Simulation of coronary circulation with special regard to the venous bed and coronary sinus occlusion

The vascular beds of the left circumflex and the left anterior descending coronary arteries are modelled by means of coupled differential equations that consider an arterial, a capillary and a venous section. In a stepwise procedure, experimental data from normal coronary perfusion and coronary sinus occlusion are used to assess the model parameters. For venous distensibility, a non-linear form of pressure-volume relationship proved vital to reproduce the characteristics of the rise in venous pressure after the onset of coronary sinus occlusion. Numerical integration was carried out for normal perfusion and for coronary sinus occlusion, yielding time courses of flows, volumes and pressures within large coronary arteries, capillaries and coronary veins. Coronary sinus occlusion reduces total mean flow by 18% and divides intramyocardial flow between the capillaries and the veins into a forward component of 3.03 mls-1 and a backward component of -1.54 mls-1. This result represents a prediction for a haemodynamic quantity which is therapeutically important but inaccessible to measurement. Varying degrees of systolic myocardial squeezing are studied to display the impact of myocardial contractility and vessel collapse on the mean values and phasic components of intra-myocardial flows.