Journal des sciences théoriques et computationnelles
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An Inductive Approximation to the Solution of Systems of Nonlinear Ordinary Differential Equations in Pharmacokinetics-Pharmacodynamics

Stephen B Duffull and Gareth Hegarty

Rapid and accurate solutions for nonlinear ordinary differential equations (ODEs) that arise in the pharmaceutical sciences are desirable. This is particularly important in the area of pharmacokinetic-pharmacodynamics modelling and design. We describe an iterative linearization to generate inductive approximations which converge to the solution. These approximations allow quick and accurate evaluations of the pharmacokinetic-pharmacodynamic PKPD models. The inductive approximations are applied to a simple nonlinear pharmacokinetic (PK) model, ie a model that is nonlinear when expressed as an ordinary differential equation, and show the utility of the method. Because the approximations depend continuously on the parameters and time, the inductive method is particularly suitable for parameter estimation and optimal design approaches.