Ebook: Cardiovascular Solid Mechanics: Cells, Tissues, and Organs

The vitality of the cardiovascular system, which consists of the heart, vas­ culature, and blood, depends on its response to a host of complex stimuli, including biological, chemical, electrical, mechanical, and thermal. The focus of this book, however, is on the response of the heart and arteries to mechanical loads from the perspective of nonlinear solid mechanics. Through my own research in this field, I have come to realize that study­ ing the complex responses of cardiovascular cells, tissues, and organs nec­ essarily requires a combined theoretical, experimental, and computational approach. Theory is needed to guide the performance and interpretation of experiments as well as to synthesize the results; experiment is needed to study the responses of the system to well-controlled loads and to test can­ didate hypotheses and theories; and due to the geometric and material non­ linearities inherent to cardiovascular mechanics, computation is needed to analyze data as well as to solve boundary and initial value problems that correspond to either experimental or in vivo conditions. One of the primary goals of this book is to introduce together basic analytical, experimental, and computational methods and to illustrate how these methods can and must be integrated to gain a more complete understanding of the bio­ mechanics of the heart and vasculature. Despite the focus on cardiovascu­ lar mechanics, the fundamental methods, indeed many of the specific results, are generally applicable to many different soft tissues.

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This text presents a general introduction to soft tissue biomechanics. One of its primary goals is to introduce basic analytical, experimental and computational methods. In doing so, it enables readers to gain a relatively complete understanding of the biomechanics of the heart and vasculature. Cardiovascular Solid Mechanics: Cells, Tissues, and Organs is a vital resource for courses on cardiovascular solid mechanics or soft tissue biomechanics. Focusing on the response of the heart and blood vessels to mechanical loads from the perspective of nonlinear solid mechanics, its primary goal is to integrate basic analytical, experimental, and computational methods to offer a more complete understanding of the underlying mechanobiology. While dealing primarily with cardiovascular mechanics, both the fundamental methods and many of the specific results are applicable to many different soft tissues, making this book an excellent general introduction to soft tissue biomechanics overall. Divided into three parts, Cardiovascular Solid Mechanics presents a practical and rational approach to biomechanics. Part I, Foundations, briefly reviews historical points of interest, basic molecular and cell biology, histology, and an overview of soft tissue mechanics. In order to provide not only a working framework, but also to give key references for those who wish to develop and extend biomechanics, included are mathematical preliminaries and salient results from continuum mechanics, finite elasticity, experimental mechanics, and finite elements. Part II, Vascular Mechanics, reviews the anatomy, histology, and physiology of arteries, illustrating and discussing constitutive formulations and stress analyses for healthy mature arteries. Considerable attention is given to the concept of residual stress and the mechanics of a number of vascular disorders, including atherosclerosis, aneurysms, and hypertension, as well as the mechanics of popular endovascular therapies such as balloon angioplasty. Part III, Cardiac Mechanics, reviews the requisite anatomy, histology, physiology, and pathology, and discusses the constitutive relations and stress analyses in the normal, mature heart. Finally, the book points the reader to areas of study that require more advanced theoretical, experimental, and computational methods, such as electromechanics, thermomechanics, mixture theory analysis of solid-fluid coupling, and damage mechanics. This book is designed as a text for an upper-division course on cardiovascular solid mechanics but will also serve as a good introduction to soft tissue biomechanics. Exercises at the end of each chapter will clarify complex concepts for both students and more experienced readers. Clinicians, life scientists, engineers, and mathematicians will also find this an invaluable guide, with concise and practical chapters, all of which are amply referenced. Cover illustration: Schema of a developing pathology of the arterial wall under mechanical stress. Excerpts Biomechanics can be defined as the development, extension, and application of mechanics to answer questions of importance in biology and medicine. It is only through biomechanics that we can understand, and thus address, many of the biophysical phenomena that occur at the molecular, cellular, tissue, and organism levels. Hence, biomechanics is as important as it is challenging. Because of the complexity of tissue structure and behavior, there is a need for sophisticated theoretical ideas; because of a continuing lack of data, there is a need for new, clever experiments; because of the geometric complexity of cells, tissues, and organs, there is a need for robust computational methods; and because of of the morbidity and mortality that results from disease and injury, there is a need for improved modalities for diagnosis and treatment. Much has been learned and accomplished, but much remains to be done. As a specialty area within biomechanics, cardiovascular solid mechanics seeks to increase our understanding of the physiology and pathophysiology of the heart and vasculature, and to improve the requisite diagnostic and therapeutic capabilities. Our approach is base on the *continuum hypothesis*, thus we assume that characteristic length scales of the microstructure are much smaller than characteristic length scales of the overall problem of interest (e.g., a vascular smooth muscle cell is orders of magnitude smaller than the thickness of the arterial wall). Given this assumption, we can define locally averaged properties at each point in the body and thereby define physical quantities of interest using continuous functions. Page 3-4, added anonymously. "This excerpt outlines the scope of the monograph and the general investigative approach used." Table of Contents Part I-Foundations 1 1. Introduction 3 1.1 Historical Prelude 4 1.2 Basic Cell Biology 14 1.3 The Extracellular Matrix 18 1.4 Soft Tissue Behavior 24 1.5 Needs and General Approach: Clinical Motivations 32 1.6 Exercises 36 1.7 References 37 2. Mathematical Preliminaries 40 2.1 A Direct Tensor Notation 40 2.2 Cartesian Components 45 2.3 Further Results in Tensor Calculus 53 2.4 Orthogonal Curvilinear Components 55 2.5 Matrix Methods 62 2.6 Exercises 65 2.7 References 66 3. Continuum Mechanics 68 3.1 Kinematics 69 3.2 Forces, Tractions, and Stresses 79 3.3 Basic Postulates 82 3.4 Constitutive Formulations 86 3.5 Boundary and Initial Conditions 101 3.6 Exercises 102 3.7 References 105 4. Finite Elasticity 107 4.1 Incompressible Isotropic Elasticity 107 4.2 Solutions in 3D Incompressible Elasticity 116 4.3 Compressible Isotropic Elasticity 131 4.4 Membrane Hyperelasticity 136 4.5 Exercises 151 4.6 References 155 5. Experimental Methods 158 5.1 General Philosophy 158 5.2 Measurement of Strain 165 5.3 Measurement of Applied Loads 179 5.4 Computer-Aided Experimentation 188 5.5 Parameter Estimation and Statistics 198 5.6 Exercises 205 5.7 References 208 6. Finite Elements 211 6.1 Fundamental Equations 213 6.2 Interpolation, Integration, and Solvers 216 6.3 An Illustrative Formulation 223 6.4 Inflation of a Membrane 234 6.5 Inverse Finite Elements 237 6.6 Exercises 239 6.7 References 244 Part II-Vascular Mechanics 247 7. The Normal Arterial Wall 249 7.1 Structure and Function 249 7.2 General Characteristics 264 7.3 Constitutive Framework 289 7.4 Experimental Methods 310 7.5 Specific Constitutive Relations 319 7.6 Stress Analyses 335 7.7 Exercises 354 7.8 References 357 8. Vascular Disorders 365 8.1 Hypertension 365 8.2 Intracranial Aneurysms 386 8.3 Atherosclerosis 429 8.4 Aortic Aneurysms 446 8.5 Additional Topics 459 8.6 Exercises 473 8.7 References 476 9. Vascular Adaptation 499 9.1 Mechanical Preliminaries 500 9.2 Cellular Responses to Applied Loads 522 9.3 Arterial Response to Hypertension 539 9.4 Arterial Response to Altered Flow 551 9.5 Vessel Response to Injury 562 9.6 Veins as Arterial Grafts 569 9.7 Aging 578 9.8 Exercises 580 9.9 References 584 Part Ill-Cardiac Mechanics 599 10. The Normal, Mature Heart 601 10.1 Structure and Function 601 10.2 General Characteristics 617 10.3 Constitutive Framework 633 10.4 Constitutive Relations 655 10.5 Stress Analysis 698 10.6 Exercises 709 10.7 References 712 11. Epilogue 725 11.1 References 729 Appendices 730 I. Nomenclature, Common Abbreviations, and Conversion Factors 730 I.1 Nomenclature 730 I.2 Common Abbreviations 733 I.3 Conversion Factors 733 II. Results for Curvilinear Coordinates 735 II.1 Cylindrical Coordinates 735 II.2 Spherical Coordinates 741 II.3 Prolate Spheroidal Coordinates 743 II.4 Exercises 744 II.5 Reference 745 III. Material Frame-Indifference 746 III.1 Exercises 749

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This a new text for bioengineering students taking a course on cardiovascular solid mechanics or soft tissue biomechanics. The focus of the book is a look at the response of the heart and arteries to mechanical loads from the perspective of nonlinear solid mechanics and one of its primary goals is to introduce basic analytical, experimental, and computational methods together so as to illustrate how these methods can and must be integrated in order to gain a more complete understanding of the biomechanics of the heart and vasculature. Despite the focus on cardiovascular mechanics, the fundamental methods, indeed many of the specific results, are generally applicable to many different soft tissues. Hence, this book can be regarded as a general introduction to soft tissue biomechanics, not just a study of cardiovascular solid mechanics.
Content:
Front Matter....Pages i-xvi
Front Matter....Pages 1-1
Introduction....Pages 3-39
Mathematical Preliminaries....Pages 40-67
Continuum Mechanics....Pages 68-106
Finite Elasticity....Pages 107-157
Experimental Methods....Pages 158-210
Finite Elements....Pages 211-246
Front Matter....Pages 247-247
The Normal Arterial Wall....Pages 249-364
Vascular Disorders....Pages 365-498
Vascular Adaptation....Pages 499-597
Front Matter....Pages 599-599
The Normal, Mature Heart....Pages 601-724
Epilogue....Pages 725-729
Back Matter....Pages 730-757
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