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world” network in analogy with the concept of the small-world phenomenon
observed more than 30 years ago in social systems. In a similar way, many types
of functional brain networks have been analyzed according to this mathematical
approach. In particular, several studies based on different imaging techniques
(fMRI, MEG and EEG) have found that the estimated functional networks
showed small-world characteristics. In the functional brain connectivity context,
these properties have been demonstrated to reflect an optimal architecture for
the information processing and propagation among the involved cerebral
structures. However, the performance of cognitive and motor tasks as well as the
presence of neural diseases has been demonstrated to affect such a small-world
topology, as revealed by the significant changes of
L
and
C
. Moreover, some
functional brain networks have been mostly found to be very unlike the random
graphs in their
degree-distribution
, which gives information about the allocation
of the functional links within the connectivity pattern. It was demonstrated that
the
degree distributions
of these networks follow a power-law trend. For this
reason those networks are called “scale-free”. They still exhibit the small-world
phenomenon but tend to contain few nodes that act as highly connected “hubs”.
Scale-free networks are known to show resistance to failure, facility of
synchronization and fast signal processing. Hence, it would be important to see
whether the scaling properties of the functional brain networks are altered under
various pathologies or experimental tasks. The present Chapter proposes a
theoretical graph approach in order to evaluate the functional connectivity
patterns obtained from high-resolution EEG signals. In this way, the “Brain
Network Analysis” (in analogy with the Social Network Analysis that has
emerged as a key technique in modern sociology) represents an effective
methodology improving the comprehension of the complex interactions in the
brain.
10.1. Cortical Activity Estimation
High-resolution EEG technology has been developed to enhance the poor spatial
information of the EEG activity on the scalp and it gives a measure of the
electrical activity on the cortical surface. Principally, this technique involves the
use of a larger number of scalp electrodes (64-256). In addition, high-resolution
EEG uses realistic MRI-constructed subject head models and spatial de-
convolution estimations which are commonly computed by solving a linear
inverse problem based on boundary-element mathematics. In the present study,
the cortical activity was estimated from EEG recordings by using a realistic head
model, whose cortical surface consisted of about 5000 triangles disposed
uniformly.
Each triangle represents the electrical dipole of a particular neuronal
population and the estimation of its current density was computed by solving the
linear inverse problem according to techniques described in previous works. In
