Dynamic left ventricular elastance: a model for integrating cardiac muscle contraction into ventricular pressure-volume relationships

Abstract

To integrate myocardial contractile processes into left ventricular (LV) function, a mathematical model was built. Muscle fiber force was set equal to the product of stiffness and elastic distortion of stiffness elements, i.e., force-bearing cross bridges (XB). Stiffness dynamics arose from recruitment of XB according to the kinetics of myofilament activation and fiber-length changes. Elastic distortion dynamics arose from XB cycling and the rate-of-change of fiber length. Muscle fiber stiffness and distortion dynamics were transformed into LV chamber elastance and volumetric distortion dynamics. LV pressure equaled the product of chamber elastance and volumetric distortion, just as muscle-fiber force equaled the product of muscle-fiber stiffness and lineal elastic distortion. Model validation was in terms of its ability to reproduce cycle-time-dependent LV pressure response, ΔP( t), to incremental step-like volume changes, ΔV, in the isolated rat heart. All ΔP( t), regardless of the time in the cycle at which ΔP( t) was elicited, consisted of three phases: phase 1, concurrent with the leading edge of ΔV; phase 2, a brief transient recovery from phase 1; and phase 3, sustained for the duration of systole. Each phase varied with the time in the cycle at which ΔP( t) was elicited. When the model was fit to the data, cooperative activation was required to sustain systole for longer periods than was possible with Ca2+ activation alone. The model successfully reproduced all major features of the measured ΔP( t) responses, and thus serves as a credible indicator of the role of underlying contractile processes in LV function.