Transcript What does delta band tell us about cognitive processes: A

A novel symbolization scheme for multichannel
recordings
with emphasis on phase information and its application
to differentiate EEG activity from different mental tasks
Stavros I. Dimitriadis,Nikolaos A. Laskaris, Vasso Tsirka, Sofia Erimaki,
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
Phase dynamics Φ
[a b b c d e a b … ]
http://users.auth.gr/~stdimitr
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Outline
Introduction
-Multichannels EEG recordings
-math calculations (control, comparison and multiplication)
-multifrequency approach (from θ to γ)
-symbolic dynamics in a multichannel fashion
Methodology
-Neural
gas for symbolization
-Different signal presentations (filtered signals, instantaneous
amplitude and phase)
-Network representation of neural-gas based symbolic dynamics
-Compute directed GE (global efficiency)
- Compare GE between the three possible pairs of conditions
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Outline
Outline of the Methodology
Results
Discussion
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Intro
Method
Results
Conclusion
s
Symbolic dynamics is a powerful tool for
studying complex dynamical systems
Many techniques of this kind have been proposed as a means to
analyze brain dynamics
but most of them are restricted to single-sensor measurements
Analyzing the dynamics in a channel-wise fashion is an invalid
approach for multisite encephalographic recordings, since it
ignores any pattern of coordinated activity that might emerge
from the coherent activation of distinct brain areas.
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Intro
Method
Results
Conclusion
s
Motivation
We suggest, here, the use of neural-gas algorithm (Martinez et al. in IEEE
Trans Neural Netw 4:558–569, 1993) for encoding brain activity
spatiotemporal dynamics in the form of a symbolic timeseries.
We intended to introduce the first multichannel approach for
symbolization brain dynamics.
Multichannel symbolization can unfold the “true” complexity
of brain functionality !!
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Intro
Method
Results
Conclusion
s
Outline of our methodology
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Intro
Method
Data acquisition: Math
Experiment
3 Conditions:
Control
Comparison
Multiplication
Results
Conclusion
s
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 condition7
Intro
Filtering
Method
Results
Conclusion
s
Using a zero-phase band-pass filter (3rd order Butterworth filter),
signals were extracted within six different narrow bands ( from 4 to 45
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
Neural-Gas algorithm
Neural-Gas algorithm provides input space representations
by constructing data summaries ( via prototypical vectors ).
Its a gradient descent procedure imitating gas dynamics
within data space to calculate the prototypes.
p
t 1
ik
 p  e
t
ik
k

 (x i  p tik )
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Intro
Method
Results
Conclusion
s
Neural-gas based symbolization
Transform a multichannel dataset into a symbolic sequence
A codebook of k code vectors is designed by applying the neural-gas
algorithm1 to the data matrix X data
The reconstructed version of X data is denoted as
X RData
To compute the fidelity of the overall encoding procedure,an index which is
the total distortion error divided by the total dispersion of the data is adopted:
In the present study,we considered as acceptable encoding the one produced
with the smallest k and simultaneously satisfied the condition that nDistortion
should be less than 8%.
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Intro
P
obs
&
P
Method
Results
Conclusion
s
exp estimation
P
We first estimated the observed probability
symbol b within the symbolic timeseries s(t).
obs
(a, b) that symbol a is followed by
To detect the significantly correlated appearance of symbols, we need to estimate the
probability of random co-occurrence of these two symbols.
We denote as p(a) and p(b) the probabilities of finding the two symbols in s(t).
The symbol a can occupy positions ranging fromthe first to the (T - 1)th
position,where T is the length of s(t). For each fixed position i of a, with i = 1, …,
(T - 1), there are (T – 1 - i) possible positions for b to appear in the sequence.
Hence, the number of possible transitions a -> b within s(t) is given by the
equation:
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Intro
Transform
exp
N
Computing
matrix CM.
to
N exp
N
exp
P
Method
Results
Conclusion
s
exp
for all the pairs of k symbols, we construct a co-occurence
P
exp
N
exp
To transform
to
, we first sum the
values of each raw of
the CM and then we divide each element of the raw with the sum.
As a result, the sum of each raw of the new matrix will be equal to 1 and will
exp
now tabulated
values.
P
w
A weight ab can be associated with the link from a to b, based on the
extent to which the number of observed transitions deviates from the
expected value
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Intro
Method
Results
Conclusion
s
Building the codebook network
Establishing links
between each pair of symbols
0.9
0.6
The process is repeated for every pair of symbols,
creating a codebook network with possible
misconnections that correspond to
forbidden patterns
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Intro
Method
Results
Conclusion
s
Computing the GE of the codebook
network
Its values range between 0 and 1, with high values indicating an
increased (with respect to randomness) number of state transitions,
and hence a highly non-stable system (Latora and Marchiori 2001).
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Intro
Method
Different signal representations
Results
Conclusion
s
Apart from the frequency range, we tested extensively if the (filtered) signal in its
original form, or in a form that either emphasizes amplitude or phase dynamics,
facilitates better the differentiation between different recording conditions.
We applied the Hilbert transform (Cohen 1995), which returns the instantaneous
amplitude A(t) and instantaneous phase φ(t) and is defined as follows:
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Intro
Method
Results
Conclusion
s
Differentiation of task-related brain dynamics
The new symbolization scheme, followed by the codebooknetwork analysis, was
applied, in a contrastive fashion, for all possible pairs of recording conditions
(control—comparison, control—multiplication and comparison—multiplication).
For every frequency band and each of the three different signal representations
(i.e. x(t), A(t), u(t)), the pair of GE-measures was derived independently for each
subject.
To summarize across subjects, the computed set of GE-pairs were analyzed via the
Wilcoxon-test (P < 0.001).
The statistical analysis of GE-values showed that phase representation was the most
suitable one for detecting taskrelated changes in brain dynamics.
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Intro
Method
Results
Conclusion
s
Global efficiency (GE) averaged values
corresponding to the three possible comparisons
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Intro
Method
Results
Conclusions
Conclusion
s
A symbolization scheme capable of handling multichannel recordings of brain
activity and useful for contrasting dynamics from different conditions was
introduced and applied to EEG data from mental calculations.
Among the outcomes of this study was that during multiplication GE
values are higher than during comparison (for all frequency bands).
Considering the emerging patterns of coordinated activity as an important aspect of
underlying mechanisms, we developed a symbolic dynamics methodology that
respects brain’s multistable character.
Moreover, our approach shares the ‘prototyping’ step with the pioneer work of
segmenting brain activity into functional microstates (Pascual-Marqui et al. 1995).
Our scheme can be readily adapted to various recording modalities (MEG, Fmri
etc.) and used for comparing dynamics between healthy and diseased brains
and based on a variety of different representations (e.g. Network metrics time
series; Dimitriadis et al. 2010a).
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References
[1]Dimitriadis SI, Laskaris NA, Tsirka V, Vourkas M, Micheloyannis S (2010a)
Tracking brain dynamics via time-dependent network analysis. J Neurosci Methods
193:145–155
[2]Latora V, Marchiori M (2001) Efficient behaviour of small-world networks. Phys
Rev Lett 87:198701
[3]Martinez T, Berkovich S, Schulten K (1993) Neural-gas network for vector
quantization and its application to time-series prediction. IEEE Trans Neural Netw
4:558–569
[4]Pascual-Marqui RD, Michel CM, Lehmann D (1995) Segmentation of brain
electrical activity into microstates: model estimation and validation. IEEE Trans
Biomed Eng 42:658–665
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