Numerical study of the behavior of an activation parameter in a sliding filament cat papillary muscle model

A previously existing model of cross-bridge kinetics is modified to make it applicable to cardiac muscle and incorporated into a macroscopic model of isolated heart muscle. Equations are formulated which describe the responses of this model during simulated isometric and isotonic contractions. These equations allow one to calculate the time variation of the activation parameter in the model when given the contraction time history, i.e. the time course of length and tension changes. The activation parameter is defined as the instantaneous rate constant for cross bridge attachment. We calculate the time course of the activation parameter with the model's responses set equal to the measured responses of isolated cat papillary muscle and the model parameters chosen appropriately for cat papillary muscle. It is found that in order for the model and muscle response to match, the degree of activation of the muscle model must first increase and then decrease with shortening. The behavior of the activation parameter in the muscle model is consistent with physiological investigations which suggest that shortening in cardiac muscle is associated with both activation and deactivation.