Efficient Estimation of the Human Circadian Phase via Kalman Filtering.

Circadian rhythms play a vital role in maintaining a person's well-being but remain difficult to quantify accurately. Numerous approaches exist to measure these rhythms, but they often suffer from performance issues on the individual level. This work implements a Steady-State Kalman Filter as a method for estimating the circadian phase shifts from biometric signals. Our framework can automatically fit the filter's parameters to biometric data obtained for each individual, and we were able to consistently estimate the phase shift within 1 hour of melatonin estimates on 100% of all subjects in this study. The estimation method opens up the possibility of real-time control and assessment of the circadian system, as well as chronotherapeutic intervention.Clinical relevance- This establishes a near real-time alternative to melatonin measurements for the estimation of circadian phase shifts, with potential applications in feedback circadian control and chronotherapeutics.

Robustness of Optimal Circadian Rhythm Entrainment under Model Perturbation.

The optimal circadian rhythm entrainment problem has been studied based on mathematical models, e.g. the Kronauer model. In this paper, we study the robustness of light-based circadian rhythm entrainment under model parameter perturbations as well as propose a feedback control law to improve the robustness of the entrainment strategy. Our study finds the model parameter whose perturbations affect the entrainment the most. We also find that feedback control reduces the sensivitity of the entrainment process to model parameter perturbations.Clinical relevance- Circadian misalignment has negative impacts on health, such as higher risks of cardiovascular disease and cancer. We present a numerical study of how well optimized circadian rhythm entrainment plans that are derived from a generic mathematical model work on personalized cases.

Trajectory Generation for Flexible-Joint Space Manipulators.

Space manipulator arms often exhibit significant joint flexibility and limited motor torque. Future space missions, including satellite servicing and large structure assembly, may involve the manipulation of massive objects, which will accentuate these limitations. Currently, astronauts use visual feedback on-orbit to mitigate oscillations and trajectory following issues. Large time delays between orbit and Earth make ground teleoperation difficult in these conditions, so more autonomous operations must be considered to remove the astronaut resource requirement and expand robotic capabilities in space. Trajectory planning for autonomous systems must therefore be considered to prevent poor trajectory tracking performance. We provide a model-based trajectory generation methodology that incorporates constraints on joint speed, motor torque, and base actuation for flexible-joint space manipulators while minimizing total trajectory time. Full spatial computer simulation results, as well as physical experiment results with a single-joint robot on an air bearing table, show the efficacy of our methodology.

Fast tuning of observer-based circadian phase estimator using biometric data.

Circadian rhythms play a vital role in maintaining an individual's well-being, and they have been shown to be the product of the master oscillator in the suprachiasmatic nuclei (SCN) located in the brain. The SCN however, is inaccessible for assessment, so existing standards for circadian phase estimation often focus on the use of indirect measurements as proxies for the circadian state. These methods often suffer from severe delays due to invasive methods of sample collection, making online estimation impossible. In this paper, we propose a linear state observer as an elegant solution for continuous phase estimation. This observer-based filter is used in isolating the frequency components of input biometric signals, which are then taken to be the circadian state. We start the design process by fixing the observer's oscillatory frequency at 24 hours, and then we tune its gains using an evolutionary optimization algorithm to extract the target components from individuals' data. The resulting filter was able to provide phase estimates with an average absolute error within 1.5 hours on all test subjects, given their minute-to-minute actigraphy data collected in ambulatory conditions.

Optimization of light exposure and sleep schedule for circadian rhythm entrainment.

The circadian rhythm, called Process C, regulates a wide range of biological processes in humans including sleep, metabolism, body temperature, and hormone secretion. Light is the dominant synchronizer of the circadian rhythm-it has been used to regulate the circadian phase to cope with jet-lag, shift work, and sleep disorder. The homeostatic oscillation of the sleep drive is called Process S. Process C and Process S together determine the sleep-wake cycle in what is known as the two-process model. This paper addresses the regulation of both Process C and Process S by scheduling light exposure and sleep based on numerical simulations of circadian rhythm and sleep mathematical models. This is a significant step beyond the existing literature that only considers the entrainment of Process C. Regulation of the two-process model poses several unique features and challenges: 1. Process S is non-smooth, i.e., the homeostatic dynamics are different in the sleep and wake regimes; 2. Light only indirectly affects Process S through Process C; 3. Light does not affect Process C during sleep. We consider two scenarios: optimizing light intensity as the control input with spontaneous (i.e., unscheduled) sleep/wake times and jointly optimizing the light intensity and the sleep/wake times, which allows limited delayed sleep and early waking as part of the decision variables. We solve the time-optimal entrainment problem for the two-process model for both scenarios using an extension of the gradient descent algorithm to non-smooth systems. To illustrate the efficacy of our time-optimal entrainment strategies, we consider two common use cases: transmeridian travelers and shift workers. For transmeridian travelers, joint optimization of the two-process model avoids the unrealistic long wake duration when only Process C is considered. The entrainment time also decreases when both the light input and the sleep schedule are optimized compared to when only the light input is optimized. For shift workers, we show that the entrainment time is significantly shortened by optimizing the night shift working light.

Actigraphy-based parameter tuning process for adaptive notch filter and circadian phase shift estimation.

We report herein the application of an adaptive notch filter (ANF) algorithm to minute-by-minute actigraphy data to estimate the continuous circadian phase of eight healthy adults. As the adaptation rates and damping factor of the ANF algorithm have large impacts on the ANF states and circadian phase estimation results, we propose a method for optimizing these parameters. The ANF with optimal parameters is further used to estimate the circadian phase shift from the actigraphy data. Dim light melatonin onset (DLMO), considered the "gold standard" method for identification of circadian phase, was determined by a serial collection of salivary samples analyzed for melatonin per standard protocol simultaneously with the collection of actigraphic data. We demonstrate our ANF algorithm, when applied to the actigraphy data, is able to estimate the circadian phase as determined by the DLMO. These results demonstrate that applying our ANF with a well-defined parameter tuning process to actigraphic data can provide accurate measurements of the circadian phase and its shift without resorting to salivary melatonin collections.

Time optimal entrainment control for circadian rhythm.

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.