Thread by @richardfbetzel

1/ Thrilled to share *two* related pre-prints in which we introduce an edge-centric approach for modeling functional brain networks. Buckle in, this thread is going to be longer than normal.

biorxiv.org/content/10.110…
biorxiv.org/content/10.110…

2/ First and foremost, I want to note that both papers are collaborations between @networks_lab and @spornslab (that’s right – the band is back together) and represent the efforts of an amazing group of graduate students and postdocs @joshfasky, @Farnaz_zm, and @Jo_Youngheun.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun 3/ The motivation for these projects were papers from @yy and @renaudlambiotte

nature.com/articles/natur…

journals.aps.org/pre/abstract/1…

Each presents a unique method for studying the interactivity of a network’s edges rather than its nodes, resulting in edge-edge networks.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte 4/There are probably many ways of focusing on brain network edges. We wanted one that a) was suitable for fully-weighted and signed data, b) operated in the time domain, c) was consistent with other FC definitions, and d) was fast to implement. This is where we had first insight

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte 5/ In most applications FC = correlation. Correlation = time-averaged element-wise product of standardized time series. If we skip the time-averaging step, we’re left with a “edge time series” for every pair of nodes whose elements = moment-to-moment fluctuations in *co*-activity

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte 6/ Our approach (in both papers) builds on edge time series.

In paper 1 we use them to estimate a novel “edge functional connectivity” matrix and characterize its properties. Edge time series are naturally resolved at a timescale of single frames.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte 7/ In paper 2, we analyze the contributions of individual time points to nodal FC, and show that FC is largely driven by rare, intermittent, and high-amplitude co-fluctuations of activity.

Let’s start with paper 1.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte 8/ In this paper we estimate edge-edge interactions from the edge time series – we call this edge functional connectivity (because we’re not creative when it comes to naming). This produces a fully-weighted and signed matrix of links between edge pairs.f

biorxiv.org/content/10.110…

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte 9/ After introducing eFC, we used @club_scan data to show that with ~30 minutes of data you can get a good estimate of eFC (similar to nFC in this way) and that eFC shows subject specificity and good reliability.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan 10/ In my opinion one of the most valuable features of eFC is that when it’s clustered, you get non-overlapping edge communities. But when they’re mapped back to regions, you naturally get overlapping regional communities!

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan 11/ This means that we can ask questions like “which brain regions/systems participate in most diverse number of clusters?” We find that sensorimotor + attention networks have greatest overlap (and replicate this result in three datasets!)

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan 12/ eFC also varies with task. We compared eFC at rest with eFC during movie-watching and found that not only were the eFC weights systematically and consistently modulated, but so was the overlap pattern, with overlap increasing in cont + dmn regions during movie-watching.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan 13/ To summarize paper 1, we developed an edge-centric framework consistent with FC but emphasizes circuit-level interactions. It naturally resolves overlapping communities, is subject specific, and modulated by task. eFC provides a new substrate to compare subjs and conditions.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan 14/ Paper 2: Edge time series are resolved at a time scale of frames (gives us tvFC without any windowing btw). FC is just the mean value of edge time series. So we can directly assess the contributions of individual frames to static, nodal FC.

biorxiv.org/content/10.110…

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan 15/ We found that the whole-brain co-fluctuation magnitude was “bursty” and exhibited a heavy tail. In other words, there are frames that contribute WAY more to time-averaged FC than others – we call these frames “events”. There are also frames that contribute virtually nothing.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan 16/ We verified this by estimating FC using only frames with high-amplitude co-fluctuations and those with low-amplitude. Sure enough, not only are the high-amplitude frames more similar to the time-averaged FC, but they also seem to drive the brain’s overall modular structure.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan 17/ At this point we got scared. Maybe the co-fluctuation “events” are cardiac or respiratory effects… maybe they’re motion? So we did comparisons with those measurements and found weak or non-existent correlations.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan 18/ Not included in the paper, but we compared the co-fluctuation amplitude during rest and movie-watching using data from @DanKennedyIU. Sure enough, co-fluctuation amplitude is correlated across subjects during movie-watching but not rest. So “events” are more than noise.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan @DanKennedyIU 19/ Because edge time series are resolved at single frames, we could compare connectivity fluctuations with *activity* fluctuations. We found that “events” corresponded to a specific mode of activity emphasizes a sort of “task-positive/task-negative” split of the brain.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan @DanKennedyIU 20/ In summary -- FC is driven by a relatively small number of frames and, specifically, by fluctuations of a particular mode of brain activity.

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan @DanKennedyIU 21/ We think there's a lot more to do here. For instance -- are events or non-events better for studying individual differences?

@networks_lab @spornslab @joshfasky @Farnaz_zm @Jo_Youngheun @yy @RenaudLambiotte @club_scan @DanKennedyIU 22/ We can also use edge time series as proxies for tvFC but with better temporal resolution. Check this out (figure not in either paper).

23/ I should add that we’re not the first to think about network edges. @martijnheuv adopted an analogous approach with SC. To my knowledge, no one has tried something similar with FC.

royalsocietypublishing.org/doi/pdf/10.109…

24/ as a final comment, I’ll note that the edge-centric approach can easily be extended to partial and lagged correlations. So if you prefer those measures, you’re in luck!