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Women in Mathematical Biology pp 49–62Cite as

A Two-Process Model for Circadian and Sleep-Dependent Modulation of Pain Sensitivity

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Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 8))

Abstract

Pain sensitivity is strongly modulated by time of day and by prior sleep behavior. These two factors, governed by the circadian rhythm and homeostatic sleep drive, respectively, likewise dictate the timing and duration of sleep. The fields of sleep and circadian research have identified much of the physiology underlying the circadian rhythm and homeostatic sleep drive with mathematical modeling playing an important role in understanding how these two processes interact to affect sleep behavior. We hypothesize that the daily rhythm of pain sensitivity and its sleep-dependent modulation reflect an interaction of the circadian rhythm and homeostatic sleep drive. To investigate this hypothesis, we adapt the formalism of a classic mathematical model for the regulation of sleep behavior by the circadian rhythm and homeostatic sleep drive, called the Two-Process model, to simulate the interaction of these two processes on pain sensitivity. To construct the model, we utilize data from experimental reports on the daily rhythmicity of pain sensitivity in humans to define a “daily pain sensitivity” function. We decompose this function into two processes: a sleep-dependent processS(t) that follows the homeostatic sleep drive and a circadian processC(t) that is dictated by the circadian rhythm. By simulating different sleep schedules with the original Two-Process model, we compute changes in the sleep-dependent processS(t) that modulates pain sensitivity. By combiningS(t) with the circadian processC(t), our model predicts resultant changes in the daily pain sensitivity rhythm. We illustrate model predictions for changes in pain sensitivity due to sleep deprivation, sleep restriction and shift work schedules. We believe that this model may be a useful tool for pain management by providing predictions of the variations in pain sensitivity due to changing sleep schedules.

The original version of this chapter was revised. An erratum to this chapter can be found at https://doi.org/10.1007/978-3-319-60304-9_13

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Acknowledgements

This work was conducted as a part of A Research Collaboration Workshop for Women in Mathematical Biology at the National Institute for Mathematical and Biological Synthesis, sponsored by the National Science Foundation through NSF Award DBI-1300426, with additional support from The University of Tennessee, Knoxville. This work was additionally partially supported by the following sources: NSF Award DMS-1412119 (VB) and the Pritzker Neuropsychiatric Disorders Research Consortium (MH). 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.

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Authors and Affiliations

  1. Biology Department, Washington and Lee University, Lexington, VA, 24450, USA

    Natalia Toporikova

  2. Molecular and Behavioral Neuroscience Institute, University of Michigan, Ann Arbor, MI, 48109, USA

    Megan Hastings Hagenauer

  3. Department of Biological Sciences, University of Alabama, Tuscaloosa, AL, 35487, USA

    Paige Ferguson

  4. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    Victoria Booth

  5. Department of Anesthesiology, University of Michigan, Ann Arbor, MI, 48109, USA

    Victoria Booth

Authors
  1. Natalia Toporikova
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  2. Megan Hastings Hagenauer
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  3. Paige Ferguson
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  4. Victoria Booth
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Corresponding author

Correspondence to Victoria Booth .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Duke University, Durham, North Carolina, USA

    Anita T. Layton

  2. Departments of Mathematics and Biology, University of North Carolina, Chapel Hill, North Carolina, USA

    Laura A. Miller

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Toporikova, N., Hagenauer, M.H., Ferguson, P., Booth, V. (2017). A Two-Process Model for Circadian and Sleep-Dependent Modulation of Pain Sensitivity. In: Layton, A., Miller, L. (eds) Women in Mathematical Biology. Association for Women in Mathematics Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-60304-9_3

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