Time optimal entrainment control for circadian rhythm

PLoS One. 2019 Dec 18;14(12):e0225988. doi: 10.1371/journal.pone.0225988. eCollection 2019.

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.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.
  • Review

MeSH terms

  • Algorithms
  • Circadian Rhythm / physiology*
  • Humans
  • Models, Biological*
  • Time Factors

Grants and funding

All authors are supported by the Army Research Office (https://www.arl.army.mil/www/default.cfm?page=29) through grant W911NF-17-1-0562, and the National Science Foundation (https://nsf.gov) through an Engineering Research Center grant EEC-0812056. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.