A mathematical model is presented describing the time-and length-dependent behavior of cardiac muscle. The model describes a wider variety of experimental data than do previously published models. It incorporates a modification of the Hill equation describing the force-velocity relation. Based on the sliding filament theory, the revised equation includes the effects of finite cross-bridge compliance proposed by A. F. Huxley. The essential simplicity of the Hill equation is retained; however, the model successfully predicts force development during both isometric and isotonic contractions, observed deactivation of the contractile element during isotonic shortening, and the apparent dependence of series elastic stiffness on time after stimulation during quick-release and quick-stretch experiments.
KEY WORDScomputer model isotonic contraction quick release cross-bridge compliance isometric contraction shortening lengthening contractile element length clamp active state• Detailed experimental studies on isolated cardiac muscle have improved our understanding of its dynamic behavior and made it feasible to relate the performance of the heart to muscle behavior. Such an analysis requires constitutive equations describing the properties of heart muscle in its passive (unstimulated) and active states. Muscle fibers are highly anisotropic, having a principal direction along which active force is generated, and most experimental studies have focused on this direction, giving little attention to properties in the plane perpendicular to force generation. The present paper presents an analytical description of the properties of heart muscle along its principal direction under uniaxial loading. The model incorporates descriptions of the forcevelocity relation during nonisotonic contractions and during lengthening, the dependence of activation on the contraction mode, and the dependence of the maximum velocity of shortening on muscle length.Previous muscle models fall into two major categories. The first category employs a kinetic model like the one proposed by A. F. Huxley (1);