Hemomath pp 295-330 | Cite as

Blood and Cancer

  • Antonio Fasano
  • Adélia Sequeira
Part of the MS&A book series (MS&A, volume 18)


In this chapter we will deal with the aspects which are specific to blood cancer, avoiding to broaden our analysis to the general area of modeling tumor growth and therapy, which is huge, though it includes many subjects involving blood too (like angiogenesis and tumors perfusion, drugs delivery to tumors, etc.) which occupy a large space in the literature of mathematical modeling of tumors. Even the restricted field of modeling leukemic disorders is extremely large for the great variety of the subjects and of the approaches that have been adopted in the literature. The reader will realize the impressive complexity of the present topic already from the sketchy classification of leukemic disorders in Sect. 8.2.


  1. 1.
    J.A. Adam, N. Bellomo (eds.), A Survey of Models for Tumor-Immune System Dynamics (MSSET Birkhäuser, Boston, 1997)zbMATHGoogle Scholar
  2. 2.
    Z. Agur, S. Vuk-Pavlovi, Mathematical modeling in immunotherapy of cancer: personalizing clinical trials. Mol. Ther. 20(1), 1–2 (2012)CrossRefGoogle Scholar
  3. 3.
    Z. Agur, Y. Daniel, Y. Ginosar, The universal properties of stem cells as pinpointed by a simple discrete model. J. Math. Biol. 44(1), 79–86 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Z. Agur, M. Elishmereni, Y. Kogan, Y. Kheifetz, I. Ziv, M. Shoham, V. Vainstein, Mathematical modeling as a new approach for improving the efficacy/toxicity profile of drugs: the thrombocytopenia case study, in Preclinical Development Handbook: ADME and Biopharmaceutical Properties, ed. by S.C. Gad, chap. 36 (Wiley, New York, 2008)Google Scholar
  5. 5.
    W.C. Aird, Discovery of the cardiovascular system: from Galen to William Harvey. J. Thromb. Haemost. 9(Suppl. s1), 118–129 (2011)Google Scholar
  6. 6.
    K. Akashi, Lineage promiscuity and plasticity in hematopoietic development. Ann. N. Y. Acad. Sci. 1044, 125–131 (2005)CrossRefGoogle Scholar
  7. 7.
    S. Balamuralitharan, S. Rajasekaran, A parameter estimation model of G-CSF: mathematical model of cyclical neutropenia. Am. J. Comput. Math. 2, 12–20 (2012)CrossRefGoogle Scholar
  8. 8.
    A.J. Becker, E. McCulloch, J. Till, Cytological demonstration of the clonal nature of spleen colonies derived from transplanted mouse marrow cells. Nature 197, 452–454 (1963)CrossRefGoogle Scholar
  9. 9.
    J. Bélair, J.M. Mahaffy, Variable maturation velocity and parameter sensitivity in a model of haematopoiesis. IMA J. Math. Appl. Med. Biol. 18, 193–211 (2001)zbMATHCrossRefGoogle Scholar
  10. 10.
    N. Bellomo, A. Bellouquid, M. Delitala, Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition. Math. Models Methods Appl. Sci. 14, 1683–1733 (2004)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    J.H. Bennett, Leucocythemia (1845). Clinical Lectures on the Principles and Practice of Medicine, Last Edinburgh edn., (S. Samuel & W. Wood, New York, 1860), pp. 814–1844Google Scholar
  12. 12.
    J.M. Bennett, D. Catovsky, M.T. Daniel, et al., Proposals for the classification of chronic (mature) B and T lymphoid leukaemias. French-American-British (FAB) Cooperative Group. J. Clin. Pathol. 42(6), 567–584 (1989)Google Scholar
  13. 13.
    E. Beretta, V. Capasso, A. Harel-Bellan, N. Morozova, Some results on the population behavior of cancer stem cells, in New Challenges for Cancer Systems Biomedicine, ed. by A. D’Onofrio, P. Cerrai, A. Gandolfi (Springer, Berlin, 2013), pp. 145–172Google Scholar
  14. 14.
    N. Bessonov, I. Demin, L. Pujo-Menjouet, V. Volpert, A multi-agent model describing self-renewal of differentiation effects on the blood cell population. Math. Comput. Model. 49, 2116–2127 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    G. Bizzozero, Sulla funzione ematopoetica del midollo delle ossa. Zentralbl. Med. Wiss. 6, 885 (1868)Google Scholar
  16. 16.
    G. Bizzozero, Sulla funzione ematopoetica del midollo delle ossa, seconda comunicazione preventiva. Zentralbl. Med. Wiss. 10, 149–150 (1869)Google Scholar
  17. 17.
    I. Borsi, A. Fasano, M. Primicerio, T. Hillen, Mathematical properties of a non-local integro-PDE model for cancer stem cells. Math. Med. Biol. 34, 59–75 (2015)Google Scholar
  18. 18.
    L. Brent, A History of Transplantation Immunology (Academic Press, London, 1997)Google Scholar
  19. 19.
    E. Campo, S.H. Swerdlow, N.L. Harris, S. Pileri, H. Stein, E.S. Jaffe, The 2008 WHO classification of lymphoid neoplasms and beyond: evolving concepts and practical applications. Blood 117(19), 5019–5032 (2011)CrossRefGoogle Scholar
  20. 20.
    A. Cappuccio, M. Elishmereni, Z. Agur, Cancer immunotherapy by Interleukin-21: potential treatment strategies evaluated in a mathematical model. Cancer Res. 66, 7293–7300 (2006)CrossRefGoogle Scholar
  21. 21.
    N. Chiorazzi, K.R. Rai, M. Ferrarini, Chronic lymphocytic leukemia. N. Engl. J. Med. 352, 804–815 (2015)CrossRefGoogle Scholar
  22. 22.
    C. Colijn, M.C. Mackey, A mathematical model of hematopoiesis - I. Periodic chronic myelogenous leukemia. J. Theor. Biol. 237, 117–132 (2005)Google Scholar
  23. 23.
    C. Colijn, M.C. Mackey, A mathematical model of hematopoiesis - II. Cyclical neutropenia. J. Theor. Biol. 237, 133–146 (2005)MathSciNetCrossRefGoogle Scholar
  24. 24.
    C. Colijn, C. Foley, M.C. Mackey, G-CSF treatment of canine cyclical neutropenia: a comprehensive mathematical model. Exp. Hematol. 35, 898–907 (2007)CrossRefGoogle Scholar
  25. 25.
    D. Coombs, O. Dushek, P.A. van der Merwe, A review of mathematical models for T cell receptor triggering and antigen discrimination, in Mathematical Models and Immune Cell Biology, Chap. 2, ed. by C. Molina-París, G. Lythe, (Springer, New York, 2011), pp. 25–45CrossRefGoogle Scholar
  26. 26.
    R. DeConde, P.S. Kim, D. Levy, P.P. Lee, Post-transplantation dynamics of the immune response to chronic myelogenous leukemia. J Theor. Biol. 236, 9–59 (2005)MathSciNetCrossRefGoogle Scholar
  27. 27.
    M.T. de la Morena, R.A. Gatti, A history of bone marrow transplantation. Hematol. Oncol. Clin. North Am. 25, 1–15 (2011)CrossRefGoogle Scholar
  28. 28.
    L.G. de Pillis, W. Gu, A.E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J. Theor. Biol. 238(4), 841–862 (2006)MathSciNetCrossRefGoogle Scholar
  29. 29.
    D. Dingli, F. Michor, Successful therapy must eradicate cancer stem cells. Stem Cells 24(12), 2603–2610 (2006)CrossRefGoogle Scholar
  30. 30.
    D. Dingli, J.M. Pacheco, Modeling the architecture and dynamics of hematopoiesis. Wiley Interdiscip. Rev. Syst. Biol. Med. 2, 235–244 (2010)CrossRefGoogle Scholar
  31. 31.
    D. Dingli, A. Traulsen, J.M. Pacheco, Compartmental architecture and dynamics of hematopoiesis. PLoS ONE 2, e345 (2007)CrossRefGoogle Scholar
  32. 32.
    T. Dittmar, K.S. Zänker, Role of Cancer Stem Cells in Cancer Biology and Therapy (CRC Press, Boca Raton, FL, 2013)Google Scholar
  33. 33.
    A. d’Onofrio, A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences. Physica D 208, 220–235 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  34. 34.
    A. d’Onofrio, U. Ledzkevicz, H. Schättler, On the dynamics of tumor-immune system interaction and combined chemo- and immunotheratpy, in New Challenges for Cancer Systems Biomedicine, ed. by A. D’Onofrio, P. Cerrai, A. Gandolfi (Springer, Mailand, 2013), pp. 249–266Google Scholar
  35. 35.
    M. Doumic-Jauffret, P.S. Kim, B. Perthame, Stability analysis of a simplified yet complete model for chronic myelogenous leukemia. Bull. Math. Biol. 72, 1732–1759 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  36. 36.
    B.J. Druker, S. Tamura, E. Buchdunger, S. Ohno, G.M. Segal, S. Fanning, J. Zimmermann, N.B. Lydon, Effects of a selective inhibitor of the Abl tyrosine kinase on the growth of Bcr-Abl positive cells. Nat. Med. 2, 561–566 (1996)CrossRefGoogle Scholar
  37. 37.
    H. Enderling, A.R.A. Anderson, M.A.J. Chaplain, A. Beheshti, L. Hlatky, P. Hahnfeldt, Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res. 69(22), 8814–8821 (2009)CrossRefGoogle Scholar
  38. 38.
    M.A. Essers, A Trumpp, Targeting leukemic stem cells by breaking their dormancy. Mol. Oncol. 4, 443–450 (2010)Google Scholar
  39. 39.
    A. Fasano, A. Mancini, M. Primicerio. Tumours with cancer stem cells: a PDE model. Math. Biosci. 272, 76–80 (2016)zbMATHMathSciNetCrossRefGoogle Scholar
  40. 40.
    T.M. Fliedner, D. Graessle, C. Paulsen, K. Reimers, Structure and function of bone marrow hemopoiesis: mechanisms of response to ionizing radiation exposure. Cancer Biother. Radiopharm. 17, 405–426 (2002)CrossRefGoogle Scholar
  41. 41.
    C. Foley, M.C. Mackey, Dynamic hematological disease: a review. J. Math. Biol. 58, 285–322 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  42. 42.
    C. Foley, S. Bernard, M.C. Mackey, Cost-effective G-CSF therapy strategies for cyclical neutropenia: mathematical modelling based hypotheses. J. Theor. Biol. 238, 754–763 (2007)CrossRefGoogle Scholar
  43. 43.
    J. Foo, M.W. Drummond, B. Clarkson, T. Holyoake, F. Michor, Eradication of chronic myeloid leukemia stem cells: a novel mathematical model predicts no therapeutic benefit of adding G-CSF to imatinib. PLoS Comput. Biol. e1000503 (2009). doi:10.1371/journal.pcbi.1000503Google Scholar
  44. 44.
    X. Gao, J.T. McDonald, L. Hlatky, H. Enderling, Cell interaction in solid tumors: the role of cancer stem cells, in New Challenges for Cancer Systems Biomedicine, ed. by A. D’Onofrio, P. Cerrai, A. Gandolfi (Springer, New York, 2013), pp. 191–204Google Scholar
  45. 45.
    I. Glauche, M. Horn, I. Roeder, Leukaemia stem cells: hit or miss? Br. J. Cancer 96, 677–678 (2007)CrossRefGoogle Scholar
  46. 46.
    M. Greaves, Return of the malingering mutants. Br. J. Cancer 109, 1391–1393 (2013)CrossRefGoogle Scholar
  47. 47.
    A. Halanay, D. Cândea, I.R. Rǎdulescu, Existence and stability of limit cycles in a two-delays model of hematopoiesis including asymmetric division. Math. Model. Nat. Phenom. 9, 58–78 (2014)zbMATHMathSciNetCrossRefGoogle Scholar
  48. 48.
    J.T. Hartmann, M. Haap, H.G. Kopp, H.P. Lipp, Tyrosine kinase inhibitors - a review on pharmacology, metabolism and side effects. Curr. Drug Metab. 10(5), 470–481 (2009)CrossRefGoogle Scholar
  49. 49.
    C. Haurie, D.C. Dale, M.C. Mackey, Cyclical neutropenia and other periodic hematological disorders: a review of mechanisms and mathematical models. Blood 92, 2629–2640 (1998)Google Scholar
  50. 50.
    C. Haurie, D.C. Dale, R. Rudnicki, M.C. Mackey, Modeling complex neutrophil dynamics in the grey collie. J. Theor. Biol. 204, 504–519 (2000)CrossRefGoogle Scholar
  51. 51.
    L. Hayflick, P.S. Moorhead, The serial cultivation of human diploid cell strains. Exp. Cell Res. 25(3), 585–621 (1961)CrossRefGoogle Scholar
  52. 52.
    T. Hearn, C. Haurie, M.C. Mackey, Cyclical neutropenia and the peripherial control of white blood cell production. J. Theor. Biol. 192, 167–181 (1998)CrossRefGoogle Scholar
  53. 53.
    T. Hillen, H. Enderling, P. Hahnfeldt, The tumor growth paradox and immune system-mediated selection for cancer stem cells. Bull. Math. Biol. 75(1), 161–184 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  54. 54.
    Th. Hodgkin, On some morbid appearances of the absorbent glands and spleen. Med. Chir. Trans. 17, 68–114 (1832)CrossRefGoogle Scholar
  55. 55.
    M. Horn, I. Glauche, M.C. M’́uller, R. Hehlmann, A. Hochhaus, M. Loeffler, I. Roeder, Model-based decision rules reduce the risk of molecular relapse after cessation of tyrosine kinase inhibitor therapy in chronic myeloid leukemia. Blood 121(2), 378–384 (2013)Google Scholar
  56. 56.
    C.A. Janeway, P. Travers, M. Walport, M. Shlomchik, Immunobiology. 6th edn. (Garland Science, New York, 2005)Google Scholar
  57. 57.
    K.R. Kampen, The discovery and early understanding of leukemia. Leuk. Res. 36, 6–13 (2012)CrossRefGoogle Scholar
  58. 58.
    P.S. Kim, P.P. Lee, D. Levy, A PDE model for imatinib-treated chronic myelogenous leukemia. Bull. Math. Biol. 70(7), 1994–2016 (2008)zbMATHMathSciNetCrossRefGoogle Scholar
  59. 59.
    P.S. Kim, P.P. Lee, D. Levy, Dynamics and potential impact of the immune response to chronic myelogenous leukemia. PLoS Comput. Biol. 4(6), e1000095 (2008). doi:10.1371/journal.pcbi.1000095Google Scholar
  60. 60.
    E.A. King-Smith, A. Morley, Computer simulation of granulopoiesis: normal and impaired granulopoiesis. Blood 36(2), 254–262 (1970)Google Scholar
  61. 61.
    D. Kirschner, J.C. Panetta, Modeling immunotherapy of the tumor-immune interaction. J. Math. Biol. 37(3), 235–252 (1998)zbMATHCrossRefGoogle Scholar
  62. 62.
    A. Kölliker, Professors Kölliker and Bennett on the discovery of leucocythemia. Mon. J. Med. Sci. 2, 374–377 (1854)Google Scholar
  63. 63.
    N.L. Komarova, Mathematical modeling of cyclic treatments of chronic myeloid leukemia. Math. Biosci. Eng. 8(2), 289–306 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  64. 64.
    N.L. Komarova, D. Wodarz, Drug resistance in cancer: principles of emergence and prevention. Proc. Natl. Acad. Sci. USA 102, 9714–9719 (2005)CrossRefGoogle Scholar
  65. 65.
    M. Loeffler, I. Roeder, Tissue stem cells: definition, plasticity, heterogeneity, self-organization and models - a conceptual approach. Cells Tissues Organs 171(1), 8–26 (2002)CrossRefGoogle Scholar
  66. 66.
    B.L. Lord, Biology of the Haemopoietic Stem Cell (Academic Press, Cambridge, 1997), pp. 401–422Google Scholar
  67. 67.
    M.C. Mackey, Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood 51(5), 941–956 (1978)Google Scholar
  68. 68.
    M.C. Mackey, Mathematical models of hematopoietic cell replication and control, in The Art of Mathematical Modelling: Case Studies in Ecology, Physiology and Biofluids ed. by H.G. Othmer, F.R. Adler, M.A. Lewis, J.C. Dallon (Prentice Hall, Upper Saddle River, 1997), pp. 149–178Google Scholar
  69. 69.
    M.C. Mackey, L. Glass, Oscillation and chaos in physiological control systems. Science 197, 287–289 (1977)CrossRefGoogle Scholar
  70. 70.
    A.L. MacLean, S. Filippi, M.P.H. Stumpf, The ecology in the hematopoietic stem cell niche determines the clinical outcome in chronic myeloid leukemia. Proc. Natl. Acad. Sci. USA 111, 3883–3888 (2014)CrossRefGoogle Scholar
  71. 71.
    J.M. Mahaffy, Age-structured modeling of hematopoiesis. Technical Report, Centre Recherches Mathematiques, Université de Montréal, CRM-2609 (1999)Google Scholar
  72. 72.
    J. Mahaffy, J. Bélair, M.C. Mackey, Hematopoietic model with moving boundary condition and state dependent delay: applications in erythropoiesis. J. Theor. Biol. 190, 135–146 (1998)CrossRefGoogle Scholar
  73. 73.
    M. Mamat, S. Kartono, A. Kartono. Mathematical model of cancer treatments using immunotherapy, chemotherapy and biochemotherapy. Appl. Math. Sci. 7(5), 247–261 (2013)MathSciNetGoogle Scholar
  74. 74.
    A. Marciniak-Czochra, T. Stiehl, A.D. Ho, W. Jaeger, W. Wagner, Modeling of asymmetric cell division in hematopoietic stem cells - regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 18, 377–385 (2009)CrossRefGoogle Scholar
  75. 75.
    A. Marciniak-Czochra, T. Stiehl, W. Wagner, Modeling of replicative senescence in hematopoietic development. Aging (Albany NY) 1(8), 723–732 (2009)Google Scholar
  76. 76.
    J. Mayer, Z. Pospíšil, Z. Kořístek, Mathematical model of peripheral blood stem cell harvest kinetics. Bone Marrow Transplant. 32:749–757 (2003)CrossRefGoogle Scholar
  77. 77.
    J.E. Menitove, J. Pereira, R. Hoffman, T. Anderson, W. Fried, R.H. Aster, Cyclic thrombocytopenia of apparent autoimmune etiology. Blood 73, 1561–1569 (1989)Google Scholar
  78. 78.
    F. Michor, Reply: the long-term response to imatinib treatment of CML. Br. J. Cancer 96, 679–680 (2007)CrossRefGoogle Scholar
  79. 79.
    J.C. Milton, M.C. Mackey, Periodic haematological diseases: mystical entities or dynamical disorders? J. R. Coll. Physicians Lond. 23, 236–241 (1989)Google Scholar
  80. 80.
    N. Misaghian, G. Ligresti, L.S. Steelman, F.E. Bertrand, J. Bäsecke, M. Libra, F. Nicoletti, F. Stivala, M. Milella, A. Tafuri, M. Cervello, A.M. Martelli, J.A. McCubre, Targeting the leukemic stem cell: the Holy Grail of leukemia therapy. Leukemia 23, 25–42 (2009)CrossRefGoogle Scholar
  81. 81.
    R. Molina-Peña, M.M. Álvarez, A simple mathematical model based on the cancer stem cell hypothesis suggests kinetic commonalities in solid tumor growth. PLoS ONE (2012). doi:10.1371/journal.pone.0026233Google Scholar
  82. 82.
    C. Molina-París, G. Lythe (eds.), Mathematical Models and Immune Cell Biology (Springer, New York, 2011)Google Scholar
  83. 83.
    C.L. Mouser, E.S. Antoniou, J. Tadros, E.K. Vassiliou, A model of hematopoietic stem cell proliferation under the influence of a chemotherapeutic agent in combination with a hematopoietic inducing agent. Theor. Biol. Med. Model. 11, 4 (2014)CrossRefGoogle Scholar
  84. 84.
    S. Nakaoka, K. Aihara, Mathematical study on kinetics of hematopoietic stem cells - theoretical conditions for successful transplantation. J. Biol. Dyn. 6, 836–854 (2012)CrossRefGoogle Scholar
  85. 85.
    S. Nanda, H. Moore, S. Lenhart, Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Math. Biosci. 210, 143–156 (2007)zbMATHMathSciNetCrossRefGoogle Scholar
  86. 86.
    S. Nanda, L. de Pillis, A. Radunskaya, B cell chronic lymphocytic leukemia: a model with immune response. Discrete Continuous Dyn. Syst. Ser. B 18, 1053–1076 (2013)zbMATHMathSciNetCrossRefGoogle Scholar
  87. 87.
    E. Neumann, Über die bedeutung des knochenmarkes für die blutbildung (Archiv der Heilkunde, Leipzig, 1869), pp. 68–102Google Scholar
  88. 88.
    J.P. Okunewick, A.L. Kretchmar. A Mathematical Model for Post-irradiation Hematopoietic Recovery. Defense Technical Information Center (1967)Google Scholar
  89. 89.
    K.M. Page, J.W. Uhr, Mathematical models of cancer dormancy. Leuk. Lymphoma 46(3), 313–327 (2005)CrossRefGoogle Scholar
  90. 90.
    E. Pefani, N. Panoskaltsis, A. Mantalaris, M.C. Georgiadis, E.N. Pistikopoulos, Chemotherapy drug scheduling for the induction treatment of patients with acute myeloid leukemia. IEEE Trans. Biomed. Eng. 61, 2049–2056 (2014)CrossRefGoogle Scholar
  91. 91.
    G.J. Piller, Leukaemia - a brief historical review from ancient times to 1950. Br. J. Haematol. 112, 282–292 (2001)CrossRefGoogle Scholar
  92. 92.
    C.A. Portell, A.S. Advani, Novel targeted therapies in acute lymphoblastic leukemia. Leuk. Lymphoma 55, 737–748 (2014)CrossRefGoogle Scholar
  93. 93.
    L. Preziosi (ed.), Cancer Modelling and Simulation (Chapman & Hall/CRC, Boca Raton, FL, 2003)Google Scholar
  94. 94.
    L. Pujo-Menjouet, M.C. Mackey, Contribution to the study of periodic chronic myelogenous leukemia. C. R. Biol. 327, 235–244 (2004)CrossRefGoogle Scholar
  95. 95.
    J. Qiu, D. Papatsenko, X- Niu, C. Schaniel, K. Moore, Divisional history and hematopoietic stem cell function during homeostasis. Stem Cell Rep. 2, 473–490 (2014)Google Scholar
  96. 96.
    A. Radunskaya, S. Hook, Modeling the kinetics of the immune response, in New Challenges for Cancer Systems Biomedicine, ed. by A. D’Onofrio, P. Cerrai, A. Gandolfi (Springer, Milan, 2013), pp. 267–284Google Scholar
  97. 97.
    V. Raia, M. Schilling, M. Bohm, B. Hahn, A. Kowarsch, A. Raue, C.Sticht, S. Bohl, M. Saile, P.Möller, N. Gretz, J. Timmer, F. Theis, W.-D. Lehmann, P. Lichter, U. Klingmüller, Dynamic mathematical modeling of IL13-induced signaling in Hodgkin and primary mediastinal B-cell lymphoma allows prediction of therapeutic targets. Cancer Res. 71, 693–704 (2011)CrossRefGoogle Scholar
  98. 98.
    M. Ramalho-Santos, H. Willenbring, On the origin of the term “Stem Cell”. Cell Stem Cell 1, 35–38 (2007)CrossRefGoogle Scholar
  99. 99.
    B. Ribba, K. Marron, Z. Agur, T. Alarcón, P.K. Maini, A mathematical model of doxorubicin treatment efficacy for non-Hodgkin’s lymphoma: investigation of the current protocol through theoretical modelling results. Bull. Math. Biol. 67, 79–99 (2005)zbMATHMathSciNetCrossRefGoogle Scholar
  100. 100.
    I. Roeder, Quantitative stem cell biology: computational studies in the hematopoietic system. Curr. Opin. Hematol. 13, 222–228 (2006)CrossRefGoogle Scholar
  101. 101.
    I. Roeder, I. Glauche, Towards an understanding of lineage specification in hematopoietic stem cells: a mathematical model for the interaction of transcription factors GATA-1 and PU.1. J. Theor. Biol. 241(4), 852–865 (2006)Google Scholar
  102. 102.
    I. Roeder, M. Loeffler, A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity. Exp. Hematol. 30, 853–861 (2002)CrossRefGoogle Scholar
  103. 103.
    I. Roeder, M. Horn, I. Glauche, A. Hochhaus, M.C. Mueller, M. Loeffler, Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nat. Med. 12, 1181–1184 (2006)CrossRefGoogle Scholar
  104. 104.
    I. Roeder, M. Herberg, M. Horn, An “age”-structured model of hematopoietic stem cell organization with application to chronic myeloid leukemia. Bull. Math. Biol. 71(3), 602–626 (2009)zbMATHMathSciNetCrossRefGoogle Scholar
  105. 105.
    C. Rozman, E. Montserrat, Chronic lymphocytic leukemia. N. Engl. J. Med. 333, 1052–1057 (1995)CrossRefGoogle Scholar
  106. 106.
    A. Safarishahrbijari, A. Gaffari, Parameter identification of hematopoiesis mathematical model – periodic chronic myelogenous leukemia. Wspolczesna Onkol. 17(1), 73–77 (2013)CrossRefGoogle Scholar
  107. 107.
    M. Santillán, J.M. Mahaffy, J. Bélair, M.C. Mackey, Regulation of platelet production: the normal response to perturbation and cyclical platelet disease. J. Theor. Biol. 206, 585–603 (2000)CrossRefGoogle Scholar
  108. 108.
    M. Scholz, A. Gross, M. Loeffler, A biomathematical model of human thrombopoiesis under chemotherapy. J. Theor. Biol. 264, 287–300 (2010)CrossRefGoogle Scholar
  109. 109.
    M. Sekimizu, Y. Yamashita, H. Ueki, N. Akita, H. Hattori, N. Maeda, K. Horibe, Nilotinib monotherapy induced complete remission in pediatric Philadelphia chromosome-positive acute lymphoblastic leukemia resistant to imatinib and dasatinib. Leuk. Lymphoma 55(7), 1652–1653 (2014)CrossRefGoogle Scholar
  110. 110.
    A.S. Silva, A.R.A. Anderson, R.A. Gatenby, A multiscale model of the bone marrow and hematopoiesis. Math. Biosci. Eng. 8, 643–658 (2011)zbMATHMathSciNetCrossRefGoogle Scholar
  111. 111.
    T. Stiehl, A. Marciniak-Czochra, Mathematical modeling of leukemogenesis and cancer stem cell dynamics. Math. Model. Nat. Phenom. 7, 166–202 (2012)zbMATHMathSciNetCrossRefGoogle Scholar
  112. 112.
    T. Stiehl, N. Baran, A.D. Ho, A. Marciniak-Czochra, Clonal selection and therapy resistance in acute leukaemias: mathematical modelling explains different proliferation patterns at diagnosis and relapse. J. R. Soc. Interface 11, 20140079 (2014). CrossRefGoogle Scholar
  113. 113.
    S.H. Swerdlow, E. Campo, N.L. Harris et al. (eds). WHO Classification of Tumours of Haematopoietic and Lymphoid Tissues (IARC, Lyon, 2008)Google Scholar
  114. 114.
    H. Swerdlow, E. Campo, S.A. Pileri, N. Lee Harris, H. Stein, R. Siebert, R. Advani, M. Ghielmini, G.A. Salles, D. Zelenetz, E.S. Jaffe, The 2016 revision of the World Health Organization (WHO) classification of lymphoid neoplasms. Blood 127, 2375–2390 (2016). doi:10.1182/blood-2016-01-643569CrossRefGoogle Scholar
  115. 115.
    R.M. Teague, J. Kline, Immune evasion in acute myeloid leukemia: current concepts and future directions. J. Immuno-Therapy Cancer 1, 13 (2013)CrossRefGoogle Scholar
  116. 116.
    X. Thomas, First contributors in the history of leukemia. World J. Hematol. 2(3), 62–70 (2013)CrossRefGoogle Scholar
  117. 117.
    A.L. Thorburn, Alfred Francois Donné, 1801–1878, discoverer of Trichomonas vaginalis and of leukaemia. Br. J. Vener. Dis. 50, 377–380 (1974)Google Scholar
  118. 118.
    T. Tian, K. Smith-Miles, Mathematical modeling of GATA-switching for regulating the differentiation of hematopoietic stem cells. BMC Syst. Biol. 8(Suppl 1), S8 (2014)Google Scholar
  119. 119.
    J. Till, E. McCulloch, A direct measurement of the radiation sensitivity of normal mouse bone marrow cells. Radiat. Res. 14, 213–222 (1961)CrossRefGoogle Scholar
  120. 120.
    V. Vainstein, Y. Ginosar, M. Shoham, A. Ianovski, A. Rabinovich, Y. Kogan,, V. Selitser, Z. Agur, Improving cancer therapy by doxorubicin and granulocyte colony-stimulating factor: insights from a computerized model of human granulopoiesis. Math. Model. Nat. Phenom. 1, 70–80 (2006)zbMATHMathSciNetCrossRefGoogle Scholar
  121. 121.
    J.W. Vardiman, J. Thiele, D.A. Arber, R.D. Brunning, M.J. Borowitz, A. Porwit, N.L. Harris, M.M. Le Beau, E. Hellstrom-Lindberg, A. Tefferi, C.D. Bloomfield, The 2008 revision of the World Health Organization (WHO) classification of myeloid neoplasms and acute leukemia: rationale and important changes. Blood 114, 937–951 (2009)CrossRefGoogle Scholar
  122. 122.
    H. Vaziri, F. Schachter, I. Uchida, L. Wei X. Zhu, R. Effros, D. Cohen, C.B. Harley, Loss of telomeric DNA during aging of normal and trisomy 21 human lymphocytes. Am. J. Hum. Genet. 52, 661–667 (1993)Google Scholar
  123. 123.
    H. Vaziri, W. Dragowska, R.C. Allsopp, T.E. Thomas, C.B. Harley, P.M. Lansorp, Evidence for a mitotic clock in human hematopoietic stem cells: loss of telomeric DNA with age. Proc. Natl. Acad. Sci. USA 91, 9857–9850 (1994)CrossRefGoogle Scholar
  124. 124.
    R.L.K. Virchow, Weisses Blut (1845), Gesammelte Abhandlungen zur Wissenschaftlichen Medicin (Meidinger Sohn, Frankfurt, 1856), pp. 149–154Google Scholar
  125. 125.
    R.L.K. Virchow, Leukämie, Gesammelte Abhandlungen zur wissenschaftlichen medicin (Meidinger Sohn, Frankfurt, 1856), pp. 190–212Google Scholar
  126. 126.
    S. Viswanathan, P.W. Zandstra, Towards predictive models of stem cell fate. Cytotechnology 41, 75–92 (2003)CrossRefGoogle Scholar
  127. 127.
    T. Walenda, T. Stiehl, H. Braun, J. Fröbel, A.D. Ho, T. Schroeder, T.W. Goecke, B. Rath, U. Germing, A. Marciniak-Czochra, W. Wagner, Feedback signals in myelodysplastic syndromes: increased self-renewal of the malignant clone suppresses normal hematopoiesis. PLoS Comput. Biol. 10, e1003599 (2014)CrossRefGoogle Scholar
  128. 128.
    J.C. Wang, J.E. Dick, Cancer stem cells: lessons from leukemia. Trends Cell Biol. 15(9), 494–501 (2005)CrossRefGoogle Scholar
  129. 129.
    T.E. Wheldon, J. Kirk, H.M. Finlay, Cyclical granulopoiesis in chronic granulocytic leukemia: a simulation study. Blood 43, 379–387 (1974)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Antonio Fasano
    • 1
  • Adélia Sequeira
    • 2
  1. 1.Fabbrica Italiana Apparecchi Biomedicali (FIAB)Università degli Studi di FirenzeFirenzeItaly
  2. 2.Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

Personalised recommendations