Finite dimensional models of drug resistant and phase specific cancer chemotherapy

• Autorzy: Ledzewicz U. , Schättler H. , Świerniak A.
• Języki publikacji: EN

Abstrakty

EN

The problem of modelling drug resistance and phase specificity of cancer chemotherapy using finite dimensional models were considered. We formulate optimal control problems arising in protocol design for such models and discuss research issues resulting from these formulations.

Słowa kluczowe

EN

chemotherapy; drug resistance; phase specificity; biomathematical modelling; optimal control

PL

chemioterapia; odporność na leki; specyfika fazy; bio-modelowanie matematyczne; optymalna kontrola

• Wydawca: University of Silesia, Institute of Informatics, Computer Systems Department
• Czasopismo: Journal of Medical Informatics & Technologies
• Rocznik: 2004
• Tom: Vol. 8
• Strony: IP5--14
• Opis fizyczny: Bibliogr. 27 poz.

Twórcy

autor

Ledzewicz U.

• Southern Illinois University at Edwardsville, Edwarsville, Il, USA

autor

Schättler H.

• Washington University, St. Louis, Il, USA

autor

Świerniak A.

• Silesian University of Technology, Gliwice, Poland

Bibliografia

• [1] BROWN P.C., BEVERLY S.M. and SCHIMKE R.T., Relationship of amplified dihydrofolate reductase genes to double minute chromosomes in unstably resistant mouse fibroblast cell lines, Molecular Cell Biology, 1, (1981), pp. 1077-1083
• [2] CALABRESI P. and SCHEIN P.S., Medical Oncology, Basic Principles and Clinical Management of Cancer, Mc Graw-Hill, New York, 1993
• [3] COLDMAN A.J. and GOLDIE J.H., A model for the resistance of tumor cells to cancer chemotherapeutic agents, Mathematical Biosciences, 65, (1983), pp. 291-307
• [4] COSTA M.I.S., BOLDRINI J.L. and BASSANEZI R.C., Drug kinetics and drug resistance in optimal chemotherapy, Mathematical Biosciences, 125, (1995), pp. 191-209
• [5] EISEN M., Mathematical Models in Cell Biology and Cancer Chemotherapy, Lecture Notes in Biomath-ematics, Vol. 30, Springer Verlag, (1979)
• [6] HARNEVO L.E. and AGUR Z., The dynamics of gene amplification described as a multitype compartmental model and as a branching process, Mathematical Biosciences, 103, (1991), pp. 115-138
• [7] HARNEVO L.E. and AGUR Z., Drug resistance as a dynamic process in a model for multistep gene amplification under various levels of selection stringency, Cancer Chemotherapy and Pharmacology, 30, (1992), pp. 469-476
• [8] KAUFMAN R.J., BROWN P.C., and SCHIMKE R.T., Loss and stabilization of amplified dihydrofolate reductase genes in mouse sarcoma S-180 cell lines, Molecular Cell Biology, 1, (1981), pp. 1084-1093
• [9] KIMMEL M and AXELROD D.E., Branching Processes in Biology, Springer Verlag, New York, NY, (2002)
• [10] KIMMEL M. and AXELROD D.E., Mathematical models of gene amplification with applications to cellular drug resistance and tumorigenicity, Genetics, 125, (1990), pp. 633-644
• [11] KIMMEL M., SWIERNIAK A. and POLANSKI A., Infinite-dimensional model of evolution of drug resistance of cancer cells, Journal of Mathematical Systems, Estimation and Control, 8, (1998), pp. 1-16
• [12] ERBEL R.S., A cancer chemotherapy resistant to resistance, Nature, 390, (1997), pp. 335-336
• [13] KIRSCHNER D. and WEBB G., A mathematical model of combined drug therapy of HIV infection, J. of Theoretical Medicine, 1, (1997), pp. 25-34
• [14] LEDZEWICZ U. and SCHATTLER H., Optimal bang-bang controls for a 2-compartment model in cancer chemotherapy, Journal of Optimization Theory and Applications - JOTA, 114, (2002), pp. 609-637
• [15] LEDZEWICZ U. and SCHATTLER H., Analysis of a cell-cycle specific model for cancer chemotherapy, J. of Biological Systems, 10, (2002), pp. 183-206
• [16] LEDZEWICZ U. and SCHATTLER H., Analysis of a class of optimal control problems arising in cancer chemotherapy, Proceedings of the American Control Conference, Anchorage, Alaska, (2002), pp. 3460-3465
• [17] LEDZEWICZ U. and SCHATTLER H., Sufficient conditions for optimality of controls in biomedical systems, Proceedings of the 41st IEEE Conference on Decision and Control (CDC), Las Vegas, Nevada, (2002), pp. 3524-3529
• [18] LEDZEWICZ U. and SCHATTLER H., Optimal control for a 3-compartment model for cancer chemotherapy with quadratic objective, in: Dynamical Systems and Differential Equations, (W. Feng, S. Hu and X. Lu, Eds.), A supplemental volume to Discrete and Continuous Dynamical Systems, (2003), pp. 544-553
• [19] LEDZEWICZ U. and SCHATTLER H., Optimal control for a bilinear model with recruiting agent in cancer chemotherapy, Proceedings of the 42nd IEEE Conference on Decision and Control (CDC), Maui, Hawaii, December 2003, to appear
• [20] PONTRYAGIN L.S., BOLTYANSKII V.G., GAMKRELIDZE R.V. and MISHCHENKO E.F., The Mathematical Theory of Optimal Processes, MacMillan, New York, (1964)
• [21] SWAN G.W., Role of optimal control in cancer chemotherapy, Math. Biosci., 101, (1990), pp. 237-284
• [22] SMIEJA J. and SWIERNIAK A., Different models of chemotherapy taking into account drug resistance stemming from gene amplification, Int. J. of Appl. Math. Comput. Sci., 13, (2003), pp. 297-305
• [23] SWIERNIAK A., Cell cycle as an object of control, Journal of Biological Systems, 3, (1995), pp. 41-54
• [24] SWIERNIAK A., LEDZEWICZ U. and SCHATTLER H., Optimal control for a class of compartmental models in cancer chemotherapy, Int. J. of Appl. Math. Comput. Sci., 13, (2003), pp. 357-368
• [25] SWIERNIAK A., POLANSKI A. and KIMMEL M., Optimal control problems arising in cell-cycle-specific cancer chemotherapy, Cell prolif., 29, (1996), pp. 117-139
• [26] SWIERNIAK A., POLANSKI A., KIMMEL M., BOBROWSKI A. and SMIEJA J., Qualitative analysis of controlled drug resistance model - inverse Laplace and semigroup approach, Control and Cybernetics 28, (1999), pp. 61-75
• [27] SWIERNIAK A. and SMIEJA J., Cancer chemotherapy optimization under evolving drug resistance, Non-linear Analysis, 47, (2000), pp. 375-386.