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.@en

By fitting of simulations with an oxygen exchange model to measured responses of the arteriovenous oxygen content difference after a flow step, coronary volumes can be estimated. In this study the dependence of the volume estimates on the choice of the oxygen exchange model for the coronary circulation was investigated. A model consisting of a single well-mixed compartment results in smaller volume estimates than a series array of mixed compartments in which Po2 declines gradually (Krogh-like model). Use of the former model for data analysis resulted in realistic volume estimates. Thus, these results indicate that the oxygen exchange vessels are better represented by a single mixed compartment than by a cylinder having Krogh characteristics. This conclusion agrees with capillary Po2 being equal to or smaller than venous Po2 which cannot be explained by a Krogh model. From these arguments we conclude that though both models are rough representations of the coronary circulation, the coronary O2 exchange vessels of the beating heart can be represented better by a single mixed compartment than by a series array of mixed compartments which has Krogh characteristics.@en