Hierarchical organization of spontaneous co-fluctuations in densely sampled individuals using fMRI

Abstract Edge time series decompose functional connectivity into its framewise contributions. Previous studies have focused on characterizing the properties of high-amplitude frames (time points when the global co-fluctuation amplitude takes on its largest value), including their cluster structure. Less is known about middle- and low-amplitude co-fluctuations (peaks in co-fluctuation time series but of lower amplitude). Here, we directly address those questions, using data from two dense-sampling studies: the MyConnectome project and Midnight Scan Club. We develop a hierarchical clustering algorithm to group peak co-fluctuations of all magnitudes into nested and multiscale clusters based on their pairwise concordance. At a coarse scale, we find evidence of three large clusters that, collectively, engage virtually all canonical brain systems. At finer scales, however, each cluster is dissolved, giving way to increasingly refined patterns of co-fluctuations involving specific sets of brain systems. We also find an increase in global co-fluctuation magnitude with hierarchical scale. Finally, we comment on the amount of data needed to estimate co-fluctuation pattern clusters and implications for brain-behavior studies. Collectively, the findings reported here fill several gaps in current knowledge concerning the heterogeneity and richness of co-fluctuation patterns as estimated with edge time series while providing some practical guidance for future studies.


FIG. S2.
Characterizing peak co-fluctuations.For every peak, we calculated its amplitude (RMS) and duration.Using a procedure developed in our previous work, also classified each peak as a high-, middle-, or low-amplitude frame.In the main text and in all panels we report statistics based on a set of 1568 co-fluctuation patterns that survived a series of quality assessments to reduce the likelihood that they are related to motion or reflect background stochastic fluctuation.In all plots, these 1568 points are opaque.For completeness, we also include the remaining 1556 detected peaks that were discarded.These points are depicted as gray and transparent.In the main text we described a correlation between duration and amplitude of peak co-fluctulations.There was, however, considerable variance around that best linear fit between those variables.(a) Here, for each duration (in units of TRs) we show the top (red) and bottom (blue) trough-to-trough curves, ranked by RMS.(b) We returned to the edge time series and calculated the correlation of each edge time series with the corresponding trough-to-trough RMS curve.We found that the mean correlation over all edges was stronger for the top 25% than for the bottom 25%, suggesting that even after controlling for duration, there is variability in the "diffusivity" of the trough-to-trough co-fluctuation, with higher amplitude co-fluctuations corresponding to tighter and more cohesive fluctuations than lower-amplitude fluctuations of identical duration.FIG.S11.Persistence and refinement of coarse clusters across hierarchical levels.In Fig. 3 and Fig. 4 we showed coarse clusters and their hierarchical divisions.We note that the coarse clusters, although they get sub-divided, are also refined across hierarchical levels.That is, strong co-fluctuations get stronger (positive and negative) but the overall pattern persists.Here, we highlight the persistence of the three large clusters identified in Fig. 3.The correlation values shown in a correspond to the correlation of each child centroid with its immediate parent.Note that an alternative possibility was that, as clusters sub-divide, the children partitions decompose their parents so that the correspondence is not as strong.We then compared different reconstructions of FC to the observed FC matrix.These included the mean co-fluctuation pattern (averaged over all patterns), the co-assignment matrix of observed bipartition, the co-assignment matrix of the best-matched system-templates, and the z-scored version of the best-matched templates.We repeated this analysis for the largest clusters detected at hierarchical level 2 (e) and for subdivisions of the largest cluster at that level (f ).In all cases, we find evidence that templates capture the specificity of divisions among co-fluctuations originally identified using the hierarchical clustering algorithm.The first level corresponds to a community that contains all nodes; the second level contains no statistically significant communities, i.e. none of the communities in the first level passed a test for statistical significance.We repeated the null model 1000 times and calculated the number of hierarchical levels detected in each run.In all cases, the number of levels was two (2).(g) Null distribution concentrated on a single value (blue) compared to the observed number of hierarchical levels (red dashed line).
FIG. S2.Characterizing peak co-fluctuations.For every peak, we calculated its amplitude (RMS) and duration.Using a procedure developed in our previous work, also classified each peak as a high-, middle-, or low-amplitude frame.In the main text and in all panels we report statistics based on a set of 1568 co-fluctuation patterns that survived a series of quality assessments to reduce the likelihood that they are related to motion or reflect background stochastic fluctuation.In all plots, these 1568 points are opaque.For completeness, we also include the remaining 1556 detected peaks that were discarded.These points are depicted as gray and transparent.(a) Definition of several quantities of interest.(b) Peak height for three peak types.(c) Trough-to-trough durations for three peaks.(d ) Maximum velocity for three peaks.(e) Relationship between peak height and duration.(f ) Relationship between velocity and duration.(g) Relationship between peak height and velocity.(h) Mean RMS trough-to-trough curves for co-fluctuation peaks.The inset depicts analogous data but for mean slope, rather than RMS.In this panel, color indicates duration.
FIG. S6.Top and bottom RMS quartiles by duration.In the main text we described a correlation between duration and amplitude of peak co-fluctulations.There was, however, considerable variance around that best linear fit between those variables.(a) Here, for each duration (in units of TRs) we show the top (red) and bottom (blue) trough-to-trough curves, ranked by RMS.(b) We returned to the edge time series and calculated the correlation of each edge time series with the corresponding trough-to-trough RMS curve.We found that the mean correlation over all edges was stronger for the top 25% than for the bottom 25%, suggesting that even after controlling for duration, there is variability in the "diffusivity" of the trough-to-trough co-fluctuation, with higher amplitude co-fluctuations corresponding to tighter and more cohesive fluctuations than lower-amplitude fluctuations of identical duration.
FIG. S7.Correlation of cluster centroids and individual patterns with static FC.In Fig. 2j we showed that larger clusters and their centroids were more strongly correlated with FC.Here, we repeat this analysis showing (a) the correlation of individual co-fluctuation patterns with FC, (b) the mean across those pattern level correlations averaged by cluster, and (c) the correlation of cluster centroids with FC.
FIG. S12.Comparison with templates and bipartitions.(a) System templates.Given 14 systems, there are exactly 8191 unique templates-i.e.ways of partitioning systems into two disjoint sets.(b) Normalized mutual information of each cofluctuation pattern with each template.Patterns are ordered by community.Note: Here we include all co-fluctuation patterns, including those with low prominence and without exclusion based on proximity to another peak.(c) For each pattern, we identified the index corresponding to the maximum NMI.Here, we show the histogram.(d )We then compared different reconstructions of FC to the observed FC matrix.These included the mean co-fluctuation pattern (averaged over all patterns), the co-assignment matrix of observed bipartition, the co-assignment matrix of the best-matched system-templates, and the z-scored version of the best-matched templates.We repeated this analysis for the largest clusters detected at hierarchical level 2 (e) and for subdivisions of the largest cluster at that level (f ).In all cases, we find evidence that templates capture the specificity of divisions among co-fluctuations originally identified using the hierarchical clustering algorithm.

FIG. S13 .
FIG. S13.Linking different hierarchical levels to FC using MSC data.In the main text we show that the correspondence with FC peaks at an intermediate hierarchical level.Here, we recapitulate that analysis using data from the individual subjects in the MSC dataset.(a) Correlation with FC at different hierarchical levels.Thick lines indicate averages across subjects while thin lines indicate data from individual subjects.(b) Mean RMS of co-fluctuation patterns at different hierarchical levels.