Analysis of linear lung models based on state-space models

Linear parametric respiratory system models have been used in the model-based analysis of the respiratory system. Although there are studies exploring the physiological correctness and fitting accuracy of the models, they are not analysed in terms of interaction between parameters and dynamics of the model. In this study we propose to use state-space modelling to yield the time-varying nature of the system incorporated by the parameters.

We tested controllability, observability and stability characteristics of the equation of motion, 2-comp. parallel, 2-comp. series, viscoelastic, 6-element and mead models while using the parameters given in the literature. In the sensitivity analysis we proposed to use dual Desensitized Linear Kalman Filter (DKF) and Extended Kalman Filter (EKF) method. In this method, state error covariance revealed the parameter sensitivities for each model.

Results showed that all models, except 2-comp. parallel and mead models, are both controllable and observable models. On the other hand all models, except mead model, are stable models. Regarding to the sensitivity analysis, dual DKF - EKF method estimated states of the models successfully with a low estimation error. Sensitivity analysis results showed that airway parameters have higher effects on the state estimation than the other parameters have.

We proved that state-space evaluation of the previously proposed parametric models of the respiratory system led us to quantitative and qualitative assessments of the respiratory models. Moreover parameter values found in the literature have different effects on the models.