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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2009, Volume 49, Number 11, Pages 1907–1919 (Mi zvmmf4778)  

This article is cited in 12 scientific papers (total in 12 papers)

Mathematical model of optimal chemotherapy strategy with allowance for cell population dynamics in a heterogeneous tumor

A. V. Antipov, A. S. Bratus'

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
References:
Abstract: A mathematical model of tumor cell population dynamics is considered. The tumor is assumed to consist of cells of two types: amenable and resistant to chemotherapeutic treatment. It is assumed that the growth of the cell populations of both types is governed by logistic equations. The effect of a chemotherapeutic drug on the tumor is specified by a therapy function. Two types of therapy functions are considered: a monotonically increasing function and a nonmonotone one with a threshold. In the former case, the effect of a drug on the tumor is stronger at a higher drug concentration. In the latter case, a threshold drug concentration exists above which the effect of the therapy reduces. The case when the total drug amount is subject to an integral constraint is also studied. A similar problem was previously studied in the case of a linear therapy function with no constraint imposed on the drug amount. By applying the Pontryagin maximum principle, necessary optimality conditions are found, which are used to draw important conclusions about the character of the optimal therapy strategy. The optimal control problem of minimizing the total number of tumor cells is solved numerically in the case of a monotone or threshold therapy function with allowance for the integral constraint on the drug amount.
Key words: mathematical model of optimal chemotherapy, optimal control problem, numerical methods.
Received: 03.09.2008
English version:
Computational Mathematics and Mathematical Physics, 2009, Volume 49, Issue 11, Pages 1825–1836
DOI: https://doi.org/10.1134/S0965542509110013
Bibliographic databases:
Document Type: Article
UDC: 519.626
Language: Russian
Citation: A. V. Antipov, A. S. Bratus', “Mathematical model of optimal chemotherapy strategy with allowance for cell population dynamics in a heterogeneous tumor”, Zh. Vychisl. Mat. Mat. Fiz., 49:11 (2009), 1907–1919; Comput. Math. Math. Phys., 49:11 (2009), 1825–1836
Citation in format AMSBIB
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\paper Mathematical model of optimal chemotherapy strategy with allowance for cell population dynamics in a~heterogeneous tumor
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\vol 49
\issue 11
\pages 1907--1919
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\jour Comput. Math. Math. Phys.
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  • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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