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goals of localizing the epileptogenic zones and predicting the impending epileptic
seizures [1, 14, 20, 26, 29]. These studies also suggest that epilepsy is a dynamical
brain disorder in which the interactions among neuron or groups of neurons in the
brain alter abruptly. Moreover, the characteristic changes in the EEG recordings
have been shown to have clear associations with the synchronization phenomena
among epileptogenic and other brain regions. When the conductivities between
two or among multiple brain regions are simultaneously considered, the univariate
analysis alone will not be able to carry out such a task. Therefore it is appropriate
to utilize multivariate analysis. Multivariate analysis has been widely used in the
field of neuroscience to study the relationships among sources obtained simulta-
neously. In this study, the cross mutual information (CMI) approach is applied to
measure the connectivity among brain regions [9]. The CMI approach is a bivari-
ate measure and has been shown to have ability for quantifying the connectivity of
the EEG signals [8, 21, 24, 25]. The brain connectivity graph is then constructed
where vertices in the graph represent the EEG electrodes.
Every distinct pair of vertices is connected by an arc with the length equal to
the connectivity quantified by CMI. After constructing a brain connectivity graph,
which is a complete graph, we then remove arcs of connectivity below a speci-
fied threshold value to preserve only strong couplings of electrode pairs. Finally,
we employ a maximum clique algorithm to find a maximum clique in which the
brain regions are strongly connected (See Section 14.4.2). The maximum clique
size can be, in turn, used to represent the amount of largest connected regions
in the brain. The maximum clique algorithm reduces the computational effort
for searching in the constructed brain connectivity graph. The proposed graph-
theoretic approach offers an easy protocol for inspecting the structures of the brain
connectivity over time and possibly identifying the brain regions where seizures
are initiated.
14.2. Epilepsy as a Dynamical Brain Disorder
Epilepsy can be caused by multiple factors. Some people may even begin having
seizures from their childhood. Epilepsy in children can result from almost every-
thing related to the brain development or function. Lack of oxygen supply can
cause cerebral palsy and seizure for example new born infants that suffer a lack
of oxygen supply to the brain before or during birth have higher risks for devel-
oping epilepsy in their lives [31]. Epilepsy can also occur in adult subjects that
have bleeding in the brain as a result of prematurity or defective blood vessels
in the brain. Some studies have also reported epilepsy can be induced by genetic
changes. Some patients are born with genes related to epilepsy that can cause them
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