Skip to main content
SpringerLink
Log in

Global dynamics of hematopoietic stem cells and differentiated cells in a chronic myeloid leukemia model

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

We consider a mathematical model describing evolution of normal and leukemic hematopoietic stem cells (HSC) and differentiated cells in bone marrow. We focus on chronic myeloid leukemia (CML), a cancer of blood cells resulting from a malignant transformation of hematopoietic stem cells. The dynamics are given by a system of ordinary differential equations for normal and leukemic cells. Homeostasis regulates the proliferation of normal HSC and leads the dynamics to an equilibrium. This mechanism is partially efficient for leukemic cells. We define homeostasis by a functional of either hematopoietic stem cells, differentiated cells or both cell lines. We determine the number of hematopoietic stem cells and differentiated cells at equilibrium. Conditions for regeneration of hematopoiesis and persistence of CML are obtained from the global asymptotic stability of equilibrium states. We prove that normal and leukemic cells can not coexist for a long time. Numerical simulations illustrate our analytical results. The study may be helpful in understanding the dynamics of normal and leukemic hematopoietic cells.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abkowitz JL, Catlin SN, McCallie MT, Guttorp P (2002) Evidence that the number of hematopoietic stem cells per animal is conserved in mammals. Blood 100: 2665–2667

    Article  Google Scholar 

  • Adimy M, Crauste F, Ruan S (2005) A mathematical study of the hematopoiesis process with applications to chronic myelogenous leukemia. SIAM J Appl Math 65: 1328–1352

    Article  MathSciNet  MATH  Google Scholar 

  • Araki M, Kondo B (1972) Stability and transient behavior of composite nonlinear systems. IEEE Trans Automat Control 17: 537–541

    Article  MathSciNet  MATH  Google Scholar 

  • Bondar T, Medzhitov R (2010) p53-Mediated hematopoietic stem and progenitor cell competition. Cell Stem Cell 6: 309–322

    Article  Google Scholar 

  • Catlin SN, Guttorp P, Abkowitz JL (2005) The kinetics of clonal dominance in myeloproliferative disorders. Blood 106: 2688–2692

    Article  Google Scholar 

  • Chen F (2006) The permanence and global attractivity of Lotka-Volterra competition system with feedback controls. Nonlinear Anal: Real World Appl 7: 133–143

    Article  MathSciNet  MATH  Google Scholar 

  • Chen L, Chen F (2009) Global stability of a Leslie-Gower predator-prey model with feedback controls. Appl Math Lett 22: 1330–1334

    Article  MathSciNet  MATH  Google Scholar 

  • Colijn C, Mackey MC (2005) A mathematical model of hematopoiesis: Periodic chronic myelogenous leukemia, part I. J Theor Biol 237: 117–132

    Article  MathSciNet  Google Scholar 

  • Coppel WA (1995) Stability and asymptotic behavior of differential equations. Health, Boston

    Google Scholar 

  • Cotta CV, Bueso-Ramos CE (2007) New insights into the pathobiology and treatment of chronic myelogenous leukemia. Ann Diagn Pathol 11: 68–78

    Article  Google Scholar 

  • Crauste F, Demin I, Gandrillon O, Volpert V (2010) Mathematical study of feedback control roles and relevance in stress erythropoiesis. J Theor Biol 263: 303–316

    Article  Google Scholar 

  • Dingli D, Michor F (2006) Successful therapy must eradicate cancer stem cells. Stem cells 24: 2603–2610

    Article  Google Scholar 

  • Dingli D, Traulsen A, Pacheco JM (2007) Stochastic dynamics of hematopoietic tumor stem cells. Cell Cycle 6: 461–466

    Article  Google Scholar 

  • Dingli D, Pacheco JM (2007) Ontogenic growth of the hematopoietic stem cell pool in humans. Proc R Sci B 274: 2497–2501

    Article  Google Scholar 

  • Fiedler M (1974) Additive compound matrices and an inequality for eigenvalues of symmetric stochastic matrices. Czechoslov Math J 24: 392–402

    MathSciNet  Google Scholar 

  • Fortin P, Mackey MC (1999) Periodic chronic myelogenous leukemia: spectral analysis of blood cell counts and aetiological implications. Br J Haematol 104: 336–345

    Article  Google Scholar 

  • Han L, Pugliese A (2009) Epidemics in two competing species. Nonlinear Anal 10: 723–744

    Article  MathSciNet  MATH  Google Scholar 

  • Ledzewicz U, Schättler H (2007) Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy. Math Biosci 206: 320–342

    Article  MathSciNet  MATH  Google Scholar 

  • Leguay T, Mahon F-X (2005) Leucémie myéloïde chronique. EMC-Hématologie 2: 187–205

    Article  Google Scholar 

  • Mackey MC (1978) A unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood 51: 941–956

    Google Scholar 

  • Mackey MC (1997) Mathematical models of hematopoietic cell replication and control. In: Othmer HG, Adler FR, Lewis MA, Dallon JC (eds) The art of mathematical modelling: case studies in ecology, physiology and biofluids. Prentice Hall, pp 149–178

  • May P, May E (1999) Rôles de p53 dans le cycle cellulaire, l’apoptose et le cancer. Revue Française des Laboratoires 311: 35–42

    Article  Google Scholar 

  • McEwen BS, Wingfield JC (2010) What is in a name? Integrating homeostasis, allostasis and stress. Horm Behav 57: 105–111

    Article  Google Scholar 

  • Michor F, Hughes TP, Iwasa Y, Branford S, Shah NP, Sawyers CL, Nowak MA (2005) Dynamics of chronic myeloid leukemia. Nature 435: 1267–1270

    Article  Google Scholar 

  • Moore H, Li NK (2004) A mathematical model of chronic myelogenous leukemia (CML) and T cell interaction. J Theor Biol 227: 513–523

    Article  MathSciNet  Google Scholar 

  • Pujo-Menjouet L, Mackey MC (2004) Contribution to the study of periodic chronic myelogenous leukemia. Comptes Rendus Biol 327: 235–244

    Article  Google Scholar 

  • Raff MC (1992) Social controls on cell survival and cell death. Nature 356: 397–400

    Article  Google Scholar 

  • Roeder I, Loeffler M (2002) A novel model of hematopoietic stem cell organization based on the concept of within-tissue plasticity. Exp Hematol 30: 853–861

    Article  Google Scholar 

  • Scheijen B, Griffin JD (2002) Tyrosine kinase oncogenes in normal hematopoiesis and hematological disease. Oncogene 21: 3314–3333

    Article  Google Scholar 

  • Spinelli L, Torricelli A, Ubezio P, Basse B (2006) Modelling the balance between quiescence and cell death in normal and tumour cell populations. Math Biosci 202: 349–370

    Article  MathSciNet  MATH  Google Scholar 

  • ten Cate B, de Bruyn M, Wei Y, Bremer E, Helfrich W, El Mourabet M, El-Hachem S, Harrison JR, Binion DG (2010) Targeted elimination of leukemia stem cells; a new therapeutic approach in hemato- oncology. Curr Drug Targets 11: 95–110

    Article  Google Scholar 

  • Wang L, Li MY (2001) Diffusion-Driven instability in reaction-diffusion systems. J Math Anal Appl 254: 138–153

    Article  MathSciNet  MATH  Google Scholar 

  • Wilson A, Laurenti E, Trumpp A (2009) Balancing dormant and self-renewing hematopoietic stem cells. Curr Opin Genet Develop 19: 461–468

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre de Recherche INRIA Bordeaux Sud-Ouest, Institut de Mathématiques de Bordeaux, UMR CNRS 5251, Université de Bordeaux, 3 ter Place de la Victoire, 33076, Bordeaux cedex, France

    Bedr’Eddine Aïnseba & Chahrazed Benosman

Authors
  1. Bedr’Eddine Aïnseba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chahrazed Benosman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chahrazed Benosman.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aïnseba, B., Benosman, C. Global dynamics of hematopoietic stem cells and differentiated cells in a chronic myeloid leukemia model. J. Math. Biol. 62, 975–997 (2011). https://doi.org/10.1007/s00285-010-0360-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00285-010-0360-x

Keywords

Mathematics Subject Classification (2000)

Search

Navigation