Comparison of linear and nonlinear formulations of the three-element windkessel model

Abstract

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 behavior in describing ascending aortic pressure-flow relationships and interpreting 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 of ascending aortic pressure and flow from three dogs under a wide variety of hemodynamic states obtained by administering 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 models A and B1 were identifiable. Fits to ascending aortic pressure obtained from model B1 were significantly better than fits obtained from model A. However, 1) the accuracy of parameter estimates, as judged from parameter estimation error 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 this relation, and 3) 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 nonlinear three-element windkessel cannot be preferred over the traditional linear version of this model.