Modeling and analysis of individualized pharmacokinetics and pharmacodynamics for volatile anesthesia

The presented procedure aims to establish an in-depth understanding of a derived mathematical model for drug distribution, pharmacokinetics, and drug effect, pharmacodynamics, during volatile anesthesia. A physiologically based, patient-specific model is derived, where the pharmacokinetic (PK) part consists of multiple blood and tissue compartmental models, each adjusted to the weight, height, gender, and age of the patient. The pharmacodynamic (PD) part is described by an effect site compartment and the Hill equation both linking the hypnotic effect measured by the Bispectral Index (BIS) to the arterial anesthetic concentration. Via a global sensitivity analysis the patient-specific PK and PD variables and parameters are analyzed regarding their influence on the measurable outputs, which are the end-tidal concentration of the volatile anesthetic and the BIS. Via this analysis, the uncertainty introduced by PD variability is identified to be more significant than the uncertainty introduced by PK variability. A case study of isoflurane-based anesthesia shows that the simulation results of the individualized PK variables are in good accordance with the measured end-tidal concentration. However, the PD parameters need to be estimated online to predict the hypnotic depth, measured by the BIS, correctly. As a result of this study, the aim should be to focus on the individual identification of the PD parameters before and during anesthesia with future application in safe and robust model predictive control.