Humphrey, Jay D. : Texas A&M University, College Station, TX

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.

The book is divided into three parts. In Part I - Foundations, the book briefly reviews some historical points of interest, molecular and cell biology, histology, and the general subject of soft tissue mechanics. Chapters 2-6 review some mathematical preliminaries and salient results from continuum mechanics, finite elasticity, experimental mechanics, and finite elements that provide not only a working framework, but also give key references for those who wish to develop and extend biomechanics, not just apply it.

Part II - Vascular Mechanics, reviews the anatomy, histology, and physiology of arteries. With this as a starting point, the foundations in Part I are illustrated by discussing constitutive formulations and stress analyses for healthy mature arteries. Considerable attention is given to the concept of residual stress which, by tending to homogenize the transmural stress field in arteries, plays a tremendous role in the growth and remodeling of blood vessels. Finally, 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 are reviewed .

Part III - Cardiac Mechanics, similarly reviews the requisite anatomy, histology, physiology, and pathology. and discusses constitutive relations and stress analyses in the normal, mature heart as well as the mechanics of various cardiac pathologies.

The book concludes by pointing 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.

The book is designed to be 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 help the student. Clinicians, life scientists, engineers and mathematicians will also find this an invaluable guide to the subject as the book is amply referenced.

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