Pharmacokinetic variability and therapeutic drug monitoring actions at steady state

Purpose. To develop a mathematical model for therapeutic drug monitoring and to assess the kinetic relationships between the intensity of corrective action and the approach of drug concentrations to target values. Methods. A mathematical model that succinctly accounts for the corrective actions and the variability inherent in the pharmacokinetics was used. Results. The validity of the variability term was tested using experimental data for steady state concentrations of the drug procainamide. The approach of the monitored process to the target value followed exponential kinetics and an analytical expression for dependence the variance with time and various dosing parameters was derived. The variance of the drug concentration depends critically on a single non-dimensional parameter containing the rate constant for the therapeutic corrective actions and a coefficient describing the variance rate. When the rate constant for the therapeutic corrective actions was less than this critical value, the variance increased indefinitely. Conclusions. From a dosing standpoint, large variances in drug concentrations are undesirable because some patients will be overdosed or underdosed. Since deterministic models cannot provide analytical solutions for the moments of drug concentration distribution functions, stochastic models can be used to provide useful insights into the design of therapeutic regimens.