Search

Structural similarity is a growing focus for magnetic resonance imaging (MRI) of connectomes. Here we propose Morphometric INverse Divergence (MIND), a new method to estimate within-subject similarity between cortical areas based on the divergence between their multivariate distributions of multiple MRI features. Compared to the prior approach of morphometric similarity networks (MSNs) on n > 11,000 scans spanning three human datasets and one macaque dataset, MIND networks were more reliable, more consistent with cortical cytoarchitectonics and symmetry and more correlated with tract-tracing measures of axonal connectivity. MIND networks derived from human T1-weighted MRI were more sensitive to age-related changes than MSNs or networks derived by tractography of diffusion-weighted MRI. Gene co-expression between cortical areas was more strongly coupled to MIND networks than to MSNs or tractography. MIND network phenotypes were also more heritable, especially edges between structurally differentiated areas. MIND network analysis provides a biologically validated lens for cortical connectomics using readily available MRI data., (© 2023. The Author(s).)

Adolescence is a time of profound changes in the physical wiring and function of the brain. Here, we analyzed structural and functional brain network development in an accelerated longitudinal cohort spanning 14 to 25 y ( n = 199). Core to our work was an advanced in vivo model of cortical wiring incorporating MRI features of corticocortical proximity, microstructural similarity, and white matter tractography. Longitudinal analyses assessing age-related changes in cortical wiring identified a continued differentiation of multiple corticocortical structural networks in youth. We then assessed structure-function coupling using resting-state functional MRI measures in the same participants both via cross-sectional analysis at baseline and by studying longitudinal change between baseline and follow-up scans. At baseline, regions with more similar structural wiring were more likely to be functionally coupled. Moreover, correlating longitudinal structural wiring changes with longitudinal functional connectivity reconfigurations, we found that increased structural differentiation, particularly between sensory/unimodal and default mode networks, was reflected by reduced functional interactions. These findings provide insights into adolescent development of human brain structure and function, illustrating how structural wiring interacts with the maturation of macroscale functional hierarchies.

Age-related changes in the brain are associated with a decline in functional flexibility. Intrinsic functional flexibility is evident in the brain's dynamic ability to switch between alternative spatiotemporal states during resting state. However, the relationship between brain connectivity states, associated psychological functions during resting state, and the changes in normal aging remain poorly understood. In this study, we analyzed resting-state functional magnetic resonance imaging (rsfMRI) data from the Human Connectome Project (HCP; N = 812) and the UK Biobank (UKB; N = 6,716). Using signed community clustering to identify distinct states of dynamic functional connectivity, and text-mining of a large existing literature for functional annotation of each state, our findings from the HCP dataset indicated that the resting brain spontaneously transitions between three functionally specialized states: sensory, somatomotor, and internal mentation networks. The occurrence, transition-rate, and persistence-time parameters for each state were correlated with behavioural scores using canonical correlation analysis. We estimated the same brain states and parameters in the UKB dataset, subdivided into three distinct age ranges: 50-55, 56-67, and 68-78 years. We found that the internal mentation network was more frequently expressed in people aged 71 and older, whereas people younger than 55 more frequently expressed sensory and somatomotor networks. Furthermore, analysis of the functional entropy - a measure of uncertainty of functional connectivity - also supported this finding across the three age ranges. Our study demonstrates that dynamic functional connectivity analysis can expose the time-varying patterns of transition between functionally specialized brain states, which are strongly tied to increasing age., Competing Interests: Declaration of Competing Interest Nothing to declare., (Copyright © 2021. Published by Elsevier Inc.)

Adolescence is a critical time for the continued maturation of brain networks. Here, we assessed structural connectome development in a large longitudinal sample ranging from childhood to young adulthood. By projecting high-dimensional connectomes into compact manifold spaces, we identified a marked expansion of structural connectomes, with strongest effects in transmodal regions during adolescence. Findings reflected increased within-module connectivity together with increased segregation, indicating increasing differentiation of higher-order association networks from the rest of the brain. Projection of subcortico-cortical connectivity patterns into these manifolds showed parallel alterations in pathways centered on the caudate and thalamus. Connectome findings were contextualized via spatial transcriptome association analysis, highlighting genes enriched in cortex, thalamus, and striatum. Statistical learning of cortical and subcortical manifold features at baseline and their maturational change predicted measures of intelligence at follow-up. Our findings demonstrate that connectome manifold learning can bridge the conceptual and empirical gaps between macroscale network reconfigurations, microscale processes, and cognitive outcomes in adolescent development., Competing Interests: BP, RB, CP, SL, RR, RV, BB No competing interests declared, EB ETB. serves on the scientific advisory board of Sosei Heptares and as a consultant for GlaxoSmithKline., (© 2021, Park et al.)

The association between stimulant drug use and aberrant reward processing is well-documented in the literature, but the nature of these abnormalities remains elusive. The present study aims to disentangle the separate and interacting effects of stimulant drug use and pre-existing familial risk on abnormal reward processing associated with stimulant drug addiction. We used the Monetary Incentive Delay task, a well-validated measure of reward processing, during fMRI scanning in four distinct groups: individuals with familial risk who were either stimulant drug-dependent (N = 41) or had never used stimulant drugs (N = 46); and individuals without familial risk who were either using stimulant drugs (N = 25) or not (N = 48). We first examined task-related whole-brain activation followed by a psychophysiological interaction analysis to further explore brain functional connectivity. For analyses, we used a univariate model with two fixed factors (familial risk and stimulant drug use). Our results showed increased task-related activation in the putamen and motor cortex of stimulant-using participants. We also found altered task-related functional connectivity between the putamen and frontal regions in participants with a familial risk (irrespective of whether they were using stimulant drugs or not). Additionally, we identified an interaction between stimulant drug use and familial risk in task-related functional connectivity between the putamen and motor-related cortical regions in potentially at-risk individuals. Our findings suggest that abnormal task-related activation in motor brain systems is associated with regular stimulant drug use, whereas abnormal task-related functional connectivity in frontostriatal brain systems, in individuals with familial risk, may indicate pre-existing neural vulnerability for developing addiction.

Functional connectomes are commonly analysed as sparse graphs, constructed by thresholding cross-correlations between regional neurophysiological signals. Thresholding generally retains the strongest edges (correlations), either by retaining edges surpassing a given absolute weight, or by constraining the edge density. The latter (more widely used) method risks inclusion of false positive edges at high edge densities and exclusion of true positive edges at low edge densities. Here we apply new wavelet-based methods, which enable construction of probabilistically-thresholded graphs controlled for type I error, to a dataset of resting-state fMRI scans of 56 patients with schizophrenia and 71 healthy controls. By thresholding connectomes to fixed edge-specific P value, we found that functional connectomes of patients with schizophrenia were more dysconnected than those of healthy controls, exhibiting a lower edge density and a higher number of (dis)connected components. Furthermore, many participants' connectomes could not be built up to the fixed edge densities commonly studied in the literature (∼5-30%), while controlling for type I error. Additionally, we showed that the topological randomisation previously reported in the schizophrenia literature is likely attributable to "non-significant" edges added when thresholding connectomes to fixed density based on correlation. Finally, by explicitly comparing connectomes thresholded by increasing P value and decreasing correlation, we showed that probabilistically thresholded connectomes show decreased randomness and increased consistency across participants. Our results have implications for future analysis of functional connectivity using graph theory, especially within datasets exhibiting heterogenous distributions of edge weights (correlations), between groups or across participants., (Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.)

Complex network topology is characteristic of many biological systems, including anatomical and functional brain networks (connectomes). Here, we first constructed a structural covariance network from MRI measures of cortical thickness on 296 healthy volunteers, aged 14-24 years. Next, we designed a new algorithm for matching sample locations from the Allen Brain Atlas to the nodes of the SCN. Subsequently we used this to define, transcriptomic brain networks by estimating gene co-expression between pairs of cortical regions. Finally, we explored the hypothesis that transcriptional networks and structural MRI connectomes are coupled. A transcriptional brain network (TBN) and a structural covariance network (SCN) were correlated across connection weights and showed qualitatively similar complex topological properties: assortativity, small-worldness, modularity, and a rich-club. In both networks, the weight of an edge was inversely related to the anatomical (Euclidean) distance between regions. There were differences between networks in degree and distance distributions: the transcriptional network had a less fat-tailed degree distribution and a less positively skewed distance distribution than the SCN. However, cortical areas connected to each other within modules of the SCN had significantly higher levels of whole genome co-expression than expected by chance. Nodes connected in the SCN had especially high levels of expression and co-expression of a human supragranular enriched (HSE) gene set that has been specifically located to supragranular layers of human cerebral cortex and is known to be important for large-scale, long-distance cortico-cortical connectivity. This coupling of brain transcriptome and connectome topologies was largely but not entirely accounted for by the common constraint of physical distance on both networks., (Copyright © 2018 The Authors. Published by Elsevier Inc. All rights reserved.)

Macroscopic cortical networks are important for cognitive function, but it remains challenging to construct anatomically plausible individual structural connectomes from human neuroimaging. We introduce a new technique for cortical network mapping based on inter-regional similarity of multiple morphometric parameters measured using multimodal MRI. In three cohorts (two human, one macaque), we find that the resulting morphometric similarity networks (MSNs) have a complex topological organization comprising modules and high-degree hubs. Human MSN modules recapitulate known cortical cytoarchitectonic divisions, and greater inter-regional morphometric similarity was associated with stronger inter-regional co-expression of genes enriched for neuronal terms. Comparing macaque MSNs with tract-tracing data confirmed that morphometric similarity was related to axonal connectivity. Finally, variation in the degree of human MSN nodes accounted for about 40% of between-subject variability in IQ. Morphometric similarity mapping provides a novel, robust, and biologically plausible approach to understanding how human cortical networks underpin individual differences in psychological functions., (Copyright © 2017 Elsevier Inc. All rights reserved.)

Schizophrenia is a disease with disruptions in thought, emotion, and behavior. The dysconnectivity hypothesis suggests these disruptions are due to aberrant brain connectivity. Many studies have identified connectivity differences but few have been able to unify gray and white matter findings into one model. Here we develop an extension of the Network-Based Statistic (NBS) called NBSm (Multimodal Network-based statistic) to compare functional and anatomical networks in schizophrenia. Structural, resting functional, and diffusion magnetic resonance imaging data were collected from 29 chronic patients with schizophrenia and 29 healthy controls. Images were preprocessed, and average time courses were extracted for 90 regions of interest (ROI). Functional connectivity matrices were estimated by pairwise correlations between wavelet coefficients of ROI time series. Following diffusion tractography, anatomical connectivity matrices were estimated by white matter streamline counts between each pair of ROIs. Global and regional strength were calculated for each modality. NBSm was used to find significant overlap between functional and anatomical components that distinguished health from schizophrenia. Global strength was decreased in patients in both functional and anatomical networks. Regional strength was decreased in all regions in functional networks and only one region in anatomical networks. NBSm identified a distinguishing functional component consisting of 46 nodes with 113 links (p < 0.001), a distinguishing anatomical component with 47 nodes and 50 links (p = 0.002), and a distinguishing intermodal component with 26 nodes (p < 0.001). NBSm is a powerful technique for understanding network-based group differences present in both anatomical and functional data. In light of the dysconnectivity hypothesis, these results provide compelling evidence for the presence of significant overlapping anatomical and functional disruption in people with schizophrenia.

Defining the organizational principles of neuronal networks at the cellular scale, or micro-connectomics, is a key challenge of modern neuroscience. In this Review, we focus on graph theoretical parameters of micro-connectome topology, often informed by economical principles that conceptually originated with Ramón y Cajal's conservation laws. First, we summarize results from studies in intact small organisms and in samples from larger nervous systems. We then evaluate the evidence for an economical trade-off between biological cost and functional value in the organization of neuronal networks. Various results suggest that many aspects of neuronal network organization are indeed the outcome of competition between these two fundamental selection pressures.

Connectomics has focused primarily on the mapping of synaptic links in the brain; yet it is well established that extrasynaptic volume transmission, especially via monoamines and neuropeptides, is also critical to brain function and occurs primarily outside the synaptic connectome. We have mapped the putative monoamine connections, as well as a subset of neuropeptide connections, in C. elegans based on new and published gene expression data. The monoamine and neuropeptide networks exhibit distinct topological properties, with the monoamine network displaying a highly disassortative star-like structure with a rich-club of interconnected broadcasting hubs, and the neuropeptide network showing a more recurrent, highly clustered topology. Despite the low degree of overlap between the extrasynaptic (or wireless) and synaptic (or wired) connectomes, we find highly significant multilink motifs of interaction, pinpointing locations in the network where aminergic and neuropeptide signalling modulate synaptic activity. Thus, the C. elegans connectome can be mapped as a multiplex network with synaptic, gap junction, and neuromodulator layers representing alternative modes of interaction between neurons. This provides a new topological plan for understanding how aminergic and peptidergic modulation of behaviour is achieved by specific motifs and loci of integration between hard-wired synaptic or junctional circuits and extrasynaptic signals wirelessly broadcast from a small number of modulatory neurons., Competing Interests: ETB is employed half-time by the University of Cambridge and half-time by GlaxoSmithKline; he holds stock in GSK. The authors have declared that no competing interests exist.

Connectome mapping using techniques such as functional magnetic resonance imaging (fMRI) has become a focus of systems neuroscience. There remain many statistical challenges in analysis of functional connectivity and network architecture from BOLD fMRI multivariate time series. One key statistic for any time series is its (effective) degrees of freedom, df, which will generally be less than the number of time points (or nominal degrees of freedom, N). If we know the df, then probabilistic inference on other fMRI statistics, such as the correlation between two voxel or regional time series, is feasible. However, we currently lack good estimators of df in fMRI time series, especially after the degrees of freedom of the "raw" data have been modified substantially by denoising algorithms for head movement. Here, we used a wavelet-based method both to denoise fMRI data and to estimate the (effective) df of the denoised process. We show that seed voxel correlations corrected for locally variable df could be tested for false positive connectivity with better control over Type I error and greater specificity of anatomical mapping than probabilistic connectivity maps using the nominal degrees of freedom. We also show that wavelet despiked statistics can be used to estimate all pairwise correlations between a set of regional nodes, assign a P value to each edge, and then iteratively add edges to the graph in order of increasing P. These probabilistically thresholded graphs are likely more robust to regional variation in head movement effects than comparable graphs constructed by thresholding correlations. Finally, we show that time-windowed estimates of df can be used for probabilistic connectivity testing or dynamic network analysis so that apparent changes in the functional connectome are appropriately corrected for the effects of transient noise bursts. Wavelet despiking is both an algorithm for fMRI time series denoising and an estimator of the (effective) df of denoised fMRI time series. Accurate estimation of df offers many potential advantages for probabilistically thresholding functional connectivity and network statistics tested in the context of spatially variant and non-stationary noise. Code for wavelet despiking, seed correlational testing and probabilistic graph construction is freely available to download as part of the BrainWavelet Toolbox at www.brainwavelet.org., (Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.)

Anatomical tract tracing methods are the gold standard for estimating the weight of axonal connectivity between a pair of pre-defined brain regions. Large studies, comprising hundreds of experiments, have become feasible by automated methods. However, this comes at the cost of positive-mean noise making it difficult to detect weak connections, which are of particular interest as recent high resolution tract-tracing studies of the macaque have identified many more weak connections, adding up to greater connection density of cortical networks, than previously recognized. We propose a statistical framework that estimates connectivity weights and credibility intervals from multiple tract-tracing experiments. We model the observed signal as a log-normal distribution generated by a combination of tracer fluorescence and positive-mean noise, also accounting for injections into multiple regions. Using anterograde viral tract-tracing data provided by the Allen Institute for Brain Sciences, we estimate the connection density of the mouse intra-hemispheric cortical network to be 73% (95% credibility interval (CI): 71%, 75%); higher than previous estimates (40%). Inter-hemispheric density was estimated to be 59% (95% CI: 54%, 62%). The weakest estimable connections (about 6 orders of magnitude weaker than the strongest connections) are likely to represent only one or a few axons. These extremely weak connections are topologically more random and longer distance than the strongest connections, which are topologically more clustered and shorter distance (spatially clustered). Weak links do not substantially contribute to the global topology of a weighted brain graph, but incrementally increased topological integration of a binary graph. The topology of weak anatomical connections in the mouse brain, rigorously estimable down to the biological limit of a single axon between cortical areas in these data, suggests that they might confer functional advantages for integrative information processing and/or they might represent a stochastic factor in the development of the mouse connectome., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests: ETB is employed half-time by GlaxoSmithKline (GSK) and half-time by the University of Cambridge; he holds stock in GSK.

How does human brain structure mature during adolescence? We used MRI to measure cortical thickness and intracortical myelination in 297 population volunteers aged 14-24 y old. We found and replicated that association cortical areas were thicker and less myelinated than primary cortical areas at 14 y. However, association cortex had faster rates of shrinkage and myelination over the course of adolescence. Age-related increases in cortical myelination were maximized approximately at the internal layer of projection neurons. Adolescent cortical myelination and shrinkage were coupled and specifically associated with a dorsoventrally patterned gene expression profile enriched for synaptic, oligodendroglial- and schizophrenia-related genes. Topologically efficient and biologically expensive hubs of the brain anatomical network had greater rates of shrinkage/myelination and were associated with overexpression of the same transcriptional profile as cortical consolidation. We conclude that normative human brain maturation involves a genetically patterned process of consolidating anatomical network hubs. We argue that developmental variation of this consolidation process may be relevant both to normal cognitive and behavioral changes and the high incidence of schizophrenia during human brain adolescence.

We introduce comparative connectomics, the quantitative study of cross-species commonalities and variations in brain network topology that aims to discover general principles of network architecture of nervous systems and the identification of species-specific features of brain connectivity. By comparing connectomes derived from simple to more advanced species, we identify two conserved themes of wiring: the tendency to organize network topology into communities that serve specialized functionality and the general drive to enable high topological integration by means of investment of neural resources in short communication paths, hubs, and rich clubs. Within the space of wiring possibilities that conform to these common principles, we argue that differences in connectome organization between closely related species support adaptations in cognition and behavior., (Copyright © 2016 Elsevier Ltd. All rights reserved.)

Abnormal brain connectivity or network dysfunction has been suggested as a paradigm to understand several psychiatric disorders. We here review the use of novel meta-analytic approaches in neuroscience that go beyond a summary description of existing results by applying network analysis methods to previously published studies and/or publicly accessible databases. We define this strategy of combining connectivity with other brain characteristics as 'meta-connectomics'. For example, we show how network analysis of task-based neuroimaging studies has been used to infer functional co-activation from primary data on regional activations. This approach has been able to relate cognition to functional network topology, demonstrating that the brain is composed of cognitively specialized functional subnetworks or modules, linked by a rich club of cognitively generalized regions that mediate many inter-modular connections. Another major application of meta-connectomics has been efforts to link meta-analytic maps of disorder-related abnormalities or MRI 'lesions' to the complex topology of the normative connectome. This work has highlighted the general importance of network hubs as hotspots for concentration of cortical grey-matter deficits in schizophrenia, Alzheimer's disease and other disorders. Finally, we show how by incorporating cellular and transcriptional data on individual nodes with network models of the connectome, studies have begun to elucidate the microscopic mechanisms underpinning the macroscopic organization of whole-brain networks. We argue that meta-connectomics is an exciting field, providing robust and integrative insights into brain organization that will likely play an important future role in consolidating network models of psychiatric disorders.

Background: Functional neuroimaging studies of schizophrenia have identified abnormal activations in many brain regions. In an effort to interpret these findings from a network perspective, we carried out a meta-analysis of this literature, mapping anatomical locations of under- and over-activation to the topology of a normative human functional connectome., Methods: We included 314 task-based functional neuroimaging studies including more than 5000 patients with schizophrenia and over 5000 controls. Coordinates of significant under- or over-activations in patients relative to controls were mapped to nodes of a normative connectome defined by a prior meta-analysis of 1641 functional neuroimaging studies of task-related activation in healthy volunteers., Results: Under-activations and over-activations were reported in a wide diversity of brain regions. Both under- and over-activations were significantly more likely to be located in hub nodes that constitute the "rich club" or core of the normative connectome. In a subset of 121 studies that reported both under- and over-activations in the same patients, we found that, in network terms, these abnormalities were located in close topological proximity to each other. Under-activation in a peripheral node was more frequently associated specifically with over-activation of core nodes than with over-activation of another peripheral node., Conclusions: Although schizophrenia is associated with altered brain functional activation in a wide variety of regions, abnormal responses are concentrated in hubs of the normative connectome. Task-specific under-activation in schizophrenia is accompanied by over-activation of topologically central, less functionally specialized network nodes, which may represent a compensatory response., (© The Author 2015. Published by Oxford University Press on behalf of the Maryland Psychiatric Research Center.)

The human connectome represents a network map of the brain's wiring diagram and the pattern into which its connections are organized is thought to play an important role in cognitive function. The generative rules that shape the topology of the human connectome remain incompletely understood. Earlier work in model organisms has suggested that wiring rules based on geometric relationships (distance) can account for many but likely not all topological features. Here we systematically explore a family of generative models of the human connectome that yield synthetic networks designed according to different wiring rules combining geometric and a broad range of topological factors. We find that a combination of geometric constraints with a homophilic attachment mechanism can create synthetic networks that closely match many topological characteristics of individual human connectomes, including features that were not included in the optimization of the generative model itself. We use these models to investigate a lifespan dataset and show that, with age, the model parameters undergo progressive changes, suggesting a rebalancing of the generative factors underlying the connectome across the lifespan., (Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.)

Brain connectomes are topologically complex systems, anatomically embedded in 3D space. Anatomical conservation of "wiring cost" explains many but not all aspects of these networks. Here, we examined the relationship between topology and wiring cost in the mouse connectome by using data from 461 systematically acquired anterograde-tracer injections into the right cortical and subcortical regions of the mouse brain. We estimated brain-wide weights, distances, and wiring costs of axonal projections and performed a multiscale topological and spatial analysis of the resulting weighted and directed mouse brain connectome. Our analysis showed that the mouse connectome has small-world properties, a hierarchical modular structure, and greater-than-minimal wiring costs. High-participation hubs of this connectome mediated communication between functionally specialized and anatomically localized modules, had especially high wiring costs, and closely corresponded to regions of the default mode network. Analyses of independently acquired histological and gene-expression data showed that nodal participation colocalized with low neuronal density and high expression of genes enriched for cognition, learning and memory, and behavior. The mouse connectome contains high-participation hubs, which are not explained by wiring-cost minimization but instead reflect competitive selection pressures for integrated network topology as a basis for higher cognitive and behavioral functions.

In recent years, pathophysiological models of brain disorders have shifted from an emphasis on understanding pathology in specific brain regions to characterizing disturbances of interconnected neural systems. This shift has paralleled rapid advances in connectomics, a field concerned with comprehensively mapping the neural elements and inter-connections that constitute the brain. Magnetic resonance imaging (MRI) has played a central role in these efforts, as it allows relatively cost-effective in vivo assessment of the macro-scale architecture of brain network connectivity. In this paper, we provide a brief introduction to some of the basic concepts in the field and review how recent developments in imaging connectomics are yielding new insights into brain disease, with a particular focus on Alzheimer's disease and schizophrenia. Specifically, we consider how research into circuit-level, connectome-wide and topological changes is stimulating the development of new aetiopathological theories and biomarkers with potential for clinical translation. The findings highlight the advantage of conceptualizing brain disease as a result of disturbances in an interconnected complex system, rather than discrete pathology in isolated sub-sets of brain regions., (Copyright © 2014 Elsevier B.V. and ECNP. All rights reserved.)

Background: We first give a brief introduction to graph theoretical analysis and its application to the study of brain network topology or connectomics. Within this framework, we review the existing empirical data on developmental changes in brain network organization across a range of experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans)., Synthesis: We discuss preliminary evidence and current hypotheses for how the emergence of network properties correlates with concomitant cognitive and behavioural changes associated with development. We highlight some of the technical and conceptual challenges to be addressed by future developments in this rapidly moving field. Given the parallels previously discovered between neural systems across species and over a range of spatial scales, we also review some recent advances in developmental network studies at the cellular scale. We highlight the opportunities presented by such studies and how they may complement neuroimaging in advancing our understanding of brain development. Finally, we note that many brain and mind disorders are thought to be neurodevelopmental in origin and that charting the trajectory of brain network changes associated with healthy development also sets the stage for understanding abnormal network development., Conclusions: We therefore briefly review the clinical relevance of network metrics as potential diagnostic markers and some recent efforts in computational modelling of brain networks which might contribute to a more mechanistic understanding of neurodevelopmental disorders in future., (© 2014 The Authors. Journal of Child Psychology and Psychiatry published by John Wiley & Sons Ltd on behalf of Association for Child and Adolescent Mental Health.)

Brain networks or 'connectomes' include a minority of highly connected hub nodes that are functionally valuable, because their topological centrality supports integrative processing and adaptive behaviours. Recent studies also suggest that hubs have higher metabolic demands and longer-distance connections than other brain regions, and therefore could be considered biologically costly. Assuming that hubs thus normally combine both high topological value and high biological cost, we predicted that pathological brain lesions would be concentrated in hub regions. To test this general hypothesis, we first identified the hubs of brain anatomical networks estimated from diffusion tensor imaging data on healthy volunteers (n = 56), and showed that computational attacks targeted on hubs disproportionally degraded the efficiency of brain networks compared to random attacks. We then prepared grey matter lesion maps, based on meta-analyses of published magnetic resonance imaging data on more than 20 000 subjects and 26 different brain disorders. Magnetic resonance imaging lesions that were common across all brain disorders were more likely to be located in hubs of the normal brain connectome (P < 10(-4), permutation test). Specifically, nine brain disorders had lesions that were significantly more likely to be located in hubs (P < 0.05, permutation test), including schizophrenia and Alzheimer's disease. Both these disorders had significantly hub-concentrated lesion distributions, although (almost completely) distinct subsets of cortical hubs were lesioned in each disorder: temporal lobe hubs specifically were associated with higher lesion probability in Alzheimer's disease, whereas in schizophrenia lesions were concentrated in both frontal and temporal cortical hubs. These results linking pathological lesions to the topological centrality of nodes in the normal diffusion tensor imaging connectome were generally replicated when hubs were defined instead by the meta-analysis of more than 1500 task-related functional neuroimaging studies of healthy volunteers to create a normative functional co-activation network. We conclude that the high cost/high value hubs of human brain networks are more likely to be anatomically abnormal than non-hubs in many (if not all) brain disorders., (© The Author (2014). Published by Oxford University Press on behalf of the Guarantors of Brain.)

Recently, there has been much interest in the community structure or mesoscale organization of complex networks. This structure is characterised either as a set of sparsely inter-connected modules or as a highly connected core with a sparsely connected periphery. However, it is often difficult to disambiguate these two types of mesoscale structure or, indeed, to summarise the full network in terms of the relationships between its mesoscale constituents. Here, we estimate a community structure with a stochastic blockmodel approach, the Erdős-Rényi Mixture Model, and compare it to the much more widely used deterministic methods, such as the Louvain and Spectral algorithms. We used the Caenorhabditis elegans (C. elegans) nervous system (connectome) as a model system in which biological knowledge about each node or neuron can be used to validate the functional relevance of the communities obtained. The deterministic algorithms derived communities with 4-5 modules, defined by sparse inter-connectivity between all modules. In contrast, the stochastic Erdős-Rényi Mixture Model estimated a community with 9 blocks or groups which comprised a similar set of modules but also included a clearly defined core, made of 2 small groups. We show that the "core-in-modules" decomposition of the worm brain network, estimated by the Erdős-Rényi Mixture Model, is more compatible with prior biological knowledge about the C. elegans nervous system than the purely modular decomposition defined deterministically. We also show that the blockmodel can be used both to generate stochastic realisations (simulations) of the biological connectome, and to compress network into a small number of super-nodes and their connectivity. We expect that the Erdős-Rényi Mixture Model may be useful for investigating the complex community structures in other (nervous) systems.

Mapping synaptic connections and projections is crucial for understanding brain dynamics and function. In a recent issue of Nature, Oh et al. present a wiring diagram of the whole mouse brain, where standardized labeling, tracing, and imaging of axonal connections reveal new details in the network organization of neuronal connectivity., (Copyright © 2014 Elsevier Inc. All rights reserved.)

There is increasing interest in topological analysis of brain networks as complex systems, with researchers often using neuroimaging to represent the large-scale organization of nervous systems without precise cellular resolution. Here we used graph theory to investigate the neuronal connectome of the nematode worm Caenorhabditis elegans, which is defined anatomically at a cellular scale as 2287 synaptic connections between 279 neurons. We identified a small number of highly connected neurons as a rich club (N = 11) interconnected with high efficiency and high connection distance. Rich club neurons comprise almost exclusively the interneurons of the locomotor circuits, with known functional importance for coordinated movement. The rich club neurons are connector hubs, with high betweenness centrality, and many intermodular connections to nodes in different modules. On identifying the shortest topological paths (motifs) between pairs of peripheral neurons, the motifs that are found most frequently traverse the rich club. The rich club neurons are born early in development, before visible movement of the animal and before the main phase of developmental elongation of its body. We conclude that the high wiring cost of the globally integrative rich club of neurons in the C. elegans connectome is justified by the adaptive value of coordinated movement of the animal. The economical trade-off between physical cost and behavioral value of rich club organization in a cellular connectome confirms theoretical expectations and recapitulates comparable results from human neuroimaging on much larger scale networks, suggesting that this may be a general and scale-invariant principle of brain network organization.

The human brain is a topologically complex network embedded in anatomical space. Here, we systematically explored relationships between functional connectivity, complex network topology, and anatomical (Euclidean) distance between connected brain regions, in the resting-state functional magnetic resonance imaging brain networks of 20 healthy volunteers and 19 patients with childhood-onset schizophrenia (COS). Normal between-subject differences in average distance of connected edges in brain graphs were strongly associated with variation in topological properties of functional networks. In addition, a club or subset of connector hubs was identified, in lateral temporal, parietal, dorsal prefrontal, and medial prefrontal/cingulate cortical regions. In COS, there was reduced strength of functional connectivity over short distances especially, and therefore, global mean connection distance of thresholded graphs was significantly greater than normal. As predicted from relationships between spatial and topological properties of normal networks, this disorder-related proportional increase in connection distance was associated with reduced clustering and modularity and increased global efficiency of COS networks. Between-group differences in connection distance were localized specifically to connector hubs of multimodal association cortex. In relation to the neurodevelopmental pathogenesis of schizophrenia, we argue that the data are consistent with the interpretation that spatial and topological disturbances of functional network organization could arise from excessive "pruning" of short-distance functional connections in schizophrenia.

Schizophrenia is frequently characterized as a disorder of brain connectivity. Neuroimaging has played a central role in supporting this view, with nearly two decades of research providing abundant evidence of structural and functional connectivity abnormalities in the disorder. In recent years, our understanding of how schizophrenia affects brain networks has been greatly advanced by attempts to map the complete set of inter-regional interactions comprising the brain's intricate web of connectivity; i.e., the human connectome. Imaging connectomics refers to the use of neuroimaging techniques to generate these maps which, combined with the application of graph theoretic methods, has enabled relatively comprehensive mapping of brain network connectivity and topology in unprecedented detail. Here, we review the application of these techniques to the study of schizophrenia, focusing principally on magnetic resonance imaging (MRI) research, while drawing attention to key methodological issues in the field. The published findings suggest that schizophrenia is associated with a widespread and possibly context-independent functional connectivity deficit, upon which are superimposed more circumscribed, context-dependent alterations associated with transient states of hyper- and/or hypo-connectivity. In some cases, these changes in inter-regional functional coupling dynamics can be related to measures of intra-regional dysfunction. Topological disturbances of functional brain networks in schizophrenia point to reduced local network connectivity and modular structure, as well as increased global integration and network robustness. Some, but not all, of these functional abnormalities appear to have an anatomical basis, though the relationship between the two is complex. By comprehensively mapping connectomic disturbances in patients with schizophrenia across the entire brain, this work has provided important insights into the highly distributed character of neural abnormalities in the disorder, and the potential functional consequences that these disturbances entail., (Copyright © 2012 Elsevier Inc. All rights reserved.)