Estimation of Three- and Four-Element Windkessel Parameters Using Subspace Model Identification

Abstract

A windkessel model is widely used to operationalize vascular characteristics. In this paper, we employ a noniterative subspace model identification (SMI) algorithm to estimate parameters in a three- and four-element windkessel model by application of physical foreknowledge. Simulation data of the systemic circulation were used to investigate systematic and random errors in the parameter estimations. Results were compared with different methods as proposed in the literature: one closed-loop and two iterative methods for the three-element model, and one iterative method for the four-element model. For the three-element model, no significant systematic errors were observed using SMI. Concerning random errors, SMI appeared more robust in parameter estimations compared with the other methods (P < 0.05 for a signal-to-noise ratio of 18 dB). For the four-element model, a significant systematic error in the estimate of the arterial inertance L was observed (P = 0.011). However, for all methods, an increasing number of outliers in parameter estimates were observed at increased noise levels. These outliers were almost exclusive due to errors in estimates of L. In conclusion, with SMI physical parameters can mathematically be derived by application of physiological foreknowledge. For a three-element windkessel model, SMI appeared a very robust method to estimate parameters. However, application to a four-element windkessel model was less accurate because of low identifiability of L. Therefore, based on the simulation results, the use of the four-element windkessel model is questionable.