Modelling Blood Pressure Uncertainty for Safety Verification of Propofol Anesthesia

Verifying safety of closed-loop drug delivery systems is a crucial step to obtain regulatory approval for such devices. Recently, we proposed a safety-preserving platform to formally verify the safety of closed-loop propofol anesthesia in the presence of uncertainty in patient models. This platform verifies that closed-loop anesthesia maintains the propofol concentration within the therapeutic window. To improve safety for at-risk patients, additional safety constraints on physiological variables, such as blood pressure, can be taken into account. To do so, an accurate description of the propofol effect on blood pressure as well as a comprehensive characterization of inter-patient variability are required. In this paper, we identify and validate a set of models characterizing the blood pressure response to propofol for 10 individual patients from clinical data. This model set shows uncertainty in the effect of propofol on blood pressure among at-risk patients. We use this model set to verify the safety of closed-loop propofol anesthesia subject to constraints on blood pressure using our safety verification platform. We show that there exists an admissible dose of propofol that maintains the propofol plasma concentration as well as blood pressure within safe bounds, without the need for additional treatment for hypotension. However, the dose of propofol which maintains safety, may not provide sufficient anesthesia for all patients and in critical cases treatment for hypotension would be required.