Nonparametric block-structured modeling of lung tissue strip mechanics

Very large amplitude pseudorandom uniaxial perturbations containing frequencies between 0.125 and 12.5 Hz were applied to five dog lung tissue strips. Three different nonlinear block-structured models in nonparametric form were fit to the data. These models consisted of (1) a static nonlinear block followed by a dynamic linear block (Hammerstein model); (2) the same blocks in reverse order (Wiener model): and (3) the blocks in parallel (parallel model). Both the Hammerstein and Wiener models performed well for a given input perturbation, each accounting for greater than 99% of the measured stress signal variance. However, the Wiener and parallel model parameters showed some dependence on the strain amplitude and the mean stress. In contrast, a single Hammerstein model accounted for the data at all strain amplitudes and operating stresses. A Hammerstein model featuring a fifth-order polynomial static nonlinearity and a linear impulse response function of 1 s duration accounted for the most output variance (99.84% ± 0.13%, mean±standard deviations for perturbations of 50% strain at 1.5 kPa stress). The static nonlinear behavior of the Hammerstein model also matched the quasistatic stressstrain behavior obtained at the same strain amplitude and operating stress. These results show that the static nonlinear behavior of the dog lung tissue strip is separable from its linear dynamic behavior.