Windkessel effect is a term used in medicine to account for the shape of the arterial blood pressure waveform in terms of the interaction between the stroke volume and the compliance of the aorta and large elastic arteries (Windkessel vessels) and the resistance of the smaller arteries and arterioles. Windkessel when loosely translated from German to English means 'air chamber', but is generally taken to imply an elastic reservoir. The walls of large elastic arteries (e.g. aorta, common carotid, subclavian, and pulmonary arteries and their larger branches) contain elastic fibers, formed of elastin. These arteries distend when the blood pressure rises during systole and recoil when the blood pressure falls during diastole. Since the rate of blood entering these elastic arteries exceeds that leaving them via the peripheral resistance, there is a net storage of blood in the aorta and large arteries during systole, which discharges during diastole. The compliance (or distensibility) of the aorta and large elastic arteries is therefore analogous to a capacitor; to put it another way, these arteries collectively act as a hydraulic accumulator. The Windkessel effect helps in damping the fluctuation in blood pressure (pulse pressure) over the cardiac cycle and assists in the maintenance of organ perfusion during diastole when cardiac ejection ceases. The idea of the Windkessel was alluded to by Giovanni Borelli, although Stephen Hales articulated the concept more clearly and drew the analogy with an air chamber used in fire engines in the 18th century. Otto Frank (physiologist), an influential German physiologist, developed the concept and provided a firm mathematical foundation. Frank's model is sometimes called a two-element Windkessel to distinguish it from more recent and more elaborate Windkessel models (e.g. three- or four-element and non-linear Windkessel models). Model types Modeling of a Windkessel Windkessel physiology remains a relevant yet dated description of important clinical interest. The historic mathematical definition of systole and diastole in the model are obviously not novel but are here elementally staged to four degrees. Reaching five would be original work. Two-element It is assumed that the ratio of pressure to volume is constant and that outflow from the Windkessel is proportional to the fluid pressure. Volumetric inflow must equal the sum of the volume stored in the capacitive element and volumetric outflow through the resistive element. This relationship is described by a differential equation: I(t) is volumetric inflow due to the pump (heart) and is measured