Modelling of the respiratory parameters in non-invasive ventilation

In this study, the respiratory system are modelled by three linear and one non-linear lumped parameter respiratory model, the equations of the models are driven and the parameters are estimated by using statistical signal processing methods. Linear RIC, Viscoelastic and Mead models and proposed basic non-linear RC model are used to resemble the respiratory system of the patient with Chronic Obstructive Pulmonary Disease (COPD) under non-invasive ventilation. Statistical signal processing methods such as Minimum Variance Unbiased Estimation (MVUE Maximum Likelihood Estimation (MLE), Kalman Filter (KF), Unscented Kalman Filter (UKF) and Extended Kalman Filter (EKF) are very powerful methods to estimate the parameters of the systems embedded in the unknown noise. In the first part of this thesis, artificial respiratory signals (airway flow and airway pressure) are used for the performance measurement criteria. Posterior Cramer Rao Lower Bound (PCRLB) is computed for the time-invariant parameters as well as the states in the dual Kalman filters. Then the error covariance matrixes of UKF and EKF are illustrated with respect to these bounds. In the second part of this thesis, the respiratory signals are acquired from 8 COPD patients and 6 healthy subjects by the measurement system. The parameters of the respiratory system are then estimated by these observed respiratory signals. Moreover, by assuming the Generalized Gaussian Distributed (GGD) measurement noise, the actual residuals that is left over when the models are fitted to the measured signals, are analyzed in the statistical sense. In the conclusion, when artificial respiratory signals are used, the best estimated parameters are the RIC model parameters when MLE or MVUE are used. It is also found that, in the real respiratory signals each group demonstrates distinguished results with both different methods and models. The other important results are RIC model parameters are estimated very consistently by MVUE and MLE; EKF and UKF are equally successful for the parameter estimation of nonlinear RC model; and the respiratory signals acquired from the Patient group is best fitted to the nonlinear RC model whereas RIC model is more suitable for the Control group?s respiratory signals.