The Worst Drug Rule Revisited: Mathematical Modeling of Cyclic Cancer Treatments

Bulletin of Mathematical Biology

Volumn 73, Issue 3, 2011, Pages 549-584

  Katouli, Allen A ^a   Komarova, Natalia L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

CML; Stochastic modeling of cancer

Indexed keywords

ANTINEOPLASTIC AGENT;

ARTICLE; DRUG ADMINISTRATION; DRUG RESISTANCE; HUMAN; NEOPLASM; STATISTICS; THEORETICAL MODEL;

ANTINEOPLASTIC AGENTS; DRUG ADMINISTRATION SCHEDULE; DRUG RESISTANCE, NEOPLASM; HUMANS; MODELS, THEORETICAL; NEOPLASMS; STOCHASTIC PROCESSES;

EID: 79952573901     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-010-9539-y     Document Type: Article

References (39)

1. Arkin, M. R., Wells, J. A. (2004). Small-molecule inhibitors of protein-protein interactions: progressing towards the dream. Nat. Rev. Drug. Discov. 3, 301-317.
2. Bailey, N. (1964). The elements of stochastic processes with applications to the natural sciences. New York: Wiley.
3. Bellomo, N., Chaplain, M., Angelis, E. D. (Eds.) (2008a). Selected topics on cancer modeling: genesis-evolution-immune competition-therapy. Basel: Birkhäuser.
4. Bellomo, N., Li, N. K., Maini, P. K. (2008b). Math. Model Method Appl. Sci. 18, 593-646.
5. Bradeen, H. A., Eide, C. A., O'Hare, T., Johnson, K. J., Willis, S. G., Lee, F. Y., Druker, B. J., Deininger, M. W. (2006). Comparison of imatinib mesylate, dasatinib (BMS-354825), and nilotinib (AMN107) in an N-ethyl-N-nitrosourea (ENU)-based mutagenesis screen: high efficacy of drug combinations. Blood108, 2332-2338.
6. Byrne, H. M., Alarcon, T., Owen, M. R., Webb, S. D., Maini, P. K. (2006). Modelling aspects of cancer dynamics: a review. Philos. Transact. A Math. Phys. Eng. Sci. 364, 1563-1578.
7. Coldman, A. J., Goldie, J. H. (1985). Role of mathematical modeling in protocol formulation in cancer chemotherapy. Cancer Treat. Rep. 69(10), 1041-1048.
8. Coldman, A. J., Goldie, J. H. (1986). A stochastic model for the origin and treatment of tumors containing drug-resistant cells. Bull. Math. Biol. 48(3-4), 279-292.
9. Colucci, G., Gebbia, V., Galetta, D., Riccardi, F., Cariello, S., Gebbia, N. (1997). Cisplatin and vinorelbine followed by ifosfamide plus epirubicin vs. the opposite sequence in advanced unresectable stage III and metastatic stage IV non-small-cell lung cancer: a prospective randomized study of the Southern Italy Oncology Group (GOIM). Br. J. Cancer76, 1509-1517.
10. Day, R. S. (1986a). A branching-process model for heterogeneous cell populations. Math. Biosci. 78, 73-90.
11. Day, R. S. (1986b). Treatment sequencing, asymmetry, and uncertainty: protocol strategies for combination chemotherapy. Cancer Res. 46, 3876-3885.
12. Deininger, M. W. (2007). Optimizing therapy of chronic myeloid leukemia. Exp. Hematol. 35, 144-154.
13. Deininger, M. W., Druker, B. J. (2003). Specific targeted therapy of chronic myelogenous leukemia with imatinib. Pharmacol. Rev. 55, 401-423.
14. Deisboeck, T. S., Zhang, L., Yoon, J., Costa, J. (2009). In silico cancer modeling: is it ready for prime time? Nat. Clin. Pract. Oncol. 6, 34-42.
15. Fulfaro, F., Valerio, M. R., Badalamenti, G., Gebbia, N., Russo, A. (2003). Antiblastic drug combinations with ifosfamide: an update. Oncology65 Suppl. 2, 21-30.
16. Gaffney, E. A. (2005). The mathematical modelling of adjuvant chemotherapy scheduling: incorporating the effects of protocol rest phases and pharmacokinetics. Bull. Math. Biol. 67(3), 563-611.
17. Gardiner, C. (2004). Handbook of stochastic methods: for physics, chemistry and the natural sciences. Berlin: Springer.
18. Gebbia, V., Galetta, D., Caruso, M., Verderame, F., Pezzella, G., Valdesi, M., Borsellino, N., Pandolfo, G., Durini, E., Rinaldi, M., Loizzi, M., Gebbia, N., Valenza, R., Tirrito, M. L., Varvara, F., Colucci, G. (2003). Gemcitabine and cisplatin versus vinorelbine and cisplatin versus ifosfamide + gemcitabine followed by vinorelbine and cisplatin versus vinorelbine and cisplatin followed by ifosfamide and gemcitabine in stage IIIB-IV non small cell lung carcinoma: a prospective randomized phase III trial of the Gruppo Oncologico Italia Meridionale. Lung Cancer39, 179-189.
19. Goldie, J. H., Coldman, A. J. (1979). A mathematic model for relating the drug sensitivity of tumors to their spontaneous mutation rate. Cancer Treat. Rep. 63(11-12), 1727-1733.
20. Goldie, J. H., Coldman, A. J. (1983a). A model for resistance of tumor cells to cancer chemotherapeutic agents. Math. Biosci. 65, 291-307.
21. Goldie, J. H., Coldman, A. J. (1983b). Quantitative model for multiple levels of drug resistance in clinical tumors. Cancer Treat. Rep. 67(10), 923-931.
22. Goldie, J. H., Coldman, A. J. (1998). Drug resistance in cancer: mechanisms and models. Cambridge: Cambridge University Press.
23. Goldie, J. H., Coldman, A. J., Gudauskas, G. A. (1982). Rationale for the use of alternating non-cross-resistant chemotherapy. Cancer Treat. Rep. 66, 439-449.
24. Grossi, F., Aita, M., Follador, A., Defferrari, C., Brianti, A., Sinaccio, G., Belvedere, O. (2007). Sequential, alternating, and maintenance/consolidation chemotherapy in advanced non-small cell lung cancer: a review of the literature. Oncologist12, 451-464.
25. Katouli, A. A., Mathematical modeling of cancer drug treatment with cross-resistance. Ph. D. thesis UCI (Expected 2009).
26. Komarova, N. L. (2006). Stochastic modeling of drug resistance in cancer. J. Theor. Biol. 239, 351-366.
27. Komarova, N. L., Wodarz, D. (2005). Drug resistance in cancer: principles of emergence and prevention. Proc. Natl. Acad. Sci. USA102, 9714-9719.
28. Komarova, N. L., Wu, L., Baldi, P. (2007). The fixed-size Luria-Delbruck model with a nonzero death rate. Math. Biosci. 210, 253-290.
29. Komarova, N. L., Katouli, A. A., Wodarz, D. (2009). Combination of two but not three current targeted drugs can improve therapy of chronic myeloid leukemia. PLoS ONE4, e4423.
30. Norton, L., Day, R. (1985). Potential innovations in scheduling of cancer chemotherapy. In: Devita, V. T., Hellman, S., Rosenberg, S. A. (Eds.), Important advances in oncology (pp. 57-72). Philadelphia: Lippincott, Williams & Wilkins.
31. Novozhilov, A. S., Karev, G. P., Koonin, E. V. (2006). Biological applications of the theory of birth-and-death processes. Brief. Bioinform. 7, 70-85.
32. O'Dwyer, M. E., Mauro, M. J., Druker, B. J. (2002). Recent advancements in the treatment of chronic myelogenous leukemia. Annu. Rev. Med53, 369-381.
33. Preziosi, L. (Ed.) (2003). Cancer modelling and simulation. London/Boca Raton: Chapman and Hall/CRC Press.
34. Quints-Cardama, A., Kantarjian, H., Cortes, J. (2007). Flying under the radar: the new wave of BCR-ABL inhibitors. Nat. Rev. Drug. Discov. 6, 834-848.
35. Sanga, S., Sinek, J. P., Frieboes, H. B., Ferrari, M., Fruehauf, J. P., Cristini, V. (2006). Mathematical modeling of cancer progression and response to chemotherapy. Expert Rev. Anticancer Ther. 6, 1361-1376.
36. Swierniak, A., Kimmel, M., Smieja, J. (2009). Mathematical modeling as a tool for planning anticancer therapy. Eur. J. Pharmacol. 625, 108-121.
37. Weisberg, E., Manley, P. W., Cowan-Jacob, S. W., Hochhaus, A., Griffin, J. D. (2007). Second generation inhibitors of BCR-ABL for the treatment of imatinib-resistant chronic myeloid leukemia. Nat. Rev. Cancer7, 345-356.
38. Wodarz, D., Komarova, N. L. (2005). Computational biology of cancer: lecture notes and mathematical modeling. Singapore: World Scientific.
39. Zhang, J., Yang, P. L., Gray, N. S. (2009). Targeting cancer with small molecule kinase inhibitors. Nat. Rev. Cancer9, 28-39.