Polynomial system identification modeling and adaptive model predictive control of arterial oxygen saturation in premature infants
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The automation of the regulation of the fraction of inspired oxygen (FiO2) in neonatal mechanical ventilation to treat respiratory distress syndrome has proven challenging due to competing objectives: maintaining arterial oxygen saturation levels (SpO2) while simultaneously not inducing complications such as retrolental fibroplasia. Historically, models of the dynamics of the neonatal respiratory system were first order transfer function approximations. This work used higher order polynomial system identification methods with the model structures of autoregressive with exogenous inputs (ARX) and Box-Jenkins (BJ) models to investigate possible improved modeling of the dynamic relationship between the FiO2, Heart Rate (HR), and Respiratory Rate (RR) to the SpO2. Through a parameter sweep of different of polynomial orders and sampling delays, 3,456 ARX models and 13,176 BJ models were created, with four being selected for comparison based upon modeling performance metrics. From these best performing models, it was concluded that the FiO2 relationship to SpO2 could still be adequately approximated by a first order transfer function model with delay. The disturbance HR, RR, and the unmodeled dynamics did require higher order approximations. It was also shown that selecting a model based off the Akaike's Information Criterion was preferred in picking a model from a collection of identified models. With a singular winning model from the four best performing models, an adaptive model predictive controller (AMPC) was designed to adhere to clinical best practices to regulate the SpO2. Through a recursive polynomial model estimator (RPME), an ARX approximation of the unknown model's dynamics for the FiO2, HR, and RR relationship to the SpO2 could be used to update the internal model of the AMPC. Through this online model estimation, the AMPC could successfully feedforward reject the HR and RR disturbances improving the simulated time within the SpO2 target limits, 67.8% of simulation time, to a baseline PI controller's 56.6%, in periodic desaturation simulations.
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