Towards an evidence-based integrative lighting score: a proposed multi-level approach

Background: Human circadian clocks are synchronized daily with the external light-dark cycle and entrained to the 24-hour day. There is increasing evidence that a lack of synchronization and circadian entrainment can lead to adverse health effects. Beyond vision, light plays a critical role in modulating many so-called non-visual functions, including sleep-wake cycles, alertness, mood and endocrine functions. To assess (and potentially optimize) the impact of light on non-visual functions, it is necessary to know the exact 'dose' (i.e. spectral irradiance and exposure duration at eye level) of 24-hour light exposures, but also to include metadata about the lighting environment, individual needs and resources.

Problem statement: To address this problem, a new assessment tool is needed that uses existing metrics to provide metadata and information about light quality and quantity from all sources. In this commentary, we discuss the need to develop an evidence-based integrative lighting score that is tailored to specific audiences and lighting environments. We will summarize the most compelling evidence from the literature and outline a future plan for developing such a lighting score using internationally accepted metrics, stakeholder and user feedback.

Conclusion: We propose a weighting system that combines light qualities with physiological and behavioral effects, and the use of mathematical modelling for an output score. Such a scoring system will facilitate a holistic assessment of a lighting environment, integrating all available light sources.

A mathematical model of melatonin synthesis and interactions with the circadian clock

A new mathematical model of melatonin synthesis in pineal cells is created and connected to a slightly modified previously created model of the circadian clock in the suprachiasmatic nucleus (SCN). The SCN influences the production of melatonin by upregulating two key enzymes in the pineal. The melatonin produced enters the blood and the cerebrospinal fluid and thus the SCN, influencing the circadian clock. We show that the model of melatonin synthesis corresponds well with extant experimental data and responds similarly to clinical experiments on bright light in the middle of the night. Melatonin is widely used to treat jet lag and sleep disorders. We show how the feedback from the pineal to the SCN causes phase resetting of the circadian clock. Melatonin doses early in the evening advance the clock and doses late at night delay the clock with a dead zone in between where the phase of the clock does not change.

The seasons within: a theoretical perspective on photoperiodic entrainment and encoding

Circadian clocks are internal timing devices that have evolved as an adaption to the omnipresent natural 24 h rhythmicity of daylight intensity. Properties of the circadian system are photoperiod dependent. The phase of entrainment varies systematically with season. Plastic photoperiod-dependent re-arrangements in the mammalian circadian core pacemaker yield an internal representation of season. Output pathways of the circadian clock regulate photoperiodic responses such as flowering time in plants or hibernation in mammals. Here, we review the concepts of seasonal entrainment and photoperiodic encoding. We introduce conceptual phase oscillator models as their high level of abstraction, but, yet, intuitive interpretation of underlying parameters allows for a straightforward analysis of principles that determine entrainment characteristics. Results from this class of models are related and discussed in the context of more complex conceptual amplitude-phase oscillators as well as contextual molecular models that take into account organism, tissue, and cell-type-specific details.

Assessing the Feasibility and Efficacy of Pre-Sleep Dim Light Therapy for Adults with Insomnia: A Pilot Study

Background: Insomnia is increasingly recognized for its marked impact on public health and is often associated with various adverse health outcomes, including cardiovascular diseases and mental health disorders. The aim of this study was to investigate the efficacy of pre-sleep dim light therapy (LT) as a non-pharmacological intervention for insomnia in adults, assessing its influence on sleep parameters and circadian rhythms. Methods: A randomized, open-label, two-arm clinical trial was conducted over two weeks with 40 participants aged 20-60 years, all of whom had sleep disorders (CRIS, KCT0008501). They were allocated into control and LT groups. The LT group received exposure to warm-colored light, minimizing the blue spectrum, before bedtime. The study combined subjective evaluation via validated, sleep-related questionnaires, objective sleep assessments via actigraphy, and molecular analyses of circadian clock gene expression in peripheral blood mononuclear cells. Baseline characteristics between the two groups were compared using an independent t-test for continuous variables and the chi-squared test for categorical variables. Within-group differences were assessed using the paired t-test. Changes between groups were analyzed using linear regression, adjusting for each baseline value and body mass index. The patterns of changes in sleep parameters were calculated using a linear mixed model. Results: The LT group exhibited significant improvements in sleep quality (difference in difference [95% CI]; -2.00 [-3.58, -0.43], and sleep efficiency (LT: 84.98 vs. control: 82.11, p = 0.032), and an advanced Dim Light Melatonin Onset compared to the control group (approximately 30 min). Molecular analysis indicated a significant reduction in CRY1 gene expression after LT, suggesting an influence on circadian signals for sleep regulation. Conclusions: This study provides evidence for the efficacy of LT in improving sleep quality and circadian rhythm alignment in adults with insomnia. Despite limitations, such as a small sample size and short study duration, the results underscore the potential of LT as a viable non-pharmacological approach for insomnia. Future research should expand on these results with larger and more diverse cohorts followed over a longer period to validate and further elucidate the value of LT in sleep medicine. Trial registration: The trial was registered with the Clinical Research Information Service (KCT0008501).

Method to determine whether sleep phenotypes are driven by endogenous circadian rhythms or environmental light by combining longitudinal data and personalised mathematical models

Sleep timing varies between individuals and can be altered in mental and physical health conditions. Sleep and circadian sleep phenotypes, including circadian rhythm sleep-wake disorders, may be driven by endogenous physiological processes, exogeneous environmental light exposure along with social constraints and behavioural factors. Identifying the relative contributions of these driving factors to different phenotypes is essential for the design of personalised interventions. The timing of the human sleep-wake cycle has been modelled as an interaction of a relaxation oscillator (the sleep homeostat), a stable limit cycle oscillator with a near 24-hour period (the circadian process), man-made light exposure and the natural light-dark cycle generated by the Earth's rotation. However, these models have rarely been used to quantitatively describe sleep at the individual level. Here, we present a new Homeostatic-Circadian-Light model (HCL) which is simpler, more transparent and more computationally efficient than other available models and is designed to run using longitudinal sleep and light exposure data from wearable sensors. We carry out a systematic sensitivity analysis for all model parameters and discuss parameter identifiability. We demonstrate that individual sleep phenotypes in each of 34 older participants (65-83y) can be described by feeding individual participant light exposure patterns into the model and fitting two parameters that capture individual average sleep duration and timing. The fitted parameters describe endogenous drivers of sleep phenotypes. We then quantify exogenous drivers using a novel metric which encodes the circadian phase dependence of the response to light. Combining endogenous and exogeneous drivers better explains individual mean mid-sleep (adjusted R-squared 0.64) than either driver on its own (adjusted R-squared 0.08 and 0.17 respectively). Critically, our model and analysis highlights that different people exhibiting the same sleep phenotype may have different driving factors and opens the door to personalised interventions to regularize sleep-wake timing that are readily implementable with current digital health technology.

Pharmacokinetic Model-Based Control across the Blood-Brain Barrier for Circadian Entrainment

The ability to shift circadian phase in vivo has the potential to offer substantial health benefits. However, the blood-brain barrier prevents the absorption of the majority of large and many small molecules, posing a challenge to neurological pharmaceutical development. Motivated by the presence of the circadian molecule KL001, which is capable of causing phase shifts in a circadian oscillator, we investigated the pharmacokinetics of different neurological pharmaceuticals on the dynamics of circadian phase. Specifically, we developed and validated five different transport models that describe drug concentration profiles of a circadian pharmaceutical at the brain level under oral administration and designed a nonlinear model predictive control (MPC)-based framework for phase resetting. Performance of the novel control algorithm based on the identified pharmacokinetic models was demonstrated through simulations of real-world misalignment scenarios due to jet lag. The time to achieve a complete phase reset for 11-h phase delay ranged between 48 and 72 h, while a 5-h phase advance was compensated in 30 to 60 h. This approach provides mechanistic insight into the underlying structure of the circadian oscillatory system and thus leads to a better understanding of the feasibility of therapeutic manipulations of the system.

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.

A review of visual sustained attention: neural mechanisms and computational models

Sustained attention is one of the basic abilities of humans to maintain concentration on relevant information while ignoring irrelevant information over extended periods. The purpose of the review is to provide insight into how to integrate neural mechanisms of sustained attention with computational models to facilitate research and application. Although many studies have assessed attention, the evaluation of humans' sustained attention is not sufficiently comprehensive. Hence, this study provides a current review on both neural mechanisms and computational models of visual sustained attention. We first review models, measurements, and neural mechanisms of sustained attention and propose plausible neural pathways for visual sustained attention. Next, we analyze and compare the different computational models of sustained attention that the previous reviews have not systematically summarized. We then provide computational models for automatically detecting vigilance states and evaluation of sustained attention. Finally, we outline possible future trends in the research field of sustained attention.

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.

Beyond the limits of circadian entrainment: Non-24-hour sleep-wake disorder, shift work, and social jet lag

While the vast majority of humans are able to entrain their circadian rhythm to the 24-hour light-dark cycle, there are numerous individuals who are not able to do so due to disease or societal reasons. We use computational and mathematical methods to analyze a well-established model of human circadian rhythms to address cases where individuals do not entrain to the 24-hour light-dark cycle, leading to misalignment of their circadian phase. For each case, we provide a mathematically justified strategy for how to minimize circadian misalignment. In the case of non-24-hour sleep-wake disorder, we show why appropriately timed bright light therapy induces entrainment. With regard to shift work, we explain why reentrainment times following transitions between day and night shifts are asymmetric, and how higher light intensity enables unusually rapid reentrainment after certain transitions. Finally, with regard to teenagers who engage in compensatory catch-up sleep on weekends, we propose a rule of thumb for sleep and wake onset times that minimizes circadian misalignment due to this type of social jet lag. In all cases, the primary mathematical approach involves understanding the dynamics of entrainment maps that measure the phase of the entrained rhythm with respect to the daily onset of lights.

A Phenomenological Mouse Circadian Pacemaker Model

Mathematical models have been used extensively in chronobiology to explore characteristics of biological clocks. In particular, for human circadian studies, the Kronauer model has been modified multiple times to describe rhythm production and responses to sensory input. This phenomenological model comprises a single set of parameters which can simulate circadian responses in humans under a variety of environmental conditions. However, corresponding models for nocturnal rodents commonly used in circadian rhythm studies are not available and may require new parameter values for different species and even strains. Moreover, due to a considerable variation in experimental data collected from mice of the same strain, within and across laboratories, a range of valid parameters is essential. This study develops a Kronauer-like model for mice by re-fitting relevant parameters to published phase response curve and period data using total least squares. Local parameter sensitivity analysis and parameter distributions determine the parameter ranges that give a near-identical model and data distribution of periods. However, the model required further parameter adjustments to match characteristics of other mouse strains, implying that the model itself detects changes in the core processes of rhythm generation and control. The model is a useful tool to understand and interpret future mouse circadian clock experiments.

Modeling melanopsin-mediated effects of light on circadian phase, melatonin suppression, and subjective sleepiness

A physiologically based model of arousal dynamics is improved to incorporate the effects of the light spectrum on circadian phase resetting, melatonin suppression, and subjective sleepiness. To account for these nonvisual effects of light, melanopic irradiance replaces photopic illuminance that was used previously in the model. The dynamic circadian oscillator is revised according to the melanopic irradiance definition and tested against experimental circadian phase resetting dose-response and phase response data. Melatonin suppression function is recalibrated against melatonin dose-response data for monochromatic and polychromatic light sources. A new light-dependent term is introduced into the homeostatic weight component of subjective sleepiness to represent the direct alerting effect of light; the new term responds to light change in a time-dependent manner and is calibrated against experimental data. The model predictions are compared to a total of 14 experimental studies containing 26 data sets for 14 different spectral light profiles. The revised melanopic model shows on average 1.4 times lower prediction error for circadian phase resetting compared to the photopic-based model, 3.2 times lower error for melatonin suppression, and 2.1 times lower error for subjective sleepiness. Overall, incorporating melanopic irradiance allowed simulation of wavelength-dependent responses to light and could explain the majority of the observations. Moving forward, models of circadian phase resetting and the direct effects of light on alertness and sleep need to use nonvisual photoreception-based measures of light, for example, melanopic irradiance, instead of the traditionally used illuminance based on the visual system.

Changes in performance and bio-mathematical model performance predictions during 45 days of sleep restriction in a simulated space mission

Lunar habitation and exploration of space beyond low-Earth orbit will require small crews to live in isolation and confinement while maintaining a high level of performance with limited support from mission control. Astronauts only achieve approximately 6 h of sleep per night, but few studies have linked sleep deficiency in space to performance impairment. We studied crewmembers over 45 days during a simulated space mission that included 5 h of sleep opportunity on weekdays and 8 h of sleep on weekends to characterize changes in performance on the psychomotor vigilance task (PVT) and subjective fatigue ratings. We further evaluated how well bio-mathematical models designed to predict performance changes due to sleep loss compared to objective performance. We studied 20 individuals during five missions and found that objective performance, but not subjective fatigue, declined from the beginning to the end of the mission. We found that bio-mathematical models were able to predict average changes across the mission but were less sensitive at predicting individual-level performance. Our findings suggest that sleep should be prioritized in lunar crews to minimize the potential for performance errors. Bio-mathematical models may be useful for aiding crews in schedule design but not for individual-level fitness-for-duty decisions.

Habitual sleep duration affects recovery from acute sleep deprivation: A modeling study

Adult humans exhibit high interindividual variation in habitual sleep durations, with short sleepers typically sleeping less than 6 h per night and long sleepers typically sleeping more than 9 h per night. Analysis of the time course of homeostatic sleep drive in habitual short and long sleepers has not identified differences between these groups, leading to the hypothesis that habitual short sleep results from increased tolerance to high levels of homeostatic sleep drive. Using a physiologically-based mathematical model of the sleep-wake regulatory network, we investigate responses to acute sleep deprivation in simulated populations of habitual long, regular and short sleepers that differ in daily levels of homeostatic sleep drive. The model predicts timing and durations of wake, rapid eye movement (REM), and non-REM (NREM) sleep episodes as modulated by the homeostatic sleep drive and the circadian rhythm, which is entrained to an external light cycle. Model parameters are fit to experimental measures of baseline sleep durations to construct simulated populations of individuals of each sleeper type. The simulated populations are validated against data for responses to specific acute sleep deprivation protocols. We use the model to predict responses to a wide range of sleep deprivation durations for each sleeper type. Model results predict that all sleeper types exhibit shorter sleep durations during recovery sleep that occurs in the morning, but, for recovery sleep times occurring later in the day, long and regular sleepers show longer and more variable sleep durations, and can suffer longer lasting disruption of daily sleep patterns compared to short sleepers. Additionally, short sleepers showed more resilience to sleep deprivation with longer durations of waking episodes following recovery sleep. These results support the hypothesis that differential responses to sleep deprivation between short and long sleepers result from differences in the tolerance for homeostatic sleep pressure.

Amplitude Effects Allow Short Jet Lags and Large Seasonal Phase Shifts in Minimal Clock Models

Mathematical models of varying complexity have helped shed light on different aspects of circadian clock function. In this work, we question whether minimal clock models (Goodwin models) are sufficient to reproduce essential phenotypes of the clock: a small phase response curve (PRC), fast jet lag, and seasonal phase shifts. Instead of building a single best model, we take an approach where we study the properties of a set of models satisfying certain constraints; here, a 1h-pulse PRC with a range of 3h and clock periods between 22h and 26h is designed. Surprisingly, almost all these randomly parameterized models showed a 4h change in phase of entrainment between long and short days and jet lag durations of three to seven days in advance and delay. Moreover, intrinsic clock period influenced jet lag duration and entrainment amplitude and phase. Fast jet lag was realized in this model by means of an interesting amplitude effect: the association between clock amplitude and clock period termed "twist." This twist allows amplitude changes to speed up and slow down clocks enabling faster shifts. These findings were robust to the addition of positive feedback to the model. In summary, the known design principles of rhythm generation - negative feedback, long delay, and switch-like inhibition (we review these in detail) - are sufficient to reproduce the essential clock phenotypes. Furthermore, amplitudes play a role in determining clock properties and must be always considered, although they are difficult to measure.

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.

Effects of light on human circadian rhythms, sleep and mood

Humans live in a 24-hour environment, in which light and darkness follow a diurnal pattern. Our circadian pacemaker, the suprachiasmatic nuclei (SCN) in the hypothalamus, is entrained to the 24-hour solar day via a pathway from the retina and synchronises our internal biological rhythms. Rhythmic variations in ambient illumination impact behaviours such as rest during sleep and activity during wakefulness as well as their underlying biological processes. Rather recently, the availability of artificial light has substantially changed the light environment, especially during evening and night hours. This may increase the risk of developing circadian rhythm sleep-wake disorders (CRSWD), which are often caused by a misalignment of endogenous circadian rhythms and external light-dark cycles. While the exact relationship between the availability of artificial light and CRSWD remains to be established, nocturnal light has been shown to alter circadian rhythms and sleep in humans. On the other hand, light can also be used as an effective and noninvasive therapeutic option with little to no side effects, to improve sleep,mood and general well-being. This article reviews our current state of knowledge regarding the effects of light on circadian rhythms, sleep, and mood.

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

Practical alternatives to gold-standard measures of circadian timing in shift workers are needed. We assessed the feasibility of applying a limit-cycle oscillator model of the human circadian pacemaker to estimate circadian phase in 25 nursing and medical staff in a field setting during a transition from day/evening shifts (diurnal schedule) to 3-5 consecutive night shifts (night schedule). Ambulatory measurements of light and activity recorded with wrist actigraphs were used as inputs into the model. Model estimations were compared to urinary 6-sulphatoxymelatonin (aMT6s) acrophase measured on the diurnal schedule and last consecutive night shift. The model predicted aMT6s acrophase with an absolute mean error of 0.69 h on the diurnal schedule (SD = 0.94 h, 80% within ±1 hour), and 0.95 h on the night schedule (SD = 1.24 h, 68% within ±1 hour). The aMT6s phase shift from diurnal to night schedule was predicted to within ±1 hour in 56% of individuals. Our findings indicate the model can be generalized to a shift work setting, although prediction of inter-individual variability in circadian phase shift during night shifts was limited. This study provides the basis for further adaptation and validation of models for predicting circadian phase in rotating shift workers.

Isostable reduction of oscillators with piecewise smooth dynamics and complex Floquet multipliers

Phase-amplitude reduction is a widely applied technique in the study of limit cycle oscillators with the ability to represent a complicated and high-dimensional dynamical system in a more analytically tractable set of coordinates. Recent work has focused on the use of isostable coordinates, which characterize the transient decay of solutions toward a periodic orbit, and can ultimately be used to increase the accuracy of these reduced models. The breadth of systems to which this phase-amplitude reduction strategy can be applied, however, is still rather limited. In this work, the theory of phase-amplitude reduction using isostable coordinates is further developed to accommodate a broader set of dynamical systems. In the first part, limit cycles of piecewise smooth dynamical systems are considered and strategies are developed to compute the associated reduced equations. In the second part, the notion of isostable coordinates for complex-valued Floquet multipliers is introduced, resulting in one phaselike coordinate and one amplitudelike coordinate for each pair of complex conjugate Floquet multipliers. Examples are given with relevance to piecewise smooth representations of excitable cardiomyocytes and the relationship between the reduced coordinate system and the emergence of cardiac alternans is discussed. Also, phase-amplitude reduction is implemented for a chaotic, externally forced pendulum with complex Floquet multipliers and a resulting control strategy for the stabilization of its periodic solution is investigated.

Responses to Intermittent Light Stimulation Late in the Night Phase Before Dawn

The circadian clock is comprised of two oscillators that independently track sunset (evening) and sunrise (morning), though little is known about how light responses differ in each. Here, we quantified the morning oscillator’s responses to 19 separate pulse trains, collecting observations from over 1300 Drosophila at ZT23. Our results show that the advances in activity onset produced by these protocols depended on the tempo of light administration even when total exposure was conserved across a 15-min window. Moreover, patterns of stimulation previously shown to optimize the evening oscillator’s delay resetting at ZT13 (an hour after dusk) were equally effective for the M oscillator at ZT23 (an hour before dawn), though the morning oscillator was by comparison more photosensitive and could benefit from a greater number of fractionation strategies that better converted light into phase-shifting drive. These data continue to build the case that the reading frames for the pacemaker’s time-of-day estimates at dusk and dawn are not uniform and suggest that the “photologic” for the evening versus morning oscillator’s resetting might be dissociable.

Circadian phase-shifting by light: Beyond photons

Circadian entrainment to the solar light:dark schedule is thought to be maintained by a simple photon counting method. According to this hypothesis, the pacemaker adjusts the phase of the body's endogenous rhythms in accordance to the intensity and duration with which it encounters a perceived twilight signal. While previous data have generally supported the hypothesis, more recent analysis has codified other factors besides irradiance that influence the magnitude of resetting responses to light delivered within the same phase of the circadian cycle. In particular, the frequency with which light is alternated with darkness, or whether it's packaged in millisecond flashes versus continuous blocks, can significantly alter the dose-response relationship. Here, we used a drosophilid model to test whether circadian photon-counting trends can be broken with light administration protocols spanning just 15 minutes. In the early part of the delay zone, a 15-min continuous light pulse was fragmented until it could no longer produce a full-magnitude shift of the flies' locomotor activity rhythms. The remaining exposure was then reorganized along various fractionation schemes that employed pulses with different widths and interstimulus intervals. Our results suggest that the pacemaker integrates the phase-shifting effects of equiluminous light differently depending on the stimulus pattern with which light is made available. For example, despite having fewer photons, certain ratios of light and darkness could be optimized on a timescale of seconds and minutes so as to achieve pacemaker resetting close to par with steady luminance. These data provide further evidence that the circadian pacemaker's responses to light entail more than photon counting and motivate continued discussion on how phototherapy can be best optimized in clinical practice to improve conditions linked to circadian impairment.

Reentrainment of the circadian pacemaker during jet lag: East-west asymmetry and the effects of north-south travel

The normal alignment of circadian rhythms with the 24-h light-dark cycle is disrupted after rapid travel between home and destination time zones, leading to sleep problems, indigestion, and other symptoms collectively known as jet lag. Using mathematical and computational analysis, we study the process of reentrainment to the light-dark cycle of the destination time zone in a model of the human circadian pacemaker. We calculate the reentrainment time for travel between any two points on the globe at any time of the day and year. We construct one-dimensional entrainment maps to explain several properties of jet lag, such as why most people experience worse jet lag after traveling east than west. We show that this east-west asymmetry depends on the endogenous period of the traveler's circadian clock as well as daylength. Thus the critical factor is not simply whether the endogenous period is greater than or less than 24 h as is commonly assumed. We show that the unstable fixed point of an entrainment map determines whether a traveler reentrains through phase advances or phase delays, providing an understanding of the threshold that separates orthodromic and antidromic modes of reentrainment. Contrary to the conventional wisdom that jet lag only occurs after east-west travel across multiple time zones, we predict that the change in daylength encountered during north-south travel can cause jet lag even when no time zones are crossed. Our techniques could be used to provide advice to travelers on how to minimize jet lag on trips involving multiple destinations and a combination of transmeridian and translatitudinal travel.

Daily Light Exposure Patterns Reveal Phase and Period of the Human Circadian Clock

Light is the most potent time cue that synchronizes (entrains) the circadian pacemaker to the 24-h solar cycle. This entrainment process is an interplay between an individual's daily light perception and intrinsic pacemaker period under free-running conditions. Establishing individual estimates of circadian phase and period can be time-consuming. We show that circadian phase can be accurately predicted (SD = 1.1 h for dim light melatonin onset, DLMO) using 9 days of ambulatory light and activity data as an input to Kronauer's limit-cycle model for the human circadian system. This approach also yields an estimated circadian period of 24.2 h (SD = 0.2 h), with longer periods resulting in later DLMOs. A larger amount of daylight exposure resulted in an earlier DLMO. Individuals with a long circadian period also showed shorter intervals between DLMO and sleep timing. When a field-based estimation of tau can be validated under laboratory studies in a wide variety of individuals, the proposed methods may prove to be essential tools for individualized chronotherapy and light treatment for shift work and jetlag applications. These methods may improve our understanding of fundamental properties of human circadian rhythms under daily living conditions.

Optimal schedules of light exposure for rapidly correcting circadian misalignment

Jet lag arises from a misalignment of circadian biological timing with the timing of human activity, and is caused by rapid transmeridian travel. Jet lag's symptoms, such as depressed cognitive alertness, also arise from work and social schedules misaligned with the timing of the circadian clock. Using experimentally validated mathematical models, we develop a new methodology to find mathematically optimal schedules of light exposure and avoidance for rapidly re-entraining the human circadian system. In simulations, our schedules are found to significantly outperform other recently proposed schedules. Moreover, our schedules appear to be significantly more robust to both noise in light and to inter-individual variations in endogenous circadian period than other proposed schedules. By comparing the optimal schedules for thousands of different situations, and by using general mathematical arguments, we are also able to translate our findings into general principles of optimal circadian re-entrainment. These principles include: 1) a class of schedules where circadian amplitude is only slightly perturbed, optimal for dim light and for small shifts 2) another class of schedules where shifting occurs along the shortest path in phase-space, optimal for bright light and for large shifts 3) the determination that short light pulses are less effective than sustained light if the goal is to re-entrain quickly, and 4) the determination that length of daytime should be significantly shorter when delaying the clock than when advancing it.

When our body's internal timekeeping system becomes misaligned with the time of day in the outside world, many negative effects can be felt, including decreased performance, improper sleep, and jet lag. When misalignment is prolonged, it can also lead to serious medical conditions, including cancer, cardiovascular disease, and possibly even late-onset diabetes. Rapid readjustment of our internal daily (circadian) clock by properly timed exposure to light, which is the strongest signal to our internal circadian clock, is therefore important to the large proportion of the population which suffers from misalignment, including transmeridian travelers, shift workers, and individuals with circadian disorders. Here we develop a methodology to determine schedules of light exposure which may shift the human circadian clock in the minimum time. By calculating thousands of schedules, we show how the human circadian pacemaker is predicted to be capable of shifting much more rapidly than previously thought, simply by adjusting the timing of the beginning and end of each day. Schedules are summarized into general principles of optimal shifting, which can be applied without knowledge of the schedules themselves.

A mathematical model of the circadian phase-shifting effects of exogenous melatonin

Melatonin is endogenously produced and released in humans during nighttime darkness and is suppressed by ocular light exposure. Exogenous melatonin is used to induce circadian phase shifts and sleep. The circadian phase-shifting ability of a stimulus (e.g., melatonin or light) relative to its timing may be displayed as a phase response curve (PRC). Published PRCs to exogenous melatonin show a transition from phase advances to delays approximately 1 h after dim light melatonin onset. A previously developed mathematical model simulates endogenous production and clearance of melatonin as a function of circadian phase, light-induced suppression, and resetting of circadian phase by light. We extend this model to include the pharmacokinetics of oral exogenous melatonin and phase-shifting effects via melatonin receptors in the suprachiasmatic nucleus of the mammalian hypothalamus. Model parameters are fit using 2 data sets: (1) blood melatonin concentration following a 0.3- or 5.0-mg dose, and (2) a PRC to a 3.0-mg dose of melatonin. After fitting to the 3.0-mg PRC, the model correctly predicts that, by comparison, the 0.5-mg PRC is slightly decreased in amplitude and shifted to a later circadian phase. This model also reproduces blood concentration profiles of various melatonin preparations that differ only in absorption rate and percentage degradation by first-pass hepatic metabolism. This model can simulate experimental protocols using oral melatonin, with potential application to guide dose size and timing to optimally shift and entrain circadian rhythms.

The Neurospora photoreceptor VIVID exerts negative and positive control on light sensing to achieve adaptation

Light adaptation in Neurospora is mediated by the photoreceptor VIVID, which exerts both a negative and positive effect on light sensing. These apparently paradoxical roles of VIVID are explained by the dynamics of a network motif that utilizes futile cycling.

The fungus Neurospora detects relative changes in light intensity by adapting to the ambient light level and remaining responsive to increases in light intensity.

Both the downregulation of the acute light response and maintained responsiveness are mediated by the photoreceptor VIVID (VVD).

Data-based mathematical modeling shows that this paradoxical function of VVD can be realized by a futile-cycle network motif that turns feedback inhibition into sensory adaptation.

The light response in Neurospora is mediated by the photoreceptor and circadian transcription factor White Collar Complex (WCC). The expression rate of the WCC target genes adapts in daylight and remains refractory to moonlight, despite the extraordinary light sensitivity of the WCC. To explain this photoadaptation, feedback inhibition by the WCC interaction partner VIVID (VVD) has been invoked. Here we show through data-driven mathematical modeling that VVD allows Neurospora to detect relative changes in light intensity. To achieve this behavior, VVD acts as an inhibitor of WCC-driven gene expression and, at the same time, as a positive regulator that maintains the responsiveness of the photosystem. Our data indicate that this paradoxical function is realized by a futile cycle that involves the light-induced sequestration of active WCC by VVD and the replenishment of the activatable WCC pool through the decay of the photoactivated state. Our quantitative study uncovers a novel network motif for achieving sensory adaptation and defines a core input module of the circadian clock in Neurospora.

Revisiting spontaneous internal desynchrony using a quantitative model of sleep physiology

Early attempts to characterize free-running human circadian rhythms generated three notable results: 1) observed circadian periods of 25 hours (considerably longer than the now established 24.1- to 24.2-hour average intrinsic circadian period) with sleep delayed to later circadian phases than during entrainment; 2) spontaneous internal desynchrony of circadian rhythms and sleep/wake cycles--the former with an approximately 24.9-hour period, and the latter with a longer (28-68 hour) or shorter (12-20 hour) period; and 3) bicircadian (48-50 hour) sleep/wake cycles. All three results are reproduced by Kronauer et al.'s (1982) coupled oscillator model, but the physiological basis for that phenomenological model is unclear. We use a physiologically based model of hypothalamic and brain stem nuclei to investigate alternative physiological mechanisms that could underlie internal desynchrony. We demonstrate that experimental observations can be reproduced by changes in two pathways: promotion of orexinergic (Orx) wake signals, and attenuation of the circadian signal reaching hypothalamic nuclei. We reason that delayed sleep is indicative of an additional wake-promoting drive, which may be of behavioral origin, associated with removal of daily schedules and instructions given to participants. We model this by increasing Orx tone during wake, which reproduces the observed period lengthening and delayed sleep. Weakening circadian input to the ventrolateral preoptic nucleus (possibly mediated by the dorsomedial hypothalamus) causes desynchrony, with observed sleep/wake cycle period determined by degree of Orx up-regulation. During desynchrony, sleep/wake cycles are driven by sleep homeostasis, yet sleep bout length maintains circadian phase dependence. The model predicts sleep episodes are shortest when started near the temperature minimum, consistent with experimental findings. The model also correctly predicts that it is possible to transition to bicircadian rhythms from either a synchronized or desynchronized state. Our findings suggest that feedback from behavioral choices to physiology could play an important role in spontaneous internal desynchrony.

Quantitative modelling of sleep dynamics

Arousal is largely controlled by the ascending arousal system of the hypothalamus and brainstem, which projects to the corticothalamic system responsible for electroencephalographic (EEG) signatures of sleep. Quantitative physiologically based modelling of brainstem dynamics theory is described here, using realistic parameters, and links to EEG are outlined. Verification against a wide range of experimental data is described, including arousal dynamics under normal conditions, sleep deprivation, stimuli, stimulants and jetlag, plus key features of wake and sleep EEGs.

Modeling light adaptation in circadian clock: prediction of the response that stabilizes entrainment

Periods of biological clocks are close to but often different from the rotation period of the earth. Thus, the clocks of organisms must be adjusted to synchronize with day-night cycles. The primary signal that adjusts the clocks is light. In Neurospora, light transiently up-regulates the expression of specific clock genes. This molecular response to light is called light adaptation. Does light adaptation occur in other organisms? Using published experimental data, we first estimated the time course of the up-regulation rate of gene expression by light. Intriguingly, the estimated up-regulation rate was transient during light period in mice as well as Neurospora. Next, we constructed a computational model to consider how light adaptation had an effect on the entrainment of circadian oscillation to 24-h light-dark cycles. We found that cellular oscillations are more likely to be destabilized without light adaption especially when light intensity is very high. From the present results, we predict that the instability of circadian oscillations under 24-h light-dark cycles can be experimentally observed if light adaptation is altered. We conclude that the functional consequence of light adaptation is to increase the adjustability to 24-h light-dark cycles and then adapt to fluctuating environments in nature.

Model-based human circadian phase estimation using a particle filter

We present a method for tracking an individual's circadian phase that integrates dynamic models of circadian physiology with physiological measurements in a Bayesian statistical framework. A model of the circadian pacemaker's response to light exposure is transformed into a nonlinear state-space model with a circadian phase state. The probability distribution of the circadian phase is estimated by a particle filter that predicts changes over time based on the model, and performs updates with information gained from physiological measurements. Simulations demonstrate how probability distributions allow flexible initialization of model states and enable statistical quantification of entrainment and divergence properties of the circadian pacemaker. The combined use of sleep-wake scheduling data and physiological measurements is demonstrated in a case study highlighting advantages for addressing the challenge of noninvasive ambulatory monitoring of circadian physiology.

Probing the mechanisms of chronotype using quantitative modeling

The physiological mechanisms underlying interindividual differences in chronotype have yet to be established, although evidence suggests both circadian and homeostatic processes are involved. A physiologically based model is developed by combining models of the sleep-wake switch and circadian pacemaker, providing a means of examining how interactions between these systems affect chronotype. Specifically, chronotype is shown to depend on the relative influences of homeostatic and circadian drives, with a stronger homeostatic drive causing morningness. Changes to intrinsic circadian and homeostatic properties, including homeostatic clearance and production rates, and circadian period and amplitude, are also shown to affect chronotype. These results provide a framework for explaining several experimentally observed phenomena, including age-related morningness, adolescent eveningness, and familial advanced and delayed sleep-phase disorders. Additionally, experimental studies have shown that healthy adults on the extremes of the morningness-eveningness spectrum fall into two subtypes: those whose circadian phase markers are unaffected by chronotype, and those whose circadian phase markers track their chronotype. The model demonstrates that this spectrum likely results from interindividual differences in homeostatic kinetics in the first group, and differences in circadian period in the second group. Physiologically based modeling can thus guide diagnosis of sleep pathologies.