We are first to compare the rsEEG mMSE features between the electrode sets corresponding to the main resting-state networks. A novel result here is also an identification of the sex/gender differences in the rsEEG complexity at the fine and the coarse scales. To the best of our knowledge, this work is the second one, following Dreszer et al. [29], that quantify ed the rsEEG signal complexity using the mMSE algorithm, i.e. an extension of the multiscale SampEn (MSE) [15] to the multivariate timeseries (signals, e.g., EEG), proposed by Ahmed and Mandic (25), [3, 4]and Looney et al. [55]. Therefore, the key property of the mMSE, not present in the SampEn and MSE methods, is that it is designed for analysis of multivariate signals whereas the SampEn and MSE are applicable to univariate signals only. Moreover, just as the MSE, the algorithm, used here, examines the complexity at both fine-grained (short) and coarse-grained (long) timescales (M.U. [2,3,4, 55]. The shape of mMSE vectors in our study (Fig. 1) resembles a typical skewed inverted U-pattern [15, 16] which is believed to result from the shortest scales representing only a random signal and the longest scales reflecting a more stable system, characterized by a reduced variance [15, 62].

The highest resting-state EEG entropy at the scalp locations corresponding to the SMN and the DAN

We found the highest, relative to other networks, AUC values, representing a total entropy, in the electrode sets corresponding to the SMN and the DAN (Fig. 1, Table 2). A similar location of the largest complexity (a central area) has been identified by other authors [32, 73, 95], however, the SMN also demonstrated relatively low entropy levels [47, 65, 67]. These inconsistent results may arise from different methodology, i.e. various brain signals (EEG,MEG or fMRI), resting-state conditions (eyes open or eyes closed) and algorithms used for data computation (e.g., Lempel–Ziv Complexity, ApEn, SampEn).

Spontaneous SMN fluctuations reflect activation of the motor system in the absence of any movement [9] whereas the DAN is involved in the top–down attention control and the expectation of objects at a particular location or with certain features [14]. The topography and strength of resting-state networks are associated with the history of network activation [22]. Therefore, the highest degrees of entropy in the SMN and DAN may reflect their increased functional connectivity with other regions or a large repertoire of possible responses to stimuli resulting from a great experience in coding features/spatial locations of the objects and motor response to these stimuli. Since the SMN and the DAN are the “task-positive” networks, their complexity levels might be more influenced by online processing and the changes in cognitive demands than the intrinsic networks such as the DMN. When there are no external tasks or stimuli, the SMN and DAN are just prepared to respond to them and in this condition there is probably no need to communicate extensively with other regions. In this context, we would be rather inclined to accept the theory postulating that greater degrees of neural complexity represent less information exchanged across brain areas [37]. Otherwise, the brain signal entropy may not directly reflect the “activity” or amount of information processing which has been already suggested by other authors (e.g., [67].

In the current study the SMN and the DAN demonstrated the greatest AvgEnt values corresponding to the complexity at the coarse scales (Fig. 1, Table 2) which might represent a greater capacity of these networks to process information globally, across distributed brain regions [17, 64, 94]. The long-range connections in the brain play an important role in perception [86] and information integration [48] which makes them crucial for the main functions of the SMN and the DAN. Congruently with [69] who found the highest positive correlations between the complexity at the coarse timescales and functional connectivity of the fMRI resting-state signal for the SMN and VN, the entropy at the scalp location corresponding to the SMN in our study might represent long-range interactions with other areas. The rsEEG signal from the electrode sets corresponding to the SMN also demonstrated the greatest complexity at the fine scales (Fig. 1, Table 2) suggesting the strongest, compared to other networks, short-distant functional couplings, and local synchronization across connected regions [64, 94].

Inconsistently with the previous results [59, 67, 69], the DMN in our study did not demonstrate the largest rsEEG complexity but, still, the AUC, MaxSlope and AvgEnt values for this network were among the highest, same as for the VAN (Fig. 1, Table 2). A relatively high entropy level in the DMN and the VAN across the timescales might be interpreted as representing greater information processing by both local and distributed neural assemblies. The DMN is considered a critical gateway for transferring information within local and across distributed networks [8, 12] which may be reflected in high degrees of entropy at the fine and the coarse scales. However, in light of the evidence showing that the DMN complexity is one of the least associated with the functional couplings [69], the interpretation of entropy in the context of functional connectivity becomes less obvious than in the case of other networks. The DMN is “active” at rest [11, 75] when its “information processing” relies on the spontaneous generation of images, voices, thoughts, and feelings that are stimulus-independent and resulted from mind wandering [58] and/or monitoring the external environment [83]. Therefore, it is even more natural to interpret a high complexity of this network in terms of extensive transitions between states and the brain’s tendency to wander [43, 63].

The lowest resting-state EEG entropy at the scalp locations corresponding to the LN, VN and the FPN

The lowest total rsEEG entropies were observed for the channel sets linked to the LN, VN and the FPN (Fig. 1, Table 2). Similar results have been obtained by other authors in the case of VN [47, 65, 67, 99] or the LN [65, 67], however, the results suggesting the highest degrees of complexity in these two networks, compared to others, have been also reported [47, 85]. In the current study the VN showed the smallest total entropy and the complexity at both fine and coarse scales. Similarly to the VN, the LN demonstrated one of the lowest AUC and AvgEnt values. These outcomes might reflect less transitions between states [31] and/or reduced (short- and long-distant) functional connections of these networks with other regions [64]. Since the VN is mainly activated by visual stimuli, it was probably not very involved at rest when the participants are asked to keep their eyes fixated on one point in space and avoid any ocular movements. Similarly, the resting protocol favors a state of relaxation and calmness where the LN might be not particularly engaged. In this context the brain entropy would directly reflect its activity.

In contrast to other authors [59, 65, 67, 69], we demonstrated that the FPN was characterized by one of the lowest entropies (Fig. 1, Table 2). The FPN is considered as an intrinsic network, recruited by executive control tasks [28], and its complexity, similarly to the DMN, is rather expected to be among the highest at rest. A relatively low FPN entropy level, found here, may be explained referring to the method of obtaining the mMSE vectors. In this context a small complexity in the FPN might represent a lack of meaningful spontaneous interactions between the frontal and parietal regions forming this network. Indeed, in our previous study [29] where the mMSE method was applied to quantify rsEEG complexity, the parietal region was characterized by the greatest entropy whereas the frontal areas demonstrated one of the lowest entropies. Thus, we might assume that the frontal and the parietal regions, analyzed together as the FPN, will demonstrate different entropy levels than the same areas examined separately. To test this assumption, an additional mMSE analysis was performed on the current database but using the channel sets from our previous work [29]. We found a similar complexity pattern in case of both former and current datasets revealing the highest degrees of total complexity and the entropy at the coarse scales separately for the frontal and parietal regions (see Additional file 1: Appendix Figs. S2 and S4 ). Therefore, we might carefully conclude that the low FPN entropy in the present study results from different spatiotemporal patterns of spontaneous fluctuations in the anterior and posterior part of this network.

Resting-state EEG entropy range between the fine and the coarse timescales

In the current study the LN showed the greatest complexity range, i.e. among the highest entropy levels at the fine scales and the lowest at the coarse scales (Fig. 1 and 3, Table 2). A similar complexity pattern was reported by McDonough and Nashiro [59] for the Cingulo-Opercular Network (CON) whose core hubs (the dorsal anterior cingulate cortex and the insula) are involved in emotional processing [27]. Such a mMSE profile of the LN, possibly reflecting the synchrony of neural assemblies at the fine scales and desynchrony at the coarse scales [7], may represent a process of emotional adaptation to the resting-state condition.

The DAN and the VN demonstrated relatively stable mMSE patterns across the timescales (had the smallest DiffEnt values, Fig. 3, Table 2) suggesting comparable amount and strength of local and global information processing. After reaching a relatively high complexity level both these networks showed a slow decrease of entropy (Fig. 1) which may reflect keeping balance between neural excitation and inhibition processes.

The DAN could be also considered as a separable, stable, internally more coherent, module in the brain [42]. The complexity of the task-positive networks such as the DAN and the VN, may change more in a task than at rest [59]. Therefore, a small differences in the entropy level at the fine and the coarse scales (low DiffEnt values) in the DAN and the VN may result from a relatively stable amount of visual stimulation and recruited cognitive resources during the resting state.

Interestingly, the DMN and the VAN in our study had almost overlapping mMSE vector shapes (Fig. 1) showing among the highest MaxSlope and AvgEnt values relative to other networks (Table 2). This effect is hard to explain in terms of sharing the same channels by these networks (the DMN and the VAN had only two common positions: T7 and T8). It is of note that we analyzed the rsEEG signal from the electrode set corresponding to the VAN, extracted by Yeo et al. (2011), and this network includes both the CON and the “classic” VAN which have demonstrated strong synchronization at rest [27, 71] possibly reflected in the great degrees of rsEEG entropy.

The DMN is considered as a part of the task-negative system whereas the VAN/CON is identified as a task-positive network [52]. In this context the DMN and the VAN/CON were supposed to indicate some inverse (anti-correlated) functionality resulting from the allocation of limited resources. As a support for this claim McDonough and Nashiro [59] found the lowest complexity at the fine scales and the highest entropy at the coarse scales in the DMN whereas for the CON the inverse neural complexity profile was obtained. In our study similar mMSE patterns in the DMN and the VAN may result from the function that they both share, e.g. tonic alertness [11, 78] which is highly involved during the resting state.

In our study the SMN and the LN had similar mMSE vector shape to the DMN/VAN (Fig. 1). While the VAN and the LN signals were acquired from very similar sets of electrodes (which may, to some extent, explain the similarity of their rsEEG complexity profiles), for the DMN or the SMN this was not the case. We might speculate then that the resemblance of mMSE patterns between particular channel sets (networks) might reflect their strong interactions or interdependencies. Conversely, different entropy patterns in given networks might represent weak connections between these systems. Therefore, in the present study, similar complexity profiles, especially in the DMN and the VAN and, to a lesser extent, in the SMN and the LN, might suggest the increased communication between these networks at rest.

Higher resting-state EEG complexity at the fine timescales and lower at the coarse scales in women compared to men

Although we did not find any significant s/g differences in the AUC values, corresponding to the total rsEEG complexity, women, relative to men, showed higher MaxSlope values (the fine scales) but lower AvgEnt values (the coarse scales) (Fig. 1). Since we are not aware of any work presenting the s/g differences in the mMSE values, we decided to quantify the complexity of the current data using exactly the same method and regions of interest as in our previous work [29]. The detailed results of this re-analysis were shown in the Additional file 1: Appendix Figs. S2–4. Basically, we found a reproducible pattern of the s/g differences in the entropy level at the fine and the coarse timescales: for both datasets, women, compared to men, produced significantly higher MaxSlope values in the frontal areas and men showed greater AvgEnt values than women for all analyzed channel sets. Considering the AUC, the outcomes across both our studies were inconsistent: females demonstrated a greater total entropy level than males only for our previous dataset and we did not observe such s/g differences in the current study.

The way how the MaxSlope is calculated (the maximum change in the EEG signal complexity at the fine scales) allows to compare this parameter with the entropy, determined using other methods and measured at a single timescale. In this context, the s/g differences in the MaxSlope value are congruent with some previous findings [32, 50, 72, 98]. Higher degrees of entropy at the short scales and lower complexity at the long scales in women might reflect enhanced information processing in local neural assemblies but reduced large-scale interactions in the resting brain [64, 93]. The previous resting-state fMRI evidence suggesting a greater overall brain integration of specialized information at a global network level in males and higher segregation, i.e. specialized processing of the brain at a local level, in females supports the aforementioned interpretation of the brain complexity [5, 45,