the implant is surrounded by bone. Therefore, the energy leakage of the ultrasonic wave out of the implant is less important. Moreover, evolution of the bone mechanical properties also influences the ultrasonic propagation at the BII, as evidenced in Sects. 17.2.1 and 17.3. Consequently, the amplitude of the ultrasonic response of the BII is influenced by the properties of the material in contact with the implant, and the variations of I are representative of the implant stability.

17.4.2 Preliminary Studies with Titanium Cylinders 17.4.2.1 In Vitro Study The validation of our QUS device was first performed in vitro using titanium cylindrical implants (Mathieu et al., 2011b). This study aimed at proposing a methodology to identify the amount of bone surrounding titanium cylinders, which would then be of interest to assess implant stability with QUS. To do so, identical implants were inserted into rabbit bone tissue with four different geometrical configurations represented in Fig. 17.13. For all configurations, a defect was drilled in bone tissue so that each configuration corresponded to a different amount of bone in contact with the implants. The QUS device was then used to analyze all samples. An approximately periodic repetition of echoes was recorded on the upper surface of the implant for all configurations. However, the amplitudes of the echoes decreased faster as a function of time when the amount of bone in contact with the implant increases, so that value of the indicator I was correlated to the amount of bone in contact with the implant. 17.4.2.2 Numerical Simulation The ultrasonic propagation in the four configurations illustrated in Fig. 17.13 was also simulated numerically in order to compare experimental and numerical results. First, a 2D numerical study was performed using the 2-D finite-difference time-domain (FDTD) algorithm (SIMSONIC, www.simsonic.fr) (Mathieu et al., 2011c). Second, a 3-D numerical study was

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Fig. 17.13 Schematic illustrations of the four drilling configurations used to mimic different configurations of primary stability

results, which may be explained by a more realistic description of the problem. In particular, a faster decay of the amplitude of the ultrasonic response was observed for the 2-D model than for the other models, and contributions due to mode conversions were lower. The 3-D numerical model proposed by (Vayron et al., 2015) was also used to simulate the changes of bone mechanical properties that are known to occur during healing (see Table 17.1). The indicator I was shown to significantly decrease as a function of healing time and thus to be sensitive to bone quality. Fig. 17.14 Variation of the normalized value of the ultrasonic indicator as a function of the configuration number corresponding to the amount of bone in contact with the implant (see Fig. 17.13) for results obtained experimentally, with 2D FDTD simulations and with the 3D finite element model. (Reprinted by permission from Springer Nature: Biomech Model Mechanobiol (Vayron et al., 2015), ©2015)

performed using an axisymmetric finite element model on COMSOL Multiphysics (Stockholm, Sweden). Figure 17.14 shows the relative evolution of the ultrasonic indicator I obtained experimentally and numerically with the 2-D FDTD and with the 3-D finite element models. A good qualitative agreement between experimental and numerical results was obtained, with I increasing when the bone quantity surrounding the implant increases for all models. However, some discrepancies were observed between the different models, and may be due to possible errors on the geometry of the configuration as well as on material properties. Numerical results obtained with the 3-D model are also closer to experimental data than 2-D

17.4.3 In Vitro Validation on Dental Implants Following the preliminary study with cylindrical implants, the QUS device was validated using dental implants. The sensitivity of QUS to the BII properties was first estimated in vitro with implants inserted in biomaterials and in bovine bone tissue.

17.4.3.1 Implants Inserted in Biomaterials Vayron et al. (2013) investigated the evolution of the ultrasonic response of dental implants embedded in the tricalcium silicate-based cement (TSBC) Biodentine™ (Koubi et al., 2012, 2013) when subjected to fatigue stress. Biodentine™ (Septodont, Saint-Maur-des Fossés, France) was considered for this study because it is a biomaterial used as bone substitute for dental implant surgery in the case of edentulous patients with poor bone quality. Six titanium dental implants were embedded in Biodentine™, and were then submitted to cyclic lateral stresses that were ap-

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plied during 24 h. The stability of the implant was regularly assessed with the QUS device. One-way analysis of variance (ANOVA) showed a significant increase of I as a function of fatigue time for all implants. This result is due to the progressive debonding of the Biodentine-implant interface, leading to a higher acoustic energy recorded at the upper surface of the implant.

17.4.3.2 Implants Inserted in Bone A second in vitro validation of the QUS device was performed with dental implants inserted in bone tissue (Vayron et al., 2014b). The aim of this study was to investigate the sensitivity of I to the amount of bone in contact with the implant. To do so, ten identical implants were fully inserted in bovine humeri, and their ultrasonic response was recorded. Implants were then progressively unscrewed in order to reduce the BIC, and their QUS response was measured after each rotation of 2π rad. Figure 17.15 compares experimental results (Vayron et al., 2014b) with numerical data obtained through finite element modeling (Vayron et al., 2016) and shows that I significantly increases when the implant is unscrewed. Therefore, this study confirms that while the wave propagation inside a dental implant is more complex than in cylindrical implants (Mathieu et al., 2011b), QUS remain sensitive to the amount of bone surrounding the implant.

Fig. 17.15 Variation of experimental and numerical values of I as a function of the number of unscrewing rotations of the dental implant in bone tissue. (Reprinted with permission from (Vayron et al., 2016). ©2016, Acoustic Society of America)

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17.4.4 Simulation of the Ultrasonic Propagation in Dental Implants The development of acoustical modeling is necessary to better understand the interaction between an ultrasonic wave and the bone– implant system. Therefore, Sect. 17.3 proposed an acoustical model of the BII for a standardized configuration of the BII, which allowed to evidence interference phenomena such as multiple scattering and phase cancellation, and to estimate an order of scale of the resolution of QUS measurements. However, the ultrasonic propagation inside a dental implant is affected by its complex structure, so that it is also of interest to consider the geometry of real implants to improve the performances of the QUS device. In the studies described below, the ultrasonic source was modeled by a broadband longitudinal velocity pulse centered at 10 MHz in the direction normal to the implant surface. Moreover, all media were assumed to have homogeneous, elastic and isotropic mechanical properties.

17.4.4.1 Guided Wave Propagation in Dental Implants A 3-D axisymmetric study was performed in (Hériveaux et al., 2020c) in order to investigate the propagation of an ultrasonic wave in a dental implant surrounded by air. In this model, the

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geometry of a TSVT4B10 implant manufactured by Zimmer Biomet (Warsaw, Indiana, USA) was considered, with an ultrasonic transducer screwed inside the dental implant. Out-of-plane displacements were simulated along the implant axis to investigate the speed of propagation and the frequency components of the ultrasonic wave. This numerical approach was coupled with an experimental approach using a laser interferometer to evaluate the amplitude of the displacements occurring at the implant surface. Both experimental and numerical approaches evidenced the propagation of a wave with a speed of around 2100 m/s and main frequency components between 300 kHz and 2 MHz along the implant axis. The low speed of propagation compared to the Pwave velocity in titanium (Cp = 5800 m/s) and the low frequency components compared to the central frequency of the ultrasonic pulse (10 MHz) evidenced the propagation of a guided wave inside the dental implant. Therefore, the propagation of the ultrasonic wave in a dental implant was guided by the implant structure. For characterization purposes, these results indicate that it is not necessary to consider high frequency transducers since ultrasound propagate at frequencies comprised between 300 kHz and 2 MHz in the dental implant. However, this study only considered one implant geometry, and did not consider the situation where the implant was surrounded by bone, which could highly affect the results.

17.4.4.2 Influence of Peri-Implant Tissues Properties Two other 3-D axisymmetric studies were performed in (Rittel et al., 2019; Vayron et al., 2016) to consider dental implants inserted in bone tissue, as illustrated in Fig. 17.16. The sensitivity of QUS to the BII conditions was evaluated for different scenarios. The ultrasonic indicator I was shown to significantly increase (i) when adding fibrous tissues around the BII (in part #L , see Fig. 17.16), (ii) when the implant was unscrewed (see Fig. 17.15), and (iii) when the longitudinal wave velocity and the mass density of bone tissue around the implant decreased. These results may be explained by a decrease of the gap of acoustic impedance between bone tissue and the implant,

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Fig. 17.16 Cross-sectional view of the 3-D axisymmetric geometrical configuration used in (Vayron et al., 2016). #L corresponds to the region where the material properties are varied. #i , #c , and #t respectively denote the implant, the cortical bone and the trabecular bone. #ca and #ta respectively correspond to absorbing layers associated to trabecular and cortical bone. The white parts inside the implant are filled with void

which leads to a higher transmission coefficient at the BII.

17.4.5 In Vivo Validation While in vitro and in silico studies demonstrated the potentiality of QUS to assess implant stability, in vivo studies are necessary to determine the sensitivity of the ultrasonic response of the BII to healing time. An initial in vivo validation of the QUS device was performed using a rabbit model (Vayron et al., 2014a). Twenty-one dental implants were inserted in the femur of eleven rabbits. Two (respectively three and six) rabbits were sacrificed after 2 weeks (respectively 6 and 11) of healing time. Ultrasonic measurements were performed for each implant directly after implantation and just before the sacrifice of the animals. The reproducibility of the method was

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Fig. 17.17 Time gated rf signals obtained on the day of the implantation and after 11 weeks of healing time

assessed by reproducing each measurement 10 times. Histological analyses were performed to determine the BIC values of each sample. Figure 17.17 shows the rf signals obtained on the day of the implantation and after 11 weeks of healing time, and evidences a decrease in the amplitude of the ultrasonic response after healing. Moreover, while no global tendency could be assessed after 2 weeks of healing time, a significant decrease of the indicator I was obtained between the initial and the final measurements for 83% (respectively for 100%) of the implants after 6 (respectively 11) weeks of healing time. The values of I obtained after 2, 6 and 13 weeks of healing were also significantly different, which confirms that QUS can be used to assess dental implant stability. Figure 17.18 shows the variation of the indicator I as function of the BIC ratio for 13 implants. A significant correlation between these two parameters was obtained. However, the coefficient of determination R2 remains relatively low because of (i) the low number of samples, (ii) the measurement of the BIC ratio for 2-D sections rather than for the whole 3-D sample and (iii) the sensitivity of QUS to changes of periimplant bone mechanical properties, which are not described by the BIC ratio.

17.4.6 Comparison of the Performances of QUS and RFA Resonance frequency analysis (RFA) is a technique widely used clinically to evaluate the stability of dental implants (Valderrama et al., 2007). It consists in applying vibrations to the implant at different frequencies and recording the amplitude of the generated displacements in order to determine the first resonance frequency of the BII, which corresponds to a bending mode. Therefore, RFA allows to assess the stiffness of the boneimplant structure. The following section will present an in vitro study and two in vivo studies comparing the performances of QUS and of RFA in order to highlight the potential of QUS to investigate the evolution of the BII properties. In all the following studies, the RFA response of the implant was measured in ISQ units (given on a scale from 1 to 100), which corresponds to the standard indicator provided by the Osstell device (Osstell, Göteborg, Sweden) to assess the implant stability.

17.4.6.1 In Vitro Studies The comparison between the performances of the QUS and RFA methods have first been assessed using bone-mimic phantoms made

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Fig. 17.18 Variation of the indicator I as function of the BIC ratio. The triangles (respectively the circles and the squares) represent the samples with 2 (respectively 6 and 11) weeks of healing time. (Data from Vayron et al., 2014a)

of rigid polyurethane foam (Orthobones; 3B Scientific, Hamburg, Germany) (Vayron et al., 2018a). The main interest of this configuration is to work under standardized and reproducible conditions. Bone test blocks with different values of bone density and of cortical thickness (1 and 2 mm) were considered in this study. In particular, three material types (# 10, # 20, and # 30 PCF) were used to model trabecular bone, which correspond to mass densities equal to 0.16, 0.32, and 0.48 g/cm3 , respectively. A mass density of 0.55 g/cm3 was chosen for cortical bone (#40 PCF). Implants were then screwed into conical cavities created in these test blocks. The influence of four parameters on the QUS and on the RFA measurements were tested in this study, namely (i) the trabecular bone density, (ii) the cortical bone thickness, (iii) the final drill diameter and (iv) the implant insertion depth. Figure 17.19 shows the variation of the values of the ISQ and of I as a function of the different input parameters. The values of ISQ (respectively I) increase (respectively decrease) as a function of the trabecular density, of the cortical thickness and of the screwing of the implant. However, ANOVA and Tukey-Kramer tests indicate that values of I obtained for all the tested trabecular densities and cortical thickness were significantly different, which was not the case for the ISQ values (see Fig. 17.19a, b). Moreover, values of I were significantly different for all considered final drill diameters except for two (see Fig. 17.19c), while the ISQ values were similar for all final drill diameters lower than 3.2 mm and higher than 3.3 mm.

Table 17.2 indicates the precision on the estimation of the different parameters through QUS and RFA measurements. The errors were between 4 and 8 times higher using RFA techniques than when using QUS. Therefore, QUS has a better sensitivity to changes of the parameters related to the implant stability and thus a higher potentiality to correctly assess the dental implant stability than the RFA technique.

17.4.6.2 In Vivo Studies Vayron et al. (2018a) used an in vitro model to prove the better performance of QUS compared to RFA techniques in order to assess dental implant stability. However, in vivo studies are required to further validate this conclusion. Therefore, Vayron et al. (2018b) used a sheep model to investigate the respective sensitivity of QUS and RFA measurements to implant stability. Compared to the previous in vivo study presented in Sect. 17.4.5 (Vayron et al., 2014a), the present study considered (i) a bigger animal model with bone properties closer to those of human tissue, (ii) a larger number of samples, and (iii) a controlled torque of insertion (3.5 N.cm) when screwing the QUS device on the implant to get a better reproducibility than former studies, where the ultrasonic probe was manually positioned. Following the insertion of 81 dental implants in the iliac crests of 11 sheep, RFA and QUS measurements were performed after different healing duration (5, 7 and 15 weeks). ISQ measurements were performed following two perpendicular directions, denoted 0◦ and 90◦ . In order to obtain an easier comparison between values of the ultrasonic indicator and of the ISQ, a new ultrasonic

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Fig. 17.19 Variations of the values of the ISQ and of the indicator I for implants inserted in bone mimicking phantoms with different values of (a) trabecular density (# 10, # 20, and # 30 PCF), (b) cortical thickness (1 or 2 mm), (c) final drill diameter and (d) screwing of the implant. Three implants are considered per test block

for (a) and (b). The stars indicate the results that are statistically similar for (c). The error bars correspond to the reproducibility of each measurement. (Figure adapted with permission from (Vayron et al., 2018a). ©2018, John Wiley and Sons)

Table 17.2 Error realized in the estimation of each parameter in (Vayron et al., 2018a)

eral implants between 5 and 15 healing weeks. This result may be related to the fact that implants were not loaded mechanically in the iliac crest, which may lead to bone resorption around the implants (Li et al., 2018). ANOVA showed that there was no correlation between the ISQ values and the healing time, with no significant variations of the ISQ for 82% of the implants. Moreover, the error on the estimation of the healing time when analyzing the results obtained with QUS was around 10 times lower than that made when using RFA, which may be explained by a better reproducibility of measurements. Therefore, this study concluded that the evolution of dental implant stability could be assessed with a better accuracy using QUS than RFA. A second in vivo study on rabbits (Hériveaux et al., 2021) aimed at comparing QUS and RFA

Trabecular Indicator density (PCF) ISQ 2.73 I 0.6

Cortical thickness (mm) 0.31 0.04

Insertion depth (mm) 0.16 0.04

indicator UI = 100–10 × I was defined so that the values of UI (i) are comprised between 1 and 100, and (ii) increase when bone quality and quantity increases around the implant. Figure 17.20 shows the variations of the ISQ and of UI as a function of healing time for two given implants. ANOVA showed a significant increase of UI from 0 to 5 healing weeks and from 0 to 7 healing weeks for 97% of implants. However, UI decreased as a function of healing time for sev-

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Fig. 17.20 Results obtained for two implants placed on the same sheep for the different healing times for UI, ISQ 0◦ and ISQ 90◦ values. Error bars show the reproducibility

of the measurements. (Reprinted from (Vayron et al., 2018b), licensed under CC BY 4.0)

Fig. 17.21 Relationship obtained (a) between UI and the BIC and (b) between ISQ0 and ISQ90 and the BIC. The solid lines correspond to a linear regression analysis. The error bars denote the reproducibility of the mea-

surements. The determination coefficients are indicated. (Figure adapted from (Hériveaux et al., 2021), licensed under CC BY 4.0)

measurements with BIC values, which is the current gold standard to investigate implant osseointegration. To do so, 22 dental implants were inserted in the knee joint of rabbits. Animals were sacrificed after a healing time comprised between 0 and 13 weeks. Prior to the sacrifice, UI and ISQ measurements were performed. RFA measurements were performed in the 0◦ and 90◦ directions. The values obtained were denoted ISQ0 and ISQ90, respectively. After the animal sacrifice, the BIC was determined for each sample using histological analyses.

Figure 17.21 shows the evolution of UI, ISQ0 and ISQ90 as a function of the BIC for the 22 implants. ANOVA indicated significant correlation between UI and the BIC and between ISQ0 and the BIC, but no correlation between ISQ90 and the BIC. It confirms that RFA results depend on the direction of the measurements and have therefore a low reliability. Moreover, the correlation between UI and the BIC was better than between ISQ0 and the BIC. Finally, the errors made on the UI estimation were around 3 times lower than errors on the ISQ, thus confirming the better performances of QUS compared to RFA.

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17.5

Conclusion

This chapter summarized in vitro, in silico and in vivo studies showing the potential of QUS methods to investigate the properties of the BII. In particular, the development of an ultrasonic device that could be used to determine dental implant stability was described, and comparisons with the RFA technique highlight the better sensitivity and precision of QUS. In the future, clinical studies would be needed to further validate this QUS device. Moreover, implant stability remains for the moment difficult to precisely define (Mathieu et al., 2014; Haïat et al., 2014). Therefore, clinical trials could help to define a target value for the ultrasonic indicator above which an implant can be considered as stable enough to be loaded. Acknowledgments This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement no 682001, project ERC Consolidator Grant 2015 BoneImplant).

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Adaptive Ultrasound Focusing Through the Cranial Bone for Non-invasive Treatment of Brain Disorders

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Thomas Bancel, Thomas Tiennot, and Jean-François Aubry

Keywords Abstract

Focused ultrasound holds great promise in therapy for its ability to target noninvasively deep seated tissues with nonionizing therapeutic beams. Nevertheless, brain applications have been hampered for decades by the presence of the skull. The skull indeed strongly reflects, refracts and absorbs ultrasound, which defocuses the therapeutic ultrasound beams. In this chapter, we will first show how the structure of the skull impacts the ultrasound beams and how it narrows the frequency range that can be envisioned for transcranial therapy. We will then introduce different methods that have been developed and optimized to compensate the defocusing effect of the bone. Finally, we will provide an overview of past, current and future treatments of brain disorders.

T. Bancel · T. Tiennot · J.-F. Aubry () Physics for Medicine Paris, INSERM U1273, ESPCI Paris, PSL University, CNRS UMR 8063, Paris, France e-mail: [email protected]; [email protected]; [email protected]; [email protected]

Therapeutic ultrasound · Transcranial focusing · Aberration correction · Brain disorders

18.1

Acoustical Properties of the Skull

Diagnostic ultrasound devices systems use a constant speed of sound when reconstructing echographic images and assume that ultrasound beams are not distorted by soft tissues (Szabo, 2004). Soft tissues are thus considered to be homogeneous with acoustically relevant parameters (local density and sound speed) close to those of water. This legitimate assumption does not hold anymore when dealing with transcranial ultrasound, as discovered during the first attempts of ultrasound brain imaging (White et al., 1968). First, there is a large change in acoustic velocities between soft and skull tissues (about 1500 m.s−1 versus 3000 m.s−1 respectively). This huge impedance mismatch at skin/bone and bone/dura mater leads to the reflection and the refraction of the incident beam (see Table 18.1). Skull bone by itself is also heterogeneous (see Fig. 18.1). It is composed of a porous trabecular region (the diploë) surrounded by two dense cortical layers (inner and outer tables). This complex

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 P. Laugier, Q. Grimal (eds.), Bone Quantitative Ultrasound, Advances in Experimental Medicine and Biology 1364, https://doi.org/10.1007/978-3-030-91979-5_18

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Table 18.1 Acoustical and thermal properties of skull bone and soft tissue (Constans et al., 2018)

Skull bone Soft tissue

Density (kg.m−3 ) 1850 1000

Sound speed (m.s−1 ) 2400 1500

Absorption (Np.m−1 .MHz−1.18 ) 31 2.4

Specific heat (J.kg−1 .K−1 ) 1300 3600

Thermal conductivity (W.m−1 .K−1 ) 0.4 0.528

Fig. 18.1 Picture of an ex-vivo human skull. The human skull is made of two dense cortical regions (inner and outer tables) surrounding a more porous region named diploë.

The thickness of the diploë varies between individuals and between regions of the same skull (see highlighted dashed region)

organization of the skull bone is the result of thousands of years of evolution to protect our brain from mechanical shocks. Unfortunately, it also affects mechanical waves like ultrasound. The speed of sound ranges between 1500 m/s in the liquid phase of porous regions and 3000 m/s in dense cortical regions (Fry & Barger, 1978). Local density ranges between 1000 kg/m3 and 2200 kg/m3 in the aforementioned regions (Fry & Barger, 1978). On one hand, the inner and outer tables have a very low porosity. Their pore size is ranging between 50 and 100 μm. For typical frequencies used in transcranial ultrasound (250 kHz to 2.25 MHz), this pore size is negligible compared to the ultrasonic wavelength in the bone

(around 3 mm at 1 MHz) and these two cortical layers can be seen as a relatively homogeneous medium for the incident wave. On the other hand, this assumption is no longer true for the trabecular layer (diploë). Pore sizes are large enough (typically 1 mm diameter) compared to the wavelength and the acoustic propagation is influenced by this inner structure of the skull bone (Aubry et al., 2003). As a result, incident waves with varying frequencies do not interact with the skull in the same manner. To illustrate this, two-dimensional numerical simulations were carried at different frequencies (see Fig. 18.2). The fluid and linear code of the k-Wave toolbox was used to model the transcranial propagation (Maimbourg et al.,

18 Adaptive Ultrasound Focusing Through the Cranial Bone for Non-invasive Treatment of Brain…

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Fig. 18.2 Two-dimensional numerical simulation of transcranial propagation without phase compensation for a focused transducer. The targeted area is marked by a cross. A 10-periods sinusoidal burst propagates for different frequencies (220 kHz, 660 kHz, 1 MHz and 2.25 MHz). The pressure field is displayed at different

time step during the propagation (left to right black dashed area). The resulting acoustic intensity field is also provided (red dashed area). These simulations show that the skull alters the propagation by scattering and attenuating the incident beam

2020; Robertson et al., 2017; Treeby et al., 2016). Wavelengths shorter than 1 mm in water (corresponding to frequencies higher than 1.5 MHz) will thus strongly interact with the diploë and suffer from multiple scattering by the diploë and absorption along the total scattered path within the skull. On the contrary, wavelengths larger than 1 mm (corresponding to frequencies lower than 1.5 MHz) will be less affected by the skull. Snapshots of the propagation of the wavefront are displayed on Fig. 18.2 (left panel) for the four frequencies ranging from 220 kHz (top row) to 2.25 MHz (bottom row) at different time-points: a few microseconds after emission (left), when the wave reaches the skull (middle) and when the wave reaches the target (right). The temporal maximum intensity recorded in a sagittal view is

displayed on the right panel. The four frequencies are representative of the frequencies used in transcranial therapy for the past 20 years: a 220 kHz clinical system is currently used to open the blood brain barrier (Mainprize et al., 2019), a 660 kHz clinical device has been approved for thalamotomy in North America, Europe and Asia (Chang et al., 2018; Elias et al., 2016; Jeanmonod et al., 2012), a MR guided 1 MHz prototype was developed (Gateau et al., 2009) and tested on cadavers (Chauvet et al., 2013), and most diagnostic transcranial devices operate at 2.25 MHz (Martin et al., 1994; Tortoli et al., 2009; Yang & Wang, 2008). Another consequence is that mode conversion, acoustic scattering (reversible phenomenon) and absorption (irreversible phenomenon) occur in

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Fig. 18.3 Speed of sound (c) and density (b) maps derived from Computed tomography scans (a)

the diploë leading to a higher attenuation than in the cortical layers. Scattering is the predominant phenomenon leading to the attenuation of the incident beam (Fry & Barger, 1978; Pinton et al., 2011a). In 1978, Fry et al. published extensive experimental results on the acoustic scattering properties of the diploë as well as the sound velocity, dispersion and attenuation in both cortical and trabecular regions (Fry & Barger, 1978). This pioneering work is still a benchmark today, providing access to the acoustic parameters of the human skull bone. It is also to note that the skull bone geometry and the acoustic properties vary across its regions and from one individual to another (see Fig. 18.3). All these aspects make the human skull bone a complex barrier to be crossed by an ultrasonic wave. The phase aberrations and attenuation due to the propagation through the skull remains a challenge to overcome when delivering therapeutic and imaging beams into the brain. To compensate for these distortions, Phillips et al. (1975) introduced in 1975 the idea of adaptive focusing by applying a phase correction to the ultrasonic beam. It will be developed in the next section.

18.2

Focusing Ultrasound to the Brain

18.2.1 Concept of Aberration Correction Three strategies have been proposed to circumvent the defocusing effect of the skull bone presented in the previous section. The first one is

drastic: perform a partial craniotomy and thus remove the skull bone in front of the emitting surface of the transducer. This approach was first used in the 1940s to perform lobotomies (Lindstrom, 1954) and it is currently used to perform ultrasound – enhanced chemotherapy delivery for glioblastoma treatments (Carpentier et al., 2016). The second strategy consists in decreasing the frequency of the ultrasound. As explained in previous section, frequencies lower than 250 kHz are scarcely affected by the skull. As the absorption in the brain decreases with frequency, inducing thermal lesions without cavitation is challenging for such low frequency ultrasound (Xu et al., 2015a) but a 220 kHz system is currently used to perform ultrasound–enhanced drug delivery in the brain (Abrahao et al., 2019). The third method consists in beamforming the therapeutic beam in order to compensate the distortions induced by the cranium. This method requires the use of programmable multi-element transducers. As explained before, the speed of sound in the skull is higher than in soft tissues. The wavefront is thus accelerated when crossing the thickest parts of the skull. The element transducers located in front of a thick portion of the skull are thus programmed to emit the acoustic wave after the ones located in front of a thin portion, so that all the beams intersect at the same time at focus. More precisely, the exact timing can be adjusted with a time reversal method (Pernot et al., 2007): (i) a needle hydrophone is first inserted at the intended target (by taking advantage of a biopsy needle for example (Aubry et al., 2003)); (ii) the hydrophone records each of the signals emitted one by one by the elements of the therapy

18 Adaptive Ultrasound Focusing Through the Cranial Bone for Non-invasive Treatment of Brain…

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Fig. 18.4 Numerical simulation of transcranial propagation with phase compensation for a focused transducer. The targeted area is marked by a cross. The parameters used in the simulations of Fig. 18.3 were kept except that a time-reversal correction was added. By tuning the

phase and the amplitude of the incident pressure field, the aberrations due to the transcranial propagation are corrected and a precise focusing is obtained behind the skull

transducer (thanks to spatial reciprocity, it corresponds to the signals that would be recorded by each element of the transducer if the hydrophone was emitting an acoustic burst); (iii) the set of signals recorded during phase (ii) is time reversed and re-emitted by the therapy transducer; (iv) the corresponding wave front refocuses back to the initial target as if the movie of the propagation in step (ii) was played backward. The efficiency of a time reversal correction is illustrated in Fig. 18.4 for four different frequencies: snapshots of the propagation of the corrected wavefront can be seen on the left panel at different time-points: a few microseconds after emission (left), when the wave reaches the skull (middle) and when the wave reaches the target (right). For sake of direct comparison, the same parameters were used

in Figs. 18.2 and 18.4 except for the additional phase correction. The temporal maximum intensity recorded in a sagittal view is displayed on the right panel: one can see that a good focusing is restored for each frequency.

18.2.2 Non-invasive Correction Taking advantage of brain biopsies to introduce a needle hydrophone in the brain and thus estimate the aberrations held promises and enabled to induce thermal lesions in the brain (Pernot et al., 2007). Nevertheless, such a protocol based on a biopsy never led to a clinical device because of its invasiveness and its specificity to brain tumors; but also because a non-invasive approach

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was developed in parallel. Instead of inserting a hydrophone in the brain at the target location, it consists in simulating numerically the propagation of the ultrasound beam between the target and the therapeutic transducer. The first proof-of-concept of non-invasive correction was published in 1998 (Sun & Hynynen, 1998) and validated on a human cadaver skull (Clement et al., 2000). The skull was modeled as a homogeneous medium whose shape and thickness was extracted from MR images. Acoustic simulation through the skull was performed with a ray-tracing algorithm. When implemented experimentally, Sun et Hynynen (Hynynen & Sun, 1999) performed transcranial focusing through a cadaver skull using a 1.1 MHz transducer composed of 72 elements. They managed to increase the energy at target by +6 dB as compared to no correction, hence making possible non-invasive thermal ablation in deep-brain regions through an in vitro human skull (Clement et al., 2000). This initial proof of concept was followed by more than 20 years of intensive research in order to refine the skull modelling and increase the energy at target. The first improvement was to change the imaging modality to CT scans instead of MR images in order to capture the heterogeneities of the human skull (Aubry et al., 2003; Clement & Hynynen, 2002). Current clinical transcranial devices rely on pre-treatment CT scans (Chang et al., 2016; Jung et al., 2019), even though recent developments on MR bone imaging allow to image the heterogeneities of the skull structure and hence get rid of any ionizing imaging modality and go back to MR-based correction (Miller et al., 2015; Wintermark et al., 2014). Several mappings were developed (Connor et al., 2002; McDannold et al., 2019; Pernot et al., 2001; Pichardo et al., 2011) to derive the density, speed of sound and attenuation coefficients inside the bone from the skull’s CT and those derived acoustic parameters were incorporated into more sophisticated acoustic propagation algorithms. In 2003, Aubry et al. (2003) developed a fullwave 3D finite difference algorithm numerically solving the linear acoustic wave equation in a heterogeneous absorbing media. Using a linear transducer composed of 128 elements operating

T. Bancel et al.

at 1.5 MHz, Aubry et al. increased the energy at target by 9.4 dB as compared to no-correction. In 2009, Marquet et al. (2009) confirmed those results using a transducer made of 300 elements distributed on a spherical transducer and operated at 1 MHz (radius of curvature 14 cm and aperture 19 cm). Since 2010, several refinements and improvements in the methodology have been achieved in order to improve the performance of the aberration correction and increase the energy focused at target. Algorithms have been tested on cadaver skulls positioned in front of the therapeutic transducer (Almquist et al., 2016; Jin et al., 2020; Maimbourg et al., 2020; Marquet et al., 2009; Marsac et al., 2017) replicating as closely as possible the clinical setups. Instead of comparing the energy restored at target with correction to the energy measured at target without correction, performance have been more and more frequently described as the ratio of the energy restored at target with correction compared to the maximum energy that would be restored if a perfect simulation were achieved, i.e. the energy restored at target with a hydrophone-based correction. Two main algorithms have thus been continuously improved in the literature: numerical resolution of the differential equations governing the wave propagation inside the skull, and heterogeneous angular spectrum simulations. So far, the first approach has exhibited the best performance. With an optimized 3D-finite difference algorithm, Marsac et al. (Marsac et al., 2017) achieved 86% pressure restoration as compared to hydrophonebased correction with a 512-element transducer operated at 900 kHz. Maimbourg et al. (Maimbourg et al., 2020) increased the performance to 90% with the same 512-element transducer with a 3D printed skull positioning setup and using a pseudo-spectral resolution scheme of the waveequation inside the skull bone (Robertson et al., 2017). In such resolution scheme, the 3D spatial derivative of the wave-equation is computed in the spectral domain (Treeby et al., 2016). Angular spectrum methods decrease the simulation time with computation taking a few millisecond to perform (Schoen & Arvanitis, 2020). However, at the time of writing, the best pub-

18 Adaptive Ultrasound Focusing Through the Cranial Bone for Non-invasive Treatment of Brain…

lished angular spectrum algorithms have a lower efficiency: only 70% of the pressure at target has been restored so far, as compared to hydrophonebased correction (Almquist et al., 2016). Current algorithms used in clinic model the skull as a fluid and non-linear effect are not taken into account. Room for improvement in algorithm performance lies in modelling the skull as an elastic solid in order to incorporate shear-wave propagation inside the skull, as well as taking into account non-linear effects. Shear-wave propagation inside the skull is known to play a significant role when the incident angles of the ultrasound beams at the skull surface reach values higher than 20◦ (Clement et al., 2004; Hayner & Hynynen, 2001). To model shear-waves in numerical simulations, several groups have worked on experimentally assessing the transverse speed of sound and attenuation inside the bone (Pichardo et al., 2017; Pinton et al., 2011a; White et al., 2006). However, so far, those approaches have been tested numerically only on 3D finite difference algorithms solving the viscoelastic wave equation (Pichardo et al., 2017; Pichardo & Hynynen, 2007; Pulkkinen et al., 2014; Treeby et al., 2014; Treeby & Saratoon, 2015). Non-linear effects such as dispersion from single frequencies into higher order harmonics (Pinton et al., 2011b) have been investigated by solving differential equations modelling non-linear effect inside the skull such as the Westervelt equation (McDannold et al., 2019) or the Khokhlov-Zabolotskaya-Kutznetsov equations (Pinton et al., 2009, 2011b). Skullguided wave generation into cortical bone layers from recombination of dispersed and differently converted waves can also occur and will be discussed in detail in Chap. 19 of this book (guided waves in the skull). However, even if none of these approaches has been used for transcranial aberration correction to date, the accuracy of the modeling of the propagation was good enough to yield to the treatment of brain disorders, as described in the next section. This chapter focuses on the impact of bone properties on transcranial focusing. We thus focused on the methods developed to concentrate acoustic waves through the cranial bone. These

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methods were successfully tested experimentally thanks to the development of multi-element transducers (Ebbini & Cain, 1989; Hynynen et al., 2006a; Pernot et al., 2003) driven by multichannel electronics (Aubry et al., 2010; Hynynen et al., 2006a; Martin et al., 2021). Such systems are expensive and current technological developments tend to decrease dramatically the cost by achieving adaptive transcranial focusing with an acoustic lens affixed to a single element transducer (Brown et al., 2020; Ferri et al., 2019; Jiménez-Gambín et al., 2019; Maimbourg et al., 2018, 2019). Of course, without delving into substantive details, clinical translation would not have been possible without extensive preclinical development and testing on phantoms (Eames et al., 2015; Paquin et al., 2013; Wintermark et al., 2014), large animal models (Elias et al., 2013b; Gateau et al., 2011; Hynynen et al., 2006b; Marquet et al., 2013; McDannold et al., 2003; Pernot et al., 2004; Xu et al., 2015b), and cadavers (Chauvet et al., 2013; Eames et al., 2014; Monteith et al., 2013).

18.2.3 Treatment of Brain Disorders Using Focused Ultrasound In parallel of 20 years of academic research on improving the aberration correction, one industrial company manufactured the first clinical device approved for thalamotomy using noninvasive transcranial focused ultrasound. The first-in-man MR-guided non-invasive ultrasound thalamotomy was performed in 2009 on patients suffering from chronic pain (Martin et al., 2009). The transducer was made of 1024 elements operating at 650 kHz and its hemispherical shape was derived from the first proof-of-concept published in 2000 (Clement et al., 2000). The transcranial aberration correction was performed using a proprietary ray-tracing algorithm based on CT images. Chronic pain is challenging to treat and the pain rarely disappears: it may decrease but it can also change and is thus difficult to assess. The tremor of Essential Tremor patients can be more reliably assessed and has been successfully treated with a focused ultrasound thalamotomy.

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Fig. 18.5 Screenshots from the clinical software used by the neuro-surgeon during an MR guided focused ultrasound transcranial treatment. (a) Coronal view of the patient. MR is registered with the CT (green overlay). The surgeon can move the yellow cross to assess the evolution of the temperature at that point during the sonication. (b) temperature monitoring during the sonication at the yellow cross positioned in (a). In green, the temperature is averaged over the neighboring voxels. During the first

11 s, ultrasounds are emitted and the temperature rises. After sonication, the temperature slowly decreases back to 37 ◦ C. (c) cavitation control. Eight large-band passive detectors located on the probe compute the spectrum of the received signal in real time. The treatment is stopped if peaks at half the treatment frequency (i.e. 330 kHz) are detected. (d) applied phase correction at the transducer level (in degrees)

The first clinical trials demonstrated a 70% reduction of the tremor score (Chang et al., 2018; Elias et al., 2013a, 2016; Gallay et al., 2018) and the treatment is now available worldwide and reimbursed in the USA (Foley et al., 2013). An example of such a treatment is displayed in Fig. 18.5 using 600 acoustic watts for 11 s. The estimated deposited energy at focus was 594 J and it yielded to a maximum peak temperature of 63 ◦ C, as measured by MRI thermometry (Fig. 18.5b). The phase correction applied to the 1024 element transducer is displayed in (Fig. 18.5d). Eight passive cavitation detectors monitor the treatment and their spectrum is displayed in real time (Fig. 18.5c). The system is automatically halted if the 330 kHz subharmonic (signature of acoustic cavitation) exceeds the safety threshold. After these firsts treatments, clinical trials followed to expand the thermal treatment to other pathologies, such as Parkinson’s disease (Martínez-Fernández et al., 2018; Moosa et al., 2019), brain tumors (Coluccia et al., 2014) or epilepsy (Abe et al., 2020). Non-thermal therapies have also been developed, such as blood brain barrier opening to deliver chemotherapy (Liu et al., 2010; Mainprize et al., 2019; Mei et al., 2009; Treat et al., 2007) or neuroactive drugs (Constans et al., 2020; McDannold et al., 2015) to

the brain or such as ultrasonic neuromodulation to trigger motor movements (Kamimura et al., 2016; Kim et al., 2012; Tufail et al., 2010; Yoo et al., 2018; Younan et al., 2013), change behavior (Deffieux et al., 2013; Folloni et al., 2019; Fouragnan et al., 2019; Kubanek et al., 2020; Verhagen et al., 2019; Wattiez et al., 2017) or stop seizures (Hakimova et al., 2015; Li et al., 2019; Min et al., 2011). These non-thermal therapies are very promising but their mode of action are beyond the scope of this book.

18.3

Conclusion

All the clinical applications of ultrasonic transcranial brain therapy discussed in this chapter have been made possible by a better understanding of the effect of the skull on ultrasound beams and by a better modeling of the propagation of ultrasound through the complex structure of the cranial bone. The technological breakthroughs that led to transcranial ultrasound focusing opened new avenues in ultrasonic brain therapy (Aryal et al., 2014; Blackmore et al., 2019; Konofagou et al., 2012; Deffieux et al., 2018) and brain imaging (Osmanski et al., 2014) that are currently revolutionizing the field of neuroscience (Rabut et al., 2020) and neurology (Piper et al., 2016).

18 Adaptive Ultrasound Focusing Through the Cranial Bone for Non-invasive Treatment of Brain… Disclosure of Interests Thomas Bancel and JeanFrancois Aubry received a grant from the company Insightec (Tirat Carmel, Israel).

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Guided Waves in the Skull

19

Héctor Estrada and Daniel Razansky

Abstract

Skull bone is the main obstacle for transcranial ultrasound therapy and imaging applications. Most efforts in characterizing ultrasonic properties of the skull have been limited to a narrow frequency range and normal incidence. On the other hand, acoustic guided waves in plates have been used in non-destructive evaluation of materials and also to assess the strength of long bones. Recent work has likewise revealed the existence of skull-guided waves (SGWs) in mice and humans when performing measurements over a broad range of frequencies and incidence angles. Here we provide an overview on the recent progress in our understanding on the propagation of SGWs, describe the measurement techniques used to detect SGWs, the experimental observations, and the accompanying modeling efforts. Finally, the outstanding challenges to harness SGWs in applications such as transcranial therapy, H. Estrada () · D. Razansky Institute of Pharmacology and Toxicology and Institute for Biomedical Engineering, University of Zurich, Zurich, Switzerland Institute for Biomedical Engineering and Department of Information Technology and Electrical Engineering, ETH Zurich, Zurich, Switzerland e-mail: [email protected]; [email protected]

imaging, and cranial bone assessment are discussed. Keywords

Skull · Bone characterization · Lamb waves · Rayleigh waves · Optoacoustics · Laser ultrasound · Transcranial ultrasound · Near-field · Laser vibrometry · Leaky waves

19.1

Introduction

The skull consists of a solid multilayered bone structure (Fig. 19.1) that encapsulates the brain to protect it from injuries, setting the intracranial pressure equilibrium and defining functional and anatomical properties of a living organism. Two cortical bone layers sandwich a small amount of calvarian vessels and bone marrow in the juvenile mouse (Fig. 19.1c) or a thick layer of trabecular bone in humans (Fig. 19.1d). Focused ultrasound therapy deep inside the human brain (Coluccia et al., 2014; Elias et al., 2016) would not have been possible without knowledge about the interaction of ultrasound waves with the human skull (see Chap. 18 of this book for more details). However, this knowledge is still incomplete, mostly due to the incredible experimental and modeling challenge posed by a curved multilayered solid with multiscale porosity such as the skull. The

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 P. Laugier, Q. Grimal (eds.), Bone Quantitative Ultrasound, Advances in Experimental Medicine and Biology 1364, https://doi.org/10.1007/978-3-030-91979-5_19

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Fig. 19.1 Skull structure. Comparison between the structure of mouse (a) and (c) and human skull (b) and (d). Due to the large difference in size, the internal skull structure

can differ substantially among individuals and varies also with age. (Mouse skull cross section courtesy of Johannes Rebling)

standard tools deployed to study ultrasound transmission through the skull have not significantly evolved over the last 40 years (Fry & Barger, 1978). In the classical setting, an ultrasound emitter of variable size generates ultrasound waves at a single frequency (Clement et al., 2004), discrete harmonics (White et al., 2006), or narrow frequency band (Pinton et al., 2012). The emitted wave impinges perpendicularly upon the skull or at varying angle to be finally detected by a needle hydrophone (see Table 19.1). The main analysis tools and models employed revolve around plane waves, neglecting internal skull reflections (Clement et al., 2004; White et al., 2006) or full wave finite-difference numerical approaches (Pichardo et al., 2017; Pinton et al., 2012) considered at normal incidence or at discrete angles. Under the simplified plane wave approach, the transcranial ultrasound problem is separated into two regimes governed either by longitudinal- or transverse waves depending on the incidence angle (Clement et al., 2004; Pichardo et al., 2017; White et al., 2006). Whilst this perspective is

accurate for a single fluid-solid interface, it does not properly describe a solid layer surrounded by fluid or soft tissue. Despite its physical inconsistency, this perspective has been demonstrated to be practical and accurate enough to produce an ultrasound focus in the thalamus (Coluccia et al., 2014; Elias et al., 2016). Guided waves in finite solid plates, also know as Rayleigh-Lamb waves (Royer & Dieulesaint, 2000; Viktorov, 1967), arise from multiple reflections and mode conversions of both longitudinal and transverse waves across the solid’s thickness. Therefore, neglecting either transverse waves (fluid skull) or internal reflections will turn our analysis blind to guided waves. Guided waves exist in long cylindrical bones, enabling the assessment of cortical bone thickness and stiffness in patients (Bochud et al., 2017) (see Chapter 7 (Talmant et al., 2011) for the basics on guided waves in cortical bone). However, the structure of the skull is considerably different from other types of bones (Brookes & Revell, 1998) and it deserves separate consideration.

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Table 19.1 Summary of ultrasound characterization methods of the skull bone. Some techniques employed to characterize guided waves in long bones are also included to give an historical perspective. Reference imaging of the skull sample is used for simulations or is required by the measurement technique. Laser vibrometry (LV) and nearfield (NF) measurements extend the angular coverage Source

beyond 90 degrees (see Reciprocal space diagram). HS: Human skull; MS: Mouse skull; FR: Frontal; PA: Parietal; TE: Temporal; OC: occipital; CT: X-Ray computed tomography; CW: Continuous wave; μCT: micro-computed tomography; US: ultrasound; FDTD: Finite differences time domain; SAFE: Semi-analytical finite element

Frequency (MHz), bandwidth (%) 1.6, 100

Angular coverage (deg)

Sample

Sample imaging

Modeling method

7

HS, PA

–

Analytical 3-layer, normal incidence

Fry and Barger (1978)

Electrostrictive

Clement and Hynynen (2003) Pinton et al. (2012) Moilanen et al. (2014)

Piezoelectric

0.7, CW

0-55

HS

CT

Forward plane wave, transverse waves

Piezoelectric Laser 1064 nm

1, 60

< 10

HS, PA

μCT

Full wave FDTD

0.03, 70

LV

Vallet et al. (2016)

Piezoarray

1, 120

< 60

Estrada et al. (2016) Estrada et al. (2018a) Sugino et al. (2020)

Laser 532 nm Laser 532 nm Wedge piezoelectric Piezoelectric

10, > 100

NF

1.5, > 100

NF

Cyl. bone phantom Human radius in vivo MS, FR, PA, OC HS, TE

3.5, 60

LV

Dry HS, PA, TE

0.47, 60

NF

HS, PA

Mazzotti et al. (2021a)

Skull-guided waves (SGWs) were first observed in a mouse skull (Estrada et al., 2016; Estrada et al., 2017) using laser excitation. Some preliminary numerical (Adams et al., 2017; Firouzi et al., 2017) and experimental (Firouzi et al., 2017) results on the use of SGWs for transcranial applications have shortly followed, although the nature of the waves involved in the experiments was not addressed whilst the classical transcranial experimental paradigm remained unaltered. SGWs were experimentally confirmed in a water-immersed human skull (Estrada et al., 2018a) and later on a dry human skull (Mazzotti et al., 2020, 2021b; Sugino et al., 2020). Advances in array technology for angled transcranial transmission have been reported (Kang et al., 2020) in an attempt to reproduce the high ultrasound transmission found

Semi-analytical fluid-coupled solid CT

2-D isotropic free plate waveguide

US

CT

3-layer fluid-coupled isotropic plate 3-layer fluid-coupled isotropic plate SAFE

μCT

SAFE 1 and 3 layers

US

in homogeneous solids. Recently, the classical transcranial experimental paradigm has been upgraded with near-field detector scanning and sophisticated signal processing tools that properly address the dispersive nature of SGWs (Mazzotti et al., 2021a).

19.2

Generation and Detection

19.2.1 Laser-Triggered Wave Propagation, Near-Field Hydrophone Scan The skull sample is immersed in water to mimic brain tissue loading and to ensure ultrasound wave coupling of the detector. A pulse echo scan of the skull (Fig. 19.2a) is required to accurately

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Fig. 19.2 Laser-triggered skull wave excitation setup. (a) A water immersed skull sample is scanned in two dimensions using a focused ultrasound transducer. The shape of the skull is then used to direct a hydrophone (b) scan in three dimensions, close to the skull’s surface. The

hydrophone detects the ultrasound waves generated at the inner side of the skull by a pulsed laser (10 ns duration) focused onto an optical absorber (Estrada et al., 2018a, 2017) (adapted from Estrada et al. (2018a))

map the skull’s surface. The three-dimensional scanning path for the needle hydrophone is traced based on the pulse-echo data to keep a constant distance between the detector and the skull and enable access to the skull’s near-field. Light can be converted into wideband ultrasound waves via thermoelastic effect when short laser pulses ( c0 , the wave will be radiated to the far-field at a specific angle between grazing and normal incidence. In terms of Snell’s law sin(θ) = c0 /cp , the angle θ has a real solution if cp ≥ c0 , but becomes complex otherwise, thus representing an evanescent wave.

19.5

Guided Waves in the Mouse Skull

Looking at the plate-like mouse skull structure (Fig. 19.1b), one may readily conclude that it should support SGWs. The ultrasound signals

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Fig. 19.4 Laser triggered SGWs in the mouse skull. (a) Hydrophone signals detected by a needle hydrophone in close proximity to the skull (right inset) at three instants as indicated by the labels. Leaky waves are enclosed by blue squares. The red curve has been filtered in reciprocal space to allow the visualization of the non-leaky waves. (b) Dispersion diagram showing the laser-triggered SGWs and the prediction of the 3-layer model overlaid in orange (Adapted from Estrada et al. (2017))

were measured covering the left frontal, parietal, and occipital bones (Fig. 19.4a) for the different time instants following the laser pulse (Estrada et al., 2016; Estrada et al., 2017). One can indeed observe the leaky waves (blue squares) propagating faster than the speed of sound in water and therefore, being radiated at a certain angle. The traces of the non-leaky waves, propagating at a subsonic speed, are only evident after filtering in reciprocal space (red curves). After applying a two-dimensional Fourier transform, the mode dispersion is disentangled (Fig. 19.4b). The existence of subsonic (non-leaky) modes is even clearer. In addition, the asymmetry with respect to the propagation direction is expected due to the inhomogeneous conformation of the skull. A flat 3-layered solid immersed in a fluid using

plane waves (Fig. 19.4b orange curves) provides the physical insight required to prove, for the first time, the existence of SGWs (Estrada et al., 2016).

19.6

Guided Waves in the Human Skull

Due to its structure (Fig. 19.1d), the SGWs propagation in the human skull is more complicated than in the mouse case. For a 6 mm thick human skull sample (Estrada et al., 2018a), leaky waves can be clearly identified (Fig. 19.5a), as well as waves propagating with the speed of sound of water. However, subsonic waves are obscured by many oscillations, presumably due to scattering

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Fig. 19.5 Laser-triggered SGW in human skull. (a) Space time amplitude of the signal detected by the hydrophone, scanned in close proximity to the skull. The initial time delay from the laser pulse (t = 0) is due to the elastic waves crossing through the skull bone. (b)

Measured dispersion with SGW calculation overlaid as white and light blue lines. The inset shows the zoomedin dispersion at low frequencies. The most relevant quasi Lamb and Rayleigh modes are labeled (Adapted from Estrada et al. (2018a))

events due to skull inhomogeneities. In the dispersion diagram (Fig. 19.5b), several non-leaky modes are distinguishable and in good agreement with the flat multilayered solid model predictions. The modes asymptotically approach the quasi-Rayleigh wave propagating at 1343 (m/s) at frequencies higher than 0.5 MHz. The quasiRayleigh wave is localized mostly at the outer cortical layer. How does the diploe bridge the guided modes existing in the two cortical layers is not clear from this measurements. Comparing the results from human and mouse skulls (Fig. 19.6), we can observe how the difference in structure (Fig. 19.1) is visible already in the prediction of the model. The agreement is better for the mouse skull because the model’s assumptions are closer to the real skull and due to limitations of the laser method to efficiently excite waves below 0.5 MHz. We can gain some insight in the role of the diploe by considering wedge-triggered SGWs measured in a dry skull (Mazzotti et al., 2020, 2021b; Sugino et al., 2020) (Fig. 19.7). A skull with average thickness of 5.8 mm is excited with a short pulse centered at 0.5 MHz. There

is a good agreement between the measurements and the model when there is no water coupling. The role of partial coupling (water only on the inner side of the skull) substantially changed the number of leaky modes detected by the laser Doppler vibrometer (Sugino et al., 2020) as they are readily radiated to water (Fig. 4a) instead of continue propagating through the skull. Revisiting the transcranial transmission paradigm after knowing SGW exist and deploying suitable analysis tools (Mazzotti et al., 2021a) reveals more details on the effect of the diploe on SGWs. Even at low frequencies, the single layer model fails to predict the angle of the mode by more than 10 degrees. Modeling the dispersion with 3layers provides a more reasonable prediction, although it does not provide enough information regarding which modes are effectively radiating at a given frequency. The experimental evidence suggest that even for a 7 mm thick diploe (10.1 mm total skull thickness) the radiation follows a SGW pattern and not a single interface longitudinal/transverse wave scheme (White et al., 2006).

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Fig. 19.6 Comparison between human and mouse skull results. Laser-triggered measurements from Fig. 4b and Fig. 5b in gray scale with the dispersion from a 3 layered model overlayed in red. Speed of sound in the water

represented by dashed blue line. Wavenumber (k|| ) and frequency (ω) are normalized by the skull thickness (h) to allow an adequate comparison

Fig. 19.7 Wedge-triggered SGW in a dry human skull. (a) Experimental dispersion with modes extracted by the matrix pencil method (dots) and the semi-analytical finite

element prediction (SAFE) (solid curves) overlaid. (b) Out-of-plane displacement profiles for the different modes (Reproduced from Mazzotti et al. (2021b))

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Challenges and Outlook

The discovery of SGWs represents a paradigm shift in what was previously considered common knowledge in the field of transcranial ultrasound. Internal skull reflections, that were systematically neglected, have now been reconsidered (Deng et al., 2020) to solve problems such as skull overheating during hyperthermal ultrasound therapy (McDannold et al., 2019). However, the SGW perspective does not seem to reduce complexity of the transcranial problem but rather offers an opportunity to develop more accurate, physically consistent and computationally efficient approximations beneficial for solving the outstanding challenges in the transcranial ultrasound problem. Beyond informing the established transcranial ultrasound methods, SGWs could open new application areas, particularly for shallow brain regions like the cortex. Taking advantage of SGWs for transcranial ultrasound applications implies considerable modeling challenges. For example, design of novel transducer array geometries requires physically realistic simulations. Current SGW modeling methods have not dealt with absorption losses in bone, thus it is still not clear whether leaky SGWs can be transmitted more efficiently than for conventional normal incidence case (Firouzi et al., 2017; Kang et al., 2020; Kilinc et al., 2020; Xiang-Da et al., 2018). The other aspects of attenuation and diploe scattering, should further be included to provide the transcranial transmission efficiency of the different modes and compare them to normal incidence. The effect of the scalp (Gupta et al., 2020) in the coupling of SGWs is to be further elucidated. Previous experience with cortical guided waves in long bones (Bochud et al., 2017) might be of great help. In-situ measurement of the skull’s elastic properties and its thickness could also be assessed using non-leaky SGWs to calibrate Xray CT- or MRI-based transcranial propagation simulations (Maimbourg et al., 2020; Webb et al., 2018), needed to predict the focusing in transcranial ultrasound therapy. SGWs are also a plausible mechanism for the auditory confound in ultrasound neuromodulation (Guo et al., 2018;

Sato et al., 2018; Airan & Pauly, 2018; Braun et al., 2020; Mohammadjavadi et al., 2019). Either via direct non-leaky SGW propagation or due to evanescent fields reaching the cochlea (Sugino et al., 2020), the detailed mechanism would require the analysis of the carrier (between 250 kHz and 2 MHz) and modulation frequency (from 100 Hz to 5 kHz). Despite the challenges ahead, the already established measurement and data processing techniques reviewed here together with a significant acceleration of the computational capacities in the years to come are a solid basis to continue exploring the underlying physics of the skull bone transmission and find suitable applications for the SGWs. Acknowledgments The authors acknowledge grant support from European Research Council (under grant agreement ERC-2015-CoG-682379).

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Index

A Aberration, 215, 400–401, 403 aBMD. see Areal bone mineral density (aBMD) Absorption, 63, 67, 127, 164, 179, 182–186, 329, 330, 336, 342, 398–400, 414 ABTF. see Apparent Backscatter Transfer Function (ABTF) Achilles, 13–17, 37, 41, 47 Acoustic impedance, 78, 95, 98, 163, 187, 188, 200, 229, 231, 233, 234, 319, 339, 375, 388 Adaptive beamforming approach, 62, 126 Adaptive focusing, 400 Adolescent, 36, 138, 299–305, 350, 362 AIB. see Apparent integrated backscatter (AIB) A0-mode. see Antisymmetric Lamb mode (A0-mode) Anisotropic, 3, 48, 62, 64, 65, 67, 72, 73, 83, 84, 120, 122, 128, 168–170, 200, 201, 254, 256, 261, 268, 269, 271, 273–275, 279–292, 301–305, 330, 337, 416 Anisotropic free plate model, 67 Anisotropic stiffness, 3, 67, 73, 83, 256, 268, 269, 271, 274, 279–292 Anisotropic stiffness ratio, 64 Anisotropy, 67, 122, 125, 127, 167–169, 198, 200–205, 214, 215, 218–219, 221, 228, 254, 256, 257, 261, 269, 273, 274, 283–287, 298, 302, 303, 306, 308, 312, 324, 327, 337, 339, 340, 384, 416 Anisotropy ratio, 283–287, 289 Antisymmetric Lamb mode (A0-mode), 45, 58, 62, 63, 67 Apparent Backscatter Transfer Function (ABTF), 164–166 Apparent integrated backscatter (AIB), 164–167, 169, 170, 186, 331 Areal bone mineral density (aBMD), 56, 80–82 Arthrosis, 156–157, 159 Asymptotic homogenization, 64 Athlete, 137–138 Attenuation, 2, 10–11, 19, 21, 25, 36–41, 43, 44, 49, 57, 68, 81, 85, 115, 121, 122, 128, 129, 131, 132, 134, 137, 164–166, 168, 179–189, 193, 236, 244, 247, 255, 319, 331, 336, 400, 402, 420 ATU. see Axial transmission ultrasound (ATU) Autofocus, 207, 215–219

Axial transmission, 11–12, 23–24, 36, 38, 39, 44–48, 55–86, 95–115, 179, 334 Axial transmission ultrasound (ATU), 95–115

B Backprojection, 232, 233, 235, 236 Backscatter, 2, 11, 12, 36, 46–49, 128, 139, 148, 151, 163–167, 169–170, 177, 179, 181, 182, 186–194, 201, 221, 319, 331, 332, 337, 340 Backscatter coefficient, 163–167, 179, 186–189, 319 Backscattered signals. see Backscatter Backscattered Spectral Centroid Shift (BSCS), 164, 165, 167, 169, 170 Bayesian, 126, 127, 130, 258, 265–271, 274, 282, 291–292, 310 BDAT. see Bi-directional axial transmission (BDAT) Bi-directional axial transmission (BDAT), 38, 45, 48, 59, 60, 62, 63, 70, 73, 75, 76, 78–85, 113 Bilateral laminae, 351, 359 Bilayer model, 66, 73–75 Bilayer waveguide, 65, 66, 75, 83, 112 Bindex, 12, 25, 26 Biochemistry, 314 Biomaterial, 291, 386–387 Biot, 2, 120–122, 138, 168 Biot-JKD theory, 121, 122 Biot’s theory, 2, 120–122, 168 Blood flow, 1, 197–223 Blood vessels, 120, 201, 221, 299, 300 BMD. see Bone mineral density (BMD) B-mode, 2, 47, 151, 227–229, 234, 235, 351, 352, 359, 362, 368 B-mode ultrasound imaging, 228, 229, 234, 235, 351 Bone curvature, 63, 64, 73 Bone growth, 138, 139, 198, 219, 298–302, 320 Bone-implant interface, 373–393 Bone matrix, 56, 64, 65, 78, 180, 182, 186, 187, 201, 273, 300, 301, 303, 337, 340 Bone-mimicking phantom, 71, 83, 109, 125, 128, 165, 167, 168, 229, 235, 391 Bone mineral density (BMD), 2, 7, 9–13, 17, 19, 22, 24, 25, 35, 38, 39, 43, 47–49, 56–58, 78–82, 145–146, 148–151, 153, 154, 156–159, 164, 165, 167, 169, 170, 177–179, 189, 331–337

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 P. Laugier, Q. Grimal (eds.), Bone Quantitative Ultrasound, Advances in Experimental Medicine and Biology 1364, https://doi.org/10.1007/978-3-030-91979-5

423

424 Bone quality, vi, vii, 10, 38, 56, 59, 67, 70, 76–79, 81, 83–85, 138, 148, 150, 314, 340, 351, 384, 386, 391 Bone remodeling, 198, 201, 219, 280, 299, 301 Bone strength, 1, 22, 35, 36, 39, 47, 48, 56, 138, 149, 159, 178, 194, 280, 312 Bone volume fraction (BV/TV), 43, 121, 122, 125, 127, 131, 164, 166, 167, 331 Born approximation, 229, 231, 234, 239, 242, 247 Brain, 3, 85, 330, 397–404, 411, 413, 416, 420 Brillouin scattering, 320, 329, 337–340, 375, 376 Broadband ultrasound attenuation (BUA), 11, 12, 14, 16, 18, 19, 21, 22, 37, 38, 40, 41, 47, 128, 131, 164, 167, 168, 180, 336 Broadband ultrasound backscatter (BUB), 11, 164, 167 BSCS. see Backscattered spectral centroid shift (BSCS) BUA. see Broadband ultrasound attenuation (BUA) BUB. see Broadband ultrasound backscatter (BUB) Bulk modulus, 65 BV/TV. see Bone volume fraction (BV/TV)

C Calcaneus, 2, 11, 13, 36, 37, 39, 40, 120, 125, 131, 138, 165, 167–169 Cancellous bone, 8, 36, 43, 44, 47, 119–139, 163–171, 325–329, 331, 333, 336, 339, 341 Cancellous bone density, 44, 134–139 Cancellous bone elasticity, 131, 134, 136, 138 Cancellous-bone-mimicking phantoms, 125, 165, 167, 168 Cartilage, 299–301, 340–342 CAS. see Linear combination of AIB and BSCS Case-finding, 26, 27, 47 Cauchy norm, 103, 107, 108 Child bone, 298, 299, 301–306, 308, 311–313 Children, 3, 36, 125, 138, 228, 229, 282, 291, 298–305, 309, 311, 312, 368 Chronic kidney disease, 136 Circumferential wave, 38, 42, 125 Clinical devices, 35–49, 139, 399, 401 Clinical risk factors, 13, 22–28 CNR. see Contrast-to-noise ratio (CNR) Cobb, 350–353, 355–361, 364, 367–369 Coda, 183, 186, 189 Collagen, 201, 273, 274, 279, 298, 301, 304–305, 314, 321–324, 331, 337, 341, 342 Compound-mode USCT, 240–242 Compressibility, 230 Compression, 44, 45, 48, 64, 200–206, 208, 209, 214, 215, 219, 240, 241, 243–245, 247, 262, 270, 273, 280, 306, 309, 314, 341, 377 Compression bulk wave, 64 Compression wave, 44, 45, 200–204, 206, 214, 215, 219, 240, 241, 244, 245, 262 Contrast, 45, 48, 55, 62, 66, 76, 79, 80, 82, 97, 98, 130, 136, 163, 165, 169, 198, 200, 210, 216–218, 229, 232–235, 239, 242, 272, 322, 330, 340, 341, 351, 364, 367, 414 Contrast-to-noise ratio (CNR), 234, 236

Index Conventional echography, 148 Coronal, 280, 349, 350, 352–364, 366–368, 404 Coronal deformity, 355, 357 Cortical axial transmission, 11, 23–24, 38, 39, 44–46 Cortical bone, v, vi, 2, 3, 8, 11, 12, 24, 26, 36, 42–49, 55–65, 67, 68, 70–86, 97, 102, 106, 109, 110, 113, 115, 120, 121, 125, 128–129, 131, 134–139, 177–194, 198, 200–207, 212–215, 217–219, 228, 236, 237, 243, 253–275, 280–282, 284, 286, 287, 290, 291, 297–315, 321, 324, 325, 331, 333, 334, 336–338, 340, 376, 378, 388, 390, 403, 411, 412 Cortical bone thickness, 12, 40, 109, 131, 134–139, 243, 390, 412 Cortical porosity, vi, 46, 48, 56, 57, 64, 70, 72, 76, 78, 79, 83, 178, 179, 186, 193, 194, 340 Cortical pulse-echo, 38, 39, 46–47 Cortical shell, 42, 43, 45, 56, 57, 62, 97, 106, 165, 240, 254, 281, 321 Cortical thickness, 2, 38, 39, 43, 46, 48, 49, 57–59, 63, 65, 67, 70, 72, 76, 78 Cortical transverse transmission, 11, 37, 39, 41–44 Cramer-Rao bound (CRB), 239 Cranial bone. see Skull Crazy-climber algorithm, 100 Critical angle, vi, 45, 207, 208, 218 Cross-links, 298, 312–315 Curvature, 63, 64, 73, 206, 350–352, 355–366, 368, 369, 402, 416 Cylindrical-scatterer model, 168

D DA. see Degree of anisotropy DBM Sonic, 14, 16, 17, 37, 41 Deep learning, 84, 113, 237, 238, 247 Deep neural network (DNN), 113 Defatting, 261 Degree of anisotropy, 122, 127 Delay-and-sum (DAS), 48, 199, 210, 214–216 Demineralization, 57, 85, 324, 331, 332 Denosumab, 10, 156 Density index (DI), 12, 38, 46, 47 Dentin, 254–256, 261, 270, 274, 279–287, 290–292, 386, 387 DI. see Density index (DI) Diabetes, vii, 8, 9, 340 Diabetes mellitus, 10, 136, 137 Diaphysis, 61, 78, 201, 204, 206, 208, 209, 211–213, 220–222, 240, 242, 282, 284, 285, 287, 289, 299, 300 Diffracted field, 231, 234, 241 Diffraction, 40, 164, 165, 228, 229, 232 Diffusion constant, 169, 170, 189, 190, 193 Diffusivity, 179, 189–193 Diploe, 397–400, 416, 418, 420 Dispersion, 2, 40, 48, 57–62, 64–66, 68, 72, 73, 75, 76, 85, 97–100, 102–114, 168, 339, 400, 403, 416–419 Dispersion characteristics, 57, 58, 100, 114

Index Dispersion compensation, 100 Dispersion curve imaging, 97, 108 Dispersion curve inversion, 97, 112 Dispersion curves, 59–62, 68, 73, 75, 85, 97, 98, 100, 104, 106, 108, 109, 112, 114 Dispersion equations, 64–66 Dispersion inversion, 108–113 Dispersive Radon transform (DRT), 62, 108–110 Dissipation, 121, 272 Distal radius, 11, 14, 17, 18, 24, 38, 42, 43, 45–47, 56, 60, 61, 80, 81, 113, 131, 132, 135–137, 287 Distal tibia, 38, 46, 80 DNN. see Deep neural network (DNN) DRT. see Dispersive Radon transform (DRT) 2D-spatial Fourier transform, 234 2D spatio-temporal Fourier transform, 45, 62 2D transverse isotropic homogeneous free plate waveguide, 63, 64 Dual-energy X-ray absorptiometry (DXA), 9, 10, 12–13, 21, 24–28, 35, 39, 47–49, 56, 58, 80, 82, 85, 113, 135, 136, 145–159, 169 Dual-frequency, 12, 46, 58, 165, 235 Dual frequency axial transmission, 46 3D ultrasound, 351–355, 357, 359, 360, 362, 367–369 DXA. see Dual-energy X-ray absorptiometry (DXA)

425

E Echolight, 12, 38, 47, 48 μCT. see Micro-computed tomography (μCT) Elastic constant of cancellous bone, 43 Elastic FDTD, 126–127 Elasticity, 3, 7, 10, 12, 37, 48, 64, 65, 67, 72, 77–79, 131, 134, 136, 138, 202, 206, 218, 253–275, 280, 282, 290, 291, 297–315, 329, 340 Elastic modulus, 274, 313 Electromechanical effect, 320–329 Electro-mechanical properties, 322, 323, 325 Endosteal, 46, 48, 58, 76, 77, 81, 84, 189, 191, 302, 303 Excitability, 72, 84, 112, 115 Extracellular matrix, 299, 300

260, 271, 273, 282–292, 301, 321–326, 333, 334, 339, 340, 388 FFGW. see Fundamental flexural guided wave (FFGW) Fibula, 235–237, 245, 282–287, 291, 301–305, 309–313 Finger phalanges, 24, 36, 37, 44 Finite difference, 128, 130 Finite-difference time-domain (FDTD), 67, 113, 126–128, 130, 167, 180, 182, 186, 187, 193, 327, 385, 386, 413 Finite element analysis (FEA), 128, 167 Finite element method, 416 Finite element modeling, 167 First arriving signal (FAS), 45, 57–59, 81, 336 Fluctuation of the compressibility, 230 Fluctuation of the mass density, 230 Fluid-solid bilayer waveguide model, 65, 66 Forearm, 9, 19, 42, 56, 60, 71, 109, 113 Forward problem, 73, 74, 241, 242, 244 Fracture healing, 36, 198, 324 Fracture repair, 299, 301 Fracture risk, 7–28, 36, 39, 44, 47–49, 56, 70, 76, 109, 159 Fracture risk assessment, 22, 25 Fracture risk prediction, 13–27, 36, 49, 114, 153–155 Fracture score (FS), 25 Fragility fracture, 9, 10, 25, 47–49, 82, 150, 151, 153, 154, 158, 178 Frail, 146, 149–152, 158 FRAX, 10, 22–25, 27, 146, 149–151 Free plate model, 67, 73–76, 83, 85 Frequency-dependent attenuation, 40, 49, 131, 179–180 Frequency slope of apparent backscatter (FSAB), 164–167, 169, 170 FS. see Fracture score (FS) FSAB. see Frequency Slope of Apparent Backscatter (FSAB) Full waveform inversion (FWI), 115, 229, 242–247 Fundamental flexural guided wave (FFGW), 45, 58, 59, 102, 334 Fundamental scattering mechanisms, 163 FWI. see Full waveform inversion (FWI)

F Far-field, 231, 233, 416 FAS. see First arriving signal Fast and slow waves, 40, 121, 122, 125, 127, 129–132, 167, 168 Fast Iterative Shrinkage Thresholding Algorithm (FISTA), 99 Fast wave (FW), 42, 43, 120, 122, 124, 125, 127–131, 134, 138, 167 FDTD. see Finite-difference time-domain (FDTD) FEA. see Finite element analysis (FEA) Femoral head, 341, 342 Femoral neck, 9, 11, 12, 22, 24, 25, 28, 38, 47, 48, 80, 81, 113, 136, 147–151, 153–158, 282, 283 Femur, 8, 24–26, 36, 39, 48, 49, 56, 65, 78, 80, 81, 84, 99, 120, 122, 125, 133, 136, 145–159, 167, 169, 178, 186, 189–192, 203, 238, 241, 255,

G Gamma function, 187 Genetic algorithm, 69–71, 73, 83, 111 Gestational age, 170 Global search, 70, 72, 112 Green function, 231, 240, 241 Green’s functions, 190, 233 Group velocity, 97, 98, 100, 203, 205 Group velocity filtering (GVF), 102 Guided mode filtering, 97, 101 Guided modes, 58–62, 66, 68–74, 76, 79, 84, 99, 100, 102, 106, 107, 110, 112, 418 Guided waves, 2, 3, 36, 45, 55–64, 66, 67, 70, 76, 77, 79, 80, 82–85, 96, 97, 99–102, 104, 114, 115, 411–420 GVF. see Group velocity filtering

426 H Hazard ratio (HR), 228 Head wave, 197, 208, 209, 219 Healing, 36, 98, 198, 280, 324, 330, 340, 374–376, 380, 384, 386, 388–392 Heel, 11–17, 19, 20, 24, 39, 40, 47 Heel QUS, 12, 13, 20–27 Hexagonal symmetry. see Transverse isotropic elastic symmetry High-resolution peripheral quantitative computed tomography (HR-pQCT), 133, 178 High-resolution Radon transform (HRRT), 104, 106 Hip, 2, 9, 12–14, 16, 18–25, 36, 39, 47, 48, 56, 61, 80–82, 85, 113, 136, 137, 145–148, 155, 157, 169, 170, 280, 353 Hip fractures, 19, 21–25, 36, 61, 80 Hooke’s law, 274, 275, 304, 308 HR. see Hazard ratio (HR) HR-pQCT. see High-resolution peripheral quantitative computed tomography (HR-pQCT) HRRT. see High-resolution Radon transform (HRRT)

I ICBA. see Intercepting Canonical Body Approximation (ICBA) Idiopathic scoliosis (IS), 349, 350, 359 IF. see Instantaneous frequency (IF) Imaging, 1, 12, 36, 82, 95, 157, 169, 178, 227, 261, 290, 305, 329, 349, 374, 397, 413 Impedance, 44, 78, 95, 97, 98, 163, 187–189, 200, 229, 231, 233–235, 239, 319, 339, 375, 385, 388, 397 Impedance contrast, 97, 98, 229, 235, 239 Implant, 3, 36, 280, 324, 355, 373 Implant stability, 373–375, 384–393 Independent Scattering Approximation (ISA), 168, 181–183 Infants, 36, 170, 301, 350 Inhomogeneity, 234, 235, 237, 418 Instantaneous frequency (IF), 131 Integrated Reflection Coefficient (IRC), 164, 165, 167, 186 Intercepting canonical body approximation (ICBA), 242, 243 International Society for Clinical Densitometry (ISCD), 13, 26, 153, 157 Inverse problem, 2, 62, 64, 67–68, 70, 71, 73–77, 79, 84, 97, 98, 103, 111, 180–182, 184, 188, 189, 231, 244, 247, 255, 257, 258, 260, 264, 266–271, 275, 282, 291, 309, 416 IRC. see Integrated Reflection Coefficient (IRC) ISA. see Independent Scattering Approximation (ISA) ISCD. see International Society for Clinical Densitometry (ISCD) Isotropic, 3, 45, 99, 120, 168, 191, 200, 230, 279, 298, 319, 384, 413 Isotropic plate model, 65, 67

Index J JADE. see joint approximate diagonalization of eigenmatrices (JADE) Joint approximate diagonalization of eigenmatrices (JADE), 100 Joint spectrogram segmentation and ridge-extraction (JSSRE), 101 JSSRE. see Joint spectrogram segmentation and ridge-extraction (JSSRE)

K Kirchhoff migration, 210, 211, 214 k-means, 237, 238

L Lamb mode, 45, 58, 65–69, 71, 72, 100, 108, 110, 111, 334 Lamina, 349, 351, 359, 361, 368 Laser, 256, 271, 320, 329–331, 333, 334, 336, 338, 375, 380, 381, 388, 413, 414 LD-100, 37, 43, 48, 131, 132, 134–138 Leaky wave, 66, 417 LFV. see Low-frequency velocity (LFV) Linear combination of AIB and BSCS, 164 Lippman-Schwinger, 231 LIPUS. see Low-intensity pulsed ultrasound (LIPUS) LL scattering, 164, 179 1 norm, 98, 107, 108 2 norm, 98 Longitudinal waves, 2, 58, 120–122, 130, 164, 168, 271, 272, 307, 337, 339–341 Low-frequency axial transmission, 46 Low-frequency velocity (LFV), 23 Low-intensity pulsed ultrasound (LIPUS), 324 LS scattering, 164 Lumbar lordosis, 350, 353, 361 Lumbar spine, 12, 25, 26, 56, 80, 81, 136, 145–148, 150, 151, 153–159, 169 Lumbar vertebrae, 12, 147, 148, 151, 153, 350

M Machine learning, 2, 85, 113, 115, 130 Major trabecular alignment (MTA), 122, 123, 125, 127 Marrow, 8, 62, 63, 67, 97, 120, 122, 126, 131, 163, 165, 168, 214, 228, 229, 234, 236, 241, 244, 247, 299, 300, 325, 331, 336, 337, 411 Mass density, 58, 64–66, 75, 120, 202, 203, 206, 218, 230, 236, 242–245, 247, 254, 255, 257, 258, 266, 273, 280–290, 305, 306, 339, 376, 388, 390 Material characterization, 75, 215, 319, 337, 342 Matrix. see Extracellular matrix Matrix elasticity, 77–79 Matrix stiffness, 72, 79

Index MCC-CNN. see Multi-channel crossed convolutional neural network (MCC-CNN) Mean intercept length (MIL), 122, 123 Mean trabecular thickness (Tb.Th), 164, 168 Mechanical testing, 254, 271, 273, 280, 281, 290, 298, 305 Medullary cavity, 41–43, 221, 300, 301 Micro-computed tomography (μCT), 72, 125, 126, 130, 164, 261, 305, 313, 332, 413 Microcracks, 129, 280 Microscopy, 8, 78, 166, 178, 187, 190, 325, 329, 330, 336–339, 341, 375, 377, 380, 382, 383 Microstructure, vi, vii, 2, 83, 85, 120, 122, 126, 127, 167, 177–181, 185–190, 193, 194, 198, 221, 290, 291, 301, 312–314, 324, 333, 336 Mid-tibia, 44, 57 MIL. see Mean intercept length (MIL) Mineral, vi, 2, 8, 9, 19, 35, 43, 56, 78, 79, 145, 164, 177, 179, 273, 280, 288, 299, 301, 311, 331, 334, 375 Modal filtering, 100–102 Mode conversion, 84, 100, 200, 205–207, 399, 412 MTA. see Major trabecular alignment (MTA) Multi-channel crossed convolutional neural network (MCC-CNN), 113 Multimode guided waves, 59, 62, 67–70, 75 Multiple scattering, 48, 167–169, 171, 181–183, 189, 190, 199, 200, 380, 387, 399 Multiple transmitter-receiver configuration, 97 Multiridge-based analysis, 100 Multi-wavelet decomposition, 98

N nBUA. see Normalized BUA (nBUA) Near-field, 191, 233, 413–416 Negative dispersion, 168 Neonates, 36, 170, 171 Net time delay (NTD), 38, 43 Neural network, 113, 367 Non-frail, 151, 152, 158 Non-leaky modes, 417, 418, 420 Non-linear Distorted Born Iterative Method, 242 Normalized BUA (nBUA), 41, 164, 167, 168 Norm function, 61–63, 70, 107 NTD. see Net time delay (NTD)

O Object function, 232, 233, 239, 241, 244 Objective function, 59, 68–70, 75, 84, 110–112, 115 Occupancy rate, 69, 72, 111 Odds ratio (OR), 24 Omnisense, 12, 17, 18, 23, 38, 44, 45 One-third distal radius, 45, 60, 61, 80, 81 One-third radius, 44 Opto-acoustic, 3, 319–342 OR. see Odds ratio (OR) OS. see Osteoporotic score (OS) OSI. see Osteo-Sono-assessment Index (OSI)

427 Osseointegration, 36, 280, 374–376, 378, 380, 384, 392 Osteoarthritis (OA), 156, 157, 341 Osteopenia, 109, 146, 150, 157, 177 Osteoporosis, 1, 8, 36, 55, 109, 120, 145, 177, 298, 333 Osteoporosis management, 9, 26–27 Osteoporotic score (OS), 25 Osteo-Sono-assessment Index (OSI), 38, 41 Ostu, 364 Otsu, 237, 238, 364 Overlying soft tissue, 24, 57, 59, 60, 68, 72, 334

P Parametrization, vii, 65, 82 Periosteal, vii, 46, 77, 186, 187, 191, 228, 301–303 Periosteum, 206, 211–214, 216, 219, 223, 228, 299, 301, 302 Peripheral skeletal sites, 56, 96, 135 Phalanx, 8, 14, 16–18, 24, 25, 27, 37, 38, 41, 42, 44, 311, 312 Phased array, 61, 205, 208, 209, 212, 213, 221, 329, 368 Phased-array transducer, 205, 208, 209, 212, 213, 221 Phase velocity, 41, 58, 62, 63, 67, 72, 73, 103–106, 112, 113, 125, 168, 202, 203, 219, 306 Photoacoustic, 85, 215, 320, 329–337, 342, 375 Piezoelectric, 3, 198, 256, 319–342, 413–415 Piezoelectricity, 319–323, 342 Plate model, 65–67, 73–76, 83, 85 Poisson’s ratio, 65, 273, 275, 284, 285, 306 Population screening, 158 Pore density, 178, 180–186, 189, 192–194 Pore diameter, 178, 180–183, 185–187, 189, 191 Pore size, 3, 49, 184, 188, 189, 193, 302, 314, 398 Porosity, 2, 8, 39, 56, 97, 120, 164, 177, 198, 273, 291, 301, 340, 398 Pregnancy, 158 Prescreening, 26 Prony, 126, 130 Proximal femur, 25, 36, 39, 48, 49, 56, 122, 136, 150, 152–154, 156, 167, 178, 189 Proximal tibia, 46, 47 Pseudo-spectral, 129, 402 Pulse-echo, 11, 12, 25, 36, 38, 39, 43, 44, 46–47, 73, 82, 145–159, 164, 169, 179, 227 Pulse-echo imaging, 36, 48, 82, 228 Pulse-echo radiofrequency signals, 25

Q QCT. see Quantitative computed tomography (QCT) Quality factor, 56, 146, 263, 269, 272, 309 Quantitative Computed Tomography (QCT), 133 Quantitative ultrasound (QUS), 1, 3, 7–28, 36, 38, 46, 56, 96, 102, 179, 192, 291, 334, 335, 374, 376 Quantitative ultrasound index (QUI), 11, 14, 16, 18, 19, 21, 22, 37, 38, 41 QUI. see Quantitative ultrasound index (QUI) QUS. see Quantitative ultrasound (QUS)

428 R Radiofrequency (RF), 1, 11, 25, 47, 63, 114, 385 Radiofrequency Echographic Multi Spectrometry (REMS), 11, 12, 147–148 Radius, 8, 36, 56, 96, 122, 203, 228, 254, 282, 301, 402, 413 Radon, 102–105, 110, 229, 230, 239 Radon transform, 62, 102, 104, 106, 108, 109, 230, 232 Real-time imaging, 115, 211, 214–215 Reference point indentation, 56 Reflection, 10, 36, 43, 45, 46, 96, 165, 186, 189, 205–209, 211, 215, 216, 218, 219, 229, 234–236, 239, 240, 338, 374, 378, 379, 381, 397, 412, 414, 415, 420 Reflection coefficient, 165, 186, 207, 217, 377–384 Refraction, 48, 200, 206, 212–214, 235, 240, 397 REMS. see Radiofrequency Echographic Multi Spectrometry (REMS) Resonance frequency analysis (RFA), 374, 375, 389–393 Resonant ultrasound spectroscopy (RUS), 3, 203, 204, 253–275, 279–292, 308–312 Resorption cavities, 76, 81, 84 RF. see Radiofrequency (RF) Risk assessment, 22, 25, 47, 59, 84, 136, 159 Risk assessment tools, 146 Roughness, 240, 376–384

S SAFE. see Semi-analytical finite-element (SAFE) Sagittal, 349, 350, 352, 353, 355, 359, 361, 362, 368, 399, 401 Sagittal curvature, 350, 352, 359 Sahara, 15–17, 37, 41, 47 Sawbone, 229, 235, 271 Scanning acoustic microscopy (SAM), 78, 79, 178, 187, 189–192, 337, 339, 340 Scattering, 2, 3, 36, 47, 48, 77, 86, 126, 130, 163–171, 177–194, 200, 210, 216, 234, 237–239, 270, 272, 320, 329, 331, 336–342, 375, 376, 380, 381, 387, 399, 400, 416, 417, 420 Scattering cross-section, 182 Scattering mean free path, 169, 179 Scolioscan, 351–368 Scoliosis, 3, 349, 350, 353, 355, 359, 362, 363, 367, 369 Segmentation, 101, 148, 150–152, 214, 236, 237, 364, 366 Semi-analytical finite-element (SAFE), 84, 111–113, 413, 416, 419 Shear, 64, 65, 202, 208, 243, 256, 261, 262, 269–275, 282–284, 286, 288, 289, 291, 312, 314, 321, 323, 338 Shear wave, 2, 36, 66, 126, 131, 164, 197, 200–204, 206, 217, 219, 239–241, 244, 247, 262, 270–272, 280, 290, 306, 307, 309, 380, 403 Short time Fourier transform (STFT), 98–100 SI. see Stiffness index (SI) SimSonic, 187, 191, 208, 385 Single scattering, 165–168, 171 Single Transmitter-Receiver Configuration, 97–102

Index Singular value decomposition (SVD), 61–63, 104, 107, 108, 110, 113, 219, 221, 415 Singular values, 61, 107 Singular vectors, 61, 107 Skull, 3, 8, 85, 120, 299, 330, 397–404, 411–420 Slow wave, 40, 120–122, 125, 127–132, 134, 138, 167, 168 Smoothed-pseudo Wigner-Ville (SPWV), 98 Soft tissue, 1, 24, 40, 57, 95, 156, 165, 186, 198, 228, 320, 378, 397, 412 Soft tissue coating, 63, 64, 76 SOS. see Speed-of-sound (SOS) SoundScan, 38, 44 Sparse SVD (SSVD), 62, 106–108, 110 Sparsity, 68, 70, 98, 99, 106 Spectra, 1, 40, 41, 47, 97–100, 104, 108, 110, 113, 129, 148–152, 164, 165, 186, 187, 262, 264–265, 274, 330, 333, 334, 336, 337, 341, 342, 402 Spectra models, 47, 148–152 Spectroscopy, 329, 330, 337, 338 Speed of sound (m/s), 131 Speed-of-sound (SOS), 10, 11, 19–21, 38, 40–42, 45, 57, 62, 128, 132, 178, 186, 199, 200, 206, 280, 311, 336, 397, 398, 400, 403, 416, 417, 419 Spinal curve, 350, 359, 360, 364 Spinal flexibility, 359 Spine, 2, 9, 36, 56, 113, 136, 146, 169, 349 Spine phantom, 351–353, 359, 368 Spinous process, 349, 351–364, 366, 367 SPWV. see Smoothed-pseudo Wigner-Ville (SPWV) SSVD. see Sparse SVD (SSVD) STFT. see Short time Fourier transform (STFT) Stiffness coefficient, 64–66, 82, 108, 254, 256, 260, 261, 265–267, 269–271, 274, 280, 281, 305, 306, 308–314 Stiffness index (SI), 11, 14, 16, 18–22, 37, 38, 41 Stiffness tensor, 64, 65, 255, 272, 274, 281, 282, 290, 304 Strain gradient elasticity, 67 Stratified bone model, 131 Support vector machine (SVM), 85, 113, 114 SVD. see Singular value decomposition (SVD) SVM. see Support vector machine (SVM) SWT. see Synchrosqueezing wavelet transform (SWT) Synchrosqueezing wavelet transform (SWT), 100, 101 Synchrotron radiation, 261

T TBS. see Trabecular Bone Score (TBS) Tb.Th. see Mean trabecular thickness (Tb.Th) Teeth, 282, 284, 288, 330 TFR. see Time-frequency representation (TFR) Thalamotomy, 399, 403 Therapeutic monitoring, 156 Thickness of cortical bone, 12, 109, 131, 135–139, 243, 412 Thoracic kyphosis, 350, 359, 361 Three-dimensional ultrasound, 3 TI. see Transmission Index (TI)

Index Tibia, 11, 36, 57, 96, 120, 147, 178, 203, 228, 254, 282, 301, 324, 376 Tikhonov regularization process, 244 Time-Distance Matrix, 182 Time-frequency representation (TFR), 98, 100, 101 Time-of-flight (TOF), 40, 42, 57, 58, 62 Time reversal, 400, 401 Toeplitz matrix, 107 TOF. see Time-of-flight (TOF) Tomography, 2, 39, 72, 110, 125, 178, 228, 261, 330, 400, 413 Tortuosity, 121 τ -p transform, 102–104 Trabeculae, 12, 38, 120, 122, 128–133, 163, 164, 168, 182, 299, 300, 333, 339, 377 Trabecular bone, 2, 8, 11, 24, 27, 43, 47, 55, 79, 125, 128, 177, 179, 181, 182, 291, 302, 332, 338, 339, 341, 342, 377, 388, 390 Trabecular Bone Score (TBS), 10, 27, 246 Trabecular network, 43, 120, 129 Trabecular pulse-echo, 39, 47 Trabecular transverse transmission (Tr.TT), 11, 37, 39–41 Transcranial, 397–399, 401–404, 415, 418, 420 Transfer function, 164, 188, 231, 232, 234, 264 Transmission, 10, 36, 56, 96, 122, 179, 198, 229, 306, 334, 388 Transmission coefficient, 207, 217, 388 Transmission Index (TI), 38 Transverse isotropic elastic symmetry, 283 Transverse isotropy. see Transverse isotropic elastic symmetry Transverse transmission, 11, 13, 36, 43, 47 Trochanteric fracture, 136 T-score, 9, 12, 24–28, 38, 56, 153–158 Two-dimensional Fourier transform, 102, 415, 417 Two-phase composite material, 64 Two-wave phenomenon, 2, 119–139

U UBPS. see Ultrasound Bone Profile Score (UBPS) UGW. see Ultrasonic guided waves (UGW) UGW inversion, 97 Ultradistal radius, 82 Ultrascan, 37, 42 Ultrasonic guided waves (UGW), 85, 96–102, 104, 108, 109, 113, 114 Ultrasound Bone Profile Score (UBPS), 37, 38 Ultrasound computed tomography (USCT), 227–247

429 USCT. see Ultrasound computed tomography (USCT)

V Velocity dispersion, 2, 98, 104, 339, 400 Vertebrae, 8, 12, 120, 122, 147, 148, 151–153, 155, 156, 169, 299, 349–356, 361, 364, 368, 369 Viscoelastic. see Viscoelasticity Viscoelasticity, 271–274, 342 Viscosity, 120, 129, 272 Voigt notation, 274, 283, 304

W Waveguide, 57–59, 62, 66–68, 72–77, 79, 83, 84, 96, 97, 110, 112, 413 Waveguide model, 62–67, 70, 71, 73, 75–77, 81–85, 114 Waveguide modeling, 62–70, 72, 114 Wavelet, 97, 98, 237, 238, 245, 364 Wavelet-based Coded-Excitation (WCE), 236 Wavelet decomposition, 98, 99, 237 Wavelet transform (WT), 99, 130 Wavenumber, 57, 60–63, 65, 70, 73, 97, 102, 107–109, 111, 113, 182, 187, 382, 419 Wave number, 182, 231 Wave-speed. see Wave velocity Wave velocity, 44, 64, 65, 67, 73, 121, 122, 179, 218–219, 228, 230, 233, 234, 240, 241, 243–245, 247, 254, 258, 266, 269, 271, 280–282, 306, 307, 319, 337–341, 375, 380, 382, 388 WCE. see Wavelet-based Coded-Excitation (WCE) WDR. see wideband dispersion reversal (WDR) Weak scattering, 234 Weak scattering model, 163 Wideband dispersion reversal (WDR), 100 World Health Organization (WHO), 9, 10, 26, 146, 159 Wrist, 19, 80, 82, 132, 134, 147 WT. See Wavelet transform (WT)

Y 10-year fracture risk probability, 27 Young modulus, 273, 291, 298, 306, 375, 376 Young’s moduli. see Young’s modulus Young’s modulus, 273, 291, 298, 306, 375, 376

Z Z-score, 12, 22, 23, 25, 38