Mechanics of Active Contraction in Cardiac Muscle: Part I—Constitutive Relations for Fiber Stress That Describe Deactivation

Constitutive relations for active fiber stress in cardiac muscle are proposed and parameters are found that allow these relations to fit experimental data from the literature, including the tension redeveloped following rapid deactivating length perturbations. Contraction is driven by a length-independent free calcium transient. The number of actin sites available to react with myosin is determined from the total number of actin sites (available and inhibited), free calcium and the length history-dependent association and dissociation rates of two Ca²⁺ ions and troponin as governed by a first-order, classical kinetics, differential equation. Finally, the relationship between active tension and the number of available actin sites is described by a general cross-bridge model. Bridges attach in a single configuration at a constant rate, the force within each cross-bridge varies linearly with position, and the rate constant of bridge detachment depends both on position and time after onset of contraction. In Part II, these constitutive relations for active stress are incorporated in a continuum mechanics model of the left ventricle that predicted end-systolic transmural strain distributions as observed experimentally.