Nonlinear Elimination of Drugs in One-Compartment Pharmacokinetic Models: Nonstandard Finite Difference Approach for Various Routes of Administration

Abstract

The motivation for this study is to introduce and motivate the use of nonstandard finite difference (NSFD) schemes, capable of solving one-compartment pharmacokinetic models. These models are modeled by both linear and nonlinear ordinary differential equations. “Exact” finite difference schemes, which are a special NSFD, are provided for the linear models while we apply the NSFD rules, based on Mickens’ idea of transferring nonlinear models into discrete schemes. The method used was compared with other established methods to verify its efficiency and accuracy. One-compartment pharmacokinetic models are considered for different routes of administration: I.V. bolus injection, I.V. bolus infusion and extravascular administration.

Keywords

• pharmacokinetics
• intravenous bolus injection
• intravenous bolus infusion
• extravascular
• nonstandard finite difference
• Michaelis-Menten elimination