The dynamics of drug resistance: A mathematical perspective

Drug Resistance Updates

Volumn 15, Issue 1-2, 2012, Pages 90-97

  Lavi, Orit ^a   Gottesman, Michael M ^a   Levy, Doron ^b  

^a NATIONAL CANCER INSTITUTE   (United States)

^b University of Maryland   (United States)

Author keywords

Drug scheduling and sequencing; Drug dependent independent resistance; Evolution of resistance; Mathematical modeling; Multidrug resistance

Indexed keywords

CYCLOPHOSPHAMIDE; DOCETAXEL; DOXORUBICIN; FLAVOPIRIDOL; FLUOROURACIL; METHOTREXATE; PACLITAXEL;

ACUTE LYMPHOBLASTIC LEUKEMIA; ALGORITHM; BREAST CANCER; DRUG RESPONSE; HUMAN; INTERMETHOD COMPARISON; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MULTIDRUG RESISTANCE; MULTIPLE CYCLE TREATMENT; PRIORITY JOURNAL; QUANTITATIVE ANALYSIS; REVIEW; STATISTICAL MODEL; STOMACH CANCER;

EID: 84860692880     PISSN: 13687646     EISSN: 15322084     Source Type: Journal    
DOI: 10.1016/j.drup.2012.01.003     Document Type: Article

References (77)

1. Z. Agur From the evolution of toxin resistance to virtual clinical trials: the role of mathematical models in oncology Future Oncol. 6 2010 917 927
2. R.P. Araujo, E.F. Petricoin, and L.A. Liotta A mathematical model of combination therapy using the EGFR signaling network Biosystems 80 2005 57 69
3. B.G. Birkhead, and W.M. Gregory A mathematical model of the effects of drug resistance in cancer chemotherapy Math. Biosci. 72 1984 59 69
4. G. Bonadonna, M. Zambetti, A. Moliterni, L. Gianni, and P. Valagussa Clinical relevance of different sequencing of doxorubicin and cyclophosphamide, methotrexate, and fluorouracil in operable breast cancer J. Clin. Oncol. 22 2004 1614 1620
5. G. Bonadonna, M. Zambetti, and P. Valagussa Sequential or alternating doxorubicin and CMF regimens in breast cancer with more than three positive nodes. Ten-year results JAMA 273 1995 542 547
6. P. Castorina, D. Carco, C. Guiot, and T.S. Deisboeck Tumor growth instability and its implications for chemotherapy Cancer Res. 69 2009 8507 8515
7. S.J. Chapman, T. Roose, and P.K. Maini Mathematical models of avascular tumor growth Siam Rev. 49 2007 179 208
8. M.L. Citron Dose-dense chemotherapy: principles. clinical results and future perspectives Breast Care (Basel) 3 2008 251 255
9. M.L. Citron, D.A. Berry, C. Cirrincione, C. Hudis, E.P. Winer, W.J. Gradishar, N.E. Davidson, S. Martino, R. Livingston, J.N. Ingle, E.A. Perez, J. Carpenter, D. Hurd, J.F. Holland, B.L. Smith, C.I. Sartor, E.H. Leung, J. Abrams, R.L. Schilsky, H.B. Muss, and L. Norton Randomized trial of dose-dense versus conventionally scheduled and sequential versus concurrent combination chemotherapy as postoperative adjuvant treatment of node-positive primary breast cancer: first report of Intergroup Trial C9741/Cancer and Leukemia Group B Trial 9741 J. Clin. Oncol. 21 2003 1431 1439
10. S.E. Clare, F. Nakhlis, and J.C. Panetta Molecular biology of breast cancer metastasis. The use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer Breast Cancer Res. 2 2000 430 435
11. P. Crivori, B. Reinach, D. Pezzetta, and I. Poggesi Computational models for identifying potential P-glycoprotein substrates and inhibitors Mol. Pharm. 3 2006 33 44
12. R.S. Day Treatment sequencing, asymmetry, and uncertainty: protocol strategies for combination chemotherapy Cancer Res. 46 1986 3876 3885
13. 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
14. E.J. Demant, M. Sehested, and P.B. Jensen A model for computer simulation of P-glycoprotein and transmembrane delta pH-mediated anthracycline transport in multidrug-resistant tumor cells Biochim. Biophys. Acta 1055 1990 117 125
15. M.A. Demel, O. Kramer, P. Ettmayer, E.E. Haaksma, and G.F. Ecker Predicting ligand interactions with ABC transporters in ADME Chem. Biodivers. 6 2009 1960 1969
16. R. Demicheli, M.W. Retsky, D.E. Swartzendruber, and G. Bonadonna Proposal for a new model of breast cancer metastatic development Ann. Oncol. 8 1997 1075 1080
17. K.R. Fister, and J.C. Panetta Optimal control applied to cell-cycle-specific cancer chemotherapy Siam J. Appl. Math. 60 2000 1059 1072
18. J. Foo, and F. Michor Evolution of resistance to anti-cancer therapy during general dosing schedules J. Theor. Biol. 263 2010 179 188
19. S.N. Gardner Cell cycle phase-specific chemotherapy: computational methods for guiding treatment Cell Cycle 1 2002 369 374
20. S.N. Gardner Modeling multi-drug chemotherapy: tailoring treatment to individuals J. Theor. Biol. 214 2002 181 207
21. S.N. Gardner Scheduling chemotherapy: catch 22 between cell kill and resistance evolution J. Theor. Med. 2 2000 215 232
22. S.N. Gardner, and M. Fernandes New tools for cancer chemotherapy: computational assistance for tailoring treatments Mol. Cancer Ther. 2 2003 1079 1084
23. J.P. Gillet, and M.M. Gottesman Mechanisms of multidrug resistance in cancer Methods Mol. Biol. 596 2010 47 76
24. J.H. Goldie, and A.J. Coldman Drug Resistance in Cancer: Mechanisms and Models 1998 Cambridge University Press Cambridge/New York
25. 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
26. 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
27. C. Guiot, P.G. Degiorgis, P.P. Delsanto, P. Gabriele, and T.S. Deisboeck Does tumor growth follow a "universal law"? J. Theor. Biol. 225 2003 147 151
28. D. Hart, E. Shochat, and Z. Agur The growth law of primary breast cancer as inferred from mammography screening trials data Br. J. Cancer 78 1998 382 387
29. A. Hochhaus, S.G. O'Brien, F. Guilhot, B.J. Druker, S. Branford, L. Foroni, J.M. Goldman, M.C. Muller, J.P. Radich, M. Rudoltz, M. Mone, I. Gathmann, T.P. Hughes, and R.A. Larson Six-year follow-up of patients receiving imatinib for the first-line treatment of chronic myeloid leukemia Leukemia 23 2009 1054 1061
30. M. Horio, I. Pastan, M.M. Gottesman, and J.S. Handler Transepithelial transport of vinblastine by kidney-derived cell lines. Application of a new kinetic model to estimate in situ Km of the pump Biochim. Biophys. Acta 1027 1990 116 122
31. M. Kimmel, A. Swierniak, and A. Polanski Infinite-dimensional model of evolution of drug resistance of cancer cells J. Math. Syst. Estim. Control 8 1998 1 16
32. 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
33. D.W. Kufe, J.F. Holland, E. Frei American Cancer Society Cancer Medicine 6 2003 B.C. Decker Hamilton, Ont./London
34. N.V. Mantzaris, S. Webb, and H.G. Othmer Mathematical modeling of tumor-induced angiogenesis J. Math. Biol. 49 2004 111 187
35. S. Michelson Mathematical models for multidrug resistance and its reversal Cytotechnology 12 1993 315 324
36. S. Michelson, and D. Slate Emergence of the drug-resistant phenotype in tumor subpopulations: a hybrid model J. Natl. Cancer Inst. 81 1989 1392 1401
37. S. Michelson, and D. Slate A mathematical model for the inhibition of the multidrug resistance-associated P-glycoprotein pump Bull. Math. Biol. 56 1994 207 223
38. S. Michelson, and D. Slate A mathematical model of the P-glycoprotein pump as a mediator of multidrug resistance Bull. Math. Biol. 54 1992 1023 1038
39. F. Michor, Y. Iwasa, and M.A. Nowak Dynamics of cancer progression Nat. Rev. Cancer 4 2004 197 205
40. F. Michor, M.A. Nowak, and Y. Iwasa Evolution of resistance to cancer therapy Curr. Pharm. Des. 12 2006 261 271
41. T.S. Mikkelsen, A. Sparreboom, C. Cheng, Y. Zhou, J.M. Boyett, S.C. Raimondi, J.C. Panetta, W.P. Bowman, J.T. Sandlund, C.H. Pui, M.V. Relling, and W.E. Evans Shortening infusion time for high-dose methotrexate alters antileukemic effects: a randomized prospective clinical trial J. Clin. Oncol. 29 2011 1771 1778
42. A.I. Minchinton, and I.F. Tannock Drug penetration in solid tumours Nat. Rev. Cancer 6 2006 583 592
43. H.C. Monro, and E.A. Gaffney Modelling chemotherapy resistance in palliation and failed cure J. Theor. Biol. 257 2009 292 302
44. J.M. Murray Some optimal control problems in cancer chemotherapy with a toxicity limit Math. Biosci. 100 1990 49 67
45. L. Norton, and R. Simon The Norton-Simon hypothesis revisited Cancer Treat. Rep. 70 1986 163 169
46. L. Norton, and R. Simon Tumor size, sensitivity to therapy, and design of treatment schedules Cancer Treat. Rep. 61 1977 1307 1317
47. L. Norton, R. Simon, H.D. Brereton, and A.E. Bogden Predicting the course of Gompertzian growth Nature 264 1976 542 545
48. V. Panagiotopoulou, G. Richardson, O.E. Jensen, and C. Rauch On a biophysical and mathematical model of Pgp-mediated multidrug resistance: understanding the "space-time" dimension of MDR Eur. Biophys. J. 39 2010 201 211
49. J.C. Panetta A mathematical model of breast and ovarian cancer treated with paclitaxel Math. Biosci. 146 1997 89 113
50. J.C. Panetta A mathematical model of drug resistance: heterogeneous tumors Math. Biosci. 147 1998 41 61
51. J.C. Panetta, A. Sparreboom, C.H. Pui, M.V. Relling, and W.E. Evans Modeling mechanisms of in vivo variability in methotrexate accumulation and folate pathway inhibition in acute lymphoblastic leukemia cells PLoS Comput. Biol. 6 2010 e1001019
52. J.C. Panetta, Y. Yanishevski, C.H. Pui, J.T. Sandlund, J. Rubnitz, G.K. Rivera, R. Ribeiro, W.E. Evans, and M.V. Relling A mathematical model of in vivo methotrexate accumulation in acute lymphoblastic leukemia Cancer Chemother. Pharmacol. 50 2002 419 428
53. M.J. Piccart-Gebhart Mathematics and oncology: a match for life? J. Clin. Oncol. 21 2003 1425 1428
54. M. Retsky, R. Demicheli, W. Hrushesky, J. Speer, D. Swartzendruber, and R. Wardwell Recent translational research: computational studies of breast cancer Breast Cancer Res. 7 2005 37 40
55. M.W. Retsky, R. Demicheli, D.E. Swartzendruber, P.D. Bame, R.H. Wardwell, G. Bonadonna, J.F. Speer, and P. Valagussa Computer simulation of a breast cancer metastasis model Breast Cancer Res. Treat. 45 1997 193 202
56. M.W. Retsky, D.E. Swartzendruber, R.H. Wardwell, and P.D. Bame Is Gompertzian or exponential kinetics a valid description of individual human cancer growth? Med. Hypotheses 33 1990 95 106
57. R. Roe-Dale, D. Isaacson, and M. Kupferschmid A mathematical model of breast cancer treatment with CMF and doxorubicin Bull. Math. Biol. 73 2011 585 608
58. R. Roe-Dale, D. Isaacson, and M. Kupferschmid A mathematical model of cell cycle effects in gastric cancer chemotherapy Bull. Math. Biol. 74 2012 159 174
59. E. Shochat, D. Hart, and Z. Agur Using computer simulations for evaluating the efficacy of breast cancer chemotherapy protocols Math. Models Meth. App. Sci. 9 1999 599 615
60. R. Simon, and L. Norton The Norton-Simon hypothesis: designing more effective and less toxic chemotherapeutic regimens Nat. Clin. Pract. Oncol. 3 2006 406 407
61. D. Slate, and S. Michelson Drug resistance-reversal strategies: comparison of experimental data with model predictions J. Natl. Cancer Inst. 83 1991 1574 1580
62. J. Smieja, A. Swierniak, and Z. Duda Gradient method for finding optimal scheduling in infinite dimensional models of chemotherapy J. Theor. Med. 3 2000 25 36
63. E.C. Spoelstra, H.V. Westerhoff, H. Dekker, and J. Lankelma Kinetics of daunorubicin transport by P-glycoprotein of intact cancer cells Eur. J. Biochem. 207 1992 567 579
64. J.A. Spratt, D. von Fournier, J.S. Spratt, and E.E. Weber Decelerating growth and human breast cancer Cancer 71 1993 2013 2019
65. G.W. Swan Role of optimal control theory in cancer chemotherapy Math. Biosci. 101 1990 237 284
66. G.W. Swan, and T.L. Vincent Optimal control analysis in the chemotherapy of IgG multiple myeloma Bull. Math. Biol. 39 1977 317 337
67. A. Swierniak, M. Kimmel, and J. Smieja Mathematical modeling as a tool for planning anticancer therapy Eur. J. Pharmacol. 625 2009 108 121
68. A. Swierniak, A. Polanski, M. Kimmel, A. Bobrowski, and J. Smieja Qualitative analysis of controlled drug resistance model - inverse Laplace and semigroup approach Control Cybern. 28 1999 61 75
69. A. Swierniak, and J. Smieja Analysis and optimization of drug resistant and phase-specific cancer chemotherapy models Math. Biosci. Eng. 2 2005 657 670
70. B.A. Teicher Cancer Drug Resistance 2006 Humana Press Totowa, N.J.
71. C. Tomasetti A new hypothesis: imatinib affects leukemic stem cells in the same way it affects all other leukemic cells Blood Cancer J. 1 2011 e19
72. C. Tomasetti, and D. Levy Role of symmetric and asymmetric division of stem cells in developing drug resistance Proc. Natl. Acad. Sci. U.S.A. 107 2010 16766 16771
73. O. Tredan, C.M. Galmarini, K. Patel, and I.F. Tannock Drug resistance and the solid tumor microenvironment J. Natl. Cancer Inst. 99 2007 1441 1454
74. R. Venkatasubramanian, M.A. Henson, and N.S. Forbes Integrating cell-cycle progression, drug penetration and energy metabolism to identify improved cancer therapeutic strategies J. Theor. Biol. 253 2008 98 117
75. L.M. Wein, J.T. Wu, A.G. Ianculescu, and R.K. Puri A mathematical model of the impact of infused targeted cytotoxic agents on brain tumours: implications for detection, design and delivery Cell Prolif. 35 2002 343 361
76. D. Wodarz, and N.L. Komarova Emergence and prevention of resistance against small molecule inhibitors Semin. Cancer Biol. 15 2005 506 514
77. E.L. Woodahl, and R.J. Ho The role of MDR1 genetic polymorphisms in interindividual variability in P-glycoprotein expression and function Curr. Drug Metab. 5 2004 11 19