A frequency domain approach to nonlinear and structure identification for long memory systems: application to lung mechanics

From the input-output point of view, many nonlinear biological systems display long memory characteristics which can become a critical issue using nonparametric time-domain kernel identification due to inevitable truncation of memory length. To avoid these limitations, we present an alternative approach in the frequency domain with application to lung mechanics. Generally, if the system is excited with a periodic wave form, the response will approach a steady state which dominates the long memory transients. Thus, we hypothesized that the kernels at discrete frequencies will not be significantly affected by memory truncation. To test this, we extended the frequency kernel analysis of Victor and Shapley (Biophys. J. 29:459-484, 1980) to a nonwhite input spectrum and developed a new structure test in the frequency domain to differentiate between Wiener and Hammerstein models. These techniques were applied to measured pressure-flow data of isolated lung lobes. The results showed that (1) the important nonlinearities in the pressure-flow relation are of second order, (2) the frequency kernels of the lobes were similar for flat and ventilatory-like input spectra, and (3) the structure test strongly suggested that the pressure-flow relationship during tidal-like excursions is consistent with a Wiener structure.