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Rationale: Focal onset epileptic seizures are due to abnormal interactions
between distributed brain areas. By estimating the cross-correlation matrix of
multi-site intra-cerebral EEG recordings (iEEG), one can quantify these
interactions. To assess the topology of the underlying functional network, the
binary connectivity matrix has to be derived from the cross-correlation matrix
by use of a threshold. Classically, a unique threshold is used that constrains
the topology [1]. Our method aims to set the threshold in a data-driven way by
separating genuine from random cross-correlation. We compare our approach to
the fixed threshold method and study the dynamics of the functional
topology. Method: We investigate the iEEG of patients suffering from focal
onset seizures who underwent evaluation for the possibility of surgery. The
equal-time cross-correlation matrices are evaluated using a sliding time
window. We then compare 3 approaches assessing the corresponding binary
networks. For each time window: - Our parameter-free method derives from the cross-correlation strength matrix (CCS)[2]. It aims at disentangling genuine from random correlations (due to finite length and varying frequency content of the signals). In practice, a threshold is evaluated for each pair of channels independently, in a data-driven way. -The fixed mean degree (FMD) uses a unique threshold on the whole connectivity matrix so as to ensure a user defined mean degree. -The varying mean degree (VMD) uses the mean degree of the CCS network to set a unique threshold for the entire connectivity matrix. - Finally, the connectivity (c), connectedness (given by k, the number of disconnected sub-networks), mean global and local efficiencies (Eg, El, resp.) are computed from FMD, CCS, VMD, and their corresponding random and lattice networks. Results: Compared to FMD and VMD, CCS networks present: - topologies that are different in terms of c, k, Eg and El. - from the pre-ictal to the ictal and then post-ictal period, topological features time courses that are more stable within a period, and more contrasted from one period to the next. For CCS, pre-ictal connectivity is low, increases to a high level during the seizure, then decreases at offset. k shows a "U-curve" underlining the synchronization of all electrodes during the seizure. Eg and El time courses fluctuate between the corresponding random and lattice networks values in a reproducible manner. Conclusions: The definition of a data-driven threshold provides new insights into the topology of the epileptic functional networks. 1. Schindler, K.A., et al., Chaos, 2008. 18: p. 033119. 2. Rummel, C., Müller, M., Baier, G., Amor, F., Schindler, K., submitted, 2009. |
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