title: Differential equations with small parameter with applications in radioimmunotherapy.
abstract: 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 chemotherapy, 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 epsilon. 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.
authors.affiliation: Department of Medical Bioinstrumentation, School of Medical Bioengineering, Gr.T. Popa University of Medicine and Pharmacy Iaşi.
authors.forename: M
authors.initials: M
authors.lastname: Ilea
authors.forename: M
authors.initials: M
authors.lastname: Turnea
authors.forename: D
authors.initials: D
authors.lastname: Arotăriţei
authors.forename: C M
authors.initials: CM
authors.lastname: Toma
mesh_terms: D000465:Algorithms; D006801:Humans; D009369:Neoplasms / Q000276:immunology* / Q000628:therapy*; D009716:Numerical Analysis, Computer-Assisted; D016499:Radioimmunotherapy / Q000379:methods*