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Research Article

An Inductive Approximation to the Solution of Systems of Nonlinear Ordinary Differential Equations in Pharmacokinetics-Pharmacodynamics

Stephen B Duffull1* and Gareth Hegarty2

1School of Pharmacy, University of Otago, Dunedin 9054, New Zealand

2Department of Mathematics and Statistics, University of Otago, Dunedin 9054, New Zealand

*Corresponding Author:
Stephen B Duffull
School of Pharmacy
University of Otago, P.O. Box 56
Dunedin 9054, New Zealand
Tel: +6434797258
Fax: +64 3 4797258
E-mail: [email protected]

Received date: June 17, 2014; Accepted date: October 06, 2014; Published date: October 14, 2014

Citation: Stephen B Duffull, Gareth Hegarty (2014) An Inductive Approximation to the Solution of Systems of Nonlinear Ordinary Differential Equations in Pharmacokinetics-Pharmacodynamics. J Theor Comput Sci 2:119. doi:10.4172/2376-130X.1000119

Copyright: © 2014 Stephen B Duffull, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Abstract

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.

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