A simple kinetic model of muscle contraction is suggested. The rates of cross-bridge transitions from one kinetic state to another one are supposed to depend on the strain averaged over an ensemble...

An axisymmetric model is suggested to simulate mechanical performance of the left ventricle of the heart. Cardiac muscle is treated as incompressible anisotropic material with active tension directed along muscle fibres. This tension depends on kinetic variables that characterize interaction of contractile proteins and regulation of muscle contraction by calcium ions. For numerical simulation of heartbeats the finite element method was implemented. The model reproduces well changes in ventricle geometry between systole and diastole, ejection fraction, pulse wave of ventricular and arterial pressure typical for normal human heart. The model also reproduces well the dependence of the stroke volume on end-diastolic and arterial pressures (the Frank–Starling law of the heart and Anrep effect). The results demonstrate that our model of cardiac muscle can be successfully applied to multiscale 3D simulation of the heart.

A model of myocardial electromechanics is suggested. It combines modified and simplified versions of previously published models of cardiac electrophysiology, excitation-contraction coupling, and mechanics. The mechano-calcium and mechano-electrical feedbacks, including the strain-dependence of the propagation velocity of the action potential, are also accounted for. The model reproduces changes in the twitch amplitude and Ca²⁺-transients upon changes in muscle strain including the slow response. The model also reproduces the Bowditch effect and changes in the twitch amplitude and duration upon changes in the interstimulus interval, including accelerated relaxation at high stimulation frequency. Special efforts were taken to reduce the stiffness of the differential equations of the model. As a result, the equations can be integrated numerically with a relatively high time step making the model suitable for multiscale simulation of the human heart and allowing one to study the impact of myocardial mechanics on arrhythmias.

A kinetic model of cardiac muscle contraction is suggested. It is based on our earlier simplified model of the kinetics of the actin-myosin interaction. We examined the kinetics of formation of calcium-troponin complexes that open the binding sites-on actin for myosin heads. The model also takes into account the cooperativity of this process and the influence of myosin heads on it. It was shown that with proper choice of its parameters the model appropriately describes the dependence of myocardium activation.on sarcomeres length that underlies the Frank-Starling law of the heart. The model fits both steady state experiments on myocardial specimens with permeable membrane and twitch contractions of intact cardiac muscle. It also describes well the myocardium load-dependent relaxation.