Cardiac muscle fiber force versus length determined by a cardiac muscle crossbridge model

A mathematical model incorporating Huxley's sliding filament crossbridge muscle model coupled with parallel and series elastic components was simulated to examine force-length relations under different external calcium concentrations. Several researchers have determined experimentally in both papillary muscle preparations and in situ heart experiments that the calcium concentration (or effective concentration from inotropic agents) will affect the strength and convexity of the cardiac muscle fiber force-length relations. Simulations were performed over a several-order-of-magnitude range of calcium concentrations in isometric contractions and these showed that the force-length curve convexity was changed. Simulation results demonstrated that increasing the stiffness in the model contractile element or series elasticity element did not change the force-length convexity. Increasing the series elasticity element stiffness did slightly change the shape of the force-length curve. The model predicts that the curve convexity changes as a result of the calcium-troponin interactions.