Few models exist that accurately reproduce the complex rhythms of the thalamocortical system that are apparent in measured scalp EEG and at the same time, are suitable for large-scale simulations of brain activity. Here, we present a neural mass model of the thalamocortical system during natural non-REM sleep, which is able to generate fast sleep spindles (12–15 Hz), slow oscillations (<1 Hz) and K-complexes, as well as their distinct temporal relations, and response to auditory stimuli. We show that with the inclusion of detailed calcium currents, the thalamic neural mass model is able to generate different firing modes, and validate the model with EEG-data from a recent sleep study in humans, where closed-loop auditory stimulation was applied. The model output relates directly to the EEG, which makes it a useful basis to develop new stimulation protocols.

NREM sleep is characterized by two hallmarks, namely K-complexes (KCs) during sleep stage N2 and cortical slow oscillations (SOs) during sleep stage N3. While the underlying dynamics on the neuronal level is well known and can be easily measured, the resulting behavior on the macroscopic population level remains unclear. On the basis of an extended neural mass model of the cortex, we suggest a new interpretation of the mechanisms responsible for the generation of KCs and SOs. As the cortex transitions from wake to deep sleep, in our model it approaches an oscillatory regime via a Hopf bifurcation. Importantly, there is a canard phenomenon arising from a homoclinic bifurcation, whose orbit determines the shape of large amplitude SOs. A KC corresponds to a single excursion along the homoclinic orbit, while SOs are noise-driven oscillations around a stable focus. The model generates both time series and spectra that strikingly resemble real electroencephalogram data and points out possible differences between the different stages of natural sleep.

In mammals, sleep is categorized by two main sleep stages, rapid eye movement (REM) and non-REM (NREM) sleep that are known to fulfill different functional roles, the most notable being the consolidation of memory. While REM sleep is characterized by brain activity similar to wakefulness, the EEG activity changes drastically with the emergence of K-complexes, sleep spindles and slow oscillations during NREM sleep. These changes are regulated by circadian and ultradian rhythms, which emerge from an intricate interplay between multiple neuronal populations in the brainstem, forebrain and hypothalamus and the resulting varying levels of neuromodulators. Recently, there has been progress in the understanding of those rhythms both from a physiological as well as theoretical perspective. However, how these neuromodulators affect the generation of the different EEG patterns and their temporal dynamics is poorly understood. Here, we build upon previous work on a neural mass model of the sleeping cortex and investigate the effect of those neuromodulators on the dynamics of the cortex and the corresponding transition between wakefulness and the different sleep stages. We show that our simplified model is sufficient to generate the essential features of human EEG over a full day. This approach builds a bridge between sleep regulatory networks and EEG generating neural mass models and provides a valuable tool for model validation.

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