Continuum rheology of muscle contraction and its application to cardiac contractility

Abstract

A set of constitutive equations is proposed to describe the mechanics of contraction of skeletal and heart muscle. Fiber tension is assumed to depend on the degree of chemical activation, the stretch ratio, and the rate of stretching of the fibers. The time rate of change of activation is governed by a differential equation. The proposed constitutive equations are used to model the time courses of isotonic and isometric twitches during contraction and relaxation phases of the muscle response to stimulation. Various contractility indices of the left ventricle are considered next by using the proposed constitutive equations. The present analysis introduces a new interpretation of the index of contractility (dP/dt)/P used in cardiac literature. It is shown that this index may not be related at all to the maximum speed of shortening and that it may be dependent on both preload and afterload. The development of pressure during isovolumetric contraction of the left ventricle is shown to be governed by a differential equation describing the time rate of change of tension during isometric contraction of myocardium fibers.