State dependent properties of epileptic brain networks: Comparative graph–theoretical analyses of simultaneously recorded EEG and MEG

Abstract

Objective

To investigate whether functional brain networks of epilepsy patients treated with antiepileptic medication differ from networks of healthy controls even during the seizure-free interval.

Methods

We applied different rules to construct binary and weighted networks from EEG and MEG data recorded under a resting-state eyes-open and eyes-closed condition from 21 epilepsy patients and 23 healthy controls. The average shortest path length and the clustering coefficient served as global statistical network characteristics.

Results

Independent on the behavioral condition, epileptic brains exhibited a more regular functional network structure. Similarly, the eyes-closed condition was characterized by a more regular functional network structure in both groups. The amount of network reorganization due to behavioral state changes was similar in both groups. Consistent findings could be achieved for networks derived from EEG but hardly from MEG recordings, and network construction rules had a rather strong impact on our findings.

Conclusions

Despite the locality of the investigated processes epileptic brain networks differ in their global characteristics from non-epileptic brain networks. Further methodological developments are necessary to improve the characterization of disturbed and normal functional networks.

Significance

An increased regularity and a diminished modulation capability appear characteristic of epileptic brain networks.

Introduction

During the last years evidence has accumulated that time-variant interactions between different regions within the complex network brain not only subserve higher cognitive functions (Varela et al., 2001, Robertson, 2003, Schnitzler and Gross, 2005) but are also of high relevance for cognitive dysfunctions and pathophysiology (Uhlhaas and Singer, 2006). An improved characterization of brain networks may be achieved with graph–theoretical approaches (see Boccaletti et al., 2006, Reijneveld et al., 2007, Ioannides, 2007, Arenas et al., 2008, Bullmore and Sporns, 2009 for an overview). Within this framework a network (or graph) is considered as a set of nodes and a set of links, connecting the nodes. Functional brain networks can be derived from direct (EEG or MEG) or indirect measurements of neural activity (e.g. fMRI), and the connectedness between any pair of brain regions (nodes) can be assessed by evaluating interdependencies between their neural activities. A variety of network measures is now available that allow one to characterize complex connection schemes. Among these measures the average shortest path length L and the clustering coefficient C are important statistical characteristics of network structure. L is the average shortest distance between two nodes. In this context the term “distance” can imply a physical distance, but can also be interpreted as a functional distance. C is the average probability that any pair of nodes is linked to a third common node by a single edge and thus describes the tendency of nodes to form local clusters. Large values of both L and C are characteristic for an ordered, lattice-like structure, while low values of L and C are related to random networks. A low value of L and a high value of C is characteristic for so-called small-world networks, which can emerge from a lattice-like structure by rewiring some connections randomly (Watts and Strogatz, 1998).

Since a small-world network is well-connected both locally and globally, it has been repeatedly proposed that the anatomical structure of the human brain resembles a small-world topology which enables efficient local and spatially distributed information processing (Bassett and Bullmore, 2006, He et al., 2007, Guye et al., 2008). Moreover, analyses of functional brain networks suggest that their topology resembles a small-world-like structure (Stam, 2004, Bassett et al., 2006) and can be influenced by different behavioral or functional states (Bassett et al., 2006, Micheloyannis et al., 2006, Ferri et al., 2007). Brain pathologies such as Alzheimer’s disease, tumors, or schizophrenia are reflected in alterations of the topology of functional brain networks (Stam et al., 2007a, Bartolomei et al., 2006a, Bartolomei et al., 2006b, Liu et al., 2008, Stam et al., 2009).

Epilepsy is a brain pathology that is strongly related to neural synchronization phenomena (see Lehnertz et al., 2009a, Lehnertz et al., 2009b for comprehensive overviews). Epileptic seizures reflect transient, strongly enhanced collective activity of spatially extended neural networks. Clinical and anatomical findings, together with invasive electroencephalography and functional neuroimaging now provide increasing evidence for the existence of specific cortical and subcortical epileptic networks in the genesis and expression of not only primary generalized but also focal onset seizures (Bertram et al., 1998, Bragin et al., 2000, Bartolomei et al., 2001, Spencer, 2002, Blumenfeld et al., 2004, Guye et al., 2006, Monto et al., 2007, Schevon et al., 2007, Gotman, 2008, Luat and Chugani, 2008, Bettus et al., 2008). Studies evaluating functional brain networks derived from intracerebral EEG recordings from patients with focal epilepsies indicated a more regular, ordered structure during seizures as compared to pre- and postictal intervals (Wu et al., 2006, Ponten et al., 2007, Schindler et al., 2008, Kramer et al., 2008). The most recent study derived similar conclusions from an analysis of non-invasively recorded EEG during absence seizures (Ponten et al., 2009). Modeling studies revealed that seizures emerge more easily from small-world-like network configurations and that transitions between different epileptiform activities may result from both synaptic properties and varying connection topologies (Netoff et al., 2004, Percha et al., 2005, Srinivas et al., 2007, Dyhrfjeld-Johnsen et al., 2007, Feldt et al., 2007, Morgan and Soltesz, 2008, Rothkegel and Lehnertz, 2009).

Taking into account the aforementioned findings we hypothesized that functional brain networks of patients suffering from focal epilepsies differ from networks of healthy controls even during the seizure-free interval and despite the locality of the epileptic disturbance. We also hypothesized that changes of the behavioral state are accompanied by a reorganization of functional networks which, however, acts differentially on epileptic and non-epileptic brain networks. We investigated these hypotheses by examining global statistical characteristics of functional brain networks derived from EEG and MEG signals that we recorded non-invasively in epilepsy patients and in healthy subjects during controlled conditions. A priori, it is neither clear which type of network construction, if at all, would be best suited for a differentiation between different networks, nor whether differentiability depends on the frequency content or other (e.g. nonlinear) properties of EEG/MEG signals, and particularly for EEG recordings, on the chosen reference. We therefore used different interdependence measures – capturing linear and nonlinear aspects of brain electromagnetic activity in a frequency-selective manner – to define functional network links and applied different rules to construct binary networks (where links either exist or not) and weighted networks (where the link weight reflects the strength of interactions between two nodes). We estimated – in a time-resolved manner – the global network characteristics L and C as well as the amount of network reorganization accompanying changes in the behavioral state.