COMPARISON OF LINEAR AND NONLINEAR FORMULATIONS OF THE 3-ELEMENT WINDKESSEL MODEL

The three-element windkessel model incorporating a constant compliance (model A) was compared with two nonlinear versions of the same model (models B1 and B2) incorporating a pressure-dependent compliance. The aim was to test whether nonlinear elasticity yielded better model beha vior in describing ascending aortic pressure-flow relationships and in terpreting the physical properties of the arterial system. Exponential and bell-shaped compliance vs. pressure curves were assumed in models B1 and B2, respectively. To test these models, we used measurements o f ascending aortic pressure and flow from three dogs under a wide vari ety of hemodynamic states obtained by administering vasoactive drugs a nd by pacing the heart. These data involved pressure waves with and wi thout an evident oscillation during diastole. Model parameters were es timated by fitting experimental and model-predicted ascending aortic p ressures. Our results indicated that only models A and B1 were identif iable. Fits to ascending aortic pressure obtained from model B1 were s ignificantly better than fits obtained from model A. However, 1) the a ccuracy of parameter estimates, as judged from parameter estimation er ror analysis, was better in model A than in model B1, 2) the estimates of characteristic parameters of the compliance vs. pressure relation in model B1 were inconsistent with expected physiological trends of th is relation, and 3) model B1 did not improve the approximation of dias tolic pressure in the presence of an evident oscillation. We conclude that, even in the presence of better data fit, the nonlinear three-ele ment windkessel cannot be preferred over the traditional linear versio n of this model.