Multiscale simulation of the effects of atrioventricular block and valve diseases on heart performance

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.

A simple model of cardiac muscle for multiscale simulation: Passive mechanics, crossbridge kinetics and calcium regulation

A simple model of cardiac muscle was designed for multiscale simulation of heart mechanics. Relaxed cardiac muscle was described as a transversally isotropic hyperelastic material. Active tension caused by actin-myosin crossbridges depends on the ensemble averaged strain of myosin heads bound to actin. Calcium activation was modeled by Ca²⁺ binding to troponin-C. To account for the dependence of troponin affinity for Ca²⁺ on myosin heads strongly bound to actin, the kinetics of troponin binding to Ca²⁺ in the overlap zone of the thin and thick filaments and outside it were separated. The changes in the length of these zones during muscle shortening or lengthening were accounted for explicitly. Simplified version of the model contains only 5 ordinary differential equations (ODE). Model parameters were estimated from a limited set of experiments with skeletal and cardiac muscle. Simulations have shown that model reproduces qualitatively a number of experimental observations: steady-state force-velocity and stiffness-velocity relations; mechanical responses to step changes in muscle length or load; steep Ca²⁺-tension relationship and its dependence on sarcomere length tension (the Frank-Starling mechanism); tension, shortening and Ca²⁺-transients in twitch isometric and isotonic contractions, tension development and redevelopment upon fast change in Ca²⁺ concentration or muscle release followed by re-stretch. We believe that the model can be effectively used for modeling contraction and relaxation of the heart.