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Since the node i does not belong to the sub-graph A i , this measure reveals the
level of fault-tolerance of the system, showing how the communication is
efficient between the first neighbors of i when i is removed. Global- ( E g ) and
local-efficiency ( E l ) were demonstrated to reflect the same properties of the
inverse of the average shortest path 1/L and the clustering index C . In addition,
this new definition is attractive since it takes into account the full information
contained in the weighted links of the graph and provides an elegant solution to
handle disconnected vertices.
10.4. Application to Real Data
In the following, two applications are presented in order to study the significant
features of the functional connectivity networks estimated with the use of
advanced high-resolution EEG methodologies.
10.4.1. Cortical network structure in tetraplegics
The first study aims at analyzing the structure of cortical connectivity during the
attempt to move a paralyzed limb by a group of spinal cord injured patients. Five
healthy (CTRL) subjects and five spinal cord injured (SCI) patients participated
to the present study. In particular, spinal cord injuries were of traumatic etiology
and located at the cervical level (C6 in three cases, C5 and C7 in two cases,
respectively); patients had not suffered for a head or brain lesion associated with
the trauma leading to the injury. The informed consent statement was signed by
each patient after the explanation of the study, which was approved by the local
institutional ethics committee. For the EEG data acquisition, subjects were
comfortably seated on a reclining chair, in an electrically shielded and dimly lit
room. They were asked to perform a brisk protrusion of their lips while they were
performing (healthy subjects) or attempting (SCI patients) a right foot movement.
By means of the lips protrusion, the SCI patients provided an evident trigger in
correspondence of their attempt to move. For each subject, the cortical activity
was estimated according to the high-resolution EEG technique (see paragraph
X.1). By using the passage through the Tailairach coordinates system, twelve
Regions Of Interest (ROIs) were then obtained by segmentation of the Brodmann
areas (B.A.) on the accurate cortical model utilized for each subject. Bilateral
ROIs considered in this analysis are the primary motor areas for foot (MIF) and
lip movement (MIL), the proper supplementary motor area (SMAp), the standard
pre-motor area (BA6), the cingulated motor area (CMA) and the associative area
(BA7).
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