Development of a recursive finite difference pharmacokinetic model from an exponential model: Application to a propofol bolus*

Propofol is commonly administered, as a single bolus dose, for the induction of general anesthesia. The purpose of this study was to mathematically assess the ability to model propofol induction-dose serum levels with a recursive finite difference equation (RFDE). Using data obtained from a prior published study, propofol induction pharmacokinetics were accurately modeled, on a subject-specific basis, with a third-order homogeneous finite difference equation with constant coefficients: P(k + 3) = AP(k + 2) + BP(k + 1) + CP(k). Furthermore, each RFDE model is derived directly from the coefficients of a traditional three-compartment pharmacokinectic exponential equation. Based on this study, third-order RFDE models can have identical accuracy as three-compartment exponential models. In this particular application, it should be noted that each RFDE model required only three coefficients whereas each exponential model required six. Also, there was overall less patient-to-patient variability of the coefficients of the RFDE models. In general, it appears that RFDE models uniquely allow for predicting subsequent drug levels from preexisting ones. However, RFDE models require initial conditions whereas exponential models do not. Additional studies and applications of exponentially-derived RFDE pharmacokinetic models may be warranted.