Artículos de revistas
Chemotherapeutic Treatments With Time Increasing Mutation Rate To Drug Resistance
Registro en:
Journal Of Biological Systems. , v. 5, n. 1, p. 49 - 62, 1997.
2183390
2-s2.0-3042877096
Autor
Boldrini J.L.
Costa M.I.S.
Institución
Resumen
A system of differential equations for the control of tumor growth cells in a cycle non-specific chemotherapy is analyzed. Spontaneously acquired drug resistance is taken into account by means of a mutation rate increasingly dependent on time. For general tumor growth and drug kill rates the optimal treatment consists of maximum allowable drug concentration throughout, supporting the conjecture that variable mutation rate to drug resistance does not basically alter the corresponding results of constant mutation rate. 5 1 49 62 Goldman, A.J., Goldie, J.H., A model for the resistance of tumor cells to cancer chemoterapeutic agents (1983) Math. Biosci., 65, p. 291 Goldman, A.J., Goldie, J.H., A stochastic model for the origin and treatment of tumors containing drug-resistant cells (1986) Bull. Math. Biol., 48, p. 279 Costa, M.I.S., Boldrini, J.L., Bassanezi, R.C., Optimal chemical control of populations developing drug resistance (1992) IMA J. Math. Appl. Med. Biol., 9, p. 215 Costa, M.I.S., Boldrini, J.L., Bassanezi, R.C., Optimal chemotherapy: A case study with drug resistance, saturation effect and toxicity (1994) IMA J. Math. Appl. Med. Biol., 11, p. 45 Costa, M.I.S., Boldrini, J.L., Bassanezi, R.C., Drug kinetics and drug resistance in optimal chemotherapy (1995) Math. Biosc., 125, p. 191 Costa, M.I.S., Boldrini, J.L., Bassanezi, R.C., Chemotherapeutic treatments involving drug resistance and level of normal cells as a criterion of toxicity (1995) Math. Biosci., 125, p. 211 Costa, M.I.S., Boldrini, J.L., Chemotherapeutic treatments: A study of the interplay among drug resistance, toxicity and recuperation from side effects (1997) Bull. Math. Biol., , in print Costa, M.I.S., Boldrini, J.L., Conflicting objectives in chemotherapeutic treatments with drug resistance (1997) Bull. Math. Biol., , in print Fidler, I.J., The evolution of biological heterogeneity in metastatic neoplasms (1984) Cancer Invasion and Metastasis: Biologic and Therapeutic Aspects, pp. 421-435. , ed. by G. L. Nicolson and L. Milas Raven Press, New York Fidler, I.J., Talmadge, J.E., The origin and progression of cancer metastasis (1984) Genes and Cancer, pp. 239-251. , ed. by J. M. Bishop, Alan R. Liss, New York Goldie, J.H., Goldman, A.J., A mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate (1979) Cancer Treat. Rep., 63, p. 1727 Hale, J.K., (1980) Ordinary Differential Equations, 2nd Edn., , Huntington, New York Harnevo, L., Agur, Z., Drug resistance as a dynamic process in a model for multistep gene amplification under various levels of selection stringency (1992) Cancer Chemother. Pharmacol., 30, p. 469 Kimmel, M., Axelrod, D.E., Mathematical models for gene amplification with application to cellular drug resistance and tumorigenicity (1980) Genetics, 125, p. 633 Kimmel, M., Axelrod, D.E., Wahl, G.M., A branching process model of gene amplication following chromosome breakage (1992) Mut. Res., 276, p. 225 Ling, A.F., Chanbers, J.F., Hill, R.P., Quantitative genetic analysis of tumor progression (1985) Cancer Metastasis Rev., 4, p. 173 Marusic, M., Bajzer, Z., Vuk-Pavlovic, S., Fryer, J.P., Tumor growth in vivo and as multicellular spheroids compared by mathematical models (1994) Bull. Math. Biol., 56, p. 617 Murray, J.M., An example of the effects of drug resistance on the optimal schedule for a single drug in cancer chemotherapy (1995) IMA J. Math. Appl. Med. Biol., 12, p. 55 Nowell, P.C., Mechanisms of tumor progression (1986) Cancer Res., 46, p. 2203 Sage, A.P., (1968) Optimum System Control, , Prentice-Hall, Inc., Englewood Cliffs, NJ Skipper, H.E., The forty year old mutation theory of Luria and Delbruck and its pertinence to cancer chemotherapy (1983) Adv. Cancer Research, 40, p. 331 Swan, G.W., Vincent, T.L., Optimal control analysis in the chemotherapy of I gG multiple myeloma (1977) Bull. Math. Biol., 39, p. 317 Swan, G.W., Role of optimal control theory in cancer chemotherapy (1990) Math. Biosc., 101, p. 237 Tan, W.Y., Cancer chemotherapy with immunostimulation: A nonhomogeneous stochastic model for drug resistance I. One drug case (1989) Math. Biosc., 97, p. 145 Vendite, L.L., (1988) Modelagem Matemática para o Crescimento Tumoral e o Problema de Resistência Celular aos Fármacos Anti-blásticos, , Ph. D. Thesis Faculdade de Engenharia Elétrica. Universidade Estadual de Campinas, SP, Brazil