Characterization of K-Complexes and Slow Wave Activity in a Neural Mass Model

Abstract

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.

A Thalamocortical Neural Mass Model of the EEG during NREM Sleep and Its Response to Auditory Stimulation

“…We adopt the view of [30], where KCs were characterized as transient events—reversed spikes—initiated by a canard explosion. Consequently the down state is never stable in our model.…”

Effects of Cholinergic Neuromodulation on Thalamocortical Rhythms During NREM Sleep: A Model Study

“…which is similar to the classical conductance-based form of Hodgkin and Huxley (1952) with one leak and two synaptic currents (say, ξ ∈ {AMPA, GABA}) (Weigenand et al, 2014). Moreover, for the convenience of calculating the convolution ⊗, r ξ (t) can be equivalently obtained by solving the following second-order differential equation…”

“…Suffczynski et al (2004) proposed a thalamocortical NMM to explain the relation between mechanisms that generate sleep spindles and those for that generate spike-wave activity. More recently, Weigenand et al (2014) extended a cortical NMM to explore the mechanisms for generating K-complexes and slow oscillations. Cona et al (2014) presented a new NMM to describe the sleeping thalamocortical system, where thalamic neurons exhibit two firing modes: bursting and tonic.…”

Timing matters: open‐loop stimulation does not improve overnight consolidation of word pairs in humans

“…Together with hippocampal ripples they play a key role in the sleep‐dependent consolidation of declarative memories and synaptic plasticity (Rosanova & Ulrich, ; Chauvette et al ., ; Rasch & Born, ). Underlying slow oscillations (SO) are widespread transient alternations of cortical networks between active and silent phases at around 1 Hz (Contreras & Steriade, ; Weigenand et al ., ). Spindles are thought to arise from interactions between neurons of the thalamic reticular nucleus and thalamocortical neurons of other thalamic nuclei (Destexhe & Sejnowski, ).…”