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. Statement of Significance Sleep deprivation is prevalent in modern society, leading to an increased risk of accidents due to lapses in attention. In many scenarios, like shiftwork, simply getting more sleep is not an option, so a better understanding of mechanisms is needed. Our study, for the first time, shows a bimodality of response rates during sleep deprivation. We explain this by the co-existence of two vigilance states in the brain. The first state corresponds to typical reaction times in all individuals, while the second state is linked to unresponsiveness with reaction times ≳1.5 s and is observed in ∼60% of individuals. Our model enables new approaches to predict and prevent accidents and new insights into the physiology of sustained attention.