Transcript Slide 1

Tracking brain dynamics via timedependent network analysis
Stavros I. Dimitriadis,Nikolaos A. Laskaris, Vasso Tsirka,
Michael Vourkas, Sifis Micheloyannis, Spiros Fotopoulos
Electronics Laboratory, Department of Physics, University of Patras, Patras 26500,
Greece
Artificial Intelligence & Information Analysis Laboratory, Department of Informatics,
Aristotle University, Thessaloniki, Greece
Medical Division (Laboratory L.Widιn), University of Crete, 71409 Iraklion/Crete,
Greece
Technical High School of Crete, Estavromenos, Iraklion, Crete, Greece
http://users.auth.gr/~stdimitr
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Outline
Introduction
-Multichannels EEG recordings
-math calculations (comparison and multiplication)
-multi frequency band analysis (from theta to gamma)
Methodology
- a frequency-dependent time window
- a novel, parameter-free method was introduced to derive the
required adjacency matrices (Dijkstra algorithm)
-a summarizing procedure that was based on replicator
dynamics and applied in consecutive adjacency matrices was
introduced where consistent hubs were identified
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Outline
Results
Conclusions
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Intro
Method
Results
Conclusion
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Mathematical thinking, as a cognitive process, activates local and
spatially distributed cortical networks
Exact calculations are correlated with language function activating
language specific regions located in the left hemisphere
During mental calculations different processes are necessary, such as
the
-recognition of the numbers in their Arabic form,
-the comprehension of verbal representation of numbers,
-the assignment of magnitudes to numerical quantities,
-attention, memory, and other more specialized processes
During difficult math calculations, additional cortical regions,
particularly of the left hemisphere, show increased activation.
These calculations demand retrieval of simple mathematical fact
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Intro
Method
Results
Conclusion
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Motivation
to introduce a methodology for tracking brain dynamics via network
measures derived from time-evolving graphs
to experimentally compare the obtained description – i.e., the
network-metric time series (NMTS) – against the description
from a single static graph or from a few successive snapshots of
functional connectivity
to detect consistent hubs based on a summarization procedure
called replicator dynamics
To introduce a novel parameter –free threshold scheme based on
Dijkstra’s algorithm
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Intro
Method
Results
Conclusion
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Outline of our methodology
We introduced the concept of time-dependent network analysis based on
weighted graphs constructed from EEG-signals using the Phase Locking
Index (PLI)
and metrics reflecting functional segregation (clustering coefficient and local
efficiency) and integration (characteristic path length and global efficiency).
The key idea was the employment of a sliding, frequency-dependent timewindow, and its application has shown that the network metrics (i.e., the
resulting time-series (NMTS)) were subject to modulations following the
characteristic oscillations of each frequency band
Interestingly, brain dynamics evolved under the constraints of a ‘small-world’topology that was ever-changing but consistent with the demands of local
processing and global integration.
Such trends are lost by approaches in which network characterization is
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attempted through static topologies or using signal segments of arbitrary length
Intro
Method
Results
Conclusion
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Evaluation of our methodology:
-our frequency dependent time window was compared with a
static and fixed time window (100 ms) without overlapping in
terms of the small – world index γ values across subjects and
for each frequency band which was estimated for 2 pairs of
networks metrics
-our parameter free algorithm for the detection of significant
edges was compared with 3 highly used threshold schemes in
terms of the quality of the fit of the degree distribution to wellknown forms of distribution (here power-law)
-Replicator dynamics showed consistent hubs in areas
related to brain rhythms and tasks.
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Intro
Method
Data acquisition: Math
Experiment
3 Conditions:
Control
Comparison
Multiplication
Results
Conclusion
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18 subjects
30 EEG electrodes
Horizontal and Vertical EOG
Trial duration: 3 x 8 seconds
Single trial analysis
The recording was terminated when at least an EEG-trace
without visible artifacts had been recorded for each condition8
Intro
Filtering
Method
Results
Conclusion
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Using a zero-phase band-pass filter (3rd order Butterworth filter),
signals were extracted for six different narrow bands : θ(4–8 Hz), α1 (8–
10 Hz),α2(10–13 Hz), β1 (13–20 Hz), β2 (20–30 Hz) and γ(30–45 Hz).
Artifact Correction
artifact reduction was performed using ICA employing runica
EEGLAB (Delorme & Makeig,2004),
-Components related to eye movement were identified based on their
scalp topography which included frontal sites and their temporal course
which followed the EOG signals.
-Components reflecting cardiac activity were recognized
from the regular rythmic pattern in their time course widespread
in the corresponding ICA component.
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Intro
Method
Results
Signal Power (SP)
Conclusion
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Calculation of SP for each recording site
The SP values corresponding to each single electrode were
contrasted for every subband and additionally the whole
delta-band. Significant changes were captured via one-tailed
paired t-tests (p < 0.001).
Τhe functional connectivity graph (FCG) describes
coordinated brain activity
In order to setup the FCG, we have to establish connections
between the nodes (i.e. the 30 EEG electrodes).
Phase synchronization, is a mode of neural synchronization,
that can be easily quantified through EEG signals
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Intro
Method
Results
Conclusion
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Phase-locking Value (PLV)
PLV quantifies the frequency-specific synchronization between two
neuroelectric signals (Mormann et al., 2000 ; Lachaux et. al. 1999).
We obtain the phase of each signal using the Hilbert transform.
(t, n) is the phase difference φ1(t, n) - φ2(t, n) between the
signals.
PLV measures the inter-trial variability of this phase
difference at t.
If the phase difference varies little across the trials,
PLV is close to 1; otherwise is close to 0
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Intro
Method
Results
Conclusion
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PLV procedure for a pair of
electrodes
Adopted from Lachaux et
al,1999
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Intro
Method
Results
Building the FCG
Conclusion
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Establishing links
for a single electrode
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0.6
The process is repeated for every electrode,
creating a complete graph.
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Intro
Surrogate Analysis
Method
Results
Conclusion
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-To detect significant connections, we utilized surrogate data to form
a distribution of PLI values, for each electrode-pair separately, that
corresponds to the case in which there is no functional coupling
- Functional connections that showed significant differences, with
respect to the distribution of PLI values generated by a
randomization procedure corresponding to each electrode pair,were
only considered.
-Since our analysis was based on a single sweep, we shuffled the time
series of the second electrode for each pair (in contrast to the case of
multiple trials where one shuffles the trials of the second electrode as
described in Lachaux et al., 2000).
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Intro
Method
Results
Surrogate Analysis
Conclusion
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-Finally, the original PLI values were compared against the
emerged baseline distribution (surrogate data) and this
comparison was expressed via a p-value which was set at p <
0.001.
-Graph
edges where the above criterion was not met, were
assigned a zero-weighted link.
To reduce computational effort of the
surrogate analysis one can employ FDR
5%
(false discovery rate)
Nonparametric Null Distribution
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Intro
Method
Results
Conclusion
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Network Analysis
The clustering coefficient C of network is defined as :
 ( wij w jh wih )1 / 3
C
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j , hGi , j , h  i

N iN
ki ( ki 1)
in which ki is the degree of the current node
The characteristic path length L is defined (through integration
across all nodes) as:
 ( wij w jh wih )1 / 3
C
1
j , hGi , j , h  i

N iN
ki ( ki 1)
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Intro
Method
Results
Conclusion
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Network Analysis
The global efficiency GE of network is defined as :
in which ki is the degree of the current node
The local efficiency LE is defined (through integration across all
nodes) as:
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Intro
Method
Results
Small – World network measures
Conclusion
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-We rewired each network 1000 times using the algorithm
proposed in (Maslov & Sneppen, 2002)
-Derived Cr and Lr as the averages corresponding to the ensemble of randomized
graphs. The two (normalized) ratios γ= C/Cr and λ= L/Lr were used in the
summarizing measure of “small-worldness”, defined as σ= γ/λ, which becomes
greater than 1 in the case of networks with small-world topology.The above
commputations were based for both pairs of network metrics.
-The above described computations were performed for
each subject/frequecy band separately and for each of the 3 approaches:
-static
-frequency dependent overlapping windows
-fixed windows without overlapping
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Intro
Method
Results
Conclusion
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General scheme
Connections in biological neural networks might fluctuate
over time
therefore, surveillance can provide a more useful picture of
brain dynamics than the standard approach that relies on a
static graph to represent functional connectivity.
Fixed time window vs frequency dependent (Cycle Criterion)
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Intro
Method
Results
Conclusion
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Unfolding the non-stationarity of brain EEG dynamics via the
frequency dependent analysis
Interestingly, the resulting NMTS (network metrics time series)
appeared to follow the characteristic oscillations of each
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frequency band.
Intro
Method
Results
Conclusion
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Threshold schemes
The selection of a threshold is not trivial
Various threshold schemes were proposed:
-mean degree K
- absolute threshold
-keep a % of strongest connections
- take the value that maximize the global cost efficiency
(gce=global efficiency - cost) versus cost (the ratio of
existing (anatomical connections ) or surviving edges
(after applying a threshold) divided by the total number
of possible connections )
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Intro
Method
Results
Conclusion
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Dijkstra’s algorithm
Construct the FCG (functional connectivity graph)
Construct distance matrix by inversing each entry of the FCG
Why ?
For instance, in a weighted correlation network, higher
correlations are more naturally interpreted as shorter
distances, and the input matrix should consequently be
some inverse of the connectivity matrix.
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Finally, we draw shortest path lengths in an adjacency matrix
Intro
Method
Results
Conclusion
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Replication dynamics
Despite the rapidly growing number of data-analysis techniques in
functional imaging, the field lacks formal mathematical tools for the
aggregation of the results from single-subject data to group data or from
single-sweep analysis to ensembles.
For the particular purpose of identifying commonalities in the hubs defined
across individual subjects, the most popular approach consists of plotting
hub regions from each subject into a single figure and recognizing the
overall average trend.
The above technique relies on visual inspection.
Solution ??
Replicator dynamics which helps to identify hubs appearing
consistently within and across subjects
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Intro
Method
Results
Conclusion
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Replication dynamics
-Applying Dijkstra’a algorithm to each
time instant FCG
-Summarizing in a co-occurrence
matrix the number of times that two
regions appeared simultaneously as
hubs in the adjacency matrix.
A node is characterized as hub if its
degree overcome the value = mean + 1
std of the overall graph.
This procedure was followed firstly at
each subject and in a second step
across subjects.
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Intro
Method
Results
Conclusion
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Small - Worldness
For the static and time-varying approaches to be comparable, the mean
of the values obtained across time was estimated in the latter cases.
Significant differences (p < 0.001) were detected for S via one-tailed
paired-t tests (applied across subjects) comparing our approach against
the piecewise approach (i.e., t2 versus t1) and the approach based on
static graphs (i.e., t2 versus s).
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Intro
NMTS
Method
Results
Conclusion
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Functional snapshots incorporate a
time-varying structure that can be
attributed to the related cognitive
task (comparison or multiplication)
because the values of the related
network metric are significantly
higher than the control condition.
The obtained time-dependent measurements seem to provide us with a more
reliable characterization of the network topology, which is closer to a smallworld network when the employed topological descriptor has not collapsed
the time-related variations.
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Intro
Method
Results
Conclusion
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Broadband scale-free character of math
calculations across subjects
Our approach based on Dijksta’s algorithm resulted in
systematically higher R2-values (is a statistical measure that
shows how well the regression curve represents the actual
measurements)
Our approach and max(cost efficiency) are the only threshold
scheme that quarantee the connectness of the nodes.
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Intro
Method
Results
Conclusion
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Broadband scale-free character of math
calculations across subjects
No difference was observed
between the 2 math tasks
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Intro
Method
Results
Conclusion
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Scalp distribution of hubs
Τhe θ-band hubs are located within the frontal region that is related to
working memory
the a2-band hubs are located bilaterally over the parieto-occipital regions
and, presumably, can be attributed to visual attention
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Intro
Method
Results
Conclusions
Conclusion
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Our methodology included the following elements:
-a frequency-dependent definition of a time-window,
-a phase-locking estimator for the pair-wise assessment of
functional connectivity from signal segments,
-the computation of standard network metrics from the timevarying graphs, and
-a novel method to reveal the most significant edges in a given
network to construct the required adjacency matrices without a
threshold selection step.
-Moreover, the individual time-dependent adjacency matrices were utilized in
a new aggregation scheme (replicator dynamics) that identified keynote
nodes (brain regions) for the observed connectivity patterns across subjects
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(i.e.,group analysis).
Future research
The incorporation of empirical techniques for the tracking and
extraction of time-varying oscillations (Fine et al., 2010), such
as Empirical Mode Decomposition
The incorporation of connectivity estimators that can take
into consideration the complexity and the non-stationary/nonlinear character of brain signals are among the necessary
improvements that should be pursued in the future.
and the replacement of the oversimplifying notion of pair-wise
interactions with the combinatorial n-way synchrony (Jung et al.,
2010), will enrich our knowledge of actual brain dynamics
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