A mathematical model for analysis of pharmacologically induced changes in the kinetics of cardiac muscle

A mathematical model of the isometric contraction of cardiac muscle is developed and utilized to characterize the inotropic and lusitropic effects of cardioactive compounds in isolated guinea pig left atria. In contrast to metrics that are based on minima and maxima of an isometric twitch and its derivative function, the entire time course of the twitch is used to quantify the kinetics of the contraction-relaxation cycle. The model relates observed tension to a time-dependent activation function that describes generation of internal force and a coupling function that determines mechanical response to the activation function. The model is structured so that it is suitable for nonlinear curve fitting to observed data. Results obtained using the model for fitting experimental data from tissues treated with different classes of cardioactive compounds agree with more qualitative results presented by other authors. Experiments using the model to fit data over an extended (90 min) time course revealed differences in the kinetic profiles of milrinone and forskolin. Computer simulations that demonstrate the effect of each model parameter on twitch kinetics are presented, and the relationships between the model and other theoretical and empirical models of cardiac muscle are discussed. The mathematical model is useful to enable a more quantitative understanding of the kinetics of cardiac muscle contraction and relaxation and identify compounds that may be selective for inotropic or lusitropic effects.