Analysis of flow in coronary epicardial arterial tree and intramyocardial circulation

A mathematical model combining the coronary flow in the epicardial arterial tree and the intramyocardial circulation is presented. The epicardial arterial tree is represented by a resistive capacitive network based on its realistic anatomy. The intramyocardial flow is affected by the pump action of the contracting myocardium through the extravascular compressive pressure (ECP), which, in turn, affects the dynamic resistance and compliance changes based on the relationship between the transmural pressure and the cross-sectional area of a vessel. The model accounts for the autoregulatory mechanism of the intramyocardial compartments (arteriolar, microvascular and venular) and is structured according to the epicardial coronary anatomy. Realistic coronary epicardial arterial flow patterns are obtained, which compare well to experimentally measured data in six dogs under basal conditions and during reactive hyperemic response. Simulations of the average transmural flow in the three intramyocardial vascular compartments show that the flow in the arterial side is predominantly diastolic, with a systolic retrograde component, and is dominantly systolic antegrade flow in the venular side, consistent with experimental data. Interestingly, the transmurally average microcirculatory flow is continuous, with very small change throughout the cardiac cycle, and is practically insensitive to changes in the model parameters. The model presents a quantitative tool that describes the dynamic patterns of coronary flow in relationship to muscular and extravascular parameters.