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Biomechanics of Living Organs
Biomechanics of human soft tissues has been an emerging research field since the publication, in 1981, of the book Biomechanics: Mechanical Properties of Living Tissues by Yuan-Cheng Fung. 1 Since that date, many groups in the world have proposed biomechanical models of soft organs to study their physiology 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, inhomogeneous, 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 framework?”; “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 hyperelasticity, 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” 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.
- Covers hyper elastic frameworks for large tissue deformations
- Considers which strain energy functions are the most appropriate to model the passive and active states of living tissue
- Evaluates the physical meaning of proposed energy functions
Chapter 1 – Hyperelasticity Modeling for Incompressible Passive Biological Tissues is available on ScienceDirect for a limited time.
Soft tissues are mainly composed of organized biological media giving them an anisotropic mechanical behavior. Soft tissues also have the ability to undergo large elastic reversible deformations. Many constitutive models were developed to describe these phenomena. In this chapter, we discuss several varying models and their constitutive equations which are defined by means of strain components or strain invariants. The notion of tangent moduli will be plotted for two well-known constitutive equations, and we will illustrate how to implement explicitly a structural kinematics constraint in a constitutive law to derive the resulting Cauchy stress tensor.
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