Brain networks, dimensionality, and global signal averaging in resting-state fMRI: Hierarchical network structure results in low-dimensional spatiotemporal dynamics

One of the most controversial practices in resting-state fMRI functional connectivity studies is whether or not to regress out the global average brain signal (GS) during artifact removal. Some groups have argued that it is absolutely essential to regress out the GS in order to fully remove head motion, respiration, and other global imaging artifacts. Others have argued that removing the GS distorts the resulting correlation matrices and inappropriately alters the results of group comparisons and relationships to behavior. At the core of this argument is the assessment of dimensionality in terms of the number of brain networks with uncorrelated time series. If the dimensionality is high, then the distortions due to GS removal could be effectively negligible. In the current paper, we examine the dimensionality of resting-state fMRI data using principal component analyses (PCA) and network clustering analyses. In two independent datasets (Set 1: N = 62, Set 2: N = 32), scree plots of the eigenvalues level off at or prior to 10 principal components, with prominent elbows at 3 and 7 components. While network clustering analyses have previously demonstrated that numerous networks can be distinguished with high thresholding of the voxel-wise correlation matrices, lower thresholding reveals a lower-dimensional hierarchical structure, with the first prominent branch at 2 networks (corresponding to the previously described task-positive/task-negative distinction) and further stable subdivisions at 4, 7 and 17. Since inter-correlated time series within these larger branches do not cancel to zero when averaged, the hierarchical nature of the correlation structure results in low effective dimensionality. Consistent with this, partial correlation analyses revealed that network-specific variance remains present in the GS at each level of the hierarchy, accounting for at least 14-18% of the overall GS variance in each dataset. These results demonstrate that GS regression is expected to remove substantial portions of network-specific brain signals along with artifacts, not simply whole-brain signals corresponding to arousal levels. We highlight alternative means of controlling for residual global artifacts when not removing the GS.