Abstract
We review the basic characteristics of four periodic hematological disorders (periodic auto-immune hemolytic anemia, cyclical thrombocytopenia, cyclical neutropenia and periodic chronic myelogenous leukemia) and examine the role that mathematical modeling and numerical simulations have played in our understanding of the origin of these diseases and in the regulation of hematopoiesis.
Similar content being viewed by others
References
Adimy, M., Crauste, F.: Global stability of a partial differential equation with distributed delay due to cellular replication. Nonlinear Anal. 54, 1469–1491 (2003)
Adimy, M., Crauste, F.: Modeling and asymptotic stability of a growth factor-dependent stem cell dynamics model with distributed delay. Disc. Cont. Dyn. Syst. Ser B 8 (2007)
Adimy, M., Crauste, F., Ruan, S.: A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J. Appl. Math. 65 (2005)
Adimy, M., Crauste, F., Ruan, S.: Stability and hopf bifurcation in a mathematical model of pluripotent stem cell dynamics. Nonlinear Anal. Real World Appl. 6, 651–670 (2005)
Adimy, M., Crauste, F., Ruan, S.: Modelling hematopoiesis mediated by growth factors with applications to periodic hematological diseases. Bull. Math. Biol. 68 (2006)
Adimy, M., Pujo-Menjouet, L.: A singular transport model describing cellular division. C. R. Acad. Sci. Paris 332, 1071–1076 (2001)
Adimy, M., Pujo-Menjouet, L.: A mathematical model describing cellular division with a proliferating phase duration depending on the maturity of cells. Electron. J. Diff. Equ. p. 14 (2003)
Apostu, R., Mackey, M.: Understanding cyclical thrombocytopenia: A mathematical modeling approach. J. Theor. Biol. (2008) (in press)
Balduini, C., Stella, C., Rosti, V., Bertolino, G., Noris, P., Ascari, E.: Acquired cyclic thrombocytopenia thrombocytosis with periodic defect of platelet function. Br. J. Haematol. 85, 718–722 (1993)
Basu, S., Hodgson, G., Katz, M., Dunn, A.R.: Evaluation of role of G-CSF in the production, survival, and release of neutrophils from bone marrow into circulation. Blood 100(3), 854–861 (2002)
Bélair, J., Mackey, M.: A model for the regulation of mammalian platelet production. Ann. N. Y. Acad. Sci. 504, 280–282 (1987)
Bélair, J., Mackey, M., Mahaffy, J.: Age-structured and two-delay models for erythropoiesis. Math. Biosci. 128, 317–346 (1995)
Bernard, J., Caen, J.: Purpura thrombopénique et megacaryocytopénie cycliques mensuels. Nouv. Rev. franc. Hémat. 2, 378–386 (1962)
Bernard, S., Belair, J., Mackey, M.: Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. J. Theor. Biol. 223, 283–298 (2003)
Bessonov, N., Ducrot, A., Volpert, V.: Modeling of leukemia development in the bone marrow. In: Proceedings of the annual symposium on “Mathematics applied in biology and biophysics (Tom XLVIII, v.2) pp. 79–8 (2005)
Bessonov, N., Pujo-Menjouet, L., Volpert, V.: Cell modeling of hematopoiesis. J. Math. Model. Nat. Phenomena 1 (2006)
Beuter, A., Glass, L., Mackey, M., Titcombe, M.: Nonlinear Dynamics in Physiology and Medicine. Springer, Heidelberg (2003)
Beutler, E., Lichtman, M.A., Coller, B.S., Kipps, T.: Williams Hematology. McGraw-Hill, New York (1995)
Blythe, S.P., Nisbet, R.M., Gurney, W.S.C.: The dynamics of population models with distributed maturation periods. Theor. Popul. Biol. 25, 289–311 (1984)
Chikkappa, G., Borner, G., Burlington, H., Chanana, A.D., Cronkite, E.P., Ohl, S., Pavelec, M., Robertso, J.S.: Periodic oscillation of blood leukocytes, platelets, and reticulocytes in a patient with chronic myelocytic leukemia. Blood 47, 1023–1030 (1976)
Cohen, T., Cooney, D.P.: Cyclical thrombocytopenia: case report and review of literature. Scand. J. Haematol. 16, 133–138 (1974)
Colijn, C., Dale, D.C., Foley, C., Mackey, M.: Observations on the pathophysiology and mechanisms for cyclic neutropenia. Math. Model. Nat. Phenomena 1 (2006)
Colijn, C., Foley, C., Mackey, M.: G-CSF treatment of canine cyclical neutropenia: a comprehensive mathematical model. Exp. Hematol. 35, 898–907 (2007)
Colijn, C., Fowler, A., Mackey, M.C.: High frequency spikes in long period blood cell oscillations. J. Math. Biol. 53, 499–519 (2006)
Colijn, C., Mackey, M.: A mathematical model of hematopoiesis: I. Periodic chronic myelogenous leukemia. J. Theor. Biol. 237, 117–132 (2005)
Colijn, C., Mackey, M.: A mathematical model of hematopoiesis: II. Cyclical neutropenia. J. Theor. Biol. 237, 133–146 (2005)
Dan, K., Inokuchi, K., An, E., Nomura, T.: Cell mediated cyclic thrombocytopenia treated with azathioprine. Br. J. Haematol. 77, 365–379 (1991)
Ducrot, A., Volpert, V.: On a model of leukemia development with a spatial cell distribution. J. Math. Model. Nat. Phenomena (2008) (in press)
Dunn, C.D.R.: Cyclic hematopoiesis: the biomathematics. Exp. Hematol. 11, 779–791 (1983)
Dyson, J., Villela-Bressan, Webb, G.: An age and maturity structured model of cell population dynamics. In: Horn, M., Simonnett, G., Webb, G.F. (eds.) Mathematical models in medical and health science, pp. 99–16 (1998)
Eller, J., Györi, I., Zollei, J., Krizsa, F.: Modelling thrombopoiesis regulation I: Model description and simulation results. Comput. Math. Appl. 14, 841–848 (1987)
Engel, C., Scholz, M., Loeffler, M.A.: Computational model of human granulopoiesis to simulate the hematotoxic effects of multicycle polychemotherapy. Blood 104, 2323–2331 (2004)
Engstrom, K., Lundquist, A., Soderstrom, N.: Periodic thrombocytopenia or tidal platelet dysgenesis in a man. Scand. J. Haematol. 3, 290–(1966)
Fargue, D.: Reductibilité des systèmes héréditaires à des systémes dynamiques. Comptes Rendus de l’Académie des Sci B277, 471–473 (1973)
Fargue, D.: Reductibilité des systèmes héréditaires. Inter. J. Nonlinear Mech. 9, 331–338 (1974)
Fisher, G.: An introduction to chaos theory and some haematological applications. Comp. Haematol. Int. 3, 43–51 (1993)
Foley, C., Bernard, S., Mackey, M.: Cost-effective G-CSF therapy strategies for cyclical neutropenia: Mathematical modelling based hypotheses. J. Theor. Biol. 238, 754–763 (2006)
Fortin, P., Mackey, M.: Periodic chronic myelogenous leukemia: spectral analysis of blood cell counts and etiological implications. Brit. J. Haematol. 104, 336–245 (1999)
Glass, L., Mackey, M.: From Clocks to Chaos: The Rhythms of Life. Princeton University Press, Princeton (1988)
Gray, W., Kirk, J.: Analysis by analogue and digital computers of the bone marrow stem cell and platelet control mechanisms. In: Proceedings on conference on computers for analysis and control in medical and biological research, pp. 120–24. IEEE, UK (1971)
Grignani, F.: Chronic myelogenous leukemia. Crit. Rev. Oncology-Hematol 4, 31–66 (1985)
Guerry, D., Dale, D., Omine, D.C., Perry, S., Wolff, S.M.: Periodic hematopoiesis in human cyclic neutropenia. J. Clin. Invest. 52, 3220–3230 (1973)
Györi, I., Eller, J.: Modelling thrombopoiesis regulation II: Mathematical investigation of the model. Comput. Math. Appl. 14, 849–859 (1987)
Hammond, W.P., Price, T.H., Souza, L.M., Dale, D.C.: Treatment of cyclic neutropenia with granulocyte colony stimulating factor. N. Eng. J. Med. 320, 1306–1311 (1989)
Hardee, M.E., Arcasoy, M.O., Blackwell, K.L., Kirkpatrick, J.P., Dewhirst, M.W.: Erythropoietin biology in cancer. Clin. Cancer Res. 12(2), 332–39 (2006). doi:10.1158/1078-0432.CCR-05-1771 URL http://clincancerres.aacrjournals.org/cgi/content/abstract/12/2/332
Haurie, C., Dale, D.C., Rudnicki, R., Mackey, M.C.: Modeling complex neutrophil dynamics in the grey collie. J. Theor. Biol. 204, 504–519 (2000)
Haurie, C., Mackey, M.C., Dale, D.C.: Cyclical neutropenia and other periodic hematological diseases: a review of mechanisms and mathematical models. Blood 92, 2629–2640 (1998)
Haurie, C., Mackey, M.C., Dale, D.C.: Occurrence of periodic oscillations in the differential blood counts of congenital, idiopathic and cyclical neutropenic patients before and during treatment with G-CSF. Exp. Hematol. (1999)
Haurie, C., Person, R., Dale, D.C., Mackey, M.: Haematopoietic dynamics in grey collies. Exp. Hematol. 27, 1139–1148 (1999)
Hearn, T., Haurie, C., Mackey, M.: Cyclical neutropenia and the peripherial control of white blood cell production. J. Theor. Biol. 192, 167–181 (1998)
Henderson, E.S., Lister, T.A., Greaves, M.F. (eds.): Leukemia. Saunders (1996)
Hoffman, R., Bridell, R., van Besien, K., Srour, E., Guscar, T., Hudson, N., Ganser, A.: Acquired cyclic amegakaryocytic thrombocytopenia associated with an immunoglobulin blocking the action of granulocyte-macrophage colony-stimulating factor. N. Engl. J. Med. 321, 97–102 (1989)
Kaushansky, K., Lin, N., Grossmann, A., Humes, J., Sprugel, K., Broudy, V.: Thrombopoietin expands erythroid, granulocyte-macrophage, and megakaryocyte progenitor cells in normal and myelosuppressed mice. Exp. Hematol. 24, 256–269 (1996)
Kazarinoff, N.D., van den Driessche, P.: Control of oscillations in hematopoiesis. Science 203, 1348–1350 (1979)
Kearns, C.M., Wang, W.C., Stute, N., Ihle, J.N., Evans, W.E.: Disposition of recombinant human granulocyte colony stimulating factor in children with severe chronic neutropenia. J. Pediatr. 123, 471–479 (1993)
Kimura, F., Nakamura, Y., Sato, K., Wakimoto, N., Kato, T., Tahara, T., Yamada, M., Nagata, N., Motoyoshi, K.: Cyclic change of cytokines in a patient with cyclic thrombocytopenia. Br. J. Haematol. 94, 171–174 (1996)
King-Smith, E.A., Morley, A.: Computer simulation of granulopoiesis: normal and impaired granulopoiesis. Blood 36, 254–262 (1970)
Koury, M., Bondurant, M.: The mechanisms of erythropoietin action. Am. J. Kidney Dis. 18, 20–23 (1991)
Lasota, A., Mackey, M.: Global asymptotic properties of proliferating cell populations. J. Math. Biol. 19, 43–62 (1984)
Lewis, M.L.: Cyclic thrombocytopenia: a thrombopoietin deficiency. J. Clin. Path. 27, 242–246 (1974)
Loeffler, M., Pantel, K.: A mathematical model of erythropoiesis suggests an altered plasma volume control as cause for anemia in aged mice. Exp. Gerontol. 25, 483–495 (1990)
Loeffler, M., Pantel, K., Wulff, H., Wichmann, H.: A mathematical model of erythropoiesis in mice and rats, part i: Structure of the model. Cell Tissue Kinet. 22, 13–20 (1989)
Lord, B.I., Bronchud, M.H., Owens, S., Chang, J., Howell, A., Souza, L., Dexter, T.M.: The kinetics of human granulopoiesis following treatment with granulocyte colony stimulating factor in vivo. Proc. Natl. Acad. Sci. USA 86, 9499–9503 (1989)
MacDonald, N.: Cyclical neutropenia: Models with two cell types and two time lags. In: Valleron, A., Macdonald, P.(eds) Biomathematics and Cell Kinetics., pp. 287–295. Elsevier/North-Holland, Amsterdam (1978)
MacDonald, N.: Time Lags in Biological Models. Springer, Heidelberg (1978)
Mackey, M., Rudnicki, A.: Global stability in a delayed partial differential equation describing cellular replication. J. Math. Biol. 33, 89–109 (1994)
Mackey, M.C.: A unified hypothesis for the origin of aplastic anemia and periodic haematopoiesis. Blood 51, 941–956 (1978)
Mackey, M.C.: Dynamic haematological disorders of stem cell origin. In: Vassileva-Popova, J.G., Jensen, E.V.(eds) Biophysical and Biochemical Information Transfer in Recognition., pp. 373–409. Plenum, New York (1979)
Mackey, M.C.: Periodic auto-immune hemolytic anemia: an induced dynamical disease. Bull. Math. Biol. 41, 829–834 (1979)
Mackey, M.C., Glass, L.: Oscillations and chaos in physiological control systems. Science 197, 287–289 (1977)
Mahaffy, J., Belair, J., Mackey, M.: Hematopoietic model with moving boundary condition and state dependent delay: applications in erythropoiesis. J. Theor. Biol. 190, 135–146 (1998)
Mahaffy, J.M., Bélair, J., Mackey, M.: Hematopoietic model with moving boundary condition and state dependent delay. J. Theor. Biol. 190, 135–146 (1998)
Melo, J.: The diversity of BCR–ABL fusion proteins and their relationship to leukemia phenotype. Blood 88, 2375 (1996)
Mempel, K., Pietsch, T., Menzel, T., Zeidler, C., Welte, K.: Increased serum levels of granulocyte colony stimulating factor in patients with severe congenital neutropenia. Blood 77, 1919–1922 (1991)
Morley, A.: A platelet cycle in normal individuals. Aust. Ann. Med. 18, 127–129 (1969)
Morley, A.: Cyclic hemopoiesis and feedback control. Blood Cells 5, 283–296 (1979)
Morley, A., King-Smith, E.A., Stohlman, F.: The oscillatory nature of hemopoiesis. In: Stohlman, F. (ed.) Hemopoietic Cellular Proliferation, pp. 3–4. Grune & Stratton, New York (1969)
Morley, A., Stohlman, F.: Cyclophosphamide induced cyclical neutropenia. N. Engl. J. Med. 282, 643–646 (1970)
O’Dwyer, M., Druker, B.J., Mauro, M., Talpaz, M., Resta, D., Peng, B., Buchdunger, E., Ford, J., Reese, S.F., Capdeville, R., Sawyers, C.L.: STI571: a tyrosine kinase inhibitor for the treatment of CML. Ann. Oncol. 11, 155 (2000)
Orr, J.S., Kirk, J., Gray, K., Anderson, J.: A study of the interdependence of red cell and bone marrow stem cell populations. Br. J. Haematol. 15, 23–24 (1968)
Ostby, I., Kvalheim, G., Rusten, L.S., Grottum, P.: Mathematical modeling of granulocyte reconstitution after high-dose chemotherapy with stem cell support: effect of posttransplant G-CSF treatment. J. Theor. Biol. 231, 69–83 (2004)
Ostby, I., Rusten, L.S., Kvalheim, G., Grottum, P.: A mathematical model for reconstitution of granulopoiesis after high dose chemotherapy with autologous stem cell transplantation. J. Math. Biol. 47, 101–136 (2003)
Palmer, S.E., Stephens, K., Dale, D.C.: Genetics, phenotype, and natural history of autosomal dominant cyclichematopoiesis. Am. J. Med. Genet. 66, 413–422 (1996)
Price, T.H., Chatta, G.S., Dale, D.C.: Effect of recombinant granulocyte colony stimulating factor on neutrophil kinetics in normal young and elderly humans. Blood 88, 335–340 (1996)
Pujo-Menjouet, L., Bernard, S., Mackey, M.: Long period oscillations in a G 0 model of hematopoietic stem cells. SIAM J. Appl. Dyn. Syst. 4, 312–32 (2005)
Pujo-Menjouet, L., Mackey, M.: Contribution to the study of periodic chronic myelogenous leukemia. C. R. Biol. 327, 235–244 (2004)
Ranlov, P., Videbaek, A.: Cyclic haemolytic anaemia synchronous with Pel-Ebstein fever in a case of Hodgkin’s disease. Acta Med. Scand. 100 (1963)
Reeve, J.: An analogue model of granulopoiesis for the analysis of isotopic and other data obtained in the non-steady state. Br. J. Haematol. 25, 15–32 (1973)
Ritchie, A., Gotoh, A., Gaddy, J., Braun, S., Broxmeyer, H.: Thrombopoietin upregulates the promoter conformation of p53 in a proliferation-independent manner coincident with a decreased expression of bax: potential mechanisms for survival enhancing effects. Blood 90, 4394–4402 (1997)
Roeder, I.: Quantitative stem cell biology: computational studies in the hematopoietic system. Curr. Opin. Hematol. 13, 222–228 (2006)
Rubinow, S., Lebowitz, J.: A mathematical model of neutrophil production and control in normal man. J. Math. Biol. 1, 187–225 (1975)
Santillan, M., Mahaffy, J., Belair, J., Mackey, M.: Regulation of platelet production: the normal response to perturbation and cyclical platelet disease. J. Theor. Biol. 206, 585–603 (2000)
Schmitz, S.: Ein mathematisches modell der zyklischen haemopoese. Ph.D. thesis, Universitat Koln (1988)
Schmitz, S., Franke, H., Brusis, J., Wichmann, H.E.: Quantification of the cell kinetic effects of G-CSF using a model of human granulopoiesis. Exp. Hematol. 21, 755–760 (1993)
Schmitz, S., Franke, H., Loeffler, M., Wichmann, H.E., Diehl, V.: Reduced variance of bone-marrow transit time of granulopoiesis: a possible pathomechanism of human cyclic neutropenia. Cell Prolif. 27, 655–667 (1994)
Schmitz, S., Franke, H., Wichmann, H.E., Diehl, V.: The effect of continuous G-CSF application in human cyclic neutropenia: a model analysis. Br. J. Haematol. 90, 41–47 (1995)
Schmitz, S., Loeffler, M., Jones, J.B., Lange, R.D., Wichmann, H.E.: Synchrony of bone marrow proliferation and maturation as the origin of cyclic haemopoiesis. Cell Tissue Kinet. 23, 425–441 (1990)
Scholz, M., Engel, C., Loeffler, M.: Modelling human granulopoiesis under polychemotherapy with G-CSF support. J. Math. Biol. 50, 397–439 (2005)
Shvitra, D., Laugalys, R., Kolesov, Y.S.: Mathematical modeling of the production of white blood cells. In: G. Marchuk, L. Belykh (eds.) Mathematical Modeling in Immunology and Medicine, pp. 211–23. North-Holland, Amsterdam (1983)
Skomorovski, K., Agur, Z.: A new method for predicting and optimizing thrombopoietin (tpo) therapeutic protocols in thrombocytopenic patients and in platelet donors [abstract]. Hematol.J. Suppl 1, 185 (2001)
Skomorovski, K., Harpak, H., Ianovski, A., Vardi, M., Visser, T., Hartong, S., van Vliet, H.H., Wagemaker, G., Agur, Z.: New tpo treatment schedules of increased safety and efficacy: pre-clinical validation of a thrombopoiesis simulation model. Br. J. Haematol 123, 683–691 (2003)
Swinburne, J., Mackey, M.: Cyclical thrombocytopenia: characterization by spectral analysis and a review. J. Theor. Med. 2, 81–91 (2000)
Takatani, H., Soda, H., Fukuda, M., Watanabe, M., Kinoshita, A., Nakamura, T., Oka, M.: Levels of recombinant human granulocyte colony stimulating factor in serum are inversely correlated with circulating neutrophil counts. Antimicrob. Agents Chemother. 40, 988–991 (1996)
Vainstein, V., Ginosara, Y., Shohamb, M., Ranmara, D., Ianovskib, A., Agur, Z.: The complex effect of granulocyte colony-stimulating factor on human granulopoiesis analyzed by a new physiologically based mathematical model. J. Theor. Biol. 234(3), 311–327 (2005)
Viswanathan, S., Zandstra, P.W.: Towards predictive models of stem cell fate. Cytotechnology 41, 75–92 (2003)
von Schulthess, G.K., Mazer, N.A.: Cyclic neutropenia (CN): a clue to the control of granulopoiesis. Blood 59, 27–37 (1982)
von Schulthess, G., Gessner, U.: Oscillating platelet counts in healthy individuals: experimental investigation and quantitative evaluation of thrombocytopoietic feedback control. Scand. J. Haematol. 36, 473–479 (1986)
Watari, K., Asano, S., Shirafuji, N., Kodo, H., Ozawa, K., Takaku, F., Kamachi, S.: Serum granulocyte colony stimulating factor levels in healthy volunteers and patients with various disorders as estimated by enzyme immunoassay. Blood 73, 117–122 (1989)
Webb, G.: Theory of nonlinear age-dependent population dynamics. Monographs and Textbooks in Pure and Applied Mathematics, no. 89 (1985)
Wichmann, H., Gerhardts, M., Spechtmeyer, H., Gross, R.: A mathematical model of thrombopoiesis in the rat. Cell Tissue Kinet. 12, 551–567 (1979)
Wichmann, H.E., Loeffler, M., Schmitz, S.: A concept of hemopoietic regulation and its biomathematical realization. Blood Cells 14, 411–429 (1988)
Yanabu, M., Nomura, S., Fukuroi, T., Kawakatsu, T., Kido, H., Yamaguchi, K., Suzuki, M., Kokawa, T., Yasunaga, K.: Periodic production of antiplatelet autoantibody directed against GP IIIa in cyclic thrombocytopenia. Acta Haematol. 89, 155–159 (1993)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Foley, C., Mackey, M.C. Dynamic hematological disease: a review. J. Math. Biol. 58, 285–322 (2009). https://doi.org/10.1007/s00285-008-0165-3
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00285-008-0165-3