Network topology of symbolic and nonsymbolic number comparison

Studies of brain activity during number processing suggest symbolic and nonsymbolic numerical stimuli (e.g., Arabic digits and dot arrays) engage both shared and distinct neural mechanisms. However, the extent to which number format influences large-scale functional network organization is unknown. In this study, using 7 Tesla MRI, we adopted a network neuroscience approach to characterize the whole-brain functional architecture supporting symbolic and nonsymbolic number comparison in 33 adults. Results showed the degree of global modularity was similar for both formats. The symbolic format, however, elicited stronger community membership among auditory regions, whereas for nonsymbolic, stronger membership was observed within and between cingulo-opercular/salience network and basal ganglia communities. The right posterior inferior temporal gyrus, left intraparietal sulcus, and two regions in the right ventromedial occipital cortex demonstrated robust differences between formats in terms of their community membership, supporting prior findings that these areas are differentially engaged based on number format. Furthermore, a unified fronto-parietal/dorsal attention community in the nonsymbolic condition was fractionated into two components in the symbolic condition. Taken together, these results reveal a pattern of overlapping and distinct network architectures for symbolic and nonsymbolic number processing.


Contents of this
-Region table with community assignments

Region Exclusion based on Signal Dropout
Signal dropout is common in orbitofrontal and inferior temporal areas in fMRI due to close proximity to air-tissue interfaces. This is problematic because signal attenuation will lead to unreliable activation estimates in affected regions and thus subsequent connectivity measures could be driven by noise. While studies of functional connectivity seldom report whether they have accounted for signal dropout (e.g., through EPI masking), this procedure has recently been discussed as an important step in connectivity analyses (Peer, Abboud, Hertz, Amedi, & Arzy, 2016). To address this, we took a quantitative approach to characterizing signal dropout and determining regions to exclude from whole-brain network analyses. First, we sought to determine the optimal fraction of signal to consider as "usable" via AFNI's 3dAutomask function (i.e., the "clip fraction" parameter). We found the default clip fraction of 0.5 to be suboptimal, as it excluded relatively more voxels in our 7T EPI data compared to its application in 3T data, due to a much higher range of values across the brain and a heavy-tailed distribution whereby exterior areas of cortex had as much as four times the signal as those located more centrally/inferiorly. We can consider the histogram of voxel-wise signals in EPI images as a mixture of two distributions, one encompassing non-brain/attenuated-signal voxels and another encompassing brain/water-signal voxels. We varied the clip fraction in 3dAutomask across a range of values and looked for the first setting at which the overall group mean distribution showed no local minima (i.e., the surviving voxels can be expected to come from the second, brain/water distribution), arriving at a clip fraction of 0.32. As a second step, we used the resulting EPI masks to determine the percentage of usable voxels in each region for each subject.
We set an exclusion criterion such that every subject had to have at least 50% usable voxels in a region for that region to be included in further analyses. One subject had 41 of 246 regions with less than 50% coverage due to significant dropout artifacts. This was more than 3.5 × the median absolute deviation (MAD), a robust metric for outlier detection, and was excluded from further analyses (median number of regions excluded across subjects = 24 ± 3.5 MAD) (Leys, Ley, Klein, Bernard, & Licata, 2013). We justified a stringent cutoff of 50% coverage based on the idea that if we aim to adequately characterize the function/connectivity of a region, we should do so based on usable signal from at least half of the voxels in this region. A similar cutoff has been employed in previous studies (e.g., Geerligs, Rubinov, Cam-CAN, & Henson, 2015). This procedure resulted in a final set of 202 regions out of 246 from the Brainnetome atlas (Fan et al., 2016).

Community Selection
Using the final group-level partitions, we computed the modularity contribution ( " * ) of each community, c, in the subject-level connectivity matrices, with " * defined as follows: Null distributions were created by reshuffling the partition vector 10 4 times, preserving the number and size of communities across permutations, and recalculating Q*c for each community, in accordance with the procedure performed by Betzel et al. (2017). Z-scores were calculated for each true value by subtracting the mean and dividing by the standard deviation across permutations. This was done for each subject, and we selected a community if its modularity contribution exceeded the 99 th percentile of the null distribution in more than half of subjects, with the reasoning that, to be considered for further analyses, the group-level communities must demonstrate significant connectivity at the subject level.

Supplementary Results
Supplementary Figure Fig. 2A, B. Partitions were relabeled at each step based on their maximal overlap with the communities at = 2.45 within each format respectively, which was our setting of interest for the community-level analyses (see Fig. 2 and 3 in the main manuscript). Note that at the low end of the range, FPN/DAN regions are subsumed by a hierarchical task-positive/task-negative community structure where the task-negative community includes primarily default mode regions (red) and the task-positive community includes visual (blue) and DAN (green) regions.

Supplementary Figure S3 -Median Connectivity in Selected Communities -Comparison
Between Formats. The median region-to-region connectivity values (i.e., median across subjectlevel correlation z-score matrices) within or between each community were vectorized, and compared between formats using paired t-tests. Non-parametric significance was determined using Monte Carlo permutations of the subject-level matrices from each format, with 50,000 iterations to mirror the group-level allegiance analysis presented in Fig. 3E, F. The z-score for CdD represents that of the simple difference between formats, since there was only one regionto-region connection within this community and a paired t-test was not possible.

Supplementary Figure S4 -Relationship of Region-level Allegiance Profile Differences to
Connectivity Dissimilarity. The median region-to-region connectivity matrices (i.e., median across subject-level correlation z-score matrices) were constructed for the symbolic and nonsymbolic condition (same data used in Supplementary Fig. S3). Each region's connectivity profile (pairwise connectivity strength with all other regions) was extracted and correlated between formats. The resulting Fisher Z values provided a measure of (dis)similarity in connectivity profile between formats. The Monte Carlo procedure with 50,000 permutations was performed to derive dissimilarity z-scores (higher z-score indicates lower Fisher Z compared to chance). Scatter plot shows a small, but significant relationship between these z-scores and the total count of steps over the resolution sweep showing a significant difference in allegiance profile between formats (see Fig. 4 in the main manuscript). However, note that the regions showing the strongest differences in connectivity profile (top left of plot) do not show robust differences in community allegiance. It could be the case, for instance, that a region demonstrates a significant difference between formats in overall connectivity strength, but this region's community membership remains stable. Furthermore, the regions showing the most robust differences in community allegiance (red) (Fig. 4) (Fan et al., 2016) are listed, with information including their lobe, gyrus, anatomic description and center of gravity coordinates in MNI space. Colored coded community assignments from the symbolic and nonsymbolic conditions are indicated in the rightmost columns. Unselected = region was assigned to community which did not reach our criteria for selection based on a significant modularity contribution at the subject-level (see Supplementary   Fig S1