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 new mathematical model of the cardiovascular system is proposed. The left ventricle is described by an axisymmetric multiscale model where myocardium is treated as an incompressible transversely isotropic medium with a realistic distribution of fibre orientation. Active tension and its regulation by Ca2+ ions are described by our recent kinetic model. A lumped parameter model is used for the simulation of blood circulation, in which the left and right atria and the right ventricle are described by a system of ordinary differential equations for active pressure‐volume relationships. The stress and strain of the left ventricle myocardium were calculated by the finite element method implemented by the authors. The changes in the haemodynamics upon changes in preload of a healthy heart, upon physical exercise, and in case of atrioventricular block with different types of arrhythmias were simulated. To simulate the effect of stenosis or regurgitation of the aortic or mitral valves, the hydraulic and inertial flow resistances of the heart valves were set as functions of their orifice areas. The model reproduced a number of phenomena observed in clinical practice, including the classification of the severity of valve disease.
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