Cross-Bridge Cycling Energy of Cardiac Muscle Estimated from an Active Cross-Bridge Model

Abstract

A mathematical formula was derived from an active cross-bridge model to express the changes in the active myocardial force which occurred during systole. Using the formula and the assumption that the energy expenditure for cross-bridge cycling (Um) was a linear function of the force-time integral (FTI), we developed formulae describing the left ventricular Um versus FTI relation, the Um versus force relation, and the Um versus pressure-volume area (PVA) relation. There were strong disagreements between the model predictions and the experimental findings relating oxygen consumption of the heart versus the PVA relation. These differences may have resulted from the oversimplification of important mechanical and/or biochemical properties of the myocardium in the model. However, the model appeared to accurately reproduce the Fenn effect (effect of contraction modes on energy liberation) for the myocardium as well as the effect of catecholamine infusion, hypothermia, and hypothyroidism on the changes in the binding rate of Ca²⁺ with the regulatory proteins, the myosin ATPase activity, the peak force developed, and the myocardial energy expenditure. We present this work as an intermediate step towards a complete theoretical linkage between the molecular biology, dynamics, and energetics of the human heart.