A cardiac model convenient for vascular load coupling

Abstract

To answer the question of optimal matching between the ventricle and arterial load, we developed a framework of analysis which uses simplified models of ventricular contraction and arterial input impedance. The ventricular model consists only of a single volume (or chamber) elastance which increases to an endsystolic value E _es with each heart beat. With this elastance, stroke volume SV is represented as a linearly decreasing function of ventricular endsystolic pressure. Arterial input impedance is represented by a 3-element Windkessel model which is in turn approximated to describe arterial end systolic pressure as a linearly increasing function of stroke volume injected per heart beat. The slope of this relationship is E _a. Superposition of the ventricular and arterial endsystolic pressure-stroke volume relationships yields stroke volume and stroke work expected when the ventricle and the arterial load are coupled. From theoretical consideration, a maximum energy transfer should occur from the contracting ventricle to the arterial load under the condition E _es = E _a. Experimental data on the external work that a ventricle performed on extensively varied arterial impedance loads supported the validity of this matched condition. The matched condition also dictated that the ventricular ejection fraction should be nearly 50%, a well-known fact under normal condition. We conclude that the ventricular contractile property, as represented by E _es, is matched to the arterial impedance property, represented by a three-element windkessel model, under normal conditions.