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sequently applied to find the clique that contained a group of highly connected
brain regions that is represented by a clique with maximum size. The CMI is
known to have the ability to capture the connectivity between EEG signals. The
adopted maximum clique algorithm can reduce the complexity of the cluster-
ing procedure for finding the maximum connected brain regions. The proposed
graph-theoretic approach offers better assessments to visualize the structure of
the brain connectivity over time. The results indicate that the maximum con-
nected brain regions prior to seizure onsets were where the impending seizure
was initiated. Furthermore, the proposed approach may be used to improve the
outcome of the epilepsy surgery by identifying the seizure onset region(s) cor-
rectly.
14.1. Introduction
Neural activity is manifested by electrical signals known as graded and action po-
tentials. Berger's [3] demonstration in 1929 has shown that it is possible to record
the electrical activity from the human brain, particularly the neurons located near
the surface of the brain. While we often think of electrical activity in neurons in
terms of action potentials, the action potentials do not usually contribute directly
to the electroencephalogram (EEG) recordings. In fact, for scalp EEG recordings,
the EEG patterns are mainly the graded potentials accumulated from hundreds of
thousands of neurons. The EEG patterns vary greatly in both amplitude and fre-
quency. The amplitude of the EEG reflects the degree of synchronous firing of the
neurons located around the recording electrodes. In general, the high EEG am-
plitude indicates that neurons are activated simultaneously. Low EEG frequency
indicates less responses of the brain, such as sleep, whereas higher EEG frequency
implies the increased alertness. Given the above descriptions, an acquired EEG
time series can be defined as a record of the fluctuating brain activity measured
at different times and spaces. The high degree of synchronicity for two different
brain regions implies strong connectivity among them and vice versa. We will in-
terchangeably use the terms synchronicity and connectivity for rest of the chapter.
Epileptic seizures involve the synchronization of large populations of neu-
rons [13]. Measuring the connectivity and synchronicity among different brain
regions through EEG recordings has been well documented [21, 22, 26]. The
structures and the behaviors of the brain connectivity have been shown to contain
rich information related to the functionality of the brain [4, 16, 30]. More recently,
the mathematical principles derived from information theory and nonlinear dy-
namical systems have allowed us to investigate the synchronization phenomena
in highly non-stationary EEG recordings. For example, a number of synchroniza-
tion measures were used for analyzing the epileptic EEG recordings to reach the
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