A mathematical model for chronic myelogenous leukemia (CML) and T cell interaction

Journal of Theoretical Biology

Volumn 227, Issue 4, 2004, Pages 513-523

  Moore, Helen ^a   Li, Natasha K ^b  

^a AMERICAN INSTITUTE OF MATHEMATICS   (United States)

^b STANFORD UNIVERSITY   (United States)

Author keywords

Cancer; Chronic myelogenous leukemia (CML); Differential equations; Dynamics; Latin hypercube sampling (LHS); Mathematical modeling; T cells

Indexed keywords

BLOOD; CANCER; MATHEMATICAL ANALYSIS;

ARTICLE; CANCER CELL; CANCER REGRESSION; CELL INTERACTION; CELL POPULATION; CHRONIC MYELOID LEUKEMIA; EFFECTOR CELL; MATHEMATICAL MODEL; MORTALITY; PRIORITY JOURNAL; T LYMPHOCYTE; TUMOR GROWTH;

CELL DEATH; CELL DIVISION; HUMANS; LEUKEMIA, MYELOID, CHRONIC; MATHEMATICS; MODELS, BIOLOGICAL; NUMERICAL ANALYSIS, COMPUTER-ASSISTED; T-LYMPHOCYTE SUBSETS; T-LYMPHOCYTES;

EID: 1642344491     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jtbi.2003.11.024     Document Type: Article

References (37)

1. Afenya E., Calderón C. Diverse ideas on the growth kinetics of disseminated cancer cells. Bull. Math. Biol. 62:2000;527-542.
2. Athens J.W., Raab S.O., Haab O.P., Boggs D.R., Ashenbruker H., Cartwright G.E., Wintrobe M.M. Leukokinetic studies. X. Blood granulocyte kinetics in chronic myelocytic leukemia. Leukemia. 44(5):1965;765-777.
3. Bassukas I.D., Maurer-Schultze B. The recursion formula of the Gompertz function. a simple method for the estimation and comparison of tumor growth curves Growth Develop. Aging. 52:1988;113-122.
4. Blower S., Dowlatabadi H. Sensitivity and uncertainty analysis of complex models of disease transmission. an HIV model, as an example Int. Stat. Rev. 2:1994;229-243.
5. Borrelli R., Coleman C. Differential Equations: A Modeling Perspective. 1998;Wiley, New York.
6. Cronkite E.P., Vincent P.C. Granulocytopoiesis. Ser. Haematol. 2:1969;3-43.
7. Duvall C.P., Perry S. The use of 51-chromium in the study of leukocyte kinetics in chronic myelocytic leukemia. J. Lab. Clin. Med. 71:1968;614-628.
8. Edelstein-Keshet L. Mathematical Models in Biology. 1988;Random House, New York.
9. + T-cell subpopulations J. Theor. Biol. 170:1994;367-391.
10. Faderl S., Talpaz M., Estrov Z., O'Brien S., Kurzrock R., Kantarjian H. The biology of chronic myeloid leukemia. New Engl. J. Med. 341(3):1999;164-172.
11. Fokas A.S., Keller J.B., Clarkson B.D. A mathematical model of granulocytopoiesis and chronic myelogenous leukemia. Cancer Res. 51(8):1991;2084-2091.
12. Freedman H. Deterministic Mathematical Models in Population Ecology. 1980;Marcel Dekker, New York.
13. Gordon, M.Y., Dazzi, F., Marley, S.B., Lewis, J.L., Nguyen, D., Grand, F.H., Davidson, R.J., Goldman, J.M., 1999. Cell biology of CML cells. Leukemia. Apr;13 Suppl 1:S65-71.
14. Haase A.T., Henry K., Zupancic M., Sedgewick G., Faust R.A., Melroe H., Cavert W., Gebhard K., Staskus K., Zhang Z.Q., Dailey P.J., Balfour H.H. Jr., Erice A., Perelson A.S. Quantitative image analysis of HIV-1 infection in lymphoid tissue. Science. 274:1996;985-989.
15. Janeway C.A., Travers P., Walport M., Shlomchik M. Immunobiology: The Immune System in Health and Disease. 2001;Garland Publishing, New York.
16. Kantarjian, H., Sawyers, C., Hochhaus, A., Guilhot, F., Schiffer, C., Gambacorti-Passerini, C., Niederwieser, D., Resta, D., Capdeville, R., Zoellner, U., Talpaz, M., Druker, B., Goldman, J., O'Brien, S.G., Russell, N., Fischer, T., Ottmann, O., Cony-Makhoul, P., Facon, T., Stone, R., Miller, C., Tallman, M., Brown, R., Schuster, M., Loughran, T., Gratwohl, A., Mandelli, F., Saglio, G., Lazzarino, M., Russo, D., Baccarani, M., Morra, E., International STI571 CML Study Group, 2002. Hematologic and cytogenetic responses in patients with accelerated phase chronic myeloid leukemia: results of a phase 2 study. New Engl. J. Med. 346, 645-652.
17. Kirschner D., Panetta J.C. Modeling immunotherapy of the tumor-immune interaction. J. Math. Biol. 37:1998;235-252.
18. Kirschner D., Webb G.F. A model for treatment strategy in the chemotherapy of AIDS. Bull. Math. Biol. 58(2):1996;367-390.
19. Kreuzer K.A., Le Coutre P., Landt O., Na I.K., Schwartz M., Schultheis K., Hochhaus A., Dorken B. Preexistence and evolution of imatinib mesylate-resistant clones in chronic myelogenous leukemia detected by PNA-based PCR clamping technique. Ann. Hematol. 82(5):2003;284-289.
20. Kuznetsov V., Makalkin I., Taylor M., Perelson A. Nonlinear dynamics of immunogenic tumors. parameter estimation and global bifurcation analysis Bull. Math. Biol. 56(2):1994;295-321.
21. Lee, G.R., Foerster, J., Lukens, J., Paraskevas, F., Greer, J.P., Rodgers, G., Wintrobe, M.M. (Eds.), 1999. Wintrobe's Clinical Hematology. Lippincott, Williams & Wilkins, Philadelphia, PA.
22. Lee, P., 2001. Pers. comm.
23. Mohri, H., Perelson, A., Tung, K., Ribeiro, R., Ramratnam, B., Markowitz, M., Kost, R., Hurley, A., Weinberger, L., Cesar, D., Hellerstein, M., Ho, D., 2001. Increased turnover of T lymphocytes in HIV-1 infection and its reduction by antiretroviral therapy. J. Exp. Med. 194 (9) (November 5), 1277-1287.
24. Nowak M.A., Bonhoeffer S., Hill A.M., Boehme R., Thomas H.C., McDade H. Viral dynamics in hepatitis B virus infection. Proc. Natl. Acad. Sci. USA. 93:1996;4398-4402.
25. Nowak M.A., May R.M. Virus Dynamics: Mathematical Principles of Immunology and Virology. 2000;Oxford University Press, Oxford, UK.
26. Othmer H.G., Adler F.R., Lewis M.A., Dallon J.C. Case Studies in Mathematical Modeling Ecology, Physiology, and Cell Biology. 1997;Englewood Cliffs, Prentice-Hall, NJ.
27. Perelson A.S., Nelson P.W. Mathematical analysis of HIV-I dynamics in vivo. SIAM Rev. 41(1):1999;3-44.
28. Perelson A.S., Essunger P., Cao Y., Vesanen M., Hurley A., Saksela K., Markowitz M., Ho D.D. Decay characteristics of HIV-1-infected compartments during combination therapy. Nature. 387:1997;188-191.
29. Perelson A.S., Kirschner D., De Boer R. Dynamics of HIV infection of CD4+ T cells. Math. Biosci. 114:1993;81-125.
30. Rubinow S.I. A simple model of steady state differentiating cell system. J. Cell Biol. 43:1969;32-39.
31. Rubinow S.I., Lebowitz J.L. A mathematical model of neutrophil production and control in normal man. J. Math. Biol. 1:1975;187-225.
32. Sawyers C.L. Chronic myeloid leukemia. New Engl. J. Med. 340(17):1999;1330-1340.
33. Schiffer C.A., Hehlmann R., Larson R. Perspectives on the treatment of chronic phase and advanced phase CML and Philadelphia chromosome positive ALL. Leukemia. 17:2003;691-699.
34. Steel G.G. Growth of Kinetic Tumors. 1977;Oxford University Press, Oxford, UK.
35. Stryckmans P.A., Debusscher L., Collard E. Cell kinetics in chronic granuclotyci leukaemia (CGL). Clin. Haematol. 6(1):1977;21-40.
36. Wigginton J.E., Kirschner D. A model to predict cell-mediated immune regulatory mechanisms during human infection with Mycobacterium tuberculosis. J. Immunol. 166(3):2001;1951-1967.
37. Xu X.L., Ling Y.B. A study on the expectational model for tumor growth. Int. J. Biomed. Comput. 22(2):1988;135-141.