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Evaluation of the Brain Network Organization From EEG SignalsA Preliminary Evidence in Stroke Patient.

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THE ANATOMICAL RECORD 292:2023–2031 (2009)
Evaluation of the Brain Network Organization
From EEG Signals: A Preliminary Evidence
in Stroke Patient
FABRIZIO DE VICO FALLANI,1,2 LAURA ASTOLFI,1,3 FEBO CINCOTTI,1 DONATELLA MATTIA,1
DARIA LA ROCCA,1 ELIRA MAKSUTI,1 SERENELLA SALINARI,3 FABIO BABILONI,1,2*
BALAZS VEGSO,4 GYORGY KOZMANN,4 AND ZOLTAN NAGY4
1
Laboratory of ‘‘Neurofisiopatologia Clinica,’’ IRCCS ‘‘Fondazione Santa Lucia,’’ Roma, Italy
2
Department of Human Physiology and Pharmacology, University ‘‘Sapienza,’’ Rome, Italy
3
Department of ‘‘Informatica e Sistemistica,’’ University ‘‘Sapienza,’’ Rome, Italy
4
Department of Information Systems, University of Pannonia, Veszprem, Hungary
ABSTRACT
Synchronous brain activity in motor cortex in perception or in complex cognitive processing has been the subject of several studies. The
advanced analysis of cerebral electro-physiological activity during the
course of planning (PRE) or execution of movement (EXE) in a high temporal resolution could reveal interesting information about the brain
functional organization in patients following stroke damage. High-power
(128 channels) electroencephalography registration was carried out on 8
healthy subjects and on a patient with stroke with capsular lacuna in the
right hemisphere. For activation of motor cortex, the finger tapping paradigm was used. In this preliminary study, we tested a theoretical graph
approach to characterize the task-related spectral coherence. All of the
obtained brain functional networks were analyzed by the connectivity
degree, the degree distribution, and efficiency parameters in the Theta,
Alpha, Beta, and Gamma bands during the PRE and EXE intervals. All
the brain networks were found to hold a regular and ordered topology.
However, significant differences (P < 0.01) emerged between the patient
with stroke and the control subjects, independently of the neural processes related to the PRE or EXE periods. In the Beta (13–29 Hz) and
Gamma (30–40 Hz) bands, the significant (P < 0.01) decrease in globaland local-efficiency in the patient’s networks, reflected a lower capacity to
integrate communication between distant brain regions and a lower tendency to be modular. This weak organization is principally due to the significant (P < 0.01 Bonferroni corrected) increase in disconnected nodes
together with the significant increase in the links in some other crucial
C 2009 Wiley-Liss, Inc.
vertices. Anat Rec, 292:2023–2031, 2009. V
Key words: cerebral disorder; functional connectivity; graph
theory
Sequential activation of parietal, premotor, and supplementary motor areas as well as subcortical extrapyramidal system and cerebellum before activation of motor
cortex is well documented in different experimental,
neuromorphological studies. In the clinical praxis, the
low temporal resolution of widely used neuroimaging
Grant sponsor: Hungarian Research Foundation; Grant
number: NKFP 2/004/04 and OTKA K69240; Grant sponsor:
COST EU Project NEUROMATH; Grant number: BM0601.
*Correspondence to: Fabio Babiloni, Laboratorio Neurofisiopatologia Clinica, IRCCS ‘‘Fondazione Santa Lucia,’’ Via Ardeatina, 306 I-00179 Rome, Italy. Fax: þ39 06 5150 1465. E-mail:
fabio.babiloni@uniroma1.it
Received 18 February 2009; Accepted 10 June 2009
DOI 10.1002/ar.20965
Published online in Wiley InterScience (www.interscience.wiley.
com).
C 2009 WILEY-LISS, INC.
V
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DE VICO FALLANI ET AL.
technologies like photon emission tomography (PET),
single photon emission computerized tomography (SPECT),
or even functional magnetic resonance imaging (fMRI) do
not allow to visualize activated loops or networks in the
course of movement. Other technologies, like magnetoencephalography (MEG) or electroencephalography (EEG) with
high temporal resolution offer new insight into mechanisms of movement-organization and execution in the
brain. These methods could characterize compromised
brain function in patients with paretic stroke.
The functional connectivity networks estimated from
brain-imaging technologies (MEG, fMRI, and EEG) can
be investigated by using graph theory (Stam, 2004;
Salvador et al., 2005; Eguiluz et al., 2005; Bartolomei et
al., 2006; Micheloyannis et al., 2006; Achard and Bullmore, 2007; De Vico Fallani et al., 2008a). As a graph is
a mathematical representation of a network essentially
reduced to nodes and connections between them, the use
of a graph-theoretical approach is potentially relevant
and useful, as first demonstrated on a set of anatomical
brain networks (Strogatz, 2001; Sporns, 2002). In those
studies, the authors employed two characteristic features, the average shortest path L and the clustering
index C, to extract the global and local properties of the
network structure, respectively (Watts and Strogatz,
1998). They found that anatomical brain networks exhibit many local connections (i.e., a high C) and few random long distance connections (i.e., a low L),
characterizing a particular model that interpolates
between a regular lattice and a random structure. Such
a topological property of the network (designated as
small-world) has a strong impact on neurosciences, as it
is related to optimal architectures for information processing and signal transmission among different cerebral
structures (Lago-Fernandez et al., 2000; Sporns, 2002).
Advances in brain imaging technologies, such as MEG
and EEG have shown that activity takes place in different
parts of the human brain. In several domains of engagement, these areas of activity are disparate in geography
yet analogous in context. In particular, several studies
(Classen et al. 1998; Andres and Gerloff, 1999; Lachaux et
al., 1999; Miltner et al., 1999; Ghilardi et al., 2000) have
examined synchronous brain activity using EEG technology. Varela et al. (Lachaux et al., 1999; Thompson and
Varela, 2001) and others (Rappelsberger et al., 1994;
Singer, 1999) have shown the role that synchronous cerebral activity plays in higher cognitive function including
associative memory, emotional tone, and motor planning
(Rodriguez et al., 1999). Such a synchronous cooperation
between two or more distant brain regions to achieve a
particular result may be referred to as a form of functional
connectivity, which can be treated as a complex network.
In this study, we show results from a novel analysis of
functional networks estimated from a set of scalp EEG signals in a stroke patient and in a group of healthy subjects
during the performance of a self-paced motor task. This
study wishes to ascertain if the cerebral lesion changed
the functional organization of the brain network related to
the performance of a self-paced movement of the hand.
MATERIALS AND METHODS
Experimental Design
To test the method of EEG graph analysis, eight
healthy male subjects (age 30.75 15.39 years) and one
stroke male patient (age 65 years) were recruited. The
stroke patient had poorly controlled hypertension.
Besides his index lacunar stroke in the right capsula, he
had multiple lacunas in the white matter in both hemispheres without focal neurological symptoms. The first
step in the recording procedure was to inform the subject of what participation in the study would entail. A
consent form was then signed by the subjects.
For the EEG data acquisition, subjects were comfortably
seated on a reclining chair, in an electrically shielded,
dimly lit room. They were asked to perform a rapid extension of their second finger with the right hand. This task
was repeated every 10 sec in a self-paced manner and 60
repetitions (trials) were recorded, digitalized, and stored
in a hard disk. EEG signals were recorded with a sampling frequency of 2,048 Hz from 128 scalp electrodes disposed according to the scheme in Fig. 1. After the artifact
removal in the present study, we analyzed separately the
EEG segments of the preparation (PRE) and the execution
(EXE) of the finger movement. In particular, we considered 2 sec before the movement onset for the PRE period
and 2 sec after the onset for the EXE period. Before the
computation of the spectral properties, all the EEG signals
were downsampled—through an antialiasing (low-pass)
FIR filter to compensate for the filter’s delay—to 128 Hz
to allow a more efficient data processing, given that the
frequencies of interest were below 50 Hz.
Brain Functional Synchronization
Brain functional connectivity is achieved through the
computation of task-related coherence. Andres and
Gerloff (1999) describe task-related coherence as the
‘‘analysis of systematic interregional correlations of oscillatory cortical activity.’’ As described earlier several
studies have suggested that such interregional correlations are associated with conscious cognitive processing
and active perception. Task-related coherence in the context of our study is essentially a measure of similarity
that provides us with an estimation of the level of synchronicity between two or more regions of the brain. The
estimation is based on a mathematical manipulation of
electrical signals obtained from the regions of the brain
under investigation.
Spectral coherence is a function that operates in the
frequency domain and generates a value between 0 and
1. Given two signals x and y, spectral coherence is calculated for a particular frequency f by taking the square of
the cross-spectrum |Sxy(f)|2 and then dividing by the
product of the two corresponding auto power spectra.
SCxy ðf Þ ¼
Sxy ðf Þ2
Sxxðf ÞSyyðf Þ
(1)
In the present study, the spectral coherence (SC) is
calculated by estimating the value of linear correlation
between each possible pairs of EEG channels with
respect to each single frequency bin. The spectral resolution was fixed to 1 Hz, thus for each channel pair the
spectral range was from 0 to 64 Hz. To compute the correlation of a pair of time series, each trial was considered as a unique not overlapped section and a ‘‘hanning’’
window of 2 sec was employed to smooth the noise due
to the finite-size trials.
FUNCTIONAL CONNECTIVITY DURING SIMPLE MOTOR ACTS
2025
Fig. 1. The EEG cap map of the active-two recording system from Biosemi.
Afterward, the coherence values were stored opportunely in a matrix with 128 rows and 128 columns (i.e.,
128 channels) for each PRE and EXE intervals and for
each frequency bin (see Fig. 2).
To study the level of synchronization in specific physiological frequency ranges, we considered a frequencyaveraged coherence map in the bands of interest Theta y
(4–7 Hz), Alpha a (8–12 Hz), Beta b (13–29 Hz), and
Gamma c (30–40 Hz).
Network Analysis
The theoretical representation of a network is the
graph. A graph consists of a set of vertices (or nodes)
and a set of edges (or connections) indicating the presence of some sort of interaction between the vertices.
The adjacency matrix A contains the information about
the connectivity structure of the graph. When a link connects two nodes i and j, the corresponding entry of the
adjacency matrix is aij ¼ 1; otherwise aij ¼ 0.
Node degree. The simplest attribute of a node is its
connectivity degree, which is the total number of connec-
Fig. 2. Schematic representation of the obtained spectral coherence connectivity maps.
2026
DE VICO FALLANI ET AL.
tions with other vertices. The formulation of the degree
index d(i) can be introduced as follows:
dðiÞ ¼
X
ai;j
(2)
j2V
V is the set of the available nodes and aij indicates the
presence of the arc connecting the point j to the point i.
Thus, it represents the total amount of links connected
to the vertex i.
The node degree has an obvious functional interpretation because it gives an index of the importance of that
node within the network.
Degree distribution. To get information about the
behavior of degree within the system, it is useful to
introduce P(d), the fraction of vertices in the graph that
have degree d. Equivalently, P(d) is the probability that
a vertex chosen uniformly at random has degree d. A
plot of P(d) for any given network can be constructed by
making a histogram of the degrees of vertices. This histogram is the degree distribution for the graph and it
allows better understanding of the degree allocation in
the system.
Efficiency. Two measures are frequently used to
characterize the local and global structure of unweighted
graphs: the average shortest path L and the clustering
index C (Watts and Strogatz, 1998; Newman, 2003;
Grigorov, 2005). The former measures the efficiency of
the passage of information among the nodes and the latter indicates the tendency of the network to form highly
connected clusters of vertices. Recently, a more general
setup has been examined to investigate weighted networks (Boccaletti et al., 2006). In particular, Latora and
Marchiori (2001) considered weighted networks and
defined the efficiency coefficient e of the path between
two vertices as the inverse of the shortest distance (dist)
between the vertices (note that in weighted graphs the
shortest path is not necessarily the path with the smallest number of edges). In the case where a path does not
exist, the distance is infinite and e ¼ 0. The average of
all the pair-wise efficiencies eij is the global-efficiency Eg
of the graph. Thus, global-efficiency can be defined as:
Eg ðAÞ ¼
X 1
1
NðN 1Þ i6¼j2V disti;j
1X
Eg ðAi Þ
N i2V
between the first neighbors of i when i is removed.
Global- (Eg) and local-efficiency (El) were demonstrated
to reflect the same properties of the inverse of the average shortest path 1/L and the clustering index C
(Latora and Marchiori, 2003). Hence, the definition of
small-world can be rephrased and generalized in terms
of the efficiency indexes (Boccaletti et al., 2006; Stam
and Reijneveld, 2007). Small-world networks have high
Eg (i.e., high 1/L) and high El (i.e., high C). This new
definition is attractive because it takes into account the
full information contained in the weighted links of the
graph and provides an elegant solution to handle disconnected vertices (Latora and Marchiori, 2001).
Contrast with random graphs. Also the comparison
with 100 random graphs has been addressed by comparing the original brain networks with connectivity patterns holding the same number of nodes and the same
number of links arranged in a random fashion (Erdos
and Renyi, 1960). This contrast has the power to evaluate statistically the distance of the real brain network
from structures obtained in a casual way.
(3)
where N is the number of vertices composing the graph.
As the efficiency e also applies to disconnected graphs,
the local properties of the graph can be characterized by
evaluating for every vertex i the efficiency coefficients of
Ai, which is the subgraph composed by the neighbors of
the node i. The local-efficiency El is the average of all
the subgraphs global-efficiencies:
El ðAÞ ¼
Fig. 3. Functional networks of the stroke patient in the Alpha band
during the PRE and EXE intervals of left side finger tapping. Each
node represents a scalp electrode. Each link represents a significant
coherence between the signals of two electrodes. Yellow links represent connections common to both the intervals, whereas black links
are the changing connections.
(4)
As the node i does not belong to the subgraph Ai, this
measure reveals the level of fault tolerance of the system, showing how the communication is efficient
Connections filtering. In the present study, we
dealt with brain networks holding the same number of
connections. This should be done when one wants to prevent that a different number of connections could bias
the comparison of two conditions or subjects. For this
reason, the resulting values of SC were filtered defining
a threshold. An edge between two channels was drawn
only if the corresponding coherence value is higher than
the specified threshold. In particular, each coherence
matrix was filtered by maintaining only the strongest
585 links (0.07197 of connection density), which were
subsequently converted to logical values (0, absence of
link; 1, presence of link). See ‘‘Methodological considerations’’ paragraph, in the Discussion section, for more
details.
The resulting coherence maps, which represent the
functional interactions between all the EEG signals, can
2027
FUNCTIONAL CONNECTIVITY DURING SIMPLE MOTOR ACTS
TABLE 1. Statistical comparisons of global- and local-efficiency
Theta
Eg
El
Alpha
Beta
PRE
EXE
PRE
EXE
PRE
0.80
1.81
1.50
1.99
0.34
1.80
1.06
2.37
2.83
2.72a
a
Gamma
EXE
PRE
EXE
2.01
3.42a
4.89
2.67a
a
3.43a
3.42a
Values are represented by the z-score.
a
Significant difference between the stroke and control graphs (|Z| > 2.58, P < 0.01).
be drawn through a set of vertices disposed in a circle.
Figure 3 illustrates the connectivity networks in the
Alpha band for the stroke patient during the PRE and
EXE period.
RESULTS
The main theoretical graph indexes obtained from the
brain networks of the stroke patient were contrasted
statistically (Z-score) with the distribution of values
obtained from the healthy population in the same frequency bands and conditions.
The analysis of the network topology through the efficiency indexes revealed a significant (P < 0.01) difference between the stroke patient and the control healthy
subjects.
Table 1 shows the obtained Z-values for Eg and El in
all the frequency bands and conditions. The differences
involve mainly the highest spectral contents (Beta and
Gamma band). In those bands, both the global- and
local-efficiency of the patient are statistically (P < 0.01)
lower with respect to control subjects during both the
PRE and EXE intervals. Only in the Beta band during
the execution (EXE) was this difference less strong.
Figure 4 shows the original Eg and El values in the Beta
and Gamma bands and during both situations. The
decrease in efficiency in the patient’s brain network is
maintained either during the PRE or EXE periods.
Eventually, all the estimated brain networks were contrasted with a distribution of 100 random graphs having
the same number of nodes and links. The results demonstrate that all the brain networks present a statistically
different topology when compared with random networks. In particular, the Z-test revealed a significant (P
< 0.01) lower Eg and a significant (P < 0.01) higher El
(data not shown here).
The different structural properties observed in the
patient’s brain are due to a different arrangement of the
links within the functional network. The evaluation of
how these connections are distributed within the network was addressed through the degree-distribution
indexes.
Figure 5 shows the obtained Z-values for P in the
Beta and Gamma bands and during the PRE and EXE
periods. The general outcome suggests in the patient’s
brain network the presence of many nodes (Z < 0) with
a lower degree, that is, d [ (1,25), than control subjects
and few nodes (Z > 0) with a higher degree, d [ (26,55).
Also, it can be noted how the number of disconnected
nodes (d ¼ 0) is significantly higher (P < 0.01, Bonferroni corrected for multiple comparisons). Moreover, a
significant increase (P < 0.01, Bonferroni corrected) of
the nodes with 32 and 38 links can be observed in the
Beta band during the PRE interval (Fig. 5a). In the
Fig. 4. Comparison between the efficiency values of the stroke
patient and the control subjects. (a) Contrast for the Eg indexes in the
Beta band during the PRE and EXE intervals. The red bar represents
the value of the stroke patient. The blue bar represents the mean
value of the control subjects; the vertical line measures the standard
deviation. The asterisk indicates a significant difference (P < 0.01). (b)
Contrast for the El indexes in the Beta band during the PRE and EXE
intervals. (c) Contrast for the Eg indexes in the Gamma band during
the PRE and EXE intervals. (d) Contrast for the El indexes in the
Gamma band during the PRE and EXE intervals.
same band, we can find a significant increase in the vertices (P < 0.01, Bonferroni corrected) with 26 and 40
connections (Fig. 5b). A significant increase (P < 0.01,
Bonferroni corrected) of the nodes with 28, 29, 33, and
41 links can be observed in the Gamma band during the
PRE interval (Fig. 5c). In the same band, we can find
also a significant increase in the vertices (P < 0.01, Bonferroni corrected) with 23 and 29 connections (Fig. 5d).
To identify the main nodes, that is, the electrodes on
the scalp, which are responsible for the observed structural change in the brain functional networks of the
stroke patient, we evaluated the degree indexes of each
vertex.
Figure 6 shows the obtained d values for the stroke
patient in the Beta and Gamma bands and during the
PRE and EXE intervals. Each degree value is represented through a sphere located on the schematic map
of the EEG electrodes cap at the respective sensor position. The size of the sphere measures the role of the electrode in the brain functional network. The larger
spheres indicate those electrodes in the stroke patient’s
network whose number of links was significantly higher
(P < 0.01 Bonferroni corrected) than control subjects.
Thus, according to the degree distribution findings the
main nodes in the Beta band during the PRE period are
2028
DE VICO FALLANI ET AL.
Fig. 5. Statistical contrast (Z-test) of the degree distributions of the
stroke patient and control subjects. (a) comparison for the P indexes
in the Beta band during the PRE period. On x-axes, the degree values,
on y-axes the Z-values of the P indexes. The numbers at the line
peaks indicate those connections that responsible of a significant dif-
ference (P < 0.01, Bonferroni corrected) between the brain network of
the patient and control subjects. (b) Comparison for the P indexes in
the Beta band during the EXE interval. (c) Comparison for the P
indexes in the Gamma band during the PRE period. (d) Comparison
for the P indexes in the Gamma band during the EXE interval.
those with 32 and 38 links, that is, A18, B17, D17, and
D29 (Fig. 6a); the main vertices in the Beta band during
the EXE interval are those with 26 and 40 connections,
that is, A29, C1, C29, D12, D28, and D29 (Fig. 6b); the
main nodes in the Gamma band during the PRE period
are those with 28, 29, 33, and 41 links, that is, A7, B1,
B7, B17, B18, C12, C17, C29, D1, and D17 (Fig. 6c); the
main vertices in the Gamma band during the EXE interval are those with 23 and 29 connections, that is, B23,
B29, C7, D8, and D23 (Fig. 6d).
In the present work, we characterized the functional
networks through a theoretical graph approach in a
stroke patient and in eight healthy subjects during a finger-tapping task from scalp EEG signals.
All the estimated networks were found to be very
unlikely from random graphs. In particular, the brain
functional networks presented a more regular and ordered structure, as revealed by the significant (P < 0.01)
higher values of local-efficiency and lower values of
global-efficiency.
Brain networks have been widely demonstrated as differing from random graphs in several studies (Stam,
2004; Salvador et al., 2005; Eguiluz et al., 2005; Bartolomei
et al,. 2006; Micheloyannis et al., 2006; Achard and
Bullmore, 2007; De Vico Fallani et al., 2008b); however,
this aspect does not represent the focus of this article.
The theoretical graph approach we used for analysis
of 128 channels EEG recording aimed at evaluating the
level of degeneration in the brain functional network of
a stroke patient. Results suggest a significant change in
the structural properties of the brain network in the
stroke patient either in the PRE or in the EXE interval
of the motor act. This means that the network topology
in the patient’s brain could be generally affected by the
stroke lesion independently of the neural processes
DISCUSSION
The possibility to adopt a mathematical approach
improves the capability of detecting the topological features from real complex networks. The topology of a network describes the organization and the architecture of
the links within the system. In the neuroscience, this aspect has a strong impact as the arrangement of the functional links between different brain sites could affect the
level of information processing and signal synchronization. In this respect, the graph theory may facilitate the
analysis of the functional connectivity patterns estimated from actual neuroimaging technologies.
FUNCTIONAL CONNECTIVITY DURING SIMPLE MOTOR ACTS
2029
Fig. 6. Patterns of degree values for the stroke patient. Each
degree value is represented through a sphere located on the schematic map of the EEG electrodes cap at the respective sensor position. The darker is the color, the higher is the degree value according
to the colorbar. The larger spheres indicate those electrodes in the
stroke patient’s network whose number of links was significantly
higher (P < 0.01 Bonferroni corrected) than control subjects. (a)
Degree values in the Beta band during the PRE interval. (b) Degree
values in the Beta band during the EXE period. (c) Degree values in
the Gamma band during the PRE interval. (d) Degree values in the
Gamma band during the EXE period.
related to preparation or execution of the movement.
These changes are particularly prominent in the Beta
band (13–29 Hz), which is already known to be involved
in motor tasks (Pfurtsheller and Lopes da Silva, 1999),
but also in the Gamma (30–40 Hz) band. This would
demonstrate that this type of cerebral damage would
affect the functional network mainly in the highest spectral contents.
In particular, the significant (P < 0.01) decrease in
global- and local-efficiency in the patient’s networks
reflects a lower capacity to integrate the communication
between distant brain regions and a lower tendency to
be modular. This weak organization is principally due to
the different arrangement of the functional links within
the network, as the number of connections was the same
in the stroke patient and in the healthy subjects. The
significant (P < 0.01 Bonferroni corrected) increase of
disconnected nodes, that is, electrodes, together with the
significant (P < 0.01 Bonferroni corrected) increase of
the links in some other crucial vertices, is thought to be
the main aspect responsible for the observed structural
and organizational degeneration. This change indicates
that the overall connectivity in the patient’s network is
ruled by a lower number of brain regions. A possible
interpretation of this preliminary evidence is that the
capsular lacunas could affect the rapid oscillating activities (13–40 Hz) of the standard cortical areas involved
during the motor task by inhibiting their degree of connectivity. The subsequent increase in connectivity in a
limited number of brain regions does not seem sufficient
to avoid a drastic reduction in the information propagation in the functional networks of the patient’s brain.
Methodological considerations
The spectral coherence, the method we used in this
study, is one of the simplest measures to detect functional connectivity between signals. It is straightforward
and it does not need restrictive a-priori hypotheses.
However, despite its intuitive nature it only gives undirected links between electrodes. No information can be
achieved about the direction of the functional relationship. Other interesting methods, based on multivariate
autoregressive models (MVAR) models (Sameshima and
Baccala, 1999; Kaminski et al., 2001), could give the
direction of the information, but there is a restrictive
2030
DE VICO FALLANI ET AL.
relation between the number of the elements among
which it is possible estimate the connectivity and the
available data. Eventually, it should be very hard to
have reliable estimates with the MVAR model on 128
electrodes. Furthermore, a serious limitation of extracranial EEG coherence measures is contamination by volume conduction through the tissues separating sources
and electrodes (Urbano et al., 1997, 1998; Babiloni et al.,
2001; Astolfi et al., 2005, 2007; De Vico Fallani et al.,
2007). However, as the main effect seems to be a coherence elevation in the highest frequencies >40 Hz
(Ramesh et al., 2007), the estimates in the present study
should be relatively stable, as we considered EEG spectral contents up to 40 Hz.
The choice of the ‘‘optimum’’ connection-density of the
estimated networks was surely the most favorable condition for the significance of the network structure indexes
(De Vico Fallani et al., in press). In fact, at this connection-density the efficiency indexes describing the structural properties of the network are maximally separated
and independent (data not shown here), thus giving a
more robust analysis. This is not trivial as arbitrary
thresholding methods could still lead to highly connected
networks or vice versa, to very sparse networks. This
possibility dramatically affects the independence and the
separation of the efficiency indexes (i.e., in a full connected graph both the global- and local-efficiency are
equal to 1, in an empty graph they are both equal to 0),
which could give misleading results across different subjects or tasks.
Eventually, it is worth to mention that previous studies showed that age affects the structure of the healthy
brain functional network (Achard and Bullmore, 2007)
obtained from fMRI signals during resting state conditions. Even if in the present study there is a sensible difference between the age of the stroke patient and the
mean age of the healthy subjects, we would like to state
that we are dealing with functional networks obtained
from a totally different brain imaging technique (i.e.,
EEG) and that the experimental conditions deviate
actually from a simple resting state. For these reasons,
we would not be able to assess exactly the role of the
age in the present study, which mainly focuses on the
possible structural changes in the brain functional network of the stroke patient.
ACKNOWLEDGEMENTS
Dr. Fabrizio De Vico Fallani whishes to thank Ing.
Alessandro Tabarrini for his support in the last computational steps.
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