Pharmacokinetic variability and therapeutic drug monitoring actions at steady state

Purpose. To develop a mathematical model for therapeutic drug monitoring an d to assess the kinetic relationships between the intensity of corrective a ction and the approach of drug concentrations to target values. Methods. A mathematical model that succinctly accounts for the corrective a ctions 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 approac h of the monitored process to the target value followed exponential kinetic s and an analytical expression for dependence the variance with time and va rious dosing parameters was derived. The variance of the drug concentration depends critically on a single nondimensional parameter containing the rat e constant for the therapeutic corrective actions and a coefficient describ ing the variance rate. When the rate constant for the therapeutic correctiv e actions was less than this critical value, the variance increased indefin itely. Conclusions. From a dosing standpoint, large variances in drug concentratio ns are undesirable because some patients will be overdosed or underdosed. S ince deterministic models cannot provide analytical solutions for the momen ts of drug concentration distribution functions, stochastic models can be u sed to provide useful insights into the design of therapeutic regimens.