Some drug-resistant models for cancer chemotherapy Part 1: Cycle-nonspecific drugs

IMA Journal of Mathemathics Applied in Medicine and Biology

Volumn 13, Issue 2, 1996, Pages 99-126

  Usher, J R ^a   Henderson, D ^a  

^a ROBERT GORDON UNIVERSITY   (United Kingdom)

Author keywords

Chemotherapy; Cycle nonspecific; Drug resistance; Increased drug sensitivity

Indexed keywords

CANCER CELLS; CELL CULTURE; CELL PROLIFERATION; CLONE CELLS; DISEASES;

CELL SUBPOPULATIONS; CELL-BE; CELL/B.E; CELL/BE; CYCLE-NONSPECIFIC; DRUG CONCENTRATION; DRUG-RESISTANCE; DRUG-SENSITIVITY; INCREASED DRUG SENSITIVITY; RESISTANT CELLS;

CHEMOTHERAPY;

ANTINEOPLASTIC AGENT;

ARTICLE; CELL CYCLE; CELL DIVISION; DRUG RESISTANCE; HUMAN; MATHEMATICS; NEOPLASM; PATHOLOGY; THEORETICAL MODEL;

ANTINEOPLASTIC AGENTS; CELL CYCLE; CELL DIVISION; DRUG RESISTANCE, NEOPLASM; HUMANS; MATHEMATICS; MODELS, THEORETICAL; NEOPLASMS;

EID: 0030160435     PISSN: 02650746     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb/13.2.99     Document Type: Article

References (26)

1. AGUR, Z., ARNON, R., & SCHECHTER, B., 1988. Reduction of cytotoxicity to normal tissues by new regimens of cell-cycle phase-specific drugs. Math. Biosci. 92, 1-15.
2. AROESTY, J., LINCOLN, T., SHAPIRO, N., & BOCCIA, G., 1973. Tumour growth and chemotherapy: mathematical methods, computer simulation and experimental foundation. Math. Biosci. 17, 243-300.
3. BAUMLER, E., 1967. Cancer - A review of international research. London: Queen Anne Press.
4. CALMAN, K. C., SMYTH, J. F., & TATTERSHALL, M. H. N., 1980. Basic Principles of Cancer Chemotherapy. London: Macmillan.
5. CASSIDY, J., 1994. Chemotherapy administration: doses, infusions and choice of schedule. Ann. Oncol. 5, S25-S30.
6. COJACARU, L., & AGUR, Z., 1992. A theoretical analysis of interval drug dosing for cell-cycle-phase-specific drugs. Math. Biosci. 109, 85-97.
7. GOLDIE, J. H., & COLDMAN, A. J., 1979. A mathematical model for relating the drug sensitivity of tumours to their spontaneous mutation rate. Cancer Treat. Rep. 63, 1727-33.
8. GOLDIE, J. H., & COLDMAN, A. J., 1983. Quantitative model for multiple levels of drug resistance in clinical tumors. Cancer Treat. Rep. 67, 923-31.
9. HARNEVO, L. E., & AGUR, Z., 1991. The dynamics of gene amplification described as a multitype compartmental model and as a branching process. Math. Biosci. 103, 115-38.
10. HARNEVO, L. E., & AGUR, Z., 1992. Drug resistance as a dynamic process in a model for multistep gene amplification under various levels of selection stringency. Cancer Chemotherapy Pharmacol. 30, 469-76.
11. JAMES, G., 1992. Modern Engineering Mathematics. Wokingham: Addison Wesley.
12. KAYE, S., & MERRY, S., 1985. Tumour cell resistance to anthracyclines - a review. Cancer Chemotherapy, Pharmacol. 14, 96-103.
13. KNOLLE, H., 1988. Cell kinetic Modeling and the Chemotherapy of Cancer. Lecture Notes in Biomathematics, Vol. 75. Springer-Verlag. New York.
14. LUM, B. L., GOSLAND, M. P., KAUBISCH, S., & SIKIC, B. I., 1993. Molecular targets in oncology: implications of the multidrug resistance gene. Pharmacotherapy, 13, 88-109.
15. MORROW, C. S., & COWAN, K., 1993. Drug resistance and cancer. Adv. Exp. Med. Biol. 330, 287-305.
16. MURRAY, J. M., 1990. Some optimal control problems in cancer chemotherapy with a toxicity limit. Math. Biosci. 100, 49-67.
17. OWENS, A. H., COFFEY, D. S., & BAYLIN, S. B. (eds.) 1982. Tumour Cell Heterogeneity: Origins and implications. New York: Academic Press.
18. PANETTA, J. C., 1994. A mathematical model of periodically-pulsed chemotherapy: tumour recurrence in a competitive environment. Private communication.
19. ROWSON, K. E. K., 1975. The role of viruses in cancer. Biology of Cancer (E. J. Ambrose and F. J. C. Roe eds.), pp. 217-51. Chichester: Ellis Horwood.
20. SIKIC, B. I., 1993. Modulation of multidrug resistance: at the threshold. J. Clin. Oncol. 11, 1629-35.
21. STEEL, G. G., 1977. Growth Kinetics of Tumours. Oxford: Clarendon.
22. SWAN, G. W., 1987. Tumour growth models and cancer chemotherapy. Cancer Modeling (J. R. Thompson and B. Brown, eds.), pp. 91-179. New York: Marcel Dekker.
23. USHER, J. R., 1994. Some mathematical models for cancer chemotherapy. Comput. Math. Applic. 28, 73-80.
24. WEBB, G. F., 1992a. A nonlinear cell population model of periodic chemotherapy treatment. Recent Trends in Ordinary Differential Equations. Series in Applicable Analysis, Vol. 1, pp. 569-83. World Scientific.
25. WEBB, G. F., 1992b. A cell population model of periodic chemotherapy treatment. Biomedical Modeling and Simulation, pp. 83-92. Elsevier Science.
26. WHELDON, T., 1988. Mathematical Models in Cancer Research: Bristol: Adam Hilger.