Table Of ContentBiomechanics of
Living Organs
Biomechanics of
Living Organs
Hyperelastic Constitutive Laws for
Finite Element Modeling
Edited by
Yohan Payan
Jacques Ohayon
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Contributors
Clayton Adam
Queensland University of Technology, Brisbane, Australia
Davide Ambrosi
Politecnico di Milano, Milano, Italy
Peter Anderson
University of British Columbia, Vancouver, BC, Canada
Stephane Avril
Ecole Nationale Superieure des Mines de Saint-Etienne, CIS-EMSE, SAINBIOSE; INSERM, U1059;
Universite de Lyon, SAINBIOSE, Saint-Etienne, France
Thiranja P. Babarenda Gamage
University of Auckland, Auckland, New Zealand
Pierre Badel
Ecole Nationale Superieure des Mines de Saint-Etienne, CIS-EMSE, SAINBIOSE; INSERM, U1059;
Universite de Lyon, SAINBIOSE, Saint-Etienne, France
Chiara Bellini
Yale University, New Haven, CT, United States
Silvia S. Blemker
University of Virginia, Charlottesville, VA, United States
Mohamed Bader Boubaker
Universite de Montpellier, Montpellier, France
Peter H.M. Bovendeerd
Eindhoven University of Technology, Eindhoven, The Netherlands
Marek Bucki
TexiSense, Montceau-les-Mines France
Begona˜ Calvo
University of Zaragoza, Zaragoza; Centro de Investigacio´ n en Red en Bioingenierı´a,
Biomateriales y Nanomedicina, Spain
Francis Cannard
TexiSense, Montceau-les-Mines France
Matthieu Chabanas
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble, France
Gregory Chagnon
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble, France
Simon Chatelin
University of Strasbourg, Strasbourg, France
Hadrien Courtecuisse
AVR-ICube, University of Strasbourg, CNRS, Strasbourg, France
xix
xx Contributors
Nicolas Curt
Ecole Nationale Superieure des Mines de Saint-Etienne, CIS-EMSE, SAINBIOSE; INSERM, U1059;
Universite de Lyon, SAINBIOSE, Saint-Etienne, France
Christian J. Cyron
Technical University of Munich, Garching, Germany
Tammo Delhaas
Maastricht University, Maastricht, The Netherlands
Herve Delingette
Universite C^ote d’Azur, Inria, Asclepios Team, France
Elena S. Di Martino
University of Calgary, Calgary, AB, Canada
Raphae¨l Dumas
Univ Lyon, Universite Claude Bernard Lyon 1, IFSTTAR, UMR_T9406, LBMC, Lyon, France
Olivier Dupuis
Universite de Lyon, Pierre Benite, France
Denis Favier
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble, France
Sidney Fels
University of British Columbia, Vancouver, BC, Canada
Behrooz Fereidoonnezhad
Sharif University of Technology, Tehran, Iran
Gerard Finet
Hospices Civils de Lyon and Claude Bernard University Lyon1, INSERM Unit 886, Lyon, France
Cormac Flynn
Wintec, Hamilton, New Zealand
Fanny Frauziols
Ecole Nationale Superieure des Mines de Saint-Etienne, CIS-EMSE, SAINBIOSE; INSERM, U1059;
Universite de Lyon, SAINBIOSE, Saint-Etienne, France
Jean-Franc¸ois Ganghoffer
Universite de Lorraine, Nancy, France
Alberto Garcia
University of Zaragoza, Zaragoza, Spain
Thomas C. Gasser
KTH Royal Institute of Technology, Stockholm, Sweden
Ahmed M. Gharib
National Institute of Diabetes Digestive and Kidney Diseases, National Institutes of Health,
Bethesda, MD, United States
Paul Glass
nanoGriptech Inc, Pittsburgh, PA, United States
Contributors xxi
Hans Gregersen
Chongqing University, Chongqing, China; The Chinese University of Hong Kong, Shatin,
Hong Kong
Negar M. Harandi
University of British Columbia, Vancouver, BC, Canada
Nicolas Hermant
Univ. del Valle, Cali, Colombia
Belen Herna´ndez-Gasco´n
University of Zaragoza, Zaragoza, Spain
Andrew Ho
University of British Columbia, Vancouver, BC, Canada
Gerhard A. Holzapfel
Graz University of Technology, Graz, Austria; Norwegian University of Science and Technology,
Trondheim, Norway
Jay D. Humphrey
Yale University, New Haven, CT, United States
Yoann Lafon
Univ Lyon, Universite Claude Bernard Lyon 1, IFSTTAR, UMR_T9406, LBMC, Lyon, France
Sebastien Laporte
Arts et Metiers ParisTech LBM/Institut de Biomecanique Humaine Georges Charpak, Paris,
France
Donghua Liao
Aarhus University, Aarhus, Denmark
Vincent Luboz
TexiSense, Montceau-les-Mines France
Mauro Malve`
Public University of Navarra, Pamplona, Spain
Stephanie Marchesseau
Clinical Imaging Research Centre, A*STAR-NUS, Singapore, Singapore
Jean-Louis Martiel
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble, France
Scott Moisik
Nanyang Technological University, Singapore, Singapore
Jer^ome Molimard
Ecole Nationale Superieure des Mines de Saint-Etienne, CIS-EMSE, SAINBIOSE; INSERM, U1059;
Universite de Lyon, SAINBIOSE, Saint-Etienne, France
Fanny Morin
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble; AVR-ICube, University of
Strasbourg, CNRS, Strasbourg, France
xxii Contributors
Martyn P. Nash
University of Auckland, Auckland, New Zealand
Laurent Navarro
Ecole Nationale Superieure des Mines de Saint-Etienne, CIS-EMSE, SAINBIOSE; INSERM, U1059;
Universite de Lyon, SAINBIOSE, Saint-Etienne, France
Mohammad Ali Nazari
University of Tehran, Tehran, Iran
Poul M.F. Nielsen
University of Auckland, Auckland, New Zealand
Jacques Ohayon
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble; University of Savoie
Mont-Blanc, Engineering School Polytech Annecy-Chambery, Le Bourget du Lac, France
Cees W.J. Oomens
Eindhoven University of Technology, Eindhoven, The Netherlands
Yohan Payan
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble, France
Estefanı´a Pen˜a
University of Zaragoza, Zaragoza; Centro de Investigacio´ n en Red en Bioingenierı´a,
Biomateriales y Nanomedicina, Spain
Pascal Perrier
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble, France
Antoine Perrier
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS; TexiSense,
Montceau-les-Mines; Univ. Grenoble Alpes, AGEIS, Grenoble, France
Gerrit W.M. Peters
Eindhoven University of Technology, Eindhoven, The Netherlands
Roderic I. Pettigrew
National Institute of Diabetes Digestive and Kidney Diseases, National Institutes of Health,
Bethesda, MD, United States
Dominique P. Pioletti
Institute of Bioengineering, EPFL, Lausanne, Switzerland
Marieke Pluijmert
Maastricht University, Maastricht; Eindhoven University of Technology, Eindhoven,
The Netherlands
Lalao Rakotomanana
IRMAR, University of Rennes I, Rennes Cedex, France
Pierre-Yves Rohan
Arts et Metiers ParisTech LBM/Institut de Biomecanique Humaine Georges Charpak, Paris, France
Philippe Rouch
Arts et Metiers ParisTech LBM/Institut de Biomecanique Humaine Georges Charpak, Paris, France
Contributors xxiii
C. Antonio Sa´nchez
University of British Columbia, Vancouver, BC, Canada
Wafa Skalli
Arts et Metiers ParisTech LBM/Institut de Biomecanique Humaine Georges Charpak, Paris, France
Ian Stavness
University of Saskatchewan, Saskatoon, SK, Canada
Julien Stelletta
Univ Lyon, Universite Claude Bernard Lyon 1, IFSTTAR, UMR_T9406, LBMC, Lyon, France
Keyi Tang
University of British Columbia, Vancouver, BC, Canada
Maxim Van den Abbeele
Arts et Metiers ParisTech LBM/Institut de Biomecanique Humaine Georges Charpak, Paris, France
Marc van Vijven
Eindhoven University of Technology, Eindhoven, The Netherlands
Arne Vogel
Institute of Bioengineering, EPFL, Lausanne, Switzerland
Nicolas Vuillerme
Univ. Grenoble Alpes, AGEIS, Grenoble; Institut Universitaire de France, Paris, France
John S. Wilson
Emory University, Atlanta, GA, United States
Saami K. Yazdani
University of South Alabama, Mobile, AL, United States
Florence Zara
Universite de Lyon, CNRS, Villeurbanne, France
Jingbo Zhao
Aarhus University, Aarhus, Denmark
Preface
Biomechanics of human soft tissues has been an emerging research field since the publication, in 1981,
1
of the book Biomechanics: Mechanical Properties of Living Tissues by Yuan-Cheng Fung. Since that
date, many groups in the world have proposed biomechanical models of soft organs to study their phys-
iology and mechanical behavior. Such organs indeed deform under physiological conditions (such as
muscle activations or interactions with other tissues) or because of the mechanical interaction with the
surgical gesture. For example, modeling human heart deformations requires an accurate description of
the passive and active behaviors of cardiac fibers and their coupling with the blood flow. Assisting a
surgical gesture to compensate for brain shift during tumor resection needs to model the brain’s
deformations and its mechanical interactions with the skull surface and with the surgical tools.
Human soft tissues are complex materials that can exhibit nonlinear, time dependent, inhomo-
geneous, and anisotropic behaviors. Modeling such behaviors is usually proposed with the partial
differential equations (PDE) of continuum mechanics that are numerically solved through the Finite
Element (FE) Method. Elaborating a subject-specific FE model is a long and tedious task that requires
(1) collecting data as concerns the geometry of the organ, (2) proposing a constitutive model and
estimating its parameters for the organ soft tissues, (3) defining boundary conditions describing the
mechanical interactions with the organ, and (4) solving the PDE with the FE method, using a 3D
meshing of the organ’s geometry, and a numerical simulation. While estimating the subject-specific
3D geometry of the organ (mainly using segmentation techniques applied to 3D images such as CT
or MRI) and solving the PDE (using dedicated FE software) are now quite straightforward tasks,
the choice for a constitutive model of the organ is still an open question source of many works. Indeed,
for each organ of the human body, various constitutive models have been proposed, raising questions
such as: “Should we consider the tissue deformations as large enough to need a hyperelastic frame-
work?”; “If yes, which strain energy functions are the most appropriate to model the passive and active
states of the living tissue?”; “How can we model muscle contraction, damaged biological tissues, soft
tissue growth, and remodeling?”; “Should we take into account viscosity?”; “Do the proposed energy
functions have a physical meaning?”
Biomechanics of Living Organs: Hyperelastic Constitutive Laws for Finite Element Modeling is the
first book to cover finite element biomechanical modeling of each organ in the human body. This book
aims at (1) introducing the basic notions about the hyperelastic constitutive laws for biological living
tissues and (2) describing the main human organs, from the head to the foot, and proposing for each
organ the most adapted constitutive model. For this, we have gathered the scientific key opinion leaders
who propose review chapters focused on the constitutive laws that should be considered as a reference
for each organ. The first part of the book is a basic description of the equations that govern hyperelas-
ticity, with focuses on isotropic vs. anisotropic passive or active tissues, visco-hyperelastic constitutive
models, and formulations for soft tissue growth and remodeling, as well as damaged tissues. Then, part
2 provides review chapters for the reference constitutive models of “passive” soft organs, from the
brain to the uterus. For all these organs, tissue deformations are from external loading, such as gravity,
mechanical interactions with surrounding tissues, or with the surgical tools. Part 3 concerns “active”
1Fung, Y.C., 1981. Biomechanics: Mechanical Properties of Living Tissues. Springer, New York.
xxv
xxvi Preface
organs, the shapes of which are also determined by the recruitment of muscles, some of them being
internal to the structure, in such a way that, as for the elephant trunk, part of the organ is responsible
for its own deformation. This is the case for the face, the tongue, the upper airways, and the heart.
Finally, part 4 or the book describes the constitutive models that should be provided when modeling
musculoskeletal structures such as the spine, the thigh, the calf, and the foot.
It is important to note that the scientific key opinion leaders who have reviewed the most efficient
constitutive models of the human organs in this book have all provided full FE implementations of
organ models. They should, to our point of view, be considered as references for students, researchers,
clinicians, and industrial partners who want to build and use organ biomechanical models in the future.
It is our hope this book will provide the reader a comprehensive overview of the state-of-the-art in
hyperelastic constitutive laws for organs’ FE modeling. We would like to thank all the authors and
reviewers for their contributions and their enthusiasm during the writing of this book.
Yohan Payan
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble France
Jacques Ohayon
TIMC-IMAG Laboratory, University Grenoble Alpes, CNRS, Grenoble France
University Savoie Mont-Blanc, Polytech Annecy-Chambery, Le Bourget du Lac, France
