Application of a Limit-Cycle Oscillator Model for Prediction of Circadian Phase in Rotating Night Shift Workers

SleepSync: Early Testing of a Personalised Sleep-Wake Management Smartphone Application for Improving Sleep and Cognitive Fitness in Defence Shift Workers

Shift work, long work hours, and operational tasks contribute to sleep and circadian disruption in defence personnel, with profound impacts on cognition. To address this, a digital technology, the SleepSync app, was designed for use in defence. A pre-post design study was undertaken to examine whether four weeks app use improved sleep and cognitive fitness (high performance neurocognition) in a cohort of shift workers from the Royal Australian Air Force. In total, 13 of approximately 20 shift-working personnel from one base volunteered for the study. Sleep outcomes were assessed using the Insomnia Severity Index (ISI), the Patient-Reported Outcomes Measurement Information System (PROMIS), Sleep Disturbance and Sleep-Related Impairment Scales, the Glasgow Sleep Effort Scale, the Sleep Hygiene Index, and mental health was assessed using the Depression, Anxiety, and Stress Scale-21. Sustained attention was measured using the 3-min Psychomotor Vigilance Task (PVT) and controlled response using the NBack. Results showed significant improvements in insomnia (ISI scores 10.31 at baseline and 7.50 after app use), sleep-related impairments (SRI T-scores 53.03 at baseline to 46.75 post-app use), and healthy sleep practices (SHI scores 21.61 at baseline to 18.83 post-app use; all p < 0.001). Trends for improvement were recorded for depression. NBack incorrect responses reduced significantly (9.36 at baseline; reduced by -3.87 at last week of app use, p < 0.001), but no other objective measures improved. These findings suggest that SleepSync may improve sleep and positively enhance cognitive fitness but warrants further investigation in large samples. Randomised control trials with other cohorts of defence personnel are needed to confirm the utility of this intervention in defence settings.

Association of Rest-Activity Rhythm and Risk of Developing Dementia or Mild Cognitive Impairment in the Middle-Aged and Older Population: Prospective Cohort Study

BACKGROUND

The relationship between 24-hour rest-activity rhythms (RARs) and risk for dementia or mild cognitive impairment (MCI) remains an area of growing interest. Previous studies were often limited by small sample sizes, short follow-ups, and older participants. More studies are required to fully explore the link between disrupted RARs and dementia or MCI in middle-aged and older adults.

OBJECTIVE

We leveraged the UK Biobank data to examine how RAR disturbances correlate with the risk of developing dementia and MCI in middle-aged and older adults.

METHODS

We analyzed the data of 91,517 UK Biobank participants aged between 43 and 79 years. Wrist actigraphy recordings were used to derive nonparametric RAR metrics, including the activity level of the most active 10-hour period (M10) and its midpoint, the activity level of the least active 5-hour period (L5) and its midpoint, relative amplitude (RA) of the 24-hour cycle [RA=(M10-L5)/(M10+L5)], interdaily stability, and intradaily variability, as well as the amplitude and acrophase of 24-hour rhythms (cosinor analysis). We used Cox proportional hazards models to examine the associations between baseline RAR and subsequent incidence of dementia or MCI, adjusting for demographic characteristics, comorbidities, lifestyle factors, shiftwork status, and genetic risk for Alzheimer's disease.

RESULTS

During the follow-up of up to 7.5 years, 555 participants developed MCI or dementia. The dementia or MCI risk increased for those with lower M10 activity (hazard ratio [HR] 1.28, 95% CI 1.14-1.44, per 1-SD decrease), higher L5 activity (HR 1.15, 95% CI 1.10-1.21, per 1-SD increase), lower RA (HR 1.23, 95% CI 1.16-1.29, per 1-SD decrease), lower amplitude (HR 1.32, 95% CI 1.17-1.49, per 1-SD decrease), and higher intradaily variability (HR 1.14, 95% CI 1.05-1.24, per 1-SD increase) as well as advanced L5 midpoint (HR 0.92, 95% CI 0.85-0.99, per 1-SD advance). These associations were similar in people aged <70 and >70 years, and in non-shift workers, and they were independent of genetic and cardiovascular risk factors. No significant associations were observed for M10 midpoint, interdaily stability, or acrophase.

CONCLUSIONS

Based on findings from a large sample of middle-to-older adults with objective RAR assessment and almost 8-years of follow-up, we suggest that suppressed and fragmented daily activity rhythms precede the onset of dementia or MCI and may serve as risk biomarkers for preclinical dementia in middle-aged and older adults.

Longitudinal associations of diurnal rest-activity rhythms with fatigue, insomnia, and health-related quality of life in survivors of colorectal cancer up to 5 years post-treatment

BACKGROUND

There is a growing population of survivors of colorectal cancer (CRC). Fatigue and insomnia are common symptoms after CRC, negatively influencing health-related quality of life (HRQoL). Besides increasing physical activity and decreasing sedentary behavior, the timing and patterns of physical activity and rest over the 24-h day (i.e. diurnal rest-activity rhythms) could also play a role in alleviating these symptoms and improving HRQoL. We investigated longitudinal associations of the diurnal rest-activity rhythm (RAR) with fatigue, insomnia, and HRQoL in survivors of CRC.

METHODS

In a prospective cohort study among survivors of stage I-III CRC, 5 repeated measurements were performed from 6 weeks up to 5 years post-treatment. Parameters of RAR, including mesor, amplitude, acrophase, circadian quotient, dichotomy index, and 24-h autocorrelation coefficient, were assessed by a custom MATLAB program using data from tri-axial accelerometers worn on the upper thigh for 7 consecutive days. Fatigue, insomnia, and HRQoL were measured by validated questionnaires. Confounder-adjusted linear mixed models were applied to analyze longitudinal associations of RAR with fatigue, insomnia, and HRQoL from 6 weeks until 5 years post-treatment. Additionally, intra-individual and inter-individual associations over time were separated.

RESULTS

Data were available from 289 survivors of CRC. All RAR parameters except for 24-h autocorrelation increased from 6 weeks to 6 months post-treatment, after which they remained relatively stable. A higher mesor, amplitude, circadian quotient, dichotomy index, and 24-h autocorrelation were statistically significantly associated with less fatigue and better HRQoL over time. A higher amplitude and circadian quotient were associated with lower insomnia. Most of these associations appeared driven by both within-person changes over time and between-person differences in RAR parameters. No significant associations were observed for acrophase.

CONCLUSIONS

In the first five years after CRC treatment, adhering to a generally more active (mesor) and consistent (24-h autocorrelation) RAR, with a pronounced peak activity (amplitude) and a marked difference between daytime and nighttime activity (dichotomy index) was found to be associated with lower fatigue, lower insomnia, and a better HRQoL. Future intervention studies are needed to investigate if restoring RAR among survivors of CRC could help to alleviate symptoms of fatigue and insomnia while enhancing their HRQoL.

TRIAL REGISTRATION

EnCoRe study NL6904 ( https://www.onderzoekmetmensen.nl/ ).

Causal dynamics of sleep, circadian rhythm, and mood symptoms in patients with major depression and bipolar disorder: insights from longitudinal wearable device data

BACKGROUND

Sleep and circadian rhythm disruptions are common in patients with mood disorders. The intricate relationship between these disruptions and mood has been investigated, but their causal dynamics remain unknown.

METHODS

We analysed data from 139 patients (76 female, mean age = 23.5 ± 3.64 years) with mood disorders who participated in a prospective observational study in South Korea. The patients wore wearable devices to monitor sleep and engaged in smartphone-delivered ecological momentary assessment of mood symptoms. Using a mathematical model, we estimated their daily circadian phase based on sleep data. Subsequently, we obtained daily time series for sleep/circadian phase estimates and mood symptoms spanning >40,000 days. We analysed the causal relationship between the time series using transfer entropy, a non-linear causal inference method.

FINDINGS

The transfer entropy analysis suggested causality from circadian phase disturbance to mood symptoms in both patients with MDD (n = 45) and BD type I (n = 35), as 66.7% and 85.7% of the patients with a large dataset (>600 days) showed causality, but not in patients with BD type II (n = 59). Surprisingly, no causal relationship was suggested between sleep phase disturbances and mood symptoms.

INTERPRETATION

Our findings suggest that in patients with mood disorders, circadian phase disturbances directly precede mood symptoms. This underscores the potential of targeting circadian rhythms in digital medicine, such as sleep or light exposure interventions, to restore circadian phase and thereby manage mood disorders effectively.

FUNDING

Institute for Basic Science, the Human Frontiers Science Program Organization, the National Research Foundation of Korea, and the Ministry of Health & Welfare of South Korea.

State of the science and recommendations for using wearable technology in sleep and circadian research

Wearable sleep-tracking technology is of growing use in the sleep and circadian fields, including for applications across other disciplines, inclusive of a variety of disease states. Patients increasingly present sleep data derived from their wearable devices to their providers and the ever-increasing availability of commercial devices and new-generation research/clinical tools has led to the wide adoption of wearables in research, which has become even more relevant given the discontinuation of the Philips Respironics Actiwatch. Standards for evaluating the performance of wearable sleep-tracking devices have been introduced and the available evidence suggests that consumer-grade devices exceed the performance of traditional actigraphy in assessing sleep as defined by polysomnogram. However, clear limitations exist, for example, the misclassification of wakefulness during the sleep period, problems with sleep tracking outside of the main sleep bout or nighttime period, artifacts, and unclear translation of performance to individuals with certain characteristics or comorbidities. This is of particular relevance when person-specific factors (like skin color or obesity) negatively impact sensor performance with the potential downstream impact of augmenting already existing healthcare disparities. However, wearable sleep-tracking technology holds great promise for our field, given features distinct from traditional actigraphy such as measurement of autonomic parameters, estimation of circadian features, and the potential to integrate other self-reported, objective, and passively recorded health indicators. Scientists face numerous decision points and barriers when incorporating traditional actigraphy, consumer-grade multi-sensor devices, or contemporary research/clinical-grade sleep trackers into their research. Considerations include wearable device capabilities and performance, target population and goals of the study, wearable device outputs and availability of raw and aggregate data, and data extraction, processing, and analysis. Given the difficulties in the implementation and utilization of wearable sleep-tracking technology in real-world research and clinical settings, the following State of the Science review requested by the Sleep Research Society aims to address the following questions. What data can wearable sleep-tracking devices provide? How accurate are these data? What should be taken into account when incorporating wearable sleep-tracking devices into research? These outstanding questions and surrounding considerations motivated this work, outlining practical recommendations for using wearable technology in sleep and circadian research.

Mathematical Analysis of Light-sensitivity Related Challenges in Assessment of the Intrinsic Period of the Human Circadian Pacemaker

Accurate assessment of the intrinsic period of the human circadian pacemaker is essential for a quantitative understanding of how our circadian rhythms are synchronized to exposure to natural and man-made light-dark (LD) cycles. The gold standard method for assessing intrinsic period in humans is forced desynchrony (FD) which assumes that the confounding effect of lights-on assessment of intrinsic period is removed by scheduling sleep-wake and associated dim LD cycles to periods outside the range of entrainment of the circadian pacemaker. However, the observation that the mean period of free-running blind people is longer than the mean period of sighted people assessed by FD (24.50 ± 0.17 h vs 24.15 ± 0.20 h, p < 0.001) appears inconsistent with this assertion. Here, we present a mathematical analysis using a simple parametric model of the circadian pacemaker with a sinusoidal velocity response curve (VRC) describing the effect of light on the speed of the oscillator. The analysis shows that the shorter period in FD may be explained by exquisite sensitivity of the human circadian pacemaker to low light intensities and a VRC with a larger advance region than delay region. The main implication of this analysis, which generates new and testable predictions, is that current quantitative models for predicting how light exposure affects entrainment of the human circadian system may not accurately capture the effect of dim light. The mathematical analysis generates new predictions which can be tested in laboratory experiments. These findings have implications for managing healthy entrainment of human circadian clocks in societies with abundant access to light sources with powerful biological effects.

Uncovering personal circadian responses to light through particle swarm optimization

BACKGROUND AND OBJECTIVES

Kronauer's oscillator model of the human central pacemaker is one of the most commonly used approaches to study the human circadian response to light. Two sources of error when applying it to a personal light exposure have been identified: (1) as a populational model, it does not consider inter-individual variability, and (2) the initial conditions needed to integrate the model are usually unknown, and thus subjectively estimated. In this work, we evaluate the ability of particle swarm optimization (PSO) algorithms to simultaneously uncover the optimal initial conditions and individual parameters of a pre-defined Kronauer's oscillator model.

METHODS

A Canonical PSO, a Dynamic Multi-Swarm PSO and a novel modification of the latter, namely Hierarchical Dynamic Multi-Swarm PSO, are evaluated. Two different target models (under a regular and an irregular schedule) are defined, and the same realistic light profile is fed to them. Based on their output, a fitness function is proposed, which is minimized by the algorithms to find the optimum set of parameters and initial conditions of the model.

RESULTS

We demonstrate that Dynamic Multi-Swarm and Hierarchical Dynamic Multi-Swarm algorithms can accurately uncover personal circadian parameters under both regular and irregular schedules, but as expected, optimization is easier under a regular schedule. Circadian parameters play the most important role in the optimization process and should be prioritized over initial conditions, although assessment of the impact of misestimating the latter is recommended. The log-log linear relationship between mean absolute error and computational cost shows that the number of particles to use is at the discretion of the user.

CONCLUSIONS

The robustness and low errors achieved by the algorithms support their further testing, validation and systematic application to empirical data under a regular or irregular schedule. Uncovering personal circadian parameters can improve the assessment of the circadian status of a person and the applicability of personalized light therapies, as well as help to discover other factors that may lie behind the interindividual variability in the circadian response to light.

A real-time, personalized sleep intervention using mathematical modeling and wearable devices

The prevalence of artificial light exposure has enabled us to be active any time of the day or night, leading to the need for high alertness outside of traditional daytime hours. To address this need, we developed a personalized sleep intervention framework that analyzes real-world sleep-wake patterns obtained from wearable devices to maximize alertness during specific target periods. Our framework utilizes a mathematical model that tracks the dynamic sleep pressure and circadian rhythm based on the user's sleep history. In this way, the model accurately predicts real-time alertness, even for shift workers with complex sleep and work schedules (N = 71, t = 13~21 days). This allowed us to discover a new sleep-wake pattern called the adaptive circadian split sleep, which incorporates a main sleep period and a late nap to enable high alertness during both work and non-work periods of shift workers. We further developed a mobile application that integrates this framework to recommend practical, personalized sleep schedules for individual users to maximize their alertness during a targeted activity time based on their desired sleep onset and available sleep duration. This can reduce the risk of errors for those who require high alertness during nontraditional activity times and improve the health and quality of life for those leading shift work-like lifestyles.

Pilot feasibility testing of biomathematical model recommendations for personalising sleep timing in shift workers

Sleep disturbances and circadian disruption play a central role in adverse health, safety, and performance outcomes in shift workers. While biomathematical models of sleep and alertness can be used to personalise interventions for shift workers, their practical implementation is undertested. This study tested the feasibility of implementing two biomathematical models-the Phillips-Robinson Model and the Model for Arousal Dynamics-in 28 shift-working nurses, 14 in each group. The study examined the overlap and adherence between model recommendations and sleep behaviours, and changes in sleep following the implementation of recommendations. For both groups combined, the mean (SD) percentage overlap between when a model recommended an individual to sleep and when sleep was obtained was 73.62% (10.24%). Adherence between model recommendations and sleep onset and offset times was significantly higher with the Model of Arousal Dynamics compared to the Phillips-Robinson Model. For the Phillips-Robinson model, 27% of sleep onset and 35% of sleep offset times were within ± 30 min of model recommendations. For the Model of Arousal Dynamics, 49% of sleep onset, and 35% of sleep offset times were within ± 30 min of model recommendations. Compared to pre-study, significant improvements were observed post-study for sleep disturbance (Phillips-Robinson Model), and insomnia severity and sleep-related impairments (Model of Arousal Dynamics). Participants reported that using a digital, automated format for the delivery of sleep recommendations would enable greater uptake. These findings provide a positive proof-of-concept for using biomathematical models to recommend sleep in operational contexts.

Nurse rostering with fatigue modelling : Incorporating a validated sleep model with biological variations in nurse rostering

We use a real Nurse Rostering Problem and a validated model of human sleep to formulate the Nurse Rostering Problem with Fatigue. The fatigue modelling includes individual biologies, thus enabling personalised schedules for every nurse. We create an approximation of the sleep model in the form of a look-up table, enabling its incorporation into nurse rostering. The problem is solved using an algorithm that combines Mixed-Integer Programming and Constraint Programming with a Large Neighbourhood Search. A post-processing algorithm deals with errors, to produce feasible rosters minimising global fatigue. The results demonstrate the realism of protecting nurses from highly fatiguing schedules and ensuring the alertness of staff. We further demonstrate how minimally increased staffing levels enable lower fatigue, and find evidence to suggest biological complementarity among staff can be used to reduce fatigue. We also demonstrate how tailoring shifts to nurses' biology reduces the overall fatigue of the team, which means managers must grapple with the issue of fairness in rostering.

The circadian stimulus-oscillator model: Improvements to Kronauer’s model of the human circadian pacemaker

Modeling how patterns of light and dark affect circadian phase is important clinically and organizationally (e.g., the military) because circadian disruption can compromise health and performance. Limit-cycle oscillator models in various forms have been used to characterize phase changes to a limited set of light interventions. We approached the analysis of the van der Pol oscillator-based model proposed by Kronauer and colleagues in 1999 and 2000 (Kronauer99) using a well-established framework from experimental psychology whereby the stimulus (S) acts on the organism (O) to produce a response (R). Within that framework, using four independent data sets utilizing calibrated personal light measurements, we conducted a serial analysis of the factors in the Kronauer99 model that could affect prediction accuracy characterized by changes in dim-light melatonin onset. Prediction uncertainty was slightly greater than 1 h for the new data sets using the original Kronauer99 model. The revised model described here reduced prediction uncertainty for these same data sets by roughly half.

Circadian rhythms and disorders of the timing of sleep

The daily alternation between sleep and wakefulness is one of the most dominant features of our lives and is a manifestation of the intrinsic 24 h rhythmicity underlying almost every aspect of our physiology. Circadian rhythms are generated by networks of molecular oscillators in the brain and peripheral tissues that interact with environmental and behavioural cycles to promote the occurrence of sleep during the environmental night. This alignment is often disturbed, however, by contemporary changes to our living environments, work or social schedules, patterns of light exposure, and biological factors, with consequences not only for sleep timing but also for our physical and mental health. Characterised by undesirable or irregular timing of sleep and wakefulness, in this Series paper we critically examine the existing categories of circadian rhythm sleep-wake disorders and the role of the circadian system in their development. We emphasise how not all disruption to daily rhythms is driven solely by an underlying circadian disturbance, and take a broader, dimensional approach to explore how circadian rhythms and sleep homoeostasis interact with behavioural and environmental factors. Very few high-quality epidemiological and intervention studies exist, and wider recognition and treatment of sleep timing disorders are currently hindered by a scarcity of accessible and objective tools for quantifying sleep and circadian physiology and environmental variables. We therefore assess emerging wearable technology, transcriptomics, and mathematical modelling approaches that promise to accelerate the integration of our knowledge in sleep and circadian science into improved human health.

Cryptochrome 1 as a state variable of the circadian clockwork of the suprachiasmatic nucleus: Evidence from translational switching

The suprachiasmatic nucleus (SCN) of the hypothalamus is the principal clock driving circadian rhythms of physiology and behavior that adapt mammals to environmental cycles. Disruption of SCN-dependent rhythms compromises health, and so understanding SCN time keeping will inform management of diseases associated with modern lifestyles. SCN time keeping is a self-sustaining transcriptional/translational delayed feedback loop (TTFL), whereby negative regulators inhibit their own transcription. Formally, the SCN clock is viewed as a limit-cycle oscillator, the simplest being a trajectory of successive phases that progresses through two-dimensional space defined by two state variables mapped along their respective axes. The TTFL motif is readily compatible with limit-cycle models, and in Neurospora and Drosophila the negative regulators Frequency (FRQ) and Period (Per) have been identified as state variables of their respective TTFLs. The identity of state variables of the SCN oscillator is, however, less clear. Experimental identification of state variables requires reversible and temporally specific control over their abundance. Translational switching (ts) provides this, the expression of a protein of interest relying on the provision of a noncanonical amino acid. We show that the negative regulator Cryptochrome 1 (CRY1) fulfills criteria defining a state variable: ts-CRY1 dose-dependently and reversibly suppresses the baseline, amplitude, and period of SCN rhythms, and its acute withdrawal releases the TTFL to oscillate from a defined phase. Its effect also depends on its temporal pattern of expression, although constitutive ts-CRY1 sustained (albeit less stable) oscillations. We conclude that CRY1 has properties of a state variable, but may operate among several state variables within a multidimensional limit cycle.

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.

Distinct Circadian Assessments From Wearable Data Reveal Social Distancing Promoted Internal Desynchrony Between Circadian Markers

Mobile measures of human circadian rhythms (CR) are needed in the age of chronotherapy. Two wearable measures of CR have recently been validated: one that uses heart rate to extract circadian rhythms that originate in the sinoatrial node of the heart, and another that uses activity to predict the laboratory gold standard and central circadian pacemaker marker, dim light melatonin onset (DLMO). We first find that the heart rate markers of normal real-world individuals align with laboratory DLMO measurements when we account for heart rate phase error. Next, we expand upon previous work that has examined sleep patterns or chronotypes during the COVID-19 lockdown by studying the effects of social distancing on circadian rhythms. In particular, using data collected from the Social Rhythms app, a mobile application where individuals upload their wearable data and receive reports on their circadian rhythms, we compared the two circadian phase estimates before and after social distancing. Interestingly, we found that the lockdown had different effects on the two ambulatory measurements. Before the lockdown, the two measures aligned, as predicted by laboratory data. After the lockdown, when circadian timekeeping signals were blunted, these measures diverged in 70% of subjects (with circadian rhythms in heart rate, or CRHR, becoming delayed). Thus, while either approach can measure circadian rhythms, both are needed to understand internal desynchrony. We also argue that interventions may be needed in future lockdowns to better align separate circadian rhythms in the body.

Prediction of shiftworker alertness, sleep, and circadian phase using a model of arousal dynamics constrained by shift schedules and light exposure

STUDY OBJECTIVES

The study aimed to, for the first time, (1) compare sleep, circadian phase, and alertness of intensive care unit (ICU) nurses working rotating shifts with those predicted by a model of arousal dynamics; and (2) investigate how different environmental constraints affect predictions and agreement with data.

METHODS

The model was used to simulate individual sleep-wake cycles, urinary 6-sulphatoxymelatonin (aMT6s) profiles, subjective sleepiness on the Karolinska Sleepiness Scale (KSS), and performance on a Psychomotor Vigilance Task (PVT) of 21 ICU nurses working day, evening, and night shifts. Combinations of individual shift schedules, forced wake time before/after work and lighting, were used as inputs to the model. Predictions were compared to empirical data. Simulations with self-reported sleep as an input were performed for comparison.

RESULTS

All input constraints produced similar prediction for KSS, with 56%-60% of KSS scores predicted within ±1 on a day and 48%-52% on a night shift. Accurate prediction of an individual's circadian phase required individualized light input. Combinations including light information predicted aMT6s acrophase within ±1 h of the study data for 65% and 35%-47% of nurses on diurnal and nocturnal schedules. Minute-by-minute sleep-wake state overlap between the model and the data was between 81 ± 6% and 87 ± 5% depending on choice of input constraint.

CONCLUSIONS

The use of individualized environmental constraints in the model of arousal dynamics allowed for accurate prediction of alertness, circadian phase, and sleep for more than half of the nurses. Individual differences in physiological parameters will need to be accounted for in the future to further improve predictions.

Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory

Optimal entrainment of limit-cycle oscillators by strong periodic inputs is studied on the basis of the phase-amplitude reduction and Floquet theory. Two methods for deriving the input waveforms that keep the system state close to the original limit cycle are proposed, which enable the use of strong inputs for entrainment. The first amplitude-feedback method uses feedback control to suppress deviations of the system state from the limit cycle, while the second amplitude-penalty method seeks an input waveform that does not excite large deviations from the limit cycle in the feedforward framework. Optimal entrainment of the van der Pol and Willamowski-Rössler oscillators with real or complex Floquet exponents is analyzed as examples. It is demonstrated that the proposed methods can achieve considerably faster entrainment and provide wider entrainment ranges than the conventional method that relies only on phase reduction.

A classification approach to estimating human circadian phase under circadian alignment from actigraphy and photometry data

The time of dim light melatonin onset (DLMO) is the gold standard for circadian phase assessment in humans, but collection of samples for DLMO is time and resource-intensive. Numerous studies have attempted to estimate circadian phase from actigraphy data, but most of these studies have involved individuals on controlled and stable sleep-wake schedules, with mean errors reported between 0.5 and 1 hour. We found that such algorithms are less successful in estimating DLMO in a population of college students with more irregular schedules: Mean errors in estimating the time of DLMO are approximately 1.5-1.6 hours. We reframed the problem as a classification problem and estimated whether an individual's current phase was before or after DLMO. Using a neural network, we found high classification accuracy of about 90%, which decreased the mean error in DLMO estimation-identifying the time at which the switch in classification occurs-to approximately 1.3 hours. To test whether this classification approach was valid when activity and circadian rhythms are decoupled, we applied the same neural network to data from inpatient forced desynchrony studies in which participants are scheduled to sleep and wake at all circadian phases (rather than their habitual schedules). In participants on forced desynchrony protocols, overall classification accuracy dropped to 55%-65% with a range of 20%-80% for a given day; this accuracy was highly dependent upon the phase angle (ie, time) between DLMO and sleep onset, with the highest accuracy at phase angles associated with nighttime sleep. Circadian patterns in activity, therefore, should be included when developing and testing actigraphy-based approaches to circadian phase estimation. Our novel algorithm may be a promising approach for estimating the onset of melatonin in some conditions and could be generalized to other hormones.

The interindividual variability of sleep timing and circadian phase in humans is influenced by daytime and evening light conditions

Human cognitive functioning shows circadian variations throughout the day. However, individuals largely differ in their timing during the day of when they are more capable of performing specific tasks and when they prefer to sleep. These interindividual differences in preferred temporal organization of sleep and daytime activities define the chronotype. Since a late chronotype is associated with adverse mental and physical consequences, it is of vital importance to study how lighting environments affect chronotype. Here, we use a mathematical model of the human circadian pacemaker to understand how light in the built environment changes the chronotype distribution in the population. In line with experimental findings, we show that when individuals spend their days in relatively dim light conditions, this not only results in a later phase of their biological clock but also increases interindividual differences in circadian phase angle of entrainment and preferred sleep timing. Increasing daytime illuminance results in a more narrow distribution of sleep timing and circadian phase, and this effect is more pronounced for longer photoperiods. The model results demonstrate that modern lifestyle changes the chronotype distribution towards more eveningness and more extreme differences in eveningness. Such model-based predictions can be used to design guidelines for workplace lighting that help limiting circadian phase differences, and craft new lighting strategies that support human performance, health and wellbeing.

Light-based methods for predicting circadian phase in delayed sleep-wake phase disorder

Methods for predicting circadian phase have been developed for healthy individuals. It is unknown whether these methods generalize to clinical populations, such as delayed sleep-wake phase disorder (DSWPD), where circadian timing is associated with functional outcomes. This study evaluated two methods for predicting dim light melatonin onset (DLMO) in 154 DSWPD patients using ~ 7 days of sleep-wake and light data: a dynamic model and a statistical model. The dynamic model has been validated in healthy individuals under both laboratory and field conditions. The statistical model was developed for this dataset and used a multiple linear regression of light exposure during phase delay/advance portions of the phase response curve, as well as sleep timing and demographic variables. Both models performed comparably well in predicting DLMO. The dynamic model predicted DLMO with root mean square error of 68 min, with predictions accurate to within ± 1 h in 58% of participants and ± 2 h in 95%. The statistical model predicted DLMO with root mean square error of 57 min, with predictions accurate to within ± 1 h in 75% of participants and ± 2 h in 96%. We conclude that circadian phase prediction from light data is a viable technique for improving screening, diagnosis, and treatment of DSWPD.

Predicting circadian phase across populations: a comparison of mathematical models and wearable devices

From smart work scheduling to optimal drug timing, there is enormous potential in translating circadian rhythms research results for precision medicine in the real world. However, the pursuit of such effort requires the ability to accurately estimate circadian phase outside of the laboratory. One approach is to predict circadian phase non-invasively using light and activity measurements and mathematical models of the human circadian clock. Most mathematical models take light as an input and predict the effect of light on the human circadian system. However, consumer-grade wearables that are already owned by millions of individuals record activity instead of light, which prompts an evaluation of the accuracy of predicting circadian phase using motion alone. Here, we evaluate the ability of four different models of the human circadian clock to estimate circadian phase from data acquired by wrist-worn wearable devices. Multiple datasets across populations with varying degrees of circadian disruption were used for generalizability. Though the models we test yield similar predictions, analysis of data from 27 shift workers with high levels of circadian disruption shows that activity, which is recorded in almost every wearable device, is better at predicting circadian phase than measured light levels from wrist-worn devices when processed by mathematical models. In those living under normal living conditions, circadian phase can typically be predicted to within 1 hour, even with data from a widely available commercial device (the Apple Watch). These results show that circadian phase can be predicted using existing data passively collected by millions of individuals with comparable accuracy to much more invasive and expensive methods.

Predicting circadian misalignment with wearable technology: validation of wrist-worn actigraphy and photometry in night shift workers

STUDY OBJECTIVES

A critical barrier to successful treatment of circadian misalignment in shift workers is determining circadian phase in a clinical or field setting. Light and movement data collected passively from wrist actigraphy can generate predictions of circadian phase via mathematical models; however, these models have largely been tested in non-shift working adults. This study tested the feasibility and accuracy of actigraphy in predicting dim light melatonin onset (DLMO) in fixed night shift workers.

METHODS

A sample of 45 night shift workers wore wrist actigraphs before completing DLMO in the laboratory (17.0 days ± 10.3 SD). DLMO was assessed via 24 hourly saliva samples in dim light (<10 lux). Data from actigraphy were provided as input to a mathematical model to generate predictions of circadian phase. Agreement was assessed and compared to average sleep timing on non-workdays as a proxy of DLMO. Model code and an open-source prototype assessment tool are available (www.predictDLMO.com).

RESULTS

Model predictions of DLMO showed good concordance with in-lab DLMO, with Lin's concordance coefficient of 0.70, which was twice as high as agreement using average sleep timing as a proxy of DLMO. The absolute mean error of the predictions was 2.88 h, with 76% and 91% of the predictions falling with 2 and 4 h, respectively.

CONCLUSION

This study is the first to demonstrate the use of wrist actigraphy-based estimates of circadian phase as a clinically useful and valid alternative to in-lab measurement of DLMO in fixed night shift workers. Future research should explore how additional predictors may impact accuracy.

Optimal adjustment of the human circadian clock in the real world

Which suggestions for behavioral modifications, based on mathematical models, are most likely to be followed in the real world? We address this question in the context of human circadian rhythms. Jet lag is a consequence of the misalignment of the body’s internal circadian (~24-hour) clock during an adjustment to a new schedule. Light is the clock’s primary synchronizer. Previous research has used mathematical models to compute light schedules that shift the circadian clock to a new time zone as quickly as possible. How users adjust their behavior when provided with these optimal schedules remains an open question. Here, we report data collected by wearables from more than 100 travelers as they cross time zones using a smartphone app, Entrain. We find that people rarely follow the optimal schedules generated through mathematical modeling entirely, but travelers who better followed the optimal schedules reported more positive moods after their trips. Using the data collected, we improve the optimal schedule predictions to accommodate real-world constraints. We also develop a scheduling algorithm that allows for the computation of approximately optimal schedules "on-the-fly" in response to disruptions. User burnout may not be critically important as long as the first parts of a schedule are followed. These results represent a crucial improvement in making the theoretical results of past work viable for practical use and show how theoretical predictions based on known human physiology can be efficiently used in real-world settings.

Jet lag, a significant problem for travelers and shift workers, occurs when our body’s internal circadian (~24-hour) clock is misaligned with the time of day in the environment. Such circadian misalignment can lead to decreased performance, impaired sleep, and increased risk for severe health conditions, ranging from cancer to cardiovascular disease. Previous work has proposed mathematically optimal schedules, based on mathematical models of the human circadian pacemaker, to overcome jet lag in minimal time. Here, we use data collected from over 100 travelers by a mobile app to track when users followed or deviated from optimal schedules. Better adherence to the schedules yielded better outcomes. We also propose more practical schedules, which can be adjusted to the real-world challenges in overcoming jet lag. Our work sets the stage for changing human behaviors in other domains by computing personalized recommendations from mathematical models.

The Role of Light Sensitivity and Intrinsic Circadian Period in Predicting Individual Circadian Timing

There is large interindividual variability in circadian timing, which is underestimated by mathematical models of the circadian clock. Interindividual differences in timing have traditionally been modeled by changing the intrinsic circadian period, but recent findings reveal an additional potential source of variability: large interindividual differences in light sensitivity. Using an established model of the human circadian clock with real-world light recordings, we investigated whether changes in light sensitivity parameters or intrinsic circadian period could capture variability in circadian timing between and within individuals. Healthy participants (n = 12, aged 18-26 years) underwent continuous light monitoring for 3 weeks (Actiwatch Spectrum). Salivary dim-light melatonin onset (DLMO) was measured each week. Using the recorded light patterns, a sensitivity analysis for predicted DLMO times was performed, varying 3 model parameters within physiological ranges: (1) a parameter determining the steepness of the dose-response curve to light (p), (2) a parameter determining the shape of the phase-response curve to light (K), and (3) the intrinsic circadian period (tau). These parameters were then fitted to obtain optimal predictions of the three DLMO times for each individual. The sensitivity analysis showed that the range of variation in the average predicted DLMO times across participants was 0.65 h for p, 4.28 h for K, and 3.26 h for tau. The default model predicted the DLMO times with a mean absolute error of 1.02 h, whereas fitting all 3 parameters reduced the mean absolute error to 0.28 h. Fitting the parameters independently, we found mean absolute errors of 0.83 h for p, 0.53 h for K, and 0.42 h for tau. Fitting p and K together reduced the mean absolute error to 0.44 h. Light sensitivity parameters captured similar variability in phase compared with intrinsic circadian period, indicating they are viable targets for individualizing circadian phase predictions. Future prospective work is needed that uses measures of light sensitivity to validate this approach.

Prediction of individual differences in circadian adaptation to night work among older adults: application of a mathematical model using individual sleep-wake and light exposure data

Circadian misalignment remains a distinct challenge for night shift workers. Variability in individual sleep-wake/light-dark patterns might contribute to individual differences in circadian alignment in night shift workers. In this simulation study, we compared the predicted phase shift from a mathematical model of the effect of light on the human circadian pacemaker to the observed melatonin phase shift among individuals who completed one of four interventions during simulated night shift work. Two inputs to the model were used to simulate circadian phase: sleep-wake/light-dark patterns measured from a wrist monitor (Simulation 1) and sleep-wake/light-dark patterns measured from a wrist monitor enhanced by known light levels measured at the level of the eye during simulated night shifts (Simulation 2). The estimated phase shift from the model was within 2 hours of the observed phase shift in ~80% of night shift workers for both simulations; none of the model-predicted phase shifts was more than ~3 hours from the observed phase shift. Overall, the root-mean-square error between observed and predicted phase shifts was better for Simulation 1. The light input from the wrist monitor informed by actual light level measured at the eye performed better in the sub-group exposed to bright light during their night shifts. The findings from this simulation study suggest that using a mathematical model combined with sleep-wake and light exposure data from a wrist monitor can facilitate the design of shift work schedules to enhance circadian alignment, which is expected to improve sleep, alertness, and performance.

A population-based gene expression signature of molecular clock phase from a single epidermal sample

BACKGROUND

For circadian medicine to influence health, such as when to take a drug or undergo a procedure, a biomarker of molecular clock phase is required--one that is easily measured and generalizable across a broad population. It is not clear that any circadian biomarker yet satisfies these criteria.

METHODS

We analyzed 24-h molecular rhythms in human dermis and epidermis at three distinct body sites, leveraging both longitudinal (n = 20) and population (n = 154) data. We applied cyclic ordering by periodic structure (CYCLOPS) to order the population samples where biopsy time was not recorded. With CYCLOPS-predicted phases, we used ZeitZeiger to discover potential biomarkers of clock phase.

RESULTS

Circadian clock function was strongest in the epidermis, regardless of body site. We identified a 12-gene expression signature that reported molecular clock phase to within 3 h (mean error = 2.5 h) from a single sample of epidermis--the skin's most superficial layer. This set performed well across body sites, ages, sexes, and detection platforms.

CONCLUSIONS

This research shows that the clock in epidermis is more robust than dermis regardless of body site. To encourage ongoing validation of this putative biomarker in diverse populations, diseases, and experimental designs, we developed SkinPhaser--a user-friendly app to test biomarker performance in datasets ( https://github.com/gangwug/SkinPhaser ).

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.

Novel Approaches for Assessing Circadian Rhythmicity in Humans: A Review

The temporal organization of molecular and physiological processes is driven by environmental and behavioral cycles as well as by self-sustained molecular circadian oscillators. Quantification of phase, amplitude, period, and disruption of circadian oscillators is essential for understanding their contribution to sleep-wake disorders, social jet lag, interindividual differences in entrainment, and the development of chrono-therapeutics. Traditionally, assessment of the human circadian system, and the output of the SCN in particular, has required collection of long time series of univariate markers such as melatonin or core body temperature. Data were collected in specialized laboratory protocols designed to control for environmental and behavioral influences on rhythmicity. These protocols are time-consuming, expensive, and not practical for assessing circadian status in patients or in participants in epidemiologic studies. Novel approaches for assessment of circadian parameters of the SCN or peripheral oscillators have been developed. They are based on machine learning or mathematical model-informed analyses of features extracted from 1 or a few samples of high-dimensional data, such as transcriptomes, metabolomes, long-term simultaneous recording of activity, light exposure, skin temperature, and heart rate or in vitro approaches. Here, we review whether these approaches successfully quantify parameters of central and peripheral circadian oscillators as indexed by gold standard markers. Although several approaches perform well under entrained conditions when sleep occurs at night, the methods either perform worse in other conditions such as shift work or they have not been assessed under any conditions other than entrainment and thus we do not yet know how robust they are. Novel approaches for the assessment of circadian parameters hold promise for circadian medicine, chrono-therapeutics, and chrono-epidemiology. There remains a need to validate these approaches against gold standard markers, in individuals of all sexes and ages, in patient populations, and, in particular, under conditions in which behavioral cycles are displaced.

Recent advances in modeling sleep: from the clinic to society and disease

In the past few decades, advances in understanding sleep-wake neurophysiology have occurred hand-in-hand with advances in mathematical modeling of sleep and wake. In this review, we summarize recent updates in modeling the timing and durations of sleep and wake, the underlying neurophysiology of sleep and wake, and the application of these models in understanding cognition and disease. Throughout, we highlight the role modeling has played in developing our understanding of sleep and its underlying mechanisms. We present open questions and controversies in the field and propose the utility of individualized models of sleep for precision sleep medicine.

Generalizability of A Neural Network Model for Circadian Phase Prediction in Real-World Conditions

A neural network model was previously developed to predict melatonin rhythms accurately from blue light and skin temperature recordings in individuals on a fixed sleep schedule. This study aimed to test the generalizability of the model to other sleep schedules, including rotating shift work. Ambulatory wrist blue light irradiance and skin temperature data were collected in 16 healthy individuals on fixed and habitual sleep schedules, and 28 rotating shift workers. Artificial neural network models were trained to predict the circadian rhythm of (i) salivary melatonin on a fixed sleep schedule; (ii) urinary aMT6s on both fixed and habitual sleep schedules, including shift workers on a diurnal schedule; and (iii) urinary aMT6s in rotating shift workers on a night shift schedule. To determine predicted circadian phase, center of gravity of the fitted bimodal skewed baseline cosine curve was used for melatonin, and acrophase of the cosine curve for aMT6s. On a fixed sleep schedule, the model predicted melatonin phase to within ± 1 hour in 67% and ± 1.5 hours in 100% of participants, with mean absolute error of 41 ± 32 minutes. On diurnal schedules, including shift workers, the model predicted aMT6s acrophase to within ± 1 hour in 66% and ± 2 hours in 87% of participants, with mean absolute error of 63 ± 67 minutes. On night shift schedules, the model predicted aMT6s acrophase to within ± 1 hour in 42% and ± 2 hours in 53% of participants, with mean absolute error of 143 ± 155 minutes. Prediction accuracy was similar when using either 1 (wrist) or 11 skin temperature sensor inputs. These findings demonstrate that the model can predict circadian timing to within ± 2 hours for the vast majority of individuals on diurnal schedules, using blue light and a single temperature sensor. However, this approach did not generalize to night shift conditions.