Go with the winner: optimizing detection of modular organization differences in dynamic

functional brain networks

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S.I. Dimitriadis, N.A. Laskaris, A. Tzelepi

AIIA-Lab, Informatics dept., Aristotle University of ThessalonikiElectronics Laboratory, Department of Physics,University of Patras

ICCS, National Technical University of Athens

Outline

MethodologyWe 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

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

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

Intro Method Results Conclusions

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Motivation and problem statement

-Inaccuracies can be more severe for fast-recordingmodalities, in particular for EEG/MEG and to a lesser extent for fMRI.

Our motivation was to present a method to qualify the employed descriptors in terms of the resulting functional community structure

The vast majority of previous studies have been based on analyzing the topological properties of static graphs

Intro Method Results Conclusions

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To alleviate the above limitations, we used time–varying graphs, which describe temporally evolving networks that have fixed nodes but changeable links

Outline of our methodology

Time-varying functional communities

We introduced a framework for detecting the synchronization measure that best describes and differentiates two conditions

Discriminability was measured for different types of coupling (linear vs. nonlinear) and different forms of covariation (amplitude/phase)

Specifically, we considered the multichannel EEG recordings during an attentive and passive eye movement taskas observations from two different states of the (same) brain,

Intro Method Results Conclusions

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Data acquisition: Visual ERP experiment

5 subjects64 EEG electrodesHorizontal and Vertical EOGTrial duration: 5.5 seconds2 runs, 50 trials for each condition

2 Conditions:•Attentive•Passive•(Left/right)

Intro Method Results Conclusions

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Exploratory Analysis – Contrast functionIntro Method Results Conclusions

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Two different sets of patterns/objects {Xi} and {Yj} can be compared in three steps.

The computed quantities are finally combined to express the set

difference,as follows:

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).

Statistical approach of J-indexThe statistical significance of a specific value for the J-index can be calculated based on a randomization procedure.

Intro Method Results Conclusions

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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

Quantify communities differencesIntro Method Results Conclusions

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Adopting a synchronization measure, we estimated the connectivity strength for each pair of signals

The set of patterns of the attentive task, at each latency t, can be compared against the set ofpatterns of the passive task

AtrialsN

BtrialsN

1 2 3 2 1 ….. 2 1 3 21 2 3 1 2 …. 2 1 3 2

Graph partition algorithm

N

Attentive Task

2 3 4 1 2 … 1 2 3 22 2 3 1 2 … 1 2 2 2

Passive Task

N

AtrialsN B

trialsN

Adjust J-index to community differencesIntro Method Results Conclusions

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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:

Where H(X) is the entropy of X and MI(X,Y) is the mutual information between X and Y (Meila, 2007)

),(2)()(),( YXMIYHXHYXVI

Adjust J-index to community differencesIntro Method Results Conclusions

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N Numerator & Denominator = J-index

Adjust J-index to dynamic community differences

Intro Method Results Conclusions

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Using the latency-dependent measurements Jt and the associated p-values (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)

Τhe functional connectivity graph (FCG) describes coordinated brain activity

To accommodate the various aspects of neural synchrony, we employed different functional connectivity estimators.

Intro Method Results Conclusions

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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

Time – varying FCGsIntro Method Results Conclusions

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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.

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 windowwas moved forward, and the whole network connectivitywas re-estimated based on the new signal segments

FCG -> TVFCGs

Intro Method Results Conclusions

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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

Task-induced differences in functional segregation (TICDI)

Intro Method Results Conclusions

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The ranking of synchronization measures according to TICDI was: COH < MI < PLI < WPLI < PLV

Functionally Segregated PatternsIntro Method Results Conclusions

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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.

Participation Index identified functional hubsIntro Method Results Conclusions

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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 is the sum of weights (links) of node i to nodes in module s, is the total strength of node i and 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

isw

s

isi wW

mN

Participation Index identified functional hubsIntro Method Results Conclusions

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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) andc) the eye – movement preparatory period until the initiation of the antisaccade (attentive condition) ([0.2 3.5]sec).

Brain rhythm interpretationIntro Method Results Conclusions

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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)

Participation Index identified functional hubsIntro Method Results Conclusions

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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)

ConclusionsIntro Method Results Conclusions

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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.

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Intro Method Results Conclusions

Further directions

Fusion of Fc estimators with different weight for Constructing an aggregated FCG ?

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References

[1] S.I.Dimitriadis, N.A. Laskaris, V.Tsirka, M.Vourkas, S.Micheloyannis and S.Fotopoulos,” Tracking brain dynamics via time-dependent network analysis,” Journal of Neuroscience Methods, vol.193,pp.145-155,2010. [2] Meila M (2007) Comparing clusterings-an information based distance.J Multivariate Anal 98:873–895[3]A. Von Stein and J. Sarnthein J, “Different frequencies for different scales of cortical integration: from local gamma to long-range alpha/theta synchronization,” Int. J. Psychophysiol., vol.38, pp.301–313,2000.[4]P. Sauseng,W.Klimesch, W.Stadler, M. Schabus,M. Doppelmayr M, S. Hanslmayr,W.R. Gruber and N. Birbaumer N, “A shift of visual spatial attention is selectively associated with human EEG alpha activity,” Eur. J. Neurosci. vol.22, pp.2917–2926, 2005. [5] T.J.Buschman, and E.K. Miller, “Top-down versus bottom-up control of attention in the prefrontal and posterior parietal cortices,” Science., vol.315, pp.1860–1862,2007.[6] J.E. McDowell,J.M. Kissler, P.Berg, K.A.Dyckman,Y. Gao, B. RockstrohB,et.al.,”Electroencephalography/magnetoencephalography study of cortical activities preceding prosaccades and antisaccades,”NeuroReport, vol.16, pp.663–668,2005.[7] Pavan M, Pelillo M (2007) Dominant sets and pairwise clustering.IEEE Trans PAMI 29(1):167–172

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