Relating left ventricular dimension to maximum elastance by fiber mechanics

The dependence of the pressure-volume slope, which defines the maximum elastance (E(max)) and the zero pressure-volume intercept (V(d)) on the size and dimensions of the left ventricle (LV), is theoretically studied, and a normalizing parameter for E(max) 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 E(max) is linearly related to the maximum force that the optimal length sarcomeres can develop (σ(o)), which is a characteristic measure of the contractility. E(max) decreases and V(d) 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, E(max) decreases slightly and shifts to the left to a lower V(d) value. In pure eccentric hypertrophy, wherein chamber size increases while the wall thickness remains constant, E(max) decreases and V(d) increases. A good index for myocardial function at constant configuration ratio (h/b)(ed) is obtained by multiplying E(max) with the LV muscle volume (V(m)). (h/b)(ed) is constant (= 0.45) for the normal heart but increases for concentric hypertrophy. The elastance index [E(max) · V(m) · 0.45/(h/b)(ed)], which accounts for the muscle volume and configuration in hypertrophied hearts, demonstrates the best correlation with the muscle contractility when compared with other indexes.