Elsevier

Clinical Neurophysiology

Volume 118, Issue 2, February 2007, Pages 449-456
Clinical Neurophysiology

Small-world network organization of functional connectivity of EEG slow-wave activity during sleep

https://doi.org/10.1016/j.clinph.2006.10.021Get rights and content

Abstract

Objective

To analyze the functional connectivity patterns of the EEG slow-wave activity during the different sleep stages and Cyclic Alternating Pattern (CAP) conditions, using concepts derived from Graph Theory.

Methods

We evaluated spatial patterns of EEG slow-wave synchronization between all possible pairs of electrodes (19) placed over the scalp of 10 sleeping healthy young normal subjects using two graph theoretical measures: the clustering coefficient (Cp) and the characteristic path length (Lp). The measures were obtained during the different sleep stages and CAP conditions from the real EEG connectivity networks and randomized control (surrogate) networks (Cp-s and Lp-s).

Results

Cp and Cp/Cp-s increased significantly from wakefulness to sleep while Lp and Lp/Lp-s did not show changes. Cp/Cp-s was higher for A1 phases, compared to B phases of CAP.

Conclusions

The network organization of the EEG slow-wave synchronization during sleep shows features characteristic of small-world networks (high Cp combined with low Lp); this type of organization is slightly but significantly more evident during the CAP A1 subtypes.

Significance

Our results show feasibility of using graph theoretical measures to characterize the complexity of brain networks during sleep and might indicate sleep, and the A1 phases of CAP in particular, as a period during which slow-wave synchronization shows optimal network organization for information processing.

Introduction

The EEG slow-wave activity during sleep has been regarded for long time as one of the most important indices of the complex sleep regulation and modulation mechanisms (Borbely and Achermann, 1999); more recently, we have analyzed the neurophysiological features of this EEG band during sleep, not only in relationship to sleep stages, which only describe sleep macrostructure because of their time resolution of 30 s (Rechtschaffen and Kales, 1968), but also considering a smaller time scale (Ferri et al., 2002, Ferri et al., 2005a, Ferri et al., 2005e, Ferri et al., 2006), coded as Cyclic Alternating Pattern (CAP) (Terzano et al., 1985, Terzano et al., 1988).

According to Terzano et al. (2001) CAP is a periodic EEG activity of NREM sleep characterized by repeated spontaneous sequences of transient events (phase A) which clearly breaks away from the background rhythm of the ongoing sleep stage, with an abrupt frequency/amplitude variation, recurring at intervals up to 1 min long. The return to background activity identifies the interval that separates the repetitive elements (phase B). CAP sequences are defined as three or more A phases separated from each other by no more than 60 s. The percentage of NREM occupied by CAP sequences defines the CAP rate. All the remaining NREM sleep, not occupied by CAP sequences, is called NCAP.

CAP-A phases have been subdivided into three subtypes (Terzano et al., 2001) based on their frequency content. The most common subtype of CAP is the A1, which accounts for up to 90% of all CAP-A phases during normal sleep, occurring approximately 200–400 times per night (Bruni et al., 2002, Bruni et al., 2005, Parrino et al., 1998). CAP A1 subtype power spectrum is characterized by a predominant peak in the frequency range of 0.25–2.5 Hz (De Carli et al., 2004, Ferri et al., 2005b); these frequencies, during CAP events, are likely to be generated at the level of the frontal areas of the brain, as we have shown (Ferri et al., 2005b) by means of the low-resolution brain electromagnetic tomography method (Pascual-Marqui et al., 1994, Pascual-Marqui et al., 1999).

EEG aspects of CAP (Terzano et al., 1985, Terzano et al., 1988, Terzano et al., 2002) and its clinical correlations (Ferri et al., 2005d; Parrino et al., 1996, Parrino et al., 1997; Terzano et al., 1996, Terzano et al., 2003) have been extensively studied; however, its underlying neurophysiological aspects are a focus for research.

Interestingly, sleep EEG shows nonlinear structure only for brief periods during NREM sleep (Shen et al., 2003) which are strictly correlated with the occurrence of delta waves (Terry et al., 2004) of CAP subtypes A1, in particular (Ferri et al., 2002); we have suggested that, probably, nonlinearity in the EEG corresponds to a particular brain state during which synchronizing mechanisms are able to lower brain complexity (Ferri et al., 2002).

Functional relationships between EEG signals recorded from different scalp areas during sleep have been explored mostly by means of coherence analysis with unclear results (Achermann and Borbely, 1998a, Achermann and Borbely, 1998b, Corsi-Cabrera et al., 2003, Duckrow and Zaveri, 2005). Recently, we have analyzed EEG slow-wave spatial synchronization during sleep by means of the synchronization likelihood algorithm (Stam and van Dijk, 2002) in order to test the hypothesis that the occurrence of CAP subtypes A1 during sleep induces high levels of synchronization in the slow-wave sleep EEG activity (Ferri et al., 2005e). The results indicate a different role for each sleep stage and CAP condition in the EEG slow-wave synchronization processes of sleep which show a complex time structure correlated with its neurophysiological mechanisms. Finally, similar to the EEG power spectrum (Ferri et al., 2005b), also slow-wave synchronization shows regional differences involving mostly the anterior parts of the brain and seems to be probably based on interhemispheric interactions, possibly mediated by transcallosal connections (Ferri et al., 2006).

Based on the fact that slow-wave synchronization processes are probably characterized by a complex spatial connectivity pattern, the objective of the present study was to analyze the functional connectivity patterns of the EEG slow-wave activity during the different sleep stages and CAP conditions by means of the tools of the graph theory which are able to characterize complex networks (Amaral and Ottino, 2004, Sporns et al., 2004, Strogatz, 2001).

A graph is a basic representation of a network, which is essentially reduced to nodes (vertices) and connections (edges); in our case each recording electrode can be seen as a node. Graphs are characterized by a cluster coefficient (Cp) and a characteristic path length (Lp), among other measures. Cp is a measure of the local interconnectedness of the graph, whereas Lp is an indicator of its overall connectedness. Watts and Strogatz, 1998 have shown that graphs with many local connections and a few random long distance connections are characterized by a high cluster coefficient (like ordered networks) and a short path length (like random networks); such near-optimal networks, which are intermediate between ordered and random networks, are designated as “small-world” networks. Since then, many types of real networks have been shown to have small-world features (Amaral and Ottino, 2004, Strogatz, 2001). Patterns of anatomical connectivity in neuronal networks are particularly characterized by high clustering and a small path length (Watts and Strogatz, 1998); moreover, these tools have been successfully applied to the analysis of awake multichannel EEG and EMG recordings in different studies in normal and pathological conditions (Bartolomei et al., 2006; Micheloyannis et al., 2006a, Micheloyannis et al., 2006b; Stam, 2004, Stam et al., 2006).

Section snippets

Subjects and polysomnographic recording

Ten healthy subjects (7 females and 3 males, aged 25–35 years) were included in this study. They all had regular life routine, did not smoke and did not take any alcohol drink in the three days preceding the study.

All subjects underwent one overnight polysomnographic recording, after one adaptation night, which comprised EOG (2 channels), EEG (19 channels, Ag/AgCl electrodes placed according to the 10–20 International System referred to linked earlobes: Fp2, F4, C4, P4, O2, F8, T4, T6, Fz, Cz,

Analysis of wakefulness and the different sleep stages

The top panel of Fig. 2 shows the comparison between the graph characteristics Cp and Lp obtained in wakefulness and during the different sleep stages. Cp shows a significant increase from wakefulness to sleep; all the 3 sleep stages considered show values significantly higher than wakefulness, including REM sleep while no significant differences were found between sleep stages at the Wilcoxon test for paired data sets. Lp does not change in the different stages considered. The bottom panel of

Discussion

Before interpreting the results of this study, it is important to point out some graph theory basics. Regular coupled networks are coupled networks and have, intuitively, the longest Lp and the largest Cp; at the opposite end of the spectrum from a completely regular network is a network with a completely random graph, which has very small Lp and does not show clustering in general. Watts and Strogatz, 1998 have shown that graphs with many local connections and a few random long distance

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