Analyzing Functional Brain Connectivity by means of Commute
Times: a new approach and its application to track event-related
dynamics
Stavros I. Dimitriadis,Nikolaos A. Laskaris, Tzelepi Areti, Economou
George
Electronics Laboratory, Department of Physics, University of Patras, Patras 26500, Greece
Artificial Intelligence & Information Analysis Laboratory, Department of Informatics, Aristotle
University, Thessaloniki, Greece
Institute of Communication and Computer Systems, National Technical University of Athens,
Greece
http://users.auth.gr/~stdimitr
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Outline
Introduction
-Multichannels EEG recordings
-eye movement task
-frequency range (4 – 10 Hz)
-time varying connectivity analysis
Methodology
-PLV
-Commute Times vs Shortest path length
-Single trial approach
- Cross –Validation scheme
2
Outline
Outline of the Methodology
Results
Discussion
3
Intro
Method
Results
Conclusion
s
Analyzing connectivity in time – varying approach can unfold the
“true dynamics” of brain functionality compared to static approach
There is growing interest in studying the association of functional
connectivity patterns with particular cognitive tasks.
The ability of graphs to encapsulate relational data has been
exploited in many related studies, where functional networks
(sketched by different neural synchrony estimators) are
characterized by a rich repertoire of graph-related metrics.
4
Intro
Method
Results
Conclusion
s
We introduce commute times (CTs) as an alternative way to capture
the true interplay between the nodes of a functional connectivity
graph (FCG).
Commute time is a measure of the time taken for a random walk
to set-out and return between a pair of nodes on a graph (Qiu &
Hancock,2007).
Its computation is considered here as a robust and accurate
integration, over the FCG, of the individual pairwise measurements
of functional coupling.
To demonstrate the benefits from our approach, we attempted
the characterization of time evolving connectivity patterns
derived from EEG signals recorded while the subject was engaged
in an eye-movement task.
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Intro
Method
Results
Conclusion
s
Motivation
We attempted to introduce a new way to capture the true
interplay between the nodes of FCG.
Employing Commute Times (CTs) to characterize connectivity,
an improved detection of event-related dynamical changes is
noticeable.
CTs appear to be a promising technique for deriving temporal
fingerprints of the brain’s dynamic functional organization.
6
Intro
Method
Results
Data acquisition:Resting state
Conclusion
s
7 subjects / 64 EEG electrodes
Horizontal and Vertical EOG
Trial duration: 5.5 seconds
Multi trial analysis
2 conditions:Attentive/Passive
Baseline period : 1 sec
Appearance of flashing checkerboard at time 0
After 4 sec the disappearance of the central fixation cross indicated the “go” signal and
subjects had to make a saccade towards the opposite side of the checkerboard
(antisaccade ; attentive) or doing nothing (passive).
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Intro
Filtering
Method
Results
Conclusion
s
Using a zero-phase band-pass filter (3rd order Butterworth filter),
signals were extracted within frequency range of 4 – 10 Hz
Artifact Correction
Working individually for each subband and using EEGLAB (Delorme
& Makeig,2004), artifact reduction was performed using ICA
-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
Conclusion
s
Artifact Correction
Muscle activity related ICs were identified based on statistical
terms (the kurtosis of derived timecourses was higher than a
predefined threshold, kurtthr=12), spectral characteristics
(increased energy in the frequency range of 20 – 60 Hz) and
topographies encompassing temporal brain areas (Delorme et al.,
2007).
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Intro
Method
Results
Conclusion
s
Constructing Functional Connectivity Graphs
FCGs were constructed by adopting PLV estimator.
Detecting Significant Couplings
Average approach
- Based on a Rayleigh test for the uniformity of PLV values, we
calculated the significance of each value
(Fisher, 1989)
significance is calculated as
- To correct for multiple testing, the false discovery rate (FDR)
method was adopted (Benjamini & Hochberg, 1995 )
- A threshold of significance was set such that the expected
fraction of false positives was restricted to q<= 0.01.
10
Intro
Method
Results
Conclusion
s
Detecting Significant Couplings
Single trial approach
- significant PLV values were determined after calculating
PLV for surrogates derived by randomizing the order of
trials in one of the channels of each pair (Lachaux et al.,
2000)
- Significance levels were then extracted from the z-scores
of the difference between PLV values in the original and
surrogate data.
- Significance probabilities were corrected using the false
discovery rate (FDR) method in order to correct for
multiple comparisons
- The expected fraction of false positives was restricted
again to q<= 0.01.
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Intro
Method
Results
Conclusion
s
Weighted shortest path length vs CTs
- We constructed an artificial five-module graph
- Scatter plot of Wspl with CTs
From this plot it is clear that Commute Time varies more smoothly
than the shortest path length and has also a wider range of
values.
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Intro
Method
Results
Conclusion
s
Tracking dynamical changes in functional
organization
The relative change of Frobenious norm (Fn) of CT matrix in the
attentive task was calculated, at every latency t, with respect to the
corresponding matrix from the passive task
To fully justify the merits of CTs, we replaced CT(t) timeseries with
W(t) and Wspl(t)
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Intro
Method
Results
Conclusion
s
Tracking dynamical changes in functional
organization
It is demonstrated that
functional connectivity
does change when
attention is employed as
early as 130 ms after
stimulus onset.
It is evident from Fig.4a,b that CTs facilitate the effortless and
accurate detection of (task-induced) changes in functional
organization.
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Intro
Method
Results
Conclusion
s
Tracking dynamical changes in functional
organization
It is demonstrated that
functional connectivity
does change when
attention is employed as
early as 130 ms after
stimulus onset.
It is evident from Fig.5a,b that CTs facilitate the effortless and accurate detection
of (task-induced) changes in functional organization.
CTs improved the detection of event-related dynamical changes with respect to
previous network descriptors (W & WSPL). In Fig.5 b) only CTs detected the
functional connectivity changes related to VEP (Visual Evoked Potential)
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Intro
Method
Results
Conclusion
s
Machine-Learning Validation
In order to justify further the previous finding about the role of attention, we
followed a machine learning methodology with the aim of showing that the
patterning of functional connectivity carries enough information to distinguish
between the attentive and passive responses
Using the latency tmax of best discrimination, as derived form the ‘across
trials’ computations and the identification of maximal difference in functional
connectivity (eq.1), we extracted the single-trial instantiations of functional
connectivity graphs.
Each connectivity matrix was first transformed to an input-vector of dimensionality [64x
63] (#sensors x (#sensors -1)) .
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Intro
Method
Results
Conclusion
s
Machine-Learning Validation
The initial dimensionality of connectivity patterns was reduced via kernel-PCA
(kPCA) (Schölkopf et al., 1999)
The classification scheme employed was a linear SVM with the cost
parameter C set as 10 (Schölkopf & Smola,2002 )
In order to achieve a reliable estimation of the generalization error, a 10-fold cross
validation scheme was adopted.
-Each subject’s trials were first split into 10 equal-sized subsets.
-Then for every fold, the classification error was measured based on a classifier
trained upon the data in the remaining 9 folds.
-After cyclically repeating this train-and-test procedure, the overall estimate of
classification performance was derived by averaging over the 10 folds.
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Intro
Method
Results
Conclusion
s
Machine-Learning Validation
Table 1. Classification performance regarding the task of discriminating attentive
vs passive brain responses based on the single-trial functional-connectivity
patterns. Left /Right column corresponds to trials in which the stimuli had
appeared on the left/right.
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Intro
Conclusions
Method
Results
Conclusion
s
The suggested methodology incorporates CTs for tracking event-related
functional-connectivity pattern
Its demonstration was based on experimental data from a paradigm that both
induced evoked responses and triggered decision making.
The evoked responses consist of early and late components
-The former correspond to activation of the sensory cortex specific to each
type of stimulus and the latter, to activation of the association cortex
- That is, the former enable identification of the mechanism of simple
sensory and the latter of higher functions.
In the present study, we showed a functional organization of the network due to the
late component of the VEP (~130 ms) (see Fig. 4a,5a) and especially in brain areas
contralateral to the presentation of the visual-stimulus
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Intro
Conclusions
Method
Results
Conclusion
s
A study combining MEG-measurements with source reconstruction has recently
advanced our knowledge about spatial/nonspatial attention and its relation to
visual and auditory stimuli (Poghosyan & Ioannides,2008 )
Spatial selective attention has been shown to influence the early sensory
processing stages (Poghosyan & Ioannides,2008 )
Here it is important to stress that the effect of attentional modulation
cannot be seen in the EEG-signals (see Fig2), but can be easily detected in
the pattern of functional connectivity (Fig.4b,5b).
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Intro
Method
Results
Conclusions
We addressed two important problems in neuroimaging functional
Conclusion
s
neuroscience and connectomics:
-The first is the reliable estimation of information exchange among distinct brain
areas by means of pairwise measurements of functional dependence based on
the recorded signals.
-The second is the detection of significant changes in time-evolving connectivity
patterns and its association with neural processes underlying cognition.
We demonstrated the benefits of Commute Times, an algorithmically
tractable graph analytic approach that is well suited to weighted graphs and
therefore directly applicable to real-valued connectivity data without the
need for binarization
Finally, the introduced analysis can be applied, as well, to connectivity patterns
from well-localized brain activity (reconstructed EEG/MEG, fMRI, etc.).
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