The optimal scheduling of two drugs with simple resistance for a problem in cancer chemotherapy

IMA Journal of Mathemathics Applied in Medicine and Biology

Volumn 14, Issue 4, 1997, Pages 283-303

  Murray, J M ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Cancer chemotherapy; Drug resistance; Optimal control

Indexed keywords

ANTINEOPLASTIC AGENT;

ARTICLE; CELL DIVISION; DRUG ADMINISTRATION; DRUG RESISTANCE; HUMAN; MATHEMATICS; MULTIDRUG RESISTANCE; NEOPLASM; PATHOLOGY; THEORETICAL MODEL; TIME;

ANTINEOPLASTIC COMBINED CHEMOTHERAPY PROTOCOLS; CELL DIVISION; DRUG ADMINISTRATION SCHEDULE; DRUG RESISTANCE, MULTIPLE; DRUG RESISTANCE, NEOPLASM; HUMANS; MATHEMATICS; MODELS, THEORETICAL; NEOPLASMS; TIME FACTORS;

CHEMOTHERAPY;

CANCER CHEMOTHERAPY; CELL LOSS; DRUG-RESISTANCE; OPTIMAL CONTROLS; OPTIMAL SCHEDULE; OPTIMAL SCHEDULING; SIMPLE++;

DISEASES;

EID: 0031305690     PISSN: 02650746     EISSN: None     Source Type: Journal    
DOI: 10.1093/imammb14.4.283     Document Type: Article

References (12)

1. BIRKHEAD, B. G., RANKIN, E. M., GALLIVAN, S., DONES, L., & RUBENS, R. D., 1987. A mathematical model of the development of drug resistance to cancer chemotherapy. Europ. J. Cancer Clin, Oncol. 23, 1421-7.
2. CESARI, L., 1966. Existence theorems for weak and usual optimal solutions in Lagrange problems with unilateral constraints. I, Trans. Am. Math. Soc. 124, 369-412.
3. COLDMAN, A. J. & GOLDIE, J. H., 1983. A model for the resistance of tumor cells to cancer chemotherapeutic agents. Math. Biosci. 65, 291-307.
4. DAY, R. S., 1986. Treatment sequencing, asymmetry, and uncertainty: Protocol strategies for combination chemotherapy. Cancer Res., 46, 3876-85.
5. GOLDIE, J. H., & COLDMAN, A. J., 1984. The genetic origin of drug resistance in neoplasms: Implications for systemic therapy. Cancer Res. 44, 3643-53.
6. HOKANSON, J. A., BROWN, B. W., THOMPSON, J. R., JANSSON, B., & DREWINKO, B., 1986. Mathematical model for human myeloma relating growth kinetics and drug resistance. Cell Tissue Kin., 19, 1-10.
7. MARTIN, R. B., FISHER, M. E., MINCHIN, R. F., & TEO, K. L., 1992. Low-intensity combination chemotherapy maximizes host survival time for tumors containing drug-resistant cells. Math. Biosci. 110, 221-52.
8. MICHELSON, S., & SLATE, D., 1994. A mathematical model for the inhibition of the multidrug resistance-associated P-glycoprotein pump. Bull. Math. Biol. 56, 207-23.
9. MURRAY, J. M., 1990. Optimal control for a cancer chemotherapy problem with general growth and loss functions. Math. Biosci. 98, 273-87.
10. MURRAY, J. M., 1995. An example of the effects of drug resistance on the optimal schedule for a single drug in cancer chemotherapy. IMA J. Math. Appl. Med. Biol. 12, 55-69.
11. SCHIMKE, R. T., 1984. Gene amplification, drug resistance, and cancer. Cancer Res. 44, 1735-42.
12. STEEL, G. G., 1977. Growth Kinetics of Tumours. Oxford: Clarendon Press.