A mathematical model for the sudy of ventriculo-arterial coupling in aortic insufficiency

A role of paramount importance in the determination of the left ventricular performance is played by the ventriculo-arterial coupling. In this work the effect of aortic insufficiency on the ventriculo-arterial coupling is investigated by means of a lumped parameters model of the left ventricle and of the systemic circulation. The left ventricle is represented by a time-varying elastance, the systemic arterial and venous networks are represented by a three-elements modified windkessel, the mitral and aortic valve are represented by ideal diodes, with a reverse path to simulate the aortic regurgitation. The model has been studied during the whole cardiac cycle, reproducing the main haemodynamical features of the cardiovascular system. Three cases have been simulated: 1. a normal ventricle 2. a severe acute aortic regurgitation 3. a chronic compensated aortic regurgitation. For each case the Preload Recruitable Stroke Work (PRSW) relation has been extracted, together with the main energetic parameters and the effective aortic elastance. The chronic insufficient aortic valve resulted in a in coupling strongly reduced respect to the normal condition; besides, the coupling remains unchanged for acute severe regurgitation. The mechanical efficiency is reduced by aortic insufficiency, with a more marked decrease in severe acute regurgitation.