Sensitivity analysis for evaluating nonlinear models of lung mechanics

We present a combined theoretical and numerical procedure for sensitivity analyses of lung mechanics models that are nonlinear in both state variables and parameters. We apply the analyses to a recently proposed nonlinear lung model which incorporates a wide range of potential nonlinear identification conditions including nonlinear viscoelastic tissues, airway inhomogeneities via a parallel airway resistance distribution function, and a nonlinear block-structure paradigm. Additionally, we examine a system identification procedure which fits time- and frequency-domain data simultaneously. Model nonlinearities motivate sensitivity analyses involving numerical approximation of sensitivity coefficients. Examination of the normalized sensitivity coefficients provides direct insight on the relative importance of each model parameter, and hence the respective mechanism. More formal quantification of parameter uniqueness requires approximation of the paired and multidimensional parameter confidence regions. Combined with parameter estimation, we use the sensitivity analyses to justify tissue nonlinearities in modeling of lung mechanics for healthy and airway constricted conditions, and to justify both airway inhomogeneities and tissue nonlinearities during bronchoconstriction. The tools in this paper are general and can be applied to a wide class of nonlinear models.