Multi-model generalised predictive control for intravenous anaesthesia under inter-individual variability

Abstract

Inter-individual variability possesses a major challenge in the regulation of hypnosis in anesthesia. Understanding the variability towards anesthesia effect is expected to assist the design of controller for anesthesia regulation. However, such studies are still very scarce in the literature. This study aims to analyze the inter-individual variability in propofol pharmacokinetics/pharmacodynamics (PK/PD) model and proposed a suitable controller to tackle the variability. This study employed Sobol’ sensitivity analysis to identify significance parameters in propofol PK/PD model that affects the model output Bispectral Index (BIS). Parameters’ range is obtained from reported clinical data. Based on the finding, a multi-model generalized predictive controller was proposed to regulate propofol in tackling patient variability. $Ce_{50}$ (concentration that produces 50% of the maximum effect) was found to have a highly-determining role on the uncertainty of BIS. In addition, the Hill coefficient, $\gamma$, was found to be significant when there is a drastic input, especially during the induction phase. Both of these parameters only affect the process gain upon model linearization. Therefore, a predictive controller based on switching of model with different process gain is proposed. Simulation result shows that it is able to give a satisfactory performance across a wide population. Both the parameters $Ce_{50}$ and $\gamma$, which are unknown before anesthesia procedure, were found to be highly significant in contributing the uncertainty of BIS. Their range of variability must be considered during the design and evaluation of controller. A linear controller may be sufficient to tackle most of the variability since both $Ce_{50}$ and $\gamma$ would be translated into process gain upon linearization.