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Incorporating Asymmetric Stem Cell Division into the Roeder Model for Chronic Myeloid Leukemia

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Mathematical Models of Tumor-Immune System Dynamics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 107))

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Abstract

In this chapter we propose several modifications to the Roeder model of chronic myeloid leukemia (Roeder et al.: Nat. Med. 12(10), 1181–1184 2006). Specifically, we incorporate asymmetric division of stem cells and precursors, allow precursors to live a variable amount of time before maturing, and introduce feedback inhibition from mature cells to stem cells and precursors. These modifications result in more accurate simulations of cancer genesis and treatment. In comparison with the original model, our results indicate lower transition rates of stem cells between their quiescent and cycling states, which are supported by the rates suggested by experimental data. Decreased transition rates of stem cells translate into quiescent cancer stem cells that are better protected from imatinib, resulting in a large residual cancer burden, even after many years of therapy. Our modeling results suggest that the efficacy of imatinib would increase if it is combined with a drug that induces cancer stem cells to cycle.

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Acknowledgements

The work of GC was supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE1322106. The work of DL was supported in part by the John Simon Guggenheim Memorial Foundation and by the joint National Science Foundation/National Institute of General Medical Sciences program under Grant No. DMS-0758374. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation, the National Cancer Institute, or the National Institutes of Health.

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Geoffrey Clapp

  2. Department of Mathematics and Center for Scientific Computation and Mathematical Modeling (CSCAMM), University of Maryland, College Park, MD, 20742, USA

    Doron Levy

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  1. Geoffrey Clapp
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  2. Doron Levy
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Correspondence to Doron Levy .

Editor information

Editors and Affiliations

  1. Mathematics Department, The College of Saint Rose, Albany, New York, USA

    Amina Eladdadi

  2. School of Mathematics and Statistics, University of Sydney, Sydney, New South Wales, Australia

    Peter Kim

  3. Mathematical Sciences School, Queensland University of Technology, Brisbane, Queensland, Australia

    Dann Mallet

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Clapp, G., Levy, D. (2014). Incorporating Asymmetric Stem Cell Division into the Roeder Model for Chronic Myeloid Leukemia. In: Eladdadi, A., Kim, P., Mallet, D. (eds) Mathematical Models of Tumor-Immune System Dynamics. Springer Proceedings in Mathematics & Statistics, vol 107. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1793-8_1

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