The timing of the human circadian clock is accurately represented by the core body temperature rhythm following phase shifts to a three-cycle light stimulus near the critical zone.

A double-stimulus experiment was conducted to evaluate the phase of the underlying circadian clock following light-induced phase shifts of the human circadian system. Circadian phase was assayed by constant routine from the rhythm in core body temperature before and after a three-cycle bright-light stimulus applied near the estimated minimum of the core body temperature rhythm. An identical, consecutive three-cycle light stimulus was then applied, and phase was reassessed. Phase shifts to these consecutive stimuli were no different from those obtained in a previous study following light stimuli applied under steady-state conditions over a range of circadian phases similar to those at which the consecutive stimuli were applied. These data suggest that circadian phase shifts of the core body temperature rhythm in response to a three-cycle stimulus occur within 24 h following the end of the 3-day light stimulus and that this poststimulus temperature rhythm accurately reflects the timing of the underlying circadian clock.

Dose-response relationship between sleep duration and human psychomotor vigilance and subjective alertness.

Although it has been well documented that sleep is required for human performance and alertness to recover from low levels after prolonged periods of wakefulness, it remains unclear whether they increase in a linear or asymptotic manner during sleep. It has been postulated that there is a relation between the rate of improvement in neurobehavioral functioning and rate of decline of slow-wave sleep and/or slow-wave activity (SWS/SWA) during sleep, but this has not been verified. Thus, a cross-study comparison was conducted in which dose-response curves (DRCs) were constructed for Stanford Sleepiness Scale (SSS) and Psychomotor Vigilance Task (PVT) tests taken at 1000 hours by subjects who had been allowed to sleep 0 hours, 2 hours, 5 hours or 8 hours the previous night. We found that the DRCs to each PVT metric improved in a saturating exponential manner, with recovery rates that were similar [time constant (T) approximately 2.14 hours] for all the metrics. This recovery rate was slightly faster than, though not statistically significantly different from, the reported rate of SWS/SWA decline (T approximately 2.7 hours). The DRC to the SSS improved much more slowly than psychomotor vigilance, so that it could be fit equally well by a linear function (slope = -0.26) or a saturating exponential function (T = 9.09 hours). We conclude that although SWS/SWA, subjective alertness, and a wide variety of psychomotor vigilance metrics may all change asymptotically during sleep, it remains to be determined whether the underlying physiologic processes governing their expression are different.

Time course of sleep inertia dissipation in human performance and alertness.

Alertness and performance on a wide variety of tasks are impaired immediately upon waking from sleep due to sleep inertia, which has been found to dissipate in an asymptotic manner following waketime. It has been suggested that behavioural or environmental factors, as well as sleep stage at awakening, may affect the severity of sleep inertia. In order to determine the time course of sleep inertia dissipation under normal entrained conditions, subjective alertness and cognitive throughput were measured during the first 4 h after habitual waketime from a full 8-h sleep episode on 3 consecutive days. We investigated whether this time course was affected by either sleep stage at awakening or behavioural/environmental factors. Sleep inertia dissipated in an asymptotic manner and took 2-4 h to near the asymptote. Saturating exponential functions fitted the sleep inertia data well, with time constants of 0.67 h for subjective alertness and 1.17 h for cognitive performance. Most awakenings occurred out of stage rapid eye movement (REM), 2 or 1 sleep, and no effect of sleep stage at awakening on either the severity of sleep inertia or the time course of its dissipation could be detected. Subjective alertness and cognitive throughput were significantly impaired upon awakening regardless of whether subjects got out of bed, ate breakfast, showered and were exposed to ordinary indoor room light (approximately 150 lux) or whether subjects participated in a constant routine (CR) protocol in which they remained in bed, ate small hourly snacks and were exposed to very dim light (10-15 lux). These findings allow for the refinement of models of alertness and performance, and have important implications for the scheduling of work immediately upon awakening in many occupational settings.

Revised limit cycle oscillator model of human circadian pacemaker.

In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. This study presents several refinements to Kronauer's original model of the pacemaker that enable it to predict more accurately the experimental results from a number of different studies of the effects of the intensity, timing, and duration of light stimuli on the human circadian pacemaker. These refinements include the following: The van der Pol oscillator from Kronauer's model has been replaced with a higher order limit cycle oscillator so that the system's amplitude recovery is slower near the singularity and faster near the limit cycle; the phase and amplitude of the circadian rhythm in sensitivity to light from Kronauer's model has been refined so that the peak sensitivity to light on the limit cycle now occurs approximately 4 h before the core body temperature minimum (CBTmin) and is three times as great as the minimum sensitivity on the limit cycle; the critical phase (at which type 1 phase response curves [PRCs] can be distinguished from type 0 PRCs) that occurs at CBT,n now corresponds to 0.8 h after the minimum of x (x(min) in this refined model rather than to the exact timing of x(min) as in Kronauer's model; a direct effect of light on circadian period was incorporated into the model such that as light intensity increases, the period decreases, which is in accordance with Aschoff's rule.

Quantifying human circadian pacemaker response to brief, extended, and repeated light stimuli over the phototopic range.

The authors' previous models have been able to describe accurately the effects of extended (approximately 5 h) bright-light (>4000 lux) stimuli on the phase and amplitude of the human circadian pacemaker, but they are not sufficient to represent the surprising human sensitivity to both brief pulses of bright light and light of more moderate intensities. Therefore, the authors have devised a new model in which a dynamic stimulus processor (Process L) intervenes between the light stimuli and the traditional representation of the circadian pacemaker as a self-sustaining limit-cycle oscillator (Process P). The overall model incorporating Process L and Process P is intended to allow the prediction of phase shifts to photic stimuli of any temporal pattern (extended and brief light episodes) and any light intensity in the photopic range. Two time constants emerge in the Process L model: the characteristic duration for necessary bright-light pulses to achieve their full effect (5-10 min) and the characteristic stimulus-free (dark) interval that can be tolerated without incurring an excessive penalty in phase shifting (30-80 min). The effect of reducing light intensity is incorporated in Process L as an extension of the time necessary for the light pulse to be fully realized (a power-law relation between time and intensity). This new model generates a number of new testable hypotheses, including the surprising prediction that 24-h cycles consisting of 8 h of darkness and 16 h of only approximately 3.5 lux would be capable of entraining a large fraction of the adult population (approximately 45%). Experimental data on the response of the human circadian system to lower light intensities and briefer stimuli are needed to allow for further refinement and validation of the model proposed here.

A simpler model of the human circadian pacemaker.

Numerous studies have used the classic van der Pol oscillator, which contains a cubic nonlinearity, to model the effect of light on the human circadian pacemaker. Jewett and Kronauer demonstrated that Aschoff's rule could be incorporated into van der Pol type models and used a van der Pol type oscillator with higher order nonlinearities. Kronauer, Forger, and Jewett have proposed a model for light preprocessing, Process L, representing a biochemical process that converts a light signal into an effective drive on the circadian pacemaker. In the paper presented here, the authors use the classic van der Pol oscillator with Process L and Jewett and Kronauer's model of Aschoff's rule to model the human circadian pacemaker. This simpler cubic model predicts the results of a three-pulse human phase response curve experiment and a two-pulse amplitude reduction study with as much, or more, accuracy as the models of Jewett and Kronauer and Kronauer, Forger, and Jewett, which both employ a nonlinearity of degree 7. This suggests that this simpler cubic model should be considered as a potential alternative to other models of the human circadian system currently available.

Interactive mathematical models of subjective alertness and cognitive throughput in humans.

The authors present here mathematical models in which levels of subjective alertness and cognitive throughput are predicted by three components that interact with one another in a nonlinear manner. These components are (1) a homeostatic component (H) that falls in a sigmoidal manner during wake and rises in a saturating exponential manner at a rate that is determined by circadian phase during sleep; (2) a circadian component (C) that is a function of the output of our mathematical model of the effect of light on the circadian pacemaker, with the amplitude further regulated by the level of H; and (3) a sleep inertia component (W) that rises in a saturating exponential manner after waketime. The authors first construct initial models of subjective alertness and cognitive throughput based on the results of sleep inertia studies, sleep deprivation studies initiated across all circadian phases, 28-h forced desynchrony studies, and alertness and performance dose response curves to sleep. These initial models are then refined using data from nearly one hundred fifty 30- to 50-h sleep deprivation studies in which subjects woke at their habitual times. The interactive three-component models presented here are able to predict even the fine details of neurobehavioral data from sleep deprivation studies and, after further validation, may provide a powerful tool for the design of safe shift work and travel schedules, including those in which people are exposed to unusual patterns of light.

Commentary: model building, quantitative testing, and model comparison.

The final goal is to create mathematical models that are based on our current knowledge of the underlying physiology and that explain all of the experimental data available. To do this, we suggest a consideration of several potential mathematical structures in the formulation of models and the formal comparison of these various structures with other models in the literature. However, when making these comparisons, one must pay careful attention to the systems being modeled and the data sets chosen to represent those systems.

Refinement of a limit cycle oscillator model of the effects of light on the human circadian pacemaker.

In 1990, Kronauer proposed a mathematical model of the effects of light on the human circadian pacemaker. Although this model predicted many general features of the response of the human circadian pacemaker to light exposure, additional data now available enable us to refine the original model. We first refined the original model by incorporating the results of a dose response curve to light into the model's predicted relationship between light intensity and the strength of the drive onto the pacemaker. Data from three bright light phase resetting experiments were then used to refine the amplitude recovery characteristics of the model. Finally, the model was tested and further refined using data from an extensive phase resetting experiment in which a 3-cycle bright light stimulus was presented against a background of dim light. In order to describe the results of the four resetting experiments, the following major refinements to the original model were necessary: (i) the relationship between light intensity (I) and drive onto the pacemaker was reduced from I1/3 to I0.23 for light levels between 150 and 10,000 lux; (ii) the van der Pol oscillator from the original model was replaced with a higher-order limit cycle oscillator so that amplitude recovery is slower near the singularity and faster near the limit cycle; (iii) a direct effect of light on circadian period (tau x) was incorporated into the model such that as I increases, tau x decreases, which is in accordance with "Aschoff's rule". This refined model generates the following testable predictions: it should be difficult to enhance normal circadian amplitude via bright light; near the critical point of a type 0 phase response curve (PRC) the slope should be steeper than it is in a type 1 PRC; and circadian period measured during forced desynchrony should be directly affected by ambient light intensity.

Human circadian pacemaker is sensitive to light throughout subjective day without evidence of transients.

Fifty-six resetting trials were conducted across the subjective day in 43 young men using a three-cycle bright-light (approximately 10,000 lx). The phase-response curve (PRC) to these trials was assessed for the presence of a "dead zone" of photic insensitivity and was compared with another three-cycle PRC that had used a background of approximately 150 lx. To assess possible transients after the light stimulus, the trials were divided into 43 steady-state trials, which occurred after several baseline days, and 13 consecutive trials, which occurred immediately after a previous resetting trial. We found that 1) bright light induces phase shifts throughout subjective day with no apparent dead zone; 2) there is no evidence of transients in constant routine assessments of the fitted temperature minimum 1-2 days after completion of the resetting stimulus; and 3) the timing of background room light modulates the resetting response to bright light. These data indicate that the human circadian pacemaker is sensitive to light at virtually all circadian phases, implying that the entire 24-h pattern of light exposure contributes to entrainment.

Phase-amplitude resetting of the human circadian pacemaker via bright light: a further analysis.

We present here an analysis of strong, weak, and critical bright-light resetting trials in humans, and report not only phase but also amplitude data for the first time. For this analysis, an appropriate iterative smoothing procedure for phase transition curves is introduced, in which the data are sequenced so as to minimize the perpendicular distance from the data to the smoothed fit. From these smoothed data, we create polar phase-amplitude resetting maps (PARMs) in order to fully illustrate the effects of the resetting stimuli on both circadian amplitude and phase, and thereby to determine whether these resetting results can be described by a phase-only model or whether a phase-amplitude model is required. Our results indicate that a single 5-hr episode of bright light induces weak type 1 resetting of the human circadian pacemaker. Two cycles of exposure to the same stimulus on consecutive days induce critical resetting, in which significant amplitude reduction may be observed. A three-cycle stimulus induces strong type 0 resetting with different effects on circadian amplitude, depending on the initial phase of the stimulus application. When a three-cycle stimulus is centered near the nadir of the temperature cycle, large phase shifts are achieved via amplitude suppression. However, when this stimulus is centered away from the temperature nadir, smaller phase shifts are achieved in which both small increases and small decreases in circadian amplitude are observed. These data indicate that the human circadian pacemaker is not a simple, phase-only oscillator. Instead, a full description of human circadian resetting responses to light requires analysis of both phase and amplitude data--a finding that is consistent with a phase-amplitude model of the circadian resetting mechanism.

Torpor shortens the period of Siberian hamster circadian rhythms.

We investigated the influence of ambient and body temperature (Ta and Tb) on circadian rhythms of gonadectomized male Siberian hamsters. Animals that entered torpor (Tb < 30 degrees C) had significantly shorter circadian periods (tau s) than did nontorpid hamsters at a Ta of 13 degrees C (24.17 +/- 0.05 vs. 24.33 +/- 0.04 h). The tau s of homeothermic hamsters were not affected by Ta change. Short-term decreases in Tb, rather than changes in Ta, appear to affect tau. Access to activity wheels inhibited expression of torpor in short daylengths and was associated with significant increases in body mass. Running wheel activity can mask or block specific short-day responses.

Light-induced suppression of endogenous circadian amplitude in humans.

Winfree reported 20 years ago the intriguing finding that a light stimulus of a critical strength applied at a critical circadian phase could essentially stop the circadian clock in Drosophila pseudo-obscura by resetting the circadian oscillator close to its singularity (a phaseless position at which the amplitude of circadian oscillation is zero). Since then, similar observations of attenuated circadian amplitude in response to critical stimuli have been limited to unicells, insects and plants. Our recent demonstration that the phase of the human circadian pacemaker could be inverted using an unconventional three-cycle stimulus led us to investigate whether critically timed exposure to a more moderate stimulus could drive that oscillator towards its singularity. Here we report that exposure of humans to fewer cycles of bright light, centred around the time at which the human circadian pacemaker is most sensitive to light-induced phase shifts, can markedly attenuate endogenous circadian amplitude. In some cases this results in an apparent loss of rhythmicity, as expected to occur in the region of singularity.

Bright light induction of strong (type 0) resetting of the human circadian pacemaker.

The response of the human circadian pacemaker to light was measured in 45 resetting trials. Each trial consisted of an initial endogenous circadian phase assessment, a three-cycle stimulus which included 5 hours of bright light per cycle, and a final phase assessment. The stimulus induced strong (type 0) resetting, with responses highly dependent on the initial circadian phase of light exposure. The magnitude and direction of the phase shifts were modulated by the timing of exposure to ordinary room light, previously thought to be undetectable by the human pacemaker. The data indicate that the sensitivity of the human circadian pacemaker to light is far greater than previously recognized and have important implications for the therapeutic use of light in the management of disorders of circadian regulation.