A hypothetical-mathematical model of acute myeloid leukemia pathogenesis


Acute myeloid leukaemia is defined by the expansion of a mutated haematopoietic stem cell clone, with the inhibition of surrounding normal clones. Haematopoiesis can be seen as an evolutionary tree, starting with one cell that undergoes several divisions during the expansion phase, afterwards losing functional cells during the aging-related contraction phase. During divisions, offspring cells acquire ‘variations’, which can be either normal or abnormal. If an abnormal variation is present in more than 25% of the final cells, a monoclonal, leukemic pattern occurs. Such a pattern develops if: (A1) The abnormal variation occurs early, during the first or second divisions; (A2) The variation confers exceptional proliferative capacity; (B) A sizable proportion of the normal clones are destroyed and a previously non-significant abnormal clone gains relative dominance over a depleted environment; (C) The abnormal variation confers relative ‘immortality’, rendering it significant during the contraction phase. Combinations of these pathways further enhance the leukemic risk of the system. A simple mathematical model is used in order to characterize normal and leukemic states and to explain the above cellular processes generating monoclonal leukemic patterns.


Andrei Cucuianu

Radu Precup
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania



Paper coordinates

A. Cucuianu, R. Precup, A hypothetical-mathematical model of acute myeloid leukemia pathogenesis, Comput. Math. Methods Med. 11 (2010), 49-65, https://doi.org/10.1080/17486700902973751


About this paper


Computational and Mathematical  Methods in Medicine

Publisher Name

Hindawi Publishing Corporation

Print ISSN
Online ISSN


google scholar link

[1] J.L. Abkowitz, S.N. Catlin, M.T. McCallie, and P. Guttorp, Evidence that the number of haematopoietic stem cells per animal is conserved in mammals, Blood 100 (2002), pp. 2665–2667.
[2] M. Adimy, F. Crauste, and A. El Abdllaoui, Discrete maturity-structured model of cell differentiation with applications to acute myelogenous leukaemia, J. Biol. Systems 16 (2008), pp. 395–424.
[3] E.K. Afenya and D.E. Bentil, Some perspectives on modeling leukaemia, Math. Biosci. 150 (1998), pp. 113– 130.
[4] R.P. Agarwal and D. O’Regan, An Introduction to Ordinary Differential Equations, Springer, Berlin, 2008.
[5] M. Albitar, T. Manshouri, and Y. Shen, Myelodysplastic syndrome is not merely ‘preleukaemia’, Blood 100 (2002), pp. 791– 798.
[6] L.K. Andersen and M.C. Mackey, Resonance in periodic chemotherapy: a case study of acute myelogenous leukaemia, J. Theor. Biol. 209 (2001), pp. 113–130.
[7] J.O. Armitage, P.P. Carbone, and J.M. Connors, Treatment related myelodysplasia and acute leukaemia in non-Hodgkin’s lymphoma patients, J. Clin. Oncol. 21 (2002), pp. 897– 906.
[8] A.L. Barabassi and Z.N. Oltvai, Network biology: understanding the cell’s functional organization, Nat. Rev. Genet. 5 (2004), pp. 101–113.
[9] R. Bhatia, M. Holtz, and N. Niu, Persistence of malignant haematopoietic progenitors in chronic myelogenous leukaemia patients in complete cytogenetic remission following imatinib mesylate treatment, Blood 101 (2003), pp. 4701– 4708.
[10] D. Bonnet, Normal and leukemic CD34 negative human haematopoietic stem cells, Rev. Clin. Exp. Hematol. 5 (2001), pp. 42 – 61.
[11] F. Brauer and C. Castillo-Cha´vez, Mathematical Models in Population Biology and Epidemiology, Springer, Berlin, 2001.
[12] L. Busque, R. Mio, J. Mattioli, E. Brais, N. Blais, Y. Lalonde, M. Maragh, and D.G. Gilliland, Nonrandom X-inactivation patterns in normal females: lyonization ratios vary with age, Blood 88 (1996), pp. 59 – 65.
[13] C.A. Clarke and S.L. Glaser, Acute myeloid leukaemia, N. Eng. J. Med. 342 (2000), pp. 358–361.
[14] E.A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, Tata McGrawHill, New Delhi, 1972.
[15] D.S. Coffey, Self-organization, complexity and chaos: The new biology for medicine, Nat. Med. 4 (1998), pp. 882– 885.
[16] C. Colijn and M.C. Mackey, A mathematical model of hematopoiesis-I. Periodic chronic myelogenous leukaemia, J. Theor. Biol. 237 (2005), pp. 117–132.
[17] J. Cortes and M.E. O’Dwyer, Clonal evolution in chronic myelogenous leukaemia, Hematol. Oncol. Clin. North Am. 18 (2004), pp. 671– 684.
[18] A. Cucuianu, Cell darwinism, apoptosis, free radicals and haematological malignancies, Med. Hypotheses 56 (2001), pp. 52 – 57.
[19] A. Cucuianu, Dominant and opportunistic leukemic clones: proposal for a pathogenesisoriented classification in acute myeloid leukaemia, Med. Hypotheses 65 (2005), pp. 107–113.
[20] O. Diekmann, R. Durrett, K.P. Hadeler, P. Maini, and H.L. Smith, Mathematics Inspired by Biology, Springer, Berlin, 1999.
[21] D. Dingli and F. Michor, Successful therapy must eradicate cancer stem cells, Stem Cells 24 (2006), pp. 2603– 2610.
[22] B. Djulbegovic´ and S. Svetina, Mathematical model of acute myeloblastic leukaemia: an investigation of the relevant kinetic parameters, Cell Proliferation 18 (1985), pp. 307– 319.
[23] C.J. Eaves, J.D. Cashman, H.J. Sutherland, T. Otsuka, R.K. Humphries, D.E. Hogge, P.L. Lansdorp, and A.C. Eaves, Molecular analysis of primitive haematopoietic cell proliferation control mechanisms, Ann. NY Acad. Sci. 628 (1991), pp. 298– 306.
[24] P.J. Fialkow, J.W. Singer, and W.H. Raskind, Clonal development, stem-cell differentiation and clinical remission in acute non-lymphocytic leukaemia, N. Eng. J. Med. 317 (1987), pp. 468–473.
[25] C. Foley and M.C. Mackey, Dynamic hematological disease: a review, J. Math. Biol. 58 (2009), pp. 285– 322.
[26] R. Gazit, I.L. Weissman, and D.J. Rossi, Haematopoietic stem cells and the aging haematopoietic system, Semin. Hematol. 45 (2008), pp. 218– 224.
[27] J. Griffin and B. Lowenberg, Clonogenic cells in acute myeloblastic leukaemia, Blood 68 (1986), pp. 1185– 1195.
[28] N.L. Harris, E.S. Jaffe, J. Diebold, G. Flandrin, H.K. Muller-Hermelink, J. Vardiman, T.A. Lister, and C.D. Bloomfield, The World Health Organization Classification of Neoplasms of the Haemopoietic and Lymphoid Tissues: report of the Clinical Advisory Comitee MeetingAirlie House, Virginia, November 1997, Hematol. J. 1 (2000), pp. 53 – 66.
[29] S.M. Hart and L. Foroni, Core binding factor genes and human leukaemia, Haematologica 87 (2002), pp. 1307– 1323.
[30] D.R. Head, Revised classification of acute leukaemias, Leukemia 10 (1996), pp. 1826– 1831.
[31] E. Jabbour, J.E. Cortes, and H.M. Kantarjian, Molecular monitoring in chronic myeloid leukaemia. Response to tyrosine kinase inhibitors and prognostic implications, Cancer 15 (2008), pp. 2112– 2118.
[32] H. Kaneko and N. Kondo, Clinical features of Bloom syndrome and function of the causative gene, BLM helicase, Expert Rev. Mol. Diagn. 4 (2004), pp. 393– 401.
[33] C.P. Leith, K.J. Kopecky, and J. Goodwin, Acute myeloid leukaemia in the elderly: assessment of multidrug resistance and cytogenetics distinguishes biologic subgroups with remarkable distinct responses to standard chemotherapy. A Southwest Oncology Group Study, Blood 89 (1997), pp. 3323– 3328.
[34] M.W. Lensch, R.K. Rathburn, and S.B. Olson, Selective pressure as an essential force in molecular evolution of myeloid leukemic clones: a view from the window of Fanconi anemia, Leukemia 13 (1999), pp. 1784– 1789.
[35] B. Lowenberg, Acute myeloid leukaemia: The challenge of capturing disease variety, Hematology Am. Soc. Hematol. Educ. Program (2008), pp. 1 –11.
[36] M.C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science 197 (1977), pp. 287– 289.
[37] K.F. McCarthy, Marrow frequency of long-term repopulating cells: evidence that marrow haematopoietic cell concentration may be inversely proportional to species body weight, Blood 101 (2003), pp. 3431– 3436.
[38] J.D. Murray, Mathematical Biology II: Spatial Models and Biomedical Applications, Springer, Berlin, 2003.
[39] R. Nash, R. Storb, and P. Neiman, Polyclonal reconstitution of human marrow after allogeneic bone marrow transplantation, Blood 72 (1988), pp. 2031– 2037.
[40] F. Nolte and W.K. Hofmann, Molecular pathogenesis and genomic changes, Ann. Hematol. 10 (2008), pp. 777– 795.
[41] C. Peschle, R. Botta, R. Muller, M. Valtieri, and B. Ziegler, Purification and functional assay of pluripotent haematopoietic stem cells, Rev. Clin. Exp. Hematol. 5 (2001), pp. 3 –14.
[42] S.I. Rubinow and J.L. Lebowitz, Model of cell kinetics with applications to the acute myeloblastic leukaemia state in man, Biosystems 8 (1977), p. 265.
[43] R.F. Schlenk, K. Dohner, J. Krauter, S. Fro¨hling, A. Corbacioglu, L. Bullinger, M. Habdank, D. Spath, M. Morgan, A. Benner, B. Schlegelberger, G. Heil, A. Ganser, H. Do¨hner and GermanAustrian Acute Myeloid Leukemia Study Group, Mutations and treatment outcomes in cytogenetically normal acute myeloid leukaemia, N. Engl. J. Med. 358 (2008), pp. 1909 –1918.
[44] S.I. Swierczek, N. Agarwal, R.H. Nussenzveig, G. Rothstein, A. Wilson, A. Artz, and J.T. Prchal, Haematopoiesis is not clonal in healthy elderly women, Blood 112 (2008), pp. 3186– 3193.
[45] I. Thornley, R. Sutherland, R. Wynn, R. Nayar, L. Sung, G. Corpus, T. Kiss, J. Lipton, J. Doyle, F. Saunders, S. Kamel-Reid, M. Freedman, and H. Messner, Early haematopoietic reconstitution after clinical stem cell transplantation: evidence for stochastic stem cell behavior and limited acceleration in telomere loss, Blood 99 (2002), pp. 2387– 2396.
[46] A. Wahlin, B. Markevarn, I. Golovleva, and M. Nilsson, Improved outcomes in AML are restricted to young patients and are related mostly to bone marrow transplantation therapy, Eur. J. Hematol. 68 (2002), pp. 232–239.


Related Posts