Linear pharmacokinetic model of first order metabolism in the liver
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Date
2014-11-13
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Abstract
In this study we demonstrate the added value of mathematical model of metabolism
for drug modi cation into metabolites. We show that for speci ed parameter val-ues, the model proposed by Polkings et al. (2005) can be substituted into a
proposed metabolism model, which can describe the dynamics of drug change
in the liver. When we ingest a drug into our body, the body absorbs the drug
into the blood stream. Then the body breaks that drug into smaller pieces called
metabolites. This conversion of drugs into metabolite is the third phase of the
Pharmacokinetic phenomenon (ADME). Mathematical modeling of Pharmacoki-netics (PK) is the rate of change in concentration of a medical drug as it goes
through di erent compartments in the human body. In the third phase of drug
processing in the body, it is expected that the absorbed drug has to undergo bio-transformation in the liver before nal excretion of the metabolites through the
kidney or any other excretory system. This third phase of PK (drug metabolism)
is an inevitable processing stage of a drug in order to prevent toxicity build-up due
to re-absorption of un-metabolised active substrate (drug concentration). This
work is an extension of the study done by Polking, Boggess and Arnold (2005).
Their research ndings shows that drug substrate in the human organ or tissue
can be analytically determined using rst-order di erential equation. However
their model encapsulates only the rst two phases (AD) of the whole (ADME)
process and moreover their model hardly tells us the fate of the active substrate
after pharmacological action (healing e ect) in the human organ (tissue). We
develop a rst-order di erential equation model characterizing the metabolism
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reaction in the liver after direct transportation of active substrate from the tis-sue compartment. Primarily, this goal is achieved by using principles in mixing
problems, methods of integration factor and integration by parts. This study
combines the rst three phases (ADM) of (ADME) and our analysis reveals and
also demonstrate the critical conditions under which liver metabolism transpires.
The result of our analysis will help improve medical dosing treatment strategies
for non-linear drugs.
Description
A thesis submitted to the Department of Mathematics, Kwame Nkrumah
University of Science and Technology in partial fulfillment of the requirements
for the degree of Master of Philosophy,