Jay D. Humphrey

Cardiovascular Solid Mechanics: Cells, Tissues, and Organs

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

A CONSTRAINED MIXTURE MODEL FOR GROWTH AND REMODELING OF SOFT TISSUES

Not long ago it was thought that the most important characteristics of the mechanics of soft tissues were their complex mechanical properties: they often exhibit nonlinear, anisotropic, nearly inco...

Mechanotransduction and extracellular matrix homeostasis

Soft connective tissues at steady state are dynamic; resident cells continually read environmental cues and respond to them to promote homeostasis, including maintenance of the mechanical properties of the extracellular matrix (ECM) that are fundamental to cellular and tissue health. The mechanosensing process involves assessment of the mechanics of the ECM by the cells through integrins and the actomyosin cytoskeleton, and is followed by a mechanoregulation process, which includes the deposition, rearrangement or removal of the ECM to maintain overall form and function. Progress towards understanding the molecular, cellular and tissue-level effects that promote mechanical homeostasis has helped to identify key questions for future research.

Review Paper: Continuum biomechanics of soft biological tissues

Since its coming of age in the mid 1960s, continuum biomechanics has contributed much to our understanding of human health as well as to disease, injury, and their treatment. Nevertheless, biomechanics has yet to reach its full potential as a consistent contributor to the improvement of health–care delivery. Because of the inherent complexities of the microstructure and biomechanical behaviour of biological cells and tissues, there is a need for new theoretical frameworks to guide the design and interpretation of new classes of experiments. Because of continued advances in experimental technology, and the associated rapid increase in information on molecular and cellular contributions to behaviour at tissue and organ levels, there is a pressing need for mathematical models to synthesize and predict observations across multiple length– and time–scales. And because of the complex geometries and loading conditions, there is a need for new computational approaches to solve the boundaryand initial–value problems of clinical, industrial, and academic importance. Clearly, much remains to be done. The purpose of this paper is twofold: to review a few of the many achievements in the biomechanics of soft tissues and the tools that allowed them, but, more importantly, to identify some of the open problems that merit increased attention from those in applied mechanics, biomechanics, mathematics and mechanobiology.

Stress-Modulated Growth, Residual Stress, and Vascular Heterogeneity

A simple phenomenological model is used to study interrelations between material properties, growth-induced residual stresses, and opening angles in arteries. The artery is assumed to be a thick-walled tube composed of an orthotropic pseudoelastic material. In addition, the normal mature vessel is assumed to have uniform circumferential wall stress, which is achieved here via a mechanical growth law. Residual stresses are computed for three configurations: the unloaded intact artery, the artery after a single transmural cut, and the inner and outer rings of the artery created by combined radial and circumferential cuts. The results show that the magnitudes of the opening angles depend strongly on the heterogeneity of the material properties of the vessel wall and that multiple radial and circumferential cuts may be needed to relieve all residual stress. In addition, comparing computed opening angles with published experimental data for the bovine carotid artery suggests that the material properties change continuously across the vessel wall and that stress, not strain, correlates well with growth in arteries.

Determination of a Constitutive Relation for Passive Myocardium: II.—Parameter Estimation

In the first paper of this series, we proposed a new transversely isotropic pseudostrain-energy function W for describing the biomechanical behavior of excised noncontracting myocardium. The specific functional form of W was inferred directly from biaxial data to be a polynomial function of two coordinate invariant measures of the finite deformation and five material parameters. In this paper, best-fit values of the material parameters are determined from biaxial data using a nonlinear least-squares regression. These values of the parameters are shown to be well-determined, and the final constitutive relation is shown to have good predictive capabilities. Since the proposed constitutive relation describes much broader classes of in-vitro biaxial data than previously proposed relations, it may be better applicable to analyses of stress in the passive heart.

A Theoretical Model of Enlarging Intracranial Fusiform Aneurysms

The mechanisms by which intracranial aneurysms develop, enlarge, and rupture are unknown, and it remains difficult to collect the longitudinal patient-based information needed to improve our understanding. We submit, therefore, that mathematical models hold promise by allowing us to propose and test competing hypotheses on potential mechanisms of aneurysmal enlargement and to compare predicted outcomes with limited clinical information--in this way, we may begin to narrow the possible mechanisms and thereby focus experimental studies. In this paper, we present a constrained mixture model of evolving thin-walled, fusiform aneurysms and compare multiple competing hypotheses with regard to the production, removal, and alignment of the collagen that provides the structural integrity of the wall. The results show that this type of approach has the capability to infer potential means by which lesions enlarge and whether such changes are likely to produce a stable or unstable process. Such information can better direct the requisite histopathological examinations, particularly on the need to quantify collagen orientations as a function of lesion geometry.

Heat-Induced Changes in the Mechanics of a Collagenous Tissue: Isothermal Free Shrinkage

We present data from isothermal free-shrinkage tests (i.e., performed in the absence of mechanical loads) wherein bovine chordae tendineae were subjected to temperatures from 65 to 85 degrees C for 120 to 1200 s. These data reveal four new insights into heat-induced denaturation of a collagenous tissue. First, a characteristic time for the free shrinkage appears to exhibit an Arrhenius-type relationship with temperature. Second, scaling the actual heating time via the characteristic time results in a single correlation between free shrinkage and the duration of heating; this correlation suggests a time-temperature equivalence. Third, it is the cumulative, not current, heating time that governs the free shrinkage. And fourth, heat-induced free shrinkage is partially recovered when the tissue is returned to 37 degrees C, this recovery also being time-dependent. Although these findings will help guide future experimentation and constitutive modeling, as well as the design of new heat-based clinical therapies, there is a pressing need to collect additional isothermal data, particularly in the presence of well-defined mechanical loads.

Upregulation of Vascular Arginase in Hypertension Decreases Nitric Oxide–Mediated Dilation of Coronary Arterioles

One characteristic of hypertension is a decreased endothelium-dependent nitric oxide (NO)-mediated vasodilation; however, the underlying mechanism is complex. In endothelial cells (ECs), l-arginine is the substrate for both NO synthase (NOS) and arginase. Because arginase has recently been shown to modulate NO-mediated dilation of coronary arterioles by reducing l-arginine availability, we hypothesized that upregulation of vascular arginase in hypertension contributes to decreased NO-mediated vasodilation. To test this hypothesis, hypertension (mean arterial blood pressure >150 mm Hg) was maintained for 8 weeks in pigs by aortic coarctation. Coronary arterioles from normotensive (NT) and hypertensive (HT) pigs were isolated and pressurized for in vitro study. NT vessels dilated dose-dependently to adenosine (partially mediated by endothelial release of NO) and sodium nitroprusside (endothelium-independent vasodilator). Conversely, HT vessels exhibited reduced dilation to adenosine but dilated normally to sodium nitroprusside. Adenosine-stimulated NO release was increased ≈3-fold in NT vessels but was reduced in HT vessels. Moreover, arginase activity was 2-fold higher in HT vessels. Inhibition of arginase activity by N&ohgr;-hydroxy-nor-l-arginine or incubation with l-arginine partially restored NO release and dilation to adenosine in HT vessels. Immunohistochemistry showed that arginase expression was increased but NOS expression was decreased in arteriolar ECs of HT vessels. These results suggest that NO-mediated dilation of coronary arterioles is inhibited in hypertension by an increase in arginase activity in EC, which limits l-arginine availability to NOS for NO production. The inability of arginase blockade or l-arginine supplementation to completely restore vasodilation may be related to downregulation of endothelial NOS expression.

Mechanisms of arterial remodeling in hypertension: coupled roles of wall shear and intramural stress.

Diverse data collected over the past 4 decades suggest the existence of a mechanical homeostasis across multiple length and time scales in the vasculature. For example,1 stress fibers within endothelial and vascular smooth muscle cells appear to disassemble and then reassemble in a mechanically preferred manner when perturbed from a normal value of mechanical stress or strain; focal adhesions in smooth muscle cells and fibroblasts tend to increase in area in response to local increases in mechanical loading so as to maintain the stress constant at a preferred value; fibroblasts tend to increase the tractions that they exert on the extracellular matrix when external loads are decreased from a preferred value, thus suggesting an attempt to enforce a “tensional homeostasis”; vascular smooth muscle cells tend to relengthen to their normal, preferred values when an arteriole is forced into a vasoconstricted state for an extended period; and arteries tend to decrease in caliber in response to sustained decreases in flow-induced wall shear stress, to increase in thickness in response to sustained increases in pressure-induced circumferential stress, and to lengthen in response to extension-induced increases in axial stress. Although changes in the cytoskeleton and integrins occur within minutes, changes at the cell-cell and cell-matrix levels occur over hours, and those at the vessel level occur over days to weeks or months. Hence, despite marked differences in length scales (dimensions from nanometers to centimeters) and time scales (durations from minutes to months), mechanobiological control mechanisms in the vasculature tend to restore values of stress or strain toward preferred (homeostatic) values in response to diverse perturbations from normal.2–5 Biomechanics and mechanobiology thus play key roles in vascular development, tissue maintenance in maturity, normal adaptations, aging, disease progression, and responses to injury or clinical interventions. A current challenge in hypertension research is to …