Active cross-bridge model. Reproduction of the myocardial force-length-time relation and the left ventricular pressure-length-time relation in systole.

A mathematical model has been derived to describe cardiac contraction. This model assumes (1) a linear end-systolic force-length relation for the intact left ventricular (LV) myocardium with proportionality constant Ec, and (2) that the rate of increase in the number of active cross-bridges is proportional to the number of cross-bridges capable of being activated at that moment with a proportionality constant Ka. Quantitative evaluation of this model was performed using parameter values measured in the normal human LV. The model predictions agreed well with many earlier experimental data concerning the myocardial force-time relation, myocardial force-velocity-length relation, systolic time interval-afterload relation, time-varying elastance concept, several LV end-systolic relations, and LV dP/dtmax-end-diastolic volume relation. Moreover, two important basic properties of contractile proteins, i.e., the maximal force-generating capacity and the rate of activation of cross-bridges, were evaluated in the model from the values of Ec and Ka, respectively. Although no definitive biological proof has yet been provided for the assumptions, this model might mathematically integrate the myocardial and ventricular dynamics over the entire systole and then provides a new method for evaluation of the human LV systolic function from two basic properties of active cross-bridges.