Frequency Analysis of EEG Microstate Sequences in Wakefulness and NREM Sleep.

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.

Complexity Measures for EEG Microstate Sequences: Concepts and Algorithms.

EEG microstate sequence analysis quantifies properties of ongoing brain electrical activity which is known to exhibit complex dynamics across many time scales. In this report we review recent developments in quantifying microstate sequence complexity, we classify these approaches with regard to different complexity concepts, and we evaluate excess entropy as a yet unexplored quantity in microstate research. We determined the quantities entropy rate, excess entropy, Lempel-Ziv complexity (LZC), and Hurst exponents on Potts model data, a discrete statistical mechanics model with a temperature-controlled phase transition. We then applied the same techniques to EEG microstate sequences from wakefulness and non-REM sleep stages and used first-order Markov surrogate data to determine which time scales contributed to the different complexity measures. We demonstrate that entropy rate and LZC measure the Kolmogorov complexity (randomness) of microstate sequences, whereas excess entropy and Hurst exponents describe statistical complexity which attains its maximum at intermediate levels of randomness. We confirmed the equivalence of entropy rate and LZC when the LZ-76 algorithm is used, a result previously reported for neural spike train analysis (Amigó et al., Neural Comput 16:717-736, https://doi.org/10.1162/089976604322860677 , 2004). Surrogate data analyses prove that entropy-based quantities and LZC focus on short-range temporal correlations, whereas Hurst exponents include short and long time scales. Sleep data analysis reveals that deeper sleep stages are accompanied by a decrease in Kolmogorov complexity and an increase in statistical complexity. Microstate jump sequences, where duplicate states have been removed, show higher randomness, lower statistical complexity, and no long-range correlations. Regarding the practical use of these methods, we suggest that LZC can be used as an efficient entropy rate estimator that avoids the estimation of joint entropies, whereas entropy rate estimation via joint entropies has the advantage of providing excess entropy as the second parameter of the same linear fit. We conclude that metrics of statistical complexity are a useful addition to microstate analysis and address a complexity concept that is not yet covered by existing microstate algorithms while being actively explored in other areas of brain research.