Modular Segregation of Structural Brain Networks Supports the Development of Executive Function in Youth
Graham L. Baum, Rastko Ciric, David R. Roalf, Richard F. Betzel, Tyler M. Moore, Russel T. Shinohara, Ari E. Kahn, Megan Quarmley, Philip A. Cook, Mark A. Elliot, Kosha Ruparel, Raquel E. Gur, Ruben C. Gur, Danielle S. Bassett, Theodore D. Satterthwaite
MModular Segregation of Structural Brain Networks Supports the Development of Executive Function in Youth
Graham L. Baum, a Rastko Ciric, a David R. Roalf, a Richard F. Betzel, c Tyler M. Moore, a Russell T. Shinohara, b Ari E. Kahn, c Megan Quarmley, a Philip A. Cook, d Mark A. Elliott, d Kosha Ruparel, a Raquel E. Gur, a Ruben C. Gur, a Danielle S. Bassett, c,e * & Theodore D. Satterthwaite a* Departments of Psychiatry, a Biostatistics and Epidemiology, b Bioengineering, c Radiology, d and Electrical and Systems Engineering e of the University of Pennsylvania, Philadelphia PA 19104 USA *=Co-senior authors Address correspondence to: Theodore D. Satterthwaite, M.D., M.A. 10th floor, Gates Building Hospital of the University of Pennsylvania 34th and Spruce Street Philadelphia, PA 19104 a r X i v : . [ q - b i o . N C ] A ug UMMARY:
The human brain is organized into large-scale functional modules that have been shown to evolve in childhood and adolescence. However, it remains unknown whether structural brain networks are similarly refined during development, potentially allowing for improvements in executive function. In a sample of 882 participants (ages 8-22) who underwent diffusion imaging as part of the Philadelphia Neurodevelopmental Cohort, we demonstrate that structural network modules become more segregated with age, with weaker connections between modules and stronger connections within modules. Evolving modular topology facilitated network integration, driven by age-related strengthening of hub edges that were present both within and between modules. Critically, both modular segregation and network integration were associated with enhanced executive performance, and mediated the improvement of executive functioning with age. Together, results delineate a process of structural network maturation that supports executive function in youth.
KEYWORDS : development, network, connectome, adolescence, executive, module ! NTRODUCTION
Modularity is a fundamental feature of complex systems, including social groups, cyber-physical systems, and diverse biological networks (Newman, 2006). A network module is a group of densely interconnected nodes, which often are the basis for specialized subunits of information processing (Sporns and Betzel, 2016). Functional neuroimaging studies have demonstrated that the human brain has a well-defined modular organization, as reflected in the presence of large-scale functional networks (Biswal et al., 1995; Damoiseaux et al., 2006; Power et al., 2011; Yeo et al., 2011). While the exact number and spatial distribution of functional network modules varies somewhat by analytic approach, a remarkable convergence exists across independent datasets and laboratories (Damoiseaux et al., 2006; Power et al., 2011; Yeo et al., 2011). Commonly described modules include somatomotor (Biswal et al., 1995), visual (Corbetta et al., 1998), default mode (Raichle et al., 2001; Buckner et al., 2008), and fronto-parietal systems (Dosenbach et al., 2007; Vincent et al., 2008). While brain network modules emerge very early in life (Fair et al., 2008; van den Heuvel et al., 2015; Thomason et al., 2013), a growing body of work has shown that these functional modules are refined during youth. During childhood and adolescence, functional modules become more distinct: connectivity within modules increases while connectivity between modules declines (Power et al., 2010; Fair et al., 2007; Fair et al., 2008; Fair et al., 2009; Dosenbach et al., 2010; Gu et al., 2015; Satterthwaite et al., 2013b; Supekar et al., 2009; Anderson et al., 2011). Such development allows for functional specialization, reducing interference among systems (Fornito et al., 2012) and facilitating cognitive performance (Hampson et al., 2010). Modularity is particularly relevant for executive function, which relies on co-activation of executive regions and reciprocal suppression of non-executive regions such as the default mode network (Anticevic et al., 2010; Barber et al., 2013; Persson et al., 2007; Satterthwaite et al., 2013a). Thus, available data suggests that development of network modularity may serve as a substrate for the evolution of executive capability during youth. Despite convergent evidence for the developmental emergence of functional network modularity, there is relatively scant data regarding the maturation of underlying structural brain networks that support this functional architecture (Hermundstad et al., 2014). Prior work demonstrates substantial correspondence between functional and structural measures of brain connectivity (Goñi et al., 2014; Honey et al., 2009; Mi š i ć et al., 2016), although structural connections tend to be a subset of densely connected, polysynaptic functional networks (Betzel et al., 2014; Hermundstad et al., 2013). Structural networks in adults are highly modular (Bassett et al., 2010; Bassett et al., 2011), but it remains unknown if this topology evolves substantially during youth. Correspondence between functional and structural data intuitively suggests that, like functional networks, structural networks should become increasingly segregated during development. However, prior studies using relatively small samples report conflicting results, including declining modularity (Chen et al., 2013), increasing modularity (Chen and Deem, 2015; Huang et al., 2015), or no change with age (Hagmann et al., 2010b; Lim et al., 2015). Larger sample sizes may be necessary for resolving the variability of findings reported in previous studies. ! RESULTS
We investigated the evolution of structural brain networks in a sample of 882 youth aged 8-22 who completed neuroimaging as part of the PNC (
Figure 1A ). As expected, executive function improved markedly with age (
Figure 1B) . Structural brain networks were constructed using nodes defined based on a parcellation of each subject’s structural image into 234 anatomically defined regions; structural connectivity between these nodes was estimated using deterministic tractography (
Figure 2 ). Each network node was assigned a priori to one of the functional network modules defined by Yeo et al. (2011). Although these module partitions were defined in an independent dataset, using a different imaging modality, the modularity quality of the functional partition imposed on subject-level structural connectivity matrices ( Q Yeo ) was highly significant ( p <1 × -10 ). Furthermore, data-driven analysis of structural networks using community detection procedures produced network modules that showed significant similarity to the a priori functional modules ( p <1 × -10 ; Figure S1 ). Segregation of structural network modules increases with age
We first sought to understand whether structural network modules became more segregated with age. To do this, we calculated the average participation coefficient for each subject’s network. The participation coefficient quantifies the relative balance of a brain region’s ! Greater modular segregation is therefore indicated by lower participation coefficient values, with reduced between-module and elevated within-module connectivity. We examined the development of modular segregation using a generalized additive model with penalized splines, which allows for statistically rigorous modeling of both linear and non-linear effects while minimizing over-fitting (Wood, 2004; Wood, 2011). Based on emerging evidence that diffusion-weighted imaging measures are systematically biased by motion artifact (Yendiki et al., 2013), we included in-scanner motion as a covariate in all models in addition to participant sex. To ensure that results reflected changes in network topology, rather than global differences in network connectivity, total network strength was also included as a covariate in all analyses (Li et al., 2012). The participation coefficient declined significantly with age (
Figure 3A ; p <1 × -10 ), indicating enhanced modular segregation. Developmental increases in modular segregation were differentially distributed across modules ( Figure 3B ), with the most robust declines observed in the somatomotor and default mode modules. To further understand which regions were driving these effects, we examined the participation coefficient of individual network nodes. As expected, the nodal participation coefficient declined in many regions (Figure 3C ), with many of the most significant reductions occurring in regions within the default mode system. Two exceptions to this overall trend were observed, with increasing participation coefficient in the right rostral frontal gyrus and frontal operculum. Next, we investigated the degree to which developmental effects on modular segregation were driven by changes in within-module connectivity, between-module connectivity, or both. We found that both effects were significant: within-module connectivity increased with age (
Figure 4A ; p <1 × -10 ), whereas between-module connectivity declined ( Figure 4B ; p <1 × -10 ). Moreover, modular segregation was reflected in individual network edges ( Figure 4C ), with permutation-based analysis revealing that a higher proportion of connections that strengthened with age were located within a module (
Figure 4D ; p <0.001). Results are robust to methodological approach
Given this strong evidence for developmental modular segregation, we next pursued a set of analyses to determine if our results were dependent upon specific methodological choices. We evaluated multiple parameters, including alternative measures of network segregation, higher-resolution node systems, and different edge measures. First, we examined a complementary measure of modular segregation: the modularity quality index of the Yeo et al. partition ( Q Yeo ) applied to individual subject-level structural connectivity matrices. For this metric, greater modular segregation is denoted by a greater Q Yeo value . As expected, this analysis revealed that modular segregation increased with age (
Figure 5A ; p =1.06 × -9 ). Second, while our primary results used the functional partition defined by Yeo et al. (2011), we additionally evaluated modular segregation using a data-driven partition of the structural connectome (see Figures S1 and S2 ). As seen in
Figure 5B , age-related decline in the mean participation coefficient remained evident ( p <1 × -10 ). Third, we directly calculated the modularity quality index of a data-driven partition of each subject’s structural connectivity matrix ( Q subj ). We observed that this statistic – which provides an individualized measure of modularity that is not dependent on a group-level partition – also increased significantly with age ( Figure 5C ; p =0.0007), indicating greater modular segregation. Fourth, we investigated the impact of using a more fine-grained ! Figure 5D ; p <1 × -10 ). Fifth, we evaluated developmental effects when using different measures of structural connectivity instead of mean fractional anisotropy. Results using raw streamline count ( Figure 5E ; p =6.52 × -7 ) or volume-normalized streamline density ( Figure 5F ; p =4.56 × -8 ) remained highly similar. Lastly, in order to rule out the possibility that observed results were driven by potentially confounding variables, we included additional model covariates such as total brain volume, handedness, race, and maternal education; results were unchanged ( p <1 × -10 ). Conversely, results were consistent when covariates such as total network strength, sex, and motion were removed from the model ( p <1 × -10 ). Modular segregation contributes to global network efficiency
Having established that network modules become more segregated with age, and that this finding was not dependent on specific analytic choices, we evaluated the impact of evolving network modularity on measures of network integration. Global network efficiency ( E glob ) provides a measure of network integration by quantifying information flow across a network as the shortest path between pairs of nodes (Bassett et al., 2009). In many networks, modularity and global efficiency are inversely related, as network segregation by module partitions extends the path length. However, in some cases it is possible for networks to become both more modular and more efficient; this unusual situation occurs when connectivity within modules is efficiently organized and hub edges form strong links between otherwise segregated modules (Sporns and Betzel, 2016). To determine which scenario characterized human neurodevelopment, we first examined the relationship between global efficiency and age while controlling for the covariates described previously. Replicating previous reports (Chen et al., 2013; Hagmann et al., 2010b), we found that global efficiency increases with age ( Figure 6A ; p <1 × -10 ). Next, we calculated the correlation between modular segregation (mean participation coefficient) and global efficiency, while co-varying for age to control for shared developmental trends. Mean participation coefficient was negatively associated with global efficiency ( Figure 6B ; p <1 × -10 ), suggesting that the development of network modules does not result in fragmentation, but rather is associated with global network integration. Age effects are concentrated in hub edges that promote network integration
To better understand this highly specialized association between network modularity and efficiency, we evaluated the edge betweenness centrality for each network connection. Edge betweenness identifies hub connections by providing a measure of how much a given network edge lies upon the shortest path of communication through a network, and thus contributes to global efficiency. Here we defined hub edges as those connections within the top quartile of edge betweenness across all network edges. Critically, edges that strengthened with age were enriched for hub edges ( p <0.001; see Figure 6C ). Both within- ( p <0.001) and between-module ( p <0.001) edges that strengthened with age had higher betweenness than expected by chance ( Figure 6D ; see
Supplemental Information) . Furthermore, the average strength of all within-module (
Figure 6E ; p <1 × -10 ) and between-module ( Figure 6F ; p <1 × -10 ) edges that strengthen with age was associated with global efficiency, suggesting that developmental effects are concentrated within connections that facilitate network integration. The striking combination of increasing modular segregation and enhanced global efficiency demonstrates that structural brain networks ! and more integrated in development. These dual processes are driven by selective strengthening of network hub edges, which are present within network modules and also provide critical links between increasingly segregated modules. Modular segregation mediates development of executive function in youth
Next, we evaluated the cognitive implications of modular segregation by examining associations with individual differences in executive function. Mean whole-brain participation coefficient was associated with improved executive performance ( p =0.018). At the level of individual modules, we found that segregation of the frontoparietal control system was uniquely associated with executive ability ( Figure 7A ; p =0.005), suggesting a network-specific substrate for executive function. As a final step, we examined whether age-related changes in executive function and modularity were related. Mediation analyses revealed that this was indeed the case ( Figure 7B ; p =0.006), suggesting that the development of segregated structural brain modules mediates the age-related improvement in executive function. These mediating effects were specifically driven by the frontoparietal module ( p =0.012). Similarly, global efficiency was associated with executive functioning ( p= p =0.002). To evaluate the specificity of these results, we examined associations with other domains of cognition, such as social cognition and memory performance. While no association with memory was found, modular segregation was also significantly associated with social cognition ( p =0.022), which was driven by segregation of the default mode module ( p =0.012). This effect mediated improvements in social cognition with age ( p =0.008). Together, these results demonstrate that developmental segregation of specific structural network modules may support the development of disparate cognitive domains. DISCUSSION
Capitalizing on a large sample of youth imaged as part of the PNC, we demonstrated that modules within human structural brain networks become increasingly segregated with age. This result was robust to specific methodological choices, and driven by a combination of enhanced within-module connectivity and declining between-module connectivity. Age related changes were concentrated within specific hub edges, allowing for networks to simultaneously become more modular and more integrated with age. Critically, segregation of network modules mediated the development of executive function during adolescence.
Segregation of structural network modules parallels development of functional networks
The delineation of robust, reproducible large-scale functional networks has had a tremendous impact on human neuroscience research (Power et al., 2011; Yeo et al., 2011). As a result, functional network modules have evolved to become the dominant framework by which human imaging data is interpreted. The conceptualization of the brain as a modular entity has had a particularly pronounced effect on theories of development, where convergent results have shown that functional network modules are present early in life (Thomason et al., 2013; van den ! š i ć et al., 2016), the disparity between developmental accounts of structural and functional network modules has been difficult to reconcile. Leveraging a large sample imaged as part of the PNC, we were able to resolve this discrepancy by demonstrating that structural network modules develop in a similar manner as functional brain networks, and become increasingly segregated with age. Modular segregation was present at every scale evaluated, including the whole network, individual network modules, and specific network nodes. Importantly, results were robust to a variety of analytic choices regarding network nodes, edges, and modules; such methodological replication is critical as parameter choices may sometimes impact inference (Hagmann et al., 2010a). For example, while we employed a commonly used set of functional network modules which were defined a priori, analysis of data-driven structural modules provided highly convergent results. Follow-up analyses revealed further parallels with functional imaging studies, and demonstrated that the process of modular segregation is driven by a combination of enhanced connectivity within a module as well as diminished connectivity between modules. Notably, the network modules that demonstrated the greatest developmental segregation were the somatomotor and default mode modules. Prior work has shown that both the default mode and somatomotor systems are highly segregated systems, with a low participation coefficient (Power et al., 2011). The relative isolation of these specific systems in the network may reflect a high degree of processing specialization (Power et al., 2013). The present results thus suggest that the differential evolution of structural network modules is similarly driven by each module’s network role. Modular networks become more integrated through strengthening of hub edges
In many networks, modular segregation is associated with reduced network integration, as measured by global efficiency. We found that this was not the case in development, and that increasing modularity was in fact associated with enhanced network integration. This robust association was the result of targeted strengthening of specific hub edges. These hub edges were present within but also between modules, allowing for integration across increasingly segregated partitions. These results are congruent with prior studies that have demonstrated that connections between network hubs strengthen preferentially with age (Baker et al., 2015), and that network efficiency increases during development (Chen et al., 2013; Hagmann et al., 2010b). The present data emphasize that increasing modular segregation does not result in isolation of functional sub-systems, but is associated with global network integration through strengthening of hub edges that facilitate both intra- and inter-module connectivity. ! tructural network maturation supports the development of executive function in youth Having defined a normative process of modular segregation, we evaluated the cognitive impact of this developmental effect. While controlling for age, we found that greater modular segregation of structural networks was associated with better executive performance. Critically, modular segregation mediated the observed improvement of executive performance with age, and was driven by segregation of the frontoparietal module. Associations between module segregation and cognition were domain-specific: segregation of the default mode mediated age-related improvements in social cognition, which is reliant on regions within that network (Buckner and Carroll, 2007; Schacter et al., 2007). The process of structural network segregation may allow for functional specialization, and reduce competitive interference between brain systems (Fornito et al., 2012). Such a process is suggested by convergent data from task-based fMRI, which has shown that individual differences in performance are related to selective recruitment of executive regions and suppression of activity elsewhere (Anticevic et al., 2010; Barber et al., 2013; Persson et al., 2007; Satterthwaite et al., 2013a). Furthermore, building on prior work that reported an association between intelligence and the global efficiency of structural (Li et al., 2009) and functional networks (van den Heuvel et al., 2009) in relatively small adult samples, we found that global efficiency also mediated developmental improvements in executive function. Taken together, the current data suggest that structural brain networks re-configure with age, becoming both more modular and more integrated. This specific topology may allow for both functional specialization within modules as well as coordination across modules, which is necessary for effective implementation of dynamic executive processes (Hutchison and Morton, 2015; Braun et al., 2015).
Limitations
Notwithstanding the strengths of this study, several limitations should be noted. First and foremost, this is a cross-sectional dataset, which has inherent limitations for studies of development (Kraemer et al., 2000). The mediating role that network maturation plays in the development of executive function could be further interrogated using longitudinal data. These limitations offer clear directions for additional research. Ongoing follow-up of this cohort will yield informative data, as will other large-scale studies of brain development, including the IMAGEN consortium (Schumann et al., 2010), the NKI-Rockland sample (Nooner et al., 2012), and the forthcoming Adolescent Brain and Cognitive Development Study. Finally, it should be noted that diffusion-based tractography remains limited in its ability to fully resolve the complex architecture of the structural connectome (Jbabdi et al., 2015).
Conclusions
In this report, we demonstrated that structural brain modules become more segregated with age. Strengthening of specific within- and between-module hub edges allowed for a simultaneous process of network integration that evolves in concert with modular segregation. Finally, both modular segregation and global network integration mediated the development of executive function in youth. These data resolve an ongoing debate in the field regarding the normative development of structural brain networks, and delineate an important new mechanism for the development of executive functioning in youth. These findings may be relevant for understanding how individual differences in brain development associate with risk-taking behaviors, which are linked to failures of executive function, and are a major source of morbidity ! ! XPERIMENTAL PROCEDURES
Participants
This study included 882 subjects between 8 and 22 years of age (mean age=15.06, SD=3.15; 389 males, 493 females) who were imaged as part of the PNC (Satterthwaite et al., 2014a; Satterthwaite et al., 2015). Participants were excluded from analyses due to gross structural brain abnormalities (Gur et al., 2013), a history of inpatient psychiatric treatment, current use of psychotropic medications, and medical disorders that could impact brain function. Participants were only included if both structural (Vandekar et al., 2015) and diffusion images (Roalf et al., 2016) passed rigorous quality assurance procedures. All participants completed the Penn computerized neurocognitive battery, which included 14 tests (Gur et al., 2002; Gur et al., 2012). Cognitive performance was summarized by a recent factor analysis (Moore et al., 2014) of both speed and accuracy data, which delineated three factors corresponding to the efficiency of executive function, episodic memory, and social cognition. For further details see
Supplemental Information . Image acquisition & processing
All high-resolution structural and 64-direction diffusion images were collected on the same 3T Siemens TIM Trio scanner using the same sequences (Satterthwaite et al., 2014a). The T1 image was processed using FreeSurfer version 5.3 (Fischl, 2012), and parcellated into 234 cortical and subcortical regions (Cammoun et al., 2012). The diffusion images were distortion corrected, skull stripped, and motion and eddy current corrected with FSL’s `eddy` tool (Jenkinson et al., 2012). Native-space T1 parcels were dilated by 4mm to extend regions into white matter, and co-registered to the first non-weighted (b=0) volume using a boundary-based rigid body transformation (Greve and Fischl, 2009). The diffusion tensor was estimated in DSI Studio and whole-brain deterministic fiber tracking was implemented with 1,000,000 streamlines per subject after removing all streamlines with length less than 10mm (Yeh et al., 2013). Edge weights in the adjacency matrix were defined by mean fractional anisotropy along streamlines connecting each pair of nodes (Mi š i ć et al., 2016; Bohlken et al., 2016; Baker et al., 2015). See Figure 2 and
Supplemental Information for more detail.
Measurement of modular segregation
Nodes were assigned to modules according to their overlap with seven functional networks defined a priori (Yeo et al., 2011); subcortical nodes were assigned to their own additional module. In addition to such a priori functional assignment, network modules were defined directly from the structural connectivity data using a generalized version of the Louvain community detection algorithm (Bassett et al., 2013; Blondel et al., 2008; Mucha et al., 2010). The similarity of data-driven partitions of the structural data were compared to the functional partition using the z -score of the Rand coefficient (Traud et al., 2011). Modular segregation was quantified using the participation coefficient, which measures the balance of between- versus within-module connectivity for each brain region (Guimerà and Nunes Amaral, 2005; Rubinov and Sporns, 2010). A higher participation coefficient at a given node indicates more between-module and less within-module connectivity. Each node’s participation coefficient was averaged over modules and the whole brain in order to evaluate modular segregation at multiple scales. To ! Supplemental Information . Statistical analyses of age-related changes in modular segregation
Linear and nonlinear effects of age were flexibly modeled with penalized thin-plate splines using generalized additive models (GAMs; Wood, 2004; Wood, 2011), which provide statistically rigorous analysis of non-linear effects while minimizing over-fitting. As in previous work (Satterthwaite et al., 2014b; Vandekar et al., 2015), nonlinearity was penalized within the GAMs using restricted maximum likelihood. Developmental models of each network measure were assessed by modeling age with a spline term, while including participant sex and in-scanner motion as covariates. To ensure that changes in global connectivity strength did not drive analyses of network topology, total network strength was also included as a covariate in all analyses (Li et al., 2012). Throughout, multiple comparisons were controlled using the False Discovery Rate ( q <0.05; Genovese et al., 2002). Permutation testing was used to assess whether the a priori functional network partition fit subject-level structural connectivity matrices and whether within-module connections were enriched for age effects (see Supplemental Information ). Methodological replications
To verify that observed age-related increases in modular segregation were not simply due to specific processing choices, we repeated analyses of global network segregation using a variety of other parameters. Analyses were repeated using a subject-specific measure of modularity quality ( Q ) for both a priori functional networks and a data-driven structural partition. Using the functional network partition, we also examined age-related changes in modular segregation in a higher resolution node system (n=463 instead of n=234), and using two alternative edge definitions (streamline count and normalized streamline density). Finally, we evaluated the effect of additional model covariates (race, maternal education, handedness, and total brain volume). For additional details, see Supplemental Information . Relationship between modular segregation and global network efficiency
Global efficiency was calculated for each participant’s structural network (Latora and Marchiori, 2001; Rubinov and Sporns, 2010) and age-related effects were examined as above. The relationship between global efficiency and modular segregation was examined while controlling for age (and other covariates as above). To further describe how age-related changes in within- and between-module connectivity might drive measures of global efficiency, we calculated the edge betweenness centrality (Brandes, 2001; Rubinov and Sporns, 2010). Edge betweenness quantifies the degree to which each edge participates in the shortest paths within a network, and thus contributes to global efficiency. Normalized edge betweenness was calculated for each edge, split by type (within- versus between-module) and age effect (strengthens with age versus no change). Hub edges were defined as connections within the top quartile of edge betweenness across all network edges. Permutation tests were used to evaluate whether connections that strengthened with age were enriched for hub edges, and had higher edge betweenness than expected by chance (see
Supplemental Information ). ! ssociations with executive function To determine if network segregation was related to executive performance, a GAM was used which incorporated the factor score for executive efficiency as well as model covariates (spline age, sex, in-scanner motion, total network strength). Specificity analyses additionally evaluated relationships with other cognitive domains including episodic memory and social cognition. Global efficiency was also assessed for relationships with cognition. Linear mediation analyses investigated whether age-related improvements in cognition were mediated by modular segregation or integration; significance was assessed using bootstrapping procedures (Preacher and Hayes, 2008).
SUPPLEMENTAL INFORMATION
Supplemental Information includes Figure S1, Figure S2, and Supplemental Experimental Procedures.
ACKNOWLDGEMENTS ! EFERENCES
Alexander-Bloch, A., Lambiotte, R., Roberts, B., Giedd, J., Gogtay, N., and Bullmore, E. (2012). The discovery of population differences in network community structure: new methods and applications to brain functional networks in schizophrenia. Neuroimage , 3889-3900. Anderson, J.S., Ferguson, M.A., Lopez-Larson, M., and Yurgelun-Todd, D. (2011). Connectivity gradients between the default mode and attention control networks. Brain Connect , 147-157. Anticevic, A., Van Snellenberg, J.X., Cohen, R.E., Repovs, G., Dowd, E.C., and Barch, D.M. (2010). Amygdala Recruitment in Schizophrenia in Response to Aversive Emotional Material: A Meta-analysis of Neuroimaging Studies. Schizophr Bull Baker, S.T.E., Lubman, D.I., Yücel, M., Allen, N.B., Whittle, S., Fulcher, B.D., Zalesky, A., and Fornito, A. (2015). Developmental Changes in Brain Network Hub Connectivity in Late Adolescence. J Neurosci , 9078-9087. Barber, A.D., Caffo, B.S., Pekar, J.J., and Mostofsky, S.H. (2013). Developmental changes in within- and between-network connectivity between late childhood and adulthood. Neuropsychologia , 156-167. Bassett, D.S., Brown, J.A., Deshpande, V., Carlson, J.M., and Grafton, S.T. (2011). Conserved and variable architecture of human white matter connectivity. Neuroimage , 1262-1279. Bassett, D.S., Bullmore, E.T., Meyer-Lindenberg, A., Apud, J.A., Weinberger, D.R., and Coppola, R. (2009). Cognitive fitness of cost-efficient brain functional networks. Proc Natl Acad Sci U S A , 11747-11752. Bassett, D.S., Greenfield, D.L., Meyer-Lindenberg, A., Weinberger, D.R., Moore, S.W., and Bullmore, E.T. (2010). Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS Comput Biol , e1000748. Bassett, D.S., Porter, M.A., Wymbs, N.F., Grafton, S.T., Carlson, J.M., and Mucha, P.J. (2013). Robust detection of dynamic community structure in networks. Chaos , 013142. Betzel, R.F., Byrge, L., He, Y., Goñi, J., Zuo, X.-N., and Sporns, O. (2014). Changes in structural and functional connectivity among resting-state networks across the human lifespan. Neuroimage
102 Pt 2 , 345-357. Biswal, B., Yetkin, F.Z., Haughton, V.M., and Hyde, J.S. (1995). Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn Reson Med , 537-541. Blondel, V.D., Guillaume, J.-L., Lambiotte, R., and Lefebvre, E. (2008). Fast unfolding of communities in large networks. Journal of statistical mechanics: theory and experiment , P10008. Bohlken, M.M., Brouwer, R.M., Mandl, R.C.W., Van den Heuvel, M.P., Hedman, A.M., De Hert, M., Cahn, W., Kahn, R.S., and Hulshoff Pol, H.E. (2016). Structural Brain Connectivity as a Genetic Marker for Schizophrenia. JAMA Psychiatry , 11-19. Braun, U., Schäfer, A., Walter, H., Erk, S., Romanczuk-Seiferth, N., Haddad, L., Schweiger, J.I., Grimm, O., Heinz, A., and Tost, H. (2015). Dynamic reconfiguration of frontal brain ! , 11678-11683. Buckner, R.L., and Carroll, D.C. (2007). Self-projection and the brain. Trends Cogn Sci , 49-57. Buckner, R.L., Andrews-Hanna, J.R., and Schacter, D.L. (2008). The brain's default network: anatomy, function, and relevance to disease. Ann N Y Acad Sci , 1-38. Calkins, M.E., Merikangas, K.R., Moore, T.M., Burstein, M., Behr, M.A., Satterthwaite, T.D., Ruparel, K., Wolf, D.H., Roalf, D.R., Mentch, F.D., Qiu, H., Chiavacci, R., Connolly, J.J., Sleiman, P.M.A., Gur, R.C., Hakonarson, H., and Gur, R.E. (2015). The Philadelphia Neurodevelopmental Cohort: constructing a deep phenotyping collaborative. J Child Psychol Psychiatry Cammoun, L., Gigandet, X., Meskaldji, D., Thiran, J.P., Sporns, O., Do, K.Q., Maeder, P., Meuli, R., and Hagmann, P. (2012). Mapping the human connectome at multiple scales with diffusion spectrum MRI. J Neurosci Methods , 386-397. Casey, B.J., Hare, T.A., and Galván, A. (2011). Risky and impulsive components of adolescent decision making. Decision Making, Affect, and Learning: Attention and Performance XXIII , 425. Casey, B.J., Jones, R.M., and Hare, T.A. (2008). The Adolescent Brain. Ann N Y Acad Sci , 111-126. Casey, B.J., Oliveri, M.E., and Insel, T. (2014). A Neurodevelopmental Perspective on the Research Domain Criteria (RDoC) Framework. Biol Psychiatry , 350-353. Castellanos, F.X., and Proal, E. (2012). Large-scale brain systems in ADHD: beyond the prefrontal–striatal model. Trends Cogn Sci , 17-26. Chen, M., and Deem, M.W. (2015). Development of modularity in the neural activity of children's brains. Phys Biol , 016009. Chen, Z., Liu, M., Gross, D.W., and Beaulieu, C. (2013). Graph theoretical analysis of developmental patterns of the white matter network. Front Hum Neurosci , 716. Corbetta, M., Akbudak, E., Conturo, T.E., Snyder, A.Z., Ollinger, J.M., Drury, H.A., Linenweber, M.R., Petersen, S.E., Raichle, M.E., and Van Essen, D.C. (1998). A common network of functional areas for attention and eye movements. Neuron , 761-773. Damoiseaux, J.S., Rombouts, S.A.R.B., Barkhof, F., Scheltens, P., Stam, C.J., Smith, S.M., and Beckmann, C.F. (2006). Consistent resting-state networks across healthy subjects. Proc Natl Acad Sci U S A , 13848-13853. Di Martino, A., Fair, D.A., Kelly, C., Satterthwaite, T.D., Castellanos, F.X., Thomason, M.E., Craddock, R.C., Luna, B., Leventhal, B.L., Zuo, X.N., and Milham, M.P. (2014). Unraveling the Miswired Connectome: A Developmental Perspective. Neuron , 1335-1353. Dosenbach, N.U., Fair, D.A., Miezin, F.M., Cohen, A.L., Wenger, K.K., Dosenbach, R.A., Fox, M.D., Snyder, A.Z., Vincent, J.L., Raichle, M.E., Schlaggar, B.L., and Petersen, S.E. (2007). Distinct brain networks for adaptive and stable task control in humans. Proc Natl Acad Sci U S A , 11073-11078. Dosenbach, N.U.F., Nardos, B., Cohen, A.L., Fair, D.A., Power, J.D., Church, J.A., Nelson, S.M., Wig, G.S., Vogel, A.C., Lessov-Schlaggar, C.N., Barnes, K.A., Dubis, J.W., Feczko, E., Coalson, R.S., Pruett, J.R., Barch, D.M., Petersen, S.E., and Schlaggar, B.L. (2010). Prediction of individual brain maturity using fMRI. Science , 1358-1361. ! , 4028. Fair, D.A., Cohen, A.L., Power, J.D., Dosenbach, N.U.F., Church, J.A., Miezin, F.M., Schlaggar, B.L., and Petersen, S.E. (2009). Functional brain networks develop from a "local to distributed" organization. PLoS Comput Biol , e1000381. Fair, D.A., Dosenbach, N.U.F., Church, J.A., Cohen, A.L., Brahmbhatt, S., Miezin, F.M., Barch, D.M., Raichle, M.E., Petersen, S.E., and Schlaggar, B.L. (2007). Development of distinct control networks through segregation and integration. Proc Natl Acad Sci U S A , 13507-13512. Fischl, B. (2012). FreeSurfer. Neuroimage , 774-781. Fornito, A., Harrison, B.J., Zalesky, A., and Simons, J.S. (2012). Competitive and cooperative dynamics of large-scale brain functional networks supporting recollection. Proc Natl Acad Sci U S A , 12788-12793. Genovese, C.R., Lazar, N.A., and Nichols, T. (2002). Thresholding of statistical maps in functional neuroimaging using the false discovery rate. Neuroimage , 870-878. Goñi, J., van den Heuvel, M.P., Avena-Koenigsberger, A., de Mendizabal, N.V., Betzel, R.F., Griffa, A., Hagmann, P., Corominas-Murtra, B., Thiran, J.-P., and Sporns, O. (2014). Resting-brain functional connectivity predicted by analytic measures of network communication. Proceedings of the National Academy of Sciences , 833-838. Greve, D.N., and Fischl, B. (2009). Accurate and robust brain image alignment using boundary-based registration. Neuroimage , 63-72. Gu, S., Satterthwaite, T.D., Medaglia, J.D., Yang, M., Gur, R.E., Gur, R.C., and Bassett, D.S. (2015). Emergence of system roles in normative neurodevelopment. Proc Natl Acad Sci U S A , 13681-13686. Guimerà, R., and Nunes Amaral, L.A. (2005). Functional cartography of complex metabolic networks. Nature , 895-900. Gur, R.C., Richard, J., Calkins, M.E., Chiavacci, R., Hansen, J.A., Bilker, W.B., Loughead, J., Connolly, J.J., Qiu, H., Mentch, F.D., Abou-Sleiman, P.M., Hakonarson, H., and Gur, R.E. (2012). Age group and sex differences in performance on a computerized neurocognitive battery in children age 8-21. Neuropsychology , 251-265. Gur, R.C., Sara, R., Hagendoorn, M., Marom, O., Hughett, P., Macy, L., Turner, T., Bajcsy, R., Posner, A., and Gur, R.E. (2002). A method for obtaining 3-dimensional facial expressions and its standardization for use in neurocognitive studies. J Neurosci Methods , 137-143. Gur, R.E., Kaltman, D., Melhem, E.R., Ruparel, K., Prabhakaran, K., Riley, M., Yodh, E., Hakonarson, H., Satterthwaite, T., and Gur, R.C. (2013). Incidental findings in youths volunteering for brain MRI research. AJNR Am J Neuroradiol , 2021-2025. Hagmann, P., Cammoun, L., Gigandet, X., Gerhard, S., Ellen Grant, P., Wedeen, V., Meuli, R., Thiran, J.-P., Honey, C.J., and Sporns, O. (2010a). MR connectomics: Principles and challenges. J Neurosci Methods Hagmann, P., Sporns, O., Madan, N., Cammoun, L., Pienaar, R., Wedeen, V.J., Meuli, R., Thiran, J.-P., and Grant, P.E. (2010b). White matter maturation reshapes structural connectivity in the late developing human brain. Proc Natl Acad Sci U S A , 19067-19072. ! , 6169-6174. Hermundstad, A.M., Brown, K.S., Bassett, D.S., Aminoff, E.M., Frithsen, A., Johnson, A., Tipper, C.M., Miller, M.B., Grafton, S.T., and Carlson, J.M. (2014). Structurally-constrained relationships between cognitive states in the human brain. PLoS Comput Biol , e1003591. Honey, C.J., Sporns, O., Cammoun, L., Gigandet, X., Thiran, J.P., Meuli, R., and Hagmann, P. (2009). Predicting human resting-state functional connectivity from structural connectivity. Proc Natl Acad Sci U S A , 2035-2040. Huang, H., Shu, N., Mishra, V., Jeon, T., Chalak, L., Wang, Z.J., Rollins, N., Gong, G., Cheng, H., Peng, Y., Dong, Q., and He, Y. (2015). Development of human brain structural networks through infancy and childhood. Cereb Cortex , 1389-1404. Hutchison, R.M., and Morton, J.B. (2015). It's a matter of time: Reframing the development of cognitive control as a modification of the brain's temporal dynamics. Dev Cogn Neurosci Insel, T.R. (2010). Rethinking schizophrenia. Nature , 187-193. Jenkinson, M., Beckmann, C.F., Behrens, T.E.J., Woolrich, M.W., and Smith, S.M. (2012). FSL. Neuroimage , 782-790. Jbabdi, S., Sotiropoulos, S.N., Haber, S.N., Van Essen, D.C., and Behrens, T.E. (2015). Measuring macroscopic brain connections in vivo. Nat Neurosci 18, 1546-1555. Kraemer, H.C., Yesavage, J.A., Taylor, J.L., and Kupfer, D. (2000). How can we learn about developmental processes from cross-sectional studies, or can we? Am J Psychiatry , 163-171. Latora, V., and Marchiori, M. (2001). Efficient behavior of small-world networks. Phys Rev Lett , 198701. Li, L., Rilling, J.K., Preuss, T.M., Glasser, M.F., and Hu, X. (2012). The effects of connection reconstruction method on the interregional connectivity of brain networks via diffusion tractography. Hum Brain Mapp , 1894-1913. Li, Y., Liu, Y., Li, J., Qin, W., Li, K., Yu, C., and Jiang, T. (2009). Brain anatomical network and intelligence. PLoS Comput Biol , e1000395. Lim, S., Han, C.E., Uhlhaas, P.J., and Kaiser, M. (2015). Preferential detachment during human brain development: age- and sex-specific structural connectivity in diffusion tensor imaging (DTI) data. Cereb Cortex , 1477-1489. Luna, B., Garver, K.E., Urban, T.A., Lazar, N.A., and Sweeney, J.A. (2004). Maturation of cognitive processes from late childhood to adulthood. Child Dev , 1357-1372. Mi š i ć , B., Betzel, R.F., de Reus, M.A., van den Heuvel, M.P., Berman, M.G., McIntosh, A.R., and Sporns, O. (2016). Network-Level Structure-Function Relationships in Human Neocortex. Cereb Cortex , 3285-3296. Moore, T.M., Reise, S.P., Gur, R.E., Hakonarson, H., and Gur, R.C. (2014). Psychometric Properties of the Penn Computerized Neurocognitive Battery. Neuropsychology ! , 876-878. Newman, M.E.J. (2006). Modularity and community structure in networks. Proc Natl Acad Sci U S A , 8577-8582. Nooner, K.B., Colcombe, S.J., Tobe, R.H., Mennes, M., Benedict, M.M., Moreno, A.L., Panek, L.J., Brown, S., Zavitz, S.T., Li, Q., Sikka, S., Gutman, D., Bangaru, S., Schlachter, R.T., Kamiel, S.M., Anwar, A.R., Hinz, C.M., Kaplan, M.S., Rachlin, A.B., Adelsberg, S., Cheung, B., Khanuja, R., Yan, C., Craddock, C.C., Calhoun, V., Courtney, W., King, M., Wood, D., Cox, C.L., Kelly, A.M.C., Di Martino, A., Petkova, E., Reiss, P.T., Duan, N., Thomsen, D., Biswal, B., Coffey, B., Hoptman, M.J., Javitt, D.C., Pomara, N., Sidtis, J.J., Koplewicz, H.S., Castellanos, F.X., Leventhal, B.L., and Milham, M.P. (2012). The NKI-Rockland Sample: A Model for Accelerating the Pace of Discovery Science in Psychiatry. Front Neurosci , 152. Persson, J., Lustig, C., Nelson, J.K., and Reuter-Lorenz, P.A. (2007). Age differences in deactivation: a link to cognitive control? J Cogn Neurosci , 1021-1032. Power, J.D., Cohen, A.L., Nelson, S.M., Wig, G.S., Barnes, K.A., Church, J.A., Vogel, A.C., Laumann, T.O., Miezin, F.M., Schlaggar, B.L., and Petersen, S.E. (2011). Functional network organization of the human brain. Neuron , 665-678. Power, J.D., Fair, D.A., Schlaggar, B.L., and Petersen, S.E. (2010). The development of human functional brain networks. Neuron , 735-748. Power, J.D., Schlaggar, B.L., Lessov-Schlaggar, C.N., and Petersen, S.E. (2013). Evidence for hubs in human functional brain networks. Neuron , 798-813. Preacher, K.J., and Hayes, A.F. (2008). Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models. Behav Res Methods , 879-891. Raichle, M.E., MacLeod, A.M., Snyder, A.Z., Powers, W.J., Gusnard, D.A., and Shulman, G.L. (2001). A default mode of brain function. Proc Natl Acad Sci U S A , 676-682. Rapoport, J.L., Giedd, J.N., and Gogtay, N. (2012). Neurodevelopmental model of schizophrenia: update 2012. Mol Psychiatry Roalf, D.R., Quarmley, M., Elliott, M.A., Satterthwaite, T.D., Vandekar, S.N., Ruparel, K., Gennatas, E.D., Calkins, M.E., Moore, T.M., Hopson, R., Prabhakaran, K., Jackson, C.T., Verma, R., Hakonarson, H., Gur, R.C., and Gur, R.E. (2016). The impact of quality assurance assessment on diffusion tensor imaging outcomes in a large-scale population-based cohort. Neuroimage , 903-919. Rubinov, M., and Sporns, O. (2010). Complex network measures of brain connectivity: uses and interpretations. Neuroimage , 1059-1069. Satterthwaite, T.D., Connolly, J.J., Ruparel, K., Calkins, M.E., Jackson, C., Elliott, M.A., Roalf, D.R., Ryan Hopsona, K.P., Behr, M., Qiu, H., Mentch, F.D., Chiavacci, R., Sleiman, P.M.A., Gur, R.C., Hakonarson, H., and Gur, R.E. (2015). The Philadelphia Neurodevelopmental Cohort: A publicly available resource for the study of normal and abnormal brain development in youth. Neuroimage Satterthwaite, T.D., Elliott, M.A., Ruparel, K., Loughead, J., Prabhakaran, K., Calkins, M.E., Hopson, R., Jackson, C., Keefe, J., Riley, M., Mentch, F.D., Sleiman, P., Verma, R., Davatzikos, C., Hakonarson, H., Gur, R.C., and Gur, R.E. (2014a). Neuroimaging of the Philadelphia neurodevelopmental cohort. Neuroimage , 544-553. ! , 16249-16261. Satterthwaite, T.D., Wolf, D.H., Ruparel, K., Erus, G., Elliott, M.A., Eickhoff, S.B., Gennatas, E.D., Jackson, C., Prabhakaran, K., Smith, A., Hakonarson, H., Verma, R., Davatzikos, C., Gur, R.E., and Gur, R.C. (2013b). Heterogeneous impact of motion on fundamental patterns of developmental changes in functional connectivity during youth. Neuroimage , 45 - 57. Schacter, D.L., Addis, D.R., and Buckner, R.L. (2007). Remembering the past to imagine the future: the prospective brain. Nat Rev Neurosci , 657-661. Schumann, G., Loth, E., Banaschewski, T., Barbot, A., Barker, G., Büchel, C., Conrod, P.J., Dalley, J.W., Flor, H., Gallinat, J., Garavan, H., Heinz, A., Itterman, B., Lathrop, M., Mallik, C., Mann, K., Martinot, J.-L., Paus, T., Poline, J.-B., Robbins, T.W., Rietschel, M., Reed, L., Smolka, M., Spanagel, R., Speiser, C., Stephens, D.N., Ströhle, A., Struve, M., and IMAGEN consortium (2010). The IMAGEN study: reinforcement-related behaviour in normal brain function and psychopathology. Mol Psychiatry , 1128-1139. Shamosh, N.A., Deyoung, C.G., Green, A.E., Reis, D.L., Johnson, M.R., Conway, A.R.A., Engle, R.W., Braver, T.S., and Gray, J.R. (2008). Individual differences in delay discounting: relation to intelligence, working memory, and anterior prefrontal cortex. Psychol Sci , 904-911. Shanmugan, S., Wolf, D.H., Calkins, M.E., Moore, T.M., Ruparel, K., Hopson, R.D., Vandekar, S.N., Roalf, D.R., Elliott, M.A., Jackson, C., Gennatas, E.D., Leibenluft, E., Pine, D.S., Shinohara, R.T., Hakonarson, H., Gur, R.C., Gur, R.E., and Satterthwaite, T.D. (2016). Common and Dissociable Mechanisms of Executive System Dysfunction Across Psychiatric Disorders in Youth. Am J Psychiatry , appiajp201515060725. Sporns, O., and Betzel, R.F. (2016). Modular Brain Networks. Annu Rev Psychol , 613-640. Supekar, K., Musen, M., and Menon, V. (2009). Development of large-scale functional brain networks in children. PLoS Biol , e1000157. Thomason, M.E., Dassanayake, M.T., Shen, S., Katkuri, Y., Alexis, M., Anderson, A.L., Yeo, L., Mody, S., Hernandez-Andrade, E., Hassan, S.S., Studholme, C., Jeong, J.-W., and Romero, R. (2013). Cross-hemispheric functional connectivity in the human fetal brain. Sci Transl Med , 173ra24. Traud, A.L., Kelsic, E.D., Mucha, P.J., and Porter, M.A. (2011). Comparing community structure to characteristics in online collegiate social networks. SIAM review , 526-543. Vandekar, S.N., Shinohara, R.T., Raznahan, A., Roalf, D.R., Ross, M., DeLeo, N., Ruparel, K., Verma, R., Wolf, D.H., Gur, R.C., Gur, R.E., and Satterthwaite, T.D. (2015). Topologically dissociable patterns of development of the human cerebral cortex. J Neurosci , 599-609. ! , 3000-3013. van den Heuvel, M.P., Stam, C.J., Kahn, R.S., and Hulshoff Pol, H.E. (2009). Efficiency of functional brain networks and intellectual performance. J Neurosci , 7619-7624. Vincent, J.L., Kahn, I., Snyder, A.Z., Raichle, M.E., and Buckner, R.L. (2008). Evidence for a frontoparietal control system revealed by intrinsic functional connectivity. J Neurophysiol , 3328-3342. Voineskos, A.N., Lobaugh, N.J., Bouix, S., Rajji, T.K., Miranda, D., Kennedy, J.L., Mulsant, B.H., Pollock, B.G., and Shenton, M.E. (2010). Diffusion tensor tractography findings in schizophrenia across the adult lifespan. Brain , 1494-1504. Wood, S.N. (2004). Stable and efficient multiple smoothing parameter estimation for generalized additive models. Journal of the American Statistical Association Wood, S.N. (2011). Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) , 3-36. Yeh, F.-C., Verstynen, T.D., Wang, Y., Fernández-Miranda, J.C., and Tseng, W.-Y.I. (2013). Deterministic diffusion fiber tracking improved by quantitative anisotropy. PLoS One , e80713. Yendiki, A., Koldewyn, K., Kakunoori, S., Kanwisher, N., and Fischl, B. (2013). Spurious group differences due to head motion in a diffusion MRI study. Neuroimage , 79-90. Yeo, B.T.T., Krienen, F.M., Sepulcre, J., Sabuncu, M.R., Lashkari, D., Hollinshead, M., Roffman, J.L., Smoller, J.W., Zöllei, L., Polimeni, J.R., Fischl, B., Liu, H., and Buckner, R.L. (2011). The organization of the human cerebral cortex estimated by intrinsic functional connectivity. J Neurophysiol , 1125-1165. ! Figure 1 . Executive functioning improves with age. A. Age distribution of 882 youth completing diffusion imaging as part of the PNC. B . Executive performance on a neurocognitive battery improves with age. Blue line represents the best fit from a general additive model; shaded area indicates 95% confidence interval. Model includes participant sex as a covariate. ! Figure 2.
Connectome construction. For each subject, the T1 image was processed using FreeSurfer and parcellated into 234 network nodes on an individualized basis. Deterministic whole-brain fiber tracking was used to create a symmetric adjacency matrix (234 × ! Figure 3 . Structural brain network modules become increasingly segregated with age. A. Modular segregation was quantified as the mean participation coefficient across all network nodes, with lower values indicating more segregation. Participation coefficient values declined significantly with age. B. Modular segregation is differentially distributed across functional systems. Age-related modular segregation is most robust in the somatomotor and default mode systems, but also present in other networks. C. Age-related changes in participation coefficient provide convergent results for individual nodes, and demonstrate widespread declines with age. The strongest age-related reductions of the participation coefficient were seen in default mode regions such as the posterior cingulate. Two exceptions to this overall trend were the right rostral frontal gyrus and frontal operculum, where participation coefficient increased with age. Blue line represents the best fit from a general additive model; shaded area indicates 95% confidence interval. All analyses control for sex, in-scanner motion, and network strength. Color palette represents z -transformed p values from a general additive model. Images are thresholded to control for multiple comparisons using the False Discovery Rate ( Q <0.05). *indicates p <0.001. ! Figure 4 . Modular segregation is driven by a combination of both enhanced within-module connectivity and reduced between-module connectivity. A. Average strength of within-module connectivity increases with age. B. Between-module connectivity decreases across development. C. Convergent effects are seen at the level of individual graph edges (image thresholded using Bonferroni corrected p <0.05 for clarity). D. A higher percentage of within-module connections (red) strengthen with age than expected by chance. All analyses include sex, in-scanner motion, and network strength as model covariates. * indicates p <0.001. ! Figure 5 . Results are robust to methodological choices. Regardless of specific processing decisions, an increase in modular segregation with age was observed. A . Convergent findings result when using an index of the modularity quality for the Yeo partition, where higher Q indicates more segregated modules. B . When using a group-level structural partition, modular segregation (mean participation coefficient) decreases with age. C . Modularity quality of subject-level connectivity matrices also increases with age. D . Results remain unaffected when a higher-dimensional parcellation is used (n=463 nodes), E . when streamline count is used instead of FA as an edge weight, and F . when normalized streamline density is used as the edge weight. Lower participation coefficient indicates more segregated modules. Blue line represents the best fit from a general additive model; shaded area indicates 95% confidence interval. All models include sex, in-scanner motion, and total network strength as covariates. ! Figure 6 . Modularity is associated with network integration, and is driven by developmental strengthening of specific hub edges. A. Replicating prior work, global network efficiency increases with age. Model includes sex, in-scanner motion, and total network strength as covariates. B. While controlling for age, lower mean participation coefficient is associated with greater network efficiency, indicating a positive association between modular segregation and network integration. C. Connections that strengthen with age are enriched for hub edges (47%). Hub edges are defined as connections in the top quartile of edge betweenness centrality, which quantifies how often a given edge lies on the shortest path between nodes and thus facilitates global efficiency. Image thresholded using Bonferroni corrected p <0.05 for clarity. D. Both within- and between-module connections that strengthen with age have higher edge betweenness centrality than expected by chance. The average weight of within- ( E ) and between-module edges ( F ) that strengthen with age are positively associated with global efficiency. Blue line represents the best fit from a general additive model, shaded area indicates 95% confidence interval; * indicates p <0.001. Error bar represents standard error of the mean. ! Figure 7 . Segregation of structural modules supports the development of executive function in youth. A. While controlling for age, greater modular segregation in the frontoparietal control network is associated with better executive performance. B. Segregation of structural modules mediates the improvement of executive function with age. Mediation results shown as unstandardized regression coefficients. Significance of indirect effect ( c’ =0.007) was assessed using bootstrapped confidence intervals [0.002-0.012]. All models also include sex, in-scanner motion, and total network strength as covariates. * indicates p <0.01. ! Figure 8 . Modular evolution of structural brain networks across youth. From childhood through adulthood, structural brain networks become increasingly modular. The targeted strengthening of specific hub edges facilitates specialized information processing within distinct modules, and simultaneously enhances integration across modules. Hub edges are indicated by thick connections. ! UPPLEMENTAL INFORMATION ! upplemental Figures Gamma R a s t k o_nu m C o mm s _n882 Zrand_n882_consensus_vs_Yeo7system N u m be r o f M odu l e s Z Rand * * * = 1.5 = 3.1 = 2.5
Supplemental Figure 1: Number of modules identified in group-level structural par-titions.
To examine alternative data-driven modular partitions of structural brain networks,we varied γ over the interval [ , ] in increments of 0.05. The number of modules identifiedin group-level consensus partitions increases as a function of γ . The similarity betweenstructural partitions and a priori functional partitions also increases with γ and the numberof identified structural modules. ∗ indicates alternative structural partitions identified atplateaus for the number of modules. Bars are colored by the z -score of the Rand coeffi-cient, which quantifies the similarity between structural partitions and the a priori func-tional partition used throughout the main text. The 9-module structural partition identifiedat γ =2.5 (marked by blue box) is used to examine age-related effects on modular segre-gation in Figure 5 . The z -score of the Rand coefficient is equal to 17.6 (p < × − )for this structural partition, suggesting a significant similarity with the functional partitionbeyond chance. 30
10 12 14 16 18 20 220.460.480.500.520.540.560.58 age_in_yrs f ( age_ i n_ y r s ) p < 1 × -10 Age (years) M ean P a r t i c i pa t i on C oe f fic i en t Module Module Module f ( age_ i n_ y r s ) Age (years) p < 1 × -10 M ean P a r t i c i pa t i on C oe f fic i en t f ( age_ i n_ y r s ) M ean P a r t i c i pa t i on C oe f fic i en t Age (years) p < 1 × -10 = 1.5 = 2.5 = 3.1 Supplemental Figure 2: Data-driven structural network modules become more seg-regated across youth.
Here we demonstrate that regardless of the group-level consensuspartition used to define modules, modular segregation increases with age, as demonstratedby a significant decrease in the mean participation coefficient. This developmental patternis replicated using a 5-module partition ( A , γ =1.5), a 9-module partition ( B , γ =2.5), and an11-module partition ( C , γ =3.1). The 9-module partition pictured in B is used to calculatemodular segregation in Figure 5 . Blue line represents the best fit from a general additivemodel; shaded area indicates 95% confidence interval. Models include participant sex,in-scanner head motion, and total network strength as covariates.31 upplemental Experimental Procedures
Subjects
Diffusion tensor imaging (DTI) datasets were acquired as part of the Philadelphia Neu-rodevelopmental Cohort (PNC), a large community-based study of brain development.1601 subjects completed the cross-sectional neuroimaging protocol (Satterthwaite et al.,2014). Datasets from 244 individuals were considered unusable due to incomplete ac-quisition or incidental findings. The remaining 1357 participants underwent a rigorousmanual and automated quality assurance protocol for DTI datasets (Roalf et al., 2016),which flagged 157 subjects for poor data quality (e.g., low temporal signal-to-noise ratio).Of the remaining 1210 participants, 93 were flagged by automated quality assurance forlow quality or incomplete FreeSurfer reconstruction of T1-weighted images. Of the re-maining 1117 participants, 235 subjects were excluded for meeting any of the followingcriteria: gross radiological abnormalities, history of medical problems that might affectbrain function, history of inpatient psychiatric hospitalization, use of psychotropic medi-cation at the time of data acquisition, missing data, and/or high levels of in-scanner headmotion (mean relative displacement between non-weighted volumes > Cognitive Assessment
The Penn computerized neurocognitive battery (Penn CNB) was administered to allparticipants. The CNB consists of 14 tests adapted from tasks applied in functional neu-roimaging to evaluate a broad range of cognitive domains (Gur et al., 2002; Gur et al.,2012). These domains include executive control (abstraction and flexibility, attention,working memory), episodic memory (verbal, facial, spatial), complex cognition (verbalreasoning, nonverbal reasoning, spatial processing), social cognition (emotion identifica-tion, emotion intensity differentiation, age differentiation) and sensorimotor and motorspeed. Accuracy and speed for each test were z-transformed. Cognitive performance wassummarized by a recent factor analysis (Moore et al., 2014) of both speed and accuracydata, which delineated three factors corresponding to the efficiency of executive function,episodic memory, and social cognition.
Data Acquisition
All MRI scans were acquired on the same 3T Siemens Tim Trio whole-body scannerand 32-channel head coil at the Hospital of the University of Pennsylvania. DTI scanswere acquired using a twice- refocused spin-echo (TRSE) single-shot echo-planar imaging32EPI) sequence (TR = 8100ms, TE = 82ms, FOV = 240mm2 /240mm ; Matrix = RL:128/AP:128/Slices:70, in-plane resolution (x and y) 1.875 mm ; slice thickness = 2mm,gap = 0; flip angle = 90 ◦ /180 ◦ /180 ◦ , volumes = 71, GRAPPA factor = 3, bandwidth =2170 Hz/pixel, PE direction = AP). This sequence used a four-lobed diffusion encodinggradient scheme combined with a 90-180-180 spin-echo sequence designed to minimizeeddy-current artifacts . DTI data were acquired in two consecutive series consisting of 32diffusion encoding gradient schemes. The complete sequence consisted of 64 diffusion-weighted directions with b=1000s/mm and 7 interspersed scans where b =0 s/mm . Theduration of DTI scans was approximately 11 minutes. The imaging volume was prescribedin axial orientation covering the entire cerebrum with the topmost slice just superior to theapex of the brain (Satterthwaite et al. 2014a). In addition to the DTI scan, a map ofthe main magnetic field (i.e., B0) was derived from a double-echo, gradient-recalled echo(GRE) sequence, allowing us to estimate field distortions in each dataset. Data Preprocessing
Two consecutive 32-direction acquisitions were merged into a single 64-direction time-series. The skull was removed for each subject by registering a binary mask of a standardfractional anisotropy (FA) map (FMRIB58 FA) to each subject’s DTI image using a rigid-body transformation (Smith et al., 2002). Eddy currents and subject motion were esti-mated and corrected using FSL’s eddy tool (Andersson and Sotiropoulos 2016). Diffusiongradient vectors were then rotated to adjust for subject motion estimated by eddy . Afterthe field map was estimated, distortion correction was applied to DTI data using FSL’sFUGUE (Jenkinson et al., 2012). Lastly, DTI data was imported into DSI Studio softwareand the diffusion tensor was estimated at each voxel.
DTI Tractography
Whole-brain fiber tracking was implemented for each subject in DSI Studio using amodified fiber assessment by continuous tracking (FACT) algorithm with Euler interpola-tion, initiating 1,000,000 streamlines after removing all streamlines with length less than10mm or greater than 400mm (Yeh et al., 2013). Fiber tracking was performed with anangular threshold of 45 ◦ , a step size of 0.9375mm, and a fractional anisotropy (FA) thresh-old determined empirically by Otzu’s method, which optimizes the contrast between fore-ground and background (Yeh et. al., 2013). Diffusivity measures (e.g., FA, mean diffusiv-ity, radial diffusivity, axial diffusivity) were calculated along the path of each reconstructedstreamline. For each subject, tractography served as the basis for constructing structuralbrain networks. 33 etwork Construction Following T1 reconstruction in FreeSurfer (version 5.3), cortical and subcortical graymatter was parcellated according to the Lausanne atlas (Cammoun et al., 2012), whichincludes whole-brain parcellations at multiple spatial scales (83, 129, 234, 463, and 1015regions). Parcellations were defined in native space and co-registered to the first b = A . Edges weredefined where at least one streamline connected a pair of nodes end-to-end. Edge weightswere primarily defined by the average FA along streamlines connecting any pair of nodes(Misic et al., 2016; Bohlken et al., 2016). See Figure 2 . Functional Module Assignment
For the 234- and 463-region parcellations, we calculated a purity index for each Lau-sanne label and corresponding voxels in the standard 7-system template image providedby Yeo et al. (2011). This measure quantifies the maximum overlap of cortical Lausannelabels and functional systems defined by Yeo et al. (2011). Each cortical Lausanne labelwas assigned to a functional system by calculating the non-zero mode of all voxels in eachbrain region. Subcortical regions were assigned to an eighth, subcortical module. Theprimary modular partition defined for 234-node networks is shown in
Figure 2 . To de-termine whether the functionally-defined network partition significantly fit the structuralconnectivity data beyond chance, we quantified the modularity quality index (formallydefined below) of the functional partition imposed on structural brain networks. Briefly,the modularity quality of a network partition quantifies how well that partition maximizesthe strength of within-module connections relative to a specified null model. Higher Q values indicate that modules are highly segregated within a network, with strong within-module connectivity and relatively weak between-module connectivity. We performed apermutation test to examine the significance of the modularity quality of the functionalpartition ( Q Yeo ) imposed on structural connectivity matrices. First, we permuted the as-signment of N nodes to functional modules 1000 times, preserving the number of nodesoriginally assigned to each module. We then calculated the modularity quality Q perm ofrandomly-defined network partitions imposed on each subject’s connectivity matrix, build-ing a null distribution for Q perm . We used the calculated mean ( µ Q perm ) and standard de-viation ( σ Q perm ) of the null distribution to derive a z -score based on the observed Q Yeo foreach subject ( z -score = ( Q Yeo − µ Qperm ) σ Qperm ). Finally, we calculated the mean z -score across allsubjects to assess the significance of Q Yeo . 34 easures of Modular Segregation
We calculated the participation coefficient to quantify the relative balance of between-module versus within-module connectivity for each brain region. Intuitively, this measuredescribes the degree to which a brain region integrates information across distinct modules,or the degree to which a brain region shows provincial connectivity among regions in itsown module. We define the participation coefficient P i of node i as P i = − ∑ m ∈ M (cid:16) k i ( m ) k i (cid:17) , (1)where m is a module in a set of modules M , and k i ( m ) is the weight of structural connec-tions between node i and all nodes in module m (Guimera and Amaral 2005; Rubinov andSporns 2010). Moreover, P i close to 1 indicates that a brain region is highly integratedwith regions in other modules, while a P i close to 0 indicates that a brain region is highlysegregated, with strong connectivity among other regions in its own module. To quantifythe segregation of specific modules, we average P i across all brain regions assigned to thesame module. To quantify global network segregation, we average P i across all nodes inthe network. Alternative Measures of Modular Segregation
To ensure that our results were not dependent on specific network metrics, we cal-culated alternative measures of modular segregation. First, we calculated the averagestrength of all within-module connections (a measure of structural coherence), and theaverage strength of all between-module connections (a measure of structural integration)in the network (Gu et al., 2015). These metrics provide additional insights into the segre-gation of information processing within distinct modules, and the degree to which modulesare integrated across the network (see
Figure 4 ). Alternatively, we calculated the subject-specific modularity quality ( Q ) of group-level functional and structural network partitions.As discussed above, this measure provides an index of how well a network can be decom-posed into a hard partition where nodes within the same module demonstrate particularlystrong connectivity beyond chance. We also calculated Q sub j for subject-specific consen-sus partitions (see detailed procedure below), which was not dependent on a group-levelpartition. We calculated the modularity Q of a network partition S based on the followingmodularity quality function: Q ( S ) = m ∑ i j (cid:104) A i j − γ P i j (cid:105) δ ( g i , g j ) , (2)where m is the total weight of A , P represents the expected strength of connections accord-ing to a specified null model (Newman, 2004), γ is a structural resolution parameter that35etermines the size of modules, and δ ( g i , g j ) is equal to unity when brain regions i and j are assigned to same community g i , and is zero otherwise. Community Detection in Structural Brain Networks
Primary analyses relied on an a priori functional partition to define network modules.We additionally estimated network modules directly from the structural connectivity datausing community detection procedures. Communities were defined by maximizing themodularity quality function using a generalization of the Louvain heuristic (Blondel etal., 2008; Mucha et al., 2010). Because the Louvain algorithm is degenerate (Good etal., 2010; Sporns and Betzel 2016), it is essential to perform modularity maximizationmultiple times in order to identify a stable consensus partition that accurately reflects thesolutions offered by each optimization. Accordingly, we applied a locally greedy Louvain-like modularity-optimization procedure (Blondel et al., 2008) 100 times for each subjectin order to define an “agreement” matrix A (cid:48) where A (cid:48) i j was equal to the probability thatnodes i and j were assigned to the same community over the 100 iterations. If A (cid:48) was de-terministic (edge weights were binary), then the algorithm had converged and the resultantpartition was defined as the consensus. Otherwise, we performed 100 iterations of modu-larity optimization on A (cid:48) in order to generate a new agreement matrix A (cid:48)(cid:48) . This procedurewas repeated until convergence (Lancichinetti and Fortunato, 2014). When performingmodularity optimization on an agreement matrix (e.g., A (cid:48) or A (cid:48)(cid:48) ), we defined an alternativenull model P (cid:48) by permuting community assignments across nodes (Bassett et al., 2013).Once a consensus partition was identified for each subject, we computed a group-level consensus across the full PNC cohort (n=882). To do this, we used a Louvain-likeprocedure to detect communities in a group-level agreement matrix A (cid:48) group . Edge weightsin A (cid:48) group were equal to the proportion of times that each pair of nodes was assigned tothe same community across subject-level consensus partitions. As above, 100 iterationsof modularity optimization were performed on A (cid:48) group until the resulting A (cid:48)(cid:48) group becamebinary, indicating that the algorithm had converged on a group-level consensus partition.Both subject-level and group-level consensus partitions were computed over a wide rangeof γ ( [ , ] , in increments of 0.05) to explore variations in community structure. We plottedthe number of group-level consensus modules as a function of γ , and found several plateausindicating partition stability (Fenn et al., 2009; see Figure S1 ). In order to directly comparethe organization of data-driven, modularity-based partitions and the a priori functionalpartition, we quantified the partition similarity using the z -score of the Rand coefficient(Traud et al., 2011). For two partitions X and Y , we calculated the Rand z -score in termsof the total number of node pairs in the network M , the number of pairs M X assigned tothe same module in partition X , the number of pairs M Y that are in the same module inpartition Y , and the number of pairs of nodes w XY that are assigned to the same module36oth in partition X and in partition Y . The z -score of the Rand coefficient is defined by: z XY = σ w XY w XY − M X M Y M , (3)where σ w XY is the standard deviation of w XY . The mean partition similarity is determinedby the mean value of z XY over all possible partition pairs for X (cid:54) = Y . Moreover, z XY denotesthe similarity of partitions X and Y beyond chance. Figure S1 shows the similarity betweenall group-level structural partitions and the primary functional partition used in this study.
Measures of Network Integration
For each subject’s structural brain network A , the topological length or distance of eachedge A i j was computed as the reciprocal of the edge weight ( A i j ). The path length betweenany pair of nodes is defined as the sum of the edge lengths along the shortest path connect-ing them (Rubinov and Sporns, 2010). Global efficiency provides a theoretical predictionof how easily information can flow across a network via the shortest path between all pairsof nodes, and is defined by E glob ( G ) = n ∑ i ∈ N ∑ j ∈ N , j (cid:54) = i (cid:18) d i j (cid:19) − n − , (4)where n is the number of nodes, and d i j is the shortest path length between node i andnode j .To examine the possible role of specific edges as integrative hub connections withinthe network, we calculated the weighted edge betweenness centrality ( EBC ) for each edge.Edge betweenness identifies important hub connections by providing a measure of howmuch a given connection participates in the shortest paths of communication through anetwork, and thus contributes to global efficiency (Brandes, 2001).
EBC = ∑ hk ρ i jhk ρ hk , (5)where ρ i jhk denotes the number of shortest paths between nodes h and k that includeedge i j , and ρ hk denotes the total number of shortest paths between h and k . After cal-culating EBC individually for each weighted network A i j (n=882), we normalized eachsubjects (cid:48) EBC values by their maximum observed
EBC , resulting in a bounded measure [ , ] (Gong et al., 2009). We calculated the mean normalized EBC for each network edgeacross subjects, and defined hub edges as those connections within the top quartile of37ormalized edge betweenness across all network edges. Following group-level analysis,which identified a subset of edges that significantly strengthened with age, we performed apermutation-based test to assess whether connections that significantly strengthened withage were enriched for hub edges (see below).
Group-level analyses
Prior work has demonstrated that brain development is not a linear process (Paus et al.,1999, Shaw et al., 2006). Accordingly, group-level analyses of structural brain networkmetrics were flexibly modeled using penalized splines within a General Additive Model(GAM) implemented in the R package “mgcv” (https://cran.r-project.org/web/packages/mgcv/index.html;Wood 2004; Wood 2011). Such an approach allows for detection of nonlinearities in therelationship between age and measures of modular segregation without defining a set offunctions a priori (such as polynomials). Importantly, the GAM estimates nonlinearitiesusing restricted maximum likelihood (REML), and determines a penalty with increasingnonlinearity in order to avoid overfitting the data. Due to this penalty, the GAM onlymodels nonlinearities when they explain additional variance in the data above and beyondlinear effects.First, we used penalized splines to estimate nonlinear developmental patterns of mod-ular segregation. Within this model we included covariates for sex, head motion, and totalnetwork strength. Accordingly, the final model equations for estimating age effects onmodular segregation (mean participation coefficient) were as follows:Modular segregation = spline(age) + sex + motion + total network strengthAn identical model was used when estimating age effects on the participation coefficientof individual brain regions. Similarly, we applied this model across all network edges inorder to assess linear and nonlinear age effects on the strength of individual connections.For all analyses, multiple comparisons were controlled using the False Discovery Rate( q < Permutation Testing
We performed permutation-based tests across network edges in order to assess (i)whether the edges that significantly strengthened with age were localized to within-moduleconnections beyond chance, (ii) whether edges that significantly strengthen with age wereenriched for hub edges, and (iii) whether these ages had elevated edge betweenness cen-trality beyond chance.First, we permuted a binary edge label specifying whether each edge connects nodeswithin or between modules 1000 times. Then for permuted samples of within- and between-module edges, we counted the number of edges that were shown to significantly strengthen38ith age in group-level analysis. We then rank-ordered the number of edges shown to sig-nificantly strengthen with age for permuted within-module edge samples, and determinedwhere the observed number of within-module edges that strengthen with age falls relativeto this null distribution.Second, we evaluated whether edges that significantly strengthen with age were en-riched for hub edges. We permuted a binary edge label defining hub or non-hub edges1000 times. For each permuted sample, we counted the number of edges that significantlystrengthened with age in group-level analysis. Then, we rank-ordered the number of per-muted hub edges shown to significantly strengthen with age, and compared these valueswith the observed number of hub edges that strengthened with age.Third, we evaluated whether edges that significantly strengthen with age had higheredge betweenness centrality than anticipated by chance. We permuted normalized edgebetweenness centrality values 1000 times. For each permuted sample, we calculated themean
EBC of within-module edges and between-module edges that significantly strength-ened with age. We rank-ordered the mean
EBC of permuted within-module and between-module edges that strengthened with age, and compared these values with the observedmeans for within- and between-module edges separately (
Figure 6D ). Methodological Replications
To verify that observed age-related increases in modular segregation were not simplydue to specific network construction choices, we repeated developmental inferences onmodular segregation using a variety of other parameters. First, we examined age effectson modular segregation (mean participation coefficient) using a data-driven structural par-tition identified at the group level (see
Figure S2B. , Figure 5B , and detailed procedureabove). Alternatively, we also calculated the modularity quality index for each subject (cid:48) soptimal partition at γ =2.5 ( Q Sub j ), where a higher Q Sub j indicates greater modular sege-gration (
Figure 5C ). Next, we examined modular segregation (mean participation coeffi-cient) using the a priori functional partition assigned to a higher-resolution parcellationof the brain (463 nodes instead of 234; see
Figure 5D ). We also measured modular seg-regation of the functional partition using structural networks with alternative edge weightdefinitions. While primary analyses focused on FA-weighted structural networks, we alsomeasured modular segregation in streamline-weighted networks (see
Figure 5E ), whereedge weights were equal to the number of streamlines connecting a pair of nodes (Bassettet al., 2011), and additionally, where edge weights were defined by streamline density:the number of connecting streamlines divided by the total regional volume of each nodepair (Baker et al., 2015; see
Figure 5F ). In addition to examining age-related patterns ofmodular segregation using alternative network measures and parameters, we also repeatedanalyses including the following additional covariates in the GAM described above: race,39aternal education, handedness, and total brain volume.
Relationship Between Modular Segregation and Global Network Efficiency
First, we examined age-related effects on global efficiency using the same GAM asabove:Global efficiency = spline(age) + sex + motion + total network strength(see
Figure 6A ). The relationship between global efficiency and modular segregation wasassessed within a GAM while controlling for age in addition to other covariates describedabove (
Figure 6B ). Moreover, the model equation was as follows:Modular segregation = Global efficiency + spline(age) + sex + motion + total networkstrengthTo assess whether global efficiency was related to the weight of specific network connec-tions that strengthened with age, we estimated the following GAMs:Global efficiency = Average strength of within-module edges + spline(age) + sex + motion+ total network strengthGlobal efficiency = Average strength of between-module edges + spline(age) + sex + mo-tion + total network strength(see
Figure 6E and
Figure 6F ). Associations with Executive Function
To examine the association between modular segregation and executive efficiency, weincluded a spline age term in the model to account for the variance associated with linearand nonlinear age-related changes in executive ability. The final model equation was asfollows:Modular segregation = spline(age) + executive efficiency + sex + motion + total networkstrengthUsing the same GAM, we also evaluated the association between the segregation of indi-vidual modules (e.g., frontoparietal) and three cognitive efficiency factor scores: executivefunction, memory, and social cognition (see
Figure 7A ). We note that 2 participants of thefull 882 sample had incomplete cognitive datasets: subsequent analyses examining associ-ations between executive function and modular segregation focused on the remaining 880participants. Visualization of GAM model fits were created using the “visreg” packagein R (https://cran.r-project.org/web/packages/visreg/). In
Figure 3A , Figure 5 , and
Figure B , one outlying datapoint was beyond the axis range, and was excluded for visualiza-tion purposes only: group-level analyses and reported results include data points for allsubjects. Mediation analyses
Linear mediation analyses investigated whether age-related improvement in execu-tive function was mediated by modular segregation and/or global efficiency (Preacher andHayes, 2008). First, we regressed out the effects of nuisance covariates (sex, head motion,and total network strength) on the independent (X), dependent (Y), and mediating (M)variables. The residuals were then used in our mediation analysis. The significance of theindirect effect was evaluated using bootstrapped confidence intervals within the R package“lavaan” (https://cran.r-project.org/web/packages/lavaan/). Specifically, we examined thetotal effect of age on executive performance (c path;
Figure 7B ), the relationship betweenage and modular segregation (a path), the relationship between modular segregation andexecutive function (b path), and the direct effect of age on executive efficiency after in-cluding modular segregation as a mediator in the model (c (cid:48) path). The significance of theindirect effect of age on executive function through the proposed mediator (modular seg-regation) was tested using bootstrapping procedures, which minimize assumptions aboutthe sampling distribution (Preacher and Hayes, 2008). This approach involves calculatingunstandardized indirect effects for each of 10,000 bootstrapped samples and calculatingthe 95% confidence interval. This procedure was repeated to assess (i) whether the seg-regation of the frontoparietal module mediated developmental improvements in executivefunction, (ii) whether the segregation of the default mode module mediated developmentalimprovements in social cognition, and (iii) whether age-related increases in global effi-ciency mediated improvements in executive function.
Data Visualization
Network partitions and regional results (
Figure 2 , Figure 3C , and
Figure S2 ) were vi-sualized on the cortical white matter surface using FreeSurfer visualization tools in MAT-LAB. While age effects on the participation coefficient for subcortical brain regions arenot visualized in
Figure 3C , these regions were included in all analyses. Brain networkvisualizations in
Figure 4 and
Figure 6 were generated using BrainNet Viewer (Xia et al.2013). 41 upplemental References
1. Andersson, J.L. and Sotiropoulos, S.N. (2016). An integrated approach to correctionfor off-resonance effects and subject movement in diffusion MR imaging. Neuroim-age, ,1063-1078.2. Bassett, D.S., Porter, M.A., Wymbs, N.F., Grafton, S.T., Carlson, J.M. and Mucha,P.J. (2013). Robust detection of dynamic community structure in networks. Chaos, , 013142.3. Fenn, D.J. Porter, M.A., McDonald, M., Williams, S., Johnson, N.F., and Jones, N.S.(2009). Dynamic communities in multichannel data: An application to the foreignexchange market during the 2007-2008 credit crisis. Chaos , 033119.4. Giedd, J.N., Blumenthal, J., Jeffries, N.O., Castellanos, F.X., Liu, H., Zijdenbos, A.,Paus, T., Evans, A.C., Rapoport, J.L. (1999). Brain development during childhoodand adolescence: a longitudinal MRI study. Nature Neuroscience , 861-3.5. Gong, G., He, Y., Concha, L., Lebel, C., Gross, D.W., Evans, A.C. and Beaulieu, C.(2009). Mapping anatomical connectivity patterns of human cerebral cortex usingin vivo diffusion tensor imaging tractography. Cerebral Cortex, , 524-536.6. Good, B. H., Montjoye, Y., and Clauset, A. (2010). Performance of modularitymaximization in practical contexts. Physical Review E , 046106.7. Gu, S., Pasqualetti, F., Cieslak, M., Telesford, Q.K., Alfred, B.Y., Kahn, A.E.,Medaglia, J.D., Vettel, J.M., Miller, M.B., Grafton, S.T. and Bassett, D.S. (2015).Controllability of structural brain networks. Nature Communications, .8. Lancichinetti, A. and Fortunato, S., 2012. Consensus clustering in complex net-works. Scientific reports, .9. Newman, M.E.J., 2004. Analysis of weighted networks. Physical Review E, ,056131.10. Paus, T., Zijdenbos, A., Worsley, K., Collins, D.L., Blumenthal, J., Giedd, J.N.,Rapoport, J.L. and Evans, A.C. (1999). Structural maturation of neural pathways inchildren and adolescents: in vivo study. Science, , 1908-1911.11. Shaw, P., Greenstein, D., Lerch, J., Clasen, L., Lenroot, R., Gogtay, N.E.E.A.,Evans, A., Rapoport, J. and Giedd, J. (2006). Intellectual ability and cortical de-velopment in children and adolescents. Nature, , 676-679.12. Xia, M., Wang, J. and He, Y. (2013). BrainNet Viewer: a network visualization toolfor human brain connectomics. PLoS One,8