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A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia

Author

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  • Lorand Gabriel Parajdi

    (Department of Mathematics, Babeş–Bolyai University, 400084 Cluj-Napoca, Romania)

  • Radu Precup

    (Department of Mathematics, Babeş–Bolyai University, 400084 Cluj-Napoca, Romania)

  • Eduard Alexandru Bonci

    (Department of Oncology, Iuliu Haţieganu University of Medicine and Pharmacy, 400012 Cluj-Napoca, Romania
    Department of Surgical Oncology, Ion Chiricuţă Clinical Cancer Center, 400015 Cluj-Napoca, Romania)

  • Ciprian Tomuleasa

    (Department of Hematology, Ion Chiricuţă Clinical Cancer Center, 400015 Cluj-Napoca, Romania)

Abstract

A mathematical model given by a two-dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated-acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated-acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.

Suggested Citation

  • Lorand Gabriel Parajdi & Radu Precup & Eduard Alexandru Bonci & Ciprian Tomuleasa, 2020. "A Mathematical Model of the Transition from Normal Hematopoiesis to the Chronic and Accelerated-Acute Stages in Myeloid Leukemia," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:376-:d:329862
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    References listed on IDEAS

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    1. Hans B Sieburg & Giulio Cattarossi & Christa E Muller-Sieburg, 2013. "Lifespan Differences in Hematopoietic Stem Cells are Due to Imperfect Repair and Unstable Mean-Reversion," PLOS Computational Biology, Public Library of Science, vol. 9(4), pages 1-15, April.
    2. Leonard I. Zon, 2008. "Intrinsic and extrinsic control of haematopoietic stem-cell self-renewal," Nature, Nature, vol. 453(7193), pages 306-313, May.
    3. Franziska Michor & Timothy P. Hughes & Yoh Iwasa & Susan Branford & Neil P. Shah & Charles L. Sawyers & Martin A. Nowak, 2005. "Dynamics of chronic myeloid leukaemia," Nature, Nature, vol. 435(7046), pages 1267-1270, June.
    4. Gregory Driessens & Benjamin Beck & Amélie Caauwe & Benjamin D. Simons & Cédric Blanpain, 2012. "Defining the mode of tumour growth by clonal analysis," Nature, Nature, vol. 488(7412), pages 527-530, August.
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    Cited by:

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