We use a dataset from the Human Connectome Project (HCP) (Barch et al. 2013), with fMRI measurements from 100 subjects undertaking an n-back working memory task. The task consists of three experimental blocks, 2-back, 0-back and fixation, with varying cognitive load. In the 2-back condition, subjects are presented with images and are asked to press a button if it matches the image presented two instances back. In the (easier) 0-back condition, they are asked to press a button when a target image is presented. During the fixation periods, no instructions are given and subjects lie passively with eyes open in a resting-state. For each subject and experimental block, we can measure a performance accuracy as the fraction of correct button presses. The duration of an experiment is just under 5 min, and measurements are taken in 405 ticks with frequency 0.72 s.
The dataset describes activity across hundreds of thousands of voxels in each subject. To reduce noise as well as the network size defined in terms of pairwise correlations we rely on techniques for describing the brain signal using fewer components. We use independent component analysis (ICA) as a method for dimensionality reduction. Using ICA we produce a set of 50 independent components (ICs) each described as a spatial map consistent over subjects (Additional file 1: Figure S1), and an accompanying time-course of component activity. ICs are under few spatial constraints and have a whole-brain spatial distribution. In practice, however, ICs are often peaked around a smaller localized region and components rarely overlap.
We represent component activity as a temporal network, by making the abstraction that ICs of the brain are physical nodes i, and correlations between their time-courses within a window are links at times α such that all intra-layer links are represented by adjacency matrices \(W_{ij}^{\alpha }\). We use a sliding window of size w=25 (each time-step is 0.72 s). Thus, the 405 original time-ticks in the data results in a temporal networks of 381 layers. Figure 1 gives a schematic overview of the experimental design and the processing procedures. Note that we use a fairly short window for correlating time-courses compared to what is recommended in the resting-state dynamic functional connectivity literature (Leonardi and Van De Ville 2015; Zalesky and Breakspear 2015). This is necessary, as the window-duration must remain shorter than the time-scale of the two tasks and fixation periods, since, if the window exceeds this time-scale, we cannot compare the temporal dynamics of communities to the experiment design. There is, however, evidence from task-based fMRI studies showing that shorter window-lengths have the necessary stability to detect changes in ongoing cognition (Gonzalez-Castillo et al. 2015). The inter-layer adjacency matrix \(D_{i}^{\alpha \beta }\) that connects states at times α and β of each physical node i is inferred with neighborhood flow coupling (NFC) (Aslak et al. 2018). In brief, NFC couples temporal states of each physical node by a strength that is proportional to the neighborhood similarities of each state-pair. If at two separate times a node has similar neighborhoods, there will be a strong link between those two time-states of the node. Consequently, time-intermittent communities (communities that repeatedly disappear and re-appear) will have many strong links between them because, at each recurrence, the member nodes have similar neighborhoods. Thus, inferring the inter-layer adjacency matrix \(D_{i}^{\alpha \beta }\) using NFC creates a temporal network that, when used as input to a community detection algorithm, can reveal intermittent communities.
We use the Infomap algorithm for community detection (Rosvall et al. 2009) which, in brief, partitions a network into modules that have maximal flow within them. Infomap minimizes a cost function called the Map Equation, which is an analytical lower bound on the per-step description length of a random walker on the network given a partition of nodes into modules. On an abstract level, it considers the network as substrate for information flow, which by analogy suits our current application well. We use the software implementation of Infomap which has built-in support for NFC (Edler and Rosvall 2014).
We find communities that are shared across subjects
One way that we can search for communities which–if they exist–are guaranteed to be universal across subjects, is to time-concatenate the networks of multiple subjects to build a larger temporal network and then find a single community detection solution. This strategy enables a functional network which activates in multiple different subjects, to be detected as a single community.
We start by performing this analysis for the ten subjects with the highest 2-back task performance accuracy, and find two highly distinct communities (Fig. 2). One community (here, community 1) appears regularly during fixation for nearly all subjects. Another, larger, community (community 0) seems to activate during task performance and turn off completely during fixation for most subjects. Communities 0 and 1 are, while not entirely disjoint, distinctly different, both in their component distributions and in their temporal activity series, where they exclude each other for many subjects (Fig. 2c). The community detection method does find more communities, but none that are very large and regular across subjects or otherwise distinguishable from noise. In Additional file 2: Figure S2 we display communities 2 and 3 to support this insight. Furthermore, since Infomap indexes communities by descending size, it is highly unlikely that any of the remaining smaller communities contain signal.
Next, we perform the same analysis on the ten subjects with the lowest 2-back task accuracy, and find that both communities 0 and 1 are recovered with largely the same component profiles (Additional file 3: Figure S3). For community 0 it appears that the time activity series is less modulated by the course of the experiment. Similarly, we perform the analysis on all 100 subjects and recover again communities 0 and 1 with almost identical component distributions (Additional file 2: Figure S2). This repeated detection of communities 0 and 1 strongly suggests that, for the chosen parameter set (see “Materials and methods” section for discussion on parameters), these communities are non-random and prominent in our population.
Task-synchrony reveals two prominent functional networks
From visual inspection of Fig. 2a, it is clear that the activity patterns of communities 0 and 1 are modulated by the experimental tasks that subjects undertake. We now quantify this correlation. Using the community detection solution obtained from all 100 subjects together (Additional file 2: Figure S2), we gauge the level of synchrony between communities and tasks. For a given subject, we measure synchrony between a community and a task as the Pearson correlation between the community’s activity level over time and a vector representing when a task is being undertaken (specifically, the proportion of a given task inside each time-window, see Fig. 1a3). We plot the distribution of community-task synchrony within the population for each combination of task (fixation, 2-back and 0-back) and community (0 and 1). We also scatter-plot synchrony values against the task performance accuracies to investigate if they co-vary. Synchronies that are insignificant after multiple comparisons correction (100 hypotheses) are rendered in gray.
We observe that, for almost all subjects, community 1 is in strong positive synchrony with the fixation period, while community 0 is in strong negative synchrony with the fixation period (Fig. 3a-b). The exact opposite is observed for the 2-back task, where we find that most subjects activate community 0 and shut down community 1 (Fig. 3c-d). Interestingly, there is no such trend in the synchrony distributions for the 0-back task, revealing that community 0 is not a general task-related community, but strictly a 2-back-task related community.
We plot the community-task synchrony values for each subject against their task performance accuracy score (recall: fraction of correct presses) and measure the Pearson correlation between these – since it is reasonable to hypothesize that if a community represents brain activity related to a specific task, then the performance accuracy of that task should modulate the dynamics of the community. However, we measure no significant correlations between task performance accuracy and community-task synchrony. Finally, as a way to correct for individual subject ability, we test the relation between performance gain (2-back performance divided by 0-back performance) and synchrony, yet find that it is not significant.
In reviewing the core components of communities 0 and 1, we found a good correspondence when matching them against brain domains that are known to activate during working memory and default mode function, respectively. Both community 0 (working memory) and community 1 (default mode) have components that together cover the regions known to activate in their associated systems. At the same time they also have a number of core components that are not associated with these, especially ones located in the occipital lobe. We perform the matching using the Neurosynth software (Yarkoni et al. 2011; Yarkoni 2011). In Additional file 4: Figure S4, we visualize the core components that best match active regions in their associated activation maps, next to the relevant z-axis slices of those maps.