Artículos de revistas
Drug Kinetics And Drug Resistance In Optimal Chemotherapy
Registro en:
Mathematical Biosciences. , v. 125, n. 2, p. 191 - 209, 1995.
255564
10.1016/0025-5564(94)00027-W
2-s2.0-0029240378
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. First-order drug kinetics and drug resistance are taken into account in a class of optimal control problems. The results show that the strategy corresponding to the maximum rate of drug injection is optimal for the Malthusian model of cell growth (which is a relatively good model for the initial phase of tumor growth). For more general models of cell growth, this strategy proved to be suboptimal under certain conditions. © 1995. 125 2 191 209 Abulesz, Lyberatos, Novel approach for determining optimal treatment regimen for cancer chemotherapy (1988) Internat. J. Syst. Sci., 19, pp. 1483-1497 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, Chemotherapeutic treatments involving drug resistance and level of normal cells as a criterion of toxicity, 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. , 2nd ed., 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 Hale, (1980) Ordinary Differential Equations, , 2nd ed., Krieger, Huntington, NY 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. 469-479 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, 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, 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. Comput., 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, Brasil