Optimal multidrug treatment in the presence of drug resistance stemming from gene amplification

• Autorzy: Śmieja J. , Świerniak A.
• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with development of optimal treatment protocols that take into account both action of several drugs and the evolution of drug resistance. It is a result of analysis of evolution of drug resistance in cancer population but presented methodology can be applied in any case involving drug resistance stemming from gene amplification. First, a biological background is given. In subsequent sections of the paper, the developed technique is presented and some early analytical results, which form a basis for more precise modeling, are shown. Afterwards, the model description is transformed into a vector integro-differential equation, which makes it possible to define necessary conditions of optimal solution to the minimization problem arising from the search for the optimal treatment. Finally, some remarks on the model applicability are presented.

Słowa kluczowe

EN

infinite dimensional systems; optimal control; biomedical modeling

PL

nieskończenie wymiarowy system; optymalna kontrola; modelowanie biomedyczne

• Wydawca: University of Silesia, Institute of Informatics, Computer Systems Department
• Czasopismo: Journal of Medical Informatics & Technologies
• Rocznik: 2002
• Tom: Vol. 3
• Strony: MI13--19
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Śmieja J.

• Department of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice, POLAND

autor

Świerniak A.

• Department of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice, POLAND

Bibliografia

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• [2] Harnevo L.E., Z. Agur, Use of mathematical models for understanding the dynamics of gene amplification, Mutat. Res., Vol. 292, 1993, pp. 17–24.
• [3] Kimmel M., D.E. Axelrod, Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity, Genetics, Vol. 125, 1990, pp. 633-644.
• [4] Kimmel M., D.N. Stivers, Time - continuous branching walk models of unstable gene amplification, Bull. Math. Biol., Vol. 56, 1994, pp. 337-357.
• [5] Smieja J., Z. Duda, A. Swierniak, Optimal Control for the Model of Drug Resistance Resulting from Gene Amplification, Preprints of 14th World Congress of IFAC, Vol. L, 1999, pp. 71-75.
• [6] Stark G.R., Regulation and mechanisms of mammalian gene amplification. Adv. Cancer Res. Vol. 61, 1993, pp. 87-113.
• [7] Swierniak A., M. Kimmel, A. Polanski, Infinite dimensional model of evolution of drug resistance of cancer cells, Journal of Mathematical Systems, Estimation and Control, Vol. 8, No. 1, 1998, pp. 1–17.
• [8] Swierniak A., A. Polanski, M. Kimmel, A. Bobrowski, J. Smieja, Qualitative analysis of controlled drug resistance model - inverse Laplace and semigroup approach, Control and Cybernetics, Vol. 28, 1999, pp. 61-74.
• [9] Swierniak A., J. Smieja, Cancer chemotherapy optimization under evolving drug resistance, Nonlinear Analysis, Vol. 47, No 1, 2001, pp. 375-386.
• [10] Windle B., G.M. Wahl, Molecular dissection of mammalian gene amplification: New mechanistic insights revealed by analysis of very early events, Mutat. Res. Vol. 276, 1992, pp. 199-224.