Model of the coronary circulation based on pressure dependence of coronary resistance and compliance

Abstract

The effect of pressure-dependent changes in vascular volume, resistance and capacitance in the coronary micro-circulation, has been studied by a distributed mathematical model of the coronary micro-vasculature in the left ventricular wall. The model does not include regulation of coronary blood flow and is evaluated only for the fully dilated coronary vasculature. The left ventricular wall was thought to consist of eight parallel layers, each of them with an arteriolar, capillary and venular compartment. The resistance of each vessel was thought to depend on the inverse of squared volume, according to Poiseuille's Law for tubes with constant length. Tissue pressure has been assumed to be equal to left ventricular cavity pressure at the endocardium and to decrease linearly to atmospheric level at the epicardium. The pressure-volume relation of the vessel compartments were assumed to be sigmoidal. There is a rest volume at transmural pressure zero and ΔV/ΔP decreases with increasing transmural pressure. Simulation of experimental protocols described by other authors yielded results which were similar to the experimental outcomes, illustrated by: (1) a parallel shift to the flow axis of the pressure-flow curves due to cardiac arrest (2) steady-state endo/epi ratio of flow as a function of heart rate. It is concluded that interpretation of transients in coronary flow and/or pressure by models containing fixed resistance and capacitance may seriously underestimate intramyocardial capacitative effects and characteristic time constants for pressure-induced resistance changes.