Interestingly, all three methods showed important similarities regarding the Default Network interactions’ properties. In (Hipp et al. 2012) it is assumed that signal components of the same source measured from different sensors will be characterized by an identical phase while in many cases, different neuron populations have a variable phase relation. This difference can be exploited to remove spurious correlation patterns due to the MEG limited spatial resolution. In particular, every considered pair of signals is orthogonalized before the computation of their power envelopes. This allows one to remove the spurious common correlation leaving a residual ‘cleaned’ spatial correlation. The activity orthogonalization is performed in the frequency domain on the estimated band limited activity but this can similarly be done in the time domain where it generalizes to broadband signals. Of practical importance is the selection of the time interval to derive the regression coefficient. This can range from the entire dataset to just a single time window during which the signals’ relation should be constant. If such stationarity is fulfilled, longer time intervals provide more robust estimates and may lead to a superior sensitivity of the method. However, it is important to stress that without stationarity, the orthogonalization step may be incomplete. Eventually, the interaction between orthogonalized signals is quantified by means of correlation of the power envelopes obtained by squaring the absolute values of the complex spectral estimates after a logarithmic transform (this makes the power more normally distributed). The correlation with a given seed is considered as significant when it is higher than a baseline value computed as the average correlation with the rest of the brain.

In Brookes et al. (2011a, b) an approach based on Beamforming and the computation of the Hilbert Envelope is presented. MEG data are frequency filtered in the typical physiological bands and covariance matrices are generated independently for each frequency band, using the whole recording session at the subject level. It is important to stress that this corresponds to assuming that sources of interest are stationary throughout the experiment. Following beamformer projection, source-space signals are normalized and Hilbert transformed. The absolute value of the analytic signal, called the “Hilbert envelope”, is computed to obtain an amplitude envelope of oscillatory power. Then, data from all subjects are concatenated in the time dimension and temporal Independent Component Analysis (ICA) is applied using the fastICA (http:www.​research.​ics.​tkk.​fi/​ica/​fastica) algorithm. The spatial signature of each IC is measured by Pearson correlation between the temporal IC (tIC) and the time course of each voxel in the concatenated dataset. This process is implemented independently for each frequency band of interest. In addition to the ICA-based approach, the authors also present a seed-based approach for DMN characterization to show that independent temporal signals arise from spatially orthogonal networks. Seed locations in the motor, fronto-parietal, and visual networks are extracted from fMRI data. Down-sampled Hilbert envelopes are extracted for each of these seed locations and in order to generate seed-based correlation maps, data are concatenated across subjects. The Pearson correlation between seed time course and down-sampled Hilbert envelopes for all other brain voxels is computed. In (Brookes et al. 2011b), the validity of correlation measurements are tested using a simulation approach in which two dipolar sources (at the seed and test locations) are repeatedly simulated. To obtain noise data to be added to these simulated data, one empty-room session is recorded (no subject in the scanner). The simulation step is repeated to assess the statistical significance of measured functional connectivity values. Simulated MEG data are projected into the brain using the same beamformer weights derived from and applied to the real MEG data. This interesting approach allows one to check whether the adopted beamformer projection generates spurious correlation due to the volume conduction and signal leakage.

Another interesting aspect of the work of Brookes and colleagues is the different metrics the authors propose to assess the functional connectivity: two are based on envelope correlation—termed Average Envelope Correlation (AEC) and Correlation of Averaged Envelopes (CAE); while two others are based on coherence—termed coherence (Coh) and Imaginary coherence (ICoh). In all cases, connectivity is measured between the projected signal at the seed voxel, and that from all other (test) voxels in the brain.

The approach presented in (de Pasquale et al. 2010, 2012a) is based on the BLP but is different from the previous ones; it is developed to take into account the non-stationarity of brain connections. This temporal non-stationarity represents an important aspect of the DMN internal and across-network interactions. In fact, based on the observation that the coupling among different RSN nodes oscillate over time, de Pasquale et al. propose an approach to estimate time epochs in which the internal connectivity of a network is optimized. In what follows, we describe the basic ingredients of this methodology.

The MEG data are pre-processed by applying a pipeline based on ICA described in (de Pasquale et al. 2010; Mantini et al. 2011), which extends an approach described in (Hironaga and Ioannides 2007). Basically, different from what was described above where each IC was related to a given resting state network, a subset of ICs is classified as artifactual and removed. Importantly, the authors do not assume that a network can be assigned single ICs but rather a combination of them. For this reason, once non-artifactual ICs are identified these are linearly combined to generate the ‘cleaned’ MEG signal. To this aim, source-space IC maps are reconstructed from the remaining ICs on a Cartesian 3D grid with 4 mm voxel side using a weighted minimum-norm least squares (WMNLS) procedure. For each voxel and each time sample, source-space signals are obtained by linear combination of IC time-courses, each weighted by its source-space map. Then, source-space signals are filtered in the typical physiological frequency bands. From these filtered signals, MEG power time series are obtained by averaging the square of source-space MEG signals.

In order to determine the time scale to adopt for the non-stationary analysis, the total interdependence function, a coherence-based measure of the functional connectivity, is examined from nodes of known network affiliation. The authors report initially for the Default Mode Network and the Dorsal Attention network (de Pasquale et al. 2010), an increase in the vicinity of 0.1 Hz. This result was then extended to the Ventral Attention, Motor and Language networks. Based on this observation the length of 10 seconds, the reciprocal of 0.1 Hz, is selected as the window duration to be used for the evaluation of time-varying node-pair correlation.

Eventually, to identify epochs of high within-RSN correlation or maximal correlation windows (MCWs), de Pasquale and colleagues developed the ‘extended maximal correlation window’ (EMCW) algorithm. This algorithm accepts as input power time-series spanning an entire MEG run from one seed and two other nodes of known network affiliation. The objective of this algorithm is to identify epochs in which the contrast between within-network, i.e. between the seed and other network input nodes, versus external node-to-network correlation, i.e. between the seed and an external node, is maximal. Specifically, the algorithm seeks epochs in which the least within-network correlation is above a threshold while the external node-to-network is minimal. This is accomplished using an iterative strategy based on the Old Bachelor Acceptance thresholding technique (Hu et al. 1995). The algorithm is run starting with different groups of input nodes to obtain a specific set of MCWs for each network by concatenating the MCWs for each input node group. Additional details on the selection of the threshold and criteria for epoch selection can be found in (de Pasquale et al. 2010, 2012a, b; Mantini et al. 2011).

The network connectivity maps and cross-network interaction matrices are based on the definition of a Z-score obtained from correlation maps computed in all the sessions of all the subjects in all the estimated MCW epochs. To obtain the final RSN connectivity maps, the strengths of the correlations in every voxel of the brain with the seed, compared to the mean correlation in the whole brain, is tested. Then, each connectivity map is corrected for false discovery rate—FDR (p < 0.05) and thresholded at a significant level to obtain a binary map. All the binary maps from the different seeds are combined together through a logic AND. This step insures that only regions of significant correlation across all nodes of a network are maintained.

Analogously, the cross-network interaction matrices are also based on Z-scores to is the strengths of the correlations between a pair of RSN nodes compared to the mean correlation of these nodes, with the rest of the brain. It must be stressed that, based on the above definitions, Z-scores are defined on specific temporal epochs including all the MCWs obtained for each specific RSN. This quantity represents the average interaction between one ‘fully engaged’ network and another network.

In (de Pasquale et al. 2012a) MEG-RSNs interactions are not only characterized on average throughout the recording period by computing matrices of node-to-node or RSN-to-RSN power correlation, but also by characterizing the dynamics of this interaction. This is achieved by computing the degree of temporal overlap between two networks, when each one is respectively in a state of high internal correlation (or MCW). Given two sets of RSN MCWs, we computed the MCW overlap as the average ratio of overlap of all the possible pairs of MCWs from the two networks. It must be noted that differently from the power correlation matrix, this matrix is symmetric by definition. To summarize, in Fig. 2 we report the flowcharts of the described ICA and seed-based approaches.