Small-world networks and epilepsy: Graph theoretical analysis of intracerebrally recorded mesial temporal lobe seizures☆
Introduction
Epilepsy is a common neurological disorder, characterized by sudden occurrence of unprovoked seizures (Hauser et al., 1993). The unforeseen and unpredictable way in which seizures occur is one of the most disabling aspects of epilepsy. The underlying pathophysiology of epileptic seizures is still poorly understood (Timofeev and Steriade, 2004). How and when the transition from an interictal to an ictal state takes place is not known. However, it is widely accepted that an abnormal synchronization of neurons is a part of seizure generation. Several findings indicate that the transition may not always occur abruptly, but may show a predisposing state called ‘preictal’ which can be characterized by either desynchronization or hypersynchronization (Mormann et al., 2003, Lopes da Silva et al., 2003, Le Van Quyen et al., 2005, Wendling et al., 2005).
Apart from changes in overall levels of synchronization the interictal–ictal transition may also be characterized by changes in the spatial organization of the involved networks. This can be studied with the use of ‘graph theory’ (see Fig. 1) (Strogatz, 2001, Wang and Chen, 2003, Boccaletti et al., 2006). Graphs are abstract representations of networks which can be characterized by a clustering coefficient (C) a measure for local connectedness and a characteristic path length (L) an indicator of overall integration. Watts and Strogatz (1998) showed that graphs with many local connections and a few random long distance connections (characterized by a high C and a short L) are near optimal networks, called ‘small-world networks’, which are intermediate between ordered (high C and long L) and random networks (low C and short L) (see Fig. 2). It has been shown that neuronal networks, like many other networks (e.g. the internet, the social network), show characteristic ‘small-world’ features (Strogatz, 2001). It is suggested that a small-world-like network may be optimal for synchronizing neuronal activity between different brain regions (Lago-Fernandez et al., 2000, Barahona and Pecora, 2002). Graph-analysis of anatomical and functional data such as fMRI, EEG and MEG showed a small-world configuration (Sporns et al., 2000, Stam, 2004, Salvador et al., 2005, Achard et al., 2006, Stam et al., 2007, Micheloyannis et al., 2006a, Micheloyannis et al., 2006b).
Recently, a relationship between the small-world phenomenon and epilepsy was suggested by two model studies. Netoff et al. (2004) simulated a small-world network model of excitatory neurons to explain seizure dynamics in a hippocampal slice. They found that seizure activity corresponded with a small-world regimen of the neurons. Moreover, the start of the bursting phase corresponded with a drop of C, and thus a random instead of small-world architecture. Percha et al. (2005) showed a potential mechanism underlying seizure generation. They used a model with a two dimensional lattice of coupled neurons to show that properties of phase synchronization change radically depending on the connectivity structure of the network. In particular, a small-world configuration was associated with a low threshold for seizure generation.
Finally, both studies showed that a small-world and even more a random structure in models are associated with an increase in synchronization and probably with seizures. However, this has never been tested in seizure recordings in patients. We investigated the hypothesis that functional neuronal networks during temporal lobe seizures change in configuration before and during seizures, by applying synchronization and graph analysis to intracerebral EEG recordings. We studied graph configuration in 5 periods of interest: interictal, preceding, during (two) and after the seizure. The characteristics of the periods around the seizure were compared with interictal EEG to investigate whether the neuronal network changes during the seizure and what the initial configuration is of the interictal network.
Section snippets
Patient selection
Seven patients were selected from a group undergoing pre-surgical evaluation of drug-resistant mesial temporal lobe epilepsy (MTLE) (see Table 1 for patient characteristics). Data from these patients were previously reported in several studies (Bartolomei et al., 2001, Bartolomei et al., 2004, Bartolomei et al., 2005, Wendling et al., 2005). The patients we selected had seizures that involved the medial temporal lobe at onset and had comparable seizure patterns. All patients had a comprehensive
Synchronization likelihood
Fig. 4 shows the mean synchronization likelihood (SL) for 5 epochs of interest (interictal, before rapid discharges (BRD), during rapid discharges (DRD), after rapid discharges (ARD) and postictal) through the seizure in broad band filtered signal (1–48 Hz) and filtered signals in separate frequency bands (1–4, 4–8, 8–13, 13–30 and 30–48 Hz). As can be seen the mean synchronization likelihood increased during the seizure in all frequency bands. For statistical analysis, we compared SL from the
Discussion
Graph theoretical analysis was used to test the hypothesis of a small-world structure of brain networks during seizures compared to interictal recordings. We found an increase of the clustering coefficient C in the lower frequency bands (1–13 Hz), and an increase of the path length L (alpha and theta bands) during and after the seizure compared to the interictal recordings. The increase of L/L-s was significant but rather small (<1,5) which is more compatible with a small-world than an ordered
Acknowledgements
We thank Prof. dr P. Chauvel (Department of clinical neurophysiology, Marseille) for clinical and electrophysiological assessment of the studied patients. We thank Prof. dr J. Régis (Neurosurgery department, Marseille) for the stereotactic placement of electrodes. Mrs E. van Deventer is thanked for her assistance with the literature search. This work was financially supported by the Dutch National Epilepsy Fund (NEF: Grant No. 05–12). We like to thank the three anonymous referees for their
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The analysis was performed in the VU University Medical Centre, but the SEEG registrations were performed in the Epilepsy Unit at Timone Hospital (Marseille, France).