Time-varying left ventricular elastance determined by a finite element model

A finite element model of the left ventricle (LV) with an axisymmetric geometry has been developed to determine LV pressures and volumes. Regional myocardial contractions defined by the finite elements are then related to the time-varying LV elastance (instantaneous pressure over volume ratio). LV geometry is modeled as a truncated ellipsoid with user-defined parameters such as wall thickness, short axis length, and long axis length. The stress-strain relationship for each element is assumed to be linear but with a time-varying Young´s modulus. Empirical values of the Young´s modulus are assigned to finite elements for simulating normal and ischemic myocardium. The mesh generation is implemented in C++ and the stress-strain computation in Matlab. The finite element model produces reasonable geometry for normal and ischemic LV walls. More importantly, the LV ejection fraction and pressure and volume curves are consistent with typical clinical observations. The simplified model developed in this study is an effective and computationally efficient way to relate regional myocardial impairments to global LV functions and to generate LV elastance curves over an entire cardiac cycle.