A bistable stochastic model quantifies performance degradation during sleep deprivation

Sleep deprivation impairs sustained attention, as measured on the psychomotor vigilance task. This is manifested in a general slowing of reaction times and an increase in periods of unresponsiveness, increasing the risk of accidents. However, the mechanisms are not fully understood. This study combines experiments and modeling to better explain and quantify the changes of sustained attention under sleep deprivation. A total of 317 male participants (age 22.1 $\pm$ 2.7 y) underwent 40 h of sleep deprivation under a constant routine protocol. A 10-minute psychomotor vigilance task was performed at 2-h intervals, and saliva melatonin was sampled every hour to monitor circadian phase. We report a bimodal distribution of reaction speed in the data. An approximately normal primary peak characterizes typical performance (reaction time ≲0.5 s), while periods of unresponsiveness correspond to reaction times ≳1.5 s and are reflected in a secondary peak which emerges after ∼20 h of wakefulness. We developed a minimal, stochastic model that accurately reproduces the data, attributing the bimodality of the distribution to bistability in vigilance state. We find general response slowing to be subject to an ultradian oscillation (∼3 cycles per day), while periods of unresponsiveness are disproportionately affected during the wake maintenance zone. Our results attribute periods of unresponsiveness to the coexistence of two vigilance states in the sleep-deprived brain, enabling new approaches in understanding vulnerability to sleep loss.