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High frequency spikes in long period blood cell oscillations

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Abstract

Several hematological diseases are characterised by oscillations of various blood cell populations. Two of these are a variant of chronic myelogenous leukemia (CML) and cyclical neutropenia (CN). These oscillations typically have long periods ranging from 20 to 60 days, despite the fact that the stem cell cycling time is thought to be of the order of 2–3 days. Clinical data from humans and laboratory data from the grey collie animal model of CN is suggestive of the idea that these long period oscillations may also contain higher frequency spiky oscillations. We show how such oscillations can be understood in the context of slow periodic stem cell oscillations, by analysing a two component differential-delay equation model of stem cell and neutrophil populations.

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Authors and Affiliations

  1. Department of Mathematics and Centre for Nonlinear Dynamics, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, Canada, H3G 1Y6

    Caroline Colijn

  2. Mathematical Institute, 24–29 St. Giles’, Oxford, OX1 3LB, UK

    A. C. Fowler

  3. Departments of Physiology, Physics and Mathematics, Centre for Nonlinear Dynamics, McGill University, 3655 Promenade Sir William Osler, Montreal, QC, Canada, H3G 1Y6

    Michael C. Mackey

Authors
  1. Caroline Colijn
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  2. A. C. Fowler
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  3. Michael C. Mackey
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Correspondence to Caroline Colijn.

Additional information

For Karl Hadeler, on his 70th birthday, leader, teacher, colleague and friend.

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Colijn, C., Fowler, A.C. & Mackey, M.C. High frequency spikes in long period blood cell oscillations. J. Math. Biol. 53, 499–519 (2006). https://doi.org/10.1007/s00285-006-0027-9

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  • DOI: https://doi.org/10.1007/s00285-006-0027-9

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