Nonparametric block-structured modeling of rat lung mechanics

The quasistatic and dynamic pressure volume characteristics of the lungs were measured in five anesthetized, paralyzed open-chest rats. Psuedo-random volume perturbations over a frequency range of 0.25 to 25 Hz and having peak-peak amplitudes of 1 to 4 ml were applied after the lungs were allowed to expire against 0.2, 0.4, 0.6, and 0.8 kPa positive end-expiratory pressure (PEEP). The lung mechanics were partitioned in two ways: a linear dynamic block followed by a static nonlinearity (Wiener model) and a static nonlinearity ahead of a linear dynamic block (Hammerstein model). It was found that a Hammerstein model featuring a third-order polynomial static nonlinearity and a linear impulse response function of 1-sec duration accounted for the greatest amount of the output variance (98.8 ± 0.6%. mean ±SD from perturbations of 4 ml amplitude and PEEP = 0.8 kPa). The static nonlinear behavior matched the measured quasistatic pressure volume behavior obtained at the same amplitude and at the same level of PEEP, provided that all direct current gain of the model was located within the static nonlinearity. Under these conditions, the linear resistance was inversely dependent on the PEEP, whereas little PEEP or amplitude dependence of the linear compartment elastance was observed. Thus, of the two block-structured models tested, the Hammerstein model accounted better for the large amplitude nonlinear mechanical behavior. However, neither model could account for the dependence of the linear block resistance on PEEP.