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

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

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

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

Estimating Representative Group Intrinsic Circadian Period from Illuminance-Response Curve Data.

The human circadian pacemaker entrains to the 24-h day, but interindividual differences in properties of the pacemaker, such as intrinsic period, affect chronotype and mediate responses to challenges to the circadian system, such as shift work and jet lag, and the efficacy of therapeutic interventions such as light therapy. Robust characterization of circadian properties requires desynchronization of the circadian system from the rest-activity cycle, and these forced desynchrony protocols are very time and resource intensive. However, circadian protocols designed to derive the relationship between light intensity and phase shift, which is inherently affected by intrinsic period, may be applied more broadly. To exploit this relationship, we applied a mathematical model of the human circadian pacemaker with a Markov-Chain Monte Carlo parameter estimation algorithm to estimate the representative group intrinsic period for a group of participants using their collective illuminance-response curve data. We first validated this methodology using simulated illuminance-response curve data in which the intrinsic period was known. Over a physiological range of intrinsic periods, this method accurately estimated the representative intrinsic period of the group. We also applied the method to previously published experimental data describing the illuminance-response curve for a group of healthy adult participants. We estimated the study participants' representative group intrinsic period to be 24.26 and 24.27 h using uniform and normal priors, respectively, consistent with estimates of the average intrinsic period of healthy adults determined using forced desynchrony protocols. Our results establish an approach to estimate a population's representative intrinsic period from illuminance-response curve data, thereby facilitating the characterization of intrinsic period across a broader range of participant populations than could be studied using forced desynchrony protocols. Future applications of this approach may improve the understanding of demographic differences in the intrinsic circadian period.

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.