When the ventricle perceives the arterial system as a Windkessel

Berger, D. S. and C. M. Quick
Biomedical Engineering Society Annual Meeting, Seattle, WA, 2000

Abstract

Consider the arterial system (AS) and a Windkessel. The former has a complex topology and distributed geometric & material properties, in which pulse waves have finite wavelength, λ. The latter has a simple hydraulic structure, in which pulses have infinite λ . The two structures could not be more different. If one were guided solely by structure, it would seem remarkable that the global behaviors (i.e., input impedance, Zas and Zw) of these models are so similar. The similarity has led to the use of the Windkessel as a true representation of the AS, and, as a corollary, to ascribe physiological meaning to the model parameters, particularly equating Windkessel compliance with total AS compliance, Ctot. However, Z as and Zw are not sufficiently similar for reliably accurate estimation of Ctot. Nevertheless, conditions exist that allow reliable Ctot estimation. These include changes that make the AS more Windkessel–like by increasing wave velocity, cph, such as increased vessel wall stiffness (E) & thickness, increased pressure (increasing E), and increased lumen area. Another way to make the AS appear more Windkessel–like is to decrease heart rate (HR). Model experiments reveal that each of these changes yields aortic pressure and flow that appear to arise from a true Windkessel. One can explain these findings on the basis of relative wavelength, λr. Given that λr α cph/HR and that AS topology is fixed, each of the above–mentioned changes yields increased λ r that, by definition, forces the AS to behave like a Windkessel.