**4. Conclusions**

and ACC and a higher APL in the ipsilateral side than the contralateral one. These results are also supported by fMRI studies [77,80], and even by results of studies of patients with

The application of topological parameters to the analysis of epilepsy turned out to be a great tool for network characterization, either in ECoG, scalp or FOE recordings. It has uncovered the dynamics and connectivity of the brain in TLE as well in the extratemporal ones. In fact, these works showed a lack of connectivity in the seizure area. In particular, in TLE the lack of connectivity in the ipsilateral side could be somehow related to the ipsilateral impairment found in the community structures analysis of FOE [49]. Moreover, loss of connectivity within specific network structures has been involved in seizure generation [82], and computational

Also, the use of the MST has provided to be of great importance in describing different types of functional architecture [68]. In that work, the MST was used to simplify the underlying network with the objective to localize particular areas of interest, as the node's degree, betweenness and local synchronization. As it was shown, critical nodes in the MST are those with highest local synchronization. Moreover, when different types of critical parameters, as maximum local synchronization, maximum betweenness, concur at a particular cortical area, resection of these area correlates with a goof post-operative outcome. **Figure 8** displays three different MST architectures with the critical nodes marked in each case. In the last case, **Figure 8C**, the three nodes with maximal local synchronization, betweenness and degree concur at the same location, that is node #2. During the surgery, a minimal cortical resection

**Figure 8.** Centrality measures and minimum spanning tree (MST) constructed from ECoG data from two different lo‐ cations. (A, B, C) Represent three examples from three patients. Electrodes are represented by gray circles (location 1) and white circles (location 2). The node with maximun local synchronization is represented by a cyan circle, the node with maximun degree by a yellow circle and The node with maximun betweenness by a red-border circle. Magenta

extratemporal seizures, which presented lower connectivity in the seizure area [81].

106 Advanced Biosignal Processing and Diagnostic Methods

models has revealed that connections deletion increases seizure likelihood [83].

involved this cortical area and the patient remained free of seizures [68].

circle represents superposition of the three centrality measures in the same node.

Although the advent of digital computation has revolutionized the whole realm of biomedical signal acquisition and preprocessing, particularly of scalp and invasive EEG, the clinical analysis and interpretation has not accompanied the rapid development experienced by the technological counterpart. Many of the current epilepsy-related protocols performed in the specialized centers around the world still rely on purely observational analyses of raw signals, depending subjectively on the neurophysiologist background and capabilities. Visual techni‐ que developed during the early years of epileptology, when computers were not yet available, has rooted so deeply in the clinical practice that it seems it could only be replaced by very efficient and objective techniques. In doing that, the new techniques should demonstrate that they performed at least as well as the classical ones. Moreover, they should provide a new framework under which the traditional view could be encompassed, but uncovering new concepts and models. Probably the little familiarity of neurophysiologists with numerical methods would help to explain to some extent the sparse use in clinical practice.

We feel that in the near future the complex network approach of epileptic processes will fit both requirements of being an encompassing framework under which the epileptogenesis and seizure spread could be fully understood and more important, it could become into a reliable therapeutic methodology to evaluate drug resistant epileptic patients, at least partially. As we have shown in this chapter, the traditional zone-oriented approach, with the seizure onset zone occupying the central position, is now shifting toward a network perspective, where network critical properties are becoming more relevant. This new framework would be applied to idiopathic or cryptogenic epilepsies, although symptomatic epilepsies (i.e. tumor induced, dysplasias, cavernomas or some types of post-traumatic seizure) probably remain better explained by the old or classical vision. In this regard, the graph theory jointly with the concept of functional connectivity is bringing new ways of thinking about the epilepsy.

Synchronization, of critical importance in constructing functional networks, has also evolved since its first use describing epileptic processes. Although epilepsy was initially related with hypersynchronization processes, today it is known that desynchronization also plays a dramatic role in the seizures dynamics. Moreover, as we have revised in this chapter, not only a single concept of synchronization exists but, on the contrary, several types of them are described.

One point which should be highlighted is the great difference existing between the traditional neurophysiological signal analysis in the field of epilepsy and the one performed under the network approach. As it is well known, interictal analysis is performed mainly in search of epileptogenic activity, i.e. sharp waves and spikes. On the contrary, synchronization of the full signals is made in construction networks.

Besides the novel knowledge provided by synchronization, the recent connectome concept has also added evidences to support the epilepsy as a truly network pathology. The analysis of EEG recordings from epilepsy patients reveals dynamical process in which network changes favor seizure creation. Centrality parameters show the presence of stable local synchronized areas that present a small-world architecture; community structures analysis revealed an increase in the ipsilateral side of desynchronized clusters, which can be related to the lower connectivity of the ipsilateral side as shown by topological parameters. All these results are at some points controversial mainly due to the different electrodes used for recordings and the small number of studies. However, they provide critical dynamical evidences to understand the underlying mechanism of epilepsy.

Although today we have the fragmented knowledge of the epilepsy as a complex network pathology, the new advances in network-related methodologies and the growing literature of its application to biomedical signals make network analyses a promising and yet powerful tool for epilepsy research with potential applications either in the diagnostic or in the therapeutic realms.
