Intrinsic near-24-h pacemaker period determines limits of circadian entrainment to a weak synchronizer in humans.

Endogenous circadian clocks are robust regulators of physiology and behavior. Synchronization or entrainment of biological clocks to environmental time is adaptive and important for physiological homeostasis and for the proper timing of species-specific behaviors. We studied subjects in the laboratory for up to 55 days each to determine the ability to entrain the human clock to a weak circadian synchronizing stimulus [scheduled activity-rest cycle in very dim (approximately 1.5 lux in the angle of gaze) light-dark cycle] at three approximately 24-h periods: 23.5, 24.0, and 24.6 h. These studies allowed us to test two competing hypotheses as to whether the period of the human circadian pacemaker is near to or much longer than 24 h. We report here that imposition of a sleep-wake schedule with exposure to the equivalent of candle light during wakefulness and darkness during sleep is usually sufficient to maintain circadian entrainment to the 24-h day but not to a 23.5- or 24.6-h day. Our results demonstrate functionally that, in normally entrained sighted adults, the average intrinsic circadian period of the human biological clock is very close to 24 h. Either exposure to very dim light and/or the scheduled sleep-wake cycle itself can entrain this near-24-h intrinsic period of the human circadian pacemaker to the 24-h day.

Thomas McMahon: a dedication in memoriam.

Thomas A. McMahon (1943-1999) was a pioneer in the field of biomechanics. He made primary contributions to our understanding of terrestrial locomotion, allometry and scaling, cardiac assist devices, orthopedic biomechanics, and a number of other areas. His work was frequently characterized by the use of simple mathematical models to explain seemingly complex phenomena. He also validated these models through creative experimentation. McMahon was a successful inventor and also published three well-received novels. He was raised in Lexington, Massachussetts, attended Cornell University as an undergraduate, and earned a PhD at MIT. From 1970 until his death, he was a member of the faculty of Harvard University, where he taught biomedical engineering. He is fondly remembered as a warm and gentle colleague and an exemplary mentor to his students.

Dynamic resetting of the human circadian pacemaker by intermittent bright light.

In humans, experimental studies of circadian resetting typically have been limited to lengthy episodes of exposure to continuous bright light. To evaluate the time course of the human endogenous circadian pacemaker's resetting response to brief episodes of intermittent bright light, we studied 16 subjects assigned to one of two intermittent lighting conditions in which the subjects were presented with intermittent episodes of bright-light exposure at 25- or 90-min intervals. The effective duration of bright-light exposure was 31% or 63% compared with a continuous 5-h bright-light stimulus. Exposure to intermittent bright light elicited almost as great a resetting response compared with 5 h of continuous bright light. We conclude that exposure to intermittent bright light produces robust phase shifts of the endogenous circadian pacemaker. Furthermore, these results demonstrate that humans, like other species, exhibit an enhanced sensitivity to the initial minutes of bright-light exposure.

Colour adaptation modifies the temporal properties of the long- and middle-wave cone signals in the human luminance mechanism.

The human luminance mechanism (LUM) detects rapid flicker and motion, summating the neurally integrated L' and M' 'contrast' signals from the long- and middle-wave cones, respectively. We previously observed large temporal phase shifts between the L' and M' signals in LUM, which were maximal and of reversed sign on green versus orange background fields and which were accompanied by large variations in the relative L' and M' contrast weights. The effects were modelled with phasic magnocellar retinal ganglion cells. The changing L' versus M' contrast weights in the model predict that the temporal dynamics of the L' and M' luminance signals will differ on green and orange fields. This is assessed with several protocols. Motion thresholds for 1 cycle deg(-1) drifting gratings or static pulsed gratings on the orange field show that the M' signal is more temporally bandpass than the L' signal; this reverses on the green field. Strong motion due to the different dynamics of the L' and M' signals is even seen with a pair of L' and M' gratings pulsed simultaneously. Impulse response functions were measured with gratings pulsed spatially in phase or antiphase. The impulse response was clearly biphasic for the M' signal on the orange field and L' signal on the green field, while the other signals were more sustained. The impulse responses predicted the motion seen with gratings pulsed in spatial quadrature.

Melatonin rhythm observed throughout a three-cycle bright-light stimulus designed to reset the human circadian pacemaker.

Exposure to light and darkness can rapidly induce phase shifts of the human circadian pacemaker. A type 0 phase response curve (PRC) to light that has been reported for humans was based on circadian phase data collected from constant routines performed before and after a three-cycle light stimulus, but resetting data observed throughout the entire resetting protocol have not been previously reported. Pineal melatonin secretion is governed by the hypothalamic circadian pacemaker via a well-defined neural pathway and is reportedly less subject to the masking effects of sleep and activity than body temperature. The authors reasoned that observation of the melatonin rhythm throughout the three-cycle light resetting trials could provide daily phase-resetting information, allowing a dynamic view of the resetting response of the circadian pacemaker to light. Subjects (n = 12) living in otherwise dim light (approximately 10-15 lux) were exposed to a noncritical stimulus of three cycles of bright light (approximately 9500 lux for 5 h per day) timed to phase advance or phase delay the human circadian pacemaker; control subjects (n = 11) were scheduled to the same protocols but exposed to three 5-h darkness cycles instead of light. Subjects underwent initial and final constant routine phase assessments; hourly melatonin samples and body temperature data were collected throughout the protocol. Average daily phase shifts of 1 to 3 h were observed in 11 of 12 subjects receiving the bright light, supporting predictions obtained using Kronauer's phase-amplitude model of the resetting response of the human circadian pacemaker. The melatonin rhythm in the 12th subject progressively attenuated in amplitude throughout the resetting trial, becoming undetectable for >32 hours preceding an abrupt reappearance of the rhythm at a shifted phase with a recovered amplitude. The data from control subjects who remained in dim lighting and darkness delayed on average -0.2 h per day, consistent with the daily delay expected due to the longer than 24-h intrinsic period of the human circadian pacemaker. Both temperature and melatonin rhythms shifted by equivalent amounts in both bright light-treated and control subjects (R = 0.968; p<0.0001; n = 23). Observation of the melatonin rhythm throughout a three-cycle resetting trial has provided a dynamic view of the daily phase-resetting response of the human circadian pacemaker. Taken together with the observation of strong type 0 resetting in humans in response to the same three-cycle stimulus applied at a critical phase, these data confirm the importance of considering both phase and amplitude when describing the resetting of the human circadian pacemaker by light.

Linear demasking techniques are unreliable for estimating the circadian phase of ambulatory temperature data.

Clinical investigators often use ambulatory temperature monitoring to assess the endogenous phase and amplitude of an individual's circadian pacemaker for diagnostic and research purposes. However, an individual's daily schedule includes changes in levels of activity, in posture, and in sleep-wake state, all of which are known to have masking or evoked effects on core body temperature (CBT) data. To compensate for or to correct these masking effects, many investigators have developed "demasking" techniques to extract the underlying circadian phase and amplitude data. However, the validity of these methods is uncertain. Therefore, the authors tested a variety of analytic methods on two different ambulatory data sets from two different studies in which the endogenous circadian pacemaker was not synchronized to the sleep-wake schedule. In both studies, circadian phase estimates calculated from CBT collected when each subject was ambulatory (i.e., free to perform usual daily activities) were compared to those calculated during the same study when the same subject's activities were controlled. In the first study, 24 sighted young and older subjects living on a 28-h scheduled "day" protocol were studied for approximately 21 to 25 cycles of 28-h each. In the second study, a blind man whose endogenous circadian rhythms were not synchronized to the 24-h day despite his maintenance of a regular 24-h sleep-wake schedule was studied for more than 80 consecutive 24-h days. During both studies, the relative phase of the endogenous (circadian) and evoked (scheduled activity-rest) components of the ambulatory temperature data changed progressively and relatively slowly, enabling analysis of the CBT rhythm at nearly all phase relationships between the two components. The analyses of the ambulatory temperature data demonstrate that the masking of the CBT rhythm evoked by changes in activity levels, posture, or sleep-wake state associated with the evoked schedule of activity and rest can significantly obscure the endogenous circadian component of the signal, the object of study. In addition, the masking effect of these evoked responses on temperature depends on the circadian phase at which they occur. These nonlinear interactions between circadian phase and sleep-wake schedule render ambulatory temperature data unreliable for the assessment of endogenous circadian phase. Even when proposed algebraic demasking techniques are used in an attempt to reveal the endogenous temperature rhythm, the phase estimates remain severely compromised.

Stability, precision, and near-24-hour period of the human circadian pacemaker.

Regulation of circadian period in humans was thought to differ from that of other species, with the period of the activity rhythm reported to range from 13 to 65 hours (median 25.2 hours) and the period of the body temperature rhythm reported to average 25 hours in adulthood, and to shorten with age. However, those observations were based on studies of humans exposed to light levels sufficient to confound circadian period estimation. Precise estimation of the periods of the endogenous circadian rhythms of melatonin, core body temperature, and cortisol in healthy young and older individuals living in carefully controlled lighting conditions has now revealed that the intrinsic period of the human circadian pacemaker averages 24.18 hours in both age groups, with a tight distribution consistent with other species. These findings have important implications for understanding the pathophysiology of disrupted sleep in older people.

Spatial masking does not reveal mechanisms selective to combined luminance and red-green color.

Detection thresholds plotted in the L and M cone-contrast plane have shown that there are two primary detection mechanisms, a red-green hue mechanism and a light-dark luminance mechanism. However, previous masking results suggest there may be additional mechanisms, responsive to combined features like bright and red or dark and green. We measured detection thresholds for a 1.2 c deg-1 sine-wave grating in the presence of a spatially matched mask grating which was either stationary, dynamically jittered or flickered. The stimuli could be set to any direction in the L,M plane. The appearance of selectivity for combined hue and luminance arose only in conditions where adding the test to the mask modified the spatial phase offset between the luminance and red-green stimulus components. Sensitivity was very high for detecting this spatial phase offset. When this extra cue was eliminated, masking contours in the L,M plane could be largely described by the classical red-green and luminance mechanisms.

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.

Second-site adaptation in the red-green detection pathway: only elicited by low-spatial-frequency test stimuli.

The red-green (RG) detection mechanism was revealed by measuring threshold detection contours in the L and M cone contrast plane for sine-wave test gratings of 0.8-6 c deg-1 on bright adapting fields of yellow or red. The slope of the RG detection contours was unity, indicating that the L and M contrast signals contribute equally (with opposite signs) on both the yellow and the red fields: this reflects first-site, cone-selective adaptation. Second-site adaptation, which may reflect saturation at a color-opponent site, was evidenced by the RG detection contours being further out from the origin of the cone contrast plane on the red field than on the yellow field. Second-site adaptation was strong (3-fold) for low spatial frequency test gratings but greatly diminished by 6 c deg-1. The disappearance of second-site adaptation with increasing spatial frequency can be explained by spatial frequency channels. The most sensitive detectors may comprise a low spatial frequency channel which is susceptible to masking by the chromatic, spatial DC component of the red field. The 6 c deg-1 patterns may be detected by a less sensitive, higher frequency channel which is less affected by the uniform red field. The RG spatial frequency channels likely arise in the cortex, implicating a partially central site for the second-site effect.

Detection of flickering edges: absence of a red-green edge detector.

Kelly ((1975) Science, 188, 371-372) showed that a centrally-fixated, contrast-reversing edge has a very different effect on the detection of luminance and red-green flicker. Red-green flicker sensitivity was approximately 3-fold greater for a uniform field than for a 'split' field with the two sides flickering out-of-phase. Just the opposite effects were observed for luminance flicker--the split field yielded a 7-fold advantage over the uniform field at 2 or 4 Hz and a 3-fold advantage at 12 Hz. Contrary to Kelly, we find that the split field offers only a very small advantage of 40% for luminance flicker at 2 Hz and virtually no advantage at 4 Hz and above. Kelly's chromatic results are surprising since one might expect that the larger color difference (or step) across the central edge would aid chromatic discrimination rather than strongly suppressing sensitivity. We show that the central chromatic edge only weakly impairs detection. Further results show that the two sides of the chromatic split field are detected essentially independently by red or green 'blob' detectors, which do not take advantage of the color difference across the edge. This has a remarkable implication: when wavelength discrimination is measured with a bipartite field whose two side are slowly modulated in opposite directions, then one side may be deleted with little adverse effect.

Facilitation between the luminance and red-green detection mechanisms: enhancing contrast differences across edges.

Previous studies have shown that detection of a red-green test pattern, such as a spot or grating, may be facilitated two to three times by a suprathreshold luminance pedestal of the same shape. We measured facilitation between the red-green (RG) and luminance (LUM) detection mechanisms using sine and square-wave gratings. Facilitation of RG by luminance pedestals was 3-fold for in phase sine-wave gratings of 0.8 cpd and a remarkable 7-fold for square-wave gratings. The latter facilitation was greatly reduced at intermediate relative phases and was generally reduced at higher spatial frequencies. We show that on a uniform field, the red or green regions of low spatial frequency test patterns are detected approximately independently, but in the presence of the LUM pedestal RG becomes sensitive to the red-green difference across the luminance edges. Under optimal conditions (with the low-frequency, square-wave luminance pedestal) this increased red-green sensitivity corresponds to a wavelength discrimination threshold as small as approximately 0.04 nm. This conversion of RG into an 'edge detector' may explain why facilitation is twice as large for square-wave gratings (bipolar patterns) than spots (unipolar patterns). The reverse facilitation, that of LUM by the red-green pedestal, is weaker and the results suggest that this is because LUM is initially sensitive to the light-dark difference across luminance edges even in the absence of the red-green pedestal.

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.

Commentary: models of sleep regulation: successes and continuing challenges.

Quantitative models have been developed to describe salient aspects of human sleep regulation. The two-process model of sleep regulation and the thermoregulatory model of sleep control highlight the interaction between sleep homeostasis and circadian rhythmicity and the association between sleep and temperature regulation, respectively. These models have been successful and inspiring, but continuing progress remains dependent on rigorous testing of some of their basic assumptions. Whereas it has been established that EEG slow-wave activity is a marker of sleep homeostasis, its causal role in regulating the timing of sleep and wakefulness remains to be demonstrated conclusively. Likewise, the causal role of the temperature regulatory system in sleep timing requires further investigation. In both models, many parameters have yet to be associated with specific physiologic processes. This makes it challenging, at least within the framework of these models, to account for interindividual differences or age-related changes in such features as sleep duration and sleep timing, as well as changes in the phase angle between the sleep-wake cycle and accepted markers of the circadian pacemaker, such as the body temperature or melatonin rhythm. Although the models may describe adequately global sleep patterns and their circadian modulation, detailed modeling of the frequent short awakenings from, and the subsequent transitions back to, sleep, as well as the variation of the propensity to awaken across the ultradian non-REM-REM cycle, is not addressed. Incoporation of these aspects of sleep in mathematical models of sleep regulation may further our understanding of a key aspect of sleep regulation, that is, its timing.

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.

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.