Advanced Search
Article Contents
Article Contents

Mathematical modeling of cyclic treatments of chronic myeloid leukemia

Abstract Related Papers Cited by
  • Cyclic treatment strategies in Chronic Myeloid Leukemia (CML) are characterized by alternating applications of two (or more) different drugs, given one at a time. One of the main causes for treatment failure in CML is the generation of drug resistance by mutations of cancerous cells. We use mathematical methods to develop general guidelines on optimal cyclic treatment scheduling, with the aim of minimizing the resistance generation. We define a condition on the drugs' potencies which allows for a relatively successful application of cyclic therapies. We find that the best strategy is to start with the stronger drug, but use longer cycle durations for the weaker drug. We further investigate the situation where a degree of cross-resistance is present, such that certain mutations cause cells to become resistant to both drugs simultaneously.
    Mathematics Subject Classification: Primary: 92C50; Secondary: 92D25, 60G35.


    \begin{equation} \\ \end{equation}
  • [1]

    M. R. Arkin and J. A. Wells, Small-molecule inhibitors of protein-protein interactions: progressing towards the dream, Nat. Rev. Drug Discov., 3 (2004), 301-317.doi: 10.1038/nrd1343.


    T. Asaki, Y. Sugiyama, T. Hamamoto, M. Higashioka, M. Umehara, H. Naito and T. Niwa, Design and synthesis of 3-substituted benzamide derivatives as Bcr-Abl kinase inhibitors, Bioorg. Med. Chem. Lett., 16 (2006), 1421-1425.doi: 10.1016/j.bmcl.2005.11.042.


    D. E. Axelrod, K. A. Baggerly and M. Kimmel, Gene amplification by unequal sister chromatid exchange: probabilistic modeling and analysis of drug resistance data, J. Theor. Biol., 168 (1994), 151-159.doi: 10.1006/jtbi.1994.1095.


    N. T. J. Bailey, "The Elements of Stochastic Processes with Applications to the Natural Sciences," Wiley, New York, 1964.


    N. Bellomo, N. K. Li and P. K. Maini, On the foundations of cancer modelling: Selected topics, speculations, and perspectives, Math. Models Methods Appl. Sci., 18 (2008), 593-646.doi: 10.1142/S0218202508002796.


    Nicola Bellomo, Mark Chaplain and Elena De Angelis (eds.), "Selected Topics on Cancer Modeling: Genesis - Evolution - Immune Competition - Therapy," Boston, Birkhauser, 2008.


    D. Bonnet and J. E. Dick, Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell, Nat. Med., 3 (1997), 730-737.doi: 10.1038/nm0797-730.


    H. A. Bradeen, C. A. Eide, T. O'Hare, K. J. Johnson, S. G.Willis, F. Y. Lee, B. J. Druker and M. W. Deininger, 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, Blood, 108 (2006), 2332-2338.doi: 10.1182/blood-2006-02-004580.


    H. M. Byrne, T. Alarcon, M. R. Owen, S. D. Webb and P. K. Maini, Modelling aspects of cancer dynamics: A review, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 364 (2006), 1563-1578.


    A. J. Coldman and J. H. Goldie, Role of mathematical modeling in protocol formulation in cancer chemotherapy, Cancer Treat. Rep., 69 (1985), 1041-1048.


    A. J. Coldman and J. H. Goldie, A stochastic model for the origin and treatment of tumors contain- ing drug-resistant cells, Bull. Math. Biol., 48 (1986), 279-292.


    R. S. Day, Treatment sequencing, asymmetry, and uncertainty: Protocol strategies for combination chemotherapy, Cancer Res., 46 (1986), 3876-3885.


    M. W. Deininger, Optimizing therapy of chronic myeloid leukemia, Experimental Hematol., 35 (2007), 144-154.doi: 10.1016/j.exphem.2007.01.023.


    M. W. Deininger and B. J. Druker, Specific targeted therapy of chronic myelogenous leukemia with imatinib, Pharmacol. Rev., 55 (2003), 401-423.doi: 10.1124/pr.55.3.4.


    T. S. Deisboeck, L. Zhang, J. Yoon and J. Costa, In silico cancer modeling: Is it ready for prime time?, Nat. Clin. Pract. Oncol., 6 (2009), 34-42.doi: 10.1038/ncponc1237.


    M. Eigen, and P. Schuster, "The Hypercycle: A Principle of Natural Self-Organization," Springer-Verlag, Berlin, New York, 1979.


    S. Faderl, M. Talpaz, Z. Estrov and H. M. Kantarjian, Chronic myelogenous leukemia: biology and therapy, Ann. Intern. Med., 131 (1999), 207-219.


    E. A. Gaffney, The application of mathematical modelling to aspects of adjuvant chemotherapy scheduling, J. Math. Biol., 48 (2004), 375-422.doi: 10.1007/s00285-003-0246-2.


    E. A. Gaffney, The mathematical modelling of adjuvant chemotherapy scheduling: incorporating the effects of protocol rest phases and pharmacokinetics, Bull. Math. Biol., 67 (2005), 563-611.doi: 10.1016/j.bulm.2004.09.002.


    C. W. Gardiner, "Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences," Springer, 2004.


    Shea N. Gardner and Michael Fernandes, New tools for cancer chemotherapy: Computational assistance for tailoring treatments, Mol. Cancer Ther., 2 (2003), 1079-1084.


    R. A. Gatenby, J. Brown and T. Vincent, Lessons from applied ecology: Cancer control using an evolutionary double bind, Cancer Res., 69 (2009), 7499-7502.doi: 10.1158/0008-5472.CAN-09-1354.


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


    J. H. Goldie and A. J. Coldman, A model for resistance of tumor cells to cancer chemotherapeutic agents, Math. Biosci., 65 (1983), 291-307.doi: 10.1016/0025-5564(83)90066-4.


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


    J. H. Goldie and A. J. Coldman, "Drug Resistance in Cancer: Mechanisms and Models," Cambridge University Press, 1998.doi: 10.1017/CBO9780511666544.


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


    L. E. Harnevo and Z. Agur, Drug resistance as a dynamic process in a model for multistep gene amplification under various levels of selection stringency, Cancer Chemother. Pharmacol., 30 (1992), 469-476.doi: 10.1007/BF00685599.


    A. A. Katouli and N. L. Komarova, The worst drug rule revisited: Mathematical modeling of cyclic cancer treatments, Bull. Math Bio., (2010), 1-36.doi: 10.1007/s11538-010-9539-y.


    M. Kimmel and D. N. Stivers, Time-continuous branching walk models of unstable gene amplification, Bull. Math. Biol., 56 (1994), 337-357.


    M. Kimmel, A. Swierniak and A. Polanski, Infinite-dimensional model of evolution of drug resistance of cancer cells, Jour. Math. Syst. Est. Contr., 8 (1998), 1-16.


    N. L. Komarova, Stochastic modeling of drug resistance in cancer, J. Theor. Biol., 239 (2006), 351-366.doi: 10.1016/j.jtbi.2005.08.003.


    N. L. Komarova, A. A. Katouli and D. Wodarz, Combination of two but not three current targeted drugs can improve therapy of chronic myeloid leukemia, PLoS ONE, 4 (2009), e4423.doi: 10.1371/journal.pone.0004423.


    N. L. Komarova and D. Wodarz, Drug resistance in cancer: Principles of emergence and prevention, Proc. Natl. Acad. Sci. U.S.A., 102 (2005), 9714-9719.doi: 10.1073/pnas.0501870102.


    L. Norton and R. Day, Potential innovations in scheduling of cancer chemotherapy, in "Important Advances in Oncology" (Vincent T. Devita, Samuel Hellman, and Steven A. Rosenberg, eds.), Lippincott, Williams & Wilkins, Philadelphia, 1985, 57-72.


    A. S. Novozhilov, G. P. Karev and E. V. Koonin, Biological applications of the theory of birth-and-death processes, Brief. Bioinformatics, 7 (2006), 70-85.doi: 10.1093/bib/bbk006.


    M. E. O'Dwyer, M. J. Mauro and B. J. Druker, Recent advancements in the treatment of chronic myelogenous leukemia, Annu. Rev. Med., 53 (2002), 369-381.


    T. O'Hare, C. A. Eide, J. W. Tyner, A. S. Corbin, M. J. Wong, S. Buchanan, K. Holme, K. A. Jessen, C. Tang, H. A. Lewis, R. D. Romero, S. K. Burley and M. W. Deininger, SGX393 inhibits the CML mutant BcrAblT315I and preempts in vitro resistance when combined with nilotinib or dasatinib, Proc. Natl. Acad. Sci. U.S.A., 105 (2008), 5507-5512.doi: 10.1073/pnas.0800587105.


    K. Peggs and S. Mackinnon, Imatinib mesylate-the new gold standard for treatment of chronic myeloid leukemia, N. Engl. J. Med., 348 (2003), 1048-1050.doi: 10.1056/NEJMe030009.


    A. Quintas-Cardama, H. Kantarjian, L. V. Abruzzo and J. Cortes, Extramedullary BCR-ABL1-negative myeloid leukemia in a patient with chronic myeloid leukemia and synchronous cytogenetic abnormalities in Philadelphia-positive and negative clones during imatinib therapy, Leukemia, 21 (2007), 2394-2396.doi: 10.1038/sj.leu.2404865.


    A. Quints-Cardama, H. Kantarjian and J. Cortes, Flying under the radar: The new wave of BCR-ABL inhibitors, Nat. Rev. Drug Discov., 6 (2007), 834-848.doi: 10.1038/nrd2324.


    T. Reya, S. J. Morrison, M. F. Clarke and I. L. Weissman, Stem cells, cancer, and cancer stem cells, Nature, 414 (2001), 105-111.doi: 10.1038/35102167.


    S. Sanga, J. P. Sinek, H. B. Frieboes, M. Ferrari, J. P. Fruehauf and V. Cristini, Mathematical modeling of cancer progression and response to chemotherapy, Expert Rev. Anticancer Ther., 6 (2006), 1361-1376.doi: 10.1586/14737140.6.10.1361.


    S. Soverini, S. Colarossi, A. Gnani, G. Rosti, F. Castagnetti, A. Poerio, I. Iacobucci, M. Amabile, E. Abruzzese, E. Orlandi, F. Radaelli, F. Ciccone, M. Tiribelli, R. di Lorenzo, C. Caracciolo, B. Izzo, F. Pane, G. Saglio, M. Baccarani and G. Martinelli, Contribution of ABL kinase domain mutations to imatinib resistance in different subsets of Philadelphia-positive patients: by the GIMEMA Working Party on Chronic Myeloid Leukemia, Clin. Cancer Res., 12 (2006), 7374-7379.doi: 10.1158/1078-0432.CCR-06-1516.


    G. W. Swan, Role of optimal control theory in cancer chemotherapy, Math. Biosci., 101 (1990), 237-284.doi: 10.1016/0025-5564(90)90021-P.


    A. Swierniak, M. Kimmel and J. Smieja, Mathematical modeling as a tool for planning anticancer therapy, Eur. J. Pharmacol., 625 (2009), 108-121.doi: 10.1016/j.ejphar.2009.08.041.


    A. Swierniak and J. Smieja, Cancer chemotherapy optimization under evolving drug resistance, Nonlin. Anal., 47 (2001), 375-386.doi: 10.1016/S0362-546X(01)00184-5.


    E. Weisberg, P. W. Manley, S. W. Cowan-Jacob, A. Hochhaus and J. D. Griffin, Second generation inhibitors of BCR-ABL for the treatment of imatinib-resistant chronic myeloid leukaemia, Nat. Rev. Cancer, 7 (2007), 345-356.doi: 10.1038/nrc2126.


    D. Wodarz and N. L. Komarova, "Computational Biology of Cancer: Lecture Notes and Mathematical Modeling," World Scientific, 2005.


    J. Zhang, P. L. Yang and N. S. Gray, Targeting cancer with small molecule kinase inhibitors, Nat. Rev. Cancer, 9 (2009), 28-39.doi: 10.1038/nrc2559.

  • 加载中

Article Metrics

HTML views() PDF downloads(61) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint