Physiological interpretation of inductance and low-resistance terms in four-element windkessel models: Assessment by generalized sensitivity function analysis

Abstract

Physiological relevance of parameters of three arterial models, denominated W4P, W4S and IVW, was assessed by computation of parameter-related generalized sensitivity functions (GSFs), which allow the definition of heart-cycle time intervals where the information content of experimental data, useful for estimation of each model parameter, is concentrated. The W4P and W4S are derived from the three-element windkessel by connecting an inductance, L, in parallel or in series, respectively, with aortic characteristic impedance, R c . In the IVW, L is placed in series at the input of a viscoelastic windkessel, incorporating a Voigt cell (a resistor, R d , in series with a capacitor, C). Pressure and flow measured in the ascending aorta of five ferrets and five dogs were used to estimate all model parameters, by fitting to pressure. For each model structure, parameter-related GSFs were generated. Focusing on controversial L, R c and R d physical meaning, our GSF analysis yielded the conclusion that, in both the W4S and the IVW, but not in the W4P, the L-term is suitable to represent the inertial properties of blood motion. Moreover, the meaning of aortic characteristic impedance ascribed to R c is questionable; while R d is likely to account for viscous losses of arterial wall motion.