Biomathematical modeling of fatigue due to sleep inertia.

Biomathematical models of fatigue capture the physiology of sleep/wake regulation and circadian rhythmicity to predict changes in neurobehavioral functioning over time. We used a biomathematical model of fatigue linked to the adenosinergic neuromodulator/receptor system in the brain as a framework to predict sleep inertia, that is, the transient neurobehavioral impairment experienced immediately after awakening. Based on evidence of an adenosinergic basis for sleep inertia, we expanded the biomathematical model with novel differential equations to predict the propensity for sleep inertia during sleep and its manifestation after awakening. Using datasets from large laboratory studies of sleep loss and circadian misalignment, we calibrated the model by fitting just two new parameters and then validated the model's predictions against independent data. The expanded model was found to predict the magnitude and time course of sleep inertia with generally high accuracy. Analysis of the model's dynamics revealed a bifurcation in the predicted manifestation of sleep inertia in sustained sleep restriction paradigms, which reflects the observed escalation of the magnitude of sleep inertia in scenarios with sleep restriction to less than âˆ¼ 4 h per day. Another emergent property of the model involves a rapid increase in the predicted propensity for sleep inertia in the early part of sleep followed by a gradual decline in the later part of the sleep period, which matches what would be expected based on the adenosinergic regulation of non-rapid eye movement (NREM) sleep and its known influence on sleep inertia. These dynamic behaviors provide confidence in the validity of our approach and underscore the predictive potential of the model. The expanded model provides a useful tool for predicting sleep inertia and managing impairment in 24/7 settings where people may need to perform critical tasks immediately after awakening, such as on-demand operations in safety and security, emergency response, and health care.

A new mathematical model for the homeostatic effects of sleep loss on neurobehavioral performance.

The two-process model of sleep regulation makes accurate predictions of sleep timing and duration for a variety of experimental sleep deprivation and nap sleep scenarios. Upon extending its application to waking neurobehavioral performance, however, the model fails to predict the effects of chronic sleep restriction. Here we show that the two-process model belongs to a broader class of models formulated in terms of coupled non-homogeneous first-order ordinary differential equations, which have a dynamic repertoire capturing waking neurobehavioral functions across a wide range of wake/sleep schedules. We examine a specific case of this new model class, and demonstrate the existence of a bifurcation: for daily amounts of wakefulness less than a critical threshold, neurobehavioral performance is predicted to converge to an asymptotically stable state of equilibrium; whereas for daily wakefulness extended beyond the critical threshold, neurobehavioral performance is predicted to diverge from an unstable state of equilibrium. Comparison of model simulations to laboratory observations of lapses of attention on a psychomotor vigilance test (PVT), in experiments on the effects of chronic sleep restriction and acute total sleep deprivation, suggests that this bifurcation is an essential feature of performance impairment due to sleep loss. We present three new predictions that may be experimentally verified to validate the model. These predictions, if confirmed, challenge conventional notions about the effects of sleep and sleep loss on neurobehavioral performance. The new model class implicates a biological system analogous to two connected compartments containing interacting compounds with time-varying concentrations as being a key mechanism for the regulation of psychomotor vigilance as a function of sleep loss. We suggest that the adenosinergic neuromodulator/receptor system may provide the underlying neurobiology.