Cardiovascular Solid Mechanics

by Humphrey, Jay Dowell

• ISBN13: 9780387951683
• ISBN10: 0387951687
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: Springer Verlag

Summary

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.

Table of Contents

Preface	vii
Acknowledgments	xi
Part I--Foundations	1	(246)
Introduction	3	(37)
Historical Prelude	4	(10)
Basic Cell Biology	14	(4)
The Extracellular Matrix	18	(6)
Soft Tissue Behavior	24	(8)
Needs and General Approach: Clinical Motivations	32	(4)
Exercises	36	(1)
References	37	(3)
Mathematical Preliminaries	40	(28)
A Direct Tensor Notation	40	(5)
Cartesian Components	45	(8)
Further Results in Tensor Calculus	53	(2)
Orthogonal Curvilinear Components	55	(7)
Matrix Methods	62	(3)
Exercises	65	(1)
References	66	(2)
Continuum Mechanics	68	(39)
Kinematics	69	(10)
Forces, Tractions, and Stresses	79	(3)
Basic Postulates	82	(4)
Constitutive Formulations	86	(15)
Boundary and Initial Conditions	101	(1)
Exercises	102	(3)
References	105	(2)
Finite Elasticity	107	(51)
Incompressible Isotropic Elasticity	107	(9)
Solutions in 3D Incompressible Elasticity	116	(15)
Compressible Isotropic Elasticity	131	(5)
Membrane Hyperelasticity	136	(15)
Exercises	151	(4)
References	155	(3)
Experimental Methods	158	(53)
General Philosophy	158	(7)
Measurement of Strain	165	(14)
Measurement of Applied Loads	179	(9)
Computer-Aided Experimentation	188	(10)
Parameter Estimation and Statistics	198	(7)
Exercises	205	(3)
References	208	(3)
Finite Elements	211	(36)
Fundamental Equations	213	(3)
Interpolation, Integration, and Solvers	216	(7)
An Illustrative Formulation	223	(11)
Inflation of a Membrane	234	(3)
Inverse Finite Elements	237	(2)
Exercises	239	(5)
References	244	(3)
Part II--Vascular Mechanics	247	(352)
The Normal Arterial Wall	249	(116)
Structure and Function	249	(15)
General Characteristics	264	(25)
Constitutive Framework	289	(21)
Experimental Methods	310	(9)
Specific Constitutive Relations	319	(16)
Stress Analyses	335	(19)
Exercises	354	(3)
References	357	(8)
Vascular Disorders	365	(134)
Hypertension	365	(21)
Intracranial Aneurysms	386	(43)
Atherosclerosis	429	(17)
Aortic Aneurysms	446	(13)
Additional Topics	459	(14)
Exercises	473	(3)
References	476	(23)
Vascular Adaptation	499	(100)
Mechanical Preliminaries	500	(22)
Cellular Responses to Applied Loads	522	(17)
Arterial Response to Hypertension	539	(12)
Arterial Response to Altered Flow	551	(11)
Vessel Response to Injury	562	(7)
Veins as Arterial Grafts	569	(9)
Aging	578	(2)
Exercises	580	(4)
References	584	(15)
Part III--Cardiac Mechanics	599	(131)
The Normal, Mature Heart	601	(124)
Structure and Function	601	(16)
General Characteristics	617	(16)
Constitutive Framework	633	(22)
Constitutive Relations	655	(43)
Stress Analysis	698	(11)
Exercises	709	(3)
References	712	(13)
Epilogue	725	(5)
References	729	(1)
Appendices	730	(21)
I. Nomenclature, Common Abbreviations, and Conversion Factors	730	(5)
I.1 Nomenclature	730	(3)
I.2 Common Abbreviations	733	(1)
I.3 Conversion Factors	733	(2)
II. Results for Curvilinear Coordinates	735	(11)
II.1 Cylindrical Coordinates	735	(6)
II.2 Spherical Coordinates	741	(2)
II.3 Prolate Spheroidal Coordinates	743	(1)
II.4 Exercises	744	(1)
II.5 Reference	745	(1)
III. Material Frame-Indifference	746	(5)
III.1 Exercises	749	(2)
Index	751