Simple model of circulatory system dynamics including heart valve mechanics

This paper describes an extension of the Windkessel model of circulatory system dynamics, which takes into account the opening action of the mitral and aortic valves, including stenotic and regurgitant orifices. The starting point for the model is the ventricular emptying/filling curve which is taken from a quasi-physiological ventricular flow relationship which incorporates variation of systolic and diastolic intervals with cycle rate. The valves are assumed to open with a linear rise in area up to maximum orifice, followed by a period at maximum orifice and then a linear fall-off in area to the closed position (which may allow regurgitation). Flow through the valves is assumed to be governed by the Gorlin equation. Peripheral resistance and compliance are considered as fixed parameters of the arterial system. The model is useful in helping to understand the complex interaction between valvular mechanics and the rest of the cardiovascular system. Applications of the model are illustrated by considering isolated aortic stenosis, isolated aortic regurgitation, cardiac adaptation in the presence of these two abnormalities and the effects of variation of peripheral resistance on pressures within the cardiovascular system.