Circadian System Modeling and Phase Control

Circadian rhythms are biological processes found in all living organisms, from plants to insects to mammals that repeat with a period close to, but not exactly, 24 hours. In the absence of environmental cues, circadian rhythms oscillate with a period slightly longer or shorter than 24 hours. The 24-hour patterns of light and dark are the strongest synchronizer of circadian rhythms to the solar day. Circadian disruption resulting from lack of synchrony between the solar day and the internal master clock that regulates and generates circadian rhythms had been linked to a variety of maladies. Circadian disruption, as experienced by night shift workers or by those traveling multiple time zones can lead to lower productivity, digestive problems and decreased sleep efficiency. Long-term circadian disruption has been linked to serious health problems, such as increased risk of cancer, cardiovascular disease, diabetes and obesity. Biochemical and empirical mathematical models describing the circadian clock and its response to light input have been developed by various research groups. Biochemical models describe the kinetics of the interaction between different proteins and may be of high order depending on the complexity of the model. Empirical models are based on nonlinear oscillators, such as the van der Pol oscillator, and are, therefore, much simpler. Though empirical models do not have a biochemical basis, it has been shown that they do represent the averaged asymptotic behavior of the biochemical models. In this paper, we analyze a simple empirical model proposed by Kronauer and colleagues and discuss how light control may be used to promote circadian entrainment. In contrast to most of the existing approaches, which are based on phase response curves, we propose a feedback-based system. Through simulation, we show that the recovery of a 12-hour jet lag can be shortened from 7 days to 2.5 days.