Model for left ventricular contraction combining the force length velocity relationship with the time varying elastance theory.

A model for the contraction of the left ventricle (LV) is developed for a spheroidal geometry. The classical force-length-velocity relationship for a single muscle fiber is assumed. The linear maximum pressure volume relationship (maximum elastance), a measure of muscle contractility, is further extended into a time-varying function. This is achieved by utilizing a mechanical activation function, assumed as half a sinusoidal wave, to describe the time-dependent isometric stress for the activated cardiac muscle. This, in turn, results in the time-varying elastance function and represents the instantaneous activity of the muscle contractile proteins. The model is tested for a set of boundary conditions that determine preload, afterload, and the inherent properties of the muscle, i.e., the contractility. The computed results of the isovolumic contraction, auxotonic contraction, and isovolumic relaxation are in agreement with the expected behavior of the LV. The relations between the simulated variations on preload, afterload, and contractility, and the set of performance indexes of the LV, are presented and discussed.