Modeling of Cardiac Muscle Contraction Based on the Cross-Bridge Mechanism

Abstract

A mathematical model was developed for the cardiac muscle contraction, assuming that the attachment and detachment cycle of the cross-bridge is activated by the internal calcium concentration and the rate constant of the cycle depends on the sliding velocity of myofilaments. The inputs of the model are the rates of calcium release and uptake, while the output is the tension curve of the muscle. The variables are factored into a series of realizable functions and most constants were determined from the dynamic constants for the tetanic contraction of frog ventricular muscle at 20° C. Using this model, the calcium transient curve as well as the change in the number of cross-bridges in each state of the cycle during a given experimental twitch tension curve was calculated with a PDP 11/60 computer, by selecting the input parameters so that the output curve fit the experimental curve. When the twitch tension was increased by increasing initial muscle length, the rate of calcium release increased and that of uptake decreased. At higher external calcium concentrations, the similar changes in the input parameters were observed. In the presence of 5×10⁻⁸ g/ml adrenalin the duration of activation was markedly prolonged, while the rates of calcium release and uptake show little change.