Fig 1.
Experimentally modulating cognitive control processes to uncover internal mechanisms of network regulation.
(A) To monitor and regulate the demands placed on neural systems, empirical evidence suggests that the brain employs cognitive control processes that gate information and select among competing representations and processes [14]. Functional brain networks that flexibly coordinate interactions between different sets of brain regions over time may be a key substrate for cognitive control, and moreover be essential for maintaining homeostasis between internally-driven brain dynamics and externally-elicited behavioral goals [8]. We present here a conceptualized diagram of the graph theoretical framework that helps us model the dynamics of cognitive control networks. Brain regions are represented as nodes and the strength of functional interactions between brain regions are represented as weighted edges. (B) Recent advances in network neuroscience [15] and machine learning [16] enable us to cluster functional brain networks into composite subgraphs—cohesive sets of graph edges (left) from the observed network (A) that tend to co-vary in strength over time. The putative role of a subgraph in cognitive control is inferred by its relative level of weighted expression in the observed network at a specific task block during cognitive processing (right). To experimentally modulate cognitive demand, we recruit 28 healthy adult human participants to perform a response inhibition, Stroop task (C) and a task-switching, local-global feature perception task based on Navon figures (D). The Stroop task entails (i) a fixation condition consisting of a black crosshair at the center of the screen, (ii) a low demand condition consisting of a matched word-color pair, and (iii) a high demand, interference condition consisting of a mismatched word-color pair. Subjects are required to report the color of the presented word. The Navon task entails (i) a fixation condition consisting of a black crosshair at the center of the screen, (ii) a low demand condition consisting of only white or green Navon figures—local shapes embedded in a non-matching global shape, and (iii) a high demand condition consisting of Navon figures randomly alternating between white or green color. Subjects are required to report the local shape if the presented figure is white or to report the global shape if the presented figure is green. Differences in task condition are thought to invoke different levels of recruitment of cognitive control mechanisms. Participant reaction time on correct trials is used to measure performance, and the difference in performance between high and low cognitive control conditions is thought to represent the costs of cognitive control.
Fig 2.
Learning functional subgraph architecture of cognitive control processes.
(A) We measure fMRI BOLD signals from 262 functional regions of interest (234 cortical and subcortical brain areas parcellated by ([31]; top) and 28 cerebellar brain areas parcellated by ([32]; bottom) as 28 healthy adult human subjects perform Stroop and Navon cognitive control tasks. (B) We concatenate BOLD signal from 6 task blocks (corresponding to 30 seconds of BOLD activity, and comprising several trials) in each of 3 task conditions (fixation, low demand, high demand) for each of 2 tasks (Stroop and Navon). (C) Next, we calculate the Pearson correlation coefficient between each pair of regional BOLD signals to create an adjacency matrix for every experimental block. We encode this information in dynamic functional networks with brain regions as graph nodes and block-varying correlation as weighted graph edges. To assess the relative role of correlated (positively weighted edges) and anticorrelated (negatively weighted edges) functional interactions during cognitive control, we threshold each adjacency matrix at the zero edge weight and group positive edges and negative edges into separate adjacency matrices (see Materials and methods). (D) We concatenate all pairwise edges over task blocks and subjects, and we generate a single network configuration matrix for the entire study cohort (left). We apply non-negative matrix factorization (NMF)—a parts-based decomposition of the dynamic network—to the configuration matrix and cluster graph edges with co-varying weights into a matrix of subgraphs (middle) and a matrix of time-varying coefficients (right) that quantify the level of expression of each subgraph in each task block. We use a cross-validation parameter optimization procedure and identify 12 subgraphs specific to the cognitive control tasks (S2 Fig). (E) For each subgraph, we reconstitute its vector of edge weights into a fully-weighted symmetric adjacency matrix (left) and track its associated positive and negative expression coefficients over task blocks (right). Briefly, the positive and negative expression coefficients signify the likelihood that the subgraph edges represent correlations or anticorrelations for each moment in time (see Materials and methods). (F) We rank functional subgraphs in decreasing order (A-L) of the difference between positive and negative expression weight, averaged over task blocks and subjects. Bar height represents the mean difference over subjects and error bars represent standard error of the mean. Red bars correspond to subgraphs that are, on average, more positively expressed and blue bars correspond to subgraphs that are, on average, more negatively expressed.
Fig 3.
Linking functional subgraphs to neuroanatomy of canonical cognitive systems.
We uncover twelve functional subgraphs whose weighted graph edges span the 262 graph nodes specified by the brain atlas. We examine functional roles of subgraphs in cognitive processing by assigning each node to a putative cognitive system [33]: dorsal attention, default mode, frontoparietal, limbic, somatosensory, subcortical, ventral attention, visual, and cerebellum. To visualize the topology of each subgraph, we construct ring graphs in which nodes are evenly spaced around the circumference of a circle—color coded by assigned cognitive system—and edges between nodes are represented by line arcs—colored by the percentile of the edge strength in the subgraph. Subgraphs are coded A through L in decreasing order of the mean relative expression weight; subgraphs expressed more positively are represented with red letters and subgraphs expressed more negatively are represented with blue letters. For system-by-system adjacency matrix representations of functional subgraphs, we refer the reader to S5 Fig. Subgraphs reflect topological states of task-related processes whereby functional interactions within a cognitive system mark a centralized network core of information that may be shared with other cognitive systems located in the network periphery. To identify core-periphery structure for a subgraph, we compute the relative difference between the mean weight of edges adjoining nodes within a cognitive system and the mean weight of edges adjoining nodes from that cognitive system to other cognitive systems—values closer to +1 indicate stronger edges within a cognitive system than between cognitive systems (core), values closer to −1 indicate stronger edges between cognitive systems than within a cognitive system (periphery), and values closer to 0 indicate equally strong edges within and between cognitive systems (core-periphery). We observe a significant positive relationship between a subgraph’s core-periphery index and its mean relative expression across task blocks and subjects (Spearman’s ρ, ρ = 0.76, p = 0.004), suggesting that subgraph topology is closely linked with subgraph dynamics. Specifically, subgraphs that exhibit greater core and core-periphery structure express more correlated dynamics (positive; red) and subgraphs that exhibit greater periphery structure express more anticorrelated dynamics (negative; blue). These results imply that subgraphs may represent putative stages of cognitive control in which correlated dynamics correspond to integrated information processes within and across cognitive systems and anticorrelated dynamics correspond to segregated information processes between different cognitive systems. For a detailed comparison of core-periphery structure across cognitive systems and subgraphs, we refer the reader to S6 Fig.
Fig 4.
Subgraphs map functional interactions specific to cognitive control tasks.
(A) Relationship between the relative subgraph expression during the Stroop task and the relative subgraph expression during the Navon task. Each point represents relative subgraph expression averaged over subjects, horizontal (vertical) error bars represent standard error of the mean for the Stroop (Navon) task. Generally, relative subgraph expression during the Stroop task is significantly associated with relative subgraph expression during the Navon task (Spearman’s ρ, ρ = 0.97, p = 1.3−7), implying that subgraphs collectively follow similar rules of dynamical expression during the Stroop and Navon tasks. However, individual subgraphs may vary in the amount they are expressed during the Stroop and Navon tasks, which is signified by the perpendicular distance between a subgraph and the shaded gray line with slope equal to one. Using paired t-tests and FDR correction for multiple comparisons, we compare the distribution of relative subgraph expression between Stroop and Navon tasks across subjects. We find greater positive expression during the Navon task than the Stroop task for subgraph B (t27 = 4.4, p = 1.4 × 10−4) and subgraph D (t27 = 2.9, p = 7.0 × 10−3), and we find greater negative expression during the Navon task than the Stroop task for subgraph K (t27 = 5.1, p = 1.4 × 10−5). Thus, the rank of a subgraph in terms of its overall expression relative to other subgraphs is similar between the Stroop and Navon tasks, but its level of expression may be different depending on the task. Specifically, we find subgraphs B and D are more strongly associated with correlated dynamics during the Navon task than the Stroop task, and we find subgraph K is more strongly associated with anticorrelated dynamics during the Navon task than the Stroop task.
Fig 5.
Modulation of subgraph expression coincides with increased cognitive demand.
(A) Relationship between relative subgraph expression during the low cognitive demand condition and the high cognitive demand condition of the Stroop task. Each point represents relative subgraph expression averaged over subjects. Horizontal (vertical) error bars represent standard error of the mean for the low (high) demand condition. Similarly plotted for the low demand condition and high demand condition of the Navon task (shown in B). Generally, relative subgraph expression during the low demand condition is significantly associated with relative subgraph expression during the high demand condition for the Stroop task (Spearman’s ρ, ρ = 0.99, p = 4.1−9) and for the Navon task (Spearman’s ρ, ρ = 0.99, p = 4.1 × 10−9). These results imply that the rank of a subgraph in terms of its overall expression relative to other subgraphs is similar between the low cognitive demand condition and the high cognitive demand condition for the Stroop task and for the Navon task. To test whether individual subgraphs vary in the amount they are expressed as cognitive demand increases, we compare the distribution of relative subgraph expression between the low demand condition and the high demand condition for each task using paired t-tests and FDR correction for multiple comparisons. For the Stroop task, we find greater positive expression during the high demand condition than the low demand condition for subgraph B (t27 = 3.3, p = 2.7 × 10−3) and subgraph E (t27 = 3.2, p = 3.6 × 10−3), and we find greater negative expression during the high demand condition than the low demand condition for subgraph L (t27 = 2.5, p = 0.01). For the Navon task, we find greater positive expression during the high demand condition than the low demand condition for subgraph G (t27 = 2.9, p = 8.2 × 10−3), and we find greater negative expression during the high demand condition than the low demand condition for subgraph F (t27 = 2.7, p = 0.01). These results collectively suggest that subgraph expression shifts alongside changes in cognitive demand in a manner that is specific to each cognitive task. Specifically, the change in subgraph expression that accompanies an increase in cognitive demand may involve an increase in correlated or anticorrelated dynamics. These dynamics potentially implicate an antagonistic network mechanism of cognitive demand whereby one set of subgraphs engage through more positive expression while another set of subgraphs disengage through more negative expression.
Fig 6.
Subgraph expression stratifies inter-individual task performance.
(A-D; left) To examine the link between subgraph dynamics and behavior, we compare subgraph expression to task-specific performance cost across individuals. Specifically, we compute the Spearman’s ρ between relative subgraph expression, averaged across low demand or high demand task blocks of each participant, and reaction time cost—difference between reaction time on high demand blocks and low demand blocks (lower is better)—averaged across task blocks of each participant. Values of ρ greater than zero imply that greater negative subgraph expression is associated with lower reaction time cost and values of ρ less than zero imply that greater positive subgraph expression is associated with lower reaction time cost. (A-B; left) Distribution of Spearman’s ρ between relative subgraph expression and reaction time cost for each subgraph during the low cognitive demand condition and the high cognitive demand condition of the Stroop task. Subgraphs with significant correlations are colored red (p < 0.05; uncorrected for multiple comparisons). (C-D; left) Distribution of Spearman’s ρ between relative subgraph expression and reaction time cost for each subgraph during the low cognitive demand condition and the high cognitive demand condition of the Navon task. Subgraphs with significant correlations are colored red (p < 0.05; uncorrected for multiple comparisons). (A-D; right) To assess which brain regions are more influential in subgraphs whose expression is associated with lower reaction time cost, we compute a participation score for each brain region by computing its node strength in each subgraph and calculating the sum of each brain region’s node strength across subgraphs, weighted by the Spearman’s ρ value. Intuitively, a more positive participation score implies that a brain region is more involved in subgraphs with greater negative expression in individuals with lower reaction time cost, and a more negative participation score implies that a brain region is more involved in subgraphs with greater positive expression in individuals with lower reaction time cost. We compare participation scores to a null distribution that is generated by permuting edges in the subgraph adjacency matrix 10000 times and recomputing the participation score for each permutation (p < 0.05; Bonferroni corrected for multiple comparisons). Brain regions with significantly positive participation scores (associated with anticorrelated dynamics) are colored in red, and brain regions with significantly negative participation scores (associated with correlated dynamics) are colored in blue.