CALCULATION OF A SHEAR STRAIN PARAMETER FOR A THREE-DIMENSIONAL FUNG-TYPE EXPONENTIAL MODEL OF THE ARTERIAL WALL UNDER TORSION

摘要

The distribution of atherosclerotic lesions within the coronary arteries is highly localized, despite the fact that risk factors (e.g., dyslipidemia) are systemic nature. The biomechanical milieu of the coronary arteries is unique in that in addition to cyclic pressure, circumferential distension and shear stress, they experience mechanical deformations of twisting, bending, and longitudinal stretching due to their tethering to the dynamic epicardial surface [1]. Biplane cineangiographic reconstruction studies have demonstrated that the coronary arteries experience as much as 20° of torsion during a cardiac cycle [2]. Spatial variations in shear and mural stresses caused by this deformation could account for the heterogeneity of atherosclerotic plaques. Finite element analysis (FEA) is the preferred method for estimation of stress distributions in bodies under various loading conditions, including torsion. FEA however, requires detailed knowledge of the material properties of the body in question. In the case of torsion, shear moduli due to twisting have been determined for pig coronary arteries [3]. However, these moduli are not constant, varying with the longitudinal stretch ratio and the applied internal pressure. In order to develop a finite element of the arterial wall under torsion a material model that incorporates this relationship between shear modulus and the other mechanical stimuli is required. The goal of this work is to utilize previously reported shear moduli to calculate a shear strain parameter in a Fung-type exponential model of the arterial wall and determine if this single constant can account for the observed behavior of arterial segments under torsion.