Mathematical modeling of cyclic treatments of chronic myeloid leukemia
Pages: 289  306,
Volume 8,
Issue 2,
April
2011
doi:10.3934/mbe.2011.8.289 Abstract
References
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Natalia L. Komarova  Department of Mathematics, University of California Irvine, Irvine CA 92697, United States (email)
1 
M. R. Arkin and J. A. Wells, Smallmolecule inhibitors of proteinprotein interactions: progressing towards the dream, Nat. Rev. Drug Discov., 3 (2004), 301317. 

2 
T. Asaki, Y. Sugiyama, T. Hamamoto, M. Higashioka, M. Umehara, H. Naito and T. Niwa, Design and synthesis of 3substituted benzamide derivatives as BcrAbl kinase inhibitors, Bioorg. Med. Chem. Lett., 16 (2006), 14211425. 

3 
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), 151159. 

4 
N. T. J. Bailey, "The Elements of Stochastic Processes with Applications to the Natural Sciences," Wiley, New York, 1964. 

5 
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), 593646. 

6 
Nicola Bellomo, Mark Chaplain and Elena De Angelis (eds.), "Selected Topics on Cancer Modeling: Genesis  Evolution  Immune Competition  Therapy," Boston, Birkhauser, 2008. 

7 
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), 730737. 

8 
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 (BMS354825), and nilotinib (AMN107) in an NethylNnitrosourea (ENU)based mutagenesis screen: high efficacy of drug combinations, Blood, 108 (2006), 23322338. 

9 
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), 15631578. 

10 
A. J. Coldman and J. H. Goldie, Role of mathematical modeling in protocol formulation in cancer chemotherapy, Cancer Treat. Rep., 69 (1985), 10411048. 

11 
A. J. Coldman and J. H. Goldie, A stochastic model for the origin and treatment of tumors contain ing drugresistant cells, Bull. Math. Biol., 48 (1986), 279292. 

12 
R. S. Day, Treatment sequencing, asymmetry, and uncertainty: Protocol strategies for combination chemotherapy, Cancer Res., 46 (1986), 38763885. 

13 
M. W. Deininger, Optimizing therapy of chronic myeloid leukemia, Experimental Hematol., 35 (2007), 144154. 

14 
M. W. Deininger and B. J. Druker, Specific targeted therapy of chronic myelogenous leukemia with imatinib, Pharmacol. Rev., 55 (2003), 401423. 

15 
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), 3442. 

16 
M. Eigen, and P. Schuster, "The Hypercycle: A Principle of Natural SelfOrganization," SpringerVerlag, Berlin, New York, 1979. 

17 
S. Faderl, M. Talpaz, Z. Estrov and H. M. Kantarjian, Chronic myelogenous leukemia: biology and therapy, Ann. Intern. Med., 131 (1999), 207219. 

18 
E. A. Gaffney, The application of mathematical modelling to aspects of adjuvant chemotherapy scheduling, J. Math. Biol., 48 (2004), 375422. 

19 
E. A. Gaffney, The mathematical modelling of adjuvant chemotherapy scheduling: incorporating the effects of protocol rest phases and pharmacokinetics, Bull. Math. Biol., 67 (2005), 563611. 

20 
C. W. Gardiner, "Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences," Springer, 2004. 

21 
Shea N. Gardner and Michael Fernandes, New tools for cancer chemotherapy: Computational assistance for tailoring treatments, Mol. Cancer Ther., 2 (2003), 10791084. 

22 
R. A. Gatenby, J. Brown and T. Vincent, Lessons from applied ecology: Cancer control using an evolutionary double bind, Cancer Res., 69 (2009), 74997502. 

23 
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), 17271733. 

24 
J. H. Goldie and A. J. Coldman, A model for resistance of tumor cells to cancer chemotherapeutic agents, Math. Biosci., 65 (1983), 291307. 

25 
J. H. Goldie and A. J. Coldman, Quantitative model for multiple levels of drug resistance in clinical tumors, Cancer Treat. Rep., 67 (1983), 923931. 

26 
J. H. Goldie and A. J. Coldman, "Drug Resistance in Cancer: Mechanisms and Models," Cambridge University Press, 1998. 

27 
J. H. Goldie, A. J. Coldman and G. A. Gudauskas, Rationale for the use of alternating noncrossresistant chemotherapy, Cancer Treat. Rep., 66 (1982), 439449. 

28 
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), 469476. 

29 
A. A. Katouli and N. L. Komarova, The worst drug rule revisited: Mathematical modeling of cyclic cancer treatments, Bull. Math Bio., (2010), 136. 

30 
M. Kimmel and D. N. Stivers, Timecontinuous branching walk models of unstable gene amplification, Bull. Math. Biol., 56 (1994), 337357. 

31 
M. Kimmel, A. Swierniak and A. Polanski, Infinitedimensional model of evolution of drug resistance of cancer cells, Jour. Math. Syst. Est. Contr., 8 (1998), 116. 

32 
N. L. Komarova, Stochastic modeling of drug resistance in cancer, J. Theor. Biol., 239 (2006), 351366. 

33 
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. 

34 
N. L. Komarova and D. Wodarz, Drug resistance in cancer: Principles of emergence and prevention, Proc. Natl. Acad. Sci. U.S.A., 102 (2005), 97149719. 

35 
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, 5772. 

36 
A. S. Novozhilov, G. P. Karev and E. V. Koonin, Biological applications of the theory of birthanddeath processes, Brief. Bioinformatics, 7 (2006), 7085. 

37 
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), 369381. 

38 
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), 55075512. 

39 
K. Peggs and S. Mackinnon, Imatinib mesylatethe new gold standard for treatment of chronic myeloid leukemia, N. Engl. J. Med., 348 (2003), 10481050. 

40 
A. QuintasCardama, H. Kantarjian, L. V. Abruzzo and J. Cortes, Extramedullary BCRABL1negative myeloid leukemia in a patient with chronic myeloid leukemia and synchronous cytogenetic abnormalities in Philadelphiapositive and negative clones during imatinib therapy, Leukemia, 21 (2007), 23942396. 

41 
A. QuintsCardama, H. Kantarjian and J. Cortes, Flying under the radar: The new wave of BCRABL inhibitors, Nat. Rev. Drug Discov., 6 (2007), 834848. 

42 
T. Reya, S. J. Morrison, M. F. Clarke and I. L. Weissman, Stem cells, cancer, and cancer stem cells, Nature, 414 (2001), 105111. 

43 
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), 13611376. 

44 
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 Philadelphiapositive patients: by the GIMEMA Working Party on Chronic Myeloid Leukemia, Clin. Cancer Res., 12 (2006), 73747379. 

45 
G. W. Swan, Role of optimal control theory in cancer chemotherapy, Math. Biosci., 101 (1990), 237284. 

46 
A. Swierniak, M. Kimmel and J. Smieja, Mathematical modeling as a tool for planning anticancer therapy, Eur. J. Pharmacol., 625 (2009), 108121. 

47 
A. Swierniak and J. Smieja, Cancer chemotherapy optimization under evolving drug resistance, Nonlin. Anal., 47 (2001), 375386. 

48 
E. Weisberg, P. W. Manley, S. W. CowanJacob, A. Hochhaus and J. D. Griffin, Second generation inhibitors of BCRABL for the treatment of imatinibresistant chronic myeloid leukaemia, Nat. Rev. Cancer, 7 (2007), 345356. 

49 
D. Wodarz and N. L. Komarova, "Computational Biology of Cancer: Lecture Notes and Mathematical Modeling," World Scientific, 2005. 

50 
J. Zhang, P. L. Yang and N. S. Gray, Targeting cancer with small molecule kinase inhibitors, Nat. Rev. Cancer, 9 (2009), 2839. 

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