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Bioengineering 2017, 4(2), 40; doi:10.3390/bioengineering4020040

Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model

DST/NRF Centre of Excellence in the Mathematical and Statistical Sciences, School of Computer Science and Applied Mathematics, University of the Witwatersrand, Johannesburg, Private Bag 3, Wits 2050, South Africa
These authors contributed equally to this work.
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Academic Editor: Gou-Jen Wang
Received: 4 March 2017 / Revised: 27 April 2017 / Accepted: 28 April 2017 / Published: 4 May 2017
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Abstract

We extend the nonstandard finite difference method of solution to the study of pharmacokinetic–pharmacodynamic models. Pharmacokinetic (PK) models are commonly used to predict drug concentrations that drive controlled intravenous (I.V.) transfers (or infusion and oral transfers) while pharmacokinetic and pharmacodynamic (PD) interaction models are used to provide predictions of drug concentrations affecting the response of these clinical drugs. We structure a nonstandard finite difference (NSFD) scheme for the relevant system of equations which models this pharamcokinetic process. We compare the results obtained to standard methods. The scheme is dynamically consistent and reliable in replicating complex dynamic properties of the relevant continuous models for varying step sizes. This study provides assistance in understanding the long-term behavior of the drug in the system, and validation of the efficiency of the nonstandard finite difference scheme as the method of choice. View Full-Text
Keywords: pharmacokinetic; standard finite difference; nonstandard finite difference; intravenous bolus injection; intravenous infusion pharmacokinetic; standard finite difference; nonstandard finite difference; intravenous bolus injection; intravenous infusion
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MDPI and ACS Style

Egbelowo, O.; Harley, C.; Jacobs, B. Nonstandard Finite Difference Method Applied to a Linear Pharmacokinetics Model. Bioengineering 2017, 4, 40.

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