Evaluation of left ventricular wall stresses during ejection using nonlinear finite elements

Abstract Wall stresses in a normal and infarcted left ventricle were calculated during ejection using nonlinear incompressible finite elements. The geometry of the left ventricle was approximated as a thick ellipsoidal shell of revolution. Tissue incompressibility was assumed and was achieved in the model by applying a constraint in each element that equated the third strain invariant as unity. Both large deformation and large strain theories were used in the analysis. A strain energy density function was assumed for the ventricular muscle. A load of 5.33 kPa (40 mm Hg) was applied at the endocardial surface, in the normal direction away from the surface. This allowed the endocardial surface to encroach upon the ventricular cavity and thus simulated ejection. In the normal left ventricle, stresses were highest in the subendocardium and decreased toward the subepicardium. The computed increase of wall thickness at the mid-ventricular level during ejection was comparable to measurements of wall thickness in anesthetized dogs. Introduction of a small simulated axisymmetric infarct into the model near the apex resulted in an appreciable stress gradient between the infarcted tissue and the adjacent normal myocardium. The estimation of the magnitude and distribution of stresses during ejection in the normal and infarcted left ventricle is useful in understanding the principles that govern left ventricular mechanics.