Comparison of linear and nonlinear formulations of the three
-element windkessel model.
Fogliardi, Roberto, Marco Di Donfrancesco, and Roberto Burattini.
Department of Electronics and Automatica, University of Ancona,
60131 Ancona, Italy, Department of Veterinary and Comparative
Anatomy, Pharmacology and Physiology, Washington State University,
Pullman, WA 99164-6520
APStracts 3:0246H, 1996.
The three-element windkessel model incorporating a constant compliance
(model A), was compared with two nonlinear versions of the same model
(models B1, B2) incorporating a pressure-dependent compliance. The
aim was to test whether nonlinear elasticity yielded a better model
behaviour in describing ascending aortic pressure-flow relationships
and interpreting the physical properties of the arterial system. An
exponential and a bell-shaped compliance vs. pressure curves were
assumed in models B1 and B2, respectively. To test these models, we
used measurements of ascending aortic pressure and flow taken from
three dogs under a wide variety of hemodynamic states obtained by
administrating vasoactive drugs and by pacing the heart. These data
involved pressure waves with and without an evident oscillation
during diastole. Model parameters were estimated by fitting
experimental and model predicted ascending aortic pressures. Our
results indicated that only model A and model B1 were identifiable.
Fits to ascending aortic pressure obtained from model B1 were
significantly better than fits obtained from model A. However, a) the
accuracy of parameter estimates, as judged from parameter estimation
error analysis, was better in model A than in model B1, b) the
estimates of characteristic parameters of the compliance vs. pressure
relation in model B1 were inconsistent with expected physiological
trends of this relation, and c) model B1 did not improve the
approximation of diastolic pressure in the presence of an evident
oscillation. We conclude that, even in the presence of better data
fit, the non-linear three-element windkessel cannot be preferred with
respect to the traditional linear version of this model.
Received 30 October 1995; accepted in final form 24 May 1996.
APS Manuscript Number H1008-5.
Article publication pending Am. J. Physiol. (Heart Circ. Physiology).
ISSN 1080-4757 Copyright 1996 The American Physiological Society.
Published in APStracts on 28 June 96