Conference Paper

Circadian System Modeling and Phase Control

Rensselaer Polytech. Inst., Troy, NY, USA
DOI: 10.1109/CDC.2010.5718105 Conference: Decision and Control (CDC), 2010 49th IEEE Conference on
Source: DBLP

ABSTRACT 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.

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    • "Feedback control of the light therapy is attractive as it could accommodate variations between individuals and disturbances from the environment . Some closed loop strategies have been suggested and demonstrated in simulation [7], [17], but a reasonable estimation of the circadian argument based on physiological sensor measurements is needed for deployment. The circadian rhythm may be assessed by measuring the circadian data. "
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    ABSTRACT: Disruption of the circadian rhythm is detrimental to human well being, with consequences ranging from lower productivity, sleep disorder, to more serious health problems. Accurate estimation of circadian argument is critical to the assessment and treatment of circadian disruption. Circadian argument estimate is also essential for light-based circadian entrainment. Direct measurements of circadian rhythm markers such as dim light melatonin onset are inconvenient and acquired at best at low rate. Wearable continuous measurement such as actigraph is convenient but is masked by many other factors. In this paper, we present a new circadian rhythm estimation scheme based on a type of frequency tracker, called adaptive notch filter (ANF) which is commonly used in signal processing. ANF is designed to track the gain and phase of a single sinusoid from noisy data. We extend the classic ANF to multiple harmonics needed in circadian rhythm tracking. The local stability and high order harmonics robustness are analyzed. The highly noisy indirect measurements result in unreliable amplitude estimate, but the phase estimate is generally quite robust. We use this phase estimate combined with the light input to construct a black-box linear time varying (LPV) system description, parameterized by the phase estimate. The LPV model predicts the circadian rhythm response to light inputs and can be used for the design of light-based feedback control. The proposed modeling and control method is applied to three different models of circadian rhythm: Kronauer's human circadian model, Leloup's Drosophila circadian model and Neurospora circadian model. Simulation shows that our approach can generate reliable circadian argument estimation and effective gain-scheduled control of the circadian rhythm without any knowledge of the underlying model. The ability to generate circadian estimate, model, and control based only on input/output data opens up the tantalizing possibility of personalized ci- cadian rhythm estimator and light therapy.
    American Control Conference (ACC), 2013; 06/2013
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    • "For the entrainment to a specified phase shift, we compare the minimum time solution with two other methods: 1) The natural 12-hr light-dark cycle entrainment, 2) The feedback algorithm that we have previously presented [13] "
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    ABSTRACT: Circadian rhythm is the biological process critical to the well being of all living organisms. The circadian rhythms oscillate with a period of approximately 24 hours due to the light-darkness pattern of the solar day. Circadian disruption, as experienced by night shift workers, travelers, submariners or miners, can lead to lower productivity, sleep disorder, and other more serious health problems. Using artificial light to regulate the circadian rhythm has long been proposed. The common approach is to use the phase response curve - the amount of steady state phase shift due to light pulses applied at specified times. In this paper, we consider a commonly used nonlinear second order oscillator model for the circadian rhythm response with light intensity as the input. Our first goal is to establish a performance bound by solving the minimum time control problem for a specified phase shift with contrained light intensity. The result is a much faster phase shift as compared to natural light-darkness pattern. We further extend the optimal control to vigilance, which is regulated in part by circadian rhythm, to maximize a vigilance lower bound for specified time and duration. Based on the two-process model of vigilance, the problem is formulated as an optimal control of switched system, and the optimization strategy is demonstrated via a simulation example.
    Decision and Control (CDC), 2012 IEEE 51st Annual Conference on; 01/2012
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    • "= z u (t + ∆T ) , r b = z f (t + ∆T ) r c = z f (t + ∆T ) − z u (t + ∆T ) . Since we do not have f 0 (z) at this point, we approximately the unforced dynamics by its describing function, ˙ z u = A DF Z u [7] "
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    ABSTRACT: Due to the 24-hour lighting-dark cycle on earth, circadian rhythm regulates the biochemical and physiological processes of almost all living organisms, including plants, insects, and mammals. Maintaining the regular cyclicity of this internal clock, called entrainment, is important to the well being of an organism. For human, circadian disruption can lead to lower productivity, digestive problems, decreased sleep efficiency and other health problems. Various models have been proposed for the circadian rhythm, from empirical oscillator type models to genetic network based biochemical models. These models are used to gain insight into the mechanism governing the circadian rhythm, but may also be used to formulate light-based control strategies for its regulation. As a first step towards our eventual goal of light based circadian rhythm regulation for human, we are conducting experiments with drosophila (fruit fly), measuring the interaction between light intensity and wavelength and its locomotive activity level. Instead of the high order biochemical models proposed in the past, we consider a second order empirical oscillator model, with light intensity as input and activity as the output. By first entraining the flies in a regular rhythm and then observe the effect of light pulses, we are able to identify the model parameters based on the input/output experimental data. The model shows promising predictive capability: Our simulation shows that two blue pulses can shift the phase of drosophila circadian pacemaker by 12 hours, while the experiment result is 13.3 hours.
    American Control Conference (ACC), 2011; 08/2011
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