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1.  Altered Structural Brain Connectivity in Healthy Carriers of the Autism Risk Gene, CNTNAP2 
Brain Connectivity  2011;1(6):447-459.
Abstract
Recently, carriers of a common variant in the autism risk gene, CNTNAP2, were found to have altered functional brain connectivity using functional MRI. Here, we scanned 328 young adults with high-field (4-Tesla) diffusion imaging, to test the hypothesis that carriers of this gene variant would have altered structural brain connectivity. All participants (209 women, 119 men, age: 23.4±2.17 SD years) were scanned with 105-gradient high-angular-resolution diffusion imaging (HARDI) at 4 Tesla. After performing a whole-brain fiber tractography using the full angular resolution of the diffusion scans, 70 cortical surface-based regions of interest were created from each individual's co-registered anatomical data to compute graph metrics for all pairs of cortical regions. In graph theory analyses, subjects homozygous for the risk allele (CC) had lower characteristic path length, greater small-worldness and global efficiency in whole-brain analyses, and lower eccentricity (maximum path length) in 60 of the 70 nodes in regional analyses. These results were not reducible to differences in more commonly studied traits such as fiber density or fractional anisotropy. This is the first study that links graph theory metrics of brain structural connectivity to a common genetic variant linked with autism and will help us understand the neurobiology of the circuits implicated in the risk for autism.
doi:10.1089/brain.2011.0064
PMCID: PMC3420970  PMID: 22500773
autism; CNTNAP2; graph theory; HARDI; structural connectivity; twins
2.  Development of Brain Structural Connectivity between Ages 12 and 30: A 4-Tesla Diffusion Imaging Study in 439 Adolescents and Adults 
NeuroImage  2012;64:671-684.
Understanding how the brain matures in healthy individuals is critical for evaluating deviations from normal development in psychiatric and neurodevelopmental disorders. The brain’s anatomical networks are profoundly re-modeled between childhood and adulthood, and diffusion tractography offers unprecedented power to reconstruct these networks and neural pathways in vivo. Here we tracked changes in structural connectivity and network efficiency in 439 right-handed individuals aged 12 to 30 (211 female/126 male adults, mean age=23.6, SD=2.19; 31 female/24 male 12 year olds, mean age=12.3, SD=0.18; and 25 female/22 male 16 year olds, mean age=16.2, SD=0.37). All participants were scanned with high angular resolution diffusion imaging (HARDI) at 4 Tesla. After we performed whole brain tractography, 70 cortical gyral-based regions of interest were extracted from each participant’s co-registered anatomical scans. The degree of fiber connections between all pairs of cortical regions, or nodes, were found to create symmetric fiber density matrices, reflecting the structural brain network. From those 70×70 matrices we computed graph theory metrics characterizing structural connectivity. Several key global and nodal metrics changed across development, showing increased network integration, with some connections pruned and others strengthened. The increases and decreases in fiber density, however, were not distributed proportionally across the brain. The frontal cortex had a disproportionate number of decreases in fiber density while the temporal cortex had a disproportionate number of increases in fiber density. This large-scale analysis of the developing structural connectome offers a foundation to develop statistical criteria for aberrant brain connectivity as the human brain matures.
doi:10.1016/j.neuroimage.2012.09.004
PMCID: PMC3603574  PMID: 22982357
HARDI; structural connectivity; graph theory; development
3.  Communication of brain network core connections altered in behavioral variant frontotemporal dementia but possibly preserved in early-onset Alzheimer’s disease 
Diffusion imaging and brain connectivity analyses can assess white matter deterioration in the brain, revealing the underlying patterns of how brain structure declines. Fiber tractography methods can infer neural pathways and connectivity patterns, yielding sensitive mathematical metrics of network integrity. Here, we analyzed 1.5-Tesla whole-brain diffusion-weighted images from 64 participants – 15 patients with behavioral variant frontotemporal dementia (bvFTD), 19 with early-onset Alzheimer’s disease (EOAD), and 30 healthy elderly controls. Using whole-brain tractography, we reconstructed structural brain connectivity networks to map connections between cortical regions. We evaluated the brain’s networks focusing on the most highly central and connected regions, also known as hubs, in each diagnostic group – specifically the “high-cost” structural backbone used in global and regional communication. The high-cost backbone of the brain, predicted by fiber density and minimally short pathways between brain regions, accounted for 81–92% of the overall brain communication metric in all diagnostic groups. Furthermore, we found that the set of pathways interconnecting high-cost and high-capacity regions of the brain’s communication network are globally and regionally altered in bvFTD, compared to healthy participants; however, the overall organization of the high-cost and high-capacity networks were relatively preserved in EOAD participants, relative to controls. Disruption of the major central hubs that transfer information between brain regions may impair neural communication and functional integrity in characteristic ways typical of each subtype of dementia.
doi:10.1117/12.2082352
PMCID: PMC4384394  PMID: 25848494
graph theory; communication cost; hub; structural network; frontotemporal dementia; Alzheimer’s disease
4.  DISCOVERY OF GENES THAT AFFECT HUMAN BRAIN CONNECTIVITY: A GENOME-WIDE ANALYSIS OF THE CONNECTOME 
Human brain connectivity is disrupted in a wide range of disorders – from Alzheimer’s disease to autism – but little is known about which specific genes affect it. Here we conducted a genome-wide association for connectivity matrices that capture information on the density of fiber connections between 70 brain regions. We scanned a large twin cohort (N=366) with 4-Tesla high angular resolution diffusion imaging (105-gradient HARDI). Using whole brain HARDI tractography, we extracted a relatively sparse 70×70 matrix representing fiber density between all pairs of cortical regions automatically labeled in co-registered anatomical scans. Additive genetic factors accounted for 1–58% of the variance in connectivity between 90 (of 122) tested nodes. We discovered genome-wide significant associations between variants and connectivity. GWAS permutations at various levels of heritability, and split-sample replication, validated our genetic findings. The resulting genes may offer new leads for mechanisms influencing aberrant connectivity and neurodegeneration.
doi:10.1109/ISBI.2012.6235605
PMCID: PMC3420975  PMID: 22903411
genetics; high angular resolution diffusion imaging (HARDI); cortical surfaces; twin modeling; human connectome
5.  SPECTRAL GRAPH THEORY AND GRAPH ENERGY METRICS SHOW EVIDENCE FOR THE ALZHEIMER’S DISEASE DISCONNECTION SYNDROME IN APOE-4 RISK GENE CARRIERS 
Our understanding of network breakdown in Alzheimer’s disease (AD) is likely to be enhanced through advanced mathematical descriptors. Here, we applied spectral graph theory to provide novel metrics of structural connectivity based on 3-Tesla diffusion weighted images in 42 AD patients and 50 healthy controls. We reconstructed connectivity networks using whole-brain tractography and examined, for the first time here, cortical disconnection based on the graph energy and spectrum. We further assessed supporting metrics - link density and nodal strength - to better interpret our results. Metrics were analyzed in relation to the well-known APOE-4 genetic risk factor for late-onset AD. The number of disconnected cortical regions increased with the number of copies of the APOE-4 risk gene in people with AD. Each additional copy of the APOE-4 risk gene may lead to more dysfunctional networks with weakened or abnormal connections, providing evidence for the previously hypothesized “disconnection syndrome”.
doi:10.1109/ISBI.2015.7163910
PMCID: PMC4578320  PMID: 26413205
graph spectrum; energy; Alzheimer’s disease; APOE-4; disconnection syndrome
6.  CHANGES IN ANATOMICAL BRAIN CONNECTIVITY BETWEEN AGES 12 AND 30: A HARDI STUDY OF 467 ADOLESCENTS AND ADULTS 
Graph theory can be applied to matrices that represent the brain’s anatomical connections, to better understand global properties of anatomical networks, such as their clustering, efficiency and “small-world” topology. Network analysis is popular in adult studies of connectivity, but only one study – in just 30 subjects – has examined how network measures change as the brain develops over this period. Here we assessed the developmental trajectory of graph theory metrics of structural brain connectivity in a cross-sectional study of 467 subjects, aged 12 to 30. We computed network measures from 70×70 connectivity matrices of fiber density generated using whole-brain tractography in 4-Tesla 105-gradient high angular resolution diffusion images (HARDI). We assessed global efficiency and modularity, and both age and age2 effects were identified. HARDI-based connectivity maps are sensitive to the remodeling and refinement of structural brain connections as the human brain develops.
doi:10.1109/ISBI.2012.6235695
PMCID: PMC3420974  PMID: 22903354
graph theory; high angular resolution diffusion imaging (HARDI); tractography; network analyses; development; structural connectivity
7.  Abnormal wiring of the connectome in adults with high-functioning autism spectrum disorder 
Molecular Autism  2015;6:65.
Background
Recent brain imaging findings suggest that there are widely distributed abnormalities affecting the brain connectivity in individuals with autism spectrum disorder (ASD). Using graph theoretical analysis, it is possible to investigate both global and local properties of brain’s wiring diagram, i.e., the connectome.
Methods
We acquired diffusion-weighted magnetic resonance imaging data from 14 adult males with high-functioning ASD and 19 age-, gender-, and IQ-matched controls. As with diffusion tensor imaging-based tractography, it is not possible to detect complex (e.g., crossing) fiber configurations, present in 60–90 % of white matter voxels; we performed constrained spherical deconvolution-based whole brain tractography. Unweighted and weighted structural brain networks were then reconstructed from these tractography data and analyzed with graph theoretical measures.
Results
In subjects with ASD, global efficiency was significantly decreased both in the unweighted and the weighted networks, normalized characteristic path length was significantly increased in the unweighted networks, and strength was significantly decreased in the weighted networks. In the local analyses, betweenness centrality of the right caudate was significantly increased in the weighted networks, and the strength of the right superior temporal pole was significantly decreased in the unweighted networks in subjects with ASD.
Conclusions
Our findings provide new insights into understanding ASD by showing that the integration of structural brain networks is decreased and that there are abnormalities in the connectivity of the right caudate and right superior temporal pole in subjects with ASD.
Electronic supplementary material
The online version of this article (doi:10.1186/s13229-015-0058-4) contains supplementary material, which is available to authorized users.
doi:10.1186/s13229-015-0058-4
PMCID: PMC4681075  PMID: 26677408
Autism spectrum disorder; Diffusion magnetic resonance imaging; White matter tract; Tractography; Connectivity; Connectome; Brain networks; Graph theoretical analysis
8.  Reproducibility of graph metrics of human brain structural networks 
Recent interest in human brain connectivity has led to the application of graph theoretical analysis to human brain structural networks, in particular white matter connectivity inferred from diffusion imaging and fiber tractography. While these methods have been used to study a variety of patient populations, there has been less examination of the reproducibility of these methods. A number of tractography algorithms exist and many of these are known to be sensitive to user-selected parameters. The methods used to derive a connectivity matrix from fiber tractography output may also influence the resulting graph metrics. Here we examine how these algorithm and parameter choices influence the reproducibility of proposed graph metrics on a publicly available test-retest dataset consisting of 21 healthy adults. The dice coefficient is used to examine topological similarity of constant density subgraphs both within and between subjects. Seven graph metrics are examined here: mean clustering coefficient, characteristic path length, largest connected component size, assortativity, global efficiency, local efficiency, and rich club coefficient. The reproducibility of these network summary measures is examined using the intraclass correlation coefficient (ICC). Graph curves are created by treating the graph metrics as functions of a parameter such as graph density. Functional data analysis techniques are used to examine differences in graph measures that result from the choice of fiber tracking algorithm. The graph metrics consistently showed good levels of reproducibility as measured with ICC, with the exception of some instability at low graph density levels. The global and local efficiency measures were the most robust to the choice of fiber tracking algorithm.
doi:10.3389/fninf.2014.00046
PMCID: PMC4019854  PMID: 24847245
structure; tractography; connectivity; brain; network; reproducibility; graph
9.  Altered functional and structural brain network organization in autism☆ 
NeuroImage : Clinical  2012;2:79-94.
Structural and functional underconnectivity have been reported for multiple brain regions, functional systems, and white matter tracts in individuals with autism spectrum disorders (ASD). Although recent developments in complex network analysis have established that the brain is a modular network exhibiting small-world properties, network level organization has not been carefully examined in ASD. Here we used resting-state functional MRI (n = 42 ASD, n = 37 typically developing; TD) to show that children and adolescents with ASD display reduced short and long-range connectivity within functional systems (i.e., reduced functional integration) and stronger connectivity between functional systems (i.e., reduced functional segregation), particularly in default and higher-order visual regions. Using graph theoretical methods, we show that pairwise group differences in functional connectivity are reflected in network level reductions in modularity and clustering (local efficiency), but shorter characteristic path lengths (higher global efficiency). Structural networks, generated from diffusion tensor MRI derived fiber tracts (n = 51 ASD, n = 43 TD), displayed lower levels of white matter integrity yet higher numbers of fibers. TD and ASD individuals exhibited similar levels of correlation between raw measures of structural and functional connectivity (n = 35 ASD, n = 35 TD). However, a principal component analysis combining structural and functional network properties revealed that the balance of local and global efficiency between structural and functional networks was reduced in ASD, positively correlated with age, and inversely correlated with ASD symptom severity. Overall, our findings suggest that modeling the brain as a complex network will be highly informative in unraveling the biological basis of ASD and other neuropsychiatric disorders.
Highlights
► Complex network analysis of resting-state fMRI and DTI tractography in autism ► Local and long-range functional connectivity is reduced in ASD. ► Reduced local efficiency and modularity of functional networks in ASD ► Altered age-related trajectory of global efficiency for structural networks in ASD
doi:10.1016/j.nicl.2012.11.006
PMCID: PMC3777708  PMID: 24179761
Resting-state functional connectivity; Diffusion tensor imaging; Graph theory; Brain networks; Autism spectrum disorders
10.  Intrinsic functional network organization in high-functioning adolescents with autism spectrum disorder 
Converging theories and data suggest that atypical patterns of functional and structural connectivity are a hallmark neurobiological feature of autism. However, empirical studies of functional connectivity, or, the correlation of MRI signal between brain regions, have largely been conducted during task performance and/or focused on group differences within one network [e.g., the default mode network (DMN)]. This narrow focus on task-based connectivity and single network analyses precludes investigation of whole-brain intrinsic network organization in autism. To assess whole-brain network properties in adolescents with autism, we collected resting-state functional connectivity MRI (rs-fcMRI) data from neurotypical (NT) adolescents and adolescents with autism spectrum disorder (ASD). We used graph theory metrics on rs-fcMRI data with 34 regions of interest (i.e., nodes) that encompass four different functionally defined networks: cingulo-opercular, cerebellar, fronto-parietal, and DMN (Fair etal., 2009). Contrary to our hypotheses, network analyses revealed minimal differences between groups with one exception. Betweenness centrality, which indicates the degree to which a seed (or node) functions as a hub within and between networks, was greater for participants with autism for the right lateral parietal (RLatP) region of the DMN. Follow-up seed-based analyses demonstrated greater functional connectivity in ASD than NT groups between the RLatP seed and another region of the DMN, the anterior medial prefrontal cortex. Greater connectivity between these regions was related to lower ADOS (Autism Diagnostic Observation Schedule) scores (i.e., lower impairment) in autism. These findings do not support current theories of underconnectivity in autism, but, rather, underscore the need for future studies to systematically examine factors that can influence patterns of intrinsic connectivity such as autism severity, age, and head motion.
doi:10.3389/fnhum.2013.00573
PMCID: PMC3777537  PMID: 24062673
autism; resting-state functional connectivity; default mode network; intrinsic network organization; graph theory; functional MRI
11.  Altered Topological Organization of White Matter Structural Networks in Patients with Neuromyelitis Optica 
PLoS ONE  2012;7(11):e48846.
Objective
To investigate the topological alterations of the whole-brain white-matter (WM) structural networks in patients with neuromyelitis optica (NMO).
Methods
The present study involved 26 NMO patients and 26 age- and sex-matched healthy controls. WM structural connectivity in each participant was imaged with diffusion-weighted MRI and represented in terms of a connectivity matrix using deterministic tractography method. Graph theory-based analyses were then performed for the characterization of brain network properties. A multiple linear regression analysis was performed on each network metric between the NMO and control groups.
Results
The NMO patients exhibited abnormal small-world network properties, as indicated by increased normalized characteristic path length, increased normalized clustering and increased small-worldness. Furthermore, largely similar hub distributions of the WM structural networks were observed between NMO patients and healthy controls. However, regional efficiency in several brain areas of NMO patients was significantly reduced, which were mainly distributed in the default-mode, sensorimotor and visual systems. Furthermore, we have observed increased regional efficiency in a few brain regions such as the orbital parts of the superior and middle frontal and fusiform gyri.
Conclusion
Although the NMO patients in this study had no discernible white matter T2 lesions in the brain, we hypothesize that the disrupted topological organization of WM networks provides additional evidence for subtle, widespread cerebral WM pathology in NMO.
doi:10.1371/journal.pone.0048846
PMCID: PMC3492259  PMID: 23144994
12.  Breakdown of Brain Connectivity Between Normal Aging and Alzheimer's Disease: A Structural k-Core Network Analysis 
Brain Connectivity  2013;3(4):407-422.
Abstract
Brain connectivity analyses show considerable promise for understanding how our neural pathways gradually break down in aging and Alzheimer's disease (AD). Even so, we know very little about how the brain's networks change in AD, and which metrics are best to evaluate these changes. To better understand how AD affects brain connectivity, we analyzed anatomical connectivity based on 3-T diffusion-weighted images from 111 subjects (15 with AD, 68 with mild cognitive impairment, and 28 healthy elderly; mean age, 73.7±7.6 SD years). We performed whole brain tractography based on the orientation distribution functions, and compiled connectivity matrices showing the proportions of detected fibers interconnecting 68 cortical regions. We computed a variety of measures sensitive to anatomical network topology, including the structural backbone—the so-called “k-core”—of the anatomical network, and the nodal degree. We found widespread network disruptions, as connections were lost in AD. Among other connectivity measures showing disease effects, network nodal degree, normalized characteristic path length, and efficiency decreased with disease, while normalized small-worldness increased, in the whole brain and left and right hemispheres individually. The normalized clustering coefficient also increased in the whole brain; we discuss factors that may cause this effect. The proportions of fibers intersecting left and right cortical regions were asymmetrical in all diagnostic groups. This asymmetry may intensify as disease progressed. Connectivity metrics based on the k-core may help understand brain network breakdown as cognitive impairment increases, revealing how degenerative diseases affect the human connectome.
doi:10.1089/brain.2012.0137
PMCID: PMC3749712  PMID: 23701292
Alzheimer's disease; asymmetry; brain connectivity; diffusion tensor imaging; efficiency; k-core; mild cognitive impairment; nodal degree; small-world; tractography
13.  Anatomical likelihood estimation meta-analysis of grey and white matter anomalies in autism spectrum disorders 
NeuroImage : Clinical  2014;7:525-536.
Autism spectrum disorders (ASD) are characterized by impairments in social communication and restrictive, repetitive behaviors. While behavioral symptoms are well-documented, investigations into the neurobiological underpinnings of ASD have not resulted in firm biomarkers. Variability in findings across structural neuroimaging studies has contributed to difficulty in reliably characterizing the brain morphology of individuals with ASD. These inconsistencies may also arise from the heterogeneity of ASD, and wider age-range of participants included in MRI studies and in previous meta-analyses. To address this, the current study used coordinate-based anatomical likelihood estimation (ALE) analysis of 21 voxel-based morphometry (VBM) studies examining high-functioning individuals with ASD, resulting in a meta-analysis of 1055 participants (506 ASD, and 549 typically developing individuals). Results consisted of grey, white, and global differences in cortical matter between the groups. Modeled anatomical maps consisting of concentration, thickness, and volume metrics of grey and white matter revealed clusters suggesting age-related decreases in grey and white matter in parietal and inferior temporal regions of the brain in ASD, and age-related increases in grey matter in frontal and anterior-temporal regions. White matter alterations included fiber tracts thought to play key roles in information processing and sensory integration. Many current theories of pathobiology ASD suggest that the brains of individuals with ASD may have less-functional long-range (anterior-to-posterior) connections. Our findings of decreased cortical matter in parietal–temporal and occipital regions, and thickening in frontal cortices in older adults with ASD may entail altered cortical anatomy, and neurodevelopmental adaptations.
Highlights
•This is a meta-analysis of voxel-based morphometry studies of individuals with autism.•Different comparisons are made for global cortical matter, grey matter, and white matter.•Thinning was present in posterior brain regions and frontal white matter paths.•Age-related thickening of frontal grey matter was seen in participants with autism.•Results fit with existing theories of frontal-posterior disconnect in autism.
doi:10.1016/j.nicl.2014.11.004
PMCID: PMC4375647  PMID: 25844306
Autism spectrum disorder; Voxel-based morphometry; Anatomical likelihood estimation; Grey matter; White matter
14.  Support Vector Machine Classification of Major Depressive Disorder Using Diffusion-Weighted Neuroimaging and Graph Theory 
Recently, there has been considerable interest in understanding brain networks in major depressive disorder (MDD). Neural pathways can be tracked in the living brain using diffusion-weighted imaging (DWI); graph theory can then be used to study properties of the resulting fiber networks. To date, global abnormalities have not been reported in tractography-based graph metrics in MDD, so we used a machine learning approach based on “support vector machines” to differentiate depressed from healthy individuals based on multiple brain network properties. We also assessed how important specific graph metrics were for this differentiation. Finally, we conducted a local graph analysis to identify abnormal connectivity at specific nodes of the network. We were able to classify depression using whole-brain graph metrics. Small-worldness was the most useful graph metric for classification. The right pars orbitalis, right inferior parietal cortex, and left rostral anterior cingulate all showed abnormal network connectivity in MDD. This is the first use of structural global graph metrics to classify depressed individuals. These findings highlight the importance of future research to understand network properties in depression across imaging modalities, improve classification results, and relate network alterations to psychiatric symptoms, medication, and comorbidities.
doi:10.3389/fpsyt.2015.00021
PMCID: PMC4332161  PMID: 25762941
major depressive disorder; diffusion-weighted imaging; graph theory; support vector machine; small world network; subgenual anterior cingulate cortex
15.  Abnormal functional connectivity during visuospatial processing is associated with disrupted organisation of white matter in autism 
Disruption of structural and functional neural connectivity has been widely reported in Autism Spectrum Disorder (ASD) but there is a striking lack of research attempting to integrate analysis of functional and structural connectivity in the same study population, an approach that may provide key insights into the specific neurobiological underpinnings of altered functional connectivity in autism. The aims of this study were (1) to determine whether functional connectivity abnormalities were associated with structural abnormalities of white matter (WM) in ASD and (2) to examine the relationships between aberrant neural connectivity and behavior in ASD. Twenty-two individuals with ASD and 22 age, IQ-matched controls completed a high-angular-resolution diffusion MRI scan. Structural connectivity was analysed using constrained spherical deconvolution (CSD) based tractography. Regions for tractography were generated from the results of a previous study, in which 10 pairs of brain regions showed abnormal functional connectivity during visuospatial processing in ASD. WM tracts directly connected 5 of the 10 region pairs that showed abnormal functional connectivity; linking a region in the left occipital lobe (left BA19) and five paired regions: left caudate head, left caudate body, left uncus, left thalamus, and left cuneus. Measures of WM microstructural organization were extracted from these tracts. Fractional anisotropy (FA) reductions in the ASD group relative to controls were significant for WM connecting left BA19 to left caudate head and left BA19 to left thalamus. Using a multimodal imaging approach, this study has revealed aberrant WM microstructure in tracts that directly connect brain regions that are abnormally functionally connected in ASD. These results provide novel evidence to suggest that structural brain pathology may contribute (1) to abnormal functional connectivity and (2) to atypical visuospatial processing in ASD.
doi:10.3389/fnhum.2013.00434
PMCID: PMC3783945  PMID: 24133425
neuroimaging; autism spectrum disorders; functional connectivity; diffusion tractography; constrained spherical deconvolution; visuospatial processing; structural connectivity; mental rotation
16.  Magnetic Resonance Field Strength Effects on Diffusion Measures and Brain Connectivity Networks 
Brain Connectivity  2013;3(1):72-86.
Abstract
The quest to map brain connectivity is being pursued worldwide using diffusion imaging, among other techniques. Even so, we know little about how brain connectivity measures depend on the magnetic field strength of the scanner. To investigate this, we scanned 10 healthy subjects at 7 and 3 tesla—using 128-gradient high-angular resolution diffusion imaging. For each subject and scan, whole-brain tractography was used to estimate connectivity between 113 cortical and subcortical regions. We examined how scanner field strength affects (i) the signal-to-noise ratio (SNR) of the non-diffusion-sensitized reference images (b0); (ii) diffusion tensor imaging (DTI)-derived fractional anisotropy (FA), mean, radial, and axial diffusivity (MD/RD/AD), in atlas-defined regions; (iii) whole-brain tractography; (iv) the 113×113 brain connectivity maps; and (v) five commonly used network topology measures. We also assessed effects of the multi-channel reconstruction methods (sum-of-squares, SOS, at 7T; adaptive recombine, AC, at 3T). At 7T with SOS, the b0 images had 18.3% higher SNR than with 3T-AC. FA was similar for most regions of interest (ROIs) derived from an online DTI atlas (ICBM81), but higher at 7T in the cerebral peduncle and internal capsule. MD, AD, and RD were lower at 7T for most ROIs. The apparent fiber density between some subcortical regions was greater at 7T-SOS than 3T-AC, with a consistent connection pattern overall. Suggesting the need for caution, the recovered brain network was apparently more efficient at 7T, which cannot be biologically true as the same subjects were assessed. Care is needed when comparing network measures across studies, and when interpreting apparently discrepant findings.
doi:10.1089/brain.2012.0114
PMCID: PMC3621300  PMID: 23205551
brain network analysis; DTI; fractional anisotropy; graph theory; high-field MRI; high angular resolution diffusion imaging (HARDI); signal-to-noise ratio; tractography
17.  The UCLA multimodal connectivity database: a web-based platform for brain connectivity matrix sharing and analysis 
Brain connectomics research has rapidly expanded using functional MRI (fMRI) and diffusion-weighted MRI (dwMRI). A common product of these varied analyses is a connectivity matrix (CM). A CM stores the connection strength between any two regions (“nodes”) in a brain network. This format is useful for several reasons: (1) it is highly distilled, with minimal data size and complexity, (2) graph theory can be applied to characterize the network's topology, and (3) it retains sufficient information to capture individual differences such as age, gender, intelligence quotient (IQ), or disease state. Here we introduce the UCLA Multimodal Connectivity Database (http://umcd.humanconnectomeproject.org), an openly available website for brain network analysis and data sharing. The site is a repository for researchers to publicly share CMs derived from their data. The site also allows users to select any CM shared by another user, compute graph theoretical metrics on the site, visualize a report of results, or download the raw CM. To date, users have contributed over 2000 individual CMs, spanning different imaging modalities (fMRI, dwMRI) and disorders (Alzheimer's, autism, Attention Deficit Hyperactive Disorder). To demonstrate the site's functionality, whole brain functional and structural connectivity matrices are derived from 60 subjects' (ages 26–45) resting state fMRI (rs-fMRI) and dwMRI data and uploaded to the site. The site is utilized to derive graph theory global and regional measures for the rs-fMRI and dwMRI networks. Global and nodal graph theoretical measures between functional and structural networks exhibit low correspondence. This example demonstrates how this tool can enhance the comparability of brain networks from different imaging modalities and studies. The existence of this connectivity-based repository should foster broader data sharing and enable larger-scale meta-analyses comparing networks across imaging modality, age group, and disease state.
doi:10.3389/fninf.2012.00028
PMCID: PMC3508475  PMID: 23226127
graph theory; data sharing; functional connectivity; structural connectivity; resting-state fMRI; diffusion-weighted MRI
18.  Distribution of language-related Cntnap2 protein in neural circuits critical for vocal learning 
Variants of the contactin associated protein-like 2 (Cntnap2) gene are risk factors for language-related disorders including autism spectrum disorder, specific language impairment, and stuttering. Songbirds are useful models for study of human speech disorders due to their shared capacity for vocal learning, which relies on similar cortico-basal ganglia circuitry and genetic factors. Here, we investigate Cntnap2 protein expression in the brain of the zebra finch, a songbird species in which males, but not females, learn their courtship songs. We hypothesize that Cntnap2 has overlapping functions in vocal learning species, and expect to find protein expression in song-related areas of the zebra finch brain. We further expect that the distribution of this membrane-bound protein may not completely mirror its mRNA distribution due to the distinct subcellular localization of the two molecular species. We find that Cntnap2 protein is enriched in several song control regions relative to surrounding tissues, particularly within the adult male, but not female, robust nucleus of the arcopallium (RA), a cortical song control region analogous to human layer 5 primary motor cortex. The onset of this sexually dimorphic expression coincides with the onset of sensorimotor learning in developing males. Enrichment in male RA appears due to expression in projection neurons within the nucleus, as well as to additional expression in nerve terminals of cortical projections to RA from the lateral magnocellular nucleus of the nidopallium. Cntnap2 protein expression in zebra finch brain supports the hypothesis that this molecule affects neural connectivity critical for vocal learning across taxonomic classes.
doi:10.1002/cne.23394
PMCID: PMC3883908  PMID: 23818387
autism; birdsong; Caspr2; speech; zebra finch
19.  Abnormal structural connectivity in the brain networks of children with hydrocephalus 
NeuroImage : Clinical  2015;8:483-492.
Increased intracranial pressure and ventriculomegaly in children with hydrocephalus are known to have adverse effects on white matter structure. This study seeks to investigate the impact of hydrocephalus on topological features of brain networks in children. The goal was to investigate structural network connectivity, at both global and regional levels, in the brains in children with hydrocephalus using graph theory analysis and diffusion tensor tractography. Three groups of children were included in the study (29 normally developing controls, 9 preoperative hydrocephalus patients, and 17 postoperative hydrocephalus patients). Graph theory analysis was applied to calculate the global network measures including small-worldness, normalized clustering coefficients, normalized characteristic path length, global efficiency, and modularity. Abnormalities in regional network parameters, including nodal degree, local efficiency, clustering coefficient, and betweenness centrality, were also compared between the two patients groups (separately) and the controls using two tailed t-test at significance level of p < 0.05 (corrected for multiple comparison). Children with hydrocephalus in both the preoperative and postoperative groups were found to have significantly lower small-worldness and lower normalized clustering coefficient than controls. Children with hydrocephalus in the postoperative group were also found to have significantly lower normalized characteristic path length and lower modularity. At regional level, significant group differences (or differences at trend level) in regional network measures were found between hydrocephalus patients and the controls in a series of brain regions including the medial occipital gyrus, medial frontal gyrus, thalamus, cingulate gyrus, lingual gyrus, rectal gyrus, caudate, cuneus, and insular. Our data showed that structural connectivity analysis using graph theory and diffusion tensor tractography is sensitive to detect abnormalities of brain network connectivity associated with hydrocephalus at both global and regional levels, thus providing a new avenue for potential diagnosis and prognosis tool for children with hydrocephalus.
Highlights
•We studied brain network in children with hydrocephalus using graph theory analysis.•We investigated structural connectivity at both global and regional levels.•Children with hydrocephalus had significantly abnormal structural connectivity.•Graph analysis using DTI is sensitive to brain damage in pediatric hydrocephalus.
doi:10.1016/j.nicl.2015.04.015
PMCID: PMC4474092  PMID: 26106573
DTI, diffusion tensor imaging; FA, fractional anisotropy; GM, gray matter; HCP, hydrocephalus; ROI, region of interest; WM, white matter; Graph theoretical analysis; Network; Pediatric hydrocephalus; Small-worldness
20.  Impaired inter-hemispheric integration in bipolar disorder revealed using brain network analyses 
Biological psychiatry  2012;73(2):183-193.
Background
This represents the first graph theory based brain network analysis study in bipolar disorder, a chronic and disabling psychiatric disorder characterized by severe mood swings. Many imaging studies have investigated white matter in bipolar disorder with results suggesting abnormal white matter structural integrity, particularly in the fronto-limbic and callosal systems. However, many inconsistencies remain in the literature, and no study to-date has conducted brain network analyses using a graph-theoretic approach.
Methods
We acquired 64-direction diffusion-weighted MRI on 25 euthymic bipolar I disorder subjects and 24 gender and age equivalent healthy subjects. White matter integrity measures including fractional anisotropy and mean diffusivity were compared in the whole brain. Additionally, structural connectivity matrices based on whole brain deterministic tractography were constructed followed by the computation of both global and local brain network measures. We also designed novel metrics to further probe inter-hemispheric integration.
Results
Network analyses revealed that the bipolar brain networks exhibited significantly longer characteristic path length, lower clustering coefficient, and lower global efficiency relative to those of controls. Further analyses revealed impaired inter-hemispheric but relatively preserved intra-hemispheric integration. These findings were supported by whole brain white matter analyses that revealed significantly lower integrity in the corpus callosum in bipolar subjects. There were also abnormalities in nodal network measures in structures within the limbic system, especially the left hippocampus, the left lateral orbito-frontal cortex, and the bilateral isthmus cingulate.
Conclusions
These results suggest abnormalities in structural network organization in bipolar disorder, particularly in inter-hemispheric integration and within the limbic system.
doi:10.1016/j.biopsych.2012.09.014
PMCID: PMC4113030  PMID: 23122540
bipolar disorder; DTI; brain network analysis; brain imaging; hemispheric integration; corpus callosum; limbic system
21.  Algebraic connectivity of brain networks shows patterns of segregation leading to reduced network robustness in Alzheimer's disease 
Measures of network topology and connectivity aid the understanding of network breakdown as the brain degenerates in Alzheimer's disease (AD). We analyzed 3-Tesla diffusion-weighted images from 202 patients scanned by the Alzheimer's Disease Neuroimaging Initiative – 50 healthy controls, 72 with early- and 38 with late-stage mild cognitive impairment (eMCI/lMCI) and 42 with AD. Using whole-brain tractography, we reconstructed structural connectivity networks representing connections between pairs of cortical regions. We examined, for the first time in this context, the network's Laplacian matrix and its Fiedler value, describing the network's algebraic connectivity, and the Fiedler vector, used to partition a graph. We assessed algebraic connectivity and four additional supporting metrics, revealing a decrease in network robustness and increasing disarray among nodes as dementia progressed. Network components became more disconnected and segregated, and their modularity increased. These measures are sensitive to diagnostic group differences, and may help understand the complex changes in AD.
doi:10.1007/978-3-319-11182-7_6
PMCID: PMC4669194  PMID: 26640830
brain network; algebraic connectivity; Fiedler value; modularity; Alzheimer's disease
22.  Loss of ‘Small-World’ Networks in Alzheimer's Disease: Graph Analysis of fMRI Resting-State Functional Connectivity 
PLoS ONE  2010;5(11):e13788.
Background
Local network connectivity disruptions in Alzheimer's disease patients have been found using graph analysis in BOLD fMRI. Other studies using MEG and cortical thickness measures, however, show more global long distance connectivity changes, both in functional and structural imaging data. The form and role of functional connectivity changes thus remains ambiguous. The current study shows more conclusive data on connectivity changes in early AD using graph analysis on resting-state condition fMRI data.
Methodology/Principal Findings
18 mild AD patients and 21 healthy age-matched control subjects without memory complaints were investigated in resting-state condition with MRI at 1.5 Tesla. Functional coupling between brain regions was calculated on the basis of pair-wise synchronizations between regional time-series. Local (cluster coefficient) and global (path length) network measures were quantitatively defined. Compared to controls, the characteristic path length of AD functional networks is closer to the theoretical values of random networks, while no significant differences were found in cluster coefficient. The whole-brain average synchronization does not differ between Alzheimer and healthy control groups. Post-hoc analysis of the regional synchronization reveals increased AD synchronization involving the frontal cortices and generalized decreases located at the parietal and occipital regions. This effectively translates in a global reduction of functional long-distance links between frontal and caudal brain regions.
Conclusions/Significance
We present evidence of AD-induced changes in global brain functional connectivity specifically affecting long-distance connectivity. This finding is highly relevant for it supports the anterior-posterior disconnection theory and its role in AD. Our results can be interpreted as reflecting the randomization of the brain functional networks in AD, further suggesting a loss of global information integration in disease.
doi:10.1371/journal.pone.0013788
PMCID: PMC2967467  PMID: 21072180
23.  Altered whole-brain white matter networks in preclinical Alzheimer's disease 
NeuroImage : Clinical  2015;8:660-666.
Surrogates of whole-brain white matter (WM) networks reconstructed using diffusion tensor imaging (DTI) are novel markers of structural brain connectivity. Global connectivity of networks has been found impaired in clinical Alzheimer's disease (AD) compared to cognitively healthy aging. We hypothesized that network alterations are detectable already in preclinical AD and investigated major global WM network properties. Other structural markers of neurodegeneration typically affected in prodromal AD but seeming largely unimpaired in preclinical AD were also examined.
12 cognitively healthy elderly with preclinical AD as classified by florbetapir-PET (mean age 73.4 ± 4.9) and 31 age-matched controls without cerebral amyloidosis (mean age 73.1 ± 6.7) from the ADNI were included. WM networks were reconstructed from DTI using tractography and graph theory. Indices of network capacity and the established imaging markers of neurodegeneration hippocampal volume, and cerebral glucose utilization as measured by fludeoxyglucose-PET were compared between the two groups. Additionally, we measured surrogates of global WM integrity (fractional anisotropy, mean diffusivity, volume).
We found an increase of shortest path length and a decrease of global efficiency in preclinical AD. These results remained largely unchanged when controlling for WM integrity. In contrast, neither markers of neurodegeneration nor WM integrity were altered in preclinical AD subjects.
Our results suggest an impairment of WM networks in preclinical AD that is detectable while other structural imaging markers do not yet indicate incipient neurodegeneration. Moreover, these findings are specific to WM networks and cannot be explained by other surrogates of global WM integrity.
Highlights
•We reconstruct WM networks using DTI fiber tractography and graph theory.•We investigate global network properties in cognitively healthy elderly.•Global network integration is decreased in subjects with amyloidosis.•In contrast, no neurodegeneration is found (FDG, hippocampus).•WM network topology may be altered already in preclinical AD.
doi:10.1016/j.nicl.2015.06.007
PMCID: PMC4536470  PMID: 26288751
Preclinical Alzheimer's disease; DTI; Brain network
24.  Altered Anatomical Network in Early Blindness Revealed by Diffusion Tensor Tractography 
PLoS ONE  2009;4(9):e7228.
The topological architecture of the cerebral anatomical network reflects the structural organization of the human brain. Recently, topological measures based on graph theory have provided new approaches for quantifying large-scale anatomical networks. Diffusion MRI studies have revealed the efficient small-world properties and modular structure of the anatomical network in normal subjects. However, no previous study has used diffusion MRI to reveal changes in the brain anatomical network in early blindness. Here, we utilized diffusion tensor imaging to construct binary anatomical networks for 17 early blind subjects and 17 age- and gender-matched sighted controls. We established the existence of structural connections between any pair of the 90 cortical and sub-cortical regions using deterministic tractography. Compared with controls, early blind subjects showed a decreased degree of connectivity, a reduced global efficiency, and an increased characteristic path length in their brain anatomical network, especially in the visual cortex. Moreover, we revealed some regions with motor or somatosensory function have increased connections with other brain regions in the early blind, which suggested experience-dependent compensatory plasticity. This study is the first to show alterations in the topological properties of the anatomical network in early blindness. From the results, we suggest that analyzing the brain's anatomical network obtained using diffusion MRI data provides new insights into the understanding of the brain's re-organization in the specific population with early visual deprivation.
doi:10.1371/journal.pone.0007228
PMCID: PMC2747271  PMID: 19784379
25.  Connectivity and tissue microstructural alterations in right and left temporal lobe epilepsy revealed by diffusion spectrum imaging 
NeuroImage : Clinical  2014;5:349-358.
Focal epilepsy is increasingly recognized as the result of an altered brain network, both on the structural and functional levels and the characterization of these widespread brain alterations is crucial for our understanding of the clinical manifestation of seizure and cognitive deficits as well as for the management of candidates to epilepsy surgery.
Tractography based on Diffusion Tensor Imaging allows non-invasive mapping of white matter tracts in vivo. Recently, diffusion spectrum imaging (DSI), based on an increased number of diffusion directions and intensities, has improved the sensitivity of tractography, notably with respect to the problem of fiber crossing and recent developments allow acquisition times compatible with clinical application.
We used DSI and parcellation of the gray matter in regions of interest to build whole-brain connectivity matrices describing the mutual connections between cortical and subcortical regions in patients with focal epilepsy and healthy controls. In addition, the high angular and radial resolution of DSI allowed us to evaluate also some of the biophysical compartment models, to better understand the cause of the changes in diffusion anisotropy.
Global connectivity, hub architecture and regional connectivity patterns were altered in TLE patients and showed different characteristics in RTLE vs LTLE with stronger abnormalities in RTLE. The microstructural analysis suggested that disturbed axonal density contributed more than fiber orientation to the connectivity changes affecting the temporal lobes whereas fiber orientation changes were more involved in extratemporal lobe changes. Our study provides further structural evidence that RTLE and LTLE are not symmetrical entities and DSI-based imaging could help investigate the microstructural correlate of these imaging abnormalities.
Highlights
•We performed a whole brain connectivity study in patients with RTLE and LTLE.•Diffusion Spectrum Imaging (DSI) was used to achieve a better angular resolution.•DSI was also used to allow investigating the tracts microstructure.•Temporal changes where more related to the neurite density.•The extratemporal changes where related to the neurite orientation dispersion.
doi:10.1016/j.nicl.2014.07.013
PMCID: PMC4519999
Diffusion MRI; Connectome; Tractography; Network measures; DSI; GFA; NODDI; Temporal lobe epilepsy

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