Biomechanics of Soft Tissue in Cardiovascular Systems PDF
Preview Biomechanics of Soft Tissue in Cardiovascular Systems
CISM COURSES AND LECTURES Series Editors: The Rectors Manuel Garcia Velarde- Madrid Mahir Sayir -Zurich Wilhelm Schneider -Wien The Secretary General Bernhard Schrefter -Padua Former Secretary General Giovanni Bianchi -Milan Executive Editor Carlo Tasso- Udine The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences. INTERNATIONAL CENTRE FOR MECHANICAL SCIENCES COURSES AND LECTURES- No. 441 BIOMECHANICS OF SOFT TISSUE IN CARDIOVASCULAR SYSTEMS EDITED BY GERHARD A. HOLZAPFEL GRAZ UNIVERSITY OF TECHNOLOGY RAYW.OGDEN UNIVERSITY OF GLASGOW t Springer-Verlag Wien GmbH This volume contains 148 illustrations This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. ISBN 978-3-211-00455-5 ISBN 978-3-7091-2736-0 (eBook) DOI 10.1007/978-3-7091-2736-0 © 2003 by Springer-Verlag Wien Originally published by CISM, Udine in 2003. SPIN 10911716 In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader. PREFACE This volume consists of the Lecture Notes for an Advanced School on "Biomechanics of Soft Tissue" held at the International Centre for Mechanical Sciences (CISM) in Udine, Italy, during the period September 10-14, 2001. The course was presented by 6 lecturers, 3 from Europe, 2 from the USA and 1 from Japan and was attended by nearly 70 participants from 20 countries. Biomechanics in general, and the biomechanics of soft tissue in particular, did not really become a clearly defined and active research field until the mid-1960s. It is suggested that there were three major events in history necessary before the modern biomechanics of soft tissue could evolve: (i) the development of the nonlinear field theory of mechanics during the 1950s and 1960s; ( ii) the development of the finite element method in the 1950s and subsequently; (iii) the rapid advances in computer technology. Analyzing the mechanical response of any soft tissue presents many fascinating challenges to various disciplines. Today's soft tissue mechanics is a distinct multidisciplinary field of rese arch involving disciplines such as experimental and applied mechanics, mathematics, biology, engineering and clinical medicine. Interdisciplinary and multidisciplinary teams provide the key to answering questions concerning the many diverse forms of biological soft tissues. What all soft tissues have in common is that they are composed of cells (the fundamental structural and functional units) plus other material such as the extracellular matrix (which serves several fun ctions in a strong symbiotic relationship with the cells). They are anisotropic, non-homogeneous and pre-strained, exhibit highly nonlinear and time-dependent responses under different loading conditions, undergo large deformations, and cannot always be treated within a purely mechani calframework. The study of both the biological and mechanical characteristics of tissue consti tuents is important for contributing a deeper understanding of soft tissue structure and function and, in particular, the underlying mechanobiology. Of course, it is the complexity and the neces sity for multidisciplinary approaches that makes the analysis of soft tissue so challenging. The focus in this volume is a review of our current knowledge of the behaviour of soft tis sues in the cardiovascular system under mechanical loads, and the importance of constitutive laws in understanding the underlying mechanics is highlighted. There are many important pro blems found in health, rehabilitation, disease, injury, and clinical intervention that require an understanding of the biomechanics of soft tissue. In particular, the clinical importance of this understanding, which should be based on physiology, cell biology, physical and computational models, and the solution of boundary and initial value problems, has never been greater. One important example is balloon angioplasty, which is a well-established interventional procedure aimed at reducing the severity of atherosclerotic stenoses. Balloon angioplasty is the most frequently used therapeutical intervention world wide and attracts great and steadily growing medical, economic and scientific interest. A total of 1,069,000 angioplasty procedures (including 601,000 coronary angioplasty procedures) were performed in 1999 in the United States alone. From 1987 to 1999 the number of procedures increased 285 percent and the number ofp atients increased 286 percent1• The knowledge that balloon angioplasty is a mecha- 1 American Heart Association. 2002 Heart and Stroke Statistical Update. American Heart Association, Dallas, Texas, 2001. nical solution for a clinical problem implies the necessity for a detailed understanding of the biomechanics and mechanobiology of the types of soft tissues and calcifications involved. It is exactly this understanding that is needed to improve such procedures, which often fail due to restenosis (about 40% within six months at the coronary site). The lectures in the course aimed to present a state-of-the-art overview of the mechanics of soft tissues, with particular reference to arteries and the cardiovascular system, but also inclu ding information on tendons, ligaments and other biological soft tissues of current research inte rest in biomechanics. The lectures included (i) essential background on the histological structure of soft tissues, important knowledge for developing both microscopic and macroscopic material models in order to understand the underlying physiological functions, ( ii) details ofe xperimental techniques and the results of experiments, which provided information about the highly nonli near mechanical response of various soft tissues (and their component cells) under different boundary loads, which are invariably spatially non-uniform and time-varying, (iii) continuum mechanical modelling, which developed the nonlinear elasticity and viscoelasticity theory back ground, with particular reference to anisotropic response associated with fibre reinforcement, (iv) computational perspectives, a particular emphasis being on the nonlinear behaviour, and the application off inite element methods to the simulation of the biomechanics of intracranial saccular aneurysms and the heart, and to clinical procedures such as balloon angioplasty and stenting, (v) the topics of tissue remodelling and growth (important for, e.g., wound healing, adaptation to arterial hypertension, aneurysm development, morphogenesis etc.), together with aspects of arterial grafting and analysis of the influence of residual stress, ageing and degene ration on the mechanical characteristics. We have pleasure in thanking our colleagues, Jay D. Humphrey, Kozabura Hayashi, Andrew D. McCulloch, Alexander Rachev for presenting their lectures and for preparing and contribu ting chapters to this volume. We are also grateful for the participants, who contributed both short talks on their own work and to lively discussions. Special thanks are due to F. Holzmann for his contribution to the editing of parts of the manuscript. We thank particularly Professor S. Kaliszky, Rector of CISM, and the staff of CISM for their assistance and hospitality, and Pro fessor C. Tasso, Executive Editor of CISM, for his encouragement to publish this collection of lecture notes. G.A. Holzapfel R.W Ogden CONTENTS Page Preface The Cardiovascular System -Anatomy, Physiology and Cell Biology by Jay D. Humphrey and Andrew D. McCulloch ................................................ I Mechanical Properties of Soft Tissues and Arterial Walls by Kozaburo Hayashi ........................................................................................ 15 Nonlinear Elasticity, Anisotropy, Material Stability and Residual Stresses in Soft Tissue by Ray W Ogden ............................................................................................... 65 Structural and Numerical Models for the (Visco )elastic Response of Arterial Walls with Residual Stresses by Gerhard A. Holzapfel ................................................................................ 109 Intracranial Saccular Aneurysms by Jay D. Humphrey ........................................................................................ 185 Remodeling of Arteries in Response to Changes in their Mechanical Environ ment by Alexander Rachev ....................................................................................... 221 Computational Methods for Soft Tissue Biomechanics by Taras P. Usyk and Andrew D. McCulloch ................................................. 273 The Cardiovascular System - Anatomy, Physiology and Cell Biology J.D. Humphreyl and A.D. McCulloch2 1 Biomedical Engineering, Texas A&M University, College Station, TX77843-3120, USA E-mail: [email protected], Home Page: http://biomed.tamu.edu/faculty/humphrey/ 2 Department of Bioengineering, University of California, San Diego, La Jolla, CA92093-0412, USA E-mail: [email protected], Home Page: http://cmrg.ucsd.edu/ Abstract. Biomechanics aims to explain the mechanics of life and living. From molecules to organisms, everything must obey the laws of mechanics-Y.C. Fung. The primary func tion of the cardiovascular system is mass transport, that is, the transport of oxygen, carbon dioxide, nutrients, waste products, hormones, etc., within the body. This system consists primarily of the heart, which serves as the pump, the blood, which serves as the conducting medium, and the vasculature, which serves as the conduit through which the blood flows. Closely related systems are the cardio-pulmonary and reno-vascular systems. The primary organs of the pulmonary system are the lungs, which facilitate the exchange of oxygen and carbon dioxide between the blood and external environment, whereas the primary organs of the renal system are the kidneys, which serve as filters to remove waste products from the blood. Although studying the pulmonary and renal systems is important, interesting, and challenging, we shall focus on the heart and vasculature in this chapter. Moreover, within the vasculature there are numerous 'special' circulations, including the cerebral, coronary, pulmonary, and fetal. Our emphasis will be on general characteristics of the vasculature and heart, however. 1 The Heart 1.1 Basic Anatomy The heart consists of four chambers, the left and right atria and left and right ventricles, the latter two being separated by the interventricular septum. The atria receive blood from the body (the left from the lungs, the right from the remainder) and the ventricles pump blood to the body (the right to the lungs, the left to the remainder). One way flow is maintained within the heart by four valves, the pulmonary, aortic, mitral, and tricuspid. The latter two valves separate the atria and ventricles; they consist of two and three leaflets, respectively, and they are stabilized in part by thin collagenous fibers (called chordae tendineae) that connect them to finger-like projections of muscle within the ventricles, the papillary muscles. In addition to the distinct papillary mus cles, the interior surface of the heart is characterized by many trabeculae, or muscular ridges. The blood supply to the wall of the heart originates via three primary vessels: the left anterior descending artery (LAD), left circumflex artery (CIRC), and right coronary artery (RCA). In general, the left coronaries supply the left atrium and the anterior and lateral portions of the left ventricle (LV) and the right coronary artery supplies the right atrium and right ventricular free wall. The posterior and inferior portions of the ventricles may receive blood from either the left 2 J.D. Humphrey and A.D. McCulloch or right coronary systems. Furthermore, the interventricular septum, which separates the left and right ventricles, is typically supplied by branches off the LAD. The veins in the heart are divided into two systems. A large superficial system, the largest vessels of which parallel the main coronary arteries, drains most of the coronary blood into the right atrium, and a smaller, deeper system (e.g., thebesian veins) drains blood directly into any of the four chambers. The wall of the heart consists of three distinct layers: an inner layer called the endocardium, a middle layer called the myocardium, and an outer layer called the epicardium. The endocardium lines the inside of each of the cardiac chambers; it is a thin serous membrane(::::::: 100 mm thick) consisting primarily of a 2-D plexus of collagen and elastin as well as a single cell layer of endothelial cells that serve as a direct interface between the blood and the heart wall. The middle layer, or myocardium, is the parenchymal (i.e., functional) tissue that endows the heart with its ability to pump blood. The myocardium consists primarily of myocytes that are arranged into locally parallel muscle fibers that are embedded in an extracellular matrix consisting largely of types I and III collagen (collagen is the most abundant protein in the body). The orientations of the muscle fibers change with position in the wall; in the equatorial region, for example, the predominant muscle fiber direction changes from about -65° in the sub-epicardial region oo to nearly in the mid-wall region to about 65° in the sub-endocardial region, all relative to the circumferential direction. This transmural splay of fiber directions causes the heart to twist during the cardiac cycle. The outermost layer, or epicardium, is also a thin(::::::: 100 mm) serous layer, consisting largely of a 2-D plexus of collagen and some elastic fibers. Noting that the epicardium is also called the visceral pericardium, the heart is surrounded by yet another serous membrane, the pericardium (or parietal pericardium). This membrane is thicker than the endocardium and epicardium, but it also consists primarily of a 2-D plexus of collagen with some elastic fibers. The pericardium is at tached to the diaphragm inferiorly and the hilum superiorly, and it creates a small potential space about the heart that is filled with a 'lubricating' pericardia] fluid (::::::: 25 ml in man). It is thought that the pericardium serves as a type of cradle that limits gross motions of the heart, which is merely suspended in the chest by its connection to the lungs and major blood vessels. These are the major anatomical structures most commonly studied in the field of cardiac mechanics. In this chapter, particular emphasis is given to the ventricular walls, which are the most important structures with regard to the pumping action of the heart. From the perspective of mechanics, the ventricles are thick-walled three-dimensional pressure vessels whose thickness and curvatures vary regionally and temporally. In the normal heart, the ventricular walls are thickest at the equator and the base of the left ventricle and thinnest at the left ventricular apex and right ventricular free wall. Ventricular geometry has been best quantified in the canine heart. The left ventricle, for example, is modeled reasonably well as a thick-walled ellipsoid of revolution that is truncated at the base. The crescentic right ventricle wraps circumferentially around the left ventricle about 180 degrees and extends longitudinally about two-thirds of the distance from the base to the apex. 1.2 Histology and Cell Biology The myocardium consists primarily of two cell types, cardiac myocytes and fibroblasts, plus an abundant extracellular matrix (ECM). Although not capable of dividing, the cardiac myocyte is The Cardiovascular System-Anatomy, Physiology and Cell Biology 3 biologically active: it is capable of synthesizing new proteins and thereby altering its size and structure in response to changes in its environment (i.e., applied loads and the chemical milieu). Indeed, myocytes may replace the bulk of their protein molecules every week or two via a bal ance between synthesis and degradation. Cardiac myocytes are typically I 0-20 J.Lm in diameter and 80-125 J.Lm in length; they contain mainly myofibrils (1-2 ttm in diameter) within their cytoplasm. Each myofibril consists of a string of tiny contractile units (::::; 2.2 J.Lm long) called sarcomeres, and it is the end-to-end organization of the sarcomeres that gives cardiac muscle its striated appearance. Each sarcomere consists of overlapping thin actin (5 nm in diameter) and thick myosin (10-12 nm in diameter) filaments, an end view of which reveals a hexagonal stacking arrangement. The sliding filament theory of 1954 suggests that the myosin has many transverse arms, or cross-bridges, that are about 13 nm long and connect to the actin. Contraction is initiated by the release of ca++, which is sequestered in the surrounding sarcoplasmic reticulum, and results in a smooth ratcheting action (at ::::; 15 J.Lm/sec) as the cross-bridges release, move forward, and reattach thus shortening the sarcomere. The release of ca++ from the sarcoplasmic reticulum is induced by an action potential that spreads from the cell membrane into the cell via T-tubules. Note, too, that the sarcomere appears to be endowed with an elastic component-the proteins titin and nebulin, which associate with the actin and myosin-that augments relaxation. Conduction of electrical signals, and thus action potentials, from cell to cell is facilitated by end-to-end and side-to-side connections (gap junctions) between myocytes. In particular, my ocytes are arranged in long columns, with the double membranes between opposing ends of the cells being the intercalated disks. The latter attach the cells via desmosomes and serve to inter connect actin filaments from cell-to-cell. Cardiac myocytes are attached to an average of 11.3 neighbors, 5.3 on the sides and 6.0 on the ends. The cardiac ECM consists primarily of the fibrillar collagens, types I (75-85%) and III (1 0- 20%), which are synthesized by the cardiac fibroblasts, the most abundant cell type in the heart. Types IV and V collagen, which constitute the basement membrane of the myocytes, are also found, however. Although once thought of as a relatively inert internal 'skeleton' for the my ocytes, it is now known that these collagens experience significant turnover, and thus endow the heart with considerable adaptability. Albeit the major structural protein in connective tissues, collagen only comprises 2-5% of the myocardium by dry weight, compared with the myocytes, which make up 90%. The collagen matrix has a hierarchical organization that has been classi fied according to conventions established for skeletal muscle into endomysium, perimysium, and epimysium. The percent of the type I collagen (relative to type III) in these three classifications is 38%, 72%, and 84%, respectively. The endomysium is associated with individual myocytes and includes a fine weave that sur rounds the cells and transverse structural connections (i.e., struts, 120-150 nm long) that connect adjacent myocytes; the attachments localize near the Z-line of the sarcomere. Additional struts appear to connect myocytes and capillaries. The primary purpose of the endomysium is proba bly to maintain registration between adjacent cells and between the myocytes and capillaries; its predominately type III composition endows it with considerable deformability. The perimysium groups cells together; it includes the collagen fibers that organize bundles of cells into laminar sheets as well as large coiled fibers typically 1-3 J.Lm in diameter that are composed of smaller collagen fibrils (4 0-50 nm ). These perimysial fibers may be the major structural elements of the extracellular matrix, consistent with the dominance of type I over type III collagen.
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