Altered white matter connectivity and network organization in polymicrogyria revealed by individual gyral topology-based analysis

NeuroImage 86 (2014) 182–193

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Altered white matter connectivity and network organization in polymicrogyria revealed by individual gyral topology-based analysis Kiho Im a,b,⁎, Michael J. Paldino c, Annapurna Poduri d, Olaf Sporns e, P. Ellen Grant a,b,c a

Division of Newborn Medicine, Boston Children's Hospital, Harvard Medical School, Boston, MA 02115, USA Fetal Neonatal Neuroimaging and Developmental Science Center, Boston Children's Hospital, Harvard Medical School, Boston, MA 02115, USA Deptartment of Radiology, Boston Children's Hospital, Harvard Medical School, Boston, MA 02115, USA d Deptartment of Neurology, Boston Children's Hospital, Harvard Medical School, Boston, MA 02115, USA e Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN 47405, USA b c

a r t i c l e

i n f o

Article history: Accepted 5 August 2013 Available online 15 August 2013 Keywords: Cortical malformation Diffusion tensor imaging Gyral pattern Polymicrogyria Structural connectivity network

a b s t r a c t Polymicrogyria (PMG) is a cortical malformation characterized by multiple small gyri and altered cortical lamination, which may be associated with disrupted white matter connectivity. However, little is known about the topological patterns of white matter networks in PMG. We examined structural connectivity and network topology using individual primary gyral pattern-based nodes in PMG patients, overcoming the limitations of an atlasbased approach. Structural networks were constructed from structural and diffusion magnetic resonance images in 25 typically developing and 14 PMG subjects. The connectivity analysis for different fiber groups divided based on gyral topology revealed severely reduced connectivity between neighboring primary gyri (short U-fibers) in PMG, which was highly correlated with the regional involvement and extent of abnormal gyral folding. The patients also showed significantly reduced connectivity between distant gyri (long association fibers) and between the two cortical hemispheres. In relation to these results, gyral node-based graph theoretical analysis revealed significantly altered topological organization of the network (lower clustering and higher modularity) and disrupted network hub architecture in cortical association areas involved in cognitive and language functions in PMG patients. Furthermore, the network segregation in PMG patients decreased with the extent of PMG and the degree of language impairment. Our approach provides the first detailed findings and interpretations on altered cortical network topology in PMG related to abnormal cortical structure and brain function, and shows the potential for an individualized method to characterize network properties and alterations in connections that are associated with malformations of cortical development. © 2013 Elsevier Inc. All rights reserved.

Introduction Polymicrogyria (PMG) is a malformation of cortical development and the result is abnormal cortical cytoarchitecture and the formation of multiple small gyri (Barkovich, 2010). As neurons in the cortical layers establish axonal connections with local and distant neurons during development in a laminar specific pattern, disorganization or absence of specific cortical layers and reduced numbers of neurons within these layers might be associated with altered axonal connectivity in the underlying white matter. Diffusion tensor imaging (DTI) studies in humans with PMG have revealed significantly decreased fractional anisotropy (FA) in the white matter subjacent to polymicrogyric cortex (Bonilha et al., 2007; Trivedi et al., 2006), with other studies reporting altered fiber tract architecture (Munakata et al., 2006; Saporta et al., 2011). However, to date, only specific fiber tracts have been examined

⁎ Corresponding author at: Boston Children's Hospital, 1 Autumn Street, Boston, MA 02115, USA. E-mail address: [email protected] (K. Im). 1053-8119/$ – see front matter © 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.neuroimage.2013.08.011

with small numbers of patients due to lack of routine use of advanced imaging and image analysis techniques (Bonilha et al., 2007; Munakata et al., 2006; Saporta et al., 2011; Trivedi et al., 2006; Widjaja et al., 2007). The human brain is a large-scale complex network, segregated and integrated via connectivity patterns allowing simultaneous global and local parallel information processing (Bullmore and Bassett, 2011; Bullmore and Sporns, 2009; Gong et al., 2009; Hagmann et al., 2008). Graph theoretical analysis provides an efficient and quantitative way to model complex brain networks and characterize their topological architecture (Bullmore and Sporns, 2009; Rubinov and Sporns, 2010). To define the nodes of a brain graph, most previous studies have parcellated cortical regions using volume- or surface-based registration to an atlas, such as the automated anatomical labeling atlas (TzourioMazoyer et al., 2002) or probabilistic surface atlas in the FreeSurfer (Desikan et al., 2006; Fischl et al., 2004). However, using such atlasbased techniques, many short fiber inter-gyral connections would be considered as self-connections and heterogeneously connected brain regions would be lumped into single nodes (Zalesky et al., 2010). In addition, typical gyral patterns cannot be identified in many patients with

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malformations of cortical development because of the abnormal cortical folding. Hence, identical labeling for parcellated regions cannot be applied to many PMG brains because anatomical and functional correspondences of labeled regions in PMG brains are unlikely to correspond with the atlas-labeled regions in normal brains (Fig. 1). Here we propose a gyral topology-based parcellation scheme as a more appropriate node definition for studying abnormally folded brains. Regional organization of specific pathways of axonal fiber bundles has been previously reported with subcortical U-fibers and long association fibers tending to project from and be located centrally within the gyri (Schmahmann and Pandya, 2006; Schmahmann et al., 2007; Takahashi et al., 2011). Particularly, short U-shaped fibers were shown to connect a given gyrus to other adjacent gyri in DTI studies (Catani et al., 2012; Guevara et al., 2011; Magro et al., 2012; Oishi et al., 2008; Zhang et al., 2010). Based on these prior post-mortem and imaging studies, we propose structural connectivity and graph theoretical network analysis based on an individual's primary gyral pattern for a more accurate description of the network in PMG brains, overcoming the limitations of the atlas-based parcellation. Furthermore, we investigated whether the structural network changes were associated with regional distribution and extent of PMG involvement as well as language impairment (deficits in comprehension, production, and use of language), which is one of the typical features of developmental delay in PMG (Guerreiro et al., 2002; Saporta et al., 2011). In order to compare with an atlas-based approach, we performed supplementary network analysis based on FreeSurfer parcellation, which has been widely used for node definition (Cheng et al., 2012; Hagmann et al., 2008, 2010; Honey et al., 2009).

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Material and methods Participants PMG patients were identified retrospectively from a search of existing patient data at the Boston Children's Hospital. Inclusion in this study was based on the following criteria: (1) age between 2 and 20 years, (2) confirmed clinical diagnosis of epilepsy, (3) diagnosis of PMG established by pathology or magnetic resonance imaging (MRI), (4) MRI examination performed at 3 T with volumetric T1-weighted image and 30 direction DTI, and (5) language development assessed by a pediatric neurologist. After inspection of image data, we excluded those with significant motion or other artifactual degradation of image quality. An age-matched typical developing control group was also retrospectively identified from existing patient data with the following inclusion criteria: (1) subjects presented for evaluation of headache, (2) subjects must have had an MRI examination of the brain performed at 3 T (identical protocol to the exam performed in the patient group), and (3) subjects must have had their language development characterized as typical by a pediatric neurologist. Exclusion criteria for the normative cohort were as follows: (1) any neurologic abnormality by history or physical exam, (2) any degree of language impairment, and (3) any MRI abnormality. The final sample of this study consisted of 14 PMG patients (n [male/ female] = 9/5, age [mean ± standard deviation (SD), range]: 11.0 ± 6.0, 2–20 years) and 25 typical controls (n = 13/12, age: 9.6 ± 4.6, 2–17 years) (Table 1). This study was approved by the Boston Children's Hospital Institutional Review Board.

Fig. 1. Atlas-based parcellation using FreeSurfer and individual gyral pattern-based parcellation for the typical control and PMG patient brains, and network construction for different fiber groups divided by gyral topology-based path length. The PMG shows irregular gyral patterns with abnormally oriented gyri. The gyral based segmentation provides a more uniform and consistent segmentation of both normal and PMG brains with regions that are similar in size and with equal respect for gyral topology. When the FreeSurfer parcellation is applied to the PMG brain, regions that are gyri in the normal brain become multiple gyral segments (for example the postcentral gyrus). Anatomical parcellation and labeling using an atlas seems not proper for the PMG brain.

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Table 1 Clinical data (age, sex, PMG lobar involvement and extent score, and language score) for individual PMG patients. Age (year)

Sex

Lobar involvement of PMG

PMG extent score

Language score

14 16 9 9 18 3 2 8 5 14 20 5 10 18

M M F M M F M F M M M F M F

R-T, R-P, R-O B-F, B-P B-F, R-T, R-P, R-O L-F, L-T, L-P B-T, B-O B-F, B-T, R-P B-F, B-T, B-P L-F, L-T, L-P B-F, B-T, B-P R-F B-T, B-P B-F R-F, R-T, R-P R-T

3 4 5 3 4 5 6 3 6 1 4 2 3 1

2 2 1 1 1 3 2 2 2 1 2 1 2 1

M: male, F: female. B: both hemispheres, L: left hemisphere, R: right hemisphere. F: frontal, T: temporal, P: parietal, O: occipital. Language score data — 1: normal to mild impairment, 2: moderate-to-severe impairment, 3: profound impairment (nonverbal).

MRI acquisition and diagnosis All imaging was performed on two MRI scanners that were the same kind from the same vendor (Siemens, Tim Trio [3 T]), running the same system software and identical pulse sequences (typical controls: n [scannerA/scannerB] = 15/10, PMG patients: n = 13/1). In addition both used the same commercial 32 channel receive coil. The following sequence was obtained for each patient: sagittal Magnetization Prepared Rapid Gradient Echo (MPRAGE; TR/TE: 2530 ms/3.39 ms; 1 acquisition; flip angle: 7°, inversion time: 1100 ms; FOV: 22 cm; acceleration factor: 2; voxel size [mm]: 1 × 1 × 1) and axial single shot echo planar DTI (TR/TE: 7000 ms/142 ms; 1 acquisition; flip angle: 90°; voxel size [mm]: 2 × 2 × 2). For DTI, a total of 35 image sets was acquired: 5 without diffusion weighting and 30 with non-collinear diffusion-weighting gradients and a b value of 1000 s/mm2. Based on standard anatomic images, the location of dysplastic cortex in PMG patients was evaluated by two pediatric neuroradiologists blinded to the connectivity analysis and language data. Specifically, each lobe in each hemisphere of each patient was categorized as involved or not-involved in PMG by visual inspection with a value of ‘1’ indicating involvement and a value of ‘0’ indicating no involvement. The extent of PMG involvement was scored as the sum of these values across all lobar regions for each hemisphere. Language development of PMG patients was qualitatively assessed from the individual medical record, and the 14 patients were divided into 3 groups: (1) normal language development to mild impairment: appropriate for age [n = 6], (2) moderate to severe impairment: language performance noticeably lower than peers [n = 7], and (3) profound impairment: nonverbal [n = 1] (Table 1). Three raters reviewed the medical record and all agreed on the language scores of 14 PMG patients, showing high inter-rater reliability.

Node definition: gyral segment parcellation To segment and define node regions based on individual gyral patterns, we used a sulcal depth map measured on the white matter surface. The FreeSurfer computed sulcal depth measure as described previously (Fischl et al., 1999). We then performed a watershed algorithm based on the depth map on triangular meshes (Im et al., 2010, 2011, in press). The algorithm initially sorted the depth values and created a list of vertices that were ordered by their depth. The vertex of the shallowest depth, gyral tip, was first defined as the initial vertex of a gyral segment. If the next vertex in the list was the neighbor of the previously identified gyral segment, it was added to this segment. If all of its neighbors were unlabeled, we created a newly labeled gyral segment. To prevent over-extraction of the gyral segments, we first reduced noisy depth variations with surface-based heat kernel smoothing with a full-width half-maximum value of 10 mm (Chung et al., 2005). Subsequently we performed segment merging in the watershed algorithm using the area of the segment. If one of the areas of two or more gyral segments was smaller than a threshold (30 mm2) when they met at a ridge point, the smaller region below the threshold was merged into the adjacent gyral region. The results of the gyral region definition are shown for typical and PMG brains in Fig. 1 and can be compared to atlas-based anatomical parcellation using FreeSurfer. The gyral pattern-based method divided the cortical surface into more regions than FreeSurfer and unlike FreeSurfer divided the cortical surface into regions that are similar in size. The average of the number and area of gyral nodes for the whole cortex is 160.3 (range: 145–174) and 9.43 cm2 (SD: 5.60 cm2) for typical controls, and 160.4 (142–178) and 8.85 cm2 (SD: 5.61 cm2) for PMG patients. In contrast, the FreeSurfer parcellation defined fewer regions (68) with larger mean area (22.80 cm2 for typical controls and 21.63 cm2 for PMG patients) and larger variation (SD: 17.24 cm2 for typical controls and SD: 17.35 cm2 for PMG patients). Some FreeSurfer regions are gyri (for example pre and postcentral gyri) or sections of gyri (for example rostral/caudal anterior and posterior cingulate gyri) but some regions are more than one gyrus such as the middle frontal and inferior parietal gyri (Fig. 1). Therefore FreeSurfer regions are more variable in size compared to our gyral parcellation and variably segment the brain into gyral segments, gyri or multiple gyri. In addition when the FreeSurfer parcellation is applied to a PMG brain, regions that were gyri in the normal brain become multiple gyral segments in the malformed PMG brains (for example the postcentral gyrus in Fig. 1). Our gyral based segmentation provides a more uniform and consistent segmentation of both normal and malformed brains with regions that are similar in size and with equal respect for gyral topology (Fig. 1). Not only does our method respect an individual's major sulci, it also segments a single gyrus into segments using a watershed algorithm based on the depth map of the cortical surface. This is possible because the gyral crests are not flat but are undulated. Parcellation of a large single gyrus, such as pre and postcentral gyri into smaller segments, may be biologically meaningful because extrinsic anatomical connections in a single gyral bank are not homogeneous. Microgyria were not represented as gyral nodes in PMG brains as the spatial resolution of the MR images was not sufficient to accurately resolve this microstructure. Gyral nodes were assigned to gyral folds on the scale of primary gyral folds and as a result the number of gyral nodes were not significantly different between the typical and PMG groups.

Cortical surface reconstruction White matter tractography The images were processed to extract cortical surfaces using the FreeSurfer pipeline (Dale et al., 1999; Fischl et al., 1999). Once the cortical models were reconstructed, they were automatically parcellated into anatomical regions based on lobar and gyral/sulcal structure (Desikan et al., 2006; Fischl et al., 2004). The same surface reconstruction method was used for sulcal pattern analysis of patients with PMG in our previous study (Im et al., in press).

Distortions in the diffusion tensor images caused by eddy currents and simple head motions were corrected by the diffusion toolbox of the FSL package (www.fmrib.ox.ac.uk/fsl/fdt). Diffusion tensor models were estimated and the FA and the apparent diffusion coefficient (ADC) were calculated at each voxel. We reconstructed whole-brain white matter fiber tracts in native diffusion space for each subject

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using the fiber assignment by continuous tracking algorithm (Mori et al., 1999), embedded in the Diffusion Toolkit (trackvis.org) (Wang et al., 2007). We terminated tracking when the angle between two consecutive orientation vectors was greater than the given threshold of 45° or when both ends of the fibers extended outside of the white matter mask which was generated by the tissue segmentation process (Hagmann et al., 2008, 2010). Edge definition and structural connectivity network construction T1-weighted images were co-registered to the b0 images using the affine registration tool from the FSL package (www.fmrib.ox.ac.uk/fsl/ flirt) in order to construct the cortical brain network. Two nodes (regions) were considered to be structurally connected by an edge, when at least the end points of 2 fiber tracts were located less than 3 mm from each of the 2 surface node regions, with self-connections excluded. A threshold of the number of fiber tracts was selected to reduce the risk of false-positive connections due to noise or the limitations in the deterministic tractography (Lo et al., 2010; Shu et al., 2011). The number of fiber tracts performed with streamline tracking may reflect the WM structure (Houenou et al., 2007); this has been used for a weight of network edges (Batalle et al., 2012; Shu et al., 2011; Yan et al., 2011; Zhang et al., 2011) but largely depends on the brain size (the number of white matter voxels) and the areas of node regions. For each edge, the connection density (number of fiber tracts per unit surface) was calculated between 2 nodes, Nij/Sij, where Nij is the number of tracts between region i and j, and Sij is the surface area of 2 regions, i and j. We also used ADC to modify strengths of interregional connections because it is an important marker of white matter development and maturation (myelin and axonal diameter changes) (Beaulieu, 2002; Hagmann et al., 2010). To weight the edge, we used the product between the connection density and mean inverse ADC (1/ADC) along all the fibers connecting a pair of regions (Hagmann et al., 2008, 2010). Weighted matrices of the structural connectivity were constructed for each individual. Gyral topology-based connectivity analysis We constructed different fiber groups and networks divided according to individual gyral pattern and topology. If two gyral segments geometrically met on the cortical surface, they were connected with an edge and became 1st neighbors to each other. We then defined the 1st, 2nd, 3rd, 4th and 5th or more neighbors for each gyral region by measuring the number of edges in the shortest paths (Fig. 1). The connections between the 1st neighboring gyri were taken to be short association U-fiber connections and the connections between distant gyri were taken to be long association fiber connections. We separately measured the mean FA and ADC values and basic network measures (mean strength and density of the network) for the connections between the nth neighboring gyri and between hemispheres (Fig. 1). For the mean strength of the nth neighbor connections, node strengths were computed as the sum of weights of links connected to the nth neighboring gyri and were averaged across all nodes. The network density was measured as the fraction of present connections to possible connections between the nth neighboring gyri without considering the connection weights. Since PMG patterns are highly heterogeneous in terms of topographic distribution, in addition to the whole brain analysis we performed a lobar regional analysis (frontal, temporal, parietal, and occipital lobes). We calculated these measurements for the connections within lobe and between all pairs of lobes in each left and right hemisphere. Network analysis Graph theoretical analyses were carried out on structural connectivity networks of patients with PMG and typical controls using the Brain

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Connectivity Toolbox (www.brain-connectivity-toolbox.net) (Rubinov and Sporns, 2010). We calculated the weighted clustering coefficient (C) and transitivity (T) as measures of network segregation (Onnela et al., 2005). To measure network integration, we calculated the average shortest path length between all pairs of nodes in the network, which is known as the characteristic path length (L) of the network (Watts and Strogatz, 1998). In addition, the global efficiency (E) was computed as the average inverse shortest path length (Latora and Marchiori, 2001). Our connectivity networks had different sizes, i.e. different numbers of nodes and edges. The graph measures were scaled against the mean values of graph measures obtained from 1000 matched random graphs that preserved the same number of nodes, edges, and degree sequence (Maslov and Sneppen, 2002): C s1 ¼ C=C rand ; T s1 ¼ T=T rand ;

Ls1 ¼ L=Lrand ;

Es1 ¼ E=Erand :

These scaled measures reflect their level in the experimental network relative to a null population with preserved node statistics but totally disordered topology. To improve the insensitivity to different network size in brain network comparisons, we used another scaling approach with both random and regular lattice networks that provides information about the extent to which the network incorporates random or regular structural features (Sporns and Zwi, 2004; van Wijk et al., 2010; Zamora-Lopez et al., 2009): C s2 ¼ ðC–C rand Þ=ðC lattice –C rand Þ; Ls2 ¼ ðL–Lrand Þ=ðLlattice –Lrand Þ;

T s2 ¼ ðT–T rand Þ=ðT lattice –T rand Þ Es2 ¼ ðE–Erand Þ=ðElattice –Erand Þ:

A small-world network is intermediate between that of random networks, the short overall path length of which is associated with a low level of local clustering, and that of regular lattice networks, the highlevel of clustering of which is accompanied by a long path length (Watts and Strogatz, 1998). To examine small-world properties, we observed if a real network had similar path length but higher clustering coefficient than a random network, that is Cs1 N 1, Ls1 ≈ 1 and 0 b Cs2 b 1, 0 b Ls2 b 1. This condition was captured by a single scalar value, the small-worldness, σ = Cs1/Ls1, which is typically larger than one in the case of small-world organization (Humphries and Gurney, 2008). We computed the assortativity coefficient for measure of network resilience, which is a correlation coefficient between the degrees of all nodes on two opposite ends of a link (Newman, 2002). For supplementary experiments, these graph measures were also computed for the networks derived from the FreeSurfer nodes parcellation. Network module analysis A brain graph can generally be subdivided or partitioned into modules of nodes. A module is defined as a group of nodes that have strong connections to other nodes within the module but weak connections to nodes outside the module. Optimal modular structure and modularity value were estimated by maximizing the ratio of within-modular to between-modular edges with optimization algorithms, and the number of modules was measured (Blondel et al., 2008). Furthermore, we measured the gyral topology-based path lengths of fiber connections and mean node strengths within the same module and between different modules for a closer examination of module structure (Hagmann et al., 2010). Statistical analysis Although the age range was wide within a group, age distribution was matched and was not statistically different between typical and PMG groups (two sample t test, P = 0.419). The male to female ratio of the two groups was different but the difference was not statistically significant (χ2 test, P = 0.458). Moreover, to further ensure that age and sex were not confounders, age and sex were regressed out as

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covariates and permutation tests were performed for all statistical analyses. Mean FA and ADC values based on gyral topology for the whole brain were compared between the typical and PMG groups. First, actual between-group differences were computed. Second, each subject was randomly assigned to one of the two groups with the same size as the original control and PMG groups at 10,000 times and group differences were calculated for each set. To assign a P value to the between-group difference, we counted the times that the actual difference was smaller than the difference obtained from the resampled sets, and divided that value by the number of random permutations (10,000). To find their relationships with the PMG extent, we performed Spearman correlation analysis in the PMG patients, which is a non-parametric test of statistical dependence between two variables. Since lobar regional involvement of PMG was visually assessed, the association between regional PMG involvement and connectivity disruption can be investigated. The PMG patients were classified into two groups, PMG-involved (PMGP) or -not involved (PMGN) group for each lobe. For within-lobe FA and ADC analyses, we compared the 3 groups (typical controls, PMGN and PMGP groups). In a between-lobe analysis, PMG patients without involvement in both lobes were classified as the PMGN group and the others as the PMGP group. The same statistical tests were performed for all pairs of lobes in each hemisphere. A Bonferroni correction was used for adjusting statistical results for multiple group comparisons. We also tested whether the FA and ADC values in PMG patients were significantly associated with the language function score using Spearman correlation analysis. Comparisons of graph measures are influenced by the number of nodes of the network (van Wijk et al., 2010; Zalesky et al., 2010). Although we used the scaling approach insensitive to different network size (van Wijk et al., 2010), we controlled for the remaining effect of number of nodes by adding it as a covariate in the analysis of network measures. Differences in graph measures of the network between the typical and PMG groups were examined using the permutation test (Bullmore and Bassett, 2011; van den Heuvel et al., 2010; Zhang et al., 2011). We examined the Spearman correlations between the network measures and the PMG involvement score in PMG patients. In case of mean strength and density of the network, we observed the connections between the nth neighboring gyri and between hemispheres, and also within- and between-lobe connections. For the lobe-based analysis, differences in the mean strength and network density were investigated between the 3 groups, typical controls, PMGN and PMGP groups, as performed in mean FA and ADC values above. The relationships between all network measures and the language function were also statistically analyzed using the Spearman correlation. A significance threshold of P = 0.05 was used for all statistical tests. For the networks constructed from the FreeSurfer parcellation, graph measures were compared between the typical and PMG groups using the same permutation test, controlling for age and sex. Distribution of hub regions We measured nodal centrality using the betweenness centrality for each node, defined as the fraction of all shortest paths in the network that pass through a given node (Brandes, 2001; Freeman, 1978). Nodes were considered as the hubs of the network if their betweenness centrality was at least one SD greater than the average betweenness centrality of the whole network (Nmean + SD) (Gong et al., 2009; Zhang et al., 2011). Previous studies detected nodes with high betweenness centrality as the hubs in a group from mean values or average connectivity matrix across all subjects (Li et al., 2009; Yan et al., 2011). However, this approach was not employed in our study because the number of nodes was not constant and node correspondence was not defined. Basic concept of our hub regions detection was to identify the hubs from all individual networks on the same space and defined the regions where the hubs were constantly detected across subjects and densely clustered. We first extracted the centers of surface gyral regions

defined as the hubs, and transformed and overlaid all individual hubs into a standardized stereotaxic space by applying a Talairach transformation matrix. The nodes were clustered by the k-means clustering algorithm using their 3D positions (x, y, z) as a feature. The number of clusters k was determined as the value of the number of all hubs Nhub over half of the number of subjects Nsubj in a group, Nhub / (Nsubj / 2). If the number of hubs in some clusters was more than Nsubj/2, these clusters of high density were defined as the hub regions for a group and their centroids were generated across the whole cerebral area (Fig. 2). However, initial seeds for the k-means clustering were randomly set, so clustering results were little different as shown in Fig. 2. The clustering was performed 100 times, and inconsistent cluster centroids were removed. Cluster centroids that had less than 20 other centroids present within 10 mm distance were discarded. Finally, a map of the regional distribution of hub regions was constructed for each group (Fig. 2). Results Structural connectivity based on gyral topological path length in the whole brain We found significantly decreased short U-fiber connections in the PMG patients when compared to the typical control group. FA and mean strength and density of the networks between the 1st neighboring gyri were significantly lower and ADC was higher in the PMG than in the typical group (FA: P = 0.013, ADC: P = 0.048, network density: P = 0.003, mean strength: P = 0.019). Decreased FA (P = 0.034) and increased ADC (P = 0.040) were found in the long association fibers between the 5th or more neighboring gyri for the PMG group. Significantly lower network density (P = 0.011) and mean strength (P = 0.001) were shown in the PMG group for the inter-hemispheric connections. Error bars are provided for comparisons of all measurements between typical and PMG groups (Fig. 3). Network density of short connections between the 1st neighboring gyri was highly correlated with the extent of PMG involvement (correlation coefficient R = −0.824, P = 0.0005), which can be shown in a scatter plot (Fig. 3). No significant association with the language score was found using all gyral connections in the whole brain. Structural connectivity within and between lobes Because the significant group differences and correlation with PMG extent were primarily shown in the short association fibers, only 1st neighboring gyral connections were considered and used for withinlobe connectivity analysis. Group difference tests for the connectivity within left and right occipital lobes were excluded from statistical analysis due to small number of subjects (n ≤ 3) in the PMGP group. This analysis revealed significantly altered structural connectivity for all other lobes in PMG. Significantly lower FA, network density, mean strength or higher ADC was mainly found in PMG-involved group (PMGP) rather than PMG-not involved group (PMGN) within left and right frontal, temporal, and parietal lobes. Although lobar involvement of PMG was not directly detected, significantly reduced connectivity (lower FA or mean strength) was revealed when compared to the typical group within the left temporal and parietal lobes and right parietal lobe (Table 2). For between-lobe connectivity measure, we excluded the 1st neighboring gyral connections (short U-fibers) that are present in the boundary between lobes. Significantly reduced connectivity (lower FA, network density, mean strength or higher ADC) was mostly revealed between frontal and temporal lobes, and between temporal and parietal lobes in left and right hemispheres in the PMGP compared to the typical or PMGN group. For the connection between left temporal and occipital lobes, higher ADC was found in the PMGP than in the typical group. The PMGN also had significantly decreased FA between the left temporal and

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Fig. 2. The overall process to construct a map of the distribution of hub regions. All individual hub nodes were transformed and overlaid in a standardized space. The nodes were clustered by the k-means clustering and the centroids of clusters with high density were generated. Inconsistent cluster centroids were removed by performing the k-means clustering many times and final hub regions map was constructed.

occipital lobes and mean strength between the right frontal and temporal lobes (Table 2). Significant correlations with the language score were primarily found around the frontal and parietal lobes. We found significant correlations between FA and the language score within the frontal and

parietal lobes, between frontal and parietal lobes, and between temporal and parietal lobes in the left hemisphere. For the right hemisphere, only network density was negatively associated with the language score within the parietal lobe. More detailed significant results for the group comparison and correlation analysis are shown in Table 2.

Fig. 3. Error bars for comparisons of FA, ADC, network density and mean strength between typical and PMG groups (*P b 0.05, **P b 0.005). Error bars display standard error of the mean. Scatter plot is provided for the significant correlation between the network density for the 1st neighboring gyral connections and the PMG extent.

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Table 2 Significant statistical results (P b 0.05) for within- and between-lobe group differences and correlations with language score. (P values) are provided for group differences, and (correlation coefficients, P values) for correlations. Left

F

T

P

F

FA Sig. corr. (−0.578, 0.033) ADC PMGN b PMGP (0.045) Network density N N PMGP (0.001) PMGN N PMGP (0.006)

FA N N PMGP (0.023) Network density N N PMGP (0.022) Mean strength N N PMGP (0.040)

FA Sig. corr. (−0.565, 0.038)

T

FA N N PMGN (0.020) Network density N N PMGP (0.0003) PMGN N PMGP (0.013)

P

FA N N PMGP (0.031) Sig. corr. (−0.600, 0.026) ADC N b PMGP (0.002)

O

FA N N PMGN (0.006) ADC N b PMGP (0.018)

FA N N PMGN (0.047) N N PMGP (0.003) Sig. corr. (−0.547, 0.046) Mean strength N N PMGP (0.014) PMGN N PMGP (0.017)

O

X

Right

F

T

F

ADC N b PMGP (0.031)

FA N N PMGP (0.005) Mean strength N N PMGN (0.030) FA N N PMGP (0.013)

T P

O

P

O

FA PMGN N PMGP (0.010) Network density N N PMGP (0.037) Sig. corr. (−0.560, 0.040) Mean strength N N PMGN (0.013) X

Sig. corr.: Significant correlation with language score. F: frontal, T: temporal, P: parietal, O: occipital. N: typical control group, PMGP: PMG-involved group, PMGN: PMG-not involved group.

Characteristics of connectivity networks Group comparisons on network measures revealed significantly lower clustering coefficient Cs2 (scaled by using both random and regular lattice networks) (P = 0.015) in the PMG patients than in the typical controls as represented in the scatter plots in Fig. 4. The connectivity networks showed Cs1 N 1, Ls1 ≈ 1, 0 b Cs2 b 1, 0 b Ls2 b 1, and σ N 1

in the typical and PMG groups, thus both groups demonstrated similar small-world attributes. There was no statistically significant difference in assortativity. Statistical results for the group comparisons of all network measures are present in Table 3. The clustering coefficient Cs1 and transitivity Ts1 (scaled by random networks) in PMG patients, although not significantly different from normal overall, were significantly correlated with the PMG extent score (Cs1: R = −0.618, P = 0.021,

Fig. 4. Significantly lower clustering coefficient Cs2 (scaled by using both random and regular lattice networks) (P = 0.015) and higher modularity (P = 0.013) in the PMG than in the typical group.

K. Im et al. / NeuroImage 86 (2014) 182–193 Table 3 Statistical results for the group comparisons of network measures and correlations with the PMG extent and language score. Network measure

Typical

PMG

Cs1

6.176 (0.534)

6.122 (0.645) Corr. with PMG extent (P = Corr. with language score (P 4.196 (0.490) Corr. with PMG extent (P = Corr. with language score (P 1.356 (0.146) 0.781 (0.035) 0.741 (0.051) 0.675 (0.066) 0.604 (0.246) 0.775 (0.128) 4.539 (0.499) 0.044 (0.078)

4.259 (0.539)

Ts1

Ls1 Es1 Cs2 Ts2 Ls2 Es2 Small-worldness Assortativity

1.323 (0.081) 0.794 (0.024) 0.784 (0.051) 0.691 (0.052) 0.577 (0.154) 0.749 (0.110) 4.677 (0.403) 0.058 (0.053)

P value 0.842 0.021) = 0.046) 0.817 0.025) = 0.018) 0.273 0.154 0.015 0.478 0.606 0.447 0.316 0.513

C: clustering coefficient, T: transitivity, L: characteristic path length, E: global efficiency. s1: scaled by random networks, s2: scaled by random and regular lattice networks. Corr.: correlation. Data: mean (standard deviation).

Ts1: R = −0.604, P = 0.025) and the language score (Cs1: R = −0.547, P = 0.046, Ts1: R = −0.631, P = 0.018) (Fig. 5). Our network module analysis found higher modularity (P = 0.013) (Fig. 4) and greater number of modules (P = 0.022) in the PMG patients than in the typical controls. Mean strengths within the same module and between different modules were both significantly lower in PMG (within-module: P = 0.020, between-module: P = 0.001). The PMG patients also exhibited significantly smaller ratio of betweenmodule to within-module strengths (P = 0.002) (Table 4). The analysis of gyral topology-based path lengths showed that within-module connections mainly consisted of short-range association fibers (1st–3rd neighboring gyral connections) in both groups. On the other hand,

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Table 4 Statistical results of the network module analysis.

Modularity Number of modules Within-module mean strength (NSw) Between-module mean strength (NSb) NSb/NSw

Typical

PMG

P value

0.680 (0.016) 9.76 (1.76) 322.884 (60.575)

0.693 (0.020) 11.43 (2.24) 283.269 (56.413)

0.013 0.022 0.020

9.544 (2.204)

7.265 (2.015)

0.001

0.029 (0.003)

0.025 (0.004)

0.002

Data: mean (standard deviation).

high ratio of long association (5th neighboring gyral connections) and inter-hemispheric fibers were observed between different modules. We finally constructed the spatial distribution of hub regions with high betweenness centrality (Fig. 6). The hub regions were predominantly identified for both groups in the medial and lateral regions of the frontal and parietal cortex, and their distribution was nearly symmetric for both hemispheres. The identified regions included portions of superior and middle frontal gyri, precuneus, and superior and inferior parietal gyri in the left and right hemispheres. We found that the hubs in the left and right anterior prefrontal regions and left posterior inferior temporal regions were detected in the typical group, but not in the PMG group. Instead, the hub region was identified in the right superior temporal region in PMG. The graph theoretical network analysis using the FreeSurfer parcellation revealed significantly lower characteristic path lengths, Ls1 (P = 0.012) and Ls2 (P = 0.023) in PMG patients. Mean clustering coefficient Cs1 was higher in PMG patients with a trend toward significance (P = 0.056). As a result, significantly higher small-worldness was shown in the connectivity networks of PMG patients (P = 0.002) (Table 5), while characteristic path length and small-worldness were not significantly different, but clustering coefficient significantly reduced in PMG in our gyral topology-based analysis.

Fig. 5. Significant negative relationships of the clustering coefficient Cs1 and transitivity Ts1 (scaled by random networks) with the PMG extent and the language score.

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Fig. 6. The hub regions distribution for the typical and PMG groups. The hub regions are shown for both groups in the portions of superior and middle frontal gyri, precuneous, and superior and inferior parietal gyri in both left and right hemispheres. The hubs are located in the left and right anterior prefrontal regions and left posterior inferior temporal regions in the typical, but not in the PMG group. The hub region can be identified in the right superior temporal region in the PMG group.

Discussion We showed significantly disrupted structural connectivity and network organization in PMG patients using a novel node region definition based on individual primary gyral patterns. Altered structural connectivity and network organization in PMG also related to abnormal cortical structure and impaired language function. Although our study was based on a small set of patients, this is the largest population of patients with a malformation of cortical development studied with high-quality imaging data and quantitative whole-brain network analysis. Disrupted white matter network organization in PMG We first found significantly decreased connectivity of short association fibers linking adjacent primary gyri in PMG patients. Altered microstructural and physiological properties of short connections were Table 5 Statistical results for the group comparisons of network measures based on FreeSurfer parcellation nodes. Network measure

Typical

PMG

P value

Cs1 Ts1 Ls1 Es1 Cs2 Ts2 Ls2 Es2 Small-worldness Assortativity

3.027 (0.249) 2.296 (0.243) 1.170 (0.088) 0.901 (0.037) 0.962 (0.093) 0.871 (0.094) 1.314 (0.732) 1.093 (0.433) 2.601 (0.283) −0.044 (0.043)

3.196 (0.325) 2.338 (0.218) 1.095 (0.078) 0.907 (0.044) 0.978 (0.084) 0.877 (0.085) 0.722 (0.605) 0.961 (0.460) 2.939 (0.430) −0.052 (0.047)

0.056 0.609 0.012 0.575 0.605 0.876 0.023 0.275 0.002 0.741

C: clustering coefficient, T: transitivity, L: characteristic path length, E: global efficiency. s1: Scaled by random networks, s2: scaled by random and regular lattice networks. Data: mean (standard deviation).

detected (decreased FA and mean strength and increased ADC). Furthermore, the basic structure and topology of these connections were significantly influenced by PMG. Fewer short association fiber pathways were identified by fiber tracking in PMG, which resulted in decreased network density. Greater termination of streamlines was not simply due to high frequency of folding in PMG because gyral nodes were not assigned to every microgyria in the typical “sawtooth” pattern of PMG but to the larger scale primary gyral folds. However, it is hard to be sure that these pathways are actually absent because tractography algorithms have uncertainty in determining orientation and geometry of fibers near the cortical gray matter boundary (Jbabdi and Johansen-Berg, 2011). A neuropathology study is needed to confirm the precise structural alterations of axonal fibers. Nonetheless, our results across all our measurements strongly suggest that the connectivity of short association fibers was impaired in PMG. In addition, network density of short connections was highly correlated with the extent of PMG in a lobar region. It significantly decreased as the severity of abnormal gyral folding increased in PMG. Along with short fiber connections, we found significantly reduced connectivity of long association (5th or more neighboring gyral connections) and inter-hemispheric fibers in PMG, which have previously been reported as not affected by PMG in human DTI study (Munakata et al., 2006). Our result is in agreement with the anatomical findings made in microgyria animal experiments, which showed the changes in callosal connectivity (Galaburda et al., 2006; Rosen et al., 2000). Further studies comparing our quantitative measures with genotype and potential biological mechanism as either axonal guidance or neuronal migration may prove helpful in better understanding the spectrum of PMG. Within-lobe short connectivity and between-lobe connectivity analyses showed that the PMG patients had decreased connectivity within the involved lobe compared to within uninvolved lobes and the lobes of typical controls in various measures. These results are consistent with previous DTI studies, reporting decreased FA values in the white matter underlying areas of cortical malformations as compared to the contralateral normal-appearing areas or normal control (Bonilha et al., 2007; Trivedi et al., 2006; Widjaja et al., 2007). Our results confirm, but also extend previous findings, showing significantly altered connectivity in uninvolved left temporal, left parietal, and right parietal lobes as well as between uninvolved left temporal and occipital lobes, and uninvolved right frontal and temporal lobes. Since the human brain is an integrated network system, these findings of abnormal connectivity of within and between normal-appearing lobes in PMG patients might be secondary to abnormal connectivity patterns with frankly abnormal regions. It is also possible that small regions of PMG may be missed by visual inspection, causing the PMGN group to include regions of PMG. A regional analysis with a larger set of patients, DTI data with higher resolution, and quantitative characterization of abnormal gyral folding would provide more reliable and complete results about the relationship between cortical malformations and fiber connectivity changes. Significantly reduced connectivity with language function impairment was detected for the fiber tracts connecting the left frontal, temporal, and parietal lobes. In the left frontal lobe and both left and right parietal lobes, short U-fiber connections were also associated with language impairment. A recent DTI study found the abnormal connectivity of arcuate fasciculus in PMG patients with severe language impairment and no speech development (Saporta et al., 2011). Since the arcuate fasciculus plays a major role in language function and it is composed of long and short fibers connecting the perisylvian cortex of the frontal, temporal, and parietal lobes (Catani and Thiebaut de Schotten, 2008), our results might be related to specific abnormalities in the development of the arcuate fasciculus. Our automatic lobar regional analysis showed the ability to detect the significant connectivity changes related to language function in PMG. Although validation with a larger sample size and more detailed formal assessment of language function are needed for future studies, the correlations between network

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measures and language function in PMG is intriguing preliminary evidence that network measures may be useful in predicting language function. We investigated the PMG-affected alterations of the global connectivity network system and revealed significantly reduced network segregation measure. The network topology of PMG brains appeared to keep the normal level of the functional integration and smallworldness. The clustering coefficient and transitivity were also significantly decreased as the PMG extent and language impairment increased. We suggest that our gyral node-based measures of the network segregation are good at reflecting the disease-related network characteristics in PMG. When reviewing the results of gyral topologybased connectivity analysis, we can suppose that low clustering coefficient in PMG is caused by the disrupted short U-fiber connectivity between neighboring regions. Conversely, the modularity was found to be significantly higher in PMG patients. Both within- and betweenmodule mean strengths were lower, but the between-module strength showed a larger group difference with higher statistical significance than the within-module strength. It was also proven by the lower ratio of between-module to within-module strengths in PMG. Withinmodule connections were mainly composed of short-range fibers and between-module connections largely consisted of long-range and inter-hemispheric fibers. Hence, modularity in PMG was likely more influenced by decreases in long-range and inter-hemispheric connectivity rather than decreases in short-range connectivity, thus resulting in higher modularity and a greater number of modules in PMG. The contrast between the two results concerning the clustering coefficient and the modularity could be interpreted more clearly by considering additional information of subdivided fiber connectivity and modular organization based on gyral segment topology. Not only the typical but also the PMG group had symmetric hub regions in the association cortex regions, such as superior and middle frontal gyri and precuneus, and superior and inferior parietal gyri. The regions that we identified for both groups have been widely reported as network hubs, which shows the consistency of our present findings with previous results (Gong et al., 2009; Hagmann et al., 2008; Shu et al., 2011; van den Heuvel et al., 2010; Yan et al., 2011; Zhang et al., 2011). The hub region detected in the left inferior temporal region from the typical group was also previously reported as a hub in normal young group (Yan et al., 2011). It is worthy of note that hub nodes were not identified in the bilateral anterior prefrontal regions and left posterior inferior temporal region in PMG. The anterior prefrontal cortex is well developed in humans compared with other primates and involved in complex cognitive function, specifically enabling more flexible cognitive control in the service of decision-making (Koechlin and Hyafil, 2007). The left posterior inferior temporal area has been reported to be implicated in reading and writing and to be part of the cortical network model of language function (Hickok and Poeppel, 2007; Rapcsak and Beeson, 2004). Loss of network hub property in these areas seems to be closely related to delayed cognitive and language development in PMG. While the superior frontal gyrus was defined as a single node in an atlas-based study, this gyrus was parcellated into several segments as a node in our methodology. As a result, we were able to identify more subdivided hub regions and reveal the absence of hubs in the prefrontal areas in PMG. Instead, PMG brains showed the hub region in the right superior temporal gyrus, not identified in the typical group. We suggest that the hub in the right superior temporal region may function as compensatory processing for the decreased centrality of the association cortex regions. Methodological issues Nodes should ideally represent brain regions with coherent patterns of extrinsic anatomical or functional connections, which can be separable from the other nodes. However, there is currently no gold standard to determine the ideal node definition in the human brain network in

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neuroimaging. In this study, we used gyral segments as node regions to better capture complex gyral topology, which can be significantly altered with cerebral malformations such as PMG. By using gyral topology, node definitions respect major sulci and are both smaller and more uniform in size, allowing characterization of individual network organization related to the gyral topology, and the ability to capture short connections between gyri. We believe this approach is biologically more meaningful than previous template approaches that combine variable numbers of gyri. In prior post-mortem and high resolution imaging studies, specific association fiber pathways seemed generally to link and project from gyral regions (Catani et al., 2012; Guevara et al., 2011; Magro et al., 2012; Schmahmann and Pandya, 2006; Schmahmann et al., 2007; Takahashi et al., 2011; Zhang et al., 2010). In addition, the number of axonal fibers connected to gyri was significantly greater than that connected to sulci in tractography data (Nie et al., 2012). Fiber tracts reconstructed from DTI represent structure at a macroscopic level and cannot completely capture the complex microscopic axonal anatomy and therefore there are false positive and negative connections due to the bias of diffusion imaging and tractography algorithms. However, DTI tractography and connectivity analysis are important and helpful approaches to explore models of the large-scale brain networks in spite of their limitations. From this point of view, we suggest that our gyral node definition provides an improved node definition compared to previous atlas-based parcellations, particularly in brain disorders where gyral patterns can be severely altered, and is supported by our supplementary experiments. We additionally constructed the connectivity networks based on the FreeSurfer parcellation and analyzed group differences of the graph measures to compare with our approach. The graph analysis in this case showed higher clustering and shorter path length of the network in PMG, which are opposite to the results using our gyral node-based analysis. In the FreeSurfer parcellation, the PMG patients also showed higher small-worldness, which could be interpreted as a combination of higher global and local network efficiency. These results seem unlikely when considering severely reduced connectivity in PMG, and might be due to coarse regional parcellation insufficient for capturing disrupted short-range connectivity in PMG patients. Thus, graph theoretical analysis simply based on a normal atlasbased parcellation may lead to distorted results in unexpected ways. The gyral node parcellation was used to investigate the connectivity changes based on primary gyral topological relationship and path length. This approach may be more appropriate than fiber length to categorize involvement into short, neighborhood, and long association fiber connections as length thresholds do not accurately classify different fiber groups and become even more ambiguous across individuals as fiber lengths vary due to different brain sizes. Short- and longrange connectivity analysis is crucial to understanding other demographic or disease-related effects on the brain network. For example, it has been suggested that people with autism may have abnormal cortical network patterns of excessive short-range connectivity but long-range disconnection (Belmonte et al., 2004; Shukla et al., 2011; Sundaram et al., 2008). Increasing long-range connectivity (integration), but decreasing short-range connectivity (segregation) with age have been reported (Dosenbach et al., 2010; Hagmann et al., 2010). Manual segmentation of fiber tracts would be the most accurate way, but very laborious and time-consuming, making assessment of large groups difficult. Therefore, it is a reasonable alternative to use the primary gyral pattern and topology to automatically analyze different groups of fibers according to connection distance. We used a single tensor-based deterministic tractography algorithm, which does not resolve fiber crossings. Single tensor approaches are likely to underestimate the probability of connections between distant regions because long-distance projections are more likely to intersect with other, differently oriented projections. More recent acquisition sequences, such as the high angular resolution diffusion imaging (HARDI) methods including diffusion spectrum imaging (DSI), where crossing fibers are included in the model (Wedeen et al., 2008), have been shown to

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generate networks with a higher probability of long-distance connections than classic DTI sequences (Zalesky et al., 2010). These higher order diffusion approaches require more time than is typically feasible in a clinical population and therefore were not available in our clinical population. However with recent acceleration methods (Setsompop et al., 2012) we hope that such advanced diffusion acquisition methods can be used in future projects to construct anatomical networks with higher quality. Our MRI data were acquired on two separate scanners. A number of studies are collecting structural MRI and DTI data from different scanners in multicenter studies. Reliability of cortical surface extraction and the surface-based structural analysis across different scanners has been established by previous studies (Dickerson et al., 2008; Han et al., 2006; Im et al., 2013a; Wonderlick et al., 2009). DTI measurements from multiple scanners were also comparable and reliable (Dyrba et al., 2013; Fox et al., 2012; Magnotta et al., 2012; Vollmar et al., 2010). All our imaging was performed on two identical MRI scanners from the same vendor, running identical pulse sequences. Additionally, gyral topology-based connectivity and graph theoretical measures were compared between typical controls on the two different scanners (15 subjects on scannerA and 10 on scannerB), and no significant difference was found. Therefore, scanner choice was unlikely to affect the large and significant group effect on structural network properties between typical controls and PMG patients. Conclusions In conclusion, our analysis provided detailed quantitative results and interpretation for the disrupted structural connectivity and resulting network related to the abnormal cortical structure and language impairment in PMG. Our approach improves on previous atlasbased approaches by enabling assessment of an individual's network properties based on their own anatomy and may provide a more rigorous means to explore changes in connectivity occurring in diseased or dysmorphic brains. Acknowledgments This work was supported by the Foundation of the American Society of Neuroradiology, Scholar Award in Neuroradiology Research 2011, and the American Society of Pediatric Neuroradiology, Annual Award for Pediatric Neuroradiology Research 2011. Conflict of interest The authors declare no competing financial interests. References Barkovich, A.J., 2010. MRI analysis of sulcation morphology in polymicrogyria. Epilepsia 51 (Suppl. 1), 17–22. Batalle, D., Eixarch, E., Figueras, F., Munoz-Moreno, E., Bargallo, N., Illa, M., Acosta-Rojas, R., Amat-Roldan, I., Gratacos, E., 2012. Altered small-world topology of structural brain networks in infants with intrauterine growth restriction and its association with later neurodevelopmental outcome. Neuroimage 60, 1352–1366. Beaulieu, C., 2002. The basis of anisotropic water diffusion in the nervous system — a technical review. NMR Biomed. 15, 435–455. Belmonte, M.K., Allen, G., Beckel-Mitchener, A., Boulanger, L.M., Carper, R.A., Webb, S.J., 2004. Autism and abnormal development of brain connectivity. J. Neurosci. 24, 9228–9231. Blondel, V.D., Guillaume, J.-L., Lambiotte, R., Lefebvre, E., 2008. Fast unfolding of communities in large networks. J. Stat. Mech. P10008. Bonilha, L., Halford, J., Rorden, C., Li, L.M., Patel, A., Rumbolt, Z., Morgan, P., 2007. Microstructural white matter abnormalities in nodular heterotopia with overlying polymicrogyria. Seizure 16, 74–80. Brandes, U., 2001. A faster algorithm for betweenness centrality. J. Math. Sociol. 25, 163–177. Bullmore, E.T., Bassett, D.S., 2011. Brain graphs: graphical models of the human brain connectome. Annu. Rev. Clin. Psychol. 7, 113–140. Bullmore, E., Sporns, O., 2009. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186–198.

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