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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.  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
4.  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
5.  ATLAS-BASED FIBER CLUSTERING FOR MULTI-SUBJECT ANALYSIS OF HIGH ANGULAR RESOLUTION DIFFUSION IMAGING TRACTOGRAPHY 
High angular resolution diffusion imaging (HARDI) allows in vivo analysis of the white matter structure and connectivity. Based on orientation distribution functions (ODFs) that represent the directionality of water diffusion at each point in the brain, tractography methods can recover major axonal pathways. This enables tract-based analysis of fiber integrity and connectivity. For multi-subject comparisons, fibers may be clustered into bundles that are consistently found across subjects. To do this, we scanned 20 young adults with HARDI at 4 T. From the reconstructed ODFs, we performed whole-brain tractography with a novel Hough transform method. We then used measures of agreement between the extracted 3D curves and a co-registered probabilistic DTI atlas to select key pathways. Using median filtering and a shortest path graph search, we derived the maximum density path to compactly represent each tract in the population. With this tract-based method, we performed tract-based analysis of fractional anisotropy, and assessed how the chosen tractography algorithm influenced the results. The resulting method may expedite population-based statistical analysis of HARDI and DTI.
doi:10.1109/ISBI.2011.5872405
PMCID: PMC4232949  PMID: 25404992
tractography; clustering; Dijkstra’s shortest path; multi-subject analysis; fiber bundles
6.  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
7.  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
8.  Pushing the limits of in vivo diffusion MRI for the Human Connectome Project 
NeuroImage  2013;80:220-233.
Perhaps more than any other “-omics” endeavor, the accuracy and level of detail obtained from mapping the major connection pathways in the living human brain with diffusion MRI depends on the capabilities of the imaging technology used. The current tools are remarkable; allowing the formation of an “image” of the water diffusion probability distribution in regions of complex crossing fibers at each of half a million voxels in the brain. Nonetheless our ability to map the connection pathways is limited by the image sensitivity and resolution, and also the contrast and resolution in encoding of the diffusion probability distribution.
The goal of our Human Connectome Project (HCP) is to address these limiting factors by re-engineering the scanner from the ground up to optimize the high b-value, high angular resolution diffusion imaging needed for sensitive and accurate mapping of the brain’s structural connections. Our efforts were directed based on the relative contributions of each scanner component. The gradient subsection was a major focus since gradient amplitude is central to determining the diffusion contrast, the amount of T2 signal loss, and the blurring of the water PDF over the course of the diffusion time. By implementing a novel 4-port drive geometry and optimizing size and linearity for the brain, we demonstrate a whole-body sized scanner with Gmax = 300mT/m on each axis capable of the sustained duty cycle needed for diffusion imaging. The system is capable of slewing the gradient at a rate of 200 T/m/s as needed for the EPI image encoding. In order to enhance the efficiency of the diffusion sequence we implemented a FOV shifting approach to Simultaneous MultiSlice (SMS) EPI capable of unaliasing 3 slices excited simultaneously with a modest g-factor penalty allowing us to diffusion encode whole brain volumes with low TR and TE. Finally we combine the multi-slice approach with a compressive sampling reconstruction to sufficiently undersample q-space to achieve a DSI scan in less than 5 minutes. To augment this accelerated imaging approach we developed a 64-channel, tight-fitting brain array coil and show its performance benefit compared to a commercial 32-channel coils at all locations in the brain for these accelerated acquisitions.
The technical challenges of developing the over-all system are discussed as well as results from SNR comparisons, ODF metrics and fiber tracking comparisons. The ultra-high gradients yielded substantial and immediate gains in the sensitivity through reduction of TE and improved signal detection and increased efficiency of the DSI or HARDI acquisition, accuracy and resolution of diffusion tractography, as defined by identification of known structure and fiber crossing.
doi:10.1016/j.neuroimage.2013.05.078
PMCID: PMC3725309  PMID: 23707579
MRI; structural connectivity; diffusion imaging; gradient hardware; HARDI; DSI
9.  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
10.  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
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.  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
13.  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
14.  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
15.  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
16.  Genetics of Path Lengths in Brain Connectivity Networks: HARDI-Based Maps in 457 Adults 
Brain connectivity analyses are increasingly popular for investigating organization. Many connectivity measures including path lengths are generally defined as the number of nodes traversed to connect a node in a graph to the others. Despite its name, path length is purely topological, and does not take into account the physical length of the connections. The distance of the trajectory may also be highly relevant, but is typically overlooked in connectivity analyses. Here we combined genotyping, anatomical MRI and HARDI to understand how our genes influence the cortical connections, using whole-brain tractography. We defined a new measure, based on Dijkstra’s algorithm, to compute path lengths for tracts connecting pairs of cortical regions. We compiled these measures into matrices where elements represent the physical distance traveled along tracts. We then analyzed a large cohort of healthy twins and show that our path length measure is reliable, heritable, and influenced even in young adults by the Alzheimer’s risk gene, CLU.
doi:10.1007/978-3-642-33530-3_3
PMCID: PMC4288784  PMID: 25584366
Structural connectivity; neuroimaging genetics; Dijkstra’s algorithm; HARDI tractography; path length
17.  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
18.  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
19.  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
20.  Quantifying diffusion MRI tractography of the corticospinal tract in brain tumors with deterministic and probabilistic methods☆ 
NeuroImage : Clinical  2013;3:361-368.
Introduction
Diffusion MRI tractography has been increasingly used to delineate white matter pathways in vivo for which the leading clinical application is presurgical mapping of eloquent regions. However, there is rare opportunity to quantify the accuracy or sensitivity of these approaches to delineate white matter fiber pathways in vivo due to the lack of a gold standard. Intraoperative electrical stimulation (IES) provides a gold standard for the location and existence of functional motor pathways that can be used to determine the accuracy and sensitivity of fiber tracking algorithms. In this study we used intraoperative stimulation from brain tumor patients as a gold standard to estimate the sensitivity and accuracy of diffusion tensor MRI (DTI) and q-ball models of diffusion with deterministic and probabilistic fiber tracking algorithms for delineation of motor pathways.
Methods
We used preoperative high angular resolution diffusion MRI (HARDI) data (55 directions, b = 2000 s/mm2) acquired in a clinically feasible time frame from 12 patients who underwent a craniotomy for resection of a cerebral glioma. The corticospinal fiber tracts were delineated with DTI and q-ball models using deterministic and probabilistic algorithms. We used cortical and white matter IES sites as a gold standard for the presence and location of functional motor pathways. Sensitivity was defined as the true positive rate of delineating fiber pathways based on cortical IES stimulation sites. For accuracy and precision of the course of the fiber tracts, we measured the distance between the subcortical stimulation sites and the tractography result. Positive predictive rate of the delineated tracts was assessed by comparison of subcortical IES motor function (upper extremity, lower extremity, face) with the connection of the tractography pathway in the motor cortex.
Results
We obtained 21 cortical and 8 subcortical IES sites from intraoperative mapping of motor pathways. Probabilistic q-ball had the best sensitivity (79%) as determined from cortical IES compared to deterministic q-ball (50%), probabilistic DTI (36%), and deterministic DTI (10%). The sensitivity using the q-ball algorithm (65%) was significantly higher than using DTI (23%) (p < 0.001) and the probabilistic algorithms (58%) were more sensitive than deterministic approaches (30%) (p = 0.003). Probabilistic q-ball fiber tracks had the smallest offset to the subcortical stimulation sites. The offsets between diffusion fiber tracks and subcortical IES sites were increased significantly for those cases where the diffusion fiber tracks were visibly thinner than expected. There was perfect concordance between the subcortical IES function (e.g. hand stimulation) and the cortical connection of the nearest diffusion fiber track (e.g. upper extremity cortex).
Discussion
This study highlights the tremendous utility of intraoperative stimulation sites to provide a gold standard from which to evaluate diffusion MRI fiber tracking methods and has provided an object standard for evaluation of different diffusion models and approaches to fiber tracking. The probabilistic q-ball fiber tractography was significantly better than DTI methods in terms of sensitivity and accuracy of the course through the white matter. The commonly used DTI fiber tracking approach was shown to have very poor sensitivity (as low as 10% for deterministic DTI fiber tracking) for delineation of the lateral aspects of the corticospinal tract in our study. Effects of the tumor/edema resulted in significantly larger offsets between the subcortical IES and the preoperative fiber tracks. The provided data show that probabilistic HARDI tractography is the most objective and reproducible analysis but given the small sample and number of stimulation points a generalization about our results should be given with caution. Indeed our results inform the capabilities of preoperative diffusion fiber tracking and indicate that such data should be used carefully when making pre-surgical and intra-operative management decisions.
Highlights
•Diffusion MRI tractography is used for presurgical brain mapping.•We use intraoperative electric stimulation as a gold standard.•We delineate motor tracts with deterministic and probabilistic DTI and q-ball models.•Probabilistic q-ball has the best sensitivity (79%).•Probabilistic q-ball fiber tracks had the smallest offset to the subcortical IES.
doi:10.1016/j.nicl.2013.08.008
PMCID: PMC3815019  PMID: 24273719
Diffusion MRI Tractography; Corticospinal tract; q-Ball; DTI; Brain tumor; Intraoperative electrical stimulation (IES)
21.  Brain connectivity and postural control in young traumatic brain injury patients: A diffusion MRI based network analysis☆☆☆ 
NeuroImage : Clinical  2012;1(1):106-115.
Our previous research on traumatic brain injury (TBI) patients has shown a strong relationship between specific white matter (WM) diffusion properties and motor deficits. The potential impact of TBI-related changes in network organization of the associated WM structural network on motor performance, however, remains largely unknown. Here, we used diffusion tensor imaging (DTI) based fiber tractography to reconstruct the human brain WM networks of 12 TBI and 17 control participants, followed by a graph theoretical analysis. A force platform was used to measure changes in body posture under conditions of compromised proprioceptive and/or visual feedback. Findings revealed that compared with controls, TBI patients showed higher betweenness centrality and normalized path length, and lower values of local efficiency, implying altered network organization. These results were not merely a consequence of differences in number of connections. In particular, TBI patients displayed reduced structural connectivity in frontal, parieto-premotor, visual, subcortical, and temporal areas. In addition, the decreased connectivity degree was significantly associated with poorer balance performance. We conclude that analyzing the structural brain networks with a graph theoretical approach provides new insights into motor control deficits following brain injury.
Highlights
► We examine the brain connectome in relation to traumatic brain injury (TBI). ► Altered structural connectivity is found in the networks of TBI patients. ► Poor balance performance is associated with decreases in structural connectivity. ► Structural connectivity analysis adds new information to standard DTI analyses.
doi:10.1016/j.nicl.2012.09.011
PMCID: PMC3757722  PMID: 24179743
Diffusion tensor imaging; Graph theoretical network analysis; Motor control; Structural network; Traumatic brain injury; Postural control
22.  Network efficiency in autism spectrum disorder and its relation to brain overgrowth 
A substantial body of evidence links differences in brain size to differences in brain organization. We have hypothesized that the developmental aspect of this relation plays a role in autism spectrum disorder (ASD), a neurodevelopmental disorder which involves abnormalities in brain growth. Children with ASD have abnormally large brains by the second year of life, and for several years thereafter their brain size can be multiple standard deviations above the norm. The greater conduction delays and cellular costs presumably associated with the longer long-distance connections in these larger brains is thought to influence developmental processes, giving rise to an altered brain organization with less communication between spatially distant regions. This has been supported by computational models and by findings linking greater intra-cranial volume, an index of maximum brain-size during development, to reduced inter-hemispheric connectivity in individuals with ASD. In this paper, we further assess this hypothesis via a whole-brain analysis of network efficiency. We utilize diffusion tractography to estimate the strength and length of the connections between all pairs of cortical regions. We compute the efficiency of communication between each network node and all others, and within local neighborhoods; we then assess the relation of these measures to intra-cranial volume, and the differences in these measures between adults with autism and typical controls. Intra-cranial volume is shown to be inversely related to efficiency for wide-spread regions of cortex. Moreover, the spatial patterns of reductions in efficiency in autism bear a striking resemblance to the regional relationships between efficiency and intra-cranial volume, particularly for local efficiency. The results thus provide further support for the hypothesized link between brain overgrowth in children with autism and the efficiency of the organization of the brain in adults with autism.
doi:10.3389/fnhum.2013.00845
PMCID: PMC3857605  PMID: 24368901
autism; brain size; network analysis; connectivity; tractography; optimal wiring; scaling
23.  TRACTOGRAPHY DENSITY AND NETWORK MEASURES IN ALZHEIMER’S DISEASE 
Brain connectivity declines in Alzheimer’s disease (AD), both functionally and structurally. Connectivity maps and networks derived from diffusion-based tractography offer new ways to track disease progression and to understand how AD affects the brain. Here we set out to identify (1) which fiber network measures show greatest differences between AD patients and controls, and (2) how these effects depend on the density of fibers extracted by the tractography algorithm. We computed brain networks from diffusion-weighted images (DWI) of the brain, in 110 subjects (28 normal elderly, 56 with early and 11 with late mild cognitive impairment, and 15 with AD). We derived connectivity matrices and network topology measures, for each subject, from whole-brain tractography and cortical parcellations. We used an ODF lookup table to speed up fiber extraction, and to exploit the full information in the orientation distribution function (ODF). This made it feasible to compute high density connectivity maps. We used accelerated tractography to compute a large number of fibers to understand what effect fiber density has on network measures and in distinguishing different disease groups in our data. We focused on global efficiency, transitivity, path length, mean degree, density, modularity, small world, and assortativity measures computed from weighted and binary undirected connectivity matrices. Of all these measures, the mean nodal degree best distinguished diagnostic groups. High-density fiber matrices were most helpful for picking up the more subtle clinical differences, e.g. between mild cognitively impaired (MCI) and normals, or for distinguishing subtypes of MCI (early versus late). Care is needed in clinical analyses of brain connectivity, as the density of extracted fibers may affect how well a network measure can pick up differences between patients and controls.
doi:10.1109/ISBI.2013.6556569
PMCID: PMC4232938  PMID: 25404994
tractography; Hadoop; MapReduce; network measures; connectivity matrix; Alzheimer’s disease; ODF
24.  FLOW-BASED NETWORK MEASURES OF BRAIN CONNECTIVITY IN ALZHEIMER’S DISEASE 
We present a new flow-based method for modeling brain structural connectivity. The method uses a modified maximum-flow algorithm that is robust to noise in the diffusion data and guided by biologically viable pathways and structure of the brain. A flow network is first created using a lattice graph by connecting all lattice points (voxel centers) to all their neighbors by edges. Edge weights are based on the orientation distribution function (ODF) value in the direction of the edge. The maximum-flow is computed based on this flow graph using the flow or the capacity between each region of interest (ROI) pair by following the connected tractography fibers projected onto the flow graph edges. Network measures such as global efficiency, transitivity, path length, mean degree, density, modularity, small world, and assortativity are computed from the flow connectivity matrix. We applied our method to diffusion-weighted images (DWIs) from 110 subjects (28 normal elderly, 56 with early and 11 with late mild cognitive impairment, and 15 with AD) and segmented co-registered anatomical MRIs into cortical regions. Experimental results showed better performance compared to the standard fiber-counting methods when distinguishing Alzheimer’s disease from normal aging.
doi:10.1109/ISBI.2013.6556461
PMCID: PMC4109645  PMID: 25067993
maximum flow; tractography; connectivity matrix; Alzheimer’s disease; ODF; projection; network measures; graph
25.  Assessment of the structural brain network reveals altered connectivity in children with unilateral cerebral palsy due to periventricular white matter lesions 
NeuroImage : Clinical  2014;5:84-92.
Background
Cerebral palsy (CP) is a term to describe the spectrum of disorders of impaired motor and sensory function caused by a brain lesion occurring early during development. Diffusion MRI and tractography have been shown to be useful in the study of white matter (WM) microstructure in tracts likely to be impacted by the static brain lesion.
Aim
The purpose of this study was to identify WM pathways with altered connectivity in children with unilateral CP caused by periventricular white matter lesions using a whole-brain connectivity approach.
Methods
Data of 50 children with unilateral CP caused by periventricular white matter lesions (5–17 years; manual ability classification system [MACS] I = 25/II = 25) and 17 children with typical development (CTD; 7–16 years) were analysed. Structural and High Angular Resolution Diffusion weighted Images (HARDI; 64 directions, b = 3000 s/mm2) were acquired at 3 T. Connectomes were calculated using whole-brain probabilistic tractography in combination with structural parcellation of the cortex and subcortical structures. Connections with altered fractional anisotropy (FA) in children with unilateral CP compared to CTD were identified using network-based statistics (NBS). The relationship between FA and performance of the impaired hand in bimanual tasks (Assisting Hand Assessment—AHA) was assessed in connections that showed significant differences in FA compared to CTD.
Results
FA was reduced in children with unilateral CP compared to CTD. Seven pathways, including the corticospinal, thalamocortical, and fronto-parietal association pathways were identified simultaneously in children with left and right unilateral CP. There was a positive relationship between performance of the impaired hand in bimanual tasks and FA within the cortico-spinal and thalamo-cortical pathways (r2 = 0.16–0.44; p < 0.05).
Conclusion
This study shows that network-based analysis of structural connectivity can identify alterations in FA in unilateral CP, and that these alterations in FA are related to clinical function. Application of this connectome-based analysis to investigate alterations in connectivity following treatment may elucidate the neurological correlates of improved functioning due to intervention.
Highlights
•Alterations in FA in children with CP were assessed using the connectome approach.•FA is reduced in corticospinal, thalamocortical, and association tracts in CP.•Higher FA is associated with better performance in bimanual tasks.
doi:10.1016/j.nicl.2014.05.018
PMCID: PMC4081979  PMID: 25003031
AHA, assisting hand assessment; CDGM, cortical and deep grey matter; CP, cerebral palsy; CTD, children with typical development; DROP-R, detection and replacement of outliers prior to resampling; FA, fractional anisotropy; FMAM, fit model to all measurements; GMFCS, gross motor function classification system; HARDI, high angular resolution diffusion imaging; HOMOR, higher order model outlier rejection; MACS, manual ability classification system; NBS, network based statistic; PWM, periventricular white matter; Congenital hemiplegia; Connectome; Diffusion MRI; Tractography; Unilateral cerebral palsy

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