Models and their uncertainty for bp maintenance during spinal anesthesia using phenylephrine

Phenylephrine is used to treat maternal hypotension induced by spinal anesthesia. Studies show that phenylephrine is able to correct hypotension but an over-dose could result in bradycardia and hypertension. The response of this drug has not been fully investigated and hence it creates significant workload for the anesthetists. They are required to adequately and continuously regulate the dose of phenylephrine. A model of blood pressure and associated uncertainty, during spinal anesthesia, is derived for use with an automatic drug delivery system. The model of input-output relationship is arranged into a 10-state multivariable model, using clinical data and the subspace identification and the prediction error method. The relationship among the output (patient's blood pressure), the primary input (phenylephrine) and measured disturbances (spinal anesthesia and heart rate) is considered. Uncertainties in the model parameters, reflecting a diverse patient population based on a 40 cases observational study, are arranged in a linear fractional structure.