Stresses and Strains Analysis in the Left Ventricular Wall with Finite Deformations

Abstract

The dysfunction of the left ventricle causes the death of a large amount of people each year. One of the most dangerous diseases is heart attack originated by ischemia. In order to specify some indices for diagnosis in clinical treatment, the material parameters of the left ventricular (LV) wall need to be determined. These indices were determined based on the understanding of material properties (stress–strain relationship) of normal heart to assess its fundamental mechanisms. In this study, transmural stress and strain distributions from base to apex in the normal canine heart during systolic and diastasis phase were determined using the previously well-established constitutive relation for the active (Hunter et al., J. Biophys. Mol. Bio. l 69,289–331, 1998) and passive (Humphrey et al., ASME J. Biomech. Eng. 112,333–141, 1990) LV wall in terms of a pseudostrain-energy function (W). A thick-walled truncated conical shell geometry was employed and LV wall was assumed to be transversely isotropic, incompressible and with a homogeneous deformation. The left ventricular anterior and posterior deformations were measured by the tetrahedron-shaped crystals implanted movement. Finite deformations including inflation, extension, twist and transmural shearing were considered in the model. Deformation parameters were considered as a linear variation from the inner to the outer LV wall. All six components of strain and three components of stress, radial stress and two components of transmural shearing stress were a function of radius. Moreover, stresses and strains relation is nonlinear due to fiber orientation changing across the LV wall. The radial strains indicate thinning and thickening of LV wall at end-diastole and end-systole, respectively. The highest circumferential stresses occur at approximately the middle surface, and also increase from the apex to the base at end-diastole and vice versa at end-systole. The highest radial stresses occur at the inner surface and decrease gradually across the LV wall.