Innovations in Biomedical Engineering [1st ed.] 9783030521790, 9783030521806

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Advances in Intelligent Systems and Computing 1223

Marek Gzik · Zbigniew Paszenda · Ewa Pietka · Ewaryst Tkacz · Krzysztof Milewski   Editors

Innovations in Biomedical Engineering

Advances in Intelligent Systems and Computing Volume 1223

Series Editor Janusz Kacprzyk, Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland Advisory Editors Nikhil R. Pal, Indian Statistical Institute, Kolkata, India Rafael Bello Perez, Faculty of Mathematics, Physics and Computing, Universidad Central de Las Villas, Santa Clara, Cuba Emilio S. Corchado, University of Salamanca, Salamanca, Spain Hani Hagras, School of Computer Science and Electronic Engineering, University of Essex, Colchester, UK László T. Kóczy, Department of Automation, Széchenyi István University, Gyor, Hungary Vladik Kreinovich, Department of Computer Science, University of Texas at El Paso, El Paso, TX, USA Chin-Teng Lin, Department of Electrical Engineering, National Chiao Tung University, Hsinchu, Taiwan Jie Lu, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, NSW, Australia Patricia Melin, Graduate Program of Computer Science, Tijuana Institute of Technology, Tijuana, Mexico Nadia Nedjah, Department of Electronics Engineering, University of Rio de Janeiro, Rio de Janeiro, Brazil Ngoc Thanh Nguyen , Faculty of Computer Science and Management, Wrocław University of Technology, Wrocław, Poland Jun Wang, Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong

The series “Advances in Intelligent Systems and Computing” contains publications on theory, applications, and design methods of Intelligent Systems and Intelligent Computing. Virtually all disciplines such as engineering, natural sciences, computer and information science, ICT, economics, business, e-commerce, environment, healthcare, life science are covered. The list of topics spans all the areas of modern intelligent systems and computing such as: computational intelligence, soft computing including neural networks, fuzzy systems, evolutionary computing and the fusion of these paradigms, social intelligence, ambient intelligence, computational neuroscience, artificial life, virtual worlds and society, cognitive science and systems, Perception and Vision, DNA and immune based systems, self-organizing and adaptive systems, e-Learning and teaching, human-centered and human-centric computing, recommender systems, intelligent control, robotics and mechatronics including human–machine teaming, knowledge-based paradigms, learning paradigms, machine ethics, intelligent data analysis, knowledge management, intelligent agents, intelligent decision making and support, intelligent network security, trust management, interactive entertainment, Web intelligence and multimedia. The publications within “Advances in Intelligent Systems and Computing” are primarily proceedings of important conferences, symposia and congresses. They cover significant recent developments in the field, both of a foundational and applicable character. An important characteristic feature of the series is the short publication time and world-wide distribution. This permits a rapid and broad dissemination of research results. ** Indexing: The books of this series are submitted to ISI Proceedings, EI-Compendex, DBLP, SCOPUS, Google Scholar and Springerlink **

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Marek Gzik Zbigniew Paszenda Ewa Pietka Ewaryst Tkacz Krzysztof Milewski •

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Editors

Innovations in Biomedical Engineering

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Editors Marek Gzik Faculty of Biomedical Engineering/ Department of Biomechatronics Silesian University of Technology Zabrze, Poland Ewa Pietka Faculty of Biomedical Engineering/ Department of Informatics and Medical Devices Silesian University of Technology Zabrze, Poland

Zbigniew Paszenda Faculty of Biomedical Engineering/ Department of Biomaterials and Medical Devices Engineering Silesian University of Technology Zabrze, Poland Ewaryst Tkacz Faculty of Biomedical Engineering/ Department of Biosensors and Processing of Biomedical Signals Silesian University of Technology Zabrze, Poland

Krzysztof Milewski American Heart of Poland Katowice, Poland The Jerzy Kukuczka Academy of Physical Education Katowice, Poland

ISSN 2194-5357 ISSN 2194-5365 (electronic) Advances in Intelligent Systems and Computing ISBN 978-3-030-52179-0 ISBN 978-3-030-52180-6 (eBook) https://doi.org/10.1007/978-3-030-52180-6 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 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

Contents

Modelling and Simulations in Biomechanics Three-Dimensional Printing of Bone Models . . . . . . . . . . . . . . . . . . . . . Angela Andrzejewska

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Isogeometric Shell Analysis of the Human Abdominal Wall . . . . . . . . . Bartosz Borzeszkowski, Thang X. Duong, Roger A. Sauer, and Izabela Lubowiecka

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Comparison of the Bone Segments Displacement Between Two Sides of the Mandible After BSSO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dominik Pachnicz and Agnieszka Szust Evaluation of Transverse Abdominal Muscles Impact on Body Posture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bożena Gzik-Zroska, Janusz Kocjan, Katarzyna Nowakowska, Patrycja Purgoł, Michał Burkacki, Sławomir Suchoń, Kamil Joszko, Robert Michnik, and Mariusz Adamek A Comparative Study of Biclustering Algorithms of Gait Data . . . . . . . Katarzyna Minta-Bielecka, Jolanta Pauk, and Agnieszka Wasilewska Assessment of Changing the Radial Forces of Biodegradable Stent in One Month Time Interval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kamil Joszko, Bożena Gzik-Zroska, Marek Gzik, Wojciech Wolański, Agata Iskra, Michał Burkacki, Sławomir Suchoń, Robert Sobota, and Arkadiusz Szarek Examination of the Impact of Vertebral Displacement on the Surface Area of Intervertebral Foramina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paweł Drapikowski, Jakub Otworowski, Adam Gramala, and Żaneta Kurowska

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Contents

The Use of Hyperelastic Material Models for Estimation of Pig Aorta Biomechanical Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sylwia Łagan and Aneta Liber-Kneć Initial Report on Numerical Modeling of Blood Flow in Myocardial Bridge Region of Coronary Artery: Concept of Model Validation . . . . . Bartłomiej Melka, Marcin Nowak, Marek Rojczyk, Maria Gracka, Wojciech Adamczyk, Ziemowit Ostrowski, and Ryszard Białecki

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Analysis of Displacements Within the Base of Mandible and Mandibular Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Anna Wybraniec and Agnieszka Szust

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Simulation Investigation of Occlusal Loads Transfer in Personalized Titanium Plates in the Case of Jaw Osteotomy . . . . . . . . . . . . . . . . . . . Grzegorz Bobik, Jarosław Żmudzki, and Tomasz Tański

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Experimental Research in Biomedical Engineering Innovations of Wireless Capsule Robots in Gastrointestinal Endoscopy: A Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ahmad Athif Mohd Faudzi, Yaser Sabzehmeidani, and Naif Khalaf Al-Shammari

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Analysis of Dynamics of the Blast Mitigation Seat . . . . . . . . . . . . . . . . . 111 Sławomir Kciuk, Grzegorz Bienioszek, and Edyta Krzystała Separation of Cancer Cells on Graphene Coated Micro-Sieves . . . . . . . 121 Barbara Nasiłowska, Artur Kowalik, Zdzisław Bogdanowicz, Krzysztof Gruszyński, Kinga Hińcza, Aneta Bombalska, Antoni Sarzyński, Zygmunt Mierczyk, and Stanisław Góźdź Variability of Postural Stability Parameters Under the Influence of School Backpack Load in Children Aged 10 Years . . . . . . . . . . . . . . 131 Szyszka Paulina, Małgorzata Lichota, and Krystyna Górniak Use of 3D Printing in Designing Sensor Overlays Used to Determine the Foot Pressure Distribution on the Ground . . . . . . . . . . . . . . . . . . . . 139 Sławomir Duda, Grzegorz Gembalczyk, Tomasz Machoczek, and Przemysław Szyszka Impact of Footwear Used in Orthoses on the Kinematics of Locomotor Functions and Energy Expenditure—Case Study . . . . . . . . . . . . . . . . . . 147 Katarzyna Jochymczyk-Woźniak, Katarzyna Nowakowska, Anna Zakałużna-Żerebecka, and Robert Michnik Changes in Thickness Versus Shear Modulus in Ultrasound Lateral Abdominal Muscle Measurements During Isometric Contraction: A Case Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 Paweł Linek and Tomasz Wolny

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Analysis of Ground Reaction Forces and Kinematic Response to Gait Perturbation During Mid- to Terminal Stance Phase of the Gait Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 Barbara Łysoń-Uklańska, Joanna Ścibek, Katarzyna Bienias, and Andrzej Wit Hand Grip Strength and Suppleness as Progress Determinants in Female Pole Dancers’ Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 Barbara Mikula, Sabina Wolny, Katarzyna Nowakowska, Agata Guzik-Kopyto, Iwona Chuchnowska, and Robert Michnik Interactive Mat an Innovative Implementation for the Rehabilitation of Disabled Children . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 Bartłomiej Burlaga, Monika Osińska, Paulina Gembara, Ewelina Smółkowska, Tomasz Merda, and Maciej Gorzkowski Analysis of the Ability to Maintain the Balance of Veterans of Stabilization Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197 Piotr Wodarski, Jacek Jurkojć, Marta Chmura, Andrzej Bieniek, Agata Guzik-Kopyto, and Robert Michnik Influence of Body Tattoo on Thermal Image—A Case Report . . . . . . . . 209 Bartłomiej Zagrodny, Łukasz Kaczorowski, and Jan Awrejcewicz Technology as a Support for Rehabilitation Patients After Stroke . . . . . 215 Damian Kania, Patrycja Romaniszyn, Anna Mańka, Daniel Ledwoń, Anna Łysień, Agnieszka Nawrat–Szołtysik, Marta Danch–Wierzchowska, Robert Michnik, Andrzej Mitas, and Andrzej Myśliwiec Engineering of Biomaterials The Surface Topography and Physicochemical and Mechanical Properties of Pure Titanium (CP Ti) Manufactured by Selective Laser Melting (SLM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Anna Woźniak, Marcin Adamiak, and Bogusław Ziębowicz Evaluation of Mechanical Properties of Hernia Surgical Mesh Implants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239 Julia Lisoń, Marcin Basiaga, Zbigniew Paszenda, Damian Nakonieczny, Witold Walke, and Magdalena Antonowicz Investigation of the Mechanical Properties of PLA as a Material for Patient-Specific Orthopaedic Equipment . . . . . . . . . . . . . . . . . . . . . . 247 Adam Gramala, Jakub Otworowski, Adam Patalas, Piotr Kulczewski, and Paweł Drapikowski

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Study of Physicochemical Properties of CoCrMo Alloy with PLCL Polymer Coating Intended for Urology . . . . . . . . . . . . . . . . . . . . . . . . . 259 Wojciech Kajzer, Paulina Niścior, Anita Kajzer, Marcin Basiaga, Janusz Szewczenko, Joanna Jaworska, Katarzyna Jelonek, and Janusz Kasperczyk Study of Strength and Fatigue of Stainless Steel and Titanium Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 Anita Kajzer, Sabina Niedźwiedź, Wojciech Kajzer, Jan Marciniak, Bożena Gzik-Zroska, Kamil Joszko, Marcin Kaczmarek, and Zbigniew Pilecki Effect of Carbon Layers Deposited by PACVD and RMS Methods on Corrosion Resistance of Ni-Ti Alloy . . . . . . . . . . . . . . . . . . . . . . . . . 279 Marcin Kaczmarek, Przemysław Kurtyka, Zbigniew Paszenda, and Marcin Basiaga Characterization of 3D Printed PLA Scaffolds Through Experimental and Modeling Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289 Aneta Liber-Kneć, Sylwia Łagan, Agnieszka Chojnacka-Brożek, and Szymon Gądek Shockwave-Generating Interdisciplinary Methods Used to Elaborate Acellular Tissue Origin Extracellular Matrix . . . . . . . . . . . . . . . . . . . . . 299 Gabriela Imbir, Roman Major, Aldona Mzyk, Piotr Wilczek, Marek Sanak, Marek Strzelec, Roman Ostrowski, and Antoni Rycyk The Study of Electrochemical Properties of Surface Modified Casting Alloys Used in Dental Prosthetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311 Anna Ziębowicz, Anna Woźniak, Bogusław Ziębowicz, Grzegorz Chladek, Paulina Boryło, and Witold Walke Informatics and Signal Analysis in Medicine Automated Classification of Axial CT Slices Using Convolutional Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 Paweł Badura, Jan Juszczyk, Paweł Bożek, and Michał Smoliński rsfMRI Study of Sensimotor Cortex in Multiple Sclerosis (MS) Using Independent Component Analysis (ICA) in GIFT Toolbox with Infomax Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 337 Ilona Karpiel and Zofia Drzazga Reconstruction of True Fetal Heart Rate Signals Obtained via Ultrasound Bedside Monitor in Relation to Fetal Electrocardiography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351 Tomasz Kupka, Adam Matonia, Krzysztof Horoba, Janusz Wrobel, and Slawomir Graczyk

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Segmentation and Registration of High-Frequency Ultrasound Images of Superficial Veins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Bartłomiej Pyciński and Joanna Czajkowska 3D Thermal Volume Reconstruction from 2D Infrared Images—a Preliminary Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Agata Sage, Daniel Ledwoń, Jan Juszczyk, and Paweł Badura Influence of Music on HRV Indices Derived from ECG and SCG . . . . . 381 Szymon Sieciński and Paweł Kostka Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

Modelling and Simulations in Biomechanics

Three-Dimensional Printing of Bone Models Angela Andrzejewska

Abstract The trabecular bone occurs, for example, in the femoral heads. Understanding the phenomenon of bone tissue degeneration can be the basis for the possibility of looking for alternative methods of surgical treatment of bone loss. The paper presents the results of the trabecular bone model, which was produced in additive manufacturing method with fused filament fabrication technology. The verification of the mechanical behavior of the trabecular bone model was based on the analysis of uniaxial compression test. The model was also conditioned under degradation process to determine the influence of the physiological fluid environment due to changes in the mechanical response of the modeled bone. The obtained results showed that the mechanical strength of the proposed spongy bone model and the method of its production allow to obtain strength values close to the natural spongy bone. In addition, the strength did not change during the 4-week degradation process. Keywords 3D printing · Bone · Mechanical testing · Hydrolytic degradation

1 Introduction Bones in terms of architecture aren’t homogeneous tissues. The surface part of the long bone shaft is a compacted bone, while in the heads of long bones, as well as in the interior of flat, irregular bone and short bones, the trabecular tissue is located. The trabecular tissue spongy consists of a network of connecting beams. The beams are crossed by arcs, which are significantly different in terms of thickness and shape. The architecture of bone beams allows the transfer of loads in the backbone system. A. Andrzejewska (B) Institution is Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Gzik et al. (eds.), Innovations in Biomedical Engineering, Advances in Intelligent Systems and Computing 1223, https://doi.org/10.1007/978-3-030-52180-6_1

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The authors of the study [12] have shown that certain factors, e.g., menopause, can significantly contribute to a faster loss of trabecular bone tissue. Resorption of the trabecular bone tissue, in this case follow into the interruption of connections between structural elements. This phenomenon causes a disproportionate loss of strength, in which only the beams with a larger thickness can partially compensate for the transferred loads. The persistent and irreversible degradation of natural bone tissue observed for years has meant that many researchers are now looking for new methods of replacing bone defects. Currently, research on the possibilities of replacing bone defects are carried out in orthopedics and traumatology [8, 22], dentistry [23], reconstructive surgery [10], pharmacy [13], or tissue engineering [20, 21]. The possibility of using the techniques of Additive Manufacturing of materials for filling bone defects is very popular. Due to the type of transferred loads, these 3D printed structures can be made of metal materials, such as titanium [7], polymers [15, 16] or ceramic–polymer composites [6, 24]. The research plan proposed in this paper is based on the application of additive manufacturing of biodegradable polymer technology. The trabecular bone models were made with the Fused Filament Fabrication method. Therefore, an overview of the current state of knowledge in the production of bone models was limited to the analysis of works in which scaffolds made of polymers were tested. In paper [14], scaffolds with dimensions of 10 mm × 10 mm × 3 mm were tested. The investigated scaffolds were made of both polylactic acid (PLA) and acrylonitrile butadiene styrene (ABS). The volume of scaffolds contained 0.7 mm × 0.7 mm × 3.5 mm pores. These constructs were used for research with chondrocytes, which were carried out for a period of 21 days. The work showed that the proposed scaffolds were characterized by good mechanical properties, and the cultured cells were characterized by high durability. Whereas in work [17] the orthogonal scaffolds were used, in which the distances between single layers were 0.5 mm and their diameter was 0.07 mm. Scaffolds with a displaced double structure were also tested. In the second case, the distance between the layers was 0.25 mm. Scaffolds made of PLA were tested for structural, mechanical and surface properties. The adhesion of cells cultured on their surface was also evaluated. The study proved that scaffolds functionality depends not only on the fabrication technique. In this case, it is also important the type of material which was used to build the 3D structure. Besides, the geometry and inner architecture of the structure influence the final surface properties. In the next study [1], bone scaffolds were made of polycaprolactone (PCL). Scaffolds were made using electrohydrodynamic (EHD) technology. Scaffolds with nominal dimensions of 60 mm × 60 mm × 2 mm was used for the investigation. The porosity of the tested model was determined at 78%, and the pore size was approximately 0.3 mm. The study proved that using PCL scaffolds it was possible to become a matrix with considerable porosity. Also thanks to the proposed structure, the high survivability of osteoblast-like cells (MG63) has been maintained. Nevertheless, the EHD method has some technical limitations. In connection with the use of an electric charge, previously produced layers of material may be destroyed.

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The paper [9] presents the results of tests carried out on scaffolds made with using the Stereolithography (SLA) technique. Two types of scaffolds with geometry 10 mm × 10 mm × 3 mm were tested, where the thickness of a single layer was 0.3 mm. The first type of scaffolds had square pores sized from 0.4 mm to 1 mm, while the second type of scaffolds were constructs with hexagonal pores with a radius of 0.6 mm. Three materials were used for the scaffolds production, where biomaterial was poly(propylene fumarate) (PPF), solvent—diethyl fumarate (DEF) and the photoinitiator—bisacrylphosphrine oxide (BAPO). The optimal production conditions for the biomaterial were determined on the basis of the conducted tests, and the SLA method brought promising results in the manufacturing field of biomedical solutions. The disadvantage of the technology used was the fact that excess resin was not always effectively removed. As a result, the scaffolds pore size was reduced. The accomplished review of the current state of knowledge showed that researchers in their investigations a square scaffolding with various geometry. The side lengths were ranging from 0.7 to 60 mm. Also, the total thickness of the tested scaffolds ranged from 2 to 3 mm. Various polymeric materials such as PLA, ABS, PCL, or PPF were used for the tests. In the presented cases, the proposed pore sizes ranging from 0.3 to 1 mm were easily obtained with each presented manufacturing method. Furthermore, in tests conducted with the use of live cells, their high survival rate was achieved. Based on the review of the current research results, the purpose of the work was defined. The purpose of the work was to determine how the behavior of the mechanical trabecular bone model changes under the influence of the simulated physiological fluid environment in the compression load conditions.

2 Materials and Methods The implementation of the work objective was possible by applying the proposed research methodology. The trabecular bone models were made in Additive Manufacturing technology in process of Fused Filament Fabrication (FFF) from the biodegradable PLA filament called 3DXPLA007 (Sigma-Aldrich, St. Louis, MO, USA). Bone models with geometry according to patent-pending P.427872 (Patent Office of the Republic of Poland, 11/23/2018) were made on the 3D Kreator Motion device (Krakow, Poland). The trabecular bone model was printed on the raft, and the geometry of the physical model was characterized by one contour path and one layer of bottom and one layer of top. The interior of the bone model was characterized by free spaces, divided by thin-film channels between upper and bottom hexagonal holes. The manufacturing process was run at 65◦ C of table temperature and at 200◦ C of extrusion temperature. Other important parameters of the printing were a nozzle diameter of 1.75 mm and a single layer height of 0.1 mm. In Fig. 1 is schematic presented the examined trabecular bone model . The dimensions of the tested model

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Fig. 1 Schematic representation of investigated trabecular bone model

were 20 mm × 20 mm × 4 mm, and the hexagonal holes were inscribed in a circle with a diameter of 2 mm. The physical trabecular bone models made in the FFF process were conditioned under hydrolytic degradation in vitro for a period of 1–4 weeks. The degradation medium was buffered sodium chloride with pH = 7.1 was used. The degradation medium was heated to a temperature of 37 ± 1◦ C [2, 3]. The models of the trabecular bone before placement in the degradation medium, followed by mechanical tests, were subjected to geometry and mass change evaluation. The mass control was carried out with the analytical balance AS 220.X2, RADWAG (Radom, Poland). Based on mass changes of the trabecular bone models, the percentage of medium uptake was determined [5]. Before measurements, each specimen was dried with a paper towel no longer than 10 min. The trabecular bone models were subjected to a monotonic compression test before degradation (T0) and its subsequent stages, designated T1, T2, T3, and T4 respectively. Five specimens were tested in each study group. Mechanical tests were carried out on the INSTRON ElectroPuls E3000 testing machine (Norwood, MA, USA) equipped with an electromagnetic actuator with a load range of ±3 kN. The traverse speed of the testing machine during the test was 1 mm/min. Direction of the compression according to Fig. 1. was in the z-axis. Mechanical tests were carried out to completely destroy the specimen. The calculation of the statistical significance of the test results was prepared in GraphPad Prism. The comparison of mass change (water uptake) and compressive strength of the trabecular bone models was determined by the one-way ANOVA test and post-hoc NIR test (LS Fisher’s LSD). The analysis was carried out at the significance level of p < 0.05.

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3 Results and Discussion The average value of the cross section of the compressed specimen was 403 mm 2 . Also, the obtained mean values of the initial mass (m 0 ), mean values of the specimen’s mass after degradation (m 1 ), and the mean values of the percentage change in their mass (Δm) are presented in Table 1. The differences of mass change (water uptake) between the trabecular bone models were statistically significant at each degradation level (p = 0.0001). The calculated values of differences between groups were ranging from 0.97% up to 7%. Based on the post-hoc test, it was noted that only for the comparison of results reached in T0 versus T3, T1 versus T4, T2 versus T3 and T2 versus T4 the difference between groups were statistically insignificant. Also, to characterize the changes in the mechanical behavior of trabecular bone models, they were investigated under static compression test. The compressive strength of the trabecular bone models was determined based on the maximum value of the compressive load. Obtained results of the compressive strength in MPa, its standard deviation, median of values, minimum (Min.), and maximum (Max.) value in the tested group and percentage coefficient of variation (VC) are summarized in Table 2. In the compression test, five trabecular bone models before and for each degradation time were used. The percentage coefficient of variation (VC) of the results in each investigated group of trabecular bone models was compared. In each investigated group of trabecular bone models, the coefficient of the variation of the results was less than 5%. Therefore, if the differences between individual measurements are

Table 1 Mean values of mass changes measurements of trabecular bone models, n = 5 Week m0, g m1, g Δm, % T0 T1 T2 T3 T4

0.687 0.694 0.693 0.695 0.693

N/A 0.742 0.717 0.710 0.734

0.00 6.88 3.46 2.20 5.92

Table 2 Calculated values of compressive strength of trabecular bone models, Rc [MPa], n = 5 Week Mean ± STD Median Min. Max. VC T0 T1 T2 T3 T4

5.90 ± 0.13 5.84 ± 0.32 5.86 ± 0.18 5.63 ± 0.12 5.81 ± 0.21

5.89 5.91 5.87 5.63 5.80

5.73 5.34 5.61 5.47 5.58

6.08 6.17 6.05 5.80 6.06

0.02 0.05 0.03 0.02 0.04

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Fig. 2 Changes of compressive strength of trabecular bone models during hydrolytic degradation

smaller than 10%, then it should be considered that the differences between bone models in the same group are statistically insignificant. Furthermore, at the significance level α= 0.05, it was shown that the results obtained in the compressive test were characterized by normal distribution. In Fig. 2 are shown box plots that present the distribution of statistical features of the determined compressive strength values. The differences of results of compressive strength between the trabecular bone models were statistically insignificant at each degradation level (p = 0.1587). The calculated values of differences were smaller than 0.3 MPa. Based on the post-hoc test, it was noted that only for the comparison of results reached in T1 versus T3 (p = 0.0374) the difference between groups were statistically significant.

4 Summary The presented investigation of trabecular bone models gives promising results in designing the synthetic bone models in additive manufacturing technology. The calculated values of the proposed bone models are convergent with the results of natural bone. The calculation values were based on the compressive strength of trabecular bone which is ranging from 5 to 10 MPa [11, 18]. In further research, the proposed bone model should be evaluated with fatigue test and compared to the results of natural trabecular bone presented in [19]. Additionally the degradation studies of biodegradable polymer material, despite a minimal decrease in compressive strength values, showed no statistically significant differences over the 4-week degradation time. The statistically insignificant

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differences in compressive strength may be related to the fact that a biodegradable polymer with a long degradation time was used for the investigation. Also, the determined results of mass changes (water uptake) show that the parameter can be strongly related to the manufacturing process and degradation time. A high value of percentage water uptake determined in investigation of porous biomaterial, in contrast to solid structures investigated in [2, 3], can be related to the method of drying before measurements. In order to unequivocally confirm the amount of the absorbed medium, it would be necessary to carry out absorption tests like was presented in work [4]. The knowledge gained in the field of material behavior after degradation may contribute to the design of further research, e.g., under changing environmental conditions, where in addition to the degradation medium, cartilage, or bone cells and substances affecting their survival may be used. Based on the presented research results, the influence of the degradation medium based on changes in the mechanical behavior of biodegradable trabecular bone models can potentially be excluded.

References 1. Ahn, S.H., Lee, H.J., Kim, G.H.: Polycaprolactone scaffolds fabricated with an advanced electrohydrodynamic direct-printing method for bone tissue regeneration. Biomacromolecules 12, 4256–4263 (2011) 2. Andrzejewska, A.: Mechanical characterization of biodegradable materials used in surgery In: Gzik M., Tkacz E., Paszenda Z., Pie˛tka E. (eds.) Innovations in Biomedical Engineering. IBE 2017. Advances in Intelligent Systems and Computing, vol. 623, pp. 399–408. Springer, Berlin (2018) 3. Andrzejewska, A., Mazurkiewicz, A., Ligaj, B.: Investigation of mechanical properties the polylactide in function its degradation rate. IOP Conf. Ser. Mater. Sci. Eng. 393, 012033 (2018) 4. Andrzejewska, A., Wirwicki, M., Andryszczyk, M., Siemianowski, P.: Procedure for determining aqueous medium absorption in biopolymers. AIP Conf. Proc. 1902, 0094–243X (2017) 5. Chlopek, J., Rosół, P., Morawska-Chochół, A.: Durability of polymer-ceramics composite implants determined in creep tests. Compos. Sci. Technol. 66, 1615–1622 (2006) 6. Huang, B., Bártolo, P.J.: Rheological characterization of polymer/ceramic blends for 3D printing of bone scaffolds. Polym. Test. 68, 365–378 (2018) ´ ˛szkowski, W.: The 7. Idaszek, J., Buhagiar, J., Szla˛zak, K., Brynk, T., Kurzydłowski, K.J., Swie influence of chemical polishing of titanium scaffolds on their mechanical strength and in-vitro cell response. Mater. Sci. Eng. C. 95, 428–439 (2019) 8. Jazayeri, H.E., Rodriguez-Romero, M., Razavi, M., Tahriri, M., Ganjawalla, K., Rasoulianboroujeni, M., Malekoshoaraie, M.H.: The cross-disciplinary emergence of 3D printed bioceramic scaffolds in orthopedic bioengineering. Ceram. Int. 44, 1–9 (2018) 9. Lee, K.W., Wang, S., Fox, B.C., Ritman, E.L., Yaszemski, M.J., Lu, L.: Poly(propylene fumarate) bone tissue engineering scaffold fabrication using stereolithography: effects of resin formulations and laser parameters. Biomacromolecules 8, 1077–1084 (2007) 10. Maroulakos, M., Kamperos, G., Tayebi, L., Halazonetis, D., Ren, Y.: Applications of 3D printing on craniofacial bone repair: a systematic review. J. Dent. 80, 1–14 (2019) 11. Murphy, W., Black, J., Hastings, G.: Handbook of Biomaterial Properties, 2nd edn, pp. 1–676 (2016)

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12. Parfitt, A.M.: Trabecular bone architecture in the pathogenesis and prevention of fracture. Am. J. Med. 82, 68–72 (1987) 13. Przekora, A., Ginalska, G.: Chitosan/β-1,3-glucan/hydroxyapatite bone scaffold enhances osteogenic differentiation through TNF-α -mediated mechanism. Mater. Sci. Eng. C. 73, 225– 233 (2017) 14. Rosenzweig, D.H., Carelli, E., Steffen, T., Jarzem, P., Haglund, L.: 3D-printed ABS and PLA scaffolds for cartilage and nucleus pulposus tissue regeneration. Int. J. Mol. Sci. 16, 15118– 15135 (2015) 15. Senatov, F.S., Chubrik, A.V., Maksimkin, A.V., Kolesnikov, E.A., Salimon, A.I.: Comparative analysis of structure and mechanical properties of porous PEEK and UHMWPE biomimetic scaffolds. Mater. Lett. 239, 63–66 (2019) 16. Senatov, F.S., Niaza, K.V., Stepashkin, A.A., Kaloshkin, S.D.: Low-cycle fatigue behavior of 3d-printed PLA-based porous scaffolds. Compos. Part B Eng. 97, 193–200 (2016) 17. Serra, T., Mateos-Timoneda, M.A., Planell, J.A., Navarro, M.: 3D printed PLA-based scaffolds: a versatile tool in regenerative medicine. Organogenesis 9, 239–244 (2013) 18. Sheikh, Z., Najeeb, S., Khurshid, Z., Verma, V., Rashid, H., Glogauer, M.: Biodegradable materials for bone repair and tissue engineering applications. Materials (Basel) 8, 5744–5794 (2015) 19. Topoli´nski, T., Cichanski, A., Mazurkiewicz, A., Nowicki, K.: Study of the behavior of the trabecular bone under cyclic compression with step-wise increasing amplitude. J. Mech. Behav. Biomed. Mater. 4, 1755–1763 (2011) 20. Wang, H., Su, K., Su, L., Liang, P., Ji, P.: The effect of 3D-printed Ti6Al4V scaffolds with various macropore structures on osteointegration and osteogenesis: A biomechanical evaluation. J. Mech. Behav. Biomed. Mater. 88, 488–496 (2018) 21. Yamachika, E., Iida, S.: Bone regeneration from mesenchymal stem cells (MSCs) and compact bone-derived MSCs as an animal model. Jpn. Dent. Sci. Rev. 49, 35–44 (2013) 22. Zhang, A.M., Yang, G., Johnson, B.N., Jia, X.: Three-dimensional (3D) printed scaffold and material selection for bone repair. Acta Biomater. 84, 16–33 (2019) 23. Zhao, L., Pei, X., Jiang, L., Hu, C., Sun, J., Xing, F., Zhou, C.: Bionic design and 3D printing of porous titanium alloy scaffolds for bone tissue repair. Compos. Part B 162, 154–161 (2019) 24. Zhou, Z., Cunningham, E., Lennon, A., Mccarthy, H.O., Buchanan, F.: Development of threedimensional printing polymer-ceramic scaffolds with enhanced compressive properties and tuneable resorption. Mater. Sci. Eng. C. 93, 975–986 (2018)

Isogeometric Shell Analysis of the Human Abdominal Wall Bartosz Borzeszkowski, Thang X. Duong, Roger A. Sauer, and Izabela Lubowiecka

Abstract In this paper, a nonlinear isogeometric Kirchhoff–Love shell model of the human abdominal wall is proposed. Its geometry is based on in vivo measurements obtained from a polygon mesh that is transformed into a NURBS surface, and then used directly for the finite element analysis. The passive response of the abdominal wall model under uniform pressure is considered. A hyperelastic membrane model based on the Gasser–Ogden–Holzapfel tissue model is used together with the Koiter bending model to describe the material behavior. Due to the mixed material formulation, different sets of constitutive parameters are examined such that the influence of each term is analyzed. The membrane contribution of the material model has a major influence on the displacement magnitude and reflects more reliably the nonlinear character of the deformation. Keywords Abdominal wall · Biomechanics · Constitutive modeling · Isogeometric analysis · Kirchhoff–Love shell theory

B. Borzeszkowski (B) · I. Lubowiecka Faculty of Civil and Environmental Engineering, Gda´nsk University of Technology, ul. Narutowicza 11/12, 80-233 Gda´nsk, Poland e-mail: [email protected] I. Lubowiecka e-mail: [email protected] T. X. Duong · R. A. Sauer Aachen Institute for Advanced Study in Computational Engineering Science (AICES), RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany e-mail: [email protected] R. A. Sauer e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Gzik et al. (eds.), Innovations in Biomedical Engineering, Advances in Intelligent Systems and Computing 1223, https://doi.org/10.1007/978-3-030-52180-6_2

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1 Introduction The abdominal wall has been investigated intensively during the past two decades, especially in the context of hernia repair [1]. The mechanical complexity of this structure includes incompressible hyperelastic anisotropy [2–4], active–passive muscle behavior [5], residual stresses [6], composite structure [7, 8], complex geometry with nontrivial boundary conditions [9, 10], and many more, including patient-specific variables, like tissue properties. Different finite element and constitutive models have been considered so far, e.g., linear elastic orthotropic membranes [11] as well as 3D electromechanical continuum models for the passive and active finite strain response of muscles [5]. CT and MRI scans for detailed segmented geometry and ABAQUS® 3D hexahedral/tetrahedral finite elements for the analysis is the primary modeling approach. [9, 12–14]. On the other hand, the future need of patient-specific solutions in hernia repairs and potential accessibility to the full-field in vivo optical measurements of the abdomen’s deformation mean that efficient and computationally less expensive shell models of the abdominal wall are necessary. This coincides with the renaissance of rotation-free Kirchhoff–Love shell formulations in the context of Isogeometric Analysis (IGA) [15, 16]. The isogeometric paradigm (same NURBS functions used both for CAD modeling and FE analysis) induces high efficiency in the geometry-analysis workflow and novel refinement strategies, coherent with patient-specific applications [17]. With the use of Bézier extraction [18], isogeometric elements can be adapted to existing FE codes with no significant changes. To the authors’ knowledge, it is the first time that the abdominal wall is modeled with isogeometric shell finite elements. This approach matches the idea of patientspecific modeling and is expected to be more practical than time consuming and computationally expensive 3D solid models. Additionally, a novel mixed-material model, described in the following section, is used, such that the membrane and shell behavior can be distinguished.

2 A Constitutive Model for Biological Shell The theoretical and computational shell formulation presented in [19, 20] is used. The formulation is based on a fully nonlinear rotation-free Kirchhoff–Love shell model, discretized with quadratic isogeometric finite elements. The constitutive relation can be either obtained via projection of 3D material laws onto a two-dimensional manifold [21], or directly derived from a 2D strain energy density function in the form (1) W = W (aαβ , bαβ ) = W M (aαβ ) + W B (bαβ ) , where W M is the membrane part dependent on the surface metric aαβ and W B is the bending part dependent on the curvature tensor bαβ [22]. Therefore, different

Isogeometric Shell Analysis of the Human Abdominal Wall

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stress–strain relationships can be assigned for bending and stretching separately. In this work, for a single biological shell layer with two families of embedded fibers, a mixed formulation that combines the bending energy of the 2-parameter (μK , ) Koiter model [23] and the membrane strain energy of the incompressible 5parameter (μGOH , k1 , k2 , κ, γ) Gasser–Ogden–Holzapfel (GOH) model [24] is used such that τ

αβ

 = μGOH A

αβ

a αβ − 2 J αβ



M0 =

+2

2  i=1

    a αβ αβ αβ , (2) E i κ A − 2 + (1 − 3κ) L i J

 T2   trKAαβ + 2 μK K αβ , 12

(3) αβ

where τ αβ are the contra-variant components of the Kirchhoff stress tensor, M0 are the contra-variant bending moment components, μGOH/K is the 2D surface shear modulus, K is the relative curvature tensor with contra-variant components K αβ , Aαβ are the contra-variant metric components of the undeformed surface, J is the surface area change, T is the undeformed shell thickness,  is a 2D Lamé constant, κ is the fibers dispersion parameter, and L αβ are the contra-variant components of the preferred fiber direction tensor, which is described in the local coordinates. Detailed derivations of Eqs. (2) and (3) and their components can be found in [21] and [25], respectively.

3 Abdominal Wall Analysis 3.1 Geometry of the Model The considered model is based on the geometry obtained in [26], where the front part of the human abdominal wall was measured in vivo. A net of points was transformed into a polygon mesh, which was further modified into a single-patch NURBS surface. The control point data was then transferred into the finite element code, where the Bézier extraction procedure provided 7 × 7 quadratic isogeometric finite element mesh (see Fig. 1). All boundary nodes were fixed and the load acting on the model was a deformation following uniform pressure.

3.2 Constitutive and Model Parameters Even though the GOH model has been used in abdominal wall modeling [14], its parameters are not well calibrated in these structures. Therefore, parameters that were

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Fig. 1 Geometry transfer from experimental data polygon mesh (left), via NURBS surface (middle) to isogeometric FE shell model (right) Table 1 Selection of parameters Variable Definition

Unit

Value/range

k2 κ γ Koiter term μ˜ K ˜ 

3D shear modulus 3D stress-like parameter Fibers dimensionless parameter Fibers dispersion parameter Angle between fiber families

kPa kPa – – deg

0.5–10 1–10 000 400 1/3 45

3D shear modulus 3D Lamé constant

kPa kPa

1–20 330

Other p T

IAP level Thickness

Pa cm

1600 3.0

GOH term μ˜ GOH k˜1

found, through a series of analyses, to have less influence on the deformation were ˜ while the remaining parameters μ˜ GOH/K , k˜1 were chosen, such fixed (T, κ, k2 , ), that membrane-dominated and bending-dominated behavior could be observed. The angle γ was chosen, such that two fiber families are orthogonal to each other (2γ = 90o ) and oriented along the linea alba. The thickness, from the reported range 3.0– 4.5 cm [10, 11, 27], was set to a constant 3 cm, while the pressure p was set to 1600 Pa, which is the reported intra-abdominal pressure (IAP) level (12 mmHG) during laparoscopic surgery [9, 27]. The 3D shear modulus μ˜ GOH/K and the Lamé constant ˜ were calculated from linear elasticity, based on the Young modulus range found  in [7, 10, 11, 27] and Poisson’s ratio ν = 0.49. The final selection of parameters is presented in Table 1 and sets of parameters for the analysis are collected in Table 2.

Isogeometric Shell Analysis of the Human Abdominal Wall Table 2 Considered sets of parameters No. μ˜ K (kPa) Membrane-dominated set1 set2 set3 set4 set5 set6 Bending-dominated set7 set8 set9 Balanced set10 set11 set12 set13

15

μ˜ GOH (kPa)

k˜1 (kPa)

1 1 1 1 1 1

0.5 5 5 5 10 10

1000 1000 10 000 100 10 1000

8 20 10

0.5 0.5 1

1 1 10

8 8 8 8

8 8 8 8

10 100 1000 10 000

3.3 Results The monitored node, the linea alba profile, and fiber orientation are shown in Fig. 2. The finite element results for selected parameter sets are presented in Figs. 3 and 4. Maximum displacement u max varies between 10 and 30 mm (sets 1–6, membranedominated), 50–60 mm (sets 7–8, bending-dominated), and 10–40 mm (sets 10–13, balanced). For comparison, u max reported in [9] was 19.9 mm (for IAP = 2260 Pa, 3D solid model, fiber-reinforced hyperelastic material), where the numerically calculated deformation was in agreement with the evidenced one on physiological abdomens in [11], i.e., u max = 16.7 mm (for IAP = 981 Pa, membrane model, linear orthotropic material). A direct comparison is impossible due to different IAP levels, geometry, material models and FE modeling considered by researchers. Therefore, the obtained results serve as an overview of the material model capabilities in the specific application of abdominal wall modeling.

4 Discussion and Conclusions The isogeometric finite element shell model of the abdominal wall, based on in vivo measurements is analyzed with the use of the mixed GOH/Koiter material model. It is shown that the Koiter bending part only has a minor influence on the

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Fig. 2 Deformed configuration (set4) with marked linea alba profile and the monitored node (left), with plotted fiber directions L 1 , L 2 (right)

Fig. 3 Load–displacement curves for the monitored node (left) and the displacement profile along the linea alba (right) for the membrane-dominated parameter sets

deformation, in comparison to the GOH membrane. It can thus be viewed merely as a membrane-stabilizing term. This is beneficial in contrast to pure membranes, where a pre-stretch is needed in order to stabilize them, which can interfere in the analysis of the residual stresses. The initial stiffness (in the linear elastic regime) is characterized by μ˜ (ground matrix), while the nonlinear stiffening effect is mainly characterized by k˜1 (fibers), which is the typical behavior of fiber-reinforced soft tissues. In order to judge if the proposed model of the composite structure of the abdominal wall is reasonable, experimental load–displacement curves should be examined and compared with computations. Also, a more detailed material model, that accounts for the different material behaviors of various tissue layers, should be

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Fig. 4 Load–displacement curves for the monitored node (left) and the displacement profile along the linea alba (right) for the bending-dominated and balanced parameter sets

chosen. Future work should also focus on defining a heterogeneous distribution of the parameters and identification method, e.g., via an inverse analysis [28, 29]. Acknowledgements This work has been partially supported by the National Science Centre (Poland) under [Grant No. 2017/27/B/ST8/02518] and the German Science Foundation (DFG) under grant GSC 111. Calculations have been carried out at the Academic Computer Centre in Gda´nsk.

References 1. Deeken, C.R., Lake, S.P.: Mechanical properties of the abdominal wall and biomaterials utilized for hernia repair. J. Mech. Behav. Biomed. Mater. 74, 411–427 (2017) 2. Gräßel, D., Prescher, A., Fitzek, S., Keyserlingk, D.G.V., Axer, H.: Anisotropy of human linea alba: a biomechanical study. J. Surg. Res. 124(1), 118–125 (2005) 3. Astruc, L., De Meulaere, M., Witz, J.F., Nováˇcek, V., Turquier, F., Hoc, T., Brieu, M.: Characterization of the anisotropic mechanical behavior of human abdominal wall connective tissues. J. Mech. Behav. Biomed. Mater. 82, 45–50 (2018) 4. Tran, D., Podwojewski, F., Beillas, P., Ottenio, M., Voirin, D., Turquier, F., Mitton, D.: Abdominal wall muscle elasticity and abdomen local stiffness on healthy volunteers during various physiological activities. J. Mech. Behav. Biomed. Mater. 60, 451–459 (2016) 5. Grasa, J., Sierra, M., Lauzeral, N., Munoz, M.J., Miana-Mena, F.J., Calvo, B.: Active behavior of abdominal wall muscles: Experimental results and numerical model formulation. J. Mech. Behav. Biomed. Mater. 61, 444–454 (2016) 6. Rausch, M.K., Kuhl, E.: On the effect of prestrain and residual stress in thin biological membranes. J. Mech. Phys. Solids 61(9), 1955–1969 (2013) 7. Tran, D., Mitton, D., Voirin, D., Turquier, F., Beillas, P.: Contribution of the skin, rectus abdominis and their sheaths to the structural response of the abdominal wall ex vivo. J. Biomech. 47(12), 3056–3063 (2014)

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8. Bielski, P., Lubowiecka, I.: Surface sliding in human abdominal wall numerical models: comparison of single-surface and multi-surface composites. Shell Structures: Theory and Applications, vol. 4, pp. 499-502. CRC Press, Gda´nsk, (2017) 9. Pachera, P., Pavan, P.G., Todros, S., Cavinato, C., Fontanella, C.G., Natali, A.N.: A numerical investigation of the healthy abdominal wall structures. J. Biomech. 49(9), 1818–1823 (2016) 10. Förstemann, T., Trzewik, J., Holste, J., Batke, B., Konerding, M.A., Wolloscheck, T., Hartung, C.: Forces and deformations of the abdominal wall. A mechanical and geometrical approach to the linea alba. J. Biomech. 44(4), 600–606 (2011) 11. Lubowiecka, I., Tomaszewska, A., Szepietowska, K., Szymczak, C., LichodziejewskaNiemierko, M., Chmielewski, M.: Membrane model of human abdominal wall. Simulations vs. in vivo measurements, pp. 503–506 (2018) 12. Hernández, B., Pena, E., Pascual, G., Rodriguez, M., Calvo, B., Doblaré, M., Bellón, J.M.: Mechanical and histological characterization of the abdominal muscle. A previous step to modelling hernia surgery. J. Mech. Behav. Biomed. Mater. 4(3), 392–404 (2011) 13. Hernández-Gascón, B., Mena, A., Pena, E., Pascual, G., Bellón, J.M., Calvo, B.: Understanding the passive mechanical behavior of the human abdominal wall. Ann. Biomed. Eng. 41(2), 433– 444 (2013) 14. Simon-Allue, R., Montiel, J.M.M., Bellon, J.M., Calvo, B.: Developing a new methodology to characterize in vivo the passive mechanical behavior of abdominal wall on an animal model. J. Mech. Behav. Biomed. Mater. 51, 40–49 (2015) 15. Kiendl, J., Bletzinger, K.U., Linhard, J., Wüchner, R.: Isogeometric shell analysis with Kirchhoff-Love elements. Comput. Methods Appl. Mech. Eng. 198(49–52), 3902–3914 (2009) 16. Cottrell, J.A., Hughes, T.J., Bazilevs, Y.: Isogeometric Analysis: Toward Integration of CAD and FEA. Wiley, Hoboken (2009) 17. Morganti, S., Auricchio, F., Benson, D.J., Gambarin, F.I., Hartmann, S., Hughes, T.J.R., Reali, A.: Patient-specific isogeometric structural analysis of aortic valve closure. Comput. Methods Appl. Mech. Eng. 284, 508–520 (2015) 18. Borden, M.J., Scott, M.A., Evans, J.A., Hughes, T.J.: Isogeometric finite element data structures based on Bézier extraction of NURBS. Int. J. Numer. Methods Eng. 87(1–5), 15–47 (2011) 19. Sauer, R.A., Duong, T.X.: On the theoretical foundations of thin solid and liquid shells. Math. Mech. Solids 22(3), 343–371 (2017) 20. Sauer, R.A.: On the computational modeling of lipid bilayers using thin-shell theory. The Role of Mechanics in the Study of Lipid Bilayers, pp. 221–286. Springer, Berlin (2018) 21. Roohbakhshan, F., Duong, T.X., Sauer, R.A.: A projection method to extract biological membrane models from 3D material models. J. Mech. Behav. Biomed. Mater. 58, 90–104 (2016) 22. Roohbakhshan, F., Sauer, R.A.: Efficient isogeometric thin shell formulations for soft biological materials. Biomech. Model. Mechanobiol. 16(5), 1569–1597 (2017) 23. Steigmann, D.: Koiter’s shell theory from the perspective of three-dimensional nonlinear elasticity. J. Elast. 111(1), 91–107 (2013) 24. Gasser, T.C., Ogden, R.W., Holzapfel, G.A.: Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3, 15–35 (2006) 25. Duong, T.X., Roohbakhshan, F., Sauer, R.A.: A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries. Comput. Methods Appl. Mech. Eng. 316, 43–83 (2017) ´ 26. Szymczak, C., Lubowiecka, I., Tomaszewska, A., Smieta´ nski, M.: Investigation of abdomen surface deformation due to life excitation: implications for implant selection and orientation in laparoscopic ventral hernia repair. Clin. Biomech. 27(2), 105–110 (2012) 27. Song, C., Alijani, A., Frank, T., Hanna, G.B., Cuschieri, A.: Mechanical properties of the human abdominal wall measured in vivo during insufflation for laparoscopic surgery. Surg. Endosc. 20(6), 987–990 (2006) 28. Kroon, M., Holzapfel, G.A.: Elastic properties of anisotropic vascular membranes examined by inverse analysis. Comput. Methods Appl. Mech. Eng. 198(45–46), 3622–3632 (2009) 29. Kroon, M.: A numerical framework for material characterisation of inhomogeneous hyperelastic membranes by inverse analysis. J. Comput. Appl. Math. 234(2), 563–578 (2010)

Comparison of the Bone Segments Displacement Between Two Sides of the Mandible After BSSO Dominik Pachnicz and Agnieszka Szust

Abstract The aim of this study was to compare displacements on both sides of the mandible after BSSO. Three different types of osteosynthesis were taken into consideration: A, 6-hole closed miniplate; B, two 6-hole straight miniplates; and C, 8-hole open miniplate. Fixations were performed using conventional monocortical screws. The distal segment of the mandible was advanced 4 mm forward. Model loading was carried out on compressive test unit, simulation of 3-point biomechanical model was performed. For all three methods, differences in displacement values on both sides of the mandible appeared. The greatest dislocation values were observed in proximal segments in transverse, horizontal axis. The differences in displacement between sides of the bone reached 49, 115, and 354% for methods C, B, and A, respectively. We found that asymmetrical work of bone fragments after orthognathic procedure may result in postoperative complications. Keywords BSSO · Miniplate · Monocortical fixation · Digital image correlation · Displacement

1 Introduction Orthognathic surgeries are common procedures performed for the correction of the maxillofacial skeleton deformities. Orthognathic procedures are carried out to improve the dysfunction of the masticatory system, joint disorders, as well as for an D. Pachnicz (B) · A. Szust Wroclaw University of Science and Technology, W10/K4, Smoluchowskiego 25, 50-370 Wroclaw, Poland e-mail: [email protected] A. Szust e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Gzik et al. (eds.), Innovations in Biomedical Engineering, Advances in Intelligent Systems and Computing 1223, https://doi.org/10.1007/978-3-030-52180-6_3

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aesthetic reasons. For health-improvement treatments for the majority of patients relief or stability in signs and symptoms are noticed [8]. Bilateral sagittal split osteotomy (BSSO) is a basic procedure allowing on the repositioning of the distal segment of the mandible in three directions. The procedure consists of setting the segment to the proper occlusal profile, keeping the proximal fragments in the correct position within the glenoid fossa [9]. This versatile technique is usually utilized in the treatment of microgenia and progenic mandible [8]. However, previous studies have reported utilization of this method also in the correction of the mandible’s asymmetry [6, 13, 15]. Similarly to all orthognathic surgeries, BSSO alters the geometry of the bone. Therefore, it results in changes in the mandible’s biomechanics. Modifications, concerning temporomandibular joint loading conditions and jaw muscle work, can lead to alteration in corresponding structures. Excessive pressure on the articular disc and different position of the condylar process can be distinguished among the negative effects on the temporomandibular joint (TMJ) [14]. During the procedure of BSSO, surgeon aims to ensure the final, correct relative position of upper jaw and mandible. Nevertheless, asymmetrical work of fragments on both sides after is highly possible. It could, therefore, be concluded that orthognathic procedures affect the left and right side of the mouth with varying degrees. Abgaje et al. [1] point on the link between the side of the mandible and frequency occurrence of postsurgical complications. The authors associate possible explanation of those differences with a surgeon’s varying performance, depending on side of the jaw. Right-handed surgeons encounter difficulties assessing a patient’s left side and vice versa. Additionally, differences between displacements can result from asymmetry in bone geometry itself. All of those factors eventually may lead to abnormalities in the treatment process, which may further result in malocclusion and complications. Miniplates and screws for the past decades have been the gold standard in osteosynthesis methods. This kind of fixation can provide sufficient stabilization significant for the proper bone healing process, early recovery of mandibular function [10–12, 18]. A considerable amount of literature has been published on BSSO fixations efficiency in vitro tests [10, 11, 21–23, 25, 26]. Previous studies, however, mainly have based their criteria for selection on parameters like fixation stiffness, yield load, and loading point displacement. The study offers some important, preliminary insights into mandible segments dislocation analysis. The aim of this in vitro study was to compare displacements on both sides of the mandible for 3 different osteosynthesis methods after bilateral sagittal split osteotomy.

2 Materials and Methods The main assumption during models preparation was recreating of the osteotomies on both sides of the bone as precise as possible. Synthetic polyurethane replicas of the human mandible Synbone 8951, which has been successfully used in a number of researches were used in this study [5]. Models were pre-cut along lines coincided with the Obwegeser osteotomy lines with Dal Pont modification. In all models, the

Comparison of the Bone Segments Displacement Between Two Sides …

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Fig. 1 Fixation models considered in the study: a closed plate, b two straight plates, c open plate

distal segment was advanced to create 4.0 mm aperture in sagittal plane view. The bone segments were fixed by three different modalities using 1.0 mm miniplates and conventional 2.0 mm thread diameter x 6-mm long monocortical screws. In the first method (A) 40 mm long, closed 6-hole sagittal split plate (SSP) was installed using 2 screws in each bone segment (Fig. 1a). In second technique (B), two straight 44 mm long 6-hole plates were fixed the same manner (Fig. 1b). In third (C), 47 mm open 8-hole SSP was installed with 6 screws, two in proximal and four in distal segment (Fig. 1c). The osteosynthesis was performed with respect to surgical art. It concerned the number of screws utilized and proper plates placement to avoid neurovascular bundle and tooth roots damage. All loadings were carried out using Instron 5944 testing unit Fig. 2a. The mandible models were stabilized in the support apparatus. The custom-fabricated support jig was designed by adapting the procedure used by Armstrong [4]. The distal segment could move freely in the occlusal surface. The proximal segments were settled on the mandibular notch allowing on their rotation around and minor movement along transverse, horizontal axis. For the purpose of dislocation measurement, Digital Image Correlation system Dantec Q-400 was used. Data management, as well as image analysis were performed using integrated software Istra 4D V4.4.6. and the authors’ own procedure written in the Wolfram Mathematica Language. In the experiment loading conditions from the first weeks after surgery, similar to the bone fracture, were recreated. Previous research has shown that at this stage of bone healing, the range of forces generated by the stomatognathic system is highly

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Fig. 2 a Biomechanical test model and loading scheme, b points of measurement

reduced due to protective neuromuscular mechanisms, responsible for the limitation in chewing muscle activity. The mean value of 62,4 N of biting force measured on the incisors was reported by Tate et al. [28] in the period of the first six weeks after bone trauma. Therefore, the reduced maximum load value of 50 N was assumed. Models were loaded by the vertical displacement of the load cell at a rate of 0.5 mm per minute. The increasing compressive force was translated to the areas of mandible angles through the metal beam. The loading scheme assumed a symmetrical distribution of force between both mandible angles. The applied force was an equivalent of the resultant muscular strength. For this reason, very significant was to ensure constant contact between beam and all bony segments. To increase the reliability of measures, each model was tested five times for each side of the mandible with a 2-minute break between loadings. Images were collected with a frequency of 2 Hz. Deformation of the bone segments was little compared to their relative dislocation. For this reason, three points in the triangular arrangement were enough for both, translational and rotation movements analysis. Values of dislocation presented in the Table 1 were collected from 3 objects on each bone segment (Fig. 2b). The choice of the measure points stemmed from the comparative character of the analysis and the authors’ own experience. Their location was a compromise between extreme displacement register and possibly close to the area of the fixation. Points were located on two borders of the mandible: upper(alveolar) and lower (inferior). They had to be placed on both sides of the bone, for three fixation methods uniformly.

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3 Results The dislocation values for three methods for the maximum loading force are presented in the Table 1. The coordinate systems are shown in the Fig. 2a. The numbers 1– 3 represent values of dislocation for proximal and 4–6 for distal segment of the mandible. There were no significant differences in displacements of distal segment on both sides of the mandible in all three fixation methods. Open plate showed the greatest stability, yet very similar to fixation with two straight plates. Significant differences in dislocations between the left and right side of the mandible can be mostly noticed for proximal segments. The greatest displacement appeared in fixation with a closed plate on the left side reaching 1.36 mm, with a difference of 354% (point 1). In methods B and C, this difference for total displacement value was 115% (point 1) and 49% (point 1) as follows. Proximal segments tend to undergo lateral displacement rather than rotate, what is represented by greater dislocations in Zaxis comparing to the X direction. In methods A and B, proximal segments show symmetrical deformation pattern with a predominance of displacements in the Zaxis. Only for method C greater anterior movement of the left proximal segment can be noticed.

4 Discussion There is a large volume of published clinical and experimental studies about the efficiency of different fixation methods after sagittal split osteotomy. Most of them have only focused on consideration of fixation rigidity and stability. Nevertheless, adequately stable and rigid fixation is not guaranteed of patient’s recovery. Different factors such as improper application of the method [30, 32], condylar malposition, loss of fixation, and condylar resorption [10] may be other determinants of postoperative complications and malocclusion. One of the challenges of in vitro tests is the proper simulation of action of masticatory muscles [22]. In many studies, 2-point biomechanical test model was used [18, 19, 21, 26, 31]. The model used in the present study is an adaptation of Armstrong [4] design for 3-point biomechanical test model. Similar models were utilized by a few authors [16, 20, 23], as a more appropriate method to recreate the masticatory forces in comparison to 2-point model (cantilever). Nevertheless, also this kind of model has its limitations and is highly inferior to the real conditions of the human mandible function. For this reason, further development of the testing model is needed [20]. The obtained results are consistent with the mobility scheme of mandible segments after BSSO surgery. It can be observed in inferior and posterior displacement of the symphysis (growing values of displacement from point 3 to 5), resulting in clockwise rotation of the distal segment. Proximal segments, on the other hand, become rotated counterclockwise, due to the action of elevator muscles attached to the ramus [22, 23]. Also, the intensive transverse displacement of the proximal segments is observed, especially in the very

Table 1 Displacement values in 6 points for three fixation methods; sides of the mandible: L- left, R- right 24 D. Pachnicz and A. Szust

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area of ramus, which is in agreement with Dai et al. [7] finite element analysis of monocortical fixation case and Motta [17] findings. The fixation with miniplates is, therefore, exposed to complex loading with additional of twisting between segments [24]. Monocortical screws and plates are currently the preferred fixation methods of mandibular sagittal spilt osteotomy [29]. Nevertheless, further investigation can concern the analysis of the same fixation methods using bicortical screws. They ensure better resistance to excessive shear force, which has a great impact on stability and may lead postoperatively to nonunion or incomplete union [23]. Bicortical screws fix both segments, so they work as one. Also, the risk of screw loosening is reduced [2, 3, 27]. Bicortical screws can be applied additionally with or in exchange for monocortical screws. The type of fixation method, as well as choice of the type of screw depends on the surgeon himself [3]. There are no specified guidelines which of them should be used. The bicortical screws ensure high biomechanical stability, though, miniplates with monocortical screws are still most accepted, much safer fixation method [19]. The purpose of the current study was to compare dislocations on both sides of the mandible after BSSO surgery. The dislocation measurement used in this study gives new insight into studies from the field of orthognathic surgeries efficiency. The most important limitation of this study lies in the small number of mandible models used. This limitation means that study findings need to be interpreted cautiously. Nevertheless, this preliminary study is also an example of Digital Image Correlation system application in the analysis of dislocations in mandible bone and shows how useful tool for quantitative characteristic of bony segments mobility it is. Considering presented results and possibility of inconvenience during the procedure mentioned in [1] can be concluded that after treatment asymmetrical work of bone fragments is highly possible, even inevitable. Differences may cause asymmetry and as a consequence of postoperative complications.

References 1. Agbaje, J.O., Sun, Y., Vrielinck, L., Schepers, S., Lambrichts, I., Politis, C.: Risk factors for the development of lower border defects after bilateral sagittal split osteotomy. J. Oral Maxillofac. Surg. 71(3), 588–596 (2013) 2. Al-Moraissi, E.A., Al-Hendi, E.A.: Are bicortical screw and plate osteosynthesis techniques equal in providing skeletal stability with the bilateral sagittal split osteotomy when used for mandibular advancement surgery? A systematic review and meta-analysis. Int. J. Oral Maxillofac. Surg. 45(10), 1195–1200 (2016) 3. Al-Moraissi, E.A.M., Ellis, E.: Stability of bicortical screw versus plate fixation after mandibular setback with the bilateral sagittal split osteotomy: a systematic review and meta-analysis. Int. J. Oral Maxillofac. Surg. 45(1), 1–7 (2016) 4. Armstrong, J.E., Lapointe, H.J., Hogg, N.J., Kwok, A.D.: Preliminary investigation of the biomechanics of internal fixation of sagittal split osteotomies with miniplates using a newly designed in vitro testing model. J. Oral Maxillofac. Surg. 59(2), 191–195 (2001)

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5. Bredbenner, T.L., Haug, R.H.: Substitutes for human cadaveric bone in maxillofacial rigid fixation research. Oral Surg. Oral Med. Oral Pathol. Oral Radiol. Endod. 90(5), 574–580 (2000) 6. Chen, Y.J., Yao, C.C., Chang, Z.C., Lai, H.H., Lu, S.C., Kok, S.H.: A new classification of mandibular asymmetry and evaluation of surgical-orthodontic treatment outcomes in class III malocclusion. J. Craniomaxillofac. Surg. 44(6), 676–683 (2016) 7. Dai, Z., Hou, M., Ma, W., Song, D.L., Zhang, C.X., Zhou, W.Y.: Evaluation of the transverse displacement of the proximal segment after bilateral sagittal split ramus osteotomy with different lingual split patterns and advancement amounts using the finite element method. J. Oral Maxillofac. Surg 74(11), 2286–e1 (2016) 8. Dujoncquoy, J.P., Ferri, J., Raoul, G., Kleinheinz, J.: Temporomandibular joint dysfunction and orthognathic surgery: a retrospective study. Head Face Med. 6(1), 27 (2010) 9. Ehrenfeld, M., Manson, P.N., Prein, J.: Principles of Internal Fixation of the Craniomaxillofacial Skeleton: Trauma and Orthognathic Surgery. AOCMF, Davos (2012) 10. Ellis, E., Esmail, N.: Malocclusions resulting from loss of fixation after sagittal split ramus osteotomies. J. Oral Maxillofac. Surg. 67(11), 2528–2533 (2009) 11. Erkmen, E., Simsek, B., Yucel, E., Kurt, A.: Comparison of different fixation methods following sagittal split ramus osteotomies using three-dimensional finite elements analysis: Part 1: advancement surgery-posterior loading. Int. J. Oral Maxillofac. Surg. 34(5), 551–558 (2005) 12. Erkmen, E., Simsek, B., Yucel, E., Kurt, A.: Three-dimensional finite element analysis used to compare methods of fixation after sagittal split ramus osteotomy: setback surgery-posterior loading. Br. J. Oral Maxillofac. Surg. 43(2), 97–104 (2005) 13. Hagensli, N., Stenvik, A., Espeland, L.: Asymmetric mandibular prognathism: outcome, stability and patient satisfaction after BSSO surgery. A retrospective study. J. Craniomaxillofac. Surg. 42(8), 1735–1741 (2014) 14. Jung, H.D., Kim, S.Y., Park, H.S., Jung, Y.S.: Orthognathic surgery and temporomandibular joint symptoms. Maxillofac. Plast. Reconstr. Surg. 37(1), 14 (2015) 15. Kim, J.W., Son, W.S., Kim, S.S., Kim, Y.I.: Proximal segment changes after bilateral sagittal split ramus osteotomy in facial asymmetry patients. J. Oral Maxillofac. Surg. 73(8), 1592–1605 (2015) 16. Klein, G.B.G., Mendes, G.C.B., Junior, P.R., Viswanath, A., Papageorge, M.: Biomechanical evaluation of different osteosynthesis methods after mandibular sagittal split osteotomy in major advancements. Int. J. Oral Maxillofac. Surg. 46(11), 1387–1393 (2017) 17. Motta, A.T., Cevidanes, L.H., Carvalho, F.A., Almeida, M.A., Phillips, C.: Three-dimensional regional displacements after mandibular advancement surgery: one year of follow-up. J. Oral Maxillofac. Surg. 69(5), 1447–1457 (2011) 18. Murphy, M.T., Haug, R.H., Barber, J.E.: An in vitro comparison of the mechanical characteristics of three sagittal ramus osteotomy fixation techniques. J. Oral Maxillofac. Surg. 55(5), 489–494 (1997) 19. Oguz, Y., Watanabe, E.R., Reis, J.M., Spin-Neto, R., Gabrielli, M.A., Pereira-Filho, V.A.: In vitro biomechanical comparison of six different fixation methods following 5-mm sagittal split advancement osteotomies. Int. J. Oral Maxillofac. Surg 44(8), 984–988 (2015) 20. Ozden, B., Alkan, A., Arici, S., Erdem, E.: In vitro comparison of biomechanical characteristics of sagittal split osteotomy fixation techniques. Int. J. Oral Maxillofac. Surg 35(9), 837–841 (2006) 21. Peterson, G.P., Haug, R.H., Van Sickels, J.: A biomechanical evaluation of bilateral sagittal ramus osteotomy fixation techniques. J. Oral Maxillofac. Surg 63(9), 1317–1324 (2005) 22. Ribeiro-Junior, P.D., Magro-Filho, O., Shastri, K.A., Papageorge, M.B.: In vitro biomechanical evaluation of the use of conventional and locking miniplate/screw systems for sagittal split ramus osteotomy. J. Oral Maxillofac. Surg. 68(4), 724–730 (2010) 23. Ribeiro-Junior, P.D., Magro-Filho, O., Shastri, K.A., Papageorge, M.B.: Which kind of miniplate to use in mandibular sagittal split osteotomy? An in vitro study. Int. J. Oral Maxillofac. Surg. 41(11), 1369–1373 (2012)

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24. Sato, F.R.L., Asprino, L., Consani, S., de Moraes, M.: Comparative biomechanical and photoelastic evaluation of different fixation techniques of sagittal split ramus osteotomy in mandibular advancement. J. Oral Maxillofac. Surg. 68(1), 160–166 (2010) 25. Sato, F.R.L., Asprino, L., Moreira, R.W.F., de Moraes, M.: Comparison of postoperative stability of three rigid internal fixation techniques after sagittal split ramus osteotomy for mandibular advancement. J. Oral Maxillofac. Surg. 42(5), e224–e229 (2014) 26. Sonego, C.L., Scheffer, M.A.R., Junior, O.C., Vetromilla, B.M., Fernandes, L.P., Ozkomur, A., Hernandez, P.A.G.: In vitro study of a modified sagittal split osteotomy fixation technique of the mandible: a mechanical test. Int. J. Oral Maxillofac. Surg. 47(10), 1330–1335 (2018) 27. Stró˙zyk, P., Nowak, R.: Zastosowanie metody elementów sko´nczonych do analizy stabilno´sci zespole´n stosowanych przy strzałkowej osteotomii gałe˛zi z˙ uchwy. Dent. Med. Probl. 48(2), 157–164 (2011) 28. Tate, G.S., Ellis III, E., Throckmorton, G.: Bite forces in patients treated for mandibular angle fractures: implications for fixation recommendations. J. Oral Maxillofac. Surg. 52(7), 734–736 (1994) 29. Ueki, K., Nakagawa, K., Takatsuka, S., Yamamoto, E.: Plate fixation after mandibular osteotomy. Int. J. Oral Maxillofac. Surg. 30(6), 490–496 (2001) 30. Van Sickels, J.E., Larsen, A.J., Thrash, W.J.: Relapse after rigid fixation of mandibular advancement. J. Oral Maxillofac. Surg. 44(9), 703–707 (1986) 31. Van Sickels, J.E., Peterson, G.P., Holms, S., Haug, R.H.: An in vitro comparison of an adjustable bone fixation system. J. Oral Maxillofac. Surg. 63(11), 1620–1625 (2005) 32. Yamashita, Y., Mizuashi, K., Shigematsu, M., Goto, M.: Masticatory function and neurosensory disturbance after mandibular correction by bilateral sagittal split ramus osteotomy: a comparison between miniplate and bicortical screw rigid internal fixation. Int. J. Oral Maxillofac. Surg. 36(2), 118–122 (2007)

Evaluation of Transverse Abdominal Muscles Impact on Body Posture Bo˙zena Gzik-Zroska, Janusz Kocjan, Katarzyna Nowakowska, Patrycja Purgoł, Michał Burkacki, Sławomir Suchon, ´ Kamil Joszko, Robert Michnik, and Mariusz Adamek

Abstract The aim of the study was to perform a comparative analysis of the transverse abdominal muscles in patients before and after resection of the lung parenchyma. As part of the work, study was carried out on a group of 32 healthy people and a 41-person study group. Zebris FDM-S platform was used for measuring the pressure of the feet on the substrate and the device measuring the abdominal circumference. Measurements on the research group were made the day before the procedure and 7 days after the procedure under the same test conditions. Due to the condition of patients after the operation, only 15 of the examined patients participated in the study. The obtained results were presented in the form of diagrams. Based on them, the impact of abdominal lateral muscles on body posture was assessed. Keywords Zebris dynamometer platform · Abdominal muscles · Body balance B. Gzik-Zroska (B) Department of Biomaterials and Medical Devices Engineering, Faculty of Biomedical Engineering, Silesian University of Technology, Roosevelta 40, 41-800 Zabrze, Poland e-mail: [email protected] URL: http://www.ib.polsl.pl J. Kocjan Chair and Department of Thoracic Surgery, Faculty of Medicine and Dentistry, Medical University of Silesia, Poniatowskiego 15, 40-055 Katowice, Poland e-mail: [email protected] K. Nowakowska · M. Burkacki · S. Sucho´n · K. Joszko · R. Michnik Department of Biomechatronics, Faculty of Biomedical Engineering, Silesian University of Technology, Roosevelta 40, 41-800 Zabrze, Poland e-mail: [email protected] M. Burkacki e-mail: [email protected] S. Sucho´n e-mail: [email protected] © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Gzik et al. (eds.), Innovations in Biomedical Engineering, Advances in Intelligent Systems and Computing 1223, https://doi.org/10.1007/978-3-030-52180-6_4

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1 Introduction Chest is an element of the torso which protects internal organs of human body. Its shape changes with age, it also depends on sex, breathing phase, body structure, and disease state [11]. Controlling body posture and maintaining balance are extremely important when doing everyday activities [2, 6, 7, 10, 12]. By balance is meant the concrete state of the postural system, which is characterized by the vertical posture of the body achieved as a result of balancing forces and moments acting on the body. The balance is controlled by the nervous system, which controls the action of antigravity muscles [1, 3]. The basic feature of the balance test is to measure the movements of the body of a person standing freely or subjected to external and internal disturbance [8]. In order to assess the balance, platforms with built-in sensors are used, thanks to which it is possible to record pressure forces and their moments acting on the ground, as well as the displacements of the center of pressure (COP) are registered [4, 7]. The aim of the study was an evaluation of transverse abdominal muscles impact on body posture

2 Materials and Methods The study was conducted on group of patients of the Independent Public Clinical Hospital No. 1 of the name of Professor Stanisława Szyszko in Katowice. Patients were residents in the thoracic surgery department with indication for lung parenchyma resection because of cancer. The group of patients consisted of 41 people, including 17 women and 24 men aged 38–76 years. Each of the subjects was able to maintain a standing posture and move independently. The measurements were made the day before the procedure and after 7 days of the procedure under the same test conditions. Due to the condition of patients after surgery, only 15 of the operated patients participated in the study. K. Joszko e-mail: [email protected] R. Michnik e-mail: [email protected] P. Purgoł Students’ Scientific Circle “Biokreatywni”, Faculty of Biomedical Engineering, Silesian University of Technology, Roosevelta 40, 41-800 Zabrze, Poland e-mail: [email protected] M. Adamek Department and Clinic of Thoracic Surgery of the Silesian Medical University in Katowice, Independent Public Clinical Hospital No. 1 named Prof. Stanisław Szyszko Silesian Medical University in Katowice, 3-go Maja 13-15, 41-800 Zabrze, Poland e-mail: [email protected]

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Fig. 1 Stages of testing using the Zebris platform and the Abdominal device: a normal, b maximum abdominal retraction, c maximum abdominal thrust

The study also included a group of healthy people, which included students of the Medical Faculty of the Silesian Medical University in Katowice and students of the Faculty of Biomedical Engineering of the Silesian University of Technology. The healthy group consisted of 32 people, including 21 women and 11 men aged 22–25 years. The test consisted of performing the Romberg test using the Zebris FDM-S stabilographic platform. Balance-related parameters are recorded and analyzed using the platform. The patient, standing on the platform with his arms lowered freely along the body, stared at the point placed on the wall at eye level. During the test, the ability to maintain balance in three phases was measured: during normal standing, standing with the abdomen being pulled up and pushed out (Fig. 1). The measurement lasted 38 s and it was started with the measurement in the free position, which lasted 15 s. Then, at mark of the person conducting the test, the patient took a deep breath with the abdomen pulled in and held such a position for 15 s, then to perform a deep exhale with the abdomen pushed out, which lasted for the next 8 s. As part of the study, the body circumference was also measured using the abdominal system, which is a original project developed by employees of the Faculty of Biomedical Engineering at the Silesian University of Technology (Fig. 1). The system allows you to evaluate the activity of the abdominal muscles. Measurements performed using this device are non-invasive and do not hinder exercise. Abdominal testing was performed in parallel with making stabilographic measurements.

3 Results Data obtained during the study were exported to a spreadsheet, where they were presented according to the division into a given phase: normal state—Phase 1, with the abdominally pulled in part—Phase 2, and with the pushed out—Phase 3.

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The following parameters were included: COP path length—Path [mm/s], COP ellipse field—Ellipse [mm2 ], left and right limb load difference—LP [%], forefoot load—Fore (the value is the average of the left and right forefoot) [%], and backfoot loading—Back (the value is the average of the left and right foot overload) [%]. Additionally, with data obtained from the abdominal system, three parameters were defined, defining the work of the abdominal muscles, described by the following formulas (1-3): Delta − Adelta =

avg pushed out − avg pull in ∗ 100[%] avg nor mal

(1)

avg nor mal − avg pull in ∗ 100[%] avg nor mal

(2)

avg nor mal − avg pushed out ∗ 100[%] avg nor mal

(3)

I ndex1 − AW 1 = I ndex2 − AW 2 =

The parameters described above for individual phases were determined for three groups: control group (N), patients before surgery (P), and patients after surgery (Pp). In order to analyze the above parameters, it was necessary to confirm the distribution of normality (p ≥ 0.05)—which allows to determine whether the given result is close to the average and choose the method of further analysis. The test was performed within the control and pre-operative groups as well as pre-operative and post-operative patients. The analysis was carried out using the Shapiro–Wilk method. Afterward, the significance of statistical differences was confirmed (p≤0.05). During the analysis two tests were performed: dependent (for individual groups between the phases: 1 and 2 and 1 and 3) and independent (between particular groups in a given phase). The Student’s T-test and the Wilcoxon test were used for analysis. During the analysis, statistically significant differences were found for the COP path length and COP ellipse field within the control group and patients before the operation in the individual phases, as well as for the COP path length and the COP ellipse field within the group of patients before and after the surgery between the first and third phases. There were no statistically significant differences for the abdominal device parameters, which indicates a large variation in the value of the subjects. On the basis of the conducted stabilographic tests, individual parameters were analyzed. Comparing the results obtained for the control group and patients before surgery, it can be concluded that when measuring the length of the path during normal standing, the values obtained are higher for patients before surgery by 16% (Fig. 2a). The values obtained while standing with the abductor being pulled in and pushed out are also higher for patients before surgery. In the second phase, the difference between the control group and the patients before the surgery was 22%, and in the third phase—32%. From the analysis of the results obtained for patients before and after the surgery, it can be concluded that the COP path length in the first and second phases is lower in patients after surgery, while in the case of a stretched belly the COP path length is lower for patients before surgery.

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Fig. 2 Graph of average values: a COP length path/time [mm/s], b COP ellipse field [mm2 ]

Based on the graph of the mean values of the COP ellipse field, it can be stated that the values obtained for the control group are the lowest for each phase (Fig. 2b). When comparing the control group and patients before surgery, it can be noticed that the values obtained for patients after surgery are higher by 74% in the first phase, while in the second phase by as much as 122%. When standing with the pushed out belly, the difference in values for these groups is 172%. Analyzing the results obtained for patients before and after surgery, a small difference in values in the second and third phases can be noticed—in the second phase, the values are 3% lower for patients after surgery and in the third phase by 6% higher than values obtained for patients before surgery. During normal standing, a 36% higher score was obtained for patients before surgery. Analyzing the graph of mean differences in the values of left and right limb loads in each phase it can be noticed that the differences between the values are not large (Fig. 3a). The highest values in each phase were observed for patients before surgery. In the first phase, this group had an average value of 8.56%, which is 12% higher than that obtained for the control group and 16% higher than the outcome of the patients after the operation. When standing with the abdomen brought in for the control group, an average score of 7.56% was achieved, while for patients before surgery the result was 9.46%, which is 25% higher. The group of patients after surgery achieved a 5% lower score than patients before surgery in this phase. In the third phase, the control group achieved a score 20% lower than patients before surgery, while patients after surgery noted a 16% lower score than patients before surgery. Analyzing the graph of the average forefoot loads in individual phases, it can be noticed that the mean value of the forefoot in each phase is the highest for patients before surgery (Fig. 3b). In comparison with the load for the control group, this value is 5% higher when standing and standing normally with the abdomen being sucked and by 10% when standing with the pushed belly. When comparing the values obtained for patients before and after the operation, it is stated that the pre-operation patient load values are higher by 3% in the first and second phases and by 4% in the third phase. Analyzing the average loads of the hindfoot during the study, it was noticed that the highest values in the individual phases were obtained for the control group Fig. 4a. Comparing it to the group of patients before the operation, it is stated that the load

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Fig. 3 Graph of mean values: a difference of left and right limb loads [%], b forefoot load [%]

Fig. 4 Graph of average values: a load on the hindfoot [%], b on the delta [%]

values were higher for the control group by 4% in the first and the second phases, and by 7% in the third phase. Analyzing the results for patients before and after the surgery, it was noticed that the mean load of the hindfoot for patients after surgery was higher by 2% when standing normal and standing with the abdomen being pulled in and by 3% when standing with the abdomen being pushed out. Based on the results of tests carried out using the abdominal system, it is possible to analyze the parameters using presented formulas. Analyzing the average delta values obtained for individual groups, it can be concluded that the mean delta value is the highest for the control group—a 25% higher value than the pre-operative value was obtained and 33% higher than the value obtained for patients after the operation (Fig. 4b). On the basis of the graph of average values of index 1, it can be concluded that the highest average value of the index was obtained for patients before surgery—3.52%, which is 127% higher than the control group and more than twice higher than for the operation (Fig. 5a). Analyzing the average values obtained for index 2, the study found that the highest average value was obtained for patients before surgery—this value is 3.48% and is 63% higher than the value obtained for the control group and 145% higher than the value for patients after surgery (Fig. 5b).

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Fig. 5 Graph of average values: a index 1 [%], b index 2 [%]

4 Discussion Based on the analysis of the results obtained during the stabilographic study, it can be concluded that an increase in the average values of individual balance parameters indicates a deterioration of the body’s stability. It is observed that the mean values of COP path length and COP ellipse fields obtained by patients are higher than the values recorded for the control group. The highest differences between the values were recorded for standing up with the abdomen pushed in—43% and 214%, respectively, which indicates an imbalance in people after removing the lung parenchyma. Statistically significant differences were found for COP path length and COP ellipse field within the control group and patients before surgery in individual phases. There were also statistically significant differences between the length of the path and the field of the COP ellipse within the group of patients before and after surgery between the first and third phases. On this basis, it can be concluded that dynamic abdominal movements affect the deterioration of the patient’s balance. In addition, during the analysis, it was noticed that in all subjects the footpath is the most loaded, regardless of the phase. The load on hindfoot is characterized by a stable posture, which has been proven by numerous scientists, including D.J. Mortona and P.R. Cavanagh and his co-workers [5, 9]. On this basis, it can be stated that the examined group properly transfers body loads. When analyzing the results obtained with the abdominal device, it was found that the mean delta values are definitely higher for the control group, while the lowest values were recorded for patients after the operation. Based on the results it is stated that the work of the abdominal muscles and diaphragm is the best in the control group. When analyzing the average values of Index 1, it can be seen that the pre-operative patients had the highest scores—127% higher than the control group and more than twofold than the results obtained for patients after surgery. Analyzing the values of Index 2, it is stated that the patients before the operation achieved the highest results. On the basis of the analysis of the average values of the index, it can be concluded that the scope of abdominal muscle work in the control group and patients after surgery was greater than in the control group. The results obtained by patients after the surgery may have been affected by the pain persisting after the surgery. During the analysis,

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however, no statistical significance of the above parameters was found. Summarizing, the variation in values among respondents was so large that no significant differences were found. The data obtained as a result of this research were not compared with other studies on abdominal muscle activity due to the fact that previous work was based mainly on strained muscles of the trunk and abdomen, and their activity was recorded using an electromyograph. Based on the performed analysis, it can be concluded that the effect on the results obtained after the surgery could have the condition of patients and a short time interval between the operation and the examination. The data obtained may also depend on weight or maintaining a correct posture. In summary, the conducted research allows to assess the impact of abdominal muscle on the posture and allow for a detailed analysis of the impact of thoracic surgery on specific parameters related to the balance. However, performing the test at longer intervals than the surgery would allow a better assessment of the parameters after the operation, and would enable measurements to be performed on a larger study group, which in turn would contribute to more reliable results.

References 1. Assländer, L., Peterka, R.J.: Sensory reweighting dynamics in human postural control. J Neurophysiol. 111(9), 1852–1864 (2014) 2. Błaszczyk, J.W.: Kontrola stabilno´sci postawy ciała (Control in postural stablility). Warszawa (1993) (in Polish) 3. Błaszczyk, J.: Biomechanika kliniczna. Podre˛cznik dla studentów medycyny i fizjoterapii (Clinical biomechanics. Handbook for Students of Medicine and Physiotherapy). Wydanie I, Wydawnictwo Lekarskie PZWL, Warszawa (2004) (in Polish) 4. Błaszczyk, J.W., Czerwosz, L.: Stabilno´sc´ posturalna w procesie starzenia (Postural stability in the aging process). Gerontologia Polska, Warszawa (2005) (in Polish) 5. Cavanagh, P.R., Rodgers M.M., Iiboshi A.: Pressure distribution under symptom-free feet during barefoot standing (1987) 6. Janssens, L., McConnell, A.K., Pijnenburg, M., Claeys, K., Goossens, N., Lysens, R., Troosters, T., et al.: Inspiratory muscle training affects proprioceptive use and low back pain. Med. Sci. Sports Exerc. 47(1), 12–19 (2015) 7. Jochymczyk-Wo´zniak, K., Nowakowska, K., Michnik, R., Nawrat-Szołtysik, A., Górka, W.: Assessment of balance of older people living at a social welfare home. In: Gzik, M., Tkacz, E., Paszenda, Z., Pie˛tka, E. (eds.) Innovation in Biomedical Engineering. Advances in Intelligent System and Computing, vol. 623, pp. 217–224. Springer, Cham (2018) 8. Kuczy´nski, M., Podbielska, M.L., Bie´c, D., Paluszak, A., Kre˛cisz, K.: Podstawy oceny równowagi ciała: czyli co, w jaki sposób i dlaczego powinni´smy mierzy´c? (Basics of body balance assessment: what, how and why we should measure) (2012) (in Polish) 9. Morton, D.J.: The Human Foot: Its Evolution, Physiology and Functional Disorders (1935) 10. Sakellari, V., Bronstein, A.M., Corna, S., Hammon, C.A., Jones, S., Wolsley, C.J.: The effects of hyperventilation on postural control mechanisms. Brain 120, 1659–1673 (1997)

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´ 11. Tejszerska, D., Swito´ nski, E., Gzik, M.: Biomechanika narza˛du ruchu człowieka (Biomechanics of the human motor apparatus). Wydawnictwo Naukowe Instytutu Technologii Eksploatacji PIB, Gliwice (2011) (in Polish) 12. Tobin, M.J., Guenther, S.M., Perez, W., Mador, M.J., Semmens, B.J., Allen, S.J., et al.: The pattern of breathing during successful and unsuccessful trials of weaning from mechanical ventilation. Am. Rev. Respir. Dis. 134, 1111–1118 (1986)

A Comparative Study of Biclustering Algorithms of Gait Data Katarzyna Minta-Bielecka, Jolanta Pauk, and Agnieszka Wasilewska

Abstract Stroke is a cause of functional and neurological impairments, which significantly limit the movement and are a cause of gait abnormalities. The objective of this study was to investigate whether hip, knee, and ankle joint angles and joint powers data could be used to estimate gait disability during every phase of gait cycle. Thirty hemiplegia patients were recruited. Gait data were measured using a motion capture system integrated with two force platforms. Biclustering algorithms CC and KMB were used to classify the hemiplegic gait patterns. Well-separated biclusters presenting similarity among the lower limb joints during the gait cycles were obtained from the data. Both CC and KMB algorithms found comparable patterns in both datasets tested. However, it can be seen that algorithm KMB can detect biclusters that may be considered as supersets of biclusters discovered by CC. Both proposed algorithms can be successfully adapted in systems to support clinical decision-making. Keywords Biclustering · Gait patterns · Hemiplegia · Bicluster · Joint angles · Joint powers

K. Minta-Bielecka · J. Pauk (B) · A. Wasilewska Białystok University of Technology, Białystok, Poland e-mail: [email protected] K. Minta-Bielecka e-mail: [email protected] A. Wasilewska e-mail: [email protected] J. Pauk Glenrose Rehabilitation Hospital, Edmonton, Canada © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021 M. Gzik et al. (eds.), Innovations in Biomedical Engineering, Advances in Intelligent Systems and Computing 1223, https://doi.org/10.1007/978-3-030-52180-6_5

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1 Introduction Cerebrovascular accident (CVA) caused by insufficient blood supply to the brain can result in severe disability including motor weakness, coordination dysfunction, and sensory impairment [9]. Post-stroke hemiplegia is a condition caused by partial brain damage that affects one side of the body. We talk about right hemiplegia if it appears as a result of injury to the right side of the brain, and left hemiplegia when the left side of the brain has been injured [13]. While typical walking patterns are characterized by similar behaviors, identification of similar gait patterns among patients with hemiplegia is still a big challenge for researchers; however, it could be very helpful in diagnosis and clinical decision-making. In recent years, a variety of techniques such as neural networks models [6, 7], support vector machines (SVM) [10], or cluster analysis [3–5, 7, 8, 11, 12, 16] were applied to classify hemiplegic gait patterns. The diversity of gait deviations in post-stroke patients presents a need to develop a gait classification methods and systems to support the diagnostic process and clinical decision-making. Most of the research on gait classification has focused on analysis of gait patterns in sagittal plane. The studies [5, 7, 8, 10] assisted the understanding of hemiplegia gait. However, because the existing classification systems depend solely on the identification of gait disturbances, but do not fully address the gait deviations in every phase of gait cycle, there are limitations to their clinical relevance. Efficient study on walking relies on the analysis of the lower limbs in all phases of the sagittal plane. The primary objectives of this study were to investigate whether hip, knee, and ankle joint angles and joint powers data could be used to assess gait disability during every phase of gait cycle.

2 Materials and Methods 2.1 Subjects The study group consisted of 30 hemiplegia patients. Patients were eligible for inclusion if they had unilateral hemiplegia caused by ischemic stroke and ability to walk 10 meters independently without a walking device. Patients were excluded if they were younger than 18 years of age or had medical complications like neurological and/or orthopedic co-morbidities impairing ambulation. Measurements included hip, knee, and ankle joint angles in sagittal plane and joint powers. Gait parameters were measured using a motion tracking system (Motion Analysis Corp., USA) and two AMTI force platforms (Advanced Mechanical Technology, Inc., USA) with sampling frequency of 120 Hz. Each patient was asked to walk barefoot at habitual speed. The measurements were repeated three times. The joint powers of the lower limbs were estimated by the formula P = M ∗ ω, where M is a joint moment and ω—angular velocity of the joint, and were normalized to the body mass. All

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data were filtered with Butterworth filter and had the same length. An ANOVA for repeated measurements was applied for gait variables to evaluate differences in gait parameters. A value of p < 0.05 was considered significant. Software Statistica 13.1 (StatSoft, Poland) was used for the analysis. The study was approved by the local ethics committee. All subjects received detailed information about the study and provided written consent.

2.2 Biclustering Methods of Gait Data For data containing gait data parameters, biclustering methods are aimed at extracting from the dataset a subset of patients behaving similarly over a subset of analyzed parameters. In the article, two biclustering methods, such as CC and KMB proposed prior in [14, 15] for joint moments data classification, have been used to extract some patterns from two datasets containing joint power and joint angle measurements collected for hip, knee, and ankle joint during the gait cycle. Both datasets included gait cycles from 30 hemiplegia patients (mean age 44.4 (SD 17.1), BMI 24.0 (SD 4.2), 66.7% of male). For both algorithms, data used for the analysis were represented as a matrix A=(R,C) of real numbers with R-rows corresponding to walking trials and C-columns corresponding to subsequent parameter measurements during a particular single cycle. Each row in data matrix contained 153 samples in time domain for a single trail of which subsequent 51 samples concerned 3 analyzed joint, such as hip, knee, and ankle, respectively. As a result of the proposed methods, a set of biclusters, each being a submatrix derived from the original dataset built of I < R rows and J < C columns, was obtained. In order to disperse sets, in both cases, all numbers in data matrix were transformed by scaling and function f (x), which for data matrix containing power and angle measurements were x → x −9 and x → x 4 , respectively. As a measure of the quality of bicluster, Cheng and Church in [2] proposed a mean square residue score H (I, J ) =

 1 (ai j − ai J − a I j + a I J )2 , |I ||J | i∈I, j∈J

(1)

where ai J , a I j , and a I J were described as mean of all the values from the i-th row, from the j-th column, and from the whole bicluster, respectively. The goal was then to find biclusters with largest volume (number of rows and columns) having the mean square residue score upper bounded by a threshold δ. Both methods are based on iterative removal and addition of bicluster nodes satisfying chosen criteria. In [2], authors introduced a coherency score measure for rows and columns similar to the mean square residue score.

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d(i) =

1  (ai j − ai J − a I j + a I J )2 , |J | j∈J

(2)

d( j) =

1  (ai j − ai J − a I j + a I J )2 , |I | i∈I

(3)

CC [14] and KMB [15] are two-phase algorithms, in which the first phase performs node deletion and the second phase adds nodes to the bicluster. The deletion stage is identical for both methods and iteratively removes rows and columns for which the calculated coherency score d(i) > α H (I, J ) until a bicluster with H (I, J )