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 $\pm$ 0.17 h vs 24.15 $\pm$ 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.