in volume per unit time, while P(t) is the pressure with respect to time measured in force per unit area, C is the ratio of volume to pressure for the Windkessel, and R is the resistance relating outflow to fluid pressure. This model is identical to the relationship between current, I(t), and electrical potential, P(t), in an electrical circuit equivalent of the two-element Windkessel model. In the blood circulation, the passive elements in the circuit are assumed to represent elements in the cardiovascular system. The resistor, R, represents the total peripheral resistance and the capacitor, C, represents total arterial compliance. During diastole there is no blood inflow since the aortic (or pulmonary valve) is closed, so the Windkessel can be solved for P(t) since I(t) = 0: where td is the time of the start of diastole and P(td) is the blood pressure at the start of diastole. This model is only a rough approximation of the arterial circulation; more realistic models incorporate more elements, provide more realistic estimates of the blood pressure waveform and are discussed below. Three-element The three-element Windkessel improves on the two-element model by incorporating another resistive element to simulate resistance to blood flow due to the characteristic resistance of the aorta (or pulmonary artery). The differential equation for the 3-element model is: where R1 is the characteristic resistance (this is assumed to be equivalent to the characteristic impedance), while R2 represents the peripheral resistance. This model is widely used as an acceptable model of the circulation. For example it has been employed to evaluate blood pressure and flow in the aorta of a chick embryo and the pulmonary artery in a pig as well as providing the basis for construction of physical models of the circulation providing realistic loads for experimental studies of isolated hearts. Four-element The three-element model overestimates the compliance and underestimates the characteristic impedance of the circulation. The four-element model includes an inductor, L, which has units of mass per length, (), into the proximal component of the circuit to account for the inertia of blood flow. This is neglected in the two- and three- element models. The relevant equation is: Applications These models relate blood flow to blood pressure through parameters of R, C (and, in the case of the four-element model, L). These equations can be easily solved (e.g. by employing MATLAB and its supplement SIMULINK) to either find the