Artículos de revistas
Chemotherapeutic Treatments Involving Drug Resistance And Level Of Normal Cells As A Criterion Of Toxicity
Registro en:
Mathematical Biosciences. , v. 125, n. 2, p. 211 - 228, 1995.
255564
10.1016/0025-5564(94)00028-X
2-s2.0-0029240198
Autor
Costa M.I.S.
Boldrini J.L.
Bassanezi R.C.
Institución
Resumen
A system of differential equations for the control of tumor cells growth in a cycle nonspecific chemotherapy is presented. Drug resistance and toxicity conveyed through the level of normal cells are taken into account in a class of optimal control problems. Alternative treatments for the exponential tumor growth are set forth for cases where optimal treatments are not available. © 1995. 125 2 211 228 Coldman, Goldie, A model for the resistance of tumor cells to cancer chemotherapeutic agents (1983) Math. Biosci., 65, pp. 291-307 Coldman, Goldie, A stochastic model for the origin and treatment of tumors containing drug-resistant cells (1986) Bull. Math. Biol., 48, pp. 279-292 M. I. S. Costa, J. L. Boldrini, and R. C. Bassanezi, Drug kinetics and drug resistance in optimal chemotherapy, Math. Biosci., in pressCosta, Boldrini, Bassanezi, Optimal chemical control of populations developing drug resistance (1992) Mathematical Medicine and Biology, 9, pp. 215-226 Costa, Boldrini, Bassanezi, Optimal Chemotherapy A Case Study with Drug Resistance Saturation Effect and Toxicity (1994) Mathematical Medicine and Biology, 11, pp. 45-59 Eisen, Mathematical Models in Cell Biology and Cancer Chemotherapy (1978) Lecture Notes in Biomathematics, 30. , Springer-Verlag Goldie, Coldman, A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate (1979) Cancer Treat. Rep., 63 (11-12), pp. 1727-1733 Harnevo, Agur, Drug resistance as a dynamic process in a model for multistep gene amplification under various levels of selection stringency (1992) Cancer Chemother. Pharmacol., 30, pp. 469-476 Kimmel, Axelrod, Mathematical models for gene amplification with application to cellular drug resistance and tumorigenicity (1990) Genetics, 125, pp. 633-644 Kimmel, Axelrod, Wahl, A branching process model of gene amplification following chromosome breakage (1992) Mutation Research/Reviews in Genetic Toxicology, 276, pp. 225-239 Kirk, (1970) Optimal Control Theory, , Prentice-Hall, Inc, Englewood Cliffs, NJ Lee, Markus, (1967) Foundations of Optimal Control Theory, , Wiley, NY Murray, Optimal control for a cancer chemotherapy problem with general growth and loss functions (1990) Math. Biosci., 98, pp. 273-287 Murray, Some optimal control problems in cancer chemotherapy with a toxicity limit (1990) Math. Biosci., 100, pp. 49-67 Sage, (1968) Optimum Systems Control, , Prentice-Hall, Inc, Englewood Cliffs, NJ Skipper, The forty year old mutation theory of Luria and Delbruck and its pertinence to cancer chemotherapy (1983) Adv. Cancer Res., 40, pp. 331-363 Swan, General applications of optimal control theory in cancer chemotherapy (1988) Mathematical Medicine and Biology, 5, pp. 303-316 Swan, Optimal control analysis of a cancer chemotherapy problem (1987) Mathematical Medicine and Biology, 4, pp. 171-184 Swan, Optimal control in some cancer chemotherapy problems (1980) International Journal of Systems Science, 11, pp. 223-237 Swan, Role of optimal control theory in cancer chemotherapy (1990) Math. Biosci., 101, pp. 237-284 Swan, Vincent, Optimal control analysis in the chemotherapy of IgG multiple myeloma (1977) Bull. Math. Biol., 39, pp. 317-337 Vaidya, Alexandro, Jr., Evaluation of some mathematical models for tumor growth (1982) Internat. J. Bio-Med. Comp., 13, pp. 19-35 Vendite, Modelagem Matemática para o Crescimento Tumoral e o Problema de Resistência Celular aos Fármacos Anti-Blásticos (1988) Ph.D. thesis, , Faculdade de Engenharia Elétrica, Universidade Estadual de Campinas, SP, Brazil Zietz, Nicolini, Mathematical approaches to optimization of cancer chemotherapy (1979) Bull. Math. Biol., 41, pp. 305-325