The Reservoir-Wave Hypothesis
Historically, separating measured blood pressure into forward and backward waves during diastole resulted in self-cancelling, physiologically contradictory waves. The reservoir-wave hypothesis resolves this by separating the measured pressure waveform into two distinct elements:
Where Pres represents Otto Frank's Windkessel reservoir pressure—which varies with time but is uniform throughout the proximal arterial tree—and Pwave (previously referred to as excess pressure) is the dynamic local pressure driving wave propagation.
By fitting the diastolic decay of pressure to an exponential curve (governed by the time constant τ = RC, representing systemic compliance and peripheral resistance), the reservoir component is resolved. Once subtracted, the residual wave pressure during diastole drops to zero, aligning with real physical flow and eliminating self-cancelling diastolic wave artifacts.
The reservoir-wave hypothesis is related conceptually to the three-element Windkessel model first proposed by Westerhof in 1970 and widely used in compartmental electrical-analogue models of the cardiovascular system.
The 3-Element Windkessel Model
The electrical analogue circuit for the three-element Windkessel is the RCR circuit is shown here, where the compliance (capacitance) of the elastic arteries and hydraulic resistance (impedance) of the vessels draining the arteries (Rres) make up the classical Windkessel model introduced by Frank in 1899. In Westerhof's model, the extra resistance represents the 'characteristic' impedance of the aorta; i.e., it is the impedance that the heart would see if there were no reflections in the aorta, shown here as Rprox.
Reservoir-Wave Separation in Practice
The figure below illustrates reservoir-wave separation applied to human aortic pressure measurements, with the reservoir pressure (blue) and excess pressure (red).
Arterial Blood Pressure Through Ventriculo-Arterial Interaction
The elastance model has been popularised to illustrate the interaction between the left ventricle and the systemic arterial system. Left ventricular stiffness and contractility are characterised by the end-diastolic pressure-volume relationship (EDPVR) and the end-systolic pressure-volume relationship (ESPVR); both of these parameters have become indicators of the performance of the human heart. The systemic arterial system is reduced to a single lumped parameter, the arterial elastance, which is closely related to systemic vascular resistance. The shared units of elastance allow this coupling between the left ventricle and the systemic arteries to be visualised.
See the effect on blood pressure & ejection fraction