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.
Highlights
The circadian rhythm is a mechanism with which living beings can synchronize their biological processes with the light and dark pattern of the terrestrial day [1]
The circadian rhythm is heavily linked to various physiological processes, including sleep, metabolism, hormone secretion, and neurobehavioral processes
In our prior work [18, 19], we study the optimal entrainment of a reduced model with second-order dynamics, which is obtained by ignoring a part of the dynamics, which is called the Process-L
Summary
The circadian rhythm is a mechanism with which living beings can synchronize their biological processes with the light and dark pattern of the terrestrial day [1]. In some later work [20, 21], we study the optimal entrainment of a further reduced model, which is obtained by ignoring the amplitude of the circadian oscillation and focusing on the phase dynamics of the oscillation. These reductions were necessary to solve the time-optimal control problem; otherwise, the solution procedures that we used were not numerically stable.
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