Modelling of residual variability in toxicokinetic studies with sparse sampling: the case of tetrahydronaphthalene

The present study describes the kinetics of tetrahydronaphthalene in male and female rats (five animals per dose per sex) at three dose levels (15, 50, and 150 mg/kg daily). Plasma concentration measurements were performed in the course of a subacute toxicity study of 28 days duration in an enriched study design. Two blood samples per animal were taken at different time points after application at day 1 and 16 (150 mg/kg daily) and at day 3 and 18 (15 and 50 mg/kg daily), respectively. Tetrahydronaphthalene was assayed by gas chromatography-mass spectrometry (GC-MS) after extraction. The data of plasma concentration time were analysed using non-linear mixed effects modelling as implemented in NONMEM. The structural model with the best fit employed one compartment kinetics with instantaneous drug input. Interindividual variability in both k and V was found to be very small [k, 0.201 h(-1), 0.013; V, 16.19 (kg), 1.77; population mean and SE]. No unequivocal evidence of dose dependence could be found. The kinetic parameter with the highest extent of variability was the extent of bioavailability which showed an coefficient of variation (CV) of 96%. Both gender and dose had no influence on the variability. The present approach is concluded to offer more insight into the relationship between dose, concentration and effect and into factors which explain variability in kinetics without additional testing or additional animals. Proposals for a refined sampling schedule are made.