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Mathematical models of drug resistance and chemotherapy effects

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Book cover Drug Resistance in Cancer Therapy

Part of the book series: Cancer Treatment and Research ((CTAR,volume 48))

Abstract

Mathematical modelling allows one to study complex processes that may not be completely amenable to direct observation. The modelling approach requires the researcher to make explicit assumptions about the phenomenon he is studying and to place these within a rigorous mathematical framework. In this paper, we will describe some of the work that has been done in the specific area of drug resistance, beginning with earlier minimal models of the phenomenon, and then going on to discuss refinements that have been incorporated into the basic model structure.

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References

  1. Hill, B.T. (1982). Biochemical and Cell Kinetic Aspects of Drug Resistance. In Drug and Hormone Resistance in Neoplasia; eds. Bruchovsky, N. and Goldie, J.H., vol. 1, pp. 21–53. CRC press, Boca Raton, Florida.

    Google Scholar 

  2. Goldie, J.H. and Coldman, A.J. (1979). The genetic origin of drug resistance in neoplasms: Implication for systemic therapy. Cancer Res. 44:3643–3653.

    Google Scholar 

  3. Goldie, J.H. and Coldman, A.J. (1979). A Mathematical model for relating the drug sensitivity of tumors to their spontaneous mutation rate. Cancer Treat. Rep. 63:1727–1733.

    PubMed  CAS  Google Scholar 

  4. Luria, S.E. and Delbruck, M. (1943). Mutation of bacteria from virus sensitivity to virus resistance. Genetics 28:491–511.

    PubMed  CAS  Google Scholar 

  5. Law, L.W. (1952). Origin of the resistance of leukemic cells to folic acid antagonists. Nature (London) 169:628–629.

    Article  CAS  Google Scholar 

  6. De Vita, V.T., Jr. (1983). The relationship between tumor mass and resistance to chemotherapy. Caner 51:1209–1220.

    Google Scholar 

  7. Skipper, H.E. (1980). ‘Some Thoughts Regarding a Recent Publication by Goldie and Coldman Entitled “A Mathematic Model for Relating the Drug Resistance of Tumors to Their Spontaneous Mutation Rate”’ In Booklet 9, Southern Research Institute, Birmingham, Ala.

    Google Scholar 

  8. Buzdar, A.U., Smith, T.L., Blumenschein, G.R., et al. (1984). Breast cancer adjuvant therapy trials of MD Anderson Hospital: Results of two studies. In Adjuvant Therapy of Cancer IV; eds. Jones, S.E. and Salmon, S.E., Grune and Stratton, New York, pp. 227–234.

    Google Scholar 

  9. Bonadonna, G., Rossi, A., Tancini, G., et al. (1984). Adjuvant chemotherapy trials in resectable breast cancer with positive axillary nodes. In The Experience of the Milan Cancer Institute in Adjuvant Therapy of Cancer IV, eds. Jones, S.E. and Salmon, S.E., Grune and Stratton, New York, pp. 193–208.

    Google Scholar 

  10. Goldie, J.H. (1983). Relevance of Drug Resistance in Cancer Treatment Strategy. In Cancer Chemotherapy I, ed. Muggia, F.M., Martinus Nejhoff, pp. 1–30.

    Google Scholar 

  11. Schackney, S., McCormack, G.W., Cuckurol, G.J., Jr. (1978). Growth rate pattern of solid tumors and their relation to responsiveness to therapy: An analytic review. Ann. Intern. Med. 89:107–121.

    Google Scholar 

  12. Goldie, J.H. and Coldman, A.J. (1983). Quantitative model for multiple levels of drug resistance in clinical tumors. Cancer Treat. Rep. 67:923–931.

    PubMed  CAS  Google Scholar 

  13. Buick, R.N. and MacKillop, W.J. (1981). Measurement of self-renewal in culture of clonogenic cells from human ovarian carcinoma. Br. J. Cancer 44:349–355.

    Article  PubMed  CAS  Google Scholar 

  14. Bush, R.S., DeBoer, G. and Hill, R.P. (1982), Long Term Survival with Gynecological Cancer. In Prolonged Arrest of Cancer; ed. Stoll, B.A., John Wiley and Sons, New York, pp. 27–58.

    Google Scholar 

  15. Goldie, J.H. and Coldman, A.J. A model for tumor response to chemotherapy: An integration of the stem cell and somatic mutation hypotheses. Cancer Invest. 3(6):553–564.

    Google Scholar 

  16. Coldman, A.J., Goldie, J.H. and Ng, V. (1983). The effect of Cellular differentiation on the development of permanent drug resistance. Math. Biosciences 74:177–198.

    Article  Google Scholar 

  17. Skipper, H.E., Schabel, F.M., Jr. and Wilcox, W.S. (1964). Experimental evaluation of potential anticancer agents XII on the criteria and kinetics associated with Curability of experimental leukemia. Cancer Chemother, Rep. 35:1–111.

    CAS  Google Scholar 

  18. Goldie, J.H., Coldman, A.J. and Gudauskas, G.A. (1982). Rationale for the use of alternating non-cros resistant chemotherapy. Cancer Treat. Rep. 66:439–449.

    PubMed  CAS  Google Scholar 

  19. Goldie, J.H. and Coldman, A.J. (1986). Application of theoretical models to chemotherapy protocol design, cancer Treat. Rep. 70:127–131.

    PubMed  CAS  Google Scholar 

  20. Evans, W.K., Feld, R., Murray, N., et al. (1987). Superiority of alternating non-cross resistant chemotherapy in extensive small cell lung cancer. Ann. Int. Med. 107:451–458.

    PubMed  CAS  Google Scholar 

  21. Day, R. (1986). Treatment Sequencing Uncertainty and Asymmetry: Protocol strategies For Combination Chemotherapy. Cancer Res. 46:3876–3885.

    PubMed  CAS  Google Scholar 

  22. Bonadonna, G., Virani, S. and Bonfante, V. (1984). Alternating chemotherapy with MOPP/ABVD in Hodgkin’s disese. Updated results. Proc. Am. Soc. Clin. Oncol. 3:254.

    Google Scholar 

  23. Klimo, P. and Connors, J.M. (1985). MOPP/ABV hybrid program: Combination chemotherapy based on early introduction of seven effective drugs for advanced Hodgkin’s disease. J. Clin. Oncol. 3:1174–1182.

    PubMed  CAS  Google Scholar 

  24. DeVita, V.T., Jr., Hubbard, S.M. and Longo, D.L. (1987). The chemotherapy of lymphoma: Looking back, moving forward. Cancer Res. 47:5810–5824.

    Google Scholar 

  25. Hyrniuk, W.M. and Bush, H. (1984). The importance of dose intensity in the chemotherapy of metastatic breast cancer. J. Clin. Oncol. 2:1281–1288.

    Google Scholar 

  26. Levin, L. and Hryniuk, W.M. (1977). Dose intensity analysis of chemotherapy regimens in ovarian cancer. J. Clin. Oncol. 5:756–769.

    Google Scholar 

  27. Coldman, A.J. and Goldie, J.H. (1988). Impact of dose-intense chemotherapy on the development of permanent drug resistance. Seminars in Oncology, in press.

    Google Scholar 

  28. Coldman, A.J., Coppin, C.M.L. and Goldie, J.H. (1988). Models of dose intensity, submitted.

    Google Scholar 

  29. Goldie, J.H. and Coldman, A.J. (1983). Clinical implications of the phenomenon of drug resistance. In Drug and Hormone Resistance in Neoplasia, eds. Bruchovsky, N. and Goldie, J.H., Boca Raton, vol. II, pp. 111–127.

    Google Scholar 

  30. Goldie, J.H., Coldman, A.J., Ng, V., Hopkins, H.A. and Looney, W.B. (1988). A Mathematical and computer based model of alternating chemotherapy and radiation therapy in experimental neoplasms. Lung Cancer Res., in press.

    Google Scholar 

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© 1989 Kluwer Academic Publishers

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Goldie, J.H. (1989). Mathematical models of drug resistance and chemotherapy effects. In: Ozols, R.F. (eds) Drug Resistance in Cancer Therapy. Cancer Treatment and Research, vol 48. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1601-5_2

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  • DOI: https://doi.org/10.1007/978-1-4613-1601-5_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8886-2

  • Online ISBN: 978-1-4613-1601-5

  • eBook Packages: Springer Book Archive

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