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Advanced hemodynamics

Physiological insight drawn from the arterial pressure waveform — separating the reservoir from the excess, and turning morphology into meaning.

Overview

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:

P(x, t) = Pres(t) + Pwave(x, t)

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.

3-element Windkessel model schematic

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).

Reservoir-wave separation diagram
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