Skip to main content
SpringerLink
Log in

Mathematical Models of Hematopoietic Reconstitution After Stem Cell Transplantation

  • Chapter
  • First Online:
Model Based Parameter Estimation

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 4))

Abstract

Transplantation of bone marrow stem cells is a widely used option to treat leukemias and other diseases. Nevertheless this intervention is linked to life-threatening complications. Numerous clinical trials have been performed to evaluate various treatment options. Since there exist strong interindividual variations in patients’ responses, results of clinical trials are hardly applicable to individual patients. In this paper a mathematical model of hematopoiesis introduced by us in(Marciniak-Czochra et al.: Stem Cells Dev. 18:377–85, 2009) is calibrated based on clinical data and applied to study several aspects of short term reconstitution after bone marrow transplantation. Parameter estimation is performed based on the data of time evolution of leukocyte counts after chemotherapy and bone marrow transplantation obtained for individual patients. The model allows to simulate various treatment options for large groups of individual patients, to compare the effects of the treatments on individual patients and to evaluate how the properties of the transplant and cytokine treatment affect the time of reconstitution.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Giebel B., Zhang T., Beckmann J., Spanholtz J., Wernet P., Ho AD, Punzel M.: Primitive human hematopoietic cells give rise to differentially specified daughter cells upon their initial cell division. Blood. 107, 2146–2152 (2006)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Till J.E., Siminovitch L., McCulloch E.A.: Stochastic Model of Stem Cell Proliferation Based on Growth of Spleen Colony-Forming Cells. PNAS 51, 29–49 (1964)

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Ostby I., Kvalheim G., Rusten L.S., Grottum P.: Mathematical modeling of granulocyte reconstitution after high-dose chemotherapy with stem cell support: effect of post-transplant G-CSF treatment. J Theor Biol. 231, 69–83 (2004)

    Article  MathSciNet  Google Scholar 

  6. Michor F., Hughes T.P., Iwasa Y., Branford S., Shah N.P., Sawyers C.L., Nowak M.A.: Dynamics of chronic myeloid leukaemia. Nature 435, 1267–1270 (2005)

    Article  Google Scholar 

  7. Wazewska-Czyzewska M.: Erythrokinetics radioisotopic methods of investigation and mathematical approach. Foreign Scientific Publications Dept. of the National Center for Scientific, Technical, and Economic Information, Springfield (1984)

    Google Scholar 

  8. Marciniak-Czochra A., Stiehl T., Ho A.D., Jäger W., Wagner W.: Modeling of asymmetric cell division in hematopoietic stem cells–regulation of self-renewal is essential for efficient repopulation. Stem Cells Dev. 18, 377–85 (2009)

    Article  Google Scholar 

  9. Stiehl, T., Marciniak-Czochra A.: Characterization of stem cells using mathematical models of multistage cell lineages, Mathematical and Computer Modelling (2010), doi:10.1016/j.mcm.2010.03.057.

    Google Scholar 

  10. Marciniak-Czochra A., Stiehl T., Wagner W.: Modeling of replicative senescence in hematopoietic development. Aging (Albany NY) 1, 723–732 (2009)

    Google Scholar 

  11. Doumic, M., Marciniak-Czochra, A., Perthame, B., Zubelli, J.: Structured population model of stem cell differentiation. Preprint available at http://hal.archives-ouvertes.fr/inria-00541860/fr/.

  12. Ho A.D., Wagner W.:The beauty of asymmetry: asymmetric divisions and self-renewal in the haematopoietic system. Curr Opin Hematol. 14,330–336 (2007)

    Google Scholar 

  13. Jandl J.H.: Blood cell formation. In: Jandl J.H., ed. Textbook of Hematology. Little, Brown and Company, Boston, MA, 1–69 (1996)

    Google Scholar 

  14. Fauci A.S., Braunwald M.D., Kasper D.I., Hauser S.I., Longo D.L., Jameson J.L., Loscalzo J.: Harrison’s Principles of Internal Medecine, 17th Edition, Mc GrawHill, New York (2008)

    Google Scholar 

  15. Metcalf D.: Hematopoietic cytokines. Blood 111, 485–91 (2008)

    Article  Google Scholar 

  16. Shinjo K., Takeshita A., Ohnishi K., Ohno R.: Granulocyte colony-stimulating factor receptor at various stages of normal and leukemic hematopoietic cells. Leuk Lymphoma. 25,37–46 (1997)

    Google Scholar 

  17. Bogner V., Keil L., Kanz K.G., Kirchhoff C., Leidel B.A., Mutschler, W., Biberthaler P.: Very early posttraumatic serum alterations are signifficantly associated to initial massive rbc substitution, injury severity, multiple organ failure and adverse clinical outcome in multiple injured patients. Eur J Med Res. 14, 284– 291 (2009)

    Article  Google Scholar 

  18. Morgan D., Desai A., Edgar B., Glotzer M., Heald R., Karsenti E., Nasmyth K., Pines J., Sherr, C.: The Cell Cycle. In: Alberts B., Johnson A., Lewis J., Raff M., Roberts K., Walter R. (Eds): Molecular Biology of the Cell, 5th Edition. Garland Science, New York (2007)

    Google Scholar 

  19. Klaus J., Herrmann D., Breitkreutz I., Hegenbart U., Mazitschek U., Egerer G., Cremer F.W., Lowenthal R.M., Huesing J., Fruehauf S., Moehler T., Ho A.D. and Goldschmidt H.: Effect of CD34 cell dose on hematopoietic reconstitution and outcome in 508 patients with multiple myeloma undergoing autologous peripheral blood stem cell transplantation. Eur J Haematol. 78, 21–28 (2007)

    Article  Google Scholar 

  20. Janz S., Potter M., Rabkin C.C.: Lymphoma- and leukemia-associated chromosomal translocations in healthy individuals. Genes Chromosomes Cancer 36, 211–223 (2003)

    Article  Google Scholar 

  21. Schueler F.,Hirt C., Doelken G.: Chromosomal translocation t(14;18) in healthy individuals. Semin Cancer Biol. 13 203–209 (2003)

    Article  Google Scholar 

  22. Reichard K.K., Zhang Q.Y., Sanchez L., Hozier J., Viswanat D., Foucar K.: Acute myeloid leukemia of donor origin after allogeneic bone marrow transplantation for precursor t-cell acute lymphoblastic leukemia: case report and review of the literature. Am J Hematol. 81 178–185 (2006)

    Article  Google Scholar 

  23. Ratajczak M.Z., Kucia M., Majka M., Reca R., Ratajczak J.: Heterogeneous populations of bone marrow stem cells-are we spotting on the same cells from the different angles? Folia Histochem Cytobiol. 42 139–146 (2004)

    Google Scholar 

  24. Ratajczak M.Z., Kucia M., Reca R., Majka M., Janowska-Wieczorek A., Ratajczak J.: Stem cell plasticity revisited: Cxcr4-positive cells expressing mrna for early muscle, liver and neural cells ’hide out’ in the bone marrow. Leukemia 18, 29–40 (2004)

    Article  Google Scholar 

  25. Kucia M., Ratajczak J., Ratajczak M.Z.: Bone marrow as a source of circulating cxcr4+ tissue-committed stem cells. Biol Cell. 97, 133–146 (2005)

    Article  Google Scholar 

  26. Kucia M., Ratajczak J., Reca R., Janowska-Wieczorek A., Ratajczak M.Z.: Tissuespecific muscle, neural and liver stem/progenitor cells reside in the bone marrow, respond to an sdf-1 gradient and are mobilized into peripheral blood during stress and tissue injury. Blood Cells Mol Dis. 32, 52–57 (2004)

    Article  Google Scholar 

  27. Roeder I., de Haan G., Engel C., Nijhof W., Dontje B., Loeffler M.: Interactions of erythropoietin, granulocyte colony-stimulating factor, stem cell factor and interleukin-11 on murine hematopoiesis during simultaneous administration. Blood, 91, 3222–3229 (1998)

    Google Scholar 

  28. Lowenthal R.M., Faberes C., Marit G., Boiron J.M., Cony-Makhoul P., Pigneux A., Agape P., Vezon G., Bouzgarou R., Dazey B., Fizet D., Bernard P., Lacombe F., Reiffers J.: Factors influencing haemopoietic recovery following chemotherapy-mobilised autologous peripheral blood progenitor cell transplantation for haematological malignancies: A retrospective analysis of a 10-year single institution experience. Bone Marrow Transplant. 1998 22, 763–770 (1998)

    Article  Google Scholar 

Download references

Acknowledgements

The authors were supported by the WIN Kolleg of Heidelberg Academy of Sciences and Humanities “A man is so old as his stem cells?” and Collaborative Research Center, SFB 873, “Maintenance and Differentiation of Stem Cells in Development and Disease.” AM-C was supported by ERC Starting Grant “Biostruct” and Emmy Noether Programme of German Research Council (DFG).

Author information

Authors and Affiliations

  1. Interdisciplinary Center for Scientific Computing, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Anna Marciniak-Czochra & Thomas Stiehl

Authors
  1. Anna Marciniak-Czochra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thomas Stiehl
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anna Marciniak-Czochra .

Editor information

Editors and Affiliations

  1. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Hans Georg Bock

  2. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 294, Heidelberg, 69120, Germany

    Thomas Carraro

  3. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Willi Jäger

  4. Interdisciplinary Center for, Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Stefan Körkel

  5. Institute for Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 293, Heidelberg, 69120, Germany

    Rolf Rannacher

  6. Interdisciplinary Center for Scientific, Computing (IWR), Heidelberg University, Im Neuenheimer Feld 368, Heidelberg, 69120, Germany

    Johannes P. Schlöder

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Marciniak-Czochra, A., Stiehl, T. (2013). Mathematical Models of Hematopoietic Reconstitution After Stem Cell Transplantation. In: Bock, H., Carraro, T., Jäger, W., Körkel, S., Rannacher, R., Schlöder, J. (eds) Model Based Parameter Estimation. Contributions in Mathematical and Computational Sciences, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30367-8_9

Download citation

Publish with us

Policies and ethics

Search

Navigation