Considerations about the Lumped Parameter Windkessel Model Applicativity in the Cardiovascular System Structure

The Windkessel model enlarges his applicativity on the whole circulatory dynamics studies. Then, the lumped parameter models allow global representation of blood flow circulation. In the vascular tree, peripheral branches are terminated by a resistance term representing smaller vessels. Blood flow and pressure are expressed by the intensity of current and voltage in an electrical analogue based on the Navier-Stokes equations for fluid flows in elastic tubes. Although the lumped parameters can be expressed according to the physical properties of the arterial tree and the rheology of the blood, the paper deal, also, the influence of various factors (infusion of the drugs and sympathetic stimulation) on the peripheral resistance. In a non-pulsatile cardiovascular model, the cardiac output, CO, is expressed as stroke volume times heart rate. Using a three-element Windkessel model as arterial load impedance of the heart, the mean arterial pressure variations is investigated. Also, some considerations relating the influence of an inotropic and a vasoactive drugs infusion rate variations upon the changes of systemic resistance is made. The sympathetic influence on peripheral resistance is a weighted sum of the afferent activities from baroreceptors, chemoreceptors and lung stretch receptors. The implementation in Matlab-Simulink allows the study of correlations between pressure and peripheral resistance variations.