Sensitivity analysis of respiratory parameter estimates in the constant-phase model

The constant-phase model is increasingly used to fit low-frequency respiratory input impedance (Zrs), highlighting the need for a better understanding of the use of the model. Of particular interest is the extent to which Zrs would be affected by changes in parameters of the model, and conversely, how reliable are parameters estimated from model fits to the measured Zrs. We performed sensitivity analysis on respiratory data from 6 adult mice, at functional residual capacity (FRC), total lung capacity (TLC), and during bronchoconstriction, obtained using a 1-25 Hz oscillatory signal. The partial derivatives of Zrs with respect to each parameter were first examined. The limits of the 95% confidence intervals, 2-dimensional pairwise and p-dimensional joint confidence regions were then calculated. It was found that airway resistance was better estimated at FRC, as determined by the confidence region limits, whereas tissue damping and elastance were better estimated at TLC. Airway inertance was poorly estimated at this frequency range, as expected. During methacholine-evoked pulmonary constriction, there was an increase in the uncertainty of airway resistance and tissue damping, but this can be compensated for by using the relative (weighted residuals) in preference over the absolute (unweighted residuals) fitting criterion. These results are consistent with experimental observation and physiological understanding.