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Time optimal entrainment control for circadian rhythm

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  • A Agung Julius
  • Jiawei Yin
  • John T Wen

Abstract

The circadian rhythm functions as a master clock that regulates many physiological processes in humans including sleep, metabolism, hormone secretion, and neurobehavioral processes. Disruption of the circadian rhythm is known to have negative impacts on health. Light is the strongest circadian stimulus that can be used to regulate the circadian phase. In this paper, we consider the mathematical problem of time-optimal circadian (re)entrainment, i.e., computing the lighting schedule to drive a misaligned circadian phase to a reference circadian phase as quickly as possible. We represent the dynamics of the circadian rhythm using the Jewett-Forger-Kronauer (JFK) model, which is a third-order nonlinear differential equation. The time-optimal circadian entrainment problem has been previously solved in settings that involve either a reduced-order JFK model or open-loop optimal solutions. In this paper, we present (1) a general solution for the time-optimal control problem of fastest entrainment that can be applied to the full order JFK model (2) an evaluation of the impacts of model reduction on the solutions of the time-optimal control problem, and (3) optimal feedback control laws for fastest entrainment for the full order Kronauer model and evaluate their robustness under some modeling errors.

Suggested Citation

  • A Agung Julius & Jiawei Yin & John T Wen, 2019. "Time optimal entrainment control for circadian rhythm," PLOS ONE, Public Library of Science, vol. 14(12), pages 1-30, December.
    • Handle: RePEc:plo:pone00:0225988
    DOI: 10.1371/journal.pone.0225988
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    Cited by:

    1. Jim Parker & Claire O’Brien & Jason Hawrelak & Felice L. Gersh, 2022. "Polycystic Ovary Syndrome: An Evolutionary Adaptation to Lifestyle and the Environment," IJERPH, MDPI, vol. 19(3), pages 1-25, January.
    2. Jiawei Yin & Agung Julius & John T. Wen & Zhen Wang & Chuanlin He & Lei Kou, 2022. "Human Alertness Optimization with a Three-Process Dynamic Model," Mathematics, MDPI, vol. 10(11), pages 1-19, June.
    3. Samuel Christensen & Yitong Huang & Olivia J Walch & Daniel B Forger, 2020. "Optimal adjustment of the human circadian clock in the real world," PLOS Computational Biology, Public Library of Science, vol. 16(12), pages 1-18, December.
    4. Jiawei Yin & A Agung Julius & John T Wen, 2021. "Optimization of light exposure and sleep schedule for circadian rhythm entrainment," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-28, June.

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