Constant infusion case of one compartment pharmacokinetic model with simultaneous first-order and Michaelis –Menten elimination: analytical solution and drug exposure formula

AbstractThe main objective of this article is to propose the closed-form solution of one-compartment pharmacokinetic model with simultaneous first-order and Michaelis –Menten elimination for the case of constant infusion. For the case of bolus administration, we have previously established a closed-form solution of the model through introducing a transcendentX function. In the same vein, we found here a closed-form solution of constant infusion could be realized through introducing another transcendentY function. For the general case of constant infusion of limited duration, the closed-form solution is then fully expressed using bothX andY functions. As direct results, several important pharmacokinetic surrogates, such as peak concentration\(C_{max}\) and total drug exposure AUC\(_{0-\infty }\), are found the closed-form expressions and ready to be analyzed. The new pharmacokinetic knowledge we have gained on these parameters, which largely exhibits in a nonlinear feature, is in clear contrast to that of the linear case. Finally, with a pharmacokinetic model adapted from that formerly reported on phenytoin, we numerically analyzed and illustrated the roles of different model parameters and discussed their influence on drug exposure. To conclude, the present findings elucidate the intrinsic quantitative structural properties of such pharmacokinetic model and provide a new avenue for future modelling and rational drug designs.
Source: Journal of Pharmacokinetics and Pharmacodynamics - Category: Drugs & Pharmacology Source Type: research