Stability of Network Communities as a Function of Task Complexity

Abstract

The analysis of the community architecture in functional brain networks has revealed important relations between specific behavioral patterns and characteristic features of the associated functional organization. Numerous studies have assessed changes in functional communities during different states of awareness, learning, information processing, and various behavioral patterns. The robustness of detected communities within a network has been an often-discussed topic in complex systems research. However, our knowledge regarding the intersubject stability of functional communities in the human brain while performing different tasks is still lacking. In this study, we examined the variability of functional communities in weighted undirected graphs based on fMRI recordings of healthy participants across three conditions: the resting state, syllable production as a simple vocal motor task, and meaningful speech production representing a complex behavioral pattern with cognitive involvement. On the basis of the constructed empirical networks, we simulated a large cohort of artificial graphs and performed a leave-one-out stability analysis to assess the sensitivity of communities in the group-averaged networks with respect to perturbations in the averaging cohort. We found that the stability of partitions derived from group-averaged networks depended on task complexity. The determined community architecture in mean networks reflected within-behavior network stability and between-behavior flexibility of the human functional connectome. The sensitivity of functional communities increased from rest to syllable production to speaking, which suggests that the approximation quality of the community structure in the average network to reflect individual per-participant partitions depends on task complexity.

Figures

Figure 1. Illustration of the utilized analytic strategy

(I) Based on a 212-region whole-brain parcellation regionally averaged BOLD time-series were extracted from fMRI recordings acquired at rest, during syllable production and while speaking. (II) NMI coefficients were calculated for each pair of ROI time-series and assembled in connectivity matrices to establish empirical functional networks. By imposing a Gaussian null model on randomly sampled empirical per-subject networks we simulated 100 artificial networks for each condition (rest, syllable, speech). The simulated networks were used in a leave-one-out analysis paradigm to compute 100 leave-one-out mean networks by omitting one graph at a time and averaging across the remaining cohort. (III) Group-averaged networks were computed for each condition in both empirical and simulated network cohorts and were considered as points of reference within the associated group. (IV) The established mean networks were used to compute group-specific resolution parameters for all subsequent modularity maximization calculations.

Figure 2. Group-specific resolution parameters were defined as maximizers of a quality function and robustness of the modular structure in group-averaged networks

(A) The resolution parameter γ was defined as the solution to an optimization problem posed for every condition (rest, syllable, speech, I-III) in both empirical (left column) and simulated (right column) networks. The value of γ that maximized a quality function f(γ) reflecting the Newman modularity Q(γ) of the respective group-averaged network with respect to the modularity score of an associated random graph Qrnd(γ ) was used in all subsequent modular decomposition calculations in the corresponding group. Thus, condition-specific resolution parameters were defined as argmax f(γ) (vertical dashed lines). (B) The quality of the computed reference partitions of the group-averaged networks was assessed using perturbation testing. Randomizing empirical (left column) and simulated (right column) mean networks, F0 and G0, respectively, with rewiring probability α yielded perturbed graphs F0(α) and G0(α), respectively. Shown is the mean partition distance (averaged across 100 rewired networks for each value of α with shaded areas indicating standard deviations from the mean) between actual and perturbed resting state (I), syllable- (II) and speech-production (III) networks (blue) in comparison to the average partition distance between the associated original and randomized null model graphs pd(R0, R0(α)) (red).

Figure 3. Spatial distribution of communities in the group-averaged empirical and simulated networks

The modular structure of empirical (I) and simulated (III) group averaged networks at rest (A), while uttering syllables (B) and during speech production (C) is shown on 3-D brain renderings in axial orientation with nodal colors illustrating regional community affiliations. Changes in module membership between empirical (F0) and simulated networks (G0) are visualized by migration flow diagrams (II). The nodes of F0 and G0 are arranged on the left and right arch, respectively, color-coded by module membership. Nodal migration between communities in the empirical and simulated networks is illustrated by color gradients between the opposing arches. Abbreviations: Acc = nucleus accumbens; Am = amygdala; Cd = caudate; mFG/MFG/SFG = medial/middle/superior frontal gyrus; GPe = external segment of globus pallidus; HipG = hippocampal gyrus; MOrG/mOrG = medial/middle orbital gyrus; THpdf/THpm/THs = prefrontal/premotor/somatosensory part of the thalamus.

Figure 4. Sensitivity of community layouts with respect to the group-averaged reference partitions

Visualization of communities in the group-averaged networks G0 (inner-most ellipse) and in the constructed 100 leave-one-out graphs (G0\k)k≥1 (surrounding concentric ellipses) at rest (A), during syllable production (B) and while speaking (C). Each ellipse consists of 212 circular disks, with each disk representing a network node, color-coded based on community affiliation. Nodes are ordered following the group-averaged reference partition to make the display consistent across ellipses, such that each individual node always occupies the same relative position in all ellipses, from center to boundary. (D) Perturbations in community structure across leave-one-out graphs (G0\k)k≥1 with respect to the reference partition of the mean networks G0 across the resting state (gray circles), syllable production (white squares), and speaking (black triangles) to the respective mean network community architecture quantified by the partition distance pd. Horizontal red lines indicate median values across the respective cohort. The range of partition distance values within each group is illustrated by whiskers extending from medians to upper and lower quartiles plus 1.5 times the respective inter-quartile range. General linear hypothesis testing of the constructed linear mixed effect models in an all-to-all Tukey contrast at p ≤ 0.05 yielded significant differences in within-group perturbation sensitivity between rest and task as well as between tasks (all p ≤ 7.1×10−6).