The nonstandard finite difference method applied to pharmacokinetic models
Date
2018
Authors
Egbelowo, Oluwaseun Francis
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Abstract
A good understanding of pharmacokinetic-pharmacodynamic can shed light on
situations where one or the other needs to be optimized in drug discovery and
development. As a result of this, pharmaceutical companies aim to develop
new tools to support drug discovery and e cacious dose for clinical use. Drugs
take a complicated journey through the body before they produce their desired
therapeutic e ects. Ultimately, these processes are usually best described by
compartment pharmacokinetic-pharmacodynamics 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 a ecting the response of these clinical drugs. These PK/PD
models leads to di erential equations. Few of these di erential equations can be
solved exactly. Therefore, a lack of exact solutions to many of these di erential
equations leads to numerical approximation been used to determine the possible
solution or behaviour of the di erential equations. The aim of this thesis is to apply
standard nite di erence (SFD) and nonstandard nite di erence (NSFD) methods
to continuous-time pharmacokinetic- pharmacodynamic models. Another aim of
this thesis is to provide a rigorous analysis of these models to gain insight into the
dynamical features. This will allow us to also comment on the impact of certain
key parameters. The NSFD method was shown to be dynamically consistent with
the original continuous-time models. Also, the NSFD method is able to predict
the concentration{time pro le of a drug when there are alterations in the dosing
regimen|this would not be possible were one to consider non-compartment analysis.
Furthermore, the NSFD method preserves signi cant properties of the analogous
models and consequently gives reliable numerical results even when analytical
solutions are not possible. The standard approaches to multi-compartment models
assume linear dynamics over the duration of each time step, whereas the NSFD
method assumes exponential dynamics. Thus, in the case of a linear model the
NSFD method recovers the model dynamics exactly. This thesis illustrates the
ability of the NSFD method to solve compartment PK models in a stable and
robust fashion.
Description
A thesis submitted in fullment of the requirements
for the degree of Doctor of Philosophy
in the School of Computer Science and Applied Mathematics
, University of the Witwatersrand, Johannesburg, July 2018
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Citation
Egbelowo, Oluwaseun Francis (2018) The nonstandard finite difference method applied to pharmacokinetic models, University of the Witwatersrand, Johannesburg, https://hdl.handle.net/10539/27306