Analysis of pseudo-profiles in organ pharmacokinetics and toxicokinetics

In general, the pharmacokinetic model parameters, like rate constants, area under the curve (AUC) etc. are estimated via a two-stage procedure, where the values obtained from concentration-time relationships within one subject (experimental unit) are considered to be functionally related to the drug concentrations measured. In many cases 'mean' estimators and their respective standard errors are calculated afterwards. The determination of drug concentrations in organs as well as in the serum of small animals (mice, rats) in dependence of the time after administration often does not permit the establishment of reasonable profiles within one subject suited for conventional pharmacokinetic analyses and tolerability studies. Frequently, only one experimental value per organ or animal is recorded. The consequence is that most pharmacokinetic parameters are to be estimated on the basis of the mean concentrations rather than via the mean of individual parameter estimates. In all cases of a non-linear relationship between a target item and the concentration, the mean-concentration based estimators and the two-stage profile based estimators need not coincide. In addition, in the former case variance estimators may be either difficult to obtain or not deducible. In order to get variance estimators as well as to enable comparisons between different treatment regimens, in addition to bioequivalence testing as a step towards human dose finding studies, various resampling techniques (parametric and non-parametric bootstrap) were applied to generate pseudo-profiles from independent measurements and compared to their more conventional counterparts where applicable. Simulation studies based on different predefined pharmacokinetic models (first-order elimination after i.v. bolus, first-order elimination after first-order absorption, simple capacity-limited kinetics) revealed that even the non-parametric pseudo-profile stratified 'bootstrap' (resampling with replacement per time point) performs quite satisfactorily.