Publication Cover
Computational and Mathematical Methods in Medicine
An Interdisciplinary Journal of Mathematical, Theoretical and Clinical Aspects of Medicine
Volume 11, 2010 - Issue 1
3
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A hypothetical-mathematical model of acute myeloid leukaemia pathogenesis

&
Pages 49-65 | Received 04 Feb 2009, Accepted 16 Apr 2009, Published online: 05 Oct 2009

References

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

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.