A tutorial in connectome analysis: Topological and spatial features of brain networks

Frustrated hierarchical synchronization and emergent complexity in the human connectome network

The spontaneous emergence of coherent behavior through synchronization plays a key role in neural function, and its anomalies often lie at the basis of pathologies. Here we employ a parsimonious (mesoscopic) approach to study analytically and computationally the synchronization (Kuramoto) dynamics on the actual human-brain connectome network. We elucidate the existence of a so-far-uncovered intermediate phase, placed between the standard synchronous and asynchronous phases, i.e. between order and disorder. This novel phase stems from the hierarchical modular organization of the connectome. Where one would expect a hierarchical synchronization process, we show that the interplay between structural bottlenecks and quenched intrinsic frequency heterogeneities at many different scales, gives rise to frustrated synchronization, metastability, and chimera-like states, resulting in a very rich and complex phenomenology. We uncover the origin of the dynamic freezing behind these features by using spectral graph theory and discuss how the emerging complex synchronization patterns relate to the need for the brain to access –in a robust though flexible way– a large variety of functional attractors and dynamical repertoires without ad hoc fine-tuning to a critical point.

Structure and function of complex brain networks

An increasing number of theoretical and empirical studies approach the function of the human brain from a network perspective. The analysis of brain networks is made feasible by the development of new imaging acquisition methods as well as new tools from graph theory and dynamical systems. This review surveys some of these methodological advances and summarizes recent findings on the architecture of structural and functional brain networks. Studies of the structural connectome reveal several modules or network communities that are interlinked by hub regions mediating communication processes between modules. Recent network analyses have shown that network hubs form a densely linked collective called a "rich club," centrally positioned for attracting and dispersing signal traffic. In parallel, recordings of resting and task-evoked neural activity have revealed distinct resting-state networks that contribute to functions in distinct cognitive domains. Network methods are increasingly applied in a clinical context, and their promise for elucidating neural substrates of brain and mental disorders is discussed.

Structural MRI connectome in development: challenges of the changing brain

MRI connectomics is an emerging approach to study the brain as a network of interconnected brain regions. Understanding and mapping the development of the MRI connectome may offer new insights into the development of brain connectivity and plasticity, ultimately leading to improved understanding of normal development and to more effective diagnosis and treatment of developmental disorders. In this review, we describe the attempts made to date to map the whole-brain structural MRI connectome in the developing brain and pay a special attention to the challenges associated with the rapid changes that the brain is undergoing during maturation. The two main steps in constructing a structural brain network are (i) choosing connectivity measures that will serve as the network "edges" and (ii) finding an appropriate way to divide the brain into regions that will serve as the network "nodes". We will discuss how these two steps are usually performed in developmental studies and the rationale behind different strategies. Changes in local and global network properties that have been described during maturation in neonates and children will be reviewed, along with differences in network topology between typically and atypically developing subjects, for example, owing to pre-mature birth or hypoxic ischaemic encephalopathy. Finally, future directions of connectomics will be discussed, addressing important steps necessary to advance the study of the structural MRI connectome in development.

Brain without anatomy: construction and comparison of fully network-driven structural MRI connectomes

MRI connectomics methods treat the brain as a network and provide new information about its organization, efficiency, and mechanisms of disruption. The most commonly used method of defining network nodes is to register the brain to a standardized anatomical atlas based on the Brodmann areas. This approach is limited by inter-subject variability and can be especially problematic in the context of brain maturation or neuroplasticity (cerebral reorganization after brain damage). In this study, we combined different image processing and network theory methods and created a novel approach that enables atlas-free construction and connection-wise comparison of diffusion MRI-based brain networks. We illustrated the proposed approach in three age groups: neonates, 6-month-old infants, and adults. First, we explored a data-driven method of determining the optimal number of equal-area nodes based on the assumption that all cortical areas of the brain are connected and, thus, no part of the brain is structurally isolated. Second, to enable a connection-wise comparison, alignment to a “reference brain” was performed in the network domain within each group using a matrix alignment algorithm with simulated annealing. The correlation coefficients after pair-wise network alignment ranged from 0.6102 to 0.6673. To test the method’s reproducibility, one subject from the 6-month-old group and one from the adult group were scanned twice, resulting in correlation coefficients of 0.7443 and 0.7037, respectively. While being less than 1 due to parcellation and noise, statistically, these values were significantly higher than inter-subject values. Rotation of the parcellation largely explained the variability. Through the abstraction from anatomy, the developed framework allows for a fully network-driven analysis of structural MRI connectomes and can be applied to subjects at any stage of development and with substantial differences in cortical anatomy.

Resolving structural variability in network models and the brain

Large-scale white matter pathways crisscrossing the cortex create a complex pattern of connectivity that underlies human cognitive function. Generative mechanisms for this architecture have been difficult to identify in part because little is known in general about mechanistic drivers of structured networks. Here we contrast network properties derived from diffusion spectrum imaging data of the human brain with 13 synthetic network models chosen to probe the roles of physical network embedding and temporal network growth. We characterize both the empirical and synthetic networks using familiar graph metrics, but presented here in a more complete statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure across scales in the network. We focus specifically on the degree distribution, degree assortativity, hierarchy, topological Rentian scaling, and topological fractal scaling—in addition to several summary statistics, including the mean clustering coefficient, the shortest path-length, and the network diameter. The models are investigated in a progressive, branching sequence, aimed at capturing different elements thought to be important in the brain, and range from simple random and regular networks, to models that incorporate specific growth rules and constraints. We find that synthetic models that constrain the network nodes to be physically embedded in anatomical brain regions tend to produce distributions that are most similar to the corresponding measurements for the brain. We also find that network models hardcoded to display one network property (e.g., assortativity) do not in general simultaneously display a second (e.g., hierarchy). This relative independence of network properties suggests that multiple neurobiological mechanisms might be at play in the development of human brain network architecture. Together, the network models that we develop and employ provide a potentially useful starting point for the statistical inference of brain network structure from neuroimaging data.

White matter tracts crisscrossing the human cortex are linked in a complex pattern that constrains human thought and behavior. Why the human brain displays the complex pattern that it does is a fascinating open question. Progress in uncovering generative mechanisms for this architecture requires greater knowledge about mechanistic drivers of anatomical networks. Here we contrast network properties derived from images of the human brain with 13 synthetic network models investigated in a progressive, branching sequence, chosen to probe the roles of physical embedding and temporal growth. We characterize both the empirical and synthetic networks using network diagnostics presented here in statistical form, as scatter plots and distributions, to reveal the full range of variability of each measure. We find that synthetic models that constrain the network nodes to be physically embedded in anatomical brain regions tend to produce distributions that are most similar to the corresponding measurements for the brain. We also find that network models hardcoded to display one network property do not in general simultaneously display a second, suggesting that multiple neurobiological mechanisms drive human brain network development. The network models that we develop and employ enable statistical inference of brain network structure from neuroimaging data.

Topological organization of the "small-world" visual attention network in children with attention deficit/hyperactivity disorder (ADHD)

Background: Attention-deficit/hyperactivity disorder (ADHD) is the most commonly diagnosed childhood psychiatric disorder. Disrupted sustained attention is one of the most significant behavioral impairments in this disorder. We mapped systems-level topological properties of the neural network responsible for sustained attention during a visual sustained task, on the premise that strong associations between anomalies in network features and clinical measures of ADHD would emerge.

Methods: Graph theoretic techniques (GTT) and bivariate network-based statistics (NBS) were applied to fMRI data from 22 children with ADHD combined-type and 22 age-matched neurotypicals, to evaluate the topological and nodal-pairing features in the functional brain networks. Correlation testing for relationships between network properties and clinical measures were then performed.

Results: The visual attention network showed significantly reduced local-efficiency and nodal-efficiency in frontal and occipital regions in ADHD. Measures of degree and between-centrality pointed to hyper-functioning in anterior cingulate cortex and hypo-functioning in orbito-frontal, middle-occipital, superior-temporal, supra-central, and supra-marginal gyri in ADHD. NBS demonstrated significantly reduced pair-wise connectivity in an inner-network, encompassing right parietal and temporal lobes and left occipital lobe, in the ADHD group.

Conclusions: These data suggest that atypical topological features of the visual attention network contribute to classic ADHD symptomatology, and may underlie the inattentiveness and hyperactivity/impulsivity that are characteristics of this syndrome.

Neurodevelopmental alterations of large-scale structural networks in children with new-onset epilepsy

Recent neuroimaging and behavioral studies have revealed that children with new onset epilepsy already exhibit brain structural abnormalities and cognitive impairment. How the organization of large-scale brain structural networks is altered near the time of seizure onset and whether network changes are related to cognitive performances remain unclear. Recent studies also suggest that regional brain volume covariance reflects synchronized brain developmental changes. Here, we test the hypothesis that epilepsy during early-life is associated with abnormalities in brain network organization and cognition. We used graph theory to study structural brain networks based on regional volume covariance in 39 children with new-onset seizures and 28 healthy controls. Children with new-onset epilepsy showed a suboptimal topological structural organization with enhanced network segregation and reduced global integration compared with controls. At the regional level, structural reorganization was evident with redistributed nodes from the posterior to more anterior head regions. The epileptic brain network was more vulnerable to targeted but not random attacks. Finally, a subgroup of children with epilepsy, namely those with lower IQ and poorer executive function, had a reduced balance between network segregation and integration. Taken together, the findings suggest that the neurodevelopmental impact of new onset childhood epilepsies alters large-scale brain networks, resulting in greater vulnerability to network failure and cognitive impairment.

The Laplacian spectrum of neural networks

The brain is a complex network of neural interactions, both at the microscopic and macroscopic level. Graph theory is well suited to examine the global network architecture of these neural networks. Many popular graph metrics, however, encode average properties of individual network elements. Complementing these "conventional" graph metrics, the eigenvalue spectrum of the normalized Laplacian describes a network's structure directly at a systems level, without referring to individual nodes or connections. In this paper, the Laplacian spectra of the macroscopic anatomical neuronal networks of the macaque and cat, and the microscopic network of the Caenorhabditis elegans were examined. Consistent with conventional graph metrics, analysis of the Laplacian spectra revealed an integrative community structure in neural brain networks. Extending previous findings of overlap of network attributes across species, similarity of the Laplacian spectra across the cat, macaque and C. elegans neural networks suggests a certain level of consistency in the overall architecture of the anatomical neural networks of these species. Our results further suggest a specific network class for neural networks, distinct from conceptual small-world and scale-free models as well as several empirical networks.

Inferring influenza global transmission networks without complete phylogenetic information

Influenza is one of the most severe respiratory infections affecting humans throughout the world, yet the dynamics of its global transmission network are still contentious. Here, I describe a novel combination of phylogenetics, time series, and graph theory to analyze 14.25 years of data stratified in space and in time, focusing on the main target of the human immune response, the hemagglutinin gene. While bypassing the complete phylogenetic inference of huge data sets, the method still extracts information suggesting that waves of genetic or of nucleotide diversity circulate continuously around the globe for subtypes that undergo sustained transmission over several seasons, such as H3N2 and pandemic H1N1/09, while diversity of prepandemic H1N1 viruses had until 2009 a noncontinuous transmission pattern consistent with a source/sink model. Irrespective of the shift in the structure of H1N1 diversity circulation with the emergence of the pandemic H1N1/09 strain, US prevalence peaks during the winter months when genetic diversity is at its lowest. This suggests that a dominant strain is generally responsible for epidemics and that monitoring genetic and/or nucleotide diversity in real time could provide public health agencies with an indirect estimate of prevalence.

Detection of preclinical neural dysfunction from functional connectivity graphs derived from task fMRI. An example from degeneration

The early, preferably pre-clinical, identification of neurodegenerative diseases is important as treatment will be most successful before substantial neuronal loss. Here, we reasoned that functional brain changes as measured using functional magnetic resonance imaging (fMRI) will precede neurodegeneration. Three independent cohorts of patients with the genetic mutation leading to Huntington's Disease (HD) but without any clinical symptoms and matched controls performed three different fMRI tasks: Sequential finger tapping engaged the motor system, which is primarily affected by HD, whereas a working-memory task and a task aiming to induce irritation represented the range of low- and high-level cognitive functions also affected by HD. Each diagnostic group of every cohort included 11-16 subjects. After segmentation into 76 cortical and 14 subcortical regions, we extracted functional connectivity patterns through pairwise correlation between the signals in the regions. The resulting coefficients were directly embedded as input to a pattern classifier aiming to separate controls from gene mutation carriers. Alternatively, graph-theory measures such as degree and clustering coefficient were used as features for the discrimination. Classification accuracy never outperformed the accuracy of a grouping based on parameter estimates from a general-linear model approach or a grouping based on features extracted from anatomical images as reported in a previous analysis. Despite good within-subject stability between two runs of the same task, a high between-subject variability led to chance-level accuracy. These results indicate that standard graph-metrics are insufficient to detect subtle disease related changes when within-group variability is high. Developing methods that reduce variability related to noise should be the focus of future studies.

Preferential detachment during human brain development: age- and sex-specific structural connectivity in diffusion tensor imaging (DTI) data

Human brain maturation is characterized by the prolonged development of structural and functional properties of large-scale networks that extends into adulthood. However, it is not clearly understood which features change and which remain stable over time. Here, we examined structural connectivity based on diffusion tensor imaging (DTI) in 121 participants between 4 and 40 years of age. DTI data were analyzed for small-world parameters, modularity, and the number of fiber tracts at the level of streamlines. First, our findings showed that the number of fiber tracts, small-world topology, and modular organization remained largely stable despite a substantial overall decrease in the number of streamlines with age. Second, this decrease mainly affected fiber tracts that had a large number of streamlines, were short, within modules and within hemispheres; such connections were affected significantly more often than would be expected given their number of occurrences in the network. Third, streamline loss occurred earlier in females than in males. In summary, our findings suggest that core properties of structural brain connectivity, such as the small-world and modular organization, remain stable during brain maturation by focusing streamline loss to specific types of fiber tracts.

A machine learning approach to automated structural network analysis: application to neonatal encephalopathy

Neonatal encephalopathy represents a heterogeneous group of conditions associated with life-long developmental disabilities and neurological deficits. Clinical measures and current anatomic brain imaging remain inadequate predictors of outcome in children with neonatal encephalopathy. Some studies have suggested that brain development and, therefore, brain connectivity may be altered in the subgroup of patients who subsequently go on to develop clinically significant neurological abnormalities. Large-scale structural brain connectivity networks constructed using diffusion tractography have been posited to reflect organizational differences in white matter architecture at the mesoscale, and thus offer a unique tool for characterizing brain development in patients with neonatal encephalopathy. In this manuscript we use diffusion tractography to construct structural networks for a cohort of patients with neonatal encephalopathy. We systematically map these networks to a high-dimensional space and then apply standard machine learning algorithms to predict neurological outcome in the cohort. Using nested cross-validation we demonstrate high prediction accuracy that is both statistically significant and robust over a broad range of thresholds. Our algorithm offers a novel tool to evaluate neonates at risk for developing neurological deficit. The described approach can be applied to any brain pathology that affects structural connectivity.

Defining nodes in complex brain networks

Network science holds great promise for expanding our understanding of the human brain in health, disease, development, and aging. Network analyses are quickly becoming the method of choice for analyzing functional MRI data. However, many technical issues have yet to be confronted in order to optimize results. One particular issue that remains controversial in functional brain network analyses is the definition of a network node. In functional brain networks a node represents some predefined collection of brain tissue, and an edge measures the functional connectivity between pairs of nodes. The characteristics of a node, chosen by the researcher, vary considerably in the literature. This manuscript reviews the current state of the art based on published manuscripts and highlights the strengths and weaknesses of three main methods for defining nodes. Voxel-wise networks are constructed by assigning a node to each, equally sized brain area (voxel). The fMRI time-series recorded from each voxel is then used to create the functional network. Anatomical methods utilize atlases to define the nodes based on brain structure. The fMRI time-series from all voxels within the anatomical area are averaged and subsequently used to generate the network. Functional activation methods rely on data from traditional fMRI activation studies, often from databases, to identify network nodes. Such methods identify the peaks or centers of mass from activation maps to determine the location of the nodes. Small (~10-20 millimeter diameter) spheres located at the coordinates of the activation foci are then applied to the data being used in the network analysis. The fMRI time-series from all voxels in the sphere are then averaged, and the resultant time series is used to generate the network. We attempt to clarify the discussion and move the study of complex brain networks forward. While the "correct" method to be used remains an open, possibly unsolvable question that deserves extensive debate and research, we argue that the best method available at the current time is the voxel-wise method.

Altered topological properties of the cortical motor-related network in patients with subcortical stroke revealed by graph theoretical analysis

Cerebral neuroplasticity after stroke has been elucidated by functional neuroimaging. However, little is known concerning how topological properties of the cortical motor-related network evolved following subcortical stroke. In the present study, we investigated 24 subcortical stroke patients with only left motor pathway damaged and 24 matched healthy controls. A cortical motor-related network consisting of 20 brain regions remote from the primary lesion was constructed using resting-state functional MRI datasets. We subsequently used graph theoretical approaches to analyze the topological properties of this network in both stroke patients and healthy controls. In addition, we divided the stroke patients into two subgroups according to their outcomes in hand function to explore relationships between topological properties of this network and outcomes in hand function. Although we observed that the cortical motor-related network in both healthy controls and stroke patients exhibited small-world topology, the local efficiency of this network in stroke patients is higher than and global efficiency is lower than those in healthy controls. In addition, striking alterations in the betweenness centrality of regions were found in stroke patients, including the contralesional supplementary motor area, dorsolateral premotor cortex, and anterior inferior cerebellum. Moreover, we observed significant correlations between betweenness centrality of regions and Fugl-Meyer assessment scores. A tendency for the cortical motor-related network to be close to a regular configuration and altered betweenness centrality of regions were demonstrated in patients with subcortical stroke. This study provided insight into functional organization after subcortical stroke from the viewpoint of network topology.

Motor imagery cognitive network after left ischemic stroke: study of the patients during mental rotation task

Although motor imagery could improve motor rehabilitation, the detailed neural mechanisms of motor imagery cognitive process of stroke patients, particularly from functional network perspective, remain unclear. This study investigated functional brain network properties in each cognitive sub-stage of motor imagery of stroke patients with ischemic lesion in left hemisphere to reveal the impact of stroke on the cognition of motor imagery. Both stroke patients and control subjects participated in mental rotation task, which includes three cognitive sub-stages: visual stimulus perception, mental rotation and response cognitive process. Event-related electroencephalograph was recorded and interdependence between two different cortical areas was assessed by phase synchronization. Both global and nodal properties of functional networks in three sub-stages were statistically analyzed. Phase synchronization of stroke patients significantly reduced in mental rotation sub-stage. Longer characteristic path length and smaller global clustering coefficient of functional network were observed in patients in mental rotation sub-stage which implied the impaired segregation and integration. Larger nodal clustering coefficient and betweenness in contralesional occipitoparietal and frontal area respectively were observed in patients in all sub-stages. In addition, patients also showed smaller betweenness in ipsilesional central-parietal area in response sub-stage. The compensatory effects on local connectedness and centrality indicated the neuroplasticity in contralesional hemisphere. The functional brain networks of stroke patients demonstrated significant alterations and compensatory effects during motor imagery.

Functional connectivity and graph theory in preclinical Alzheimer's disease

Alzheimer's disease (AD) has a long preclinical phase in which amyloid and tau cerebral pathology accumulate without producing cognitive symptoms. Resting state functional connectivity magnetic resonance imaging has demonstrated that brain networks degrade during symptomatic AD. It is unclear to what extent these degradations exist before symptomatic onset. In this study, we investigated graph theory metrics of functional integration (path length), functional segregation (clustering coefficient), and functional distinctness (modularity) as a function of disease severity. Further, we assessed whether these graph metrics were affected in cognitively normal participants with cerebrospinal fluid evidence of preclinical AD. Clustering coefficient and modularity, but not path length, were reduced in AD. Cognitively normal participants who harbored AD biomarker pathology also showed reduced values in these graph measures, demonstrating brain changes similar to, but smaller than, symptomatic AD. Only modularity was significantly affected by age. We also demonstrate that AD has a particular effect on hub-like regions in the brain. We conclude that AD causes large-scale disconnection that is present before onset of symptoms.

Prediction of rat behavior outcomes in memory tasks using functional connections among neurons

BACKGROUND

Analyzing the neuronal organizational structures and studying the changes in the behavior of the organism is key to understanding cognitive functions of the brain. Although some studies have indicated that spatiotemporal firing patterns of neuronal populations have a certain relationship with the behavioral responses, the issues of whether there are any relationships between the functional networks comprised of these cortical neurons and behavioral tasks and whether it is possible to take advantage of these networks to predict correct and incorrect outcomes of single trials of animals are still unresolved.

METHODOLOGY/PRINCIPAL FINDINGS

This paper presents a new method of analyzing the structures of whole-recorded neuronal functional networks (WNFNs) and local neuronal circuit groups (LNCGs). The activity of these neurons was recorded in several rats. The rats performed two different behavioral tasks, the Y-maze task and the U-maze task. Using the results of the assessment of the WNFNs and LNCGs, this paper describes a realization procedure for predicting the behavioral outcomes of single trials. The methodology consists of four main parts: construction of WNFNs from recorded neuronal spike trains, partitioning the WNFNs into the optimal LNCGs using social community analysis, unsupervised clustering of all trials from each dataset into two different clusters, and predicting the behavioral outcomes of single trials. The results show that WNFNs and LNCGs correlate with the behavior of the animal. The U-maze datasets show higher accuracy for unsupervised clustering results than those from the Y-maze task, and these datasets can be used to predict behavioral responses effectively.

CONCLUSIONS/SIGNIFICANCE

The results of the present study suggest that a methodology proposed in this paper is suitable for analysis of the characteristics of neuronal functional networks and the prediction of rat behavior. These types of structures in cortical ensemble activity may be critical to information representation during the execution of behavior.

Topological graph kernel on multiple thresholded functional connectivity networks for mild cognitive impairment classification

Recently, brain connectivity networks have been used for classification of Alzheimer's disease and mild cognitive impairment (MCI) from normal controls (NC). In typical connectivity-networks-based classification approaches, local measures of connectivity networks are first extracted from each region-of-interest as network features, which are then concatenated into a vector for subsequent feature selection and classification. However, some useful structural information of network, especially global topological information, may be lost in this type of approaches. To address this issue, in this article, we propose a connectivity-networks-based classification framework to identify accurately the MCI patients from NC. The core of the proposed method involves the use of a new graph-kernel-based approach to measure directly the topological similarity between connectivity networks. We evaluate our method on functional connectivity networks of 12 MCI and 25 NC subjects. The experimental results show that our proposed method achieves a classification accuracy of 91.9%, a sensitivity of 100.0%, a balanced accuracy of 94.0%, and an area under receiver operating characteristic curve of 0.94, demonstrating a great potential in MCI classification, based on connectivity networks. Further connectivity analysis indicates that the connectivity of the selected brain regions is different between MCI patients and NC, that is, MCI patients show reduced functional connectivity compared with NC, in line with the findings reported in the existing studies.

A study of brain networks associated with swallowing using graph-theoretical approaches

Functional connectivity between brain regions during swallowing tasks is still not well understood. Understanding these complex interactions is of great interest from both a scientific and a clinical perspective. In this study, functional magnetic resonance imaging (fMRI) was utilized to study brain functional networks during voluntary saliva swallowing in twenty-two adult healthy subjects (all females, [Formula: see text] years of age). To construct these functional connections, we computed mean partial correlation matrices over ninety brain regions for each participant. Two regions were determined to be functionally connected if their correlation was above a certain threshold. These correlation matrices were then analyzed using graph-theoretical approaches. In particular, we considered several network measures for the whole brain and for swallowing-related brain regions. The results have shown that significant pairwise functional connections were, mostly, either local and intra-hemispheric or symmetrically inter-hemispheric. Furthermore, we showed that all human brain functional network, although varying in some degree, had typical small-world properties as compared to regular networks and random networks. These properties allow information transfer within the network at a relatively high efficiency. Swallowing-related brain regions also had higher values for some of the network measures in comparison to when these measures were calculated for the whole brain. The current results warrant further investigation of graph-theoretical approaches as a potential tool for understanding the neural basis of dysphagia.

The potential of the human connectome as a biomarker of brain disease

The human connectome at the level of fiber tracts between brain regions has been shown to differ in patients with brain disorders compared to healthy control groups. Nonetheless, there is a potentially large number of different network organizations for individual patients that could lead to cognitive deficits prohibiting correct diagnosis. Therefore changes that can distinguish groups might not be sufficient to diagnose the disease that an individual patient suffers from and to indicate the best treatment option for that patient. We describe the challenges introduced by the large variability of connectomes within healthy subjects and patients and outline three common strategies to use connectomes as biomarkers of brain diseases. Finally, we propose a fourth option in using models of simulated brain activity (the dynamic connectome) based on structural connectivity rather than the structure (connectome) itself as a biomarker of disease. Dynamic connectomes, in addition to currently used structural, functional, or effective connectivity, could be an important future biomarker for clinical applications.

Structure-dynamics relationships in bursting neuronal networks revealed using a prediction framework

The question of how the structure of a neuronal network affects its functionality has gained a lot of attention in neuroscience. However, the vast majority of the studies on structure-dynamics relationships consider few types of network structures and assess limited numbers of structural measures. In this in silico study, we employ a wide diversity of network topologies and search among many possibilities the aspects of structure that have the greatest effect on the network excitability. The network activity is simulated using two point-neuron models, where the neurons are activated by noisy fluctuation of the membrane potential and their connections are described by chemical synapse models, and statistics on the number and quality of the emergent network bursts are collected for each network type. We apply a prediction framework to the obtained data in order to find out the most relevant aspects of network structure. In this framework, predictors that use different sets of graph-theoretic measures are trained to estimate the activity properties, such as burst count or burst length, of the networks. The performances of these predictors are compared with each other. We show that the best performance in prediction of activity properties for networks with sharp in-degree distribution is obtained when the prediction is based on clustering coefficient. By contrast, for networks with broad in-degree distribution, the maximum eigenvalue of the connectivity graph gives the most accurate prediction. The results shown for small () networks hold with few exceptions when different neuron models, different choices of neuron population and different average degrees are applied. We confirm our conclusions using larger () networks as well. Our findings reveal the relevance of different aspects of network structure from the viewpoint of network excitability, and our integrative method could serve as a general framework for structure-dynamics studies in biosciences.

Disparity between dorsal and ventral networks in patients with obsessive-compulsive disorder: evidence revealed by graph theoretical analysis based on cortical thickness from MRI

As one of the most widely accepted neuroanatomical models on obsessive-compulsive disorder (OCD), it has been hypothesized that imbalance between an excitatory direct (ventral) pathway and an inhibitory indirect (dorsal) pathway in cortico-striato-thalamic circuit underlies the emergence of OCD. Here we examine the structural network in drug-free patients with OCD in terms of graph theoretical measures for the first time. We used a measure called efficiency which quantifies how a node transfers information efficiently. To construct brain networks, cortical thickness was automatically estimated using T1-weighted magnetic resonance imaging. We found that the network of the OCD patients was as efficient as that of healthy controls so that the both networks were in the small-world regime. More importantly, however, disparity between the dorsal and the ventral networks in the OCD patients was found in terms of graph theoretical measures, suggesting a positive evidence to the imbalance theory on the underlying pathophysiology of OCD.

Topographic hub maps of the human structural neocortical network

Hubs within the neocortical structural network determined by graph theoretical analysis play a crucial role in brain function. We mapped neocortical hubs topographically, using a sample population of 63 young adults. Subjects were imaged with high resolution structural and diffusion weighted magnetic resonance imaging techniques. Multiple network configurations were then constructed per subject, using random parcellations to define the nodes and using fibre tractography to determine the connectivity between the nodes. The networks were analysed with graph theoretical measures. Our results give reference maps of hub distribution measured with betweenness centrality and node degree. The loci of the hubs correspond with key areas from known overlapping cognitive networks. Several hubs were asymmetrically organized across hemispheres. Furthermore, females have hubs with higher betweenness centrality and males have hubs with higher node degree. Female networks have higher small-world indices.

A DTI-based template-free cortical connectome study of brain maturation

Improved understanding of how the human brain is “wired” on a macroscale may now be possible due to the emerging field of MRI connectomics. However, mapping the rapidly developing infant brain networks poses challenges. In this study, we applied an automated template-free “baby connectome” framework using diffusion MRI to non-invasively map the structural brain networks in subjects of different ages, including premature neonates, term-born neonates, six-month-old infants, and adults. We observed increasing brain network integration and decreasing segregation with age in term-born subjects. We also explored how the equal area nodes can be grouped into modules without any prior anatomical information – an important step toward a fully network-driven registration and analysis of brain connectivity.

Comparing connectomes across subjects and populations at different scales

Brain connectivity can be represented by a network that enables the comparison of the different patterns of structural and functional connectivity among individuals. In the literature, two levels of statistical analysis have been considered in comparing brain connectivity across groups and subjects: 1) the global comparison where a single measure that summarizes the information of each brain is used in a statistical test; 2) the local analysis where a single test is performed either for each node/connection which implies a multiplicity correction, or for each group of nodes/connections where each subset is summarized by one single test in order to reduce the number of tests to avoid a penalizing multiplicity correction. We comment on the different levels of analysis and present some methods that have been proposed at each scale. We highlight as well the possible factors that could influence the statistical results and the questions that have to be addressed in such an analysis.

Mapping putative hubs in human, chimpanzee and rhesus macaque connectomes via diffusion tractography

Mapping anatomical brain networks with graph-theoretic analysis of diffusion tractography has recently gained popularity, because of its presumed value in understanding brain function. However, this approach has seldom been used to compare brain connectomes across species, which may provide insights into brain evolution. Here, we employed a data-driven approach to compare interregional brain connections across three primate species: 1) the intensively studied rhesus macaque, 2) our closest living primate relative, the chimpanzee, and 3) humans. Specifically, we first used random parcellations and surface-based probabilistic diffusion tractography to derive the brain networks of the three species under various network densities and resolutions. We then compared the characteristics of the networks using graph-theoretic measures. In rhesus macaques, our tractography-defined hubs showed reasonable overlap with hubs previously identified using anterograde and retrograde tracer data. Across all three species, hubs were largely symmetric in the two hemispheres and were consistently identified in medial parietal, insular, retrosplenial cingulate and ventrolateral prefrontal cortices, suggesting a conserved structural architecture within these regions. However, species differences were observed in the inferior parietal cortex, polar and medial prefrontal cortices. The potential significance of these interspecies differences is discussed.

The mind-brain relationship as a mathematical problem

This paper aims to frame certain fundamental aspects of the human mind (content and meaning of mental states) and foundational elements of brain computation (spatial and temporal patterns of neural activity) so as to enable at least in principle their integration within one and the same quantitative representation. Through the history of science, similar approaches have been instrumental to bridge other seemingly mysterious scientific phenomena, such as thermodynamics and statistical mechanics, optics and electromagnetism, or chemistry and quantum physics, among several other examples. Identifying the relevant levels of analysis is important to define proper mathematical formalisms for describing the brain and the mind, such that they could be mapped onto each other in order to explain their equivalence. Based on these premises, we overview the potential of neural connectivity to provide highly informative constraints on brain computational process. Moreover, we outline approaches for representing cognitive and emotional states geometrically with semantic maps. Next, we summarize leading theoretical framework that might serve as an explanatory bridge between neural connectivity and mental space. Furthermore, we discuss the implications of this framework for human communication and our view of reality. We conclude by analyzing the practical requirements to manage the necessary data for solving the mind-brain problem from this perspective.

The parcellation-based connectome: limitations and extensions

The human connectome is an intricate system of interconnected elements, providing the basis for integrative brain function. An essential step in the macroscopic mapping and examination of this network of structural and functional interactions is the subdivision of the brain into large-scale regions. Parcellation approaches used for the formation of macroscopic brain networks include application of predefined anatomical templates, randomly generated templates and voxel-based divisions. In this review, we discuss the use of such parcellation approaches for the examination of connectome characteristics. We specifically address the impact of the choice of parcellation scheme and resolution on the estimation of the brain's topological and spatial network features. Although organizational principles of functional and structural brain networks appear to be largely independent of the adopted parcellation approach, quantitative measures of these principles may be significantly modulated. Future parcellation-based connectome studies might benefit from the adoption of novel network tools and promising advances in connectivity-based parcellation approaches.

Disturbed resting state EEG synchronization in bipolar disorder: A graph-theoretic analysis

Disruption of functional connectivity may be a key feature of bipolar disorder (BD) which reflects disturbances of synchronization and oscillations within brain networks. We investigated whether the resting electroencephalogram (EEG) in patients with BD showed altered synchronization or network properties. Resting-state EEG was recorded in 57 BD type-I patients and 87 healthy control subjects. Functional connectivity between pairs of EEG channels was measured using synchronization likelihood (SL) for 5 frequency bands (δ, θ, α, β, and γ). Graph-theoretic analysis was applied to SL over the electrode array to assess network properties. BD patients showed a decrease of mean synchronization in the alpha band, and the decreases were greatest in fronto-central and centro-parietal connections. In addition, the clustering coefficient and global efficiency were decreased in BD patients, whereas the characteristic path length increased. We also found that the normalized characteristic path length and small-worldness were significantly correlated with depression scores in BD patients. These results suggest that BD patients show impaired neural synchronization at rest and a disruption of resting-state functional connectivity.

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Global synchronization of BD patients was reduced in the alpha-band at resting.

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De-synchronized connectivity was localized in fronto-centro-parietal connections.

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Global topology of BD had decreased network clustering and increased path length.

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BD showed the less efficient network processing.

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Network characteristics of BD patients were associated with depression severity.

Single-subject grey matter graphs in Alzheimer's disease

Coordinated patterns of cortical morphology have been described as structural graphs and previous research has demonstrated that properties of such graphs are altered in Alzheimer's disease (AD). However, it remains unknown how these alterations are related to cognitive deficits in individuals, as such graphs are restricted to group-level analysis. In the present study we investigated this question in single-subject grey matter networks. This new method extracts large-scale structural graphs where nodes represent small cortical regions that are connected by edges when they show statistical similarity. Using this method, unweighted and undirected networks were extracted from T1 weighted structural magnetic resonance imaging scans of 38 AD patients (19 female, average age 72±4 years) and 38 controls (19 females, average age 72±4 years). Group comparisons of standard graph properties were performed after correcting for grey matter volumetric measurements and were correlated to scores of general cognitive functioning. AD networks were characterised by a more random topology as indicated by a decreased small world coefficient (p = 3.53×10(-5)), decreased normalized clustering coefficient (p = 7.25×10(-6)) and decreased normalized path length (p = 1.91×10(-7)). Reduced normalized path length explained significantly (p = 0.004) more variance in measurements of general cognitive decline (32%) in comparison to volumetric measurements (9%). Altered path length of the parahippocampal gyrus, hippocampus, fusiform gyrus and precuneus showed the strongest relationship with cognitive decline. The present results suggest that single-subject grey matter graphs provide a concise quantification of cortical structure that has clinical value, which might be of particular importance for disease prognosis. These findings contribute to a better understanding of structural alterations and cognitive dysfunction in AD.

Spreading dynamics on spatially constrained complex brain networks

The study of dynamical systems defined on complex networks provides a natural framework with which to investigate myriad features of neural dynamics and has been widely undertaken. Typically, however, networks employed in theoretical studies bear little relation to the spatial embedding or connectivity of the neural networks that they attempt to replicate. Here, we employ detailed neuroimaging data to define a network whose spatial embedding represents accurately the folded structure of the cortical surface of a rat brain and investigate the propagation of activity over this network under simple spreading and connectivity rules. By comparison with standard network models with the same coarse statistics, we show that the cortical geometry influences profoundly the speed of propagation of activation through the network. Our conclusions are of high relevance to the theoretical modelling of epileptic seizure events and indicate that such studies which omit physiological network structure risk simplifying the dynamics in a potentially significant way.

Magnetic resonance imaging and graph theoretical analysis of complex brain networks in neuropsychiatric disorders

Neurological and psychiatric disorders disturb higher cognitive functions and are accompanied by aberrant cortico-cortical axonal pathways or synchronizations of neural activity. A large proportion of neuroimaging studies have focused on examining the focal morphological abnormalities of various gray and white matter structures or the functional activities of brain areas during goal-directed tasks or the resting state, which provides vast quantities of information on both the structural and functional alterations in the patients' brain. However, these studies often ignore the interactions among multiple brain regions that constitute complex brain networks underlying higher cognitive function. Information derived from recent advances of noninvasive magnetic resonance imaging (MRI) techniques and computational methodologies such as graph theory have allowed researchers to explore the patterns of structural and functional connectivity of healthy and diseased brains in vivo. In this article, we summarize the recent advances made in the studies of both structural (gray matter morphology and white matter fibers) and functional (synchronized neural activity) brain networks based on human MRI data pertaining to neuropsychiatric disorders. These studies bring a systems-level perspective to the alterations of the topological organization of complex brain networks and the underlying pathophysiological mechanisms. Specifically, noninvasive imaging of structural and functional brain networks and follow-up graph-theoretical analyses demonstrate the potential to establish systems-level biomarkers for clinical diagnosis, progression monitoring, and treatment effects evaluation for neuropsychiatric disorders.

Perfusion network shift during seizures in medial temporal lobe epilepsy

Background

Medial temporal lobe epilepsy (MTLE) is associated with limbic atrophy involving the hippocampus, peri-hippocampal and extra-temporal structures. While MTLE is related to static structural limbic compromise, it is unknown whether the limbic system undergoes dynamic regional perfusion network alterations during seizures. In this study, we aimed to investigate state specific (i.e. ictal versus interictal) perfusional limbic networks in patients with MTLE.

Methods

We studied clinical information and single photon emission computed tomography (SPECT) images obtained with intravenous infusion of the radioactive tracer Technetium- Tc 99 m Hexamethylpropyleneamine Oxime (Tc-99 m HMPAO) during ictal and interictal state confirmed by video-electroencephalography (VEEG) in 20 patients with unilateral MTLE (12 left and 8 right MTLE). Pair-wise voxel-based analyses were used to define global changes in tracer between states. Regional tracer uptake was calculated and state specific adjacency matrices were constructed based on regional correlation of uptake across subjects. Graph theoretical measures were applied to investigate global and regional state specific network reconfigurations.

Results

A significant increase in tracer uptake was observed during the ictal state in the medial temporal region, cerebellum, thalamus, insula and putamen. From network analyses, we observed a relative decreased correlation between the epileptogenic temporal region and remaining cortex during the interictal state, followed by a surge of cross-correlated perfusion in epileptogenic temporal-limbic structures during a seizure, corresponding to local network integration.

Conclusions

These results suggest that MTLE is associated with a state specific perfusion and possibly functional organization consisting of a surge of limbic cross-correlated tracer uptake during a seizure, with a relative disconnection of the epileptogenic temporal lobe in the interictal period. This pattern of state specific shift in metabolic networks in MTLE may improve the understanding of epileptogenesis and neuropsychological impairments associated with MTLE.

Network attributes for segregation and integration in the human brain

Network studies of large-scale brain connectivity have begun to reveal attributes that promote the segregation and integration of neural information: communities and hubs. Network communities are sets of regions that are strongly interconnected among each other while connections between members of different communities are less dense. The clustered connectivity of network communities supports functional segregation and specialization. Network hubs link communities to one another and ensure efficient communication and information integration. This review surveys a number of recent reports on network communities and hubs, and their role in integrative processes. An emerging focus is the shifting balance between segregation and integration over time, which manifest in continuously changing patterns of functional interactions between regions, circuits and systems.

Structure out of chaos: functional brain network analysis with EEG, MEG, and functional MRI

The brain is the characteristic of a complex structure. By representing brain function, measured with EEG, MEG, and fMRI, as an abstract network, methods for the study of complex systems can be applied. These network studies have revealed insights in the complex, yet organized, architecture that is evidently present in brain function. We will discuss some technical aspects of formation and assessment of the functional brain networks. Moreover, the results that have been reported in this respect in the last years, in healthy brains as well as in functional brain networks of subjects with a neurological or psychiatrical disease, will be reviewed.

The anatomical distance of functional connections predicts brain network topology in health and schizophrenia

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.

Hierarchical alteration of brain structural and functional networks in female migraine sufferers

BACKGROUND

Little is known about the changes of brain structural and functional connectivity networks underlying the pathophysiology in migraine. We aimed to investigate how the cortical network reorganization is altered by frequent cortical overstimulation associated with migraine.

METHODOLOGY/PRINCIPAL FINDINGS

Gray matter volumes and resting-state functional magnetic resonance imaging signal correlations were employed to construct structural and functional networks between brain regions in 43 female patients with migraine (PM) and 43 gender-matched healthy controls (HC) by using graph theory-based approaches. Compared with the HC group, the patients showed abnormal global topology in both structural and functional networks, characterized by higher mean clustering coefficients without significant change in the shortest absolute path length, which indicated that the PM lost optimal topological organization in their cortical networks. Brain hubs related to pain-processing revealed abnormal nodal centrality in both structural and functional networks, including the precentral gyrus, orbital part of the inferior frontal gyrus, parahippocampal gyrus, anterior cingulate gyrus, thalamus, temporal pole of the middle temporal gyrus and the inferior parietal gyrus. Negative correlations were found between migraine duration and regions with abnormal centrality. Furthermore, the dysfunctional connections in patients' cortical networks formed into a connected component and three dysregulated modules were identified involving pain-related information processing and motion-processing visual networks.

CONCLUSIONS

Our results may reflect brain alteration dynamics resulting from migraine and suggest that long-term and high-frequency headache attacks may cause both structural and functional connectivity network reorganization. The disrupted information exchange between brain areas in migraine may be reshaped into a hierarchical modular structure progressively.

Dynamic network structure of interhemispheric coordination

Fifty years ago Gazzaniga and coworkers published a seminal article that discussed the separate roles of the cerebral hemispheres in humans. Today, the study of interhemispheric communication is facilitated by a battery of novel data analysis techniques drawn from across disciplinary boundaries, including dynamic systems theory and network theory. These techniques enable the characterization of dynamic changes in the brain's functional connectivity, thereby providing an unprecedented means of decoding interhemispheric communication. Here, we illustrate the use of these techniques to examine interhemispheric coordination in healthy human participants performing a split visual field experiment in which they process lexical stimuli. We find that interhemispheric coordination is greater when lexical information is introduced to the right hemisphere and must subsequently be transferred to the left hemisphere for language processing than when it is directly introduced to the language-dominant (left) hemisphere. Further, we find that putative functional modules defined by coherent interhemispheric coordination come online in a transient manner, highlighting the underlying dynamic nature of brain communication. Our work illustrates that recently developed dynamic, network-based analysis techniques can provide novel and previously unapproachable insights into the role of interhemispheric coordination in cognition.

Rich club organization of macaque cerebral cortex and its role in network communication

Graph-theoretical analysis of brain connectivity data has revealed significant features of brain network organization across a range of species. Consistently, large-scale anatomical networks exhibit highly nonrandom attributes including an efficient small world modular architecture, with distinct network communities that are interlinked by hub regions. The functional importance of hubs motivates a closer examination of their mutual interconnections, specifically to examine the hypothesis that hub regions are more densely linked than expected based on their degree alone, i.e. forming a central rich club. Extending recent findings of rich club topology in the cat and human brain, this report presents evidence for the existence of rich club organization in the cerebral cortex of a non-human primate, the macaque monkey, based on a connectivity data set representing a collation of numerous tract tracing studies. Rich club regions comprise portions of prefrontal, parietal, temporal and insular cortex and are widely distributed across network communities. An analysis of network motifs reveals that rich club regions tend to form star-like configurations, indicative of their central embedding within sets of nodes. In addition, rich club nodes and edges participate in a large number of short paths across the network, and thus contribute disproportionately to global communication. As rich club regions tend to attract and disperse communication paths, many of the paths follow a characteristic pattern of first increasing and then decreasing node degree. Finally, the existence of non-reciprocal projections imposes a net directional flow of paths into and out of the rich club, with some regions preferentially attracting and others dispersing signals. Overall, the demonstration of rich club organization in a non-human primate contributes to our understanding of the network principles underlying neural connectivity in the mammalian brain, and further supports the hypothesis that rich club regions and connections have a central role in global brain communication.

Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically infeasible, even in simpler systems like dissociated neuronal cultures. We introduce an improved algorithmic approach based on Transfer Entropy to reconstruct structural connectivity from network activity monitored through calcium imaging. We focus in this study on the inference of excitatory synaptic links. Based on information theory, our method requires no prior assumptions on the statistics of neuronal firing and neuronal connections. The performance of our algorithm is benchmarked on surrogate time series of calcium fluorescence generated by the simulated dynamics of a network with known ground-truth topology. We find that the functional network topology revealed by Transfer Entropy depends qualitatively on the time-dependent dynamic state of the network (bursting or non-bursting). Thus by conditioning with respect to the global mean activity, we improve the performance of our method. This allows us to focus the analysis to specific dynamical regimes of the network in which the inferred functional connectivity is shaped by monosynaptic excitatory connections, rather than by collective synchrony. Our method can discriminate between actual causal influences between neurons and spurious non-causal correlations due to light scattering artifacts, which inherently affect the quality of fluorescence imaging. Compared to other reconstruction strategies such as cross-correlation or Granger Causality methods, our method based on improved Transfer Entropy is remarkably more accurate. In particular, it provides a good estimation of the excitatory network clustering coefficient, allowing for discrimination between weakly and strongly clustered topologies. Finally, we demonstrate the applicability of our method to analyses of real recordings of in vitro disinhibited cortical cultures where we suggest that excitatory connections are characterized by an elevated level of clustering compared to a random graph (although not extreme) and can be markedly non-local.

Unraveling the general organizing principles of connectivity in neural circuits is a crucial step towards understanding brain function. However, even the simpler task of assessing the global excitatory connectivity of a culture in vitro, where neurons form self-organized networks in absence of external stimuli, remains challenging. Neuronal cultures undergo spontaneous switching between episodes of synchronous bursting and quieter inter-burst periods. We introduce here a novel algorithm which aims at inferring the connectivity of neuronal cultures from calcium fluorescence recordings of their network dynamics. To achieve this goal, we develop a suitable generalization of Transfer Entropy, an information-theoretic measure of causal influences between time series. Unlike previous algorithmic approaches to reconstruction, Transfer Entropy is data-driven and does not rely on specific assumptions about neuronal firing statistics or network topology. We generate simulated calcium signals from networks with controlled ground-truth topology and purely excitatory interactions and show that, by restricting the analysis to inter-bursts periods, Transfer Entropy robustly achieves a good reconstruction performance for disparate network connectivities. Finally, we apply our method to real data and find evidence of non-random features in cultured networks, such as the existence of highly connected hub excitatory neurons and of an elevated (but not extreme) level of clustering.

On-chip systolic networks for real-time tracking of pairwise correlations between neurons in a large-scale network

The correlation map of neurons emerges as an important mathematical framework for a spectrum of applications including neural circuit modeling, neurologic disease bio-marking and neuroimaging. However, constructing a correlation map is computationally expensive, especially when the number of neurons is large. This paper proposes a hardware design using hierarchical systolic arrays to calculate pairwise correlations between neurons. Through mapping a computationally efficient algorithm for cross-correlation onto a massively parallel structure, the hardware is able to construct the correlation maps in a much shorter time. The proposed architecture was evaluated using a field programmable gate array. The results show that the computational delay of the hardware for constructing correlation maps increases linearly with the number of neurons, whereas the growth of delay is quadratic for a software-based serial approach. Also, the efficiency of our method for detecting abnormal behaviors of neural circuits is demonstrated by analyzing correlation maps of retinal neurons.

EEG-based functional brain networks: does the network size matter?

Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. These networks--whose nodes can vary from tens to hundreds--are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which various graph metrics depend upon the network size. To this end, EEGs from 32 normal subjects were recorded and functional networks of three different sizes were extracted. A state-space based method was used to calculate cross-correlation matrices between different brain regions. These correlation matrices were used to construct binary adjacency connectomes, which were assessed with regards to a number of graph metrics such as clustering coefficient, modularity, efficiency, economic efficiency, and assortativity. We showed that the estimates of these metrics significantly differ depending on the network size. Larger networks had higher efficiency, higher assortativity and lower modularity compared to those with smaller size and the same density. These findings indicate that the network size should be considered in any comparison of networks across studies.

Quantitative assessment of a framework for creating anatomical brain networks via global tractography

Interregional connections of the brain measured with diffusion tractography can be used to infer valuable information regarding both brain structure and function. However, different tractography algorithms can generate networks that exhibit different characteristics, resulting in poor reproducibility across studies. Therefore, it is important to benchmark different tractography algorithms to quantitatively assess their performance. Here we systematically evaluated a newly introduced tracking algorithm, global tractography, to derive anatomical brain networks in a fiber phantom, 2 post-mortem macaque brains, and 20 living humans, and compared the results with an established local tracking algorithm. Our results demonstrated that global tractography accurately characterized the phantom network in terms of graph-theoretic measures, and significantly outperformed the local tracking approach. Results in brain tissues (post-mortem macaques and in vivo humans), however, showed that although the performance of global tractography demonstrated a trend of improvement, the results were not vastly different than that of local tractography, possibly resulting from the increased fiber complexity of real tissues. When using macaque tracer-derived connections as the ground truth, we found that both global and local algorithms generated non-random patterns of false negative and false positive connections that were probably related to specific fiber systems and largely independent of the tractography algorithm or tissue type (post-mortem vs. in vivo) used in the current study. Moreover, a close examination of the transcallosal motor connections, reconstructed via either global or local tractography, demonstrated that the lateral transcallosal fibers in humans and macaques did not exhibit the denser homotopic connections found in primate tracer studies, indicating the need for more robust brain mapping techniques based on diffusion MRI data.

Graph-based network analysis in schizophrenia

Over the last few years, many studies have been published using modern network analysis of the brain. Researchers and practical doctors alike should understand this method and its results on the brain evaluation at rest, during activation and in brain disease. The studies are noninvasive and usually performed with elecroencephalographic, magnetoencephalographic, magnetic resonance imaging and diffusion tensor imaging brain recordings. Different tools for analysis have been developed, although the methods are in their early stages. The results of these analyses are of special value. Studies of these tools in schizophrenia are important because widespread and local network disturbances can be evaluated by assessing integration, segregation and several structural and functional properties. With the help of network analyses, the main findings in schizophrenia are lower optimum network organization, less efficiently wired networks, less local clustering, less hierarchical organization and signs of disconnection. There are only about twenty five relevant papers on the subject today. Only a few years of study of these methods have produced interesting results and it appears promising that the development of these methods will present important knowledge for both the preclinical signs of schizophrenia and the methods’ therapeutic effects.