Windkessel models are frequently used to describe the load faced by the heart in pumping blood through the pulmonary or systemic arterial system, and the relation between blood pressure and blood flow in the aorta or the pulmonary artery. Characterizing the pulmonary or systemic arterial load on the heart in terms of the parameters that arise in Windkessel models, such as arterial compliance and peripheral resistance, is important, for example, in quantifying the effects of vasodilator or vasoconstrictor drugs. Also, a mathematical model of the relationship between blood pressure and blood flow in the aorta and pulmonary artery is useful, for example, in the development and operation of mechanical heart and heart-lung machines. If blood is not supplied by these devices within acceptable ranges of pressure and flow, the patient will not survive.