Graph Analysis and Visualization for Brain Function Characterization Using EEG Data

Abstract

Over the past few years, there has been an increased interest in studying the underlying neural mechanism of cognitive brain activity as well as in diagnosing certain pathologies. Noninvasive imaging modalities such as functional magnetic resonance imaging (fMRI), positron emission tomography (PET), and dynamic signal acquisition techniques such as quantitative electroencephalography (EEG) have been vastly used to estimate cortical connectivity and identify functional interdependencies among synchronized brain lobes. In this area, graph-theoretic concepts and tools are used to describe large scale brain networks while performing cognitive tasks or to characterize certain neuropathologies. Such tools can be of particular value in basic neuroscience and can be potential candidates for future inclusion in a clinical setting. This paper discusses the application of the high time resolution EEG to resolve interdependence patterns using both linear and nonlinear techniques. The network formed by the statistical dependencies between the activations of distinct and often well separated neuronal populations is further analyzed using a number of graph theoretic measures capable of capturing and quantifying its structure and summarizing the information that it contains. Finally, graph visualization reveals the hidden structure of the networks and amplifies human understanding. A number of possible applications of the graph theoretic approach are also listed. A freely available standalone brain visualization tool to benefit the healthcare engineering community is also provided .gr (V. Sakkalis).information processing and mental representations [6,7], and have been studied across different conditions of rest [8,9,10] or cognitive load [11].Studies with detailed electroencephalography (EEG) and magnetoencephalography (MEG) signals have revealed local synchronization patterns and cortico-cortical interactions involved in several cognitive functions [12], with composite subtasks being triggered within different brain regions by unitary brain sources that subsequently synchronize to complete the task. Thus, the dynamics of interaction among different EEG/ MEG channels may be used for indexing neural synchrony of such local or distant brain sources [13]. Such sources act synchronously behaving similar to coupled oscillators [14] and their interactions can be measured using pair-wise linear (cross-coherence or phasecoherence) [16] or nonlinear dynamics and models [15,16,17]. Furthermore, the causality of the functional coupling of such oscillatory activities can be assessed with partially directed coherence, which reveals the direction of statistically significant relationships [18]. Synchronization can be evaluated not only on the actual recordings on the scalp electrodes but also on independent components. The later are derived from linear un-mixing transforms and are free from volume conduction effects [15,16].Networks are modeled by graphs which consist of a set of vertices and a set of pair of vertices called edges (Figure 1)....

Automated network analysis to measure brain effective connectivity estimated from EEG data of patients with alcoholism

“…All experiments showed that binary clustering coefficient and weighted average neighbourhood degree in effective networks enables us to differentiate alcoholics from normal subjects. This result is similar to results published in another research (Sakkalis et al 2010). Here, each node of weighted node betweenness centrality was compared between normal subjects and alcoholics, showing significant difference.…”

Graph-theoretic Indices of Evaluating Brain Network Synchronization: Application in an Alcoholism Paradigm

“…where k u and k v are the degrees of the end vertices u and v, respectively, of edge {u,v} ∈ E. For directed unweighted graphs the above measure can still be used if we ignore the direction of edges [7]. The assortativity coefficient r lies in the range À1 r 1, where À1 indicates totally disassortative network while 1 indicates a totally assortative network.…”

“…The clustering coefficient for the whole graph is the average of C i for each node, C ¼ ∑ i ¼ 1 n C i /n, and is a measure of the tendency of graph nodes to form local clusters [7]. For unweighted graphs, the local CC associated with a node i having k i connections is defined as the ratio of the triangles that contain this node divided by the maximum possible number of such triangles k i (k i À 1)/2.…”

“…Special interest in using graph theory to study neural and functional networks has been in focus recently, since it offers a unique perspective of studying local and distributed brain interactions [7,8]. In this study, network topology and functional connectivity are evaluated by measuring several properties of the emerged graphs, i.e., mean vertex degree, clustering coefficient index, assortativity coefficient, shortest path length, and efficiency.…”

BrainNetVis: An Open-Access Tool to Effectively Quantify and Visualize Brain Networks

“…However, more sophisticated interdependence techniques addressing not only linear but also nonlinear synchronization and causality are also available and applied in certain pathologies like Epilepsy [ 12 ]. Such measures can act complementary to graph theoretic indices that characterize brain networks as discussed in [ 19 ] and can be used as input to BrainNetVis.…”