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

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.