4.2. Microstate topographies in wakefulness and sleep
Using the well-studied modified k-means clustering algorithm (Pasqual-Marqui et al. 1995), we found microstate topographies similar to those described in most wakeful rest studies (Koenig et al. 2002; Michel and Koenig 2018). The maps presented here are based on the same data set analyzed in Brodbeck et al. (2012) but using a different preprocessing strategy. Instead of 1–40 Hz band-pass filtering (Brodbeck et al. 2012), we chose a frequency range of 0.5–20 Hz. The aim was to include broader delta frequency band content which may contain relevant information in deeper sleep stages (N3), and to exclude higher frequencies possibly contaminated by noise. The upper frequency band limit of 20 Hz is a common choice in resting state microstate studies (Koenig et al. 2002; Lehmann et al. 2005; Pasqual-Marqui et al. 2014; Diaz et al. 2016).
We chose the group maps in agreement with the canonical maps defined in the literature (Michel and Koenig 2018), even though individual trials of the permutation algorithm sometimes gave non-canonical microstate maps, for instance maps with a fronto-occipital symmetry axis. Compared to the canonical maps, their GEV values differed by less than 0.5%, only. Though label-dependent quantities such as MMD and GEV per map are dependent on the choice of the group maps, the label-independent values (Trelax, entropy rate, and the autoinformation function) should not be affected, as suggested by our previous work (von Wegner et al. 2018).
We reproduced the finding that microstate map D has a more circular pattern in sleep compared to wakefulness, a feature discussed in detail in Brodbeck et al. (2012). Brodbeck et al. (2012) reported that their N2 group maps had the lowest correlation with the wake maps, an effect mainly driven by the more circular pattern of map D. We could reproduce this finding under the current preprocessing strategy and made the additional observation that map D was not only different in N2 (correlation coefficient to W: 53.8%) but also in N1 (62.2%). There is evidence that even subtle alterations in map geometries indicate significantly different dynamic functional connectivity patterns (Abreu et al. 2021). Thus, the topography of microstate class D appears to be the best indicator of light sleep, and the actual network underlying this topography is likely to be different from the network corresponding to class D in wakefulness. Thus, the comparison of microstate class D statistics between conditions which may also reflect different vigilance levels should be interpreted accordingly, they may not correspond to the same functional network.
In contrast to Brodbeck et al. (2012), we did not reproduce the finding that map B was the most prominent in terms of GEV in sleep stage N2, and that map C predominated in all other vigilance states. In our analysis, map C had the largest GEV values in all vigilance states including N2 (W: 18.2%; N1: 20.9%; N2: 26.7%; N3: 26.5%). Similar observations were recently reported for microstate distributions in slow-wave sleep (Xu et al. 2020) and in a sleep study using five microstate maps (Bréchet et al. 2020).
The details of our data processing pipeline may have contributed to the differences described as the band-pass filter was different from the one used in Brodbeck et al. (2012), which affects the smoothness of the obtained surface topographies, and thus influences the goodness-of-fit between data vectors and microstate maps as well as the final microstate statistics.
Overall, our results confirm that microstate topographies are a robust feature of spontaneous brain activity in wake and NREM sleep. On the negative side, individual map statistics can be affected by preprocessing and the role of individual maps is still unclear. Moreover, the same map label (e.g. class D) may represent different network configurations when compared between vigilance states. Our previous observation that entropy-based microstate statistics are more robust against changes in preprocessing (von Wegner et al. 2018), and the hypothesis that dynamic microstate properties may be better suited to track vigilance changes led us to focus on temporal correlations of microstate sequences.
4.3. Slowing of microstate dynamics and loss of complexity
Sleep-related EEG changes are diverse, a common feature being an increase in the proportion of lower frequencies, although individual higher frequency events such as sleep spindles also occur. We observed EEG slowing for deeper sleep stages in the GFP time course, i.e. in the frequency of GFP peaks (local maxima) per second. Compared to the previous study by Brodbeck et al. (2012) (W: 31.2; N1: 31.8; N2: 27.6; N3: 13.4/s), our PPS values were lower (W: 18.5; N1: 16.6; N2: 15.4; N3: 11.5/s), due to the lower high-frequency cut-off of the band-pass filter in our study (20 Hz vs. 40 Hz).
To correctly interpret the mean microstate durations with respect to the literature, we must emphasize the fundamental difference between our algorithm and many other microstate studies. We fit the best matching microstate at each EEG sampling time point (von Wegner and Laufs 2018; von Wegner et al. 2021), whereas many other researchers calculate this fit at GFP peaks only, and interpolate the labels between GFP peaks (e.g. Lehmann et al. 1987, 1998; Koenig et al. 2002; Brodbeck et al. 2012). The latter approach has a smoothing effect, as switches between microstate labels are only allowed to happen in the GFP valleys between the peaks, imposing a lower limit on microstate durations, and an upper limit on the observed microstate frequencies. For example, a PPS value of 20/s implies that the interpolation method renders microstate durations below 50 ms very unlikely, by construction. Our method uses minimal assumptions and therefore allows us to observe the full bandwidth of temporal dynamics. Recent studies by us and others could show that the dynamics between GFP peaks contain relevant information about the actual continuous dynamics of the cortical electric field (Mishra et al. 2020; von Wegner et al. 2021).
A consequence of our approach is that the mean microstate durations are significantly shorter than those reported in many classical microstate papers. For all vigilance states, the MMD values in the present study were shorter than those found in Brodbeck et al. (2012), where the interpolation method was used: 17.9 vs. 44.8 (W), 24.3 vs. 44.9 ms (N1), 26.2 vs. 57.9 ms (N2), and 49.3 vs. 81.4 ms (N3). Between sleep stages, we found a higher MMD in N1 compared to W, while Brodbeck et al. (2012) found almost no difference. The MMD difference between N1 and N2 was not significant in our study. Both studies agree that the largest MMD increase exists between W and sleep stage N3, with a MMD in N3 between two times (Brodbeck et al. 2012) and three times (+ 175% in our study) higher than in wakefulness.
Our additional metrics, however, demonstrate that the transition from W to N3 is accompanied by a smooth, continuous slowing of microstate dynamics. The relaxation time of the transition probability matrix, a time constant that describes how fast a stochastic process returns to equilibrium after a perturbation, captures the continuous aspects of microstate dynamics. Its inverse, the spectral gap is shown in Fig. 2 and shows a monotone decay across the vigilance states. The limitation of the relaxation time approach is its temporal scope, which it inherits from the transition matrix, i.e. it only considers single time step dynamics (t → t + 1).
We therefore included further time steps in our analysis using the (finite) entropy rate with a time window of 24 ms. The (finite) entropy rate behaved in exactly the same way as the relaxation time, as illustrated in Fig. 2. With deepening sleep stage, the entropy rate decreased continuously, and clearly correlated with the microstate duration. The entropy rate of a microstate sequence measures the amount of surprise about the next microstate, given knowledge about its history (conditional entropy). The decreasing entropy rate during sleep means that more information about the next brain state is contained in the immediate past brain activity, rendering network transitions more predictable, and less complex. The complexity of the microstate process however can be defined in different ways and cannot be interpreted without taking into account the underlying frequency at which these processes run. When oscillatory brain activity with a given complexity slows down by a given factor, its entropy rate will decrease accordingly, yielding a more predictable process. However, the process would still be able to encode the same amount of information per oscillation cycle, it would just be stored over a longer time window. Therefore, the notion of complexity has to be used carefully, and in a well-defined context. A different definition of complexity, correcting for the underlying “carrier frequency” was recently used in Tait et al. (2020).
To what extent microstate dynamics deviate from a simple Markov model, as captured by the transition matrix/relaxation time approach, was assessed by formal Markovianity tests. Earlier analyses of wakefulness EEG demonstrated that microstate sequences show very strong deviations from Markovianity (von Wegner et al. 2017). Similar observations were obtained here for W, N1, and N2, where the Markov property was rejected in all data sets. We did not expect to find that n = 10/19 N3 recordings gave test results compatible with a second-order Markov process, as compared to a third-order process. In other words, 10 out of 19 microstate sequences had t → t + 1 transition probabilities that were fully predicted by the microstates at time points t and t-1, whereas addition of the microstate label at t-2 had no further predictive effect.
This observation, together with the lower microstate entropy rate, speak for a more restricted, and therefore more predictable trajectory of the underlying neuronal ensembles in deeper sleep stages. During complex cognitive tasks, the largest microstate entropy rates have been observed in subtasks with the highest cognitive workload and the lowest degree of cognitive control (Jia et al. 2021). The current results extend these observations while pointing in the same direction, as they suggest a further decrease in cognitive workload with deepening sleep. Our results also suggest that other than cognitive control mechanisms can restrict the degrees of freedom with which microstates are generated. We hypothesize that sleep-specific network mechanisms, including subcortical and brainstem activity, might restrict microstate dynamics in sleep, as opposed to cortical cognitive control mechanisms during cognitive task execution. It can be hypothesized that a partial isolation from external sensory stimuli as well as the synchronized slow wave activity organize and restrict cortical activity and thus, microstate dynamics.
4.4. Periodicities
Finally, the hallmark of EEG recordings are oscillations in different frequency bands, and the frequency composition of ongoing EEG in wakefulness and sleep shows marked differences (Rechtschaffen and Kales 1968; American Academy of Sleep Medicine 2007). The relationship between microstates and EEG frequencies is still unclear and has been addressed in several studies. Britz et al. (2010) reported a lack of correlation between the power of EEG frequency bands and microstate prevalence during wakefulness. Comsa et al. (2019) detected an association of microstate D with EEG functional connectivity in the theta band during the transition from wakefulness to drowsiness. Shi et al. (2020) investigated the instantaneous EEG frequency during the lifetime of individual microstates and found that five microstate classes had very similar marginal EEG spectra during propofol sedation. Abreu et al. (2021) used topographic time-frequency decomposition, a technique which yields a time-frequency plot for each microstate map (Koenig et al. 2001), and reported characteristic EEG frequency spectra for ten different microstate maps. None of these techniques, however, tests for the periodic appearance of the microstate labels themselves. We introduced and validated a technique for microstate frequency analysis in a resting-state EEG study set (von Wegner et al. 2017), and found that alpha oscillations (10 Hz) were linked to periodic microstates with twice that frequency, i.e. a minimum recurrence interval of 50 ms. Frequency doubling was explained by microstate maps matching the EEG topography twice per alpha cycle, due to the fact that alpha oscillations invert their polarity every half-cycle (50 ms), and the polarity-ignoring property of the microstate fitting algorithm (Lehmann 1971).
4.4.1. Wakeful rest
In wakefulness, we reproduced clearly defined oscillatory microstate dynamics related to the underlying alpha frequency band as described in von Wegner et al. (2017). The mutual information (autoinformation) of microstate sequences had peaks coinciding with all local extrema of the autocorrelation function of the underlying EEG. As entropy values are non-negative, local maxima of the AIF occur at the locations of local minima and maxima of the ACF. This observation confirms that the functional networks captured by microstates activate periodically during wakefulness.
4.4.2. Sleep stage N1
Microstate frequency analysis shows that the differences between W and N1 go beyond the change in microstate D topography and general EEG slowing. Even though brain activity in N1 can effectively be described by the four microstate classes, the regular periodic activation profile is almost completely lost in a brain state that corresponds to drowsiness. This observation lifts the EEG definition of sleep stage N1 to the network level. Sleep stage N1 is assigned when less than 50% of a 30 second EEG segment shows the posterior dominant rhythm, usually in the alpha band, which is replaced by low amplitude mixed frequency activity (American Academy of Sleep Medicine 2007). Our analysis shows that the loss of the occipital alpha rhythm is accompanied by a temporal disordering (loss of periodicity) on the level of EEG microstates. It can therefore be hypothesized that loss of microstate periodicity may be a useful marker in other types of drowsiness, as caused by pharmacological agents or neurological conditions. The observation that microstate sequences can be linked to N1 theta oscillations, although observed in only one subject, is a novel finding, demonstrating that sleep-related networks can also activate periodically in the theta frequency range.
4.4.3. Sleep stage N2
Microstate properties averaged over sleep stage N2 segments showed further slowing of microstate dynamics, but no spectral peaks. Isolated sleep spindle segments, however, showed periodic microstates linked to the sleep spindle frequency of 12.5 Hz. Similar to other frequency bands, the principal AIF latency coincided with half the spindle oscillation length (40 ms, or 25 Hz), suggesting that the mechanisms leading to frequency doubling, as detailed above, are also valid for sleep spindle oscillations. Sleep spindle statistics were different from other frequency bands in that the microstate AIF peaks did not exceed the Markov confidence interval, indicating that the absolute information content contained in these oscillations was not larger than that contained in the equivalent Markov model. In line with this observation, the explicit Markov tests of these short microstate sequences showed no deviation from a Markov process. However, this effect is mainly due to the low number of samples used. We tested this by using short higher-order Markov surrogates. These higher-order properties could not be detected by the Markovianity tests in sequences as short as sleep spindles, whereas longer sequences were classified correctly (analysis not shown). These statistical effects might also have played a role in early microstate studies where 15 second microstate sequences were classified as Markovian (Wackermann et al. 1993).
The statistical significance of sleep spindle associated microstate oscillations is proven by the AIF peak test that quantifies the observation that none of the Markovian surrogates had AIF peaks. The finding of periodic microstates during sleep spindles provides an interesting link between sleep spindle-linked EEG spiral waves (Muller et al. 2016) and the rotating EEG phase patterns we identified as a basic mechanism underlying periodic microstates during wake EEG (von Wegner et al. 2021).
4.4.4. Sleep stage N3
Network activity during sleep stage N3, which is characterized by delta frequencies (0.5-3 Hz), shows the same qualitative behavior as found in the other vigilance states, i.e. periodic microstates that are closely linked to the EEG frequency spectrum, but transposed into the delta frequency band. A recent study identified the four canonical microstates in slow-wave sleep and mapped them to well-known functional networks (auditory, executive control, saliency) defined by independent component analysis from fMRI data (Xu et al. 2020). Combining these results with our study, we can predict that fMRI-defined networks should also activate periodically, with an oscillation length of approximately 1 Hz. The time scale of these oscillations is still faster than the sampling rate of most fMRI sequences, which makes experimental verification challenging. Since fMRI resolves at timescales that depend on the repetition time (TR) of the scanning as well as on the blood flow rate (Demetriou et al. 2018), we believe that microstate dynamics add relevant information about the neurobiology of sleep by revealing network behavior in the sub-second range.
An earlier analysis of the data set presented here revealed that increasing delta activity was correlated with a loss of functional connectivity within occipital areas, as well as between occipital and central areas (Tagliazucchi et al. 2013) while other studies found disintegration of mediofrontal functional networks during sleep (Horovitz et al. 2009; Bréchet et al. 2020). Since different brain areas have to activate in a phase-locked manner to produce a stable microstate topography (Koenig and Valdés-Sosa 2018), these connectivity changes might explain the altered microstate map D topography in sleep, where occipital and frontal areas appear to be dissociated from the microstate D network. The exact mechanisms underlying these connectivity changes remain to be clarified. Early cellular studies suggested a role of the thalamus in generating and synchronizing cortical delta oscillations but also pointed out that the cortex can generate these frequencies without thalamic input (Amzica and Steriade 1998). On the other hand, we know that the thalamus disengages from supratentorial networks in N3, instead joining a functional module which contains the cerebellum (Tagliazucchi et al. 2013). This functional uncoupling of the thalamus from the cortex would rather suggest less synchronized cortical networks in N3, contradicting our empirical evidence from microstate analysis. This line of arguments shows that the insights obtained from different modalities (cellular recordings, surface EEG and fMRI) are not easily integrated in a framework using simple models of regional (de-)activation and functional coupling. However, within the EEG microstate framework, our analysis demonstrates that 1 Hz oscillations are a robust and statistically significant phenomenon.