Beyond the limits of circadian entrainment: Non-24-h sleep-wake disorder, shift work, and social jet lag.

While the vast majority of humans are able to entrain their circadian rhythm to the 24-h light-dark cycle, there are numerous individuals who are not able to do so due to disease or societal reasons. We use computational and mathematical methods to analyze a well-established model of human circadian rhythms to address cases where individuals do not entrain to the 24-h light-dark cycle, leading to misalignment of their circadian phase. For each case, we provide a mathematically justified strategy for how to minimize circadian misalignment. In the case of non-24-h sleep-wake disorder, we show why appropriately timed bright light therapy induces entrainment. With regard to shift work, we explain why reentrainment times following transitions between day and night shifts are asymmetric, and how higher light intensity enables unusually rapid reentrainment after certain transitions. Finally, with regard to teenagers who engage in compensatory catch-up sleep on weekends, we propose a rule of thumb for sleep and wake onset times that minimizes circadian misalignment due to this type of social jet lag. In all cases, the primary mathematical approach involves understanding the dynamics of entrainment maps that measure the phase of the entrained rhythm with respect to the daily onset of lights.