Understanding and Treating Cytopenia Through Mathematical Modeling

Chapter
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 844)

Abstract

Here, we briefly review how the study of dynamic hematological diseases with mathematical modeling tools has led to a better understanding of the origin of some types of neutropenia and thrombocytopenia and to improved treatment strategies. In addition, we have briefly discussed how these models suggest improved ways to minimize and/or treat cytopenia induced by chemotherapy.

Keywords

Anemia Chemotherapy Granulocyte colony-stimulating factor Neutropenia Thrombocytopenia Thrombopoietin 

Notes

Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council (NSERC, Canada) and the Mathematics of Information Technology and Complex Systems (MITACS, Canada), and carried out in Beijing and Montreal.

References

  1. 1.
    Glass L, Mackey MC. From clock to chaos. Princeton: Princeton University Press; 1988.Google Scholar
  2. 2.
    Foley C, Bernard S, Mackey MC. Cost-effective G-CSF therapy strategies for cyclical neutropenia: mathematical modeling based hypotheses. J Theor Biol. 2006;238:754–63. doi:10.1016/j.jtbi.2005.06.021.PubMedCrossRefGoogle Scholar
  3. 3.
    Colijn C, Mackey MC. A mathematical model of hematopoiesis: II. cyclical neutropenia. J Theor Biol. 2005;237:133–46.PubMedCrossRefGoogle Scholar
  4. 4.
    Haurie C, Dale DC, Mackey MC. Cyclical neutropenia and other periodic hematological diseases: a review of mechanisms and mathematical models. Blood. 1998;92:2629–40.PubMedGoogle Scholar
  5. 5.
    Haurie C, Dale DC, Mackey MC. 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;27:401–9.PubMedCrossRefGoogle Scholar
  6. 6.
    Haurie C, Dale DC, Rudnicki R, Mackey MC. Modeling complex neutrophil dynamics in the grey collie. J Theor Biol. 2000;204:505–19.PubMedCrossRefGoogle Scholar
  7. 7.
    Fortin P, Mackey MC. Periodic chronic myelogenous leukaemia: spectral analysis of blood cell counts and aetiological implications. Br J Haematol. 1999;104:336–45.PubMedCrossRefGoogle Scholar
  8. 8.
    Mackey MC, Glass L. Oscillation and chaos in physiological control systems. Science. 1977;197:287–9.PubMedCrossRefGoogle Scholar
  9. 9.
    Swinburne J, Mackey MC. Cyclical thrombocytopenia: characterization by spectral analysis and a review. J Theor Med. 2000;2:81–91.CrossRefGoogle Scholar
  10. 10.
    Apostu R, Mackey MC. Understanding cyclical thrombocytopenia: a mathematical modeling approach. J Theor Biol. 2008;251:297–316.PubMedCrossRefGoogle Scholar
  11. 11.
    Hsieh MM, Everhart JE, Byrd-Holt DD, Tisdale JF, Rodgers GP. Prevalence of neutropenia in the U.S. population: age, sex, smoking status, and ethnic differences. Ann Intern Med. 2007;146:486–92.PubMedCrossRefGoogle Scholar
  12. 12.
    Gill M, Ockelford P, Morris A, Bierre T, Kyle C. Diagnostic handbook-the interpretation of laboratory tests. Auckland: Diagnostic Medlab; 2000.Google Scholar
  13. 13.
    Haurie C, Person R, Dale DC, Mackey MC. Hematopoietic dynamics in grey collies. Exp Hematol. 1999;27:1139–48.PubMedCrossRefGoogle Scholar
  14. 14.
    Reimann HA, de Beradinis CT. Periodic(cyclic) neutropenia. an entity. A collection of sixteen cases. Blood. 1949;4:1109–16.PubMedGoogle Scholar
  15. 15.
    Morley AA, Carew JP, Baikie AG. Familial cyclical neutropenia. Br J Haematol. 1967;13:719–38.PubMedCrossRefGoogle Scholar
  16. 16.
    Palmer SE, Stephens K, Dale DC. Genetics, phenotype, and natural history of autosomal dominant cyclic hematopoiesis. Am J Med Genet. 1996;88:335–40.Google Scholar
  17. 17.
    Norwitz M, Benson K, Person R, Aprikyan A, Dale D. Mutations in ELA2, encoding neutrophil elastase, define a 21-day biological clock in cyclic haematopoiesis. Nat Genet. 1999;23:433–6.CrossRefGoogle Scholar
  18. 18.
    Cohen T, Cooney DP. Cyclical thrombocytopenia: case report and review of literature. Scand J Haemat. 1974;16:133–8.Google Scholar
  19. 19.
    Beutler E, Lichtman MA, Coller BS, Kipps T. Williams hematology. New York: McGraw-Hill; 1995.Google Scholar
  20. 20.
    Balduini C, Stella C, Rosti V, Bertolino G, Noris P, Ascari E. Acquired cyclic thrombocytopenia thrombocytosis with periodic defect of platelet function. Brit J Haematol. 1993;85:718–22.CrossRefGoogle Scholar
  21. 21.
    Bernard J, Caen J. Purpura thrombopénique et megacaryocytopénie cycliques mensuels. Nouv Rev franc Hémat. 1962;2:378–86.PubMedGoogle Scholar
  22. 22.
    Dan K, Inokuchi K, An E, Nomura T. Cell mediated cyclic thrombocytopenia treated with azathioprine. Brit J Haematol. 1991;77:365–79.CrossRefGoogle Scholar
  23. 23.
    Engstrom K, Lundquist A, Soderstrom N. Periodic thrombocytopenia or tidal platelet dysgenesis in a man. Scand J Haemat. 1966;3:290–2.PubMedCrossRefGoogle Scholar
  24. 24.
    Hoffman R, Bridell RA, van Besien K, Srour EF, Guscar T, Hudson NW, et al. Acquired cyclic amegakaryocytic thrombocytopenia associated with an immunoglobulin blocking the action of granulocyte-macrophage colony-stimulating factor. N Engl J Med. 1989;321:97–102.PubMedCrossRefGoogle Scholar
  25. 25.
    Lewis ML. Cyclical Thrombocytopenia: a thrombopoietin deficiency? J Clin Path. 1974;27:242–6.PubMedCentralPubMedCrossRefGoogle Scholar
  26. 26.
    Kimura F, Nakamura Y, Sato K, Wakimoto N, Kato T, Tahara T, et al. Cyclic change of cytokines in a patient with cyclic thrombocytopenia. Br J Haemat. 1996;94:171–4.CrossRefGoogle Scholar
  27. 27.
    Santillán M, Bélair J, Mahaffy JM, Mackey MC. Regulation of platelet production: the normal response to perturbation and cyclical platelet disease. J Theor Biol. 2000;206:585–603. doi:10.1006/jtbi.2000.2149.PubMedCrossRefGoogle Scholar
  28. 28.
    Ranlov P, Videbaek A. Cyclic haemolytic anaemia synchronous with Pel-Ebstein fever in a case of Hodgkin’s disease. Acta Medica Scandinavica. 1963;100.Google Scholar
  29. 29.
    Gordon RR, Varadi S. Congenital hypoplastic anemia (pure red-cell anemia) with periodic erythroblastopenia. Lancet. 1962;1:296–9.PubMedCrossRefGoogle Scholar
  30. 30.
    Gurney CW, Simmons EL, Gaston EO. Cyclic erythropoiesis in W/Wv mice following a single small dose of 89Sr. Exp Hemat. 1981;9:118–22.PubMedGoogle Scholar
  31. 31.
    Gibson CM, Gurney CW, Gaston EO, Simmons EL. Cyclic erythropoiesis in the S1/S1d mouse. Exp Hemat. 1984;12:343–8.PubMedGoogle Scholar
  32. 32.
    Gibson CM, Gurney CW, Simmons EL, Gaston EO. Further studies on cyclic erythropoiesis in mice. Exp Hemat. 1985;13:855–60.PubMedGoogle Scholar
  33. 33.
    Vácha J, Znojil V. Application of a mathematical model of erythropoiesis to the process of recovery after acute X-irradiation of mice. Biofizika. 1975;20:872–9.PubMedGoogle Scholar
  34. 34.
    Vácha J. Postirradiational oscillations of erythropoiesis in mice. Acta Sc Nat Brno. 1982;16(2):1–52.Google Scholar
  35. 35.
    Orr JS, Kirk J, Gray KG, Anderson JR. A study of the interdependence of red cell and bone marrow stem cell populations. Br J Haemat. 1968;15:23–4.CrossRefGoogle Scholar
  36. 36.
    Mackey MC. Periodic auto-immune hemolytic anemia: an induced dynamical disease. Bull Math Biol. 1979;41:829–34.PubMedCrossRefGoogle Scholar
  37. 37.
    O’Dwyer M, Druker BJ, Mauro M, Talpaz M, Resta D, Peng B, et al. STI571: a tyrosine kinase inhibitor for the treatment of CML. Ann Oncol. 2000;11:155.CrossRefGoogle Scholar
  38. 38.
    Melo J. The diversity of BCR-ABL fusion proteins and their relationship to leukemia phenotype. Blood. 1996;88:2375.PubMedGoogle Scholar
  39. 39.
    Grignani F. Chronic myelogenous leukemia. Crit Rev Oncol Hematol. 1985;4:31–66.PubMedCrossRefGoogle Scholar
  40. 40.
    Henderson ES, Lister TA, Greaves MF, editors. Leukemia. Philadelphia: Saunders; 1996.Google Scholar
  41. 41.
    Foley C, Mackey MC. Dynamic hematological disease: a review. J Math Biol. 2009;58:285–322.PubMedCrossRefGoogle Scholar
  42. 42.
    Wichard ZL, Sarkar CA, Kimmel M, Corey SJ. Hematopoiesis and its disorders: a systems biology approach. Blood. 2011;115:2339–47.CrossRefGoogle Scholar
  43. 43.
    Mackey MC, Haurie C, Bélair J. Cell replication and control. In: Beuter A, Glass L, Mackey MC, Titcombe MS, editors. Nonlinear dynamics in physiology and medicine. New York: Springer; 2003, pp. 233–69.CrossRefGoogle Scholar
  44. 44.
    Lei J, Mackey MC. Multistability in an age-structured model of hematopoiesis: cyclical neutropenia. J Theor Biol. 2011;270:143–53.PubMedCrossRefGoogle Scholar
  45. 45.
    Mackey MC. Unified hypothesis for the origin of aplastic anemia and periodic haematopiesis. Blood. 1978;51:941–56.PubMedGoogle Scholar
  46. 46.
    Mackey MC. Mathematical models of hematopoietic cell replication and control. In: Othmer H, Adler F, Lewis M, Dallon J, editors. Case studies in mathematical modeling-ecology, physiology, and cell biology. New Jersey: Prentice-Hall; 1996. pp. 149–78.Google Scholar
  47. 47.
    Hoffbrand AV, Pettit JE, Moss PAH. Essential haematology. 4th ed. Milan: Blackwell Science; 2011.Google Scholar
  48. 48.
    Mahaffy JM, Bélair J, Mackey MC. Hematopoietic model with moving boundary condition and state dependent delay: application in erythropoiesis. J Theor Biol. 1998;190:135–46.PubMedCrossRefGoogle Scholar
  49. 49.
    Bélair J. Mackey MC. A model for the regulation of mammalian platelet. Ann N Y Acad Sci. 1987;504:280–2.CrossRefGoogle Scholar
  50. 50.
    Adamson JW. The relationship of erythropoietin and iron metabolism to red blood cell production in humans. Semin Oncol. 1994;2:9–15.Google Scholar
  51. 51.
    Price TH, Chatta GS, Dale DC. Effect of recombinant granulocyte colony-stimulating factor on neutrophil kinetics in normal young and elderly humans. Blood. 1996;88:335–40.PubMedGoogle Scholar
  52. 52.
    Ratajczak MZ, Ratajczak J, Marlicz W, Jr Pletcher WC, Machalinshi B, Moore J, et al. Recombinant human thrombopoietin(TPO) stimulates erythropoiesis by inhibiting erythroid progenitor cell apoptosis. Br J Haematol. 1997;98:8–17.PubMedCrossRefGoogle Scholar
  53. 53.
    Tanimukai S, Kimura T, Stakabe H, Ohmizono Y, Kato T, Miyazaki H, et al. Recomninant human c-Mpl ligand (thrombopoietin) not only acts on megakaryocyte progenitors, but also on erythroid and multipotential progenitors in vitro. Exp Hematol. 1997;25:1025–33.PubMedGoogle Scholar
  54. 54.
    Silva M, Grillot D, Benito A, Richard C, Nunez G, Fernandez-Luna J. Erythropoietin can promote erythroid progenitor survival by repressing apoptosis through bcl-1 and bcl-2. Blood. 1996;88:1576–82.PubMedGoogle Scholar
  55. 55.
    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. 1997;90:4394–402.PubMedGoogle Scholar
  56. 56.
    Kaushansky K, Lin N, Grossmann A, Humes J, Sprugel K, Broudy V. Thrombopoietin expands erythoid, granulocyte-macrophage, and megakaryocyte progenitor cells in normal and myelosuppressed mice. Exp Hematol. 1996;24:256–69.Google Scholar
  57. 57.
    Kearns CM, Wang WC, Stute N, Ihle J, Evans W. Disposition of recombinant human granulocyte colony-stimulating factor in children with severe chronic neutropenia. J Pediatr. 1993;123(3):471–9.PubMedCrossRefGoogle Scholar
  58. 58.
    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. 1991;77:1919–22.PubMedGoogle Scholar
  59. 59.
    Takatani H, Soda H, Fukuda M, Watanabe M, Kinoshita A, Nakamura T, et al. Levels of recombinant human granulocyte colony stimulating factor in serum are inversely correlated with circulating neutrophil counts. Antimicrob Agents Chemother. 1996;40:988–91.PubMedCentralPubMedGoogle Scholar
  60. 60.
    Watari K, Asano S, Shirafuji N, Kodo H, Ozawa K, Takaku F, et al. Serum granulocyte colony stimulating factor levels in healthy volunteers and patients with various disorders as estimated by enzyme immunoassay. Blood. 1989;73:117–22.PubMedGoogle Scholar
  61. 61.
    Roeder I. Quantitative stem cell biology: computational studies in the hematopoietic system. Curr Opin Hematol. 2006;13:222–8.PubMedCrossRefGoogle Scholar
  62. 62.
    Viswanathan S, Zandstra PW. Towards predicitive models of stem cell fate. CytoTechnol. 2003;41:75–92.CrossRefGoogle Scholar
  63. 63.
    Bélair J, Mackey MC, Mahaffy JM. Age-structuredand two-delay models for erythropoiesis. Math Biosci. 1995;128:317–46.PubMedCrossRefGoogle Scholar
  64. 64.
    Colijn C, Mackey MC. A mathematical model of hematopoiesis: I. periodic chronic myelogenous leukemia. J Theor Biol. 2005;237:117–32.PubMedCrossRefGoogle Scholar
  65. 65.
    Foley C, Mackey MC. Mathematical model for G-CSF administration after chemotherapy. J Theor Biol. 2009;257:27–44.PubMedCrossRefGoogle Scholar
  66. 66.
    Brooks G, Provencher-Langlois G, Lei J, Mackey MC. Neutrophil dynamics after chemotherapy and G-CSF: the role of pharmacokinetics in shaping the response. J Theor Biol. 2012;315:97–109.PubMedCrossRefGoogle Scholar
  67. 67.
    Colijn C, Dale DC, Foley C, Mackey MC. Observations on the pathophysiology and mechanisms for cyclic neutropenia. Math Model Nat Phenomena. 2006;1:45–69.CrossRefGoogle Scholar
  68. 68.
    Dunn CDR. Cyclical hematopoiesis: the biomathematics. Exp Hematol. 1983;11:779–91.PubMedGoogle Scholar
  69. 69.
    Fisher G. An introduction to chaos theory and some haematological applications. Comp Haematol Int. 1993;3:43–51.CrossRefGoogle Scholar
  70. 70.
    Kazarinoff ND, van den Driessche P. Control of oscillations in hematopoiesis. Science. 1979;203:1348–50.PubMedCrossRefGoogle Scholar
  71. 71.
    King-Smith EA, Morley A. Computer simulation of granulopoiesis: normal and impaired granulopoiesis. Blood. 1970;36:254–62.PubMedGoogle Scholar
  72. 72.
    MacDonald N. Cyclical neutropenia: models with two cell types and two time lags. In: Valleron AJ, Macdonald PDM, editors. Biomathematics and cell kinetics. Amsterdam: Elsevier; 1978. pp. 287–95.Google Scholar
  73. 73.
    Morley A. A platelet cycle in normal individuals. Aust Ann Med. 1969;18:127–9.PubMedGoogle Scholar
  74. 74.
    Morley A. Blood-cell cycles in polycythaemia vera. Aust Ann Med. 1969;18:124.PubMedGoogle Scholar
  75. 75.
    Morley A, Stohlman F. Cyclophosphamide induced cyclical neutropenia. N Engl J Med. 1970;282:643–6.PubMedCrossRefGoogle Scholar
  76. 76.
    Morley A. Cyclic hemopoiesis and feedback control. Blood Cells.1979;5:283–96.PubMedGoogle Scholar
  77. 77.
    Reeve J. An analogue model of granulopoiesis for the analysis of isotopic and other data obtained in the non-steady state. Br J Haematol. 1973;25:15–32.PubMedCrossRefGoogle Scholar
  78. 78.
    Schmitz S. Ein mathematisches Modell der zyklischen Haemopoese. Ph.D thesis, Universitat Koln; 1988.Google Scholar
  79. 79.
    Schmitz S, Franke H, Brusis J, Wichmann HE. Quantification of the cell kinetic effects of G-CSF using a model of human granulopoiesis. Exp Hematol. 1993;21:755–60.PubMedGoogle Scholar
  80. 80.
    Schmitz S, Franke H, Loeffler M, Wichmann HE, Diehl V. Reduced variance of bone-marrow transit time of granulopoiesis: a possible pathomechanism of human cyclic neutropenia. Cell Prolif. 1994;27:655–67.CrossRefGoogle Scholar
  81. 81.
    Schmitz S, Loeffler M, Jones JB, Lange RD, Wichmann HE. Synchrony of bone marrow proliferation and maturation as the origin of cyclic haemopoiesis. Cell Tissue Kinet. 1990;23:425–41.PubMedGoogle Scholar
  82. 82.
    Schmitz S, Franke H, Wichmann HE, Diehl V. The effect of continuous G-CSF application in human cyclic neutropenia: a model analysis. Br J Haematol. 1995;90:41–7.PubMedCrossRefGoogle Scholar
  83. 83.
    Shvitra D, Laugalys R, Kolesov YS. Mathematical modeling of the production of white blood cells. In: Marchuk G, Belykh LN, editors. Mathematical modeling in immunology and medicine. Amsterdam: North-Holland; 1983. pp. 211–23.Google Scholar
  84. 84.
    von Schulthess GK, Mazer NA. Cyclic neutropenia(CN): a clue to the control of granulopoiesis. Blood. 1982;59:27–37.PubMedGoogle Scholar
  85. 85.
    Wichmann HE, Loeffler M, Schmitz S. A concept of hemopoietic regulation and its biomathematical realization. Blood Cells.1988; 14:411–29.PubMedGoogle Scholar
  86. 86.
    Hearn T, Haurie C, Mackey MC. Cyclical neutropenia and the peripherial control of white blood cell production. J Theor Biol. 1998;192:167–81.PubMedCrossRefGoogle Scholar
  87. 87.
    Bernard S, Bélair J, Mackey MC. Oscillations in cyclical neutropenia: new evidence based on mathematical modeling. J Theor Biol. 2003;223:283–98. doi:10.1016/S0022-5193(03)00090-0.PubMedCrossRefGoogle Scholar
  88. 88.
    Colijn C, Foley C, Mackey MC. G-CSF treatment of canine cyclical neutropeina: a comprehensive mathematical model. Exp Hematol. 2007;37:898–907.CrossRefGoogle Scholar
  89. 89.
    Santillan M, Mahaffy JM, Bélair J, Mackey MC. Regulation of platelet productin: the normal response to perturbation and cyclical platelet disease. J Theor Biol. 2000;206:585–603.PubMedCrossRefGoogle Scholar
  90. 90.
    Zhuge C, Lei J, Mackey MC. Neutrophil dynamics in response to chemotherapy and G-CSF. J Theor Biol. 2012;293:111–20.PubMedCrossRefGoogle Scholar
  91. 91.
    Hannun Y. Apoptosis and the dilemma of cancer chemotherapy. Blood. 1997;89:1845–53.PubMedGoogle Scholar
  92. 92.
    Hammond WP, Price TH, Souza LM, Dale DC. Treatment of cyclic neutropenia with granulocyte colony stimulating factor. N Engl J Med. 1989;320:1306–11.PubMedCrossRefGoogle Scholar
  93. 93.
    Koury MJ. Programmed cell death(apoptosis) in hematopoiesis. Exp Hematol. 1992;20:391–4.PubMedGoogle Scholar
  94. 94.
    Park JR. Cytokine regulation of apoptosis in hematopoietic precursor cells. Curr Opin Hematol. 1996;3:191–6.PubMedCrossRefGoogle Scholar
  95. 95.
    Migliaccio AR, Migliaccio G, Dale DC, Hammond WP. Hematopoietic progenitors in cyclic neutropenia: effect of granulocyte colony stimulating factor in vivo. Blood. 1990;75:1951–9.PubMedGoogle Scholar
  96. 96.
    Williams G, Smith C. Molecular regulation of apoptosis: genetic controls on cell death. Cell. 1993;74:777–9.PubMedCrossRefGoogle Scholar
  97. 97.
    Crawford J, Dale DC, Lyman GH. Chemotherapy-induced neutropenia: risks, consequences, and new directions for its management. Cancer. 2003;100:228–37.CrossRefGoogle Scholar
  98. 98.
    Ozer H, Armitage JO, Bennett CL, et al. Update of recommendations for the use of hematopoietic colony-stimulating factors: evidence-based, clinical practice guidelines. J Clin Oncol. 2000;18:3558–85.PubMedGoogle Scholar
  99. 99.
    Clark OA, Lyman GH, Castro AA, Clark LG, Djulbegovic B. Colony-stimulating factors for chemotherapy-induced febrile neutropenia: a meta-analysis of randomized controlled trials. J Clin Oncol. 2005;23:4198–214.PubMedCrossRefGoogle Scholar
  100. 100.
    Bennett CL, Weeks JA, et al. Use of hematopoietic colony-stimulating factors: comparison of the 1994 and 1997 American Society of Clinical Oncology surveys regarding ASCO clinical practice guidelines. Health Services Research Committee of the American Society of Clinical Oncology. J Clin Oncol. 1999;17:3676–81.PubMedGoogle Scholar

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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Zhou Pei-Yuan Center for Applied MathematicsTsinghua UniversityBeijingChina
  2. 2.Department of Physiology and CAMBAMMonteralCanada

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