Frequency Analysis of EEG Microstate Sequences in Wakefulness and NREM Sleep

Abstract

The majority of EEG microstate analyses concern wakefulness, and the existing sleep studies have focused on changes in spatial microstate properties and on microstate transitions between adjacent time points, the shortest available time scale. We present a more extensive time series analysis of unsmoothed EEG microstate sequences in wakefulness and non-REM sleep stages across many time scales. Very short time scales are assessed with Markov tests, intermediate time scales by the entropy rate and long time scales by a spectral analysis which identifies characteristic microstate frequencies. During the descent from wakefulness to sleep stage N3, we find that the increasing mean microstate duration is a gradual phenomenon explained by a continuous slowing of microstate dynamics as described by the relaxation time of the transition probability matrix. The finite entropy rate, which considers longer microstate histories, shows that microstate sequences become more predictable (less random) with decreasing vigilance level. Accordingly, the Markov property is absent in wakefulness but in sleep stage N3, 10/19 subjects have microstate sequences compatible with a second-order Markov process. A spectral microstate analysis is performed by comparing the time-lagged mutual information coefficients of microstate sequences with the autocorrelation function of the underlying EEG. We find periodic microstate behavior in all vigilance states, linked to alpha frequencies in wakefulness, theta activity in N1, sleep spindle frequencies in N2, and in the delta frequency band in N3. In summary, we show that EEG microstates are a dynamic phenomenon with oscillatory properties that slow down in sleep and are coupled to specific EEG frequencies across several sleep stages.

Keywords: EEG microstates; Electroencephalography (EEG); Entropy; Information theory; NREM sleep; Oscillations.

Fig. 1

EEG microstates in wakefulness (W) and NREM sleep stages N1–N3. The four vigilance states are illustrated by exemplary EEG traces (3 s) from three exemplary channels (F4, Cz, O1; black). Wakefulness is characterized by occipital alpha oscillations (8–12 Hz). Sleep stage N1 has low-amplitude mixed frequency (LAMF) activity, N2 shows a sleep spindle (first second at Cz) followed by a K-complex and N3 is characterized by generalized delta waves (0.5–3 Hz). Global field power (red line) and GFP peaks (red dots) are shown below the EEG traces. The microstate group maps A–D of each vigilance state are shown below the GFP time series (note that their polarity can be ignored)

Fig. 2

Slowing of microstate sequences with decreasing vigilance. From wake (W) to N3, the mean microstate duration (abscissa) increases, while the entropy rate (left ordinate, circles) and the spectral gap of the transition matrix (inverse of the relaxation time, right ordinate, crosses) decrease. The abscissa (MMD) uses a semi-logarithmic scaling

Fig. 3

PSD, ACF and AIF of microstate sequences in wakefulness. Left: average power spectral density (n = 32) in semi-logarithmic coordinates. Right: average EEG autocorrelation function (black) and microstate autoinformation function (red). Markov surrogate data are shown as the 95% confidence interval (blue-shaded area) and mean surrogate AIF (blue line). The PSD is characterized by an alpha frequency peak at 9.5 Hz, which corresponds to the first local minimum of the ACF at 52 ms (9.6 Hz). AIF peaks at multiples of 52 ms coincide with negative and positive ACF local extrema. The AIF peak test was significant for the first two AIF peaks (marked by asterisks); the first five AIF peaks are significant with respect to the Markov confidence interval while the surrogate AIF does not show any peaks. PSD, ACF and AIF are shown along with their confidence intervals (5–95%)

Fig. 4

PSD, ACF and AIF of microstate sequences in sleep stage N1. a Left: average power spectral density (n = 32) in semi-logarithmic coordinates. Right: average EEG autocorrelation function (black) and microstate autoinformation function (red). Markov surrogate data are shown as the 95% confidence interval (blue shaded area) and mean surrogate AIF (blue line). PSD, ACF and AIF do not show clear peaks, indicating the absence of a dominant frequency. PSD, ACF and AIF are shown along with their confidence intervals (5–95%). b Results for a single subject with a prominent theta rhythm during N1. The PSD has a 6.3 Hz peak, corresponding to a first local ACF minimum at 76 ms (6.6 Hz). AIF peaks at multiples of 76 ms coincide with negative and positive ACF local extrema. The AIF peak test was significant for the first two AIF peaks (marked by asterisks); they are as well significant with respect to the 95% Markov confidence interval (blue shaded area). AIF peaks do not appear in Markov surrogate data (blue line)

Fig. 5

PSD, ACF and AIF of microstate sequences in sleep stage N2. a Left: average power spectral density (n = 32) in semi-logarithmic coordinates. Right: average EEG autocorrelation function (black) and microstate autoinformation function (red). Markov surrogate data are shown as the 95% confidence interval (blue shaded area) and mean surrogate AIF (blue line). The PSD shows a small peak at 12.2 Hz whereas ACF and AIF show no clear oscillations. The ACF has a ‘shoulder’ (marked by arrow) outside of the Markov confidence interval. The surrogate AIF does not show any peaks. b Left: the average PSD for isolated sleep spindles (n = 32). Right: average EEG autocorrelation function (black) and microstate autoinformation function (red) for isolated sleep spindles. Markov surrogate data are shown as the 95% confidence interval (blue shaded area) and mean surrogate AIF (blue line). There is a PSD peak at 12.5 Hz, corresponding to the first local ACF minimum at 40 ms (12.5 Hz). AIF peaks at multiples of 40 ms coincide with negative and positive ACF local extrema. Microstate AIF peaks do not exceed the 95% Markov confidence interval but cannot be reproduced by Markov surrogate data (blue line); the AIF peak test was significant for first two AIF peaks (marked by asterisks). PSD, ACF and AIF in (a) and (b) are shown along with their confidence intervals (5–95%)

Fig. 6

shows the frequency analysis for sleep stage N3. The EEG spectrum in N3 was dominated by delta activity (0.5-3 Hz) which accounted for the majority of total data variance (84% of the PSD area). The first ACF local maximum was located outside the analysed area (> 1000 ms), the first ACF local minimum was at 440 ms (black curve), close to the first AIF peak at 464 ms (red curve). The AIF peak at 464 ms clearly exceeded the Markov confidence interval (blue area), indicating a large amount of shared information at 1.1. Hz, compared to surrogate Markov data. The AIF peak test confirmed the statistical significance of the peak (p < 0.001), relative to Markov surrogate AIF (blue curve)