More than just slowing: bimodal vigilance dynamics in sleep deprivation

Sleep deprivation is a critical concern in modern society, affecting not only personal health but also public safety by increasing the risk of accidents across transportation, healthcare, and industrial domains, primarily through its detrimental effects on attention. While the ubiquitous psychomotor vigilance task has been instrumental in characterizing attention impairments associated with sleep deficiency,^1,2 but its granular interpretation remains limited by the absence of physiologically grounded models. In a compelling study, Raison et al. provide a much-needed breakthrough by introducing a bistable stochastic model that elegantly quantifies the dynamics of attention under sleep deprivation.³ This study moves the field forward in at least three major ways: by empirically confirming a bimodal distribution of reaction times (RTs) during extended wakefulness, offering a theoretical model that captures this dual-state behavior, and providing a tractable mathematical framework to link latent cognitive states with behavioral performance metrics. We argue that this study provides new insights into the nature of attention and marks a significant step forward in the mathematical modeling of cognitive processes.

The authors analyzed a rich dataset of 317 healthy young males subjected to 40 h of sleep deprivation under a constant routine protocol. What stands out is the emergence of a secondary peak in the reciprocal RT distribution (rRT)—a striking signature of attentional lapses not captured by standard measures like lapse counts (RTs > 500 ms). The first, or main peak, reflects normal RTs (typically faster than 0.5 s) and represents periods when participants are attentive. In contrast, the secondary peak, which reflects very slow responses (RT ≳ 1.5 s), becomes noticeable after about 20 h of wakefulness and appears in nearly two-thirds of participants. Crucially, this bimodal pattern is not just due to averaging across individuals—it also shows up within each person’s data. By distinguishing between the main peak (attentive responses) and the secondary peak (unresponsiveness), the study shows that attention does not simply degrade uniformly, but instead shifts between distinct cognitive states.

At the heart of the study lies a bistable rate model, built upon evidence accumulation frameworks commonly used in decision-making research.^4,5 But unlike classic drift-diffusion models, this formulation explicitly integrates the concept of vigilance bistability: the brain stochastically toggles between a high-performance (task-engaged) and low-performance (task-disengaged) state. The accumulation rate is governed by a stochastic differential equation with a cubic nonlinearity modulated by a stabilizing quadratic term, enabling the system to dwell in or transition between two attractor states.

Notably, the model’s effectiveness extends beyond recapitulating the empirical rRT distributions. When combined with the two-process model (homeostatic and circadian drives), fluctuation of two attractor states—fitted from empirical rRT distribution—exhibits sensitivity to known circadian phenomena, such as the wake maintenance zone and an unexpected ultradian component (~8 h periodicity). These findings are a testament to the model’s fidelity and its potential to capture subtle internal fluctuations in cognitive states.

Importantly, the bistable dynamics posited in this study resonate with neurophysiological observations. Transitions into the low-performance state likely mirror microsleep episodes,^2,6,7 brief cortical shutdowns often undetectable through superficial behavioral metrics. The authors discuss plausible neural underpinnings, including the sleep–wake “flip-flop” switch and local cortical OFF states,⁸ situating their model within a robust neurobiological framework. This differentiation between general response slowing and discrete lapses is not just a modeling convenience—it has practical implications. For instance, operators prone to unresponsiveness may pose higher safety risks than those exhibiting only mild slowing, a nuance critical for real-world risk mitigation in aviation, medicine, and transportation.

This advancement of Raison et al.’s model provides a springboard for broadening the scope and precision of biomathematical models in cognitive science. While existing biomathematical models, including the two-process model, predict performance at coarse temporal scales,^9-12 they fail to account for intra-task fluctuations. Raison et al. propose a clear path forward: integrating their bistable framework with established alertness models to enable individual-level, real-time prediction of performance collapse. Such integration could revolutionize fatigue risk management systems and adaptive scheduling tools. For example, existing mobile-based sleep interventions could be enhanced by incorporating predictions of the transition timing into low-performance states.¹⁰

Beyond the performance state, the model’s utility may extend to other circadian-regulated outcomes, such as mood.¹³ Previous mathematical modeling studies on mood and circadian rhythms have largely relied on daily mood assessments,^13-15 often overlooking within-day fluctuations driven by sleep and circadian disruptions.¹⁶ To address this gap, the mathematical framework proposed by Raison et al. could be applied to capture within-day variability in mood states.

Naturally, the scope of the study is not without constraints. The exclusive focus on young Caucasian males limits immediate generalizability of the findings across broader populations. In addition, while the model’s assumptions—such as omitting non-decision time and simplifying evidence accumulation—are empirically justified, they necessitate further validation through neural measurements or more comprehensive behavioral paradigms. Nonetheless, these limitations do not undermine the conceptual contribution of the model. Instead, they invite future work to extend the framework across diverse populations and contexts, and to fuse it with physiological monitoring (e.g., EEG, pupillometry) for more holistic assessments.

Raison et al. offer a tour de force in mathematical neuroscience, blending elegant theory with robust empirical validation. Their bistable model illuminates the nuanced, state-dependent nature of vigilance under sleep deprivation and sets the stage for more precise, predictive, and personalized approaches to managing fatigue-related risks. By acknowledging that lapses are not merely “long RTs” but hallmarks of a fundamentally different brain state, this work invites a paradigm shift. Their new paradigm sees cognitive performance not as a continuum, but as a competition between coexisting neural modes—an insight that may reshape how we study, model, and safeguard human attention in a 24/7 world.

Disclosure statement

Financial disclosure: The authors have no financial relationships, funding, or conflicts of interest related to this work to disclose.

Non-financial disclosure: The authors have no non-financial competing interests to disclose.