**Network Theoretical Approach to Describe Epileptic Processes**

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84 Advanced Biosignal Processing and Diagnostic Methods

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Ancor Sanz-García, Rafael G. de Sola, Lorena Vega-Zelaya, Jesús Pastor and Guillermo J. Ortega

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/63914

#### **Abstract**

Epilepsy is characterized by recurrent unprovoked seizures. Recent studies suggest that seizure generation may be caused by the abnormal activity of the entire network. This new paradigm requires new tools and methods for its study. In this sense, synchroniza‐ tion by linear as well as nonlinear measures are used to determine network structure and functional connectivity of neurophysiological data. Electroencephalography (EEG) data can be analyzed using each electrode's activity as a node of the underlying cortical network. The information provided by the synchronization matrix is the basic brick upon which several lines of analysis can be performed thereafter. Detection of community struc‐ tures, identification of centrality nodes, transformation of the underlying network into a simpler one, and the identification of the basic network architecture are only some of the many lines of basic works that can be done in order to characterize the epilepsy as a network disease. This chapter describes new approaches in network epilepsy, provides mathe‐ matical concepts in order to understand the complex network analyses, and reviews the advances in network analyses and its application to epilepsy research.

**Keywords:** synchronization, temporal lobe epilepsy, electroencephalography, electro‐ corticography, graph theory, centrality measures, community structures, small-world

### **1. Introduction**

Epilepsy is one of the most common neurological disorders characterized by recurrent unprovoked seizures. It has an incidence of 50–100 cases per 100,000 persons/year in devel‐

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

opedcountries, andabout 50millionpeople aroundtheworldsufferfromepilepsy[1].Themost common type of epilepsy is temporal lobe epilepsy (TLE). Unfortunately, a high percentage of TLE patients are resistant to drug treatment presenting the so-called drug-resistant epilepsy (DRE). Surgery is recommended in such cases as the only curative/palliative alternative. Metaanalyses from literature indicate that 66% of the patients are seizure free in the first two years following the surgery [2]. However, seizures persist in one third of the operated patients; thus, an accurate localization of the epileptogenic zone (EZ) is vital for a good surgery outcome.

Traditionally, seizures in partial epilepsy have been considered to arise from a single focus that recruits other regions in order to spread. Very recently however, an alternative point of view has suggested that ictogenesis (seizure generation) may be caused by the abnormal activity of the entire network instead of being provoked by pathological isolated areas, such as the EZ [3–7]. In fact, the Commission on Classification and Terminology from the Interna‐ tional League Against Epilepsy (ILAE) has proposed a new approximation for the classification of seizures and epilepsy types [8]. The new recommended terminology redefines focal seizures as those originating at some points within networks spatially limited to only one hemisphere, or bilaterally distributed in the case of generalized seizures. This new perspective has been mostly inspired, on one hand from the network analyses of data obtained from several diagnostic tools that are routinely used nowadays in the pre-surgical evaluation of epilepsy, such as functional magnetic resonance imaging (MRI) (for review see [9]) or even from the classical one, the electroencephalography (EEG) [4,6,9]. On the other hand, the development of the connectome concept, which describes the connectivity among different brain areas in physiological conditions, has boosted this new perspective. In this regard, three types of connectivity have been defined: the anatomical, which are the structural connections linking the neurons or brain regions; the functional, which describes the statistical relations between activity of different neurons or brain regions; and lastly, the effective connectivity, which assesses the causal effects of one region or neuron to another [10].

Similarly to the impact of network analyses in seizure definition and classification, this new perspective on epilepsy has also modified the traditional pre-surgical evaluation of TLE patients. The traditional zone-oriented approach [11] has been complemented with the recent advent of the network perspective [4,5]. The zone-oriented concept of the EZ can be interpreted under this new point of view as a key property, yet unknown, of the network in charge of generating and sustaining the seizures. The new aim in epilepsy surgery would be now targeted at destroying this particular property of the network instead of being aimed at resecting a cortical area such as the EZ, as it is traditionally done. The importance of identifi‐ cation, delimitation and characterization of the epileptic network clearly shows up when the above considerations are taking into account and justify the great number of works devoted to this issue [12–18].

In this regard, EEG data obtained either invasively or non-invasively, can be now analyzed using each electrode's activity as a node of the underlying cortical network. In this framework, it is fashionable to estimate functional connectivity between cortical areas covered by neurophysiological electrodes through the correlation or synchronization – both terms are used interchangeably through the chapter, although their meanings are not exactly the same – matrix of the electrodes' time series. The information provided by the synchronization matrix is the basic brick upon which several lines of research can be built. One of them is the study of hierarchical organization, which through the construction of hierarchical trees provides insightful information of closeness and farness of node's neurophysiological activity. The application of this technique characterizes the underlying dynamical behavior of the whole network and allows to easily reveal those regions of highly synchronized nodes, i.e. synchronization clusters. Also, by combining the information provided by the synchronization matrices, and several techniques borrowed from graph theory, give us the opportunity to study the underlying cortical network as a whole entity.

It is important to emphasize that the network perspective is not only limited to EEG studies but functional MRI (fMRI) also provides evidences of this emerging view. Despite fMRI possesses a lower temporal resolution and is an indirect measure of neuronal activity, as compared with EEG, fMRI has a good spatial resolution and obviously provides critical data about the functional connectivity of the whole brain. In this regard, simultaneous fMRI and EEG studies have revealed the validity of the BOLD analysis [19], showing that changes in the epileptic network actually occur (for a review see [9]). In line with fMRI and EEG data, pathological and structural studies also corroborate the study of epilepsy as a network disorder, since histological studies have revealed neuronal cell loss, gliosis, axonal sprouting, among others in hippocampus of the TLE patients [20]. Indeed, similar changes have been described in adjacent areas to the hippocampus, as the amygdala, the entorhinal cortex, the parahippocampal cortex, certain areas of the temporal cortex, and even other cortical and thalamic areas [9]). All these results suggest that network reorganization occurs in epilepsy from a histological point of view. Similarly, anatomical and diffusion MRI studies supported the histological results, showing loss of grey matter and disorganization of fibers.

In this chapter, we review in a first step, the synchronization concept, its different types and estimators in order to provide an overview of the basic element needed to perform a network analysis of neurophysiological data. Secondly, we present the new network epilepsy approach with detailed and comprehensive explanations of the underlying mathematical concepts needed to fully understand the involved concepts and methodologies. Our aim, thus, is to present the recent advances in network analyses, covering issues such as hierarchical classifications, community detection, centrality measures identification and topological organization in order to state their outstanding relevance in a particular field of biomedical signal processing as it is the evaluation of pre-surgical neurophysiological recordings coming from DRE patients.
