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.

1. INTRODUCTION. 1.1 Historical Prelude, 1.2 Basic Cell Biology, 1.3 The Extracellular Matrix, 1.4 Soft Tissue Behavior, 1.5 Needs and General Approach, 1.6 Exercises, 1.7 References. 2. MATHEMATICAL PRELIMINARIES 2.1 A Direct Tensor Notation, 2.2 Cartesian Components, 2.3 Further Results in Tensor Calculus, 2.4 Orthogonal Curvilinear Components, 2.5 Matrix Methods, 2.6 Exercises, 2.7 References, 3. CONTINUUM MECHANICS 3.1 Kinematics, 3.2 Forces, Tractions and Stresses, 3.3 Balance Relations, 3.4 Constitutive Formulations, 3.5 Boundary and Initial Conditions, 3.6 Exercises, 3.7 References, 4. FINITE ELASTICITY 4.1 Introduction, 4.2 Incompressible Isotropic Elasticity, 4.3 Solutions in 3-D Incompressible Elasticity, 4.4 Compressible Isotropic Elasticity, 4.5 Membrane Hyperelasticity, 4.6 Exercises, 4.7 References 5. EXPERIMENTAL METHODS 5.1 General Philosophy, 5.2 Measurement of Strain, 5.3 Measurement of Applied Loads, 5.4 Testing Conditions, 5.5 Parameter Estimation and Statistics, 5.6 Exercises, 5.7 References 6. Finite Element Methods 6.1 Fundamental Equations, 6.2 Interpolation, Integration, and Solvers, 6.3 An Illustrative Formulation, 6.4 Inflation of a Membrane, 6.5 Inverse Finite Elements, 6.6 Exercises, 6.7 References PART II - VASCULAR MECHANICS 7. THE NORMAL ARTERIAL WALL 7.1 Structure and Function, 7.2 General Characteristics, 7.3 Constitutive Framework, 7.4 Experimental Methods, 7.5 Specific Constitutive Relations, 7.6 Stress Analyses, 7.7 Exercises, 7.8 References 8. VASCULAR DISORDERS 8.1 Hypertension, 8.2 Intracranial Aneurysms, 8.3 Atherosclerosis, 8.4 Aortic Aneurysms, 8.5 Additional Topics, 8.6 Exercises, 8.7 References 9. VASCULAR ADAPTATION 9.1 Mechanical Preliminaries, 9.2 Cellular Responses to Applied Loads, 9.3 Arterial Response to Hypertension, 9.4 Arterial Response to Altered Flow, 9.5 Vessel Response to Injury, 9.6 Veins as Arterial Grafts, 9.7 Aging, 9.8 Exercises, 9.9 References PART III CARDIAC MECHANICS 10. THE NORMAL HEART 10.1 Structure and Function, 10.2 General Characteristics, 10.3 Constitutive Framework, 10.4 Constitutive Relations, 10.5 Stress Analyses, 10.6 Exercises, 10.7 References 11. EPILOGUE APPENDICES I. Nomenclature, Abbreviations, and Conversions II. Results for Curvilinear Coordinates III. Material Frame Indifference 11. CARDIAC DISORDERS 11.1 Ischemia 11.2 Volume Overload 11.3 Hypertrophy 11.4 Cardiac Aneurysms 11.5 Additional Topics