The Sleep Cycle Modelled as a Cortical Phase Transition

Abstract

Abstract. We present a mean-field model of the cortex that attempts to describe the gross changes in brain electrical activity for the cycles of natural sleep. We incorporate within the model two major sleep modulatory effects: slow changes in both synaptic efficiency and in neuron resting voltage caused by the ∼90-min cycling in acetylcholine, together with even slower changes in resting voltage caused by gradual elimination during sleep of somnogens (fatigue agents) such as adenosine. We argue that the change from slow-wave sleep (SWS) to rapid-eye-movement (REM) sleep can be understood as a firstorder phase transition from a low-firing, coherent state to a high-firing, desychronized cortical state. We show that the model predictions for changes in EEG power, spectral distribution, and correlation time at the SWS-to-REM transition are consistent not only with those observed in clinical recordings of a sleeping human subject, but also with the on-cortex EEG patterns recently reported by Destexhe et al. [J. Neurosci. 19(11), (1999) [4595][4596][4597][4598][4599][4600][4601][4602][4603][4604][4605][4606][4607][4608] for the sleeping cat.

An analysis of the transitions between down and up states of the cortical slow oscillation under urethane anaesthesia

“…These phenomena are in agreement with a first-order phase transition model, in which fluctuations are predicted to grow and slow on the approach to the transition [19,20].…”

“…In such transitions, the jump is characterized by a build-up in amplitude of small, random fluctuations about the solution. The size of these fluctuations is inversely related to the stability of the solution, as described for a mean-field cortical model by Steyn-Ross et al [19].…”

“…However, this work with a conscious brain may not relate directly to an analysis of slow-wave sleep. Figure 1 shows a stylized model of a first-order phase transition [19]. The solution to a set of equations describing the system is shown by the solid line; it is characterized by having a region of parameter space with multiple (in this case, three) solutions.…”

Model and data-driven representations of the sleep cycle using locally linear embedding

“…It accomplishes this by characterizing the local structure around each data point (based on its "nearest neighbors") and then computing a nonlinear re-mapping of the data that optimally preserves that local structure [1]. Here we apply the LLE algorithm to both human EEG data recorded during sleep and simulated EEG data from a continuous mathematical model of the sleep cycle [2]. The data starts in a 7-dimensional feature space based on power in three frequency bands and several statistical measures; we then project each one into a 2-D space and compare the resulting structures.…”

Numerical modelling of plasticity induced by transcranial magnetic stimulation

“…Table 1 gives a list of standard parameters chosen for this modelling. Values for the mean-field cortical modelling have been chosen drawing from references [38,39,37,11,45,46], with smaller rates being used for α B and β B to model the long timescale GABA B inhibitory post-synaptic potentials [32,34]. Values for the STDP have been chosen with reference to [1] and [11].…”