Estimating Representative Group Intrinsic Circadian Period from Illuminance-Response Curve Data

Modeling the Effects of Napping and Non-napping Patterns of Light Exposure on the Human Circadian Oscillator

In early childhood, consolidation of sleep from a biphasic to a monophasic sleep-wake pattern, that is, the transition from sleeping during an afternoon nap and at night to sleeping only during the night, represents a major developmental milestone. Reduced napping behavior is associated with an advance in the timing of the circadian system; however, it is unknown if this advance represents a standard response of the circadian clock to altered patterns of light exposure or if it additionally reflects features of the developing circadian system. Using a mathematical model of the human circadian pacemaker, we investigated the impact of napping and non-napping patterns of light exposure on entrained circadian phases. Simulated light schedules were based on published data from 20 children (34.2 ± 2.0 months) with habitual napping or non-napping sleep patterns (15 nappers). We found the model predicted different circadian phases for napping and non-napping light patterns: both the decrease in afternoon light during the nap and the increase in evening light associated with napping toddlers' later bedtimes contributed to the observed circadian phase difference produced between napping and non-napping light schedules. We systematically quantified the effects on phase shifting of nap duration, timing, and light intensity, finding larger phase delays occurred for longer and earlier naps. In addition, we simulated phase response curves to a 1-h light pulse and 1-h dark pulse to predict phase and intensity dependence of these changes in light exposure. We found the light pulse produced larger shifts compared with the dark pulse, and we analyzed the model dynamics to identify the features contributing to this asymmetry. These findings suggest that napping status affects circadian timing due to altered patterns of light exposure, with the dynamics of the circadian clock and light processing mediating the effects of the dark pulse associated with a daytime nap.

Parameter Estimation in a Model of the Human Circadian Pacemaker Using a Particle Filter

OBJECTIVE

In the near future, real-time estimation of peoples unique, precise circadian clock state has the potential to improve the efficacy of medical treatments and improve human performance on a broad scale. Human-centric lighting can bring circadian-rhythm support using biodynamic lighting solutions that sync light with the time of day. We investigate a method to improve the tracking of individual's circadian processes.

METHODS

In literature, the human circadian physiology has been mathematically modeled using ordinary differential equations, the state of which can be tracked via the signal processing concept of a Particle Filter. We show that substantial improvements can be made if the estimator not only tracks state variables, such as the phase and amplitude of the circadian pacemaker, but also fits specific model parameters to the individual. In particular, we optimize model parameter τ_x, which reflects the intrinsic period of the circadian pacemaker ( τ). We show that both state and model parameters can be estimated based on minimally-invasive light exposure measurements and sleep-wake state observations. We also quantify the effect of inaccuracies in sensing.

RESULTS

We demonstrate improved performance by estimating τ_x for every individual, both with artificially created and human subject data. Prediction accuracy improves with every newly available observation. The estimated τ_x-s correlate well with the subjects' chronotypes, in a similar way as τ correlates.

CONCLUSION

Our results show that individualizing the estimation of model parameters can improve circadian state estimation accuracy.

SIGNIFICANCE

These findings underscore the potential improvements in personalized models over one-size fits all approaches.

Integrating wearable data into circadian models

The emergence of wearable health sensors in the last decade has the potential to revolutionize the study of sleep and circadian rhythms. In particular, recent progress has been made in the use of mathematical models in the prediction of a patient's internal circadian state using data measured by wearable devices. This is a vital step in our ability to identify optimal circadian timing for health interventions. We review the available data for fitting circadian phase models with a focus on wearable data sets. Finally, we review the current modeling paradigms and explore avenues for developing personalized parameter sets in limit cycle oscillator models in order to further improve prediction accuracy.