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

Exploring inductive linearization for pharmacokinetic–pharmacodynamic systems of nonlinear... Pharmacokinetic–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 hand. 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 pharmacokinetic 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 time-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 integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Pharmacokinetics and Pharmacodynamics Springer Journals

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

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Publisher
Springer US
Copyright
Copyright © 2017 by Springer Science+Business Media New York
Subject
Biomedicine; Pharmacology/Toxicology; Pharmacy; Veterinary Medicine/Veterinary Science; Biomedical Engineering; Biochemistry, general
ISSN
1567-567X
eISSN
1573-8744
D.O.I.
10.1007/s10928-017-9527-z
Publisher site
See Article on Publisher Site

Abstract

Pharmacokinetic–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 hand. 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 pharmacokinetic 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 time-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 integrator to the ODE system is of potential risk, then the inductive approximation method coupled with an analytical integration method would be an appropriate alternative.

Journal

Journal of Pharmacokinetics and PharmacodynamicsSpringer Journals

Published: May 26, 2017

References

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