Validation of the Entrainment Signal Regularity Index and associations with children's changes in BMI

OBJECTIVE

This study examined the validity of a novel metric of circadian health, the Entrainment Signal Regularity Index (ESRI), and its relationship to changes in BMI during the school year and summer.

METHODS

In a longitudinal observational data set, this study examined the relationship between ESRI score and children's (n = 119, 5- to 8-year-olds) sleep and physical activity levels during the school year and summer, differences in ESRI score during the school year and summer, and the association of ESRI score during the school year and summer with changes in BMI across those time periods.

RESULTS

The ESRI score was higher during the school year (0.70 ± 0.10) compared with summer (0.63 ± 0.11); t(111) = 5.484, p < 0.001. Whereas the ESRI score at the beginning of the school year did not significantly predict BMI change during the school year (β = 0.05 ± 0.09 SE, p = 0.57), having a higher ESRI score during summer predicted smaller increases in BMI during summer (β = -0.22 ± 0.10 SE, p = 0.03).

CONCLUSIONS

Overall, children demonstrated higher entrainment regularity during the school year compared with the summer. During summer, having a higher entrainment signal was associated with smaller changes in summertime BMI. This effect was independent of the effects of children's sleep midpoint, sleep regularity, and physical activity on children's BMI.

Estimating circadian phase in elementary school children: leveraging advances in physiologically informed models of circadian entrainment and wearable devices

STUDY OBJECTIVES

Examine the ability of a physiologically based mathematical model of human circadian rhythms to predict circadian phase, as measured by salivary dim light melatonin onset (DLMO), in children compared to other proxy measurements of circadian phase (bedtime, sleep midpoint, and wake time).

METHODS

As part of an ongoing clinical trial, a sample of 29 elementary school children (mean age: 7.4 ± .97 years) completed 7 days of wrist actigraphy before a lab visit to assess DLMO. Hourly salivary melatonin samples were collected under dim light conditions (<5 lx). Data from actigraphy were used to generate predictions of circadian phase using both a physiologically based circadian limit cycle oscillator mathematical model (Hannay model), and published regression equations that utilize average sleep onset, midpoint, and offset to predict DLMO. Agreement of proxy predictions with measured DLMO were assessed and compared.

RESULTS

DLMO predictions using the Hannay model outperformed DLMO predictions based on children's sleep/wake parameters with a Lin's Concordance Correlation Coefficient (LinCCC) of 0.79 compared to 0.41-0.59 for sleep/wake parameters. The mean absolute error was 31 min for the Hannay model compared to 35-38 min for the sleep/wake variables.

CONCLUSION

Our findings suggest that sleep/wake behaviors were weak proxies of DLMO phase in children, but mathematical models using data collected from wearable data can be used to improve the accuracy of those predictions. Additional research is needed to better adapt these adult models for use in children.

CLINICAL TRIAL

The i Heart Rhythm Project: Healthy Sleep and Behavioral Rhythms for Obesity Prevention https://clinicaltrials.gov/ct2/show/NCT04445740.

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.

Macroscopic Models for Human Circadian Rhythms

Mathematical models have a long and influential history in the study of human circadian rhythms. Accurate predictive models for the human circadian light response have been used to study the impact of a host of light exposures on the circadian system. However, generally, these models do not account for the physiological basis of these rhythms. We illustrate a new paradigm for deriving models of the human circadian light response. Beginning from a high-dimensional model of the circadian neural network, we systematically derive low-dimensional models using an approach motivated by experimental measurements of circadian neurons. This systematic reduction allows for the variables and parameters of the derived model to be interpreted in a physiological context. We fit and validate the resulting models to a library of experimental measurements. Finally, we compare model predictions for experimental measurements of light levels and discuss the differences between our model’s predictions and previous models. Our modeling paradigm allows for the integration of experimental measurements across the single-cell, tissue, and behavioral scales, thereby enabling the development of accurate low-dimensional models for human circadian rhythms.

Potential circadian and circannual rhythm contributions to the obesity epidemic in elementary school age children

Children gain weight at an accelerated rate during summer, contributing to increases in the prevalence of overweight and obesity in elementary-school children (i.e., approximately 5 to 11 years old in the US). Int J Behav Nutr Phys Act 14:100, 2017 explained these changes with the "Structured Days Hypothesis" suggesting that environmental changes in structure between the school year and the summer months result in behavioral changes that ultimately lead to accelerated weight gain. The present article explores an alternative explanation, the circadian clock, including the effects of circannual changes and social demands (i.e., social timing resulting from societal demands such as school or work schedules), and implications for seasonal patterns of weight gain. We provide a model for understanding the role circadian and circannual rhythms may play in the development of child obesity, a framework for examining the intersection of behavioral and biological causes of obesity, and encouragement for future research into bio-behavioral causes of obesity in children.

Macroscopic models for networks of coupled biological oscillators

The study of synchronization of coupled biological oscillators is fundamental to many areas of biology including neuroscience, cardiac dynamics, and circadian rhythms. Mathematical models of these systems may involve hundreds of variables in thousands of individual cells resulting in an extremely high-dimensional description of the system. This often contrasts with the low-dimensional dynamics exhibited on the collective or macroscopic scale for these systems. We introduce a macroscopic reduction for networks of coupled oscillators motivated by an elegant structure we find in experimental measurements of circadian protein expression and several mathematical models for coupled biological oscillators. The observed structure in the collective amplitude of the oscillator population differs from the well-known Ott-Antonsen ansatz, but its emergence can be characterized through a simple argument depending only on general phase-locking behavior in coupled oscillator systems. We further demonstrate its emergence in networks of noisy heterogeneous oscillators with complex network connectivity. Applying this structure, we derive low-dimensional macroscopic models for oscillator population activity. This approach allows for the incorporation of cellular-level experimental data into the macroscopic model whose parameters and variables can then be directly associated with tissue- or organism-level properties, thereby elucidating the core properties driving the collective behavior of the system.

Collective phase response curves for heterogeneous coupled oscillators

Phase response curves (PRCs) have become an indispensable tool in understanding the entrainment and synchronization of biological oscillators. However, biological oscillators are often found in large coupled heterogeneous systems and the variable of physiological importance is the collective rhythm resulting from an aggregation of the individual oscillations. To study this phenomena we consider phase resetting of the collective rhythm for large ensembles of globally coupled Sakaguchi-Kuramoto oscillators. Making use of Ott-Antonsen theory we derive an asymptotically valid analytic formula for the collective PRC. A result of this analysis is a characteristic scaling for the change in the amplitude and entrainment points for the collective PRC compared to the individual oscillator PRC. We support the analytical findings with numerical evidence and demonstrate the applicability of the theory to large ensembles of coupled neuronal oscillators.