Steady-State Drug Exposure of Repeated IV Bolus Administration for a One Compartment Pharmacokinetic Model with Sigmoidal Hill Elimination

Drugs exhibiting nonlinear pharmacokinetics hold significant importance in drug research and development. However, evaluating drug exposure accurately is challenging with the current formulae established for linear pharmacokinetics. This article aims to investigate the steady-state drug exposure for a one-compartment pharmacokinetic (PK) model with sigmoidal Hill elimination, focusing on three key topics: the comparison between steady-state drug exposure of repeated intravenous (IV) bolus ( \(\textrm{AUC}_{ss}\) ${\text{AUC}}_{\mathit{ss}}$ ) and total drug exposure after a single IV bolus ( \(\textrm{AUC}_{0-\infty }\) ${\text{AUC}}_{0-\infty }$ ); the evolution of steady-state drug concentration with varying dosing frequencies; and the control of drug pharmacokinetics in multiple-dose therapeutic scenarios. For the first topic, we established conditions for the existence of \(\textrm{AUC}_{ss}\) ${\text{AUC}}_{\mathit{ss}}$ , derived an explicit formula for its calculation, and compared it with \(\textrm{AUC}_{0-\infty }\) ${\text{AUC}}_{0-\infty }$ . For the second, we identified the trending properties of steady-state average and trough concentrations concerning dosing frequency. For the third, we developed formulae to compute dose and dosing time for both regular and irregular dosing scenarios. As an example, our findings were applied to a real drug model of progesterone used in lactating dairy cows. In conclusion, these results provide a theoretical foundation for designing rational dosage regimens and conducting therapeutic trials.