On the Solutions of Huxley-type Models in Cardiac Muscle Fiber Contractions

Huxleyʹs sliding filament crossbridge muscle model coupled with parallel and series elastic components was simulated to examine the effect of various solution techniques in cardiac contractions. Solutions of both isometric and isotonic contraction cases showed that the force versus time curves were not significantly altered by solving the three-element Hill model with Huxleyʹs Equation written as either an ordinary or partial differential equation (ODE or PDE), but this makes a difference in the solution time required. Various theoretical studies have used either the ODE or PDE representation. The crossbridge cycles at the end of a contraction showed approximately 25% and 15% difference in the isometric and isotonic cases when Huxleyʹs Equation was written as either an ODE or PDE. Examination of the crossbridge distribution (distribution among states of reach) showed that assuming that the crossbridge distribution is a Gaussian function is a poor approximation since the shape changes considerably between the cardiac contracting and expanding phases, and using a technique such as a distribution moment approximation is questionable. Recent experimental studies have demonstrated that solving Huxley-type relations as ordinary differential equations gives good agreement with cardiac data, implying that as a first approximation, this can be successfully used.