Reduction of a complex arterial tree into a simple Windkessel
Berger, D. S., and C. M. Quick
XIV Congress, Cardiovascular System Dynamics Society, Baltimore, MD, 2000
Abstract
Consider the arterial system (AS) and a Windkessel model. The
former has a complex topology and distributed geometric and material properties,
in which pulse waves have finite wavelength, λ. The latter is
a simple theoretical construct, consisting of a single chamber in which pulses
have infinite λ. The two systems could not be more different.
If one were guided solely by structure, it would seem remarkable that their
input impedances, Zas and Zw, can be so
similar. This similarity has led to the use of the Windkessel as a true
representation of the AS, and, accordingly, to ascribe physiological
meaning to the model parameters, particularly interpreting Windkessel compliance
as total AS compliance, Ctot. However,
Zas and Zw are not sufficiently similar for
reliably accurate estimation of Ctot. Nevertheless,
conditions do exist that allow reliable Ctot estimation.
These include changes that make the AS more Windkessel–like by
increasing pulse wave velocity, cph, such as increased vessel
wall stiffness (E, fig. A) and 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, fig.
B). Simulations, using a multibranching AS model dynamically coupled
to a model of the heart, show 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
. Because λr = cph
/HR, each of the above–mentioned changes yields increased λ
r, making the AS to appear like a Windkessel.
