## Abstract

Recent work in cognitive neuroscience has focused on analyzing the brain as a network, rather than as a collection of independent regions. Prior studies taking this approach have found that individual differences in the degree of modularity of the brain network relate to performance on cognitive tasks. However, inconsistent results concerning the direction of this relationship have been obtained, with some tasks showing better performance as modularity increases and other tasks showing worse performance. A recent theoretical model [Chen, M., & Deem, M. W. 2015. Development of modularity in the neural activity of children's brains. Physical Biology, 12, 016009] suggests that these inconsistencies may be explained on the grounds that high-modularity networks favor performance on simple tasks whereas low-modularity networks favor performance on more complex tasks. The current study tests these predictions by relating modularity from resting-state fMRI to performance on a set of simple and complex behavioral tasks. Complex and simple tasks were defined on the basis of whether they did or did not draw on executive attention. Consistent with predictions, we found a negative correlation between individuals' modularity and their performance on a composite measure combining scores from the complex tasks but a positive correlation with performance on a composite measure combining scores from the simple tasks. These results and theory presented here provide a framework for linking measures of whole-brain organization from network neuroscience to cognitive processing.

## INTRODUCTION

Recent work in cognitive neuroscience has moved away from analyzing the function of localized brain structures toward analysis of the brain as a network. Previous studies have shown that the human brain is organized into different subnetworks, termed modules (Sporns & Betzel, 2016; Power et al., 2011; Meunier, Lambiotte, & Bullmore, 2010; He et al., 2009; Meunier, Lambiotte, Fornito, Ersche, & Bullmore, 2009), which support different aspects of behavioral function, for example, modules for visual perception, motor control, and attentional processing (Bassett, Yang, Wymbs, & Grafton, 2015; Bertolero, Yeo, & D'Esposito, 2015; Bassett et al., 2011; Smith et al., 2009). Understanding the network organization of the brain has been advanced using graph theory to quantify various local and global properties of its organization, with the nodes of the network defined by brain regions and edges between nodes as connections, determined either by structural connectivity derived from diffusion tensor imaging or by functional connectivity derived from resting-state or task-based fMRI, between these regions (Rosenberg et al., 2016; Finn et al., 2015; Rubinov & Sporns, 2010; Bullmore & Sporns, 2009). The current work focuses on a global measure of network organization—modularity. Modularity characterizes the community structure of the network in terms of the relative strength of within- and between-module connections. Using Newman's algorithm, nodes in the network are sorted into modules so as to maximize this value separately for each individual (Newman, 2006; Girvan & Newman, 2002). Individuals differ in their modularity, and the degree of modularity has been found to relate to characteristics such as age (Chen & Deem, 2015; Geerligs, Renken, Saliasi, Maurits, & Lorist, 2015; Betzel et al., 2014; Chan, Park, Savalia, Petersen, & Wig, 2014; Meunier, Achard, Morcom, & Bullmore, 2009), mental state (Andric & Hasson, 2015; Godwin, Barry, & Marois, 2015), and neurological status (Fornito, Zalesky, & Breakspear, 2015; Alexander-Bloch et al., 2010, 2012).

Correlations between modularity and performance on a variety of tasks have also been reported, focusing on individuals within a developmental stage. However, there are inconsistencies regarding the direction of the relationship. For example, Stevens, Tappon, Garg, and Fair (2012) reported a positive correlation between modularity and performance on a visual working memory task, whereas Meunier et al. (2014) reported a negative correlation with odor recognition. Even within the same group of participants, the direction of the correlation varies as a function of task. Alavash, Doebler, Holling, Thiel, and Gießing (2015) report a positive correlation between modularity and visual working memory performance but a trend toward a negative correlation with a complex working memory span task. Thus, although there is accumulating evidence that whole-brain measures relate to behavioral performance (Bassett et al., 2015; Gu, Pasqualetti, et al., 2015; Gu, Satterthwaite, et al., 2015; Medaglia, Lynall, & Bassett, 2015; Power & Petersen, 2013; Power et al., 2011), the exact relationship between modularity and performance is unclear.

Deem (2013) proposed a theory derived from theoretical biology that posits that high-modularity systems afford greater evolutionary fitness at shorter timescales whereas low-modularity systems afford greater fitness at longer timescales. This general principle may help to explain why high modularity is beneficial for some tasks whereas low modularity is beneficial for others. Chen and Deem (2015) developed a computational model to examine this principle in recognition memory. Simulations showed that high-modularity architectures resulted in better performance in recognition memory with shorter response deadlines, whereas low-modularity architectures resulted in better performance with longer response deadlines. More generally, this principle leads to the prediction that high-modularity architectures are better for simple tasks, which are completed over a short timescale and draw mainly on a specific module, whereas low-modularity architectures are better for complex tasks, which take more time and that draw on the interaction of several modules. On the basis of this interpretation, the inconsistent previous findings relating modularity to performance might be due to variation in the complexity of the tasks.

## METHODS

### Participants

Fifty-two (18–26 years old, mean = 19.8 years old; 16 men and 36 women) students from Rice University participated in this study. Participants reported no neurological or psychiatric disorders. Informed consent was obtained according to procedures approved by the Rice University institutional review board. Participants were compensated \$50 for their participation.

### Resting-state fMRI

#### Imaging Data Acquisition

Resting-state fMRI scans were conducted at the Core for Advanced Magnetic Resonance Imaging at Baylor College of Medicine. Images were obtained on a 3-T Siemens (Erlangen, Germany) Magnetom Tim Trio scanner equipped with a 12-channel head coil. Foam pads were used to keep participants' heads stable during the scanning. A high-resolution T1-weighted structural image was acquired by using magnetization prepared rapid gradient-echo sequence in the sagittal direction (repetition time = 2500 msec, echo time = 4.71 msec, field of view = 256 mm, voxel size = 1 × 1 × 1 mm3). Three 7-min resting-state functional runs were obtained by using an EPI sequence as follows: repetition time = 2000 msec, echo time = 40 msec, field of view = 220 mm, voxel size = 3 × 3 mm2, and slice thickness = 4 mm. Each resting-state run had 210 volumes, and each volume had 34 slices in the axial plane to cover the whole brain. All 52 participants completed the imaging session.

#### Preprocessing

Image preprocessing was conducted using the AFNI software (AFNI version: AFNI_2011_12_21_1014; Cox, 1996). The first six volumes of each functional run were discarded to allow stabilization of the BOLD signal. Preprocessing procedures basically followed the pipelines recommended by Jo et al.'s (2013) article and AFNI's script afni_proc.py. Each functional run was preprocessed separately, including de-spiking of large fluctuations for some time points, slice timing, and head motion correction. Then, each participant's functional images were aligned to that individual's structural image, warped to the Talairach standard space, and resampled to 3-mm isotropic voxels. Next, the functional images were spatially smoothed with a 4-mm FWHM Gaussian kernel. A whole-brain mask was then generated and applied for all subsequent analyses. A multiple regression model was then applied to each voxel's time series to regress out several nuisance signals, including third-order polynomial baseline trends, six head motion correction parameters, and six derivatives of head motion.1 Band-pass (0.005–0.1 Hz) filtering and outlier censoring were conducted in the same regression model. The outlier censoring removed the time points in which head motion exceeded a distance (Euclidean norm) of 0.2 mm with respect to the previous time point or in which >10% of whole-brain voxels were considered as outliers by AFNI's 3dToutcount. The residual time series after application of the regression model were used for the following network analyses.

#### Network Reconstruction and Modularity Calculation

The whole-brain network was reconstructed based on several prominent parcellations of the brain: Brodmann's areas (BAs); Eickhoff–Zilles atlas (Eickhoff et al., 2005); functional areas identified in Power et al. (2011); spatially coherent areas identified in Craddock, James, Holtzheimer, Hu, and Mayberg (2012); and a recently published parcellation based on structural and function data from the Human Connectome Project (Glasser et al., 2016). We illustrate the network reconstruction methods for the 84 BAs (42 BAs for the left and right hemispheres, respectively). These 84 BAs were derived from the Brodmann atlas in AFNI Talairach–Daemon (AFNI version: AFNI_2011_12_21_1014; Lancaster et al., 1997, 2000). This Brodmann atlas mainly covered the cerebral cortex of the brain. Each BA served as a node of the network, and the mean time series was extracted by averaging the preprocessed time series across all voxels in that BA. The edge between any two nodes in the network was defined by functional connectivity—that is, the Pearson correlation of the time series for those two nodes. Edges for all pairs of nodes in the network were estimated, resulting in an 84 × 84 correlation matrix. The correlation matrix was calculated for each run and each participant separately, and an averaged correlation matrix across three runs was obtained for each participant (Figure 1A). We did not concatenate the three runs for each participant because this would introduce a large discontinuity in the fMRI signal at the point of concatenation, leading to spurious correlation. We applied Newman's algorithm (Newman, 2006) to each individual's averaged correlation matrix to calculate the modularity value for that participant. To do this, we first took the absolute values of each correlation and set all the diagonal elements of the correlation matrix to zero. Fewer than 0.05% of the elements in the matrix were negative. The resulting matrix was binarized by setting the largest 400 edges (i.e., 11.47% graph density) in the network to 1 and all others to 0 (Figure 1B). We also considered the top 300 (8.61%) and 500 (14.34%) edges, respectively, to assess the consistency of correlation with modularity across different numbers of edges. This binarization process has been argued to improve detection of modularity by increasing the signal-to-noise ratio (Chen & Deem, 2015). Modularity was defined as in Equation 1, where Aij is 1 if there is an edge between BAs i and j and 0 otherwise, the value of ai = ΣjAij is the degree of BA i, and e = ½ Σiai is the total number of edges, here set to 300, 400, and 500, respectively. Newman's algorithm was applied to the binarized matrix to obtain the (maximal) modularity value and the corresponding partitioning of BAs into different modules for each participant.2
$M=12e∑allmoduleareas∑i,jwithinthismoduleAij−aiaj2e$
1
Figure 1.

(A) The group average correlation matrix in which each element represents the edge (i.e., functional connectivity) between each pair of 84 Brodmann nodes. (B) The group average binarized correlation matrix by setting the off-diagonal top 400 edges of correlation matrix in A to 1, whereas all others to 0. (C) The group average whole-brain modular organization with the BAs in each module being marked by the same color. The modular partition results were mapped onto a brain surface model for display by using SUMA in AFNI. (D) The group average binarized correlation matrix sorted by the group level modular partition. The modular color markers are the same as in C.

Figure 1.

(A) The group average correlation matrix in which each element represents the edge (i.e., functional connectivity) between each pair of 84 Brodmann nodes. (B) The group average binarized correlation matrix by setting the off-diagonal top 400 edges of correlation matrix in A to 1, whereas all others to 0. (C) The group average whole-brain modular organization with the BAs in each module being marked by the same color. The modular partition results were mapped onto a brain surface model for display by using SUMA in AFNI. (D) The group average binarized correlation matrix sorted by the group level modular partition. The modular color markers are the same as in C.

A group average correlation matrix (Figure 1A) was obtained by averaging the mean correlation matrices across all participants. The partitioning into modules was also conducted at the group level. To assess individual variability in the modular structure of the brain, we maximally aligned each participant's partitioning of BAs with the partitioning identified from the group average correlation matrix. When comparing the distance between two assignments of BAs to modules, we take into account that the labeling of the modules can be permuted and that the number of modules of the two assignments need not be identical. Thus, the maximal alignment is the one that minimizes the distance over all permutations of the assignment with the greater (or equal) number of modules. The value d is the number of nodes whose modular assignment differed between the participant and the group average, as defined by Equation 2.
$d=minP∑i=1841−δm1i,Pm2i$
2
BAs are indexed by i, m1i denotes the module to which BA i belongs in Assignment 1, m2i denotes the module to which BA i belongs in Assignment 2, P is a permutation of module labeling, and we have assumed that the number of modules in Assignment 1 is not greater than that in Assignment 2. To assess which cortical regions drove this individual variation in modular structure, we also calculated, for each of the 84 BAs, the number of participants for whom that BA was assigned to a different module than the assignment for group average data.

Although BAs have the virtue of covering most of the gray matter, many of the areas are quite large, meaning that each BA likely contains multiple functionally selective regions. Given that each BA can only be assigned to one module, that modular assignment may only be appropriate for a subregion, thereby potentially reducing the relation between modularity and behavioral performance. Thus, we also calculated modularity for each participant based on another anatomical parcellation, which is available in AFNI (Eickhoff–Zilles macro labels atlas from N27 template in Talairach space; Eickhoff et al., 2005), and some functional parcellations, including Power et al. (2011), Craddock et al. (2012), and Glasser et al.'s (2016) networks. We used 90 of the 115 masks from the Eickhoff–Zilles atlas, excluding those in the cerebellum. Power et al. defined many small spheric nodes that are associated with specific cognitive functions identified by meta-analyses of task-based fMRI.3 Craddock et al. parceled the gray matter into many spatially coherent clusters, identifying clusters based on homogeneity of local functional connectivity. We chose the 100-node version of Craddock et al.'s parcellation, which has a similar number of nodes with the Brodmann network. Glasser et al. used multiple properties (e.g., cortical myelin content, cortical response to task functional MRI, resting-state functional connectivity pattern) of MRI data from the Human Connectome Project, generated feature gradient maps to identify the boundaries of structurally and functionally homogenous areas on the cortical surface model, and then created 180 areas in each hemisphere.4 The correlation matrices for functional parcellations were binarized with a threshold of percent cost (11.47%), which equates the proportion of top edges to that for the Brodmann network of 400 edges.

All 52 participants took part in the operation span and task-shifting tasks. Forty-three of them participated in the ANT task and visual arrays task, and 44 participants took part in the traffic light task, as these were done in a different session; not all participants returned to be involved in all tasks. The interval between neuroimaging and behavioral sessions varied from 0 (i.e., measuring resting-state fMRI and behavior on the same day but during different sessions) to 140 days. Forty participants completed all of the behavioral tasks.

#### Operation Span

Participants were administered the operation span task (Unsworth et al., 2005), which is a standard measure of working memory capacity with high test–retest reliability (Redick et al., 2012). On each trial, participants saw an arithmetic problem for 2 sec, for example, (2 × 3) + 1, and were instructed to solve it as quickly and accurately as possible. Participants judged whether a digit presented on the next screen was a correct solution to the previous arithmetic problem. After the arithmetic problem, a letter was presented on the screen for 800 msec that participants were instructed to remember. A single trial consisted of repeating these steps six or seven times. At the end of each trial, participants recalled the letters in the order in which they were presented. The recall screen consisted of a 3 × 4 matrix of letters, and participants used the mouse to check the boxes aside letters during recall. There were 12 trials for each set size (six or seven arithmetic problem–letter pairs, randomly presented), resulting in 156 letters and 156 arithmetic problems. The dependent measure was the total number of letters recalled at the correct position with a maximum of 156. Before the experiment, participants practiced with (1) a block involving only letter recall, (2) a block involving only arithmetic problems, and (3) a mixed block in which the trial had the same procedure as in the experimental trials. Practice blocks included only set sizes of 2, 3, or 4.

A visual arrays task was used to tap visual STM capacity. In this task, participants fixated the center of the screen. Arrays of two to five colored squares at different screen locations were presented for 500 msec, followed by a blank screen for 500 msec, and then by multicolored masks for 500 msec. A single probe square was then presented at one of the locations where the colored squares had appeared. Participants had to judge whether the probe square had the same color as the one at the same location. The order of different array sizes was random. There were 32 trials at each array size—half of which required positive responses; and half, negative. The visual STM score was calculated by averaging the accuracy across all array sizes.

Participants heard a list of spoken digits, at the rate of one per second. After the last digit in each list, a blank screen prompted participants to recall the digits in the order presented by typing them on the keyboard. Participants were tested on five trials for each set size starting at a set size of two to a maximum of nine. The program was terminated if participants scored fewer than three correct trials at a given set size (60% accuracy). Digit span was calculated by estimating the set size at which a participant would score 60% through linear interpolation between the two sizes spanning this accuracy threshold.

Participants responded to an object (blue and yellow squares and triangles) according to a preceding cue word. If the cue was “color,” participants pressed a button to indicate whether the object was blue or yellow, and if the cue was “shape,” they pressed a button to indicate whether the object was a square or a triangle. The same buttons were used for the two tasks. RT was recorded from the onset of the object. For half of the trials, the cue was the same as that in the previous trial (a repeat trial), and for the other half, the cue changed (a switch trial). For each condition, to take into account both RT and accuracy in a single measure, we calculated an inverse efficiency (IE) score (Townsend & Ashby, 1983) defined as mean RT/proportion correct. The task-shifting cost was measured as the difference in IE scores between repeat and switch trials. Cue–stimulus interval (CSI) was varied, which is the time between onset of the cue and onset of the object, using CSIs of 200, 400, 600, and 800 msec. However, as the effect of modularity on IE did not differ for different CSIs, the data were averaged across CSI. In total, there were 256 repeat trials and 256 switch trials.

#### Attention Network Test

The ANT (Fan et al., 2002) was used to measure three different attentional components: alerting, orienting, and conflict resolution. This task involves a simple visual discrimination—that is, indicating whether a central arrow is pointing left or right via a mouse press. The arrow(s) appeared above or below the fixation cross, which was in the center of the screen. The central arrow appeared alone on a third of the trials and was flanked by two arrows on the left and two on the right on the remaining two thirds of the trials. The flanking arrow trials were evenly split between a congruent condition in which they pointed in the same direction as the central arrow and an incongruent condition in which they pointed in the opposite direction. In the neutral condition, there were no flanking arrows. The timing of the appearance of the arrow(s) was cued by zero, one, or two asterisks, which appeared for 100 msec on the screen. The interval between offset of the cue and onset of the arrow was 400 msec. The four cue conditions were (1) no cue condition; (2) a cue at fixation; (3) double-cue condition, with one cue above and the other below fixation; and (4) spatial cue condition, where the cue appeared above or below the fixation to indicate where the arrows would appear, provided both timing and location information. Thus, the task had a 4 cue × 3 flanker condition factorial design. The experimental trials consisted of three sessions, with 96 trials in each session and eight trials in each cell of each condition. For half of all trials, arrows were presented above the fixation; and for the other half, below. In addition, for half of the trials, the middle arrow pointed left; and for the other half, right. The order of trials in each session was random. Before the experimental trials, 24 practice trials with feedback were given to the participants.

RTs and accuracy were recorded with mean RT based on correct trials only. IE was calculated for each condition. The alerting effect was computed by subtracting the IE for the no-cue condition from the IE for the double-cue condition. The orienting effect was computed by subtracting the IE for the center cue condition from the IE for the spatial cue condition. The conflict effect was computed by subtracting the IE for the congruent condition from the IE for the incongruent condition. To make the direction of the conflict effect the same as alerting and orienting effects, we reversed the sign of the conflict effect. Thus, the more negative the conflict effect value, the greater the interference from the incongruent flankers. The alerting and orienting effects both tap into sensitivity to exogenous, or stimulus-driven, cues within the visual domain, whereas the conflict effect taps individuals' ability to direct attention to the central cue and ignore conflicting flankers, thus drawing on endogenous, or participant-driven, attentional abilities (Raz & Buhle, 2006).

In this task, participants saw a red square in the center of screen, which was replaced after an unpredictable time delay (from 2 to 3 sec) by a green circle. Participants pressed a button as quickly as possible when they saw the green circle. There were 25 trials in total. Mean RT was calculated for each participant.

## RESULTS

### Modular Organization of Resting-state Network

For the calculations with the BA network of 400 edges (11.47%), modularity values ranged across participants from 0.33 to 0.59, with a mean of 0.47 on a scale from 0 to 1.0. For the BA network of 300 edges (8.61%) and the BA network of 500 edges (14.34%), the means were 0.53 (range = 0.39–0.64) and 0.42 (range = 0.31–0.52), respectively. With the BA network of 84 nodes and 400 edges used in our analysis, a value greater than 0.29 is taken to indicate a significant degree of modularity as random voxel data led to M = 0.25 (SD = 0.022, max value out of 52 = 0.29) for our setup. The results reported below were based on the BA network of 400 edges (11.47%) without tissue-based regression, unless indicated otherwise. Individuals differed to some degree in the number of modules, with most (31/52) having four modules but some having three modules (14/52) or five modules (7/52). The organization of brain regions into modules is described below, starting with the results from the group average data, followed by a discussion of how this organization varied across individuals.

At the group level, the 84 BAs were organized into four modules (Figure 1C and D). For all modules, the brain regions making up the module were contiguous and symmetrical, with the left and right BAs assigned to the same module for 40 of the 42 BA labels. The first module (a sensory-motor module) consisted of BAs covering bilateral primary somatosensory cortex (BAs 1, 2, and 3), primary motor cortex (BA 4), somatosensory association cortex (BA 5), premotor cortex and supplementary motor cortex (BA 6), supramarginal gyrus (BA 40), and ventromedial pFC (BA 25).5 The second module included auditory and language-related regions covering both Broca and Wernicke's areas, although areas were bilateral, consisting of bilateral auditory cortex (BAs 41 and 42), superior temporal gyrus (BA 22), temporal pole area (BA 38), insular gyrus (BA 13), primary gustatory cortex (BA 43), ventral part of dorsolateral pFC (BA 46), and inferior frontal gyrus, including pars opercularis (BA 44), pars triangularis (BA 45), and pars orbitalis (BA 47). The third module overlapped considerably with the default mode network (Raichle et al., 2001), consisting of bilateral angular gyrus (BA 39), inferior temporal gyrus (BA 20), middle temporal gyrus (BA 21), and some frontal regions, including FEFs (BA 8), the dorsal part of dorsolateral pFC (BA 9), and anterior pFC (BA 10) as well as some medial regions, such as anterior cingulate gyrus (BAs 24 and 32 and left BA 33) and a part of posterior cingulate gyrus (left BA 31). The fourth module was the largest and most diverse. It included visual, attentional, and medial memory-related areas. More specifically, this module included bilateral OFC (BA 11); posterior superior parietal cortex (BA 7); primary, secondary, and associative visual cortex (BAs 17, 18, and 19); and fusiform gyrus (BA 37) as well as some medial regions, including the posterior cingulate cortex (BAs 23, 29, and 30 and right BA 31), a part of anterior cingulate gyrus (right BA 33), piriform cortex (BA 27), entorhinal cortex (BAs 28 and 34), and perirhinal cortex (BAs 35 and 36). The four modules roughly replicated prior results on various parcellation schemes (BAs using Newman's algorithm: Chen & Deem, 2015; AAL atlas using Newman's algorithm: He et al., 2009; 8 × 8 × 8 mm3 cubic nodes within the coverage of AAL atlas using Louvain algorithm: Meunier et al., 2010; Meunier, Lambiotte, et al., 2009). We also obtained group level modular organizations for our data for other parcellations, which revealed four modules for Power and Craddock's nodes, three for Glasser's nodes, and five for the Eickhoff–Zilles nodes. The modular organization was largely consistent across these different networks for three of the four modules from BAs (i.e., the sensory-motor module, the default-mode module, and the diverse module that covered the occipital, dorsal parietal, and some frontal regions); however, the auditory/language module was not evident in all other networks (for modular organizations in other networks, see Supplementary Figure 2 available at the Open Science Framework: osf.io/9tmhc/?view_only=7bafc4494c8e49f8a1b8c51df5823b5a). Hence, the number of modules and their constituent brain regions were quite similar irrespective of whether an anatomical or functional parcellation scheme was used, although some differences were observed.

Although the above modules represent those derived from the average correlation matrix, the assignment of brain regions to modules differed considerably across participants, with some brain regions showing a high degree of variation and others showing little. Figure 2A shows for each brain area the number of individuals for which that area was in a module different from the average. In low-level sensory and motor area, for example, posterior visual cortex and primary somatosensory and motor cortex, the assignment to a module differed from the group average for only a few participants. In contrast, for brain regions associated with higher-order cognitive functions, for example, lateral pFC, there was large variation across participants. In some temporal and parietal regions, module identity differed from the group average for about half of the participants. The medial ventral frontal lobe had the most participants deviate from the group average, which most likely was due to the distorted magnetic field in this region, resulting in a poor signal-to-noise ratio with the typical EPI sequence. Notably, however, cognitive control regions that do not experience such signal loss also showed considerable variability in module assignment across individuals.

Figure 2.

(A) The distance map showing how many participants' module identities differ from group average in each BA. (B) The scatterplot showing average distance across 84 BAs for each participant against modularity value as well as the distributions for two measures.

Figure 2.

(A) The distance map showing how many participants' module identities differ from group average in each BA. (B) The scatterplot showing average distance across 84 BAs for each participant against modularity value as well as the distributions for two measures.

To quantify individuals' difference in modular organization relative to the group average, we computed the average distance of that individual's modular organization to the modular organization of the group average data, as described above. Distance ranged from 14 to 48 with a mean of 33.8. Figure 2B shows the relation between individual's modularity value (M) and this distance measure and includes a depiction of the distribution of both measures. There was a significant negative correlation (r = −.36, p = .008) between an individual's modularity score and their distance from the group average modular structure, indicating that the modules identified for high-modularity individuals were closer to the group average modules than were those for low-modularity individuals.

### Behavioral and Correlation Analyses

Figure 3 depicts the relation between modularity and the composite scores, with the complex composite score on the right and the simple composite score on the left. The results for both conformed to predictions, a marginally significant negative correlation between complex composite scores and modularity (r = −.29, p = .067) and a positive correlation between the simple composite scores and modularity (r = .41, p = .008; correlations between modularity with each of the task measures are available online at the Open Science Framework: osf.io/9tmhc/?view_only=7bafc4494c8e49f8a1b8c51df5823b5a). A test for the difference in dependent correlations (Meng, Rosenthal, & Rubin, 1992) showed that the two correlations differed significantly (z = 3.09, p = .002), confirming that the relation between modularity and performance was mediated by task complexity. We also correlated the complex and simple composite scores with the modularity values derived from the binarized matrices based on 300 and 500 edges, and similar patterns were observed: (1) 300 edges (8.61%): r = −.32 and p = .044 for complex score and r = .33 and p = .037 for simple score, difference: z = 2.84, p = .0045, and (2) 500 edges (14.34%): r = −.30 and p = .059 for complex score and r = .34 and p = .032 for simple score, difference: z = 2.80, p = .0052. Thus, the pattern of correlations was highly consistent across differences in graph density.6

Figure 3.

The relation between modularity and the composite scores with the simple on the left and the complex on the right. The center of the figure depicts the theoretical prediction from Chen and Deem (2015) relating performance to tasks at different levels of complexity for individuals with high and low modularity. The blue lines represent the linear fit.

Figure 3.

The relation between modularity and the composite scores with the simple on the left and the complex on the right. The center of the figure depicts the theoretical prediction from Chen and Deem (2015) relating performance to tasks at different levels of complexity for individuals with high and low modularity. The blue lines represent the linear fit.

Modularity derived from another anatomical network (Eickhoff–Zilles) had a marginally significant negative correlation with the complex composite score (r = −.305, p = .056) and a nonsignificant positive correlation with the simple composite score (r = .19, p = .24). The difference between the two correlations was significant (z = 2.16, p = .03). This pattern basically replicated that from the Brodmann network. Modularity derived from Power et al.'s network (Power et al., 2011) had a nonsignificant negative correlation with the complex composite score (r = −.25, p = .12) and a near-zero correlation with the simple composite score (r = −.057, p = .73). The difference between the two correlations was not significant (z = 0.85, p = .40). These findings most likely result because of the much lower coverage of gray matter for the Power et al.'s nodes than for the BAs. On the basis of our calculations of the total number of voxels of the brain areas covered by the masks from the two sets of nodes, the BAs covered about three times as much gray matter as the areas defined by Power et al.'s (2011) nodes. For modularity based on Craddock et al.'s 100-node parcellation and a recently released functional parcellation with greater gray matter coverage (Glasser et al., 2016), patterns of correlations with the behavioral composite scores were similar to that for the Brodmann network, but the correlations did not reach significance (r = −.217, p = .18 for the complex composite and r = .154, p = .343 for the simple composite for Craddock's network; r = −.257, p = .109 for the complex composite and r = .151, p = .352 for the simple composite for Glasser's network). However, there was a marginally significant difference between the two correlations (z = 1.77, p = .077) for Glasser's network, but the difference did not reach significance for Craddock's network (z = 1.61, p = .108). Aside from Power et al.'s network, the correlations with behavior for different parcellation schemes were similar in showing a negative correlation with the complex composite and a positive correlation with the simple composite, with the difference between the two being significant or marginally so.

Given that the interval between resting-state fMRI session and behavioral testing session varied substantially across participants, we investigated whether the strength of correlations with modularity differed as a function of this interval. For each task, we regressed the dependent measure on modularity, absolute value of the number of days between resting-state fMRI and task completion, because for a few participants, tasks were completed before fMRI data were collected and the interaction of these two variables. Rather than perform this analysis with all of the dependent measures of modularity described above, we used only the BA-network 400-edge modularity measure, as this network showed the strongest correlations with the simple and complex composite scores when we collapsed time interval.

Among the complex tasks, operation span and conflict from the ANT task showed a decreasing correlation with modularity as the number of days increased, with the interaction between modularity and days being significant for operation span (p = .02) and marginally so for conflict (p = .07). For both tasks, correlations were moderately high at the shortest interval but declined substantially over days. Task shifting did not show a significant interaction between modularity and days (p = .22). However, given that operation span and shift cost had the largest range of days and included the shortest intervals, we also computed a composite score combining standardized operation span and shift cost scores into a single measure. For this composite measure, there was a significant interaction between days and modularity (p = .04), with correlations within day groups ranging from −.59 (p = .04) for Day group 1 to .04 (p = .89) for Day group 4.

For the remaining tasks, visual STM and digit span showed no sign of an interaction between modularity and number of days (visual STM: p = .89, digit span: p = .92) nor did any of the simple tasks (orienting and traffic light: both ps > .73). It is unclear whether this failure to find an interaction relates to specifics of these tasks or to the fact that all of the day intervals, including the shortest one, were quite long.

Figure 4 depicts relations between modularity and the dependent variable as a function of days. Participants were divided into day groups such that the number of participants in each group was approximately equal, and then the correlations between the dependent measure and modularity were plotted for each day group. For operation span and task shifting, there were four such day groups (Group 1: 0–11 days, n = 14; Group 2: 11–31 days, n = 12; Group 3: 33–43 days, n = 12; Group 4: 44–82 days, n = 14). For the ANT, visual arrays, traffic light, and digit span tasks, there were three day groups (Group 1: 30–43 days, n = 13; Group 2: 44–82 days, n = 14; Group 3: 100–140 days, n = 16). Note that Groups 1 and 2 for the latter tasks have approximately the same range of days as for Groups 3 and 4 for operation span and shifting. The figure includes the three complex tasks that showed significant or marginally significant interactions between days and modularity and also the results for the orienting effect, which showed a significant positive correlation with modularity overall with no change across day groups.

Figure 4.

Correlation between individual differences in modularity and task performance as a function of time between neuroimaging and behavioral testing for the operation span task (green), the task-shifting task (red), conflict effect of the ANT (purple), and orienting effect of the ANT (blue). Error bars are 95% confidence intervals around the correlation values.

Figure 4.

Correlation between individual differences in modularity and task performance as a function of time between neuroimaging and behavioral testing for the operation span task (green), the task-shifting task (red), conflict effect of the ANT (purple), and orienting effect of the ANT (blue). Error bars are 95% confidence intervals around the correlation values.

## DISCUSSION

The current study examined the application to brain organization of a theory derived from theoretical biology, which posits that high-modularity systems are advantageous over short timescales, whereas low-modularity systems are advantageous over longer timescales. In testing this theory with respect to the relation of brain organization to behavior, we related timescale to task complexity, as simpler tasks have fewer cognitive steps and therefore take less time to complete than do more complex tasks that entail a greater number of steps. Using Newman's algorithm to segregate brain regions into modules, we determined the modularity value for each participant and correlated modularity with behavioral performance, testing whether we would find the predicted interaction between complexity and modularity. The modules uncovered in this process consisted of subnetworks of contiguous regions that had fairly transparent mappings to cognitive functions. Considerable variability in terms of the identity of modules and the overall modularity value was found across participants. The findings for task correlations were generally consistent with the proposed theory. Below, we summarize the findings on modularity and relation of modularity to behavior and discuss their implications for theory.

### Modular Brain Network and Individual Differences

The four modules uncovered at the group level matched to a large extent those uncovered in prior studies using modularity analyses of resting-state and task-based fMRI (Chen & Deem, 2015; Meunier et al., 2010; He et al., 2009; Meunier, Lambiotte, et al., 2009). It is also the case that the modules detected using graph theoretical tools agree with modules discovered by other analytical approaches, such as independent component analysis (Smith et al., 2009) or clustering analysis (Blank, Kanwisher, & Fedorenko, 2014; Yeo et al., 2011). Taken together, these findings indicate that the human brain is intrinsically organized into functionally different modules.

Although the group data revealed a coherent set of modules, there was considerable variability across individuals in terms of the assignment of brain regions to modules, with interesting patterns regarding which regions were more or less likely to vary in module assignment. Specifically, brain regions involving motor or primary or secondary sensory processes, such as visual, somatosensory, or auditory, showed little variability. On the other hand, regions associated with higher-level functions like cognitive control or working memory, namely, dorsolateral prefrontal or parietal regions, showed much more variability. These findings are consistent with claims that these high-level regions are domain general and can be associated with a variety of sensory or motor processes or representations depending on the current demands of the system. It is unclear, however, why these domain-general regions might be preferentially associated during resting state with different sensory or motor regions for different individuals, for instance, auditory regions for one individual but visual regions for another. Perhaps these alliances depend on whatever individuals tended to think about during their resting-state scans or they could perhaps reflect more permanent preferences in allocation of attention because of greater experience or interest in certain domains over others. There was also a tendency for individuals with lower modularity to deviate more from the group average modules than individuals with higher modularity (Figure 2B). Less modular individuals have, by definition, a smaller difference between the within-module correlations and the between-module correlations. One explanation for this trend therefore is that, for less modular individuals, it is more likely that modules are more loosely defined or that Newman's algorithm will identify an idiosyncratic set of nodes to maximize the difference between within- and between-module correlations.

### Time-sensitive Correlations

One unanticipated finding from the current study was that the relationship between modularity and task performance depended on the time interval between neuroimaging and behavioral testing. This result is clearest with the complex tasks of operation span and task shifting and the conflict measure from the ANT. In all three cases, the strongest correlations were observed for short intervals, with correlations approaching zero at long intervals.

One possible explanation for these time-sensitive correlation patterns is that neither modularity nor task performance has stable individual differences. Rather, these measures may all drift over time. Poldrack et al. reported substantial fluctuations in the connectome structure of a single individual over the course of 18 months of testing (Poldrack et al., 2015). The stability of some of the behavioral measures, for example, operation span, has also been investigated. Whereas Klein and Fiss (1999) reported significant test–retest correlations on operation span with approximately 3-, 6- to 7-, and 10-week intervals, the raw test–retest correlations were lowest with the longest interval. At a given time point, both brain and behavior measures are reliable, which can explain why a correlation is observed between modularity and task performance with a short time interval. However, as time passes, the modular organization of the brain changes, as does task performance, in a sort of random walk that drifts over time. Thus, after a long interval, the correlation between modularity and task performance weakens. To test this hypothesis, future research should investigate the stability of both resting-state modularity and behavioral measures as well as the stability of the brain–behavior correlations over different intervals. Our results suggest that, rather than measures of an individual's network structure being a fingerprint—a stable, identifying property of an individual (Finn et al., 2015)—they are probably more like a snapshot, a reflection of how the brain was organized at a specific time. Understanding how and why brain organization changes over time remains an important area for research.

### Limitations and Future Directions

Although the pattern of results across different parcellation schemes was similar (aside from the Power et al., 2011, network), the strength of the correlations with the complex and simple composites and the significance of the difference in correlations varied. The strongest results were obtained for the two anatomical parcellation schemes, with both revealing a significant difference in the correlations with the simple and complex composites in the direction predicted. It is unclear why the results for the parcellations taking into account functional connectivity resulted in weaker results. Because previous work argued that inappropriate node definition might mischaracterize brain regions that have distinctive functions (Wig, Schlaggar, & Petersen, 2011) and found that nodes derived based on task-based fMRI studies did not align well with anatomical parcellations (Power et al., 2011), one might have expected the opposite—that is, that using network nodes determined at least in part from functional activations (e.g., Glasser et al., 2016) would result in modular structures more relevant to task performance and thus higher correlations of modularity with behavior. However, although the correlations from the functional parcellations were often not substantially lower than those determined from the Brodmann parcellation, they were never substantially higher. It should be noted that the only other study correlating behavior on simple and complex tasks to graph theoretic measures (Cohen & D'Esposito, 2016) also did not find consistently higher correlations using a functional atlas than an anatomical atlas (e.g., for their relatively simple sequence tapping task, the correlation with modularity from an anatomical parcellation was significant, p = .03, whereas that for a functional parcellation was not, p = .40). One factor to keep in mind is that modularity determined from Newman's algorithm does not use modules determined on a priori functional grounds when calculating modularity, irrespective of the network used. Instead, the connectivity determined from resting-state activity is used to determine how nodes should best be sorted into modules to maximize modularity. Across the different parcellation schemes examined in our study, the number of modules and their constituent brain regions was quite similar for the most part. It must be left to future work to determine exactly how the differences that did exist in modular structure arose and what the implications of these differences were for the determination of modularity values. Another issue that needs to be addressed is whether the combination of quite different tasks into the complex and simple composites negated any advantage for network nodes determined from particular functional domains. In future work, it will be important to manipulate task complexity within a given domain (e.g., manipulating working memory demands parametrically). It would also be important to determine if using a set of nodes limited to those domain-specific (e.g., auditory processing) and domain-general (e.g., exogenous attention) networks hypothesized to be involved in a particular task would result in higher correlations with behavior than whole-brain measures. Perhaps under these conditions, modularity determined from subnetworks defined by functional parcellation schemes would result in higher correlations with behavior than those defined anatomically. On the other hand, it is possible that whole-brain measures would remain superior because connectivity to other regions plays some understudied role—for instance, in the suppression of unrelated domain-specific or domain-general subnetworks (Todd, Fougnie, & Marois, 2005).

### Conclusion

The relationship between individual differences in whole-brain modularity and performance varies as a function of task complexity. Specifically, low-modularity individuals showed an advantage on complex tasks, whereas high-modularity individuals showed an advantage on simple tasks. These observations support predictions of a theoretical model, by which high modularity increases performance for simple tasks that operate at a short timescale and low modularity increases performance for complex tasks that operate at a longer timescale. This new understanding allows previously reported, and conflicting, results relating individual differences in brain organization to behavior to be understood in a general framework. Future work is needed to examine whether modularity as defined by subnetworks of functionally relevant systems would be superior to these whole-brain measures or, rather, the whole-brain measures would maintain an advantage because of the involvement of other regions whose contributions are less clear based on current findings.

## Acknowledgments

This work was partially supported by the T. L. L. Temple Foundation. M. W. D. and F. Y. were partially supported by the Center for Theoretical Biological Physics under NSF grant #PHY-1427654. We would like to acknowledge the contributions Jill Moore, Yuan Chang, and Elizabeth Baca made to data acquisition and analysis.

Reprint requests should be sent to Randi C. Martin, Department of Psychology, MS-25, Rice University, P.O. Box 1892, Houston, TX 77251, or via e-mail: rmartin@rice.edu.

## Notes

1.

Some previous resting-state fMRI studies also included averaged signals in the white matter and ventricle as nuisance signals and regressed them out. A recent study by Aurich, Alves Filho, Marques da Silva, and Franco (2015) showed that different preprocessing strategies with respect to these tissue-based signals had an impact on some graph theoretical measures, but this study did not evaluate the effect on the modularity measure. Because of Aurich et al.'s findings, we conducted an extra analysis in which the tissue-based (e.g., white matter and ventricle) regression was included in preprocessing by following the anaticor procedure in AFNI (Jo, Saad, Simmons, Milbury, & Cox, 2010). Specifically, we segmented an individual's structural image by using FreeSurfer (Dale, Fischl, & Sereno, 1999; Fischl, Sereno, & Dale, 1999). Then, white matter and ventricle masks were created and eroded. The averaged time series in eroded ventricle mask and regionally averaged time series within a 15-mm-radius sphere in eroded white matter mask were extracted and included as two additional nuisance signals in the regression model. Results in terms of modularity–behavior correlations were similar for both analyses without and with tissue regression. In the text, we report the results without regressing out tissue-based signals, but the results with this additional preprocessing step are reported in a table available on Open Science Framework.

2.

Because of the resolution limitation issue with the current community detection algorithm (Fortunato & Barthélemy, 2007), we also estimated modularity values by using the lowest hierarchy level in the Louvain algorithm (Blondel, Guillaume, Lambiotte, & Lefebvre, 2008), which could avoid resolution limit issue (Lancichinetti & Fortunato, 2009, 2014). Results in terms of modularity–behavior correlations based on Louvain method are similar to those with modularity calculated by the method described above and are reported in a table that is available at the Open Science Framework.

3.

The original Power et al.'s network consisted of 264 nodes. To apply it to our data, we first converted the coordinates provided in Power et al.'s article from Montreal Neurological Institute space to Talairach space by using a converter tool (Lancaster et al., 2007) in software GingerALE. Then, 10-mm-diameter spheric ROIs were created around coordinates. Eight ROIs in the cerebellum in Talairach space were excluded as they were not covered by images for some of our participants, resulting to 256 nodes in our analyses.

4.

The original Glasser et al.'s parcellation was based on the 2-D cortical surface model. We obtained the volumetric parcellation (figshare.com/articles/HCP-MMP1_0_projected_on_MNI2009a_GM_volumetric_in_NIfTI_format/3501911), which was projected to the Montreal Neurological Institute space. To apply this volumetric parcellation to our data, using AFNI script @auto_tlrc, we first warped the anatomical template onto which this functional parcellation was coregistered into Talairach space and registered it to the template used in AFNI with linear interpolation. Then, a set of masks for volumetric parcellation were warped into Talairach by using the same transformation and resampled to match the resolution of our data with nearest neighbor interpolation. Craddock et al.'s parcellation was applied to our data in a similar way.

5.

Left and right BA 25 had no connection with any other nodes when we binarized the correlation matrix, resulting in random assignment of these two nodes into this module.

6.

The results for the tissue-based regression and using the Louvain algorithm for computing modularity also gave similar results, which are reported in a table that is available at the Open Science Framework.

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