Complex and frequency-dependent compliance of viscoelastic windkessel resolves contradictions in elastic windkessels

Based on simulated data, recent studies by others showed that fitting measured pulse pressure with the pulse pressure predicted by the two-element windkessel (W2-based pulse pressure method, PPM) yielded estimates of total arterial compliance closer to simulated values than other estimation methods that use either the W2 model or the three-element windkessel (W3). A later experimental application of the PPM, made by us, however, yielded relatively non pressure dependent estimates of compliance that were in contradiction with pressure dependent estimates obtained from the W2 model by fitting to the full aortic pressure wave (full pressure method, FPM). To explain these contradictory findings, in the present study we interpreted the aortic input impedance in terms of a viscoelastic windkessel (VW), where total peripheral resistance is connected in parallel to a complex and frequency dependent compliance, Cc(j omega), described by the Voigt cell. Using ascending aortic pressure and flow taken from four dogs, under a variety of haemodynamic states, we compared the estimates of compliance obtained from the W3 and VW models and from different W2-based estimation methods: the FPM (Cw2), the PPM (Cpp), the decay time method, DTM (Cdt), and the area method, AM (C(am)). The VW-based estimates of complex compliance resolved contradictions in the W2-based estimates. Static compliance of VW-model, Cvw = Cc(0), showed a good correlation (p = 0.999) with Cw2. Correlation of static compliance with C(am) and Cdt estimates was affected by distortions in diastolic pressure decay. The modulus of VW model's dynamic compliance, ¿Cc(omega(h))¿, at the heart pulsation omega(h), was well correlated (p = 0.975) with Cpp. Analysis of data fit and compliance estimates indicated that the VW model yields an improvement over the W3 in the physical interpretation of the overall arterial properties.