Relating left ventricular dimension to maximum elastance by fiber mechanics

Abstract

The dependence of the pressure-volume slope, which defines the maximum elastance (Emax) and the zero pressure-volume intercept (Vd) on the size and dimensions of the left ventricle (LV), is theoretically studied, and a normalizing parameter for Emax is suggested for normal and hypertrophied hearts. The study is based on our earlier model of the mechanics of the LV contraction, which assumes a nested-shell spheroidal shape, Streeter's fiber angle distribution, given stress-length and stress-strain rate functions of the sarcomeres, a radial propagation of the electrical activation front, and a windkessel arterial model. The study shows that Emax is linearly related to the maximum force that the optimal length sarcomeres can develop (sigma o), which is a characteristic measure of the contractility. Emax decreases and Vd increases with an increase in ventricular size, at a constant end-diastolic ratio (h/b)ed, where h is the wall thickness, and b is the semiminor axis of the prolate spheroidal LV. When the reference unstressed volume (V0) is held constant and the wall thickness increases, as in pure concentric hypertrophy, Emax decreases slightly and shifts to the left to a lower Vd value. In pure eccentric hypertrophy, wherein chamber size increases while the wall thickness remains constant, Emax decreases and Vd increases. A good index for myocardial function at constant configuration ratio (h/b)ed is obtained by multiplying Emax with the LV muscle volume (Vm). (h/b)ed is constant (= 0.45) for the normal heart but increases for concentric hypertrophy.(ABSTRACT TRUNCATED AT 250 WORDS)