Exploring inductive linearization for pharmacokinetic –pharmacodynamic systems of nonlinear ordinary differential equations

AbstractPharmacokinetic –pharmacodynamic systems are often expressed with nonlinear ordinary differential equations (ODEs). While there are numerous methods to solve such ODEs these methods generally rely on time-stepping solutions (e.g. Runge–Kutta) which need to be matched to the characteristics of the problem at han d. The primary aim of this study was to explore the performance of an inductive approximation which iteratively converts nonlinear ODEs to linear time-varying systems which can then be solved algebraically or numerically. The inductive approximation is applied to three examples, a simple nonlinear p harmacokinetic model with Michaelis–Menten elimination (E1), an integrated glucose–insulin model and an HIV viral load model with recursive feedback systems (E2 and E3, respectively). The secondary aim of this study was to explore the potential advantages of analytically solving linearized ODEs with two examples, again E3 with stiff differential equations and a turnover model of luteinizing hormone with a surge function (E4). The inductive linearization coupled with a matrix exponential solution provided accurate predictions for all examples with comparable solution time to the matched tim e-stepping solutions for nonlinear ODEs. The time-stepping solutions however did not perform well for E4, particularly when the surge was approximated by a square wave. In circumstances when either a linear ODE is particularly desirable or the uncertainty in matching the i...
Source: Journal of Pharmacokinetics and Pharmacodynamics - Category: Drugs & Pharmacology Source Type: research