Evidence of Dense Functional Connectivity in the Human Brain
Ankita Saha1, Ishaan Batta2, and Rahul Garg1

1Department of Computer Science and Engineering, Indian Institute of Technology Delhi, New Delhi, India, 2Center for Biomedical Image Computing and Analytics, University of Pennsylvania, Philadelphia, PA, United States


Aimed at studying the nature of voxel-wise interactions in the brain, this study finds the evidence of dense functional connectivity in the brain using resting state fMRI data from over 700 subjects. To study the nature of these interactions, we used a bipartite graph embedding algorithm on the connectivity network obtained with multiple pre-processing strategies with respect to global signal regression. We also analyzed interactions between and whithin grey and white matter. The results point to a dense non-bipartite network covering 74.63% of the brain leading to new insights towards understanding the human functional connectome.


Since the onset of fMRI, correlation-based functional connectivity analysis has been widely used in resting state studies to establish relations between various brain regions.1 With recent large scale projects,2-4 many studies have contributed to understanding the human connectome. Diverse techniques including graph theory,5 independent component analysis,6 parcellation7 and clustering approaches have been employed to understand the brain’s network structure. A previous study8 had pointed to the possibility of dense correlations in the brain. In this abstract, we use statistical analysis to explore this hypothesis. We find a weak but dense functional connectivity between majority of the voxels in the brain. Unlike in studies with small number of subjects and region-wise analysis,9 we found statistically significant functional connectivity among 74.63% of all pairs of brain voxels. We further analyzed the connections between and within full brain, white and grey matter (WM,GM). We characterize this connectivity with global signal removal, WM, GM signal removal and bipartite embedding.


Resting state fMRI data of 724 subjects from 1000 Functional Connectomes Project2 was used after preprocessing using standard procedures in FSL10 and removing the subjects with less than 90% of brain in the field of view. Functional data of all subjects was registered to that of one of the subjects. Pairwise correlations for all voxel-pairs were computed for all subjects followed by t-test and a suitably modified FDR correction procedure operating at the network level, at 95% confidence. Three versions of correlation computation and statistical testing were done (see Table 1). For these versions, the connection density between WM-WM, WM-GM and GM-GM as well as the percentage of positive connections were computed and reported in Table 1. A scatter plot of number negative vs positive connections in these cases is included in Figure 3.

The brain is known to be organized into inter-inhibitory task positive regions11 and task negative regions.12 If they only comprise one task-positive and one task-negative network, then the subgraph with only negative functional connectivity should be a bipartite graph. To test this hypothesis, a bipartite graph embedding algorithm on the negative (inhibitory) functional connectivity sub-graph was executed (details omitted due to space constraints). For comparison, it was also executed on a synthetic complete bipartite graph.


Table 1 shows the connection density and percentage of positively connected voxels among the WM and GM voxels for different preprocessing options. Out of all possible connections in the full brain, 69.8% were significantly active even after the global signal was regressed out, indicating dense connectivity among brain voxels. Positive WM-WM connectivity was in the range 79.5-96.3% across different preprocessing options.

The density maps (no signal removal) for positive and negative functional connectivity are shown in Figure 1. Notably, the GM voxels tend to have more negative connectivity as compared to the WM voxels. The scatter plot in Figure 3 shows a negative correlation in number of negative connections.

Figure 2 shows distribution of the bipartite embedding weights when applied to a subgraph comprising of negatively functionally connected voxels, plotted against that for a complete bipartite graph. The complete bipartite graph demonstrates just two components with weights +1 and -1 whereas the negative connectivity sub-graph shows a continuum.


While human connectomics have been studied for brain parcellation and topological study objectives7 or region-wise analysis,13 not many studies have looked into the nature of voxel-wise connectivity in full brain. Moreover, most of the studies employ datasets not larger than a hundred subjects, thus resulting in less statistical power than using large datasets.

The white matter in the brain does seem to have BOLD signal14 albeit with a different haemodynamic response function.15 Highly dense positive functional connectivity among the WM voxels is consistent with the fact that WM mostly has excitatory connections.14 Similarly, 40-50% positive connectivity among the GM voxels and between WM-GM voxels is consistent with the presence of both excitatory and inhibitory interactions. The high density of functional connectivity in brain is not surprising but uncovering its structure needs to be studied using thousands of subjects. Some connectivity might be explained by physiological16 or scanner noise.17

The failure of bipartite embedding indicates a more rich and nuanced structure in the graph to be obtained from the human functional connectome. Presence of a multi-partite structure with small number of regions as well as a continuum of network with subtly changing interactions is possible. Determining the nature of this dense full-brain functional connectivity network calls for a further detailed study into the human connectome.


No acknowledgement found.


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Figure 1: Density Maps for (a) positive correlations and (b) negative correlations in the resting state brain. Density is calculated as the percentage of statistically significant positive (or negative) correlations out of number of all possible pairs for correlations. Density of positive connections is much higher in white matter while that negative density is higher in the grey matter.

Table 1: Connection density (and percentage of positive connections out of significant connections) between and within full brain, grey and white matter regions with different pre-processing options. Connection Density for a set of voxels is the percentage of significant functional connections within the set of voxels out of total possible connections for that set. The values were computed using: (a) only standard pre-processing (b) standard pre-processing and global mean removal and (c) standard pre-processing, global mean, white and grey matter mean removal. Time series of all the voxels were orthogonalized with respect to the above mentioned mean signals.

Figure 2: Distribution of bipartite embedding weights for a synthetic complete bipartite graph and resting state fMRI negative connectivity graph. The synthetic graph has two peaks signifying a perfect embedding while the connectivity graph is a continuum, signifying a more intricate network structure.

Figure 3: Scatter plots for prevalence of negative vs positive connections between and within grey matter and white matter. In WM-WM connections in (d) are concentrated towards the lower right side, signifying the high presence of positive correlations within white matter voxels, unlike the GM-GM points in (a). R2 is the coefficient of determination, a statistical measure between 0 to 1 indicating the linearity in data. A Higher value of R2 implies more linearity in data.

Proc. Intl. Soc. Mag. Reson. Med. 26 (2018)