Eigenvector centrality mapping for analyzing connectivity patterns in fMRI data of the human brain

Local MEG networks: the missing link between protein expression and epilepsy in glioma patients?

Connectivity and network analysis in neuroscience has been applied to multiple spatial scales, but the links between these different scales have rarely been investigated. In tumor-related epilepsy, altered network topology is related to behavior, but the molecular basis of these observations is unknown. We elucidate the associations between microscopic features of brain tumors, local network topology, and functional patient status. We hypothesize that expression of proteins related to tumor-related epilepsy is directly correlated with network characteristics of the tumor area. Glioma patients underwent magnetoencephalography, and functional network topology of the tumor area was used to predict tissue protein expression patterns of tumor tissue collected during neurosurgery. Protein expression and network topology were interdependent; in particular between-module connectivity was selectively associated with two epilepsy-related proteins. Total number of seizures was related to both the role of the tumor area in the functional network and to protein expression. Importantly, classification of protein expression was predicted by between-module connectivity with up to 100% accuracy. Thus, network topology may serve as an intermediate level between molecular features of tumor tissue and symptomatology in brain tumor patients, and can potentially be used as a non-invasive marker for microscopic tissue characteristics.

The thalamus and brainstem act as key hubs in alterations of human brain network connectivity induced by mild propofol sedation

Despite their routine use during surgical procedures, no consensus has yet been reached on the precise mechanisms by which hypnotic anesthetic agents produce their effects. Molecular, animal and human studies have suggested disruption of thalamocortical communication as a key component of anesthetic action at the brain systems level. Here, we used the anesthetic agent, propofol, to modulate consciousness and to evaluate differences in the interactions of remote neural networks during altered consciousness. We investigated the effects of propofol, at a dose that produced mild sedation without loss of consciousness, on spontaneous cerebral activity of 15 healthy volunteers using functional magnetic resonance imaging (fMRI), exploiting oscillations (<0.1 Hz) in blood oxygenation level-dependent signal across functionally connected brain regions. We considered the data as a graph, or complex network of nodes and links, and used eigenvector centrality (EC) to characterize brain network properties. The EC mapping of fMRI data in healthy humans under propofol mild sedation demonstrated a decrease of centrality of the thalamus versus an increase of centrality within the pons of the brainstem, highlighting the important role of these two structures in regulating consciousness. Specifically, the decrease of thalamus centrality results from its disconnection from a widespread set of cortical and subcortical regions, while the increase of brainstem centrality may be a consequence of its increased influence, in the mildly sedated state, over a few highly central cortical regions key to the default mode network such as the posterior and anterior cingulate cortices.

Abdominal fat distribution and its relationship to brain changes: the differential effects of age on cerebellar structure and function: a cross-sectional, exploratory study

OBJECTIVES

To investigate whether the metabolically important visceral adipose tissue (VAT) relates differently to structural and functional brain changes in comparison with body weight measured as body mass index (BMI). Moreover, we aimed to investigate whether these effects change with age.

DESIGN

Cross-sectional, exploratory.

SETTING

University Clinic, Integrative Research and Treatment Centre.

PARTICIPANTS

We included 100 (mean BMI=26.0 kg/m², 42 women) out of 202 volunteers randomly invited by the city's registration office, subdivided into two age groups: young-to-mid-age (n=51, 20-45 years of age, mean BMI=24.9, 24 women) versus old (n=49, 65-70 years of age, mean BMI=27.0, 18 women).

MAIN OUTCOME MEASURES

VAT, BMI, subcutaneous abdominal adipose tissue, brain structure (grey matter density), functional brain architecture (eigenvector centrality, EC).

RESULTS

We discovered a loss of cerebellar structure with increasing VAT in the younger participants, most significantly in regions involved in motor processing. This negative correlation disappeared in the elderly. Investigating functional brain architecture showed again inverse VAT-cerebellum correlations, whereas now regions involved in cognitive and emotional processing were significant. Although we detected similar results for EC using BMI, significant age interaction for both brain structure and functional architecture was only found using VAT.

CONCLUSIONS

Visceral adiposity is associated with cerebellar changes of both structure and function, whereas the regions involved contribute to motor, cognitive and emotional processes. Furthermore, these associations seem to be age dependent, with younger adults' brains being adversely affected.

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.

Analyzing complex functional brain networks: Fusing statistics and network science to understand the brain*†

Complex functional brain network analyses have exploded over the last decade, gaining traction due to their profound clinical implications. The application of network science (an interdisciplinary offshoot of graph theory) has facilitated these analyses and enabled examining the brain as an integrated system that produces complex behaviors. While the field of statistics has been integral in advancing activation analyses and some connectivity analyses in functional neuroimaging research, it has yet to play a commensurate role in complex network analyses. Fusing novel statistical methods with network-based functional neuroimage analysis will engender powerful analytical tools that will aid in our understanding of normal brain function as well as alterations due to various brain disorders. Here we survey widely used statistical and network science tools for analyzing fMRI network data and discuss the challenges faced in filling some of the remaining methodological gaps. When applied and interpreted correctly, the fusion of network scientific and statistical methods has a chance to revolutionize the understanding of brain function.

Dynamic modulation of intrinsic functional connectivity by transcranial direct current stimulation

Transcranial direct current stimulation (tDCS) is a noninvasive brain stimulation technique capable of modulating cortical excitability and thereby influencing behavior and learning. Recent evidence suggests that bilateral tDCS over both primary sensorimotor cortices (SM1) yields more prominent effects on motor performance in both healthy subjects and chronic stroke patients than unilateral tDCS over SM1. To better characterize the underlying neural mechanisms of this effect, we aimed to explore changes in resting-state functional connectivity during both stimulation types. In a randomized single-blind crossover design, 12 healthy subjects underwent functional magnetic resonance imaging at rest before, during, and after 20 min of unilateral, bilateral, and sham tDCS stimulation over SM1. Eigenvector centrality mapping (ECM) was used to investigate tDCS-induced changes in functional connectivity patterns across the whole brain. Uni- and bilateral tDCS over SM1 resulted in functional connectivity changes in widespread brain areas compared with sham stimulation both during and after stimulation. Whereas bilateral tDCS predominantly modulated changes in primary and secondary motor as well as prefrontal regions, unilateral tDCS affected prefrontal, parietal, and cerebellar areas. No direct effect was seen under the stimulating electrode in the unilateral condition. The time course of changes in functional connectivity in the respective brain areas was nonlinear and temporally dispersed. These findings provide evidence toward a network-based understanding regarding the underpinnings of specific tDCS interventions.

Cognitive dysfunction in early multiple sclerosis: altered centrality derived from resting-state functional connectivity using magneto-encephalography

BACKGROUND

Cognitive dysfunction in multiple sclerosis (MS) is frequent. Insight into underlying mechanisms would help to develop therapeutic strategies.

OBJECTIVE

To explore the relationship of cognitive performance to patterns of nodal centrality derived from magneto-encephalography (MEG).

METHODS

34 early relapsing-remitting MS patients (median EDSS 2.0) and 28 age- and gender-matched healthy controls (HC) had a MEG, a neuropsychological assessment and structural MRI. Resting-state functional connectivity was determined by the synchronization likelihood. Eigenvector Centrality (EC) was used to quantify for each sensor its connectivity and importance within the network. A cognition-score was calculated, and normalized grey and white matter volumes were determined. EC was compared per sensor and frequency band between groups using permutation testing, and related to cognition.

RESULTS

Patients had lower grey and white matter volumes than HC, male patients lower cognitive performance than female patients. In HC, EC distribution showed highest nodal centrality over bi-parietal sensors ("hubs"). In patients, nodal centrality was even higher bi-parietally (theta-band) but markedly lower left temporally (upper alpha- and beta-band). Lower cognitive performance correlated to decreased nodal centrality over left temporal (lower alpha-band) and right temporal (beta-band) sensors, and to increased nodal centrality over right parieto-temporal sensors (beta-band). Network changes were most pronounced in male patients.

CONCLUSIONS

Partial functional disconnection of the temporal regions was associated with cognitive dysfunction in MS; increased centrality in parietal hubs may reflect a shift from temporal to possibly less efficient parietal processing. To better understand patterns and dynamics of these network changes, longitudinal studies are warranted, also addressing the influence of gender.

EEG-fMRI Methods for the Study of Brain Networks during Sleep

Modern neuroimaging methods may provide unique insights into the mechanism and role of sleep, as well as into particular mechanisms of brain function in general. Many of the recent neuroimaging studies have used concurrent EEG and fMRI, which present unique technical challenges ranging from the difficulty of inducing sleep in the MRI environment to appropriate instrumentation and data processing methods to obtain artifact free data. In addition, the use of EEG-fMRI during sleep leads to unique data interpretation issues, as common approaches developed for the analysis of task-evoked activity do not apply to sleep. Reviewed are a variety of statistical approaches that can be used to characterize brain activity from fMRI data acquired during sleep, with an emphasis on approaches that investigate the presence of correlated activity between brain regions. Each of these approaches has advantages and disadvantages that must be considered in concert with the theoretical questions of interest. Specifically, fundamental theories of sleep control and function should be considered when designing these studies and when choosing the associated statistical approaches. For example, the notion that local brain activity during sleep may be triggered by local, use-dependent activity during wakefulness may be tested by analyzing sleep networks as statistically independent components. Alternatively, the involvement of regions in more global processes such as arousal may be investigated with correlation analysis.

Electrical brain stimulation improves cognitive performance by modulating functional connectivity and task-specific activation

Excitatory anodal transcranial direct current stimulation (atDCS) can improve human cognitive functions, but neural underpinnings of its mode of action remain elusive. In a cross-over placebo ("sham") controlled study we used functional magnetic resonance imaging (fMRI) to investigate neurofunctional correlates of improved language functions induced by atDCS over a core language area, the left inferior frontal gyrus (IFG). Intrascanner transcranial direct current stimulation-induced changes in overt semantic word generation assessed behavioral modulation; task-related and task-independent (resting-state) fMRI characterized language network changes. Improved word-retrieval during atDCS was paralleled by selectively reduced task-related activation in the left ventral IFG, an area specifically implicated in semantic retrieval processes. Under atDCS, resting-state fMRI revealed increased connectivity of the left IFG and additional major hubs overlapping with the language network. In conclusion, atDCS modulates endogenous low-frequency oscillations in a distributed set of functionally connected brain areas, possibly inducing more efficient processing in critical task-relevant areas and improved behavioral performance.

Connectivity concordance mapping: a new tool for model-free analysis of FMRI data of the human brain

Functional magnetic resonance data acquired in a task-absent condition (“resting state”) require new data analysis techniques that do not depend on an activation model. Here, we propose a new analysis method called Connectivity Concordance Mapping (CCM). The main idea is to assign a label to each voxel based on the reproducibility of its whole-brain pattern of connectivity. Specifically, we compute the correlations of time courses of each voxel with every other voxel for each measurement. Voxels whose correlation pattern is consistent across measurements receive high values. The result of a CCM analysis is thus a voxel-wise map of concordance values. Regions of high inter-subject concordance can be assumed to be functionally consistent, and may thus be of specific interest for further analysis. Here we present two fMRI studies to demonstrate the possible applications of the algorithm. The first is a eyes-open/eyes-closed paradigm designed to highlight the potential of the method in a relatively simple domain. The second study is a longitudinal repeated measurement of a patient following stroke. Longitudinal clinical studies such as this may represent the most interesting domain of applications for this algorithm.

Hierarchical topological network analysis of anatomical human brain connectivity and differences related to sex and kinship

Modern non-invasive brain imaging technologies, such as diffusion weighted magnetic resonance imaging (DWI), enable the mapping of neural fiber tracts in the white matter, providing a basis to reconstruct a detailed map of brain structural connectivity networks. Brain connectivity networks differ from random networks in their topology, which can be measured using small worldness, modularity, and high-degree nodes (hubs). Still, little is known about how individual differences in structural brain network properties relate to age, sex, or genetic differences. Recently, some groups have reported brain network biomarkers that enable differentiation among individuals, pairs of individuals, and groups of individuals. In addition to studying new topological features, here we provide a unifying general method to investigate topological brain networks and connectivity differences between individuals, pairs of individuals, and groups of individuals at several levels of the data hierarchy, while appropriately controlling false discovery rate (FDR) errors. We apply our new method to a large dataset of high quality brain connectivity networks obtained from High Angular Resolution Diffusion Imaging (HARDI) tractography in 303 young adult twins, siblings, and unrelated people. Our proposed approach can accurately classify brain connectivity networks based on sex (93% accuracy) and kinship (88.5% accuracy). We find statistically significant differences associated with sex and kinship both in the brain connectivity networks and in derived topological metrics, such as the clustering coefficient and the communicability matrix.

Network centrality in the human functional connectome

The network architecture of functional connectivity within the human brain connectome is poorly understood at the voxel level. Here, using resting state functional magnetic resonance imaging data from 1003 healthy adults, we investigate a broad array of network centrality measures to provide novel insights into connectivity within the whole-brain functional network (i.e., the functional connectome). We first assemble and visualize the voxel-wise (4 mm) functional connectome as a functional network. We then demonstrate that each centrality measure captures different aspects of connectivity, highlighting the importance of considering both global and local connectivity properties of the functional connectome. Beyond "detecting functional hubs," we treat centrality as measures of functional connectivity within the brain connectome and demonstrate their reliability and phenotypic correlates (i.e., age and sex). Specifically, our analyses reveal age-related decreases in degree centrality, but not eigenvector centrality, within precuneus and posterior cingulate regions. This implies that while local or (direct) connectivity decreases with age, connections with hub-like regions within the brain remain stable with age at a global level. In sum, these findings demonstrate the nonredundancy of various centrality measures and raise questions regarding their underlying physiological mechanisms that may be relevant to the study of neurodegenerative and psychiatric disorders.

Critical comments on dynamic causal modelling

Dynamic causal modelling (DCM) (Friston et al., 2003) is a technique designed to investigate the influence between brain areas using time series data obtained by EEG/MEG or functional magnetic resonance imaging (fMRI). The basic idea is to fit various models to time series data, and select one of those models using Bayesian model comparison. Here, we present a critical evaluation of DCM in which we show that DCM can be challenged on several grounds. We will discuss three main points relating to combinatorial explosion, the validity of the model selection procedure, and problems with respect to model validation.

Human connectomics

Recent advances in non-invasive neuroimaging have enabled the measurement of connections between distant regions in the living human brain, thus opening up a new field of research: Human connectomics. Different imaging modalities allow the mapping of structural connections (axonal fibre tracts) as well as functional connections (correlations in time series), and individual variations in these connections may be related to individual variations in behaviour and cognition. Connectivity analysis has already led to a number of new insights about brain organization. For example, segregated brain regions may be identified by their unique patterns of connectivity, structural and functional connectivity may be compared to elucidate how dynamic interactions arise from the anatomical substrate, and the architecture of large-scale networks connecting sets of brain regions may be analysed in detail. The combined analysis of structural and functional networks has begun to reveal components or modules with distinct patterns of connections that become engaged in different cognitive tasks. Collectively, advances in human connectomics open up the possibility of studying how brain connections mediate regional brain function and thence behaviour.

A network-based approach to prioritize results from genome-wide association studies

Genome-wide association studies (GWAS) are a valuable approach to understanding the genetic basis of complex traits. One of the challenges of GWAS is the translation of genetic association results into biological hypotheses suitable for further investigation in the laboratory. To address this challenge, we introduce Network Interface Miner for Multigenic Interactions (NIMMI), a network-based method that combines GWAS data with human protein-protein interaction data (PPI). NIMMI builds biological networks weighted by connectivity, which is estimated by use of a modification of the Google PageRank algorithm. These weights are then combined with genetic association p-values derived from GWAS, producing what we call ‘trait prioritized sub-networks.’ As a proof of principle, NIMMI was tested on three GWAS datasets previously analyzed for height, a classical polygenic trait. Despite differences in sample size and ancestry, NIMMI captured 95% of the known height associated genes within the top 20% of ranked sub-networks, far better than what could be achieved by a single-locus approach. The top 2% of NIMMI height-prioritized sub-networks were significantly enriched for genes involved in transcription, signal transduction, transport, and gene expression, as well as nucleic acid, phosphate, protein, and zinc metabolism. All of these sub-networks were ranked near the top across all three height GWAS datasets we tested. We also tested NIMMI on a categorical phenotype, Crohn’s disease. NIMMI prioritized sub-networks involved in B- and T-cell receptor, chemokine, interleukin, and other pathways consistent with the known autoimmune nature of Crohn’s disease. NIMMI is a simple, user-friendly, open-source software tool that efficiently combines genetic association data with biological networks, translating GWAS findings into biological hypotheses.

Brain graphs: graphical models of the human brain connectome

Brain graphs provide a relatively simple and increasingly popular way of modeling the human brain connectome, using graph theory to abstractly define a nervous system as a set of nodes (denoting anatomical regions or recording electrodes) and interconnecting edges (denoting structural or functional connections). Topological and geometrical properties of these graphs can be measured and compared to random graphs and to graphs derived from other neuroscience data or other (nonneural) complex systems. Both structural and functional human brain graphs have consistently demonstrated key topological properties such as small-worldness, modularity, and heterogeneous degree distributions. Brain graphs are also physically embedded so as to nearly minimize wiring cost, a key geometric property. Here we offer a conceptual review and methodological guide to graphical analysis of human neuroimaging data, with an emphasis on some of the key assumptions, issues, and trade-offs facing the investigator.

Maturation of the language network: from inter- to intrahemispheric connectivities

Language development must go hand-in-hand with brain maturation. Little is known about how the brain develops to serve language processing, in particular, the processing of complex syntax, a capacity unique to humans. Behavioral reports indicate that the ability to process complex syntax is not yet adult-like by the age of seven years. Here, we apply a novel method to demonstrate that the basic neural basis of language, as revealed by low frequency fluctuation stemming from functional MRI data, differs between six-year-old children and adults in crucial aspects. Although the classical language regions are actively in place by the age of six, the functional connectivity between these regions clearly is not. In contrast to adults who show strong connectivities between frontal and temporal language regions within the left hemisphere, children's default language network is characterized by a strong functional interhemispheric connectivity, mainly between the superior temporal regions. These data indicate a functional reorganization of the neural network underlying language development towards a system that allows a close interplay between frontal and temporal regions within the left hemisphere.

Long-term effects of motor training on resting-state networks and underlying brain structure

Acquired motor skills are coded in fronto-parietal brain networks, but how these networks evolve through motor training is unclear. On the one hand, increased functional connectivity has been shown immediately after a training session; on the other hand, training-induced structural changes are visible only after several weeks. Based on known associations between functional and structural network development during human ontogeny, we hypothesised that learning a challenging motor task leads to long-lasting changes in functional resting-state networks and the corresponding cortical and sub-cortical brain structures. Using longitudinal functional and structural MRI at multiple time points, we demonstrate increased fronto-parietal network connectivity one week after two brief motor training sessions in a dynamic balancing task, although subjects were engaged in their regular daily activities during the week. Repeated training sessions over six consecutive weeks progressively modulate these changes in accordance with individual performance improvements. Multimodal correlation analyses showed an association between structural grey matter alterations and functional connectivity changes in prefrontal and supplementary-motor areas. These coincident changes were most prominent in the first three weeks of training. In contrast, changes in fronto-parietal functional connectivity and the underlying white matter fibre structure developed gradually during the six weeks. Our results demonstrate a tight correlation between training-induced functional and structural brain plasticity on the systems level and suggest a functional relevance of intrinsic brain activity for morphological adaptation in the human brain.

Effects of morphine and alcohol on functional brain connectivity during "resting state": a placebo-controlled crossover study in healthy young men

A major challenge in central nervous system (CNS) drug research is to develop a generally applicable methodology for repeated measurements of drug effects on the entire CNS, without task-related interactions and a priori models. For this reason, data-driven resting-state fMRI methods are promising for pharmacological research. This study aimed to investigate whether different psychoactive substances cause drug-specific effects in functional brain connectivity during resting-state. In this double blind placebo-controlled (double dummy) crossover study, seven resting-state fMRI scans were obtained in 12 healthy young men in three different drug sessions (placebo, morphine and alcohol; randomized). Drugs were administered intravenously based on validated pharmacokinetic protocols to minimize the inter- and intra-subject variance in plasma drug concentrations. Dual-regression was used to estimate whole-brain resting-state connectivity in relation to eight well-characterized resting-state networks, for each data set. A mixed effects analysis of drug by time interactions revealed dissociable changes in both pharmacodynamics and functional connectivity resulting from alcohol and morphine. Post hoc analysis of regions of interest revealed adaptive network interactions in relation to pharmacokinetic and pharmacodynamic curves. Our results illustrate the applicability of resting-state functional brain connectivity in CNS drug research.

Resting state functional connectivity correlates of inhibitory control in children with attention-deficit/hyperactivity disorder

Motor inhibition is among the most commonly studied executive functions in attention-deficit/hyperactivity disorder (ADHD). Imaging studies using probes of motor inhibition such as the stop signal task (SST) consistently demonstrate ADHD-related dysfunction within a right-hemisphere fronto-striatal network that includes inferior frontal gyrus and pre-supplementary motor area. Beyond findings of focal hypo- or hyper-function, emerging models of ADHD psychopathology highlight disease-related changes in functional interactions between network components. Resting state fMRI (R-fMRI) approaches have emerged as powerful tools for mapping such interactions (i.e., resting state functional connectivity, RSFC), and for relating behavioral and diagnostic variables to network properties. We used R-fMRI data collected from 17 typically developing controls (TDC) and 17 age-matched children with ADHD (aged 8-13 years) to identify neural correlates of SST performance measured outside the scanner. We examined two related inhibition indices: stop signal reaction time (SSRT), indexing inhibitory speed, and stop signal delay (SSD), indexing inhibitory success. Using 11 fronto-striatal seed regions-of-interest, we queried the brain for relationships between RSFC and each performance index, as well as for interactions with diagnostic status. Both SSRT and SSD exhibited connectivity-behavior relationships independent of diagnosis. At the same time, we found differential connectivity-behavior relationships in children with ADHD relative to TDC. Our results demonstrate the utility of RSFC approaches for assessing brain/behavior relationships, and for identifying pathology-related differences in the contributions of neural circuits to cognition and behavior.

The brain as a complex system: using network science as a tool for understanding the brain

Although graph theory has been around since the 18th century, the field of network science is more recent and continues to gain popularity, particularly in the field of neuroimaging. The field was propelled forward when Watts and Strogatz introduced their small-world network model, which described a network that provided regional specialization with efficient global information transfer. This model is appealing to the study of brain connectivity, as the brain can be viewed as a system with various interacting regions that produce complex behaviors. In practice, graph metrics such as clustering coefficient, path length, and efficiency measures are often used to characterize system properties. Centrality metrics such as degree, betweenness, closeness, and eigenvector centrality determine critical areas within the network. Community structure is also essential for understanding network organization and topology. Network science has led to a paradigm shift in the neuroscientific community, but it should be viewed as more than a simple "tool du jour." To fully appreciate the utility of network science, a greater understanding of how network models apply to the brain is needed. An integrated appraisal of multiple network analyses should be performed to better understand network structure rather than focusing on univariate comparisons to find significant group differences; indeed, such comparisons, popular with traditional functional magnetic resonance imaging analyses, are arguably no longer relevant with graph-theory based approaches. These methods necessitate a philosophical shift toward complexity science. In this context, when correctly applied and interpreted, network scientific methods have a chance to revolutionize the understanding of brain function.

Negative edges and soft thresholding in complex network analysis of resting state functional connectivity data

Complex network analyses of functional connectivity have consistently revealed non-random (modular, small-world, scale-free-like) behavior of hard-thresholded networks constructed from the right-tail of the similarity histogram. In the present study we determined network properties resulting from edges constrained to specific ranges across the full correlation histogram, in particular the left (negative-most) tail, and their dependence on the confound signal removal strategy employed. In the absence of global signal correction, left-tail networks comprised predominantly long range connections associated with weak correlations and were characterized by substantially reduced modularity and clustering, negative assortativity and γ<1 Deconvolution of specific confound signals (white matter, CSF and motion) resulted in the most robust within-subject reproducibility of global network parameters (ICCs~0.5). Global signal removal altered the network topology in the left tail, with the clustering coefficient and assortativity converging to zero. Networks constructed from the absolute value of the correlation coefficient were thus compromised following global signal removal since the different right-tail and left-tail topologies were mixed. These findings informed the construction of soft-thresholded networks, replacing the hard thresholding or binarization operation with a continuous mapping of all correlation values to edge weights, suppressing rather than removing weaker connections and avoiding issues related to network fragmentation. A power law adjacency function with β=12 yielded modular networks whose parameters agreed well with corresponding hard-thresholded values, that were reproducible in repeated sessions across many months and evidenced small-world-like and scale-free-like properties.

Graph analysis of epileptogenic networks in human partial epilepsy

PURPOSE

The current gold standard for the localization of the cortical regions responsible for the initiation and propagation of the ictal activity is through the use of invasive electrocorticography (ECoG). This method is utilized to guide surgical intervention in cases of medically intractable epilepsy by identifying the location and extent of the epileptogenic focus. Recent studies have proposed mechanisms in which the activity of epileptogenic cortical networks, rather than discrete focal sources, contributes to the generation of the ictal state. If true, selective modulation of key network components could be employed for the prevention and termination of the ictal state.

METHODS

Here, we have applied graph theory methods as a means to identify critical network nodes in cortical networks during both ictal and interictal states. ECoG recordings were obtained from a cohort of 25 patients undergoing presurgical monitoring for the treatment of intractable epilepsy at the Mayo Clinic (Rochester, MN, U.S.A.).

KEY FINDINGS

One graph measure, the betweenness centrality, was found to correlate with the location of the resected cortical regions in patients who were seizure-free following surgical intervention. Furthermore, these network interactions were also observed during random nonictal periods as well as during interictal spike activity. These network characteristics were found to be frequency dependent, with high frequency gamma band activity most closely correlated with improved postsurgical outcome as has been reported in previous literature.

SIGNIFICANCE

These findings could lead to improved understanding of epileptogenesis. In addition, this theoretically allows for more targeted therapeutic interventions through the selected modulation or disruption of these epileptogenic networks.

A new measure of centrality for brain networks

Recent developments in network theory have allowed for the study of the structure and function of the human brain in terms of a network of interconnected components. Among the many nodes that form a network, some play a crucial role and are said to be central within the network structure. Central nodes may be identified via centrality metrics, with degree, betweenness, and eigenvector centrality being three of the most popular measures. Degree identifies the most connected nodes, whereas betweenness centrality identifies those located on the most traveled paths. Eigenvector centrality considers nodes connected to other high degree nodes as highly central. In the work presented here, we propose a new centrality metric called leverage centrality that considers the extent of connectivity of a node relative to the connectivity of its neighbors. The leverage centrality of a node in a network is determined by the extent to which its immediate neighbors rely on that node for information. Although similar in concept, there are essential differences between eigenvector and leverage centrality that are discussed in this manuscript. Degree, betweenness, eigenvector, and leverage centrality were compared using functional brain networks generated from healthy volunteers. Functional cartography was also used to identify neighborhood hubs (nodes with high degree within a network neighborhood). Provincial hubs provide structure within the local community, and connector hubs mediate connections between multiple communities. Leverage proved to yield information that was not captured by degree, betweenness, or eigenvector centrality and was more accurate at identifying neighborhood hubs. We propose that this metric may be able to identify critical nodes that are highly influential within the network.