DIFFERENTIAL EQUATIONS WITH SMALL PARAMETER WITH APPLICATIONS IN RADIOIMMUNOTHERAPY
The Akzo Nobel research laboratories formulated
this problem in their study of the penetration of radio-labeled antibodies into a tissue that has
been infected by a tumor. This study was carried out for diagnostic as well as therapeutic
purposes. The treatment of malignant diseases, after its primary treatment by surgery, is either
by external beam radiotherapy, which is effective but local, or by chemoteraphy, which is
effective but not selective. The radiotherapy labelled antibody has to be able to penetrate the
whole of the tumour, whereas for imaging only uptake on the surface of the tumour is needed.
Factors such as dose, rate delivered, tumor size, and radiosensitivity play a major role in
determining therapeutic response, while target-to-nontarget ratios and, particularly, circulating
radioactivity to the bone marrow determine the major dose-limiting toxicities. In this article, we
introduced a system of differential equations with small parameter with applications in
radioimmunotherapy. The problem consists of two partial differential equations. Both the
equation of this system includes small parameter e. We introduce the mathematical technique
known as boundary function method for singular perturbation system. In this system, the small
parameter is an asymptotic variable, different from the independent variable. We write solution
of this system in a small parameter, and investigation of asymptotic solution for system. Using
the program Matlab and numerical method Runge-Kutta, I did various simulations for different
values of biological parameters presented in the model studied.
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