An Analytical Approach of One-Compartmental Pharmacokinetic Models with Sigmoidal Hill Elimination

In this study, we aim to develop the analytical solutions of one-compartment pharmacokinetic models with sigmoidal Hill elimination and quantitatively revisit some widely used pharmacokinetic indexes. For this purpose, we have first established the closed-form solutions of the model with intravenous bolus administration through introducing a transcendent H function, which is proved a generalized form of the Lambert W function. Then, in the case of a single dose, we have obtained the explicit formulas for several pharmacokinetic surrogates, such as the clearance, elimination half-life and partial/total drug exposure. All these surrogates are found concentration-dependent and sensitive to the Hill coefficient [Formula: see text]. Meanwhile, in establishing the closed-form formulas for multiple repeated dosing regimens, we have discovered phase transitions for steady states with different ranges of [Formula: see text] in function of the lengths of dosing intervals. Further, our results are illustrated with two drug examples. To conclude, the present findings elucidate the intrinsic quantitative structural properties of pharmacokinetic models with Hill elimination and provide new knowledge for nonlinear pharmacokinetics and guidance for rational drug designs.