A novel symbolization scheme for multichannel recordings

with emphasis on phase information and its applicationto 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, GreeceArtificial Intelligence & Information Analysis Laboratory, Department of Informatics, Aristotle University, Thessaloniki, GreeceMedical Division (Laboratory L.Widιn), University of Crete, 71409 Iraklion/Crete, GreeceTechnical High School of Crete, Estavromenos, Iraklion, Crete, Greece

http://users.auth.gr/~stdimitr

[a b b c d e a b … ]

Phase dynamics Φ

1

OutlineIntroduction-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

2

Outline of the Methodology

Results

Outline

3

Discussion

Intro Method Results Conclusions

Symbolic dynamics is a powerful tool forstudying complex dynamical systems

Many techniques of this kind have been proposed as a means toanalyze brain dynamics

but most of them are restricted to single-sensor measurements

4

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.

Intro Method Results Conclusions

MotivationWe suggest, here, the use of neural-gas algorithm (Martinez et al. in IEEE Trans Neural Netw 4:558–569, 1993) for encoding brain activityspatiotemporal dynamics in the form of a symbolic timeseries.

We intended to introduce the first multichannel approach for symbolization brain dynamics.

5

Multichannel symbolization can unfold the “true” complexity of brain functionality !!

Intro Method Results Conclusions

Outline of our methodology

6

Data acquisition: Math Experiment

Intro Method Results Conclusions

3 Conditions:ControlComparisonMultiplication

18 subjects30 EEG electrodesHorizontal and Vertical EOGTrial duration: 3 x 8 secondsSingle trial analysis

The recording was terminated when at least an EEG-trace without visible artifacts had been recorded for each condition7

Intro Method Results Conclusions

Using a zero-phase band-pass filter (3rd order Butterworth filter), signals were extracted within six different narrow bands ( from 4 to 45 Hz)

Filtering

Artifact CorrectionWorking individually for each subband and using EEGLAB (Delorme & Makeig,2004), artifact reduction was performed using ICA

8

-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.

Neural-Gas algorithmNeural-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.

)(1 tiki

ktik

tik e pxpp

Intro Method Results Conclusions

9

Intro Method Results Conclusions

Neural-gas based symbolizationTransform a multichannel dataset into a symbolic sequence

The reconstructed version of is denoted as

10

A codebook of k code vectors is designed by applying the neural-gas algorithm1 to the data matrix dataX

dataXData

RX

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 producedwith the smallest k and simultaneously satisfied the condition that should be less than 8%.

Distortionn

Intro Method Results Conclusions

11

& estimationobsP expPWe first estimated the observed probability (a, b) that symbol a is followed by symbol b within the symbolic timeseries s(t).

obsP

To detect the significantly correlated appearance of symbols, we need to estimate theprobability 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:

Intro Method Results Conclusions

12

Transform to expN expP

Computing for all the pairs of k symbols, we construct a co-occurence matrix CM.

expN

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.

expN expP expN

As a result, the sum of each raw of the new matrix will be equal to 1 and will now tabulated values.

expP

A weight 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

abw

0.9

0.6

Building the codebook network

Establishing links between each pair of symbols

Intro Method Results Conclusions

13

The process is repeated for every pair of symbols, creating a codebook network with possible misconnections that correspond to forbidden patterns

Intro Method Results Conclusions

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).

14

Computing the GE of the codebook network

Intro Method Results Conclusions

Different signal representations

15

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:

Intro Method Results Conclusions

Differentiation of task-related brain dynamics

The statistical analysis of GE-values showed that phase representation was the most suitable one for detecting taskrelated changes in brain dynamics.

To summarize across subjects, the computed set of GE-pairs were analyzed via the Wilcoxon-test (P < 0.001).

16

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 eachsubject.

Intro Method Results Conclusions

Global efficiency (GE) averaged values corresponding to the three possible comparisons

17

ConclusionsA 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.

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.

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).

Intro Method Results Conclusions

18

Moreover, our approach shares the ‘prototyping’ step with the pioneer work of segmenting brain activity into functional microstates (Pascual-Marqui et al. 1995).

Among the outcomes of this study was that during multiplication GE values are higher than during comparison (for all frequency bands).

19

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

20