Are infinite dimensional models applicable in modelling and analysis of cancer chemotherapy?

• Autorzy: Świerniak A. , Kimmel M. , Śmieja J. , Rzeszowska-Wolny J.
• Języki publikacji: EN

Abstrakty

EN

Drug resistance and phase dependence have been regarded by many authors as the main obstacles against successful cancer chemotherapy. We propose a model which takes into account both these phenomena and give a tool to use phase specificity as an advantage rather than a fault and make it resistant of drug resistance. It combines models that so far have been studied separately, taking into account both the phenomenon of gene amplification and drug specificity in chemotherapy, in their different aspects. The mathematical description is given by an infinite dimensional state equation with a system matrix, the form of which enables decomposition of the model into two interacting subsystems. While the first one, of finite dimension, can have any form, the second one is infinite dimensional and tridiagonal.

Słowa kluczowe

EN

drug resistance; branching random walk; infinite-dimensional systems; Laplace transforms

PL

odporność na leki; nieskończenie wymiarowy system; przekształcenia Laplace'a

• Wydawca: University of Silesia, Institute of Informatics, Computer Systems Department
• Czasopismo: Journal of Medical Informatics & Technologies
• Rocznik: 2004
• Tom: Vol. 8
• Strony: MM3--10
• Opis fizyczny: Bibliogr. 6 poz., rys.

Twórcy

autor

Świerniak A.

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

autor

Kimmel M.

• Department of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice, Poland
• Department of Statistics, Rice University, Houston TX 77251, USA

autor

Śmieja J.

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

autor

Rzeszowska-Wolny J.

• Department of Clinical and Experimental Biology, Institute of Oncology Branch Gliwice, 44-101 Gliwice, Poland

Bibliografia

• [1] BATE R.B., The optimal control of systems with transport lag, Advances in control systems (ed. V. Leondes), Vol. 7, 165-224, 1969.
• [2] HARNEVO L.E. and AGUR Z., Use of mathematical models for understanding the dynamics of gene amplification, Mutat. Res., Vol. 292, pp. 17-24, 1993
• [3] SMIEJA J., SWIERNIAK A., DUDA Z. Gradient Method for Finding Optimal Scheduling in Infinite Dimensional Models of Chemotherapy, Journal of Theoretical Medicine, Vol. 3, pp. 25-36, 2000
• [4] SWIERNIAK A., KIMMEL M., POLANSKI A. Infinite dimensional model of evolution of drug resistance of cancer cells, Journal of Mathematical Systems, Estimation and Control, Vol. 8, No. 1, pp. 1–17, 1998.
• [5] SWIERNIAK A., KIMMEL M., POLANSKI A, BOBROWSKI A, SMIEJA J. Qualitative analysis of controlled drug resistance model - inverse Laplace and semigroup approach, Control and Cybernetics, Vol. 28, pp. 61-74, 1998.
• [6] SWIERNIAK A., KIMMEL M., POLANSKI A, DUDA Z. Phase-Specific Chemotherapy of Cancer: Optimisation of Scheduling and Rationale for Periodic Protocols, Biocybernetics and Biomedical Engineering, Vol. 16, pp. 13-43, 1997.