Circadian rhythm modeling, estimation and control based on dynamic lighting

Abstract

Taking advantage of the signal processing algorithm, we propose a new modeling and control strategy by combining the circadian system and the signal processing algorithm as a black box. The dynamics of the black box is approximated by a linear parameter varying model, with light as input and estimated circadian signal argument as output. Gain-scheduling feedback control stabilizes the estimated argument around the desired argument. The overall modeling and control approach is demonstrated in simulation using both empirical and biomolecular circadian models.

The Earth has a regular 24-hour pattern of daylight and darkness over most of its surface. Terrestrial species have adapted to this daily pattern by evolving biological rhythms, called circadian rhythms, that repeat at approximately 24-hour intervals. The circadian rhythm governs a wide range of biological cycles, from cell division, to hormone production, to behavior (e.g., sleep-wake) that, when synchronized with the natural light/dark cycle, enables the organism to entrain these cycles to its particular photic niche (diurnal or nocturnal) and to its location on Earth. For human, the lack of synchrony between the master clock in circadian rhythm and the external environment can lead to circadian disruption, with potential detrimental consequences ranging from increased sleepiness and decreased attention span during the day, lower productivity, gastrointestinal disorders, to long-term health problems such as increased risk for cancer, diabetes, obesity, and cardiovascular disorders. The circadian disruption may be caused by, for example, irregular sleep patterns of soldiers in the battlefield, artificial deprivation of light of submariners or mine workers, frequent shifted sleep-wake cycles of night nurses, and shifted light-dark cycles for travelers across multiple time zones. Human circadian pacemaker receives inputs from a variety of environmental cues. Light is capable of shifting the circadian clock. Furthermore, light information is the major cue in the establishment and maintenance of entrainment to the natural day.

This thesis investigates circadian control algorithms using simulation and model analysis. Based on the literature review of existing circadian models, Kronauer model is employed for its simplicity and the quantified light input. In controller design, the major challenge is the nonlinearity of the system. Compared with existing control algorithms, we can demonstrate the stabilities of open loop control algorithm and our feedback control algorithm using Poincare return map and reachable set of hybrid system. We propose optimal control algorithms that theoretically satisfy the necessary conditions of optimality, and are solvable in a computationally efficient manner.

For closed loop feedback control, one critical link is to estimate the argument of the circadian signal. The challenges of the signal processing include non-sinusoidal waveform, unknown signal parameters, slowly time varying parameters and recursive estimation. We develop an adaptive signal processing algorithm which has the potential to estimate the circadian signal argument in real time. Compared with the existing algorithms, our approach can adaptively process semi-periodic signals with high order harmonics and DC bias, and are theoretically proved to be locally stable. The algorithm is tested on synthetic signals and Drosophila locomotor activity data.