Go with the winner: optimizing detection of
modular organization differences in dynamic
functional brain networks
S.I. Dimitriadis, N.A. Laskaris, A. Tzelepi
AIIA-Lab, Informatics dept., Aristotle University of Thessaloniki
Electronics Laboratory, Department of Physics,University of Patras
ICCS, National Technical University of Athens
1
Outline
Introduction
-Various studies examined modular organization based on
numerous measures of neural synchrony
-It is not known yet how to quantify the employed descriptors in
terms of functional community structure
Methodology
We introduced a framework for detecting the synchronization measure
that best describes and differentiates two conditions (or two groups
of subjects) in terms of time-varying functional communities
Results
Conclusions
2
Intro
Method
Results
Conclusions
A great variety of measures has been proposed
to quantify neural synchrony
An important question is whether the detection of modules is
influenced by the adopted synchronization measure and also
by the clustering algorithm (Pavan & Pelillo,2007).
An additional question is whether the distribution and
also the number of modules in healthy and impaired
subjects are similar or not
3
Intro
Method
Results
Conclusions
Motivation and problem statement
The vast majority of previous studies have been based on
analyzing the topological properties of static graphs
-Inaccuracies can be more severe for fast-recordingmodalities,
in particular for EEG/MEG and to a lesser extent for fMRI.
To alleviate the above limitations, we used time–varying
graphs, which describe temporally evolving networks that
have fixed nodes but changeable links
Our motivation was to present a method to qualify the employed
descriptors in terms of the resulting functional community structure
4
Intro
Method
Results
Conclusions
Outline of our methodology
We introduced a framework for detecting the synchronization
measure that best describes and differentiates two conditions
Time-varying functional communities
Specifically, we considered the multichannel EEG recordings
during an attentive and passive eye movement task
as observations from two different states of the (same) brain,
Discriminability was measured for different types of coupling
(linear vs. nonlinear) and different forms of covariation
(amplitude/phase)
5
Intro
Method
Results
Conclusions
Data acquisition: Visual ERP experiment
2 Conditions:
•Attentive
•Passive
•(Left/right)
5 subjects
64 EEG electrodes
Horizontal and Vertical EOG
Trial duration: 5.5 seconds
2 runs, 50 trials for each condition
6
Intro
Method
Results
Conclusions
Exploratory Analysis – Contrast function
Two different sets of patterns/objects {Xi} and
{Yj} can be compared in three steps.
We first established an appropriate pairwise dissimilarity
measure D(Xi,Yj).
This measure is then applied to all possible pairs to compute
the inter-set scatter (IS ATTENTIVE - PASSIVE) and the two
within-set scatters (WS ATTENTIVE and WS PASSIVE).
The computed quantities are finally combined to express the set
difference,as follows:
7
Intro
Method
Results
Conclusions
Statistical approach of J-index
The statistical significance of a specific value for the J-index
can be calculated based on a randomization procedure.
We first splitting the objects (i.e., all EEG-traces from
attentive and passive conditions) at random into two groups
and repeating the computations for J multiple times to form a
baseline distribution for the J-index indicative of random
partitioning (e.g.10.000 -> P < 0.001)
Finally, the original value of the J-index is
compared to the derived baseline distribution,
and this comparison is expressed via a P-value
8
Intro
Method
Results
Conclusions
Quantify communities differences
Adopting a synchronization measure, we estimated the connectivity
strength for each pair of signals
A
The set of N trials
patterns of the
attentive task, at each latency t, can
B
be compared against the set of N trials
patterns of the passive task
Graph partition algorithm
A
N trials
N
1 2 3 2 1 ….. 2 1 3 2
1 2 3 1 2 …. 2 1 3 2
Attentive Task
N
B
N trials
23412…1232
22312…1222
Passive Task
9
Intro
Method
Results
Conclusions
Adjust J-index to community differences
We adopted VI (Variation of Information) as a
dissimilarity measure to quantify community differences
Suppose we have two clusterings X and Y.
X=[1 1 2 1 , … 2 1] & Y=[1 3 2 1 , … 2 3]
Then the variation of information between two clusterings is:
VI ( X , Y )  H ( X )  H (Y )  2MI ( X , Y )
Where H(X) is the entropy of X and MI(X,Y) is the mutual information
between X and Y (Meila, 2007)
10
Intro
Method
Results
Conclusions
Adjust J-index to community differences
N
Numerator &
Denominator
=
J-index
11
Intro
Method
Results
Conclusions
Adjust J-index to dynamic community
differences
Using the latency-dependent measurements Jt and the associated pvalues (produced via trial-shuffling) derived for each subject
separately, we summarize the comparison between attentive and
passive task by means of the TICDI
(Time-Integrated Community Difference Index )
where Ns denotes the number of subjects and NT the total
number of discrete time points (latencies)
12
Intro
Method
Results
Conclusions
Τhe functional connectivity graph (FCG)
describes coordinated brain activity
To accommodate the various aspects of neural synchrony, we
employed different functional connectivity estimators.
Coherence (COH), Mutual Information (MI),
Phase Locking Value (PLV), Phase Lag Index
(PLI) and weighted – Phase Lag Index (wPLI)
Every estimator takes as input a pair of time series recorded at
distinct sites and derives an estimate of the strength for the
corresponding functional interaction
Such an interaction can have either linear or nonlinear
characteristics and can take the form of either amplitude or
phase covariation
13
Intro
Method
Results
Conclusions
Time – varying FCGs
We employed a frequency-dependent criterion to define the width
of the time-window (Dimitriadis et al., 2010) .
Using a regular time step, the centre of the window
was moved forward, and the whole network connectivity
was re-estimated based on the new signal segments
Each FCG was defined by the (time dependent) [64 × 64]
matrix W(t) with entries the pairwise coupling strengths FCG
(u(t),v(t)) derived based after integration within the
4–10 Hz frequency range.
FCG -> TVFCGs
14
Intro
Method
Results
Conclusions
Detecting Significant Couplings
Significant values were determined after calculating connectivity
strength for surrogates derived by randomizing the order of
trials in one of the channels of each pair
Significance levels were then extracted from the p-values
of the difference between synchronization estimates in
the original and surrogate data (e.g.1.000 -> P < 0.01)
Significance probabilities were corrected using the FDR
method in order to correct for multiple comparisons
The expected fraction of false positives was restricted to
q ≤ 0.01
15
Intro
Method
Results
Conclusions
Task-induced differences in
functional segregation (TICDI)
The ranking of synchronization measures according to
TICDI was: COH < MI < PLI < WPLI < PLV
16
Intro
Method
Results
Conclusions
Functionally Segregated Patterns
Evolution of clusterings across trials and
subjects between attentive (A) and passive
condition (P) in a) left and b) right
presentation
The most important trend is that during
the attentive condition, the number of
functional groups that are emerging is
higher compared to the passive condition.
17
Intro
Method
Results
Conclusions
Participation Index identified functional hubs
Participation Index is a feature of each nodes connectivity relative
to the modularity decomposition of the entire network. We
define the participation coefficient PI of node i as:
where wsi is the sum of weights (links) of node i to nodes in
i
W

w

module s, i s s is the total strength of node i and N m is the
total number of modules.
The participation coefficient of a node is therefore close to
one if its links are uniformly distributed among all the
modules and zero if all its links are within its own module
18
Intro
Method
Results
Conclusions
Participation Index identified functional hubs
In order to detect hubs across time and subjects,we ranked PI
values for each network and then we keep the indices of the nodes
belonging to the 20% of the highest values
Sensors belonging in at least 80% of latencies at each subject
and to the 20% highest PI-values of each network were
defined as hubs on a group level
Our analysis was divided into three parts:
a) the baseline period, ([-1 0] sec),
b) the period from the onset of the stimulus until the weakening of the Visual
Evoked Potential (VEP) ([0 0.2] sec) and
c) the eye – movement preparatory period until the initiation of the
antisaccade (attentive condition) ([0.2 3.5]sec).
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Intro
Method
Results
Conclusions
Brain rhythm interpretation
In the present study, we analyzed EEG signals in the
frequency range of 4 – 10 Hz including both θ and lower-α
(α1).
Both brain rhythms were found to be involved in attentional
processes (von Stein and Sarnthein, 2000 ; Sauseng et al., 2005)
20
Intro
Method
Results
Conclusions
Participation Index identified functional hubs
The extension of hubs :
(a)bilaterally over frontal regions
and also
(b)over parieto-occipital sites
contralaterally to the presentation
of the stimulus,
an observation that can be
attributed to attention and also to
preparatory effects of the motor
system preceding antisaccades (
Buschman and Miller, 2007 ;
McDowellet al., 2005)
21
Intro
Method
Results
Conclusions
Conclusions
Our methodology offers a novel framework for optimizing the
detection of Functional brain organization between two
conditions (or groups) using the notion of dynamic functional
brain networks
In the future, we will apply the methodology to data
from other other neuroimaging techniques as well (e.g.,
MEG, fMRI, MRI, DTI) and also to source reconstruction
techniques
The incorporation of causality measures and the replacement of
the over-simplifying notion of pairwise interactions with
multivariate synchrony should be considered in the future.
22
Intro
Method
Results
Conclusions
Further directions
Fusion of Fc estimators with different weight for
Constructing an aggregated FCG ?
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References
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