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A finite element approach for skeletal muscle using a distributed moment model of contraction

Abstract The present paper describes a geometrically and physically nonlinear continuum model to study the mechanical behaviour of passive and active skeletal muscle. The contraction is described with a Huxley type model. A Distributed Moments approach is used to convert the Huxley partial differential equation in a set of ordinary differential equations. An isoparametric brick element is developed to solve the field equations numerically. Special arrangements are made to deal with the combination of highly nonlinear effects and the nearly incompressible behaviour of the muscle. For this a Natural Penalty Method (NPM) and an Enhanced Stiffness Method (ESM) are tested. Finally an example of an analysis of a contracting tibialis anterior muscle of a rat is given. The DM-method proved to be an efficient tool in the numerical solution process. The ESM showed the best performance in describing the incompressible behaviour.

Transmural Course of Stress and Sarcomere Length in the Left Ventricle Under Normal Hemodynamic Circumstances

In this paper the dynamic behaviour of mechanical stresses and strains in the wall of the left ventricle is described. Though several investigators are rather optimistic (1), direct determination of stresses in the wall of the left ventricle is difficult and unreliable (2). A better approach is calculation of these stresses by the use of a mathematical model of the mechanics of the left ventricle (3). Following this principle, several investigators (2, 4, 5) have computed wall stress from left ventricular pressure, assuming a certain geometry of the left ventricle and certain mechanical properties of the wall. However, none of these models can be used to study the dynamic behaviour of the stresses in the wall of the left ventricle since these models are based on unrealistic approximations, such as isotropic myocardial material or inadequate geometry, while usually fibre orientation in the wall of the left ventricle and physiological contractile behaviour of the myocardial material are not taken into account. Therefore, a new model was developed in which all of these factors are considered (3).

Stiffening of the Cardiac Wall by Coronary Blood Volume Increase: A Finite Element Simulation

A porous medium finite element model of the beating left ventricle is used to simulate the influence of the intracoronary blood volume on left ventricular mechanics. The spongy material is composed of incompressible solid (myocardial tissue) and incompressible fluid (coronary blood). The model is axisymmetric and allows for finite deformation, including torsion around the axis of symmetry. The total stress in the tissue is the sum of the intramyocardial pressure, effective passive stress due to myocardial deformation and the contractile fiber stress. The model is able to simulate a full cardiac cycle. Three-dimensional end-systolic deformation computed relative to the end-diastolic state is shown to be consistent with experimental data from the literature. The direction of maximal shortening varied less than 30° fiuni endocardium to epicardium while fiber direction varied by more than 100°. It is shown that the ventricular model exhibits diastolic stiffening following an increase of intracoronary blood volume. End-diastolic left ventricular pressure increases from 1.5 kPa to 2.0 kPa when raising intracoronary blood volume from 9 to 14 ml per 100 g myocardial tissue. The model simulation suggests that the mechanism underlying the increase in end-diastolic pressure at higher coronary blood volumes, is an increase in passive stiffness of the myocardial fibers. This increased stiffness is the combined result of an overall increase in strain in myocardial tissue and the non-linear stress-strain relationship of myocardial tissue.