Frequency-dependent functional connectivity within resting-state networks: an atlas-based MEG beamformer solution

Abstract

The brain consists of functional units with more-or-less specific information processing capabilities, yet cognitive functions require the co-ordinated activity of these spatially separated units. Magnetoencephalography (MEG) has the temporal resolution to capture these frequency-dependent interactions, although, due to volume conduction and field spread, spurious estimates may be obtained when functional connectivity is estimated on the basis of the extra-cranial recordings directly. Connectivity estimates on the basis of reconstructed sources may similarly be affected by biases introduced by the source reconstruction approach. Here we propose an analysis framework to reliably determine functional connectivity that is based around two main ideas: (i) functional connectivity is computed for a set of atlas-based ROIs in anatomical space that covers almost the entire brain, aiding the interpretation of MEG functional connectivity/network studies, as well as the comparison with other modalities; (ii) volume conduction and similar bias effects are removed by using a functional connectivity estimator that is insensitive to these effects, namely the Phase Lag Index (PLI). Our analysis approach was applied to eyes-closed resting-state MEG data for thirteen healthy participants. We first demonstrate that functional connectivity estimates based on phase coherence, even at the source-level, are biased due to the effects of volume conduction and field spread. In contrast, functional connectivity estimates based on PLI are not affected by these biases. We then looked at mean PLI, or weighted degree, over areas and subjects and found significant mean connectivity in three (alpha, beta, gamma) of the five (including theta and delta) classical frequency bands tested. These frequency-band dependent patterns of resting-state functional connectivity were distinctive; with the alpha and beta band connectivity confined to posterior and sensorimotor areas respectively, and with a generally more dispersed pattern for the gamma band. Generally, these patterns corresponded closely to patterns of relative source power, suggesting that the most active brain regions are also the ones that are most-densely connected. Our results reveal for the first time, using an analysis framework that enables the reliable characterisation of resting-state dynamics in the human brain, how resting-state networks of functionally connected regions vary in a frequency-dependent manner across the cortex.

Fig. 1

Flow chart of analysis steps. The anatomical MRI is co-registered with the MEG and subsequently spatially normalised to a template MRI. Voxels in the template MRI are labelled using the Talairach Daemon Database. Voxels with the same label are defined as a ROI and transformed to the individual's co-registered MRI. The volume conductor model, based on the co-registered MRI, together with the data covariance created from selected time-frequency windows in the MEG data, is used to compute beamformer weights for the target locations in these ROIs. The MEG data are then projected through the beamformer weights in order to create time-series (virtual electrodes) for these voxels. For each frequency band separately, a single time-series is constructed for each ROI (see Methods) and the functional connectivity between the different ROIs is estimated by computing the Phase Lag Index (PLI) or Phase Coherence. Graph theory can subsequently be applied to the resulting adjacency matrix in order to characterise the functional network formed by the interacting ROIs (see Supplementary material). Flow chart of analysis steps. The anatomical MRI is co-registered with the MEG and subsequently spatially normalised to a template MRI. Voxels in the template MRI are labelled using the Talairach Daemon Database. Voxels with the same label are defined as a ROI and transformed to the individual's co-registered MRI. The volume conductor model, based on the co-registered MRI, together with the data covariance created from selected time-frequency windows in the MEG data, is used to compute beamformer weights for the target locations in these ROIs. The MEG data are then projected through the beamformer weights in order to create time-series (virtual electrodes) for these voxels. For each frequency band separately, a single time-series is constructed for each ROI (see Methods) and the functional connectivity between the different ROIs is estimated by computing the Phase Lag Index (PLI) or Phase Coherence. Graph theory can subsequently be applied to the resulting adjacency matrix in order to characterise the functional network formed by the interacting ROIs (see Supplementary material).

Fig. 2

Mean PLI (upper panel) and mean Phase Coherence (lower panel) for the alpha band, displayed as a colour-coded map (unthresholded) on a schematic of the parcellated template brain.

Fig. 3

Functional connectivity and relationship with the beamformer weights for the alpha band. a) Mean PLI adjacency matrix. The separation between anatomical groupings (from left to right: occipital, parietal/central, temporal, frontal) is denoted by a solid line, the separation between left and right hemisphere within each anatomical grouping is denoted by a dotted line (see Appendix A for details); b) mean Phase Coherence adjacency matrix; c) mean (squared) correlation between beamformer weights for each ROI (with the diagonal set to zero). Each element in this matrix was computed as follows: for each subject, the square of the correlation between the beamformer weights for a ROI and another ROI was computed. The mean over subjects of this value was then computed; d) Scatter plot of the (squared) correlation between beamformer weights and the PLI and (e) Phase Coherence.

Fig. 4

Mean PLI (left column, thresholded at p = 0.05) and mean relative power (right column) for alpha, beta and gamma bands (top to bottom), displayed as a colour-coded map on a schematic of the parcellated template brain (see Supplementary Fig. 4 for unthresholded results). See Appendix B for a list of the areas with significant mean PLI. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) Mean PLI (left column, thresholded at p = 0.05) and mean relative power (right column) for alpha, beta and gamma bands (top to bottom), displayed as a colour-coded map on a schematic of the parcellated template brain (see Supplementary Fig. 4 for unthresholded results). See Appendix B for a list of the areas with significant mean PLI.

Fig. 5

Mean PLI versus mean relative power for the different frequency bands. Note that there is a significant positive linear relationship between PLI and relative power, for all frequency bands, except the gamma band. Also note that, for each frequency band separately, the mean PLI varies over only a limited range, and that the variance in PLI that can be explained by source power is relatively small (R² = 51%, 12%, 75%, 72% and 2% for the delta, theta, alpha, beta and gamma bands respectively).