Mathematical models for drug diffusion through the compartments of blood and tissue medium

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M.A. Khanday Aasma Rafiq Khalid Nazir

Abstract

This paper is an attempt to establish the mathematical models to understand the distribution
of drug administration in human body through oral and intravenous routes. Three models
were formulated based on diffusion process using Fick’s principle and law of mass action. The rate
constants governing the law of mass action were used on the basis of the drug efficacy at different
interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the
ordinary differential equations concerning the rate of change of concentration in different compartments
viz. blood and tissue medium. The drug concentration in the different compartments has
been computed using numerical parameters. The graphs plotted illustrate the variation of drug concentration
with respect to time using MATLAB software. It has been observed from the graphs that
the drug concentration decreases in the first compartment and gradually increases in other compartments.
2016 Alexandria University Faculty of Medicine. Production and hosting by Elsevier B.V. This is an
open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

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Author Biographies

M.A. Khanday

Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu & Kashmir, India

Aasma Rafiq

Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu & Kashmir, India

Khalid Nazir

Department of Mathematics, University of Kashmir, Srinagar 190006, Jammu & Kashmir, India