Windkessel effect
Windkessel effect (German: Windkesseleffekt) 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',[1][2] but is generally taken to imply an elastic reservoir.
[3] 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.
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 (employing the hydraulic analogy); 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.
[4] Otto Frank, an influential German physiologist, developed the concept and provided a firm mathematical foundation.
[5][6] 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.
Volumetric inflow must equal the sum of the volume stored in the capacitive element and volumetric outflow through the resistive element.
I(t) is volumetric inflow due to the pump (heart) and is measured 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.
[7] 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:
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.
[5] For example it has been employed to evaluate blood pressure and flow in the aorta of a chick embryo [8] and the pulmonary artery in a pig[8] as well as providing the basis for construction of physical models of the circulation providing realistic loads for experimental studies of isolated hearts.
[9] The three-element model overestimates the compliance and underestimates the characteristic impedance of the circulation.
[7] 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.
These equations can be easily solved (e.g. by employing MATLAB and its supplement SIMULINK) to either find the values of pressure given flow and R, C, L parameters, or find values of R, C, L given flow and pressure.
An example for the two-element model is shown below, where I(t) is depicted as an input signal during systole and diastole.
Systole is represented by the sin function, while flow during diastole is zero.
The 'Windkessel effect' becomes diminished with age as the elastic arteries become less compliant, termed hardening of the arteries or arteriosclerosis, probably secondary to fragmentation and loss of elastin.
[10] The reduction in the Windkessel effect results in increased pulse pressure for a given stroke volume.
The increased pulse pressure results in elevated systolic pressure (hypertension) which increases the risk of myocardial infarction, stroke, heart failure and a variety of other cardiovascular diseases.
[11] Although the Windkessel is a simple and convenient concept, it has been largely superseded by more modern approaches that interpret arterial pressure and flow waveforms in terms of wave propagation and reflection.
[12] Recent attempts to integrate wave propagation and Windkessel approaches through a reservoir concept,[13] have been criticized[14][15] and a recent consensus document highlighted the wave-like nature of the reservoir.
