Megan E. Jewett

A phase response curve to single bright light pulses in human subjects

The circadian pacemaker is differentially sensitive to the resetting effects of retinal light exposure, depending upon the circadian phase at which the light exposure occurs. Previously reported human phase response curves (PRCs) to single bright light exposures have employed small sample sizes, and were often based on relatively imprecise estimates of circadian phase and phase resetting. In the present study, 21 healthy, entrained subjects underwent pre‐ and post‐stimulus constant routines (CRs) in dim light (∼2–7 lx) with maintained wakefulness in a semi‐recumbent posture. The 6.7 h bright light exposure stimulus consisted of alternating 6 min fixed gaze (∼10 000 lx) and free gaze (∼5000–9000 lx) exposures. Light exposures were scheduled across the circadian cycle in different subjects so as to derive a PRC. Plasma melatonin was used to determine the phase of the onset, offset, and midpoint of the melatonin profiles during the CRs. Phase shifts were calculated as the difference in phase between the pre‐ and post‐stimulus CRs. The resultant PRC of the midpoint of the melatonin rhythm revealed a characteristic type 1 PRC with a significant peak‐to‐trough amplitude of 5.02 h. Phase delays occurred when the light stimulus was centred prior to the critical phase at the core body temperature minimum, phase advances occurred when the light stimulus was centred after the critical phase, and no phase shift occurred at the critical phase. During the subjective day, no prolonged ‘dead zone’ of photic insensitivity was apparent. Phase shifts derived using the melatonin onsets showed larger magnitudes than those derived from the melatonin offsets. These data provide a comprehensive characterization of the human PRC under highly controlled laboratory conditions.

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.

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 decribed 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.

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 Kronauers 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 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 CBTmin 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.

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 Aschoffs 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 Kronauers model of Aschoffs 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.

Human circadian melatonin rhythm phase delay during a fixed sleep–wake schedule interspersed with nights of sleep deprivation

Abstract:  The human circadian pacemaker, with an intrinsic period between 23.9 and 24.5 hr, can be reset by low levels of light. Biomathematical models of the human clock predict that light–dark cycles consisting of only ∼3.5 lux during 16 hr of wakefulness and 0 lux during 8 hr of sleep should entrain ∼45% of the population. However, under real‐life conditions, sleep–wake schedules and the associated light–dark exposures are often irregular. It remains unclear whether the phase of the pacemaker would remain stable under such conditions. We investigated the stability of the circadian phase in dim light by assessing the plasma melatonin rhythm during nine consecutive circadian cycles. Ten subjects were scheduled to sleep for 8 hr (0.03 lux) and to be awake for 16 hr (5–13 lux) during all days except on days 4 and 8, during which the subjects were sleep deprived for 40 hr (5–13 lux), either in a sitting/standing or supine body posture. In all subjects, the phase of the melatonin rhythm occurred at a later clock time on day 9 than on day 2 (average delay: 1.4 hr). Largest delays in the melatonin onset were observed in subjects with low amplitude melatonin rhythms. The area under the curve during active melatonin secretion was significantly reduced when subjects were sleep deprived in the 40‐hr supine body posture condition compared with either the 40‐hr sitting/standing sleep deprivation (SD) or the ambulatory condition under non‐SD conditions. Posture differences did not significantly affect the relative phase position of the melatonin profiles. The data indicate that under conditions of reduced zeitgeber strength, the phase of the human circadian pacemaker, using plasma melatonin as a marker, can be phase delayed by one night of SD and the associated dim light exposure.

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

Adouble-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.

Commentary: The Human Circadian Response to Light-Strong and Weak Resetting

The paper by Beersma and Daan (this issue) offers a reinterpretation of our data on the circadian phase-shifting effect of bright light on humans (Czeisler et al., 1989). In our view, Beersma and Daan misunderstand the mathematical basis of the relationship between type 0 and type I resetting, and inaccurately represent not only our data but the data of other investigators. We have organized our response so as to deal separately with the issues on which we disagree.

Reply to technical note: Nonlinear interactions between circadian and homeostatic processes: Models or metrics?

Derk-Jan Dijk,* Megan E. Jewett,** Charles A. Czeisler,** and Richard E. Kronauer*** * Centre for Chronobiology, School for Biological Sciences, University of Surry, Guilford GU2 5XH, UK; **Circadian, Neuroendocrine and Sleep Disorders Section, Brigham and Women’s Hospital, 221 Longwood Avenue, Boston MA 02115; ***Division of Engineering and Applied Science, Harvard University, Cambridge, MA 02138

Comparison of Amplitude Recovery Dynamics of Two Limit Cycle Oscillator Models of the Human Circadian Pacemaker

At an organism level, the mammalian circadian pacemaker is a two‐dimensional system. For these two dimensions, phase (relative timing) and amplitude of the circadian pacemaker are commonly used. Both the phase and the amplitude (A) of the human circadian pacemaker can be observed within multiple physiological measures—including plasma cortisol, plasma melatonin, and core body temperature (CBT)—all of which are also used as markers of the circadian system. Although most previous work has concentrated on changes in phase of the circadian system, critically timed light exposure can significantly reduce the amplitude of the pacemaker. The rate at which the amplitude recovers to its equilibrium level after reduction can have physiological significance. Two mathematical models that describe the phase and amplitude dynamics of the pacemaker have been reported. These models are essentially equivalent in predictions of phase and in predictions of amplitude recovery for small changes from an equilibrium value (A=1), but are markedly different in the prediction of recovery rates when A<0.6. To determine which dynamic model best describes the amplitude recovery observed in experimental data; both models were fit to CBT data using a maximum likelihood procedure and compared using Akaikes Information Criterion (AIC). For all subjects, the model with the lower recovery rate provided a better fit to data in terms of AIC, supporting evidence that the amplitude recovery of the endogenous pacemaker is slow at low amplitudes. Experiments derived from model predictions are proposed to test the influence of low amplitude recovery on the physiological and neurobehavioral functions.