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

- A simple model of cardiac muscle is proposed.
- Relaxed cardiac muscle is described as hyperelastic transversally isotropic media.
- Active force of actin-myosin crossbridges depends on their average strain.
- Ca2+ regulation in the filament overlap zone and outside it have different kinetics.
- Despite its simplicity the model describes a wide range of experimental data.

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.