=Paper=
{{Paper
|id=Vol-2212/paper11
|storemode=property
|title=On an approach to assessing the inter-channel phase synchronization of electroencephalogram signals
|pdfUrl=https://ceur-ws.org/Vol-2212/paper11.pdf
|volume=Vol-2212
|authors=Yury Obukhov,Renata Tolmacheva,Alexandr Polupanov,Ludmila Zhavoronkova
}}
==On an approach to assessing the inter-channel phase synchronization of electroencephalogram signals ==
https://ceur-ws.org/Vol-2212/paper11.pdf
On an approach to assessing the inter-channel phase
synchronization of electroencephalogram signals
Y V Obukhov1, R A Tolmacheva1, A F Polupanov1 and L A Zhavoronkova2
1
Kotelβnikov Institute of Radioengineering and Electronics of RAS, Mokhovaya 11-7,
Moscow, Russia, 125009
2
Institute of Higher Nervous Activity and Neurophysiologyof RAS, Butlerova 5a, Moscow,
Russia, 117485
Abstract. A new approach to evaluation of the phase coherence of electroencephalogram
(EEG) signals in different channels based on the calculation and comparison of definite phase
characteristics of signals at the points of the ridges of their wavelet spectrograms is considered.
The approach is applied to evaluation of inter-channel phase coherence of EEG signals at
cognitive tests performed for a healthy subject and for a patient after a traumatic brain injury.
The method makes possible to efficiently detect phase-coupled pairs of channels of EEG and
distinguish them from phase-uncoupled ones.
1. Introduction
The study of EEG inter-channel coherence is a conventional method for diagnosing brain pathologies.
Phase connectivity or phase synchronization of signals in two EEG channels is evaluated with the help
of the coherence. Typically [1-3], the coherence of two signals is estimated using their normalized
complex cross-correlation calculated by multiplying the normalized Fourier components of the signals.
The coherence between the two channels of the EEG is defined as the linear dependence of two
signals at a certain frequency [2]. Let π₯π₯ππ (ππ) and π₯π₯ππ (ππ) are the complex Fourier transformations of time
series and of channels i and j, respectively. Then the cross-spectrum is defined as:
ππππππ (ππ) = β©π₯π₯ππ (ππ)π₯π₯ππβ (ππ)βͺ (1)
where * is the complex conjugation and <> is the mathematical expectation.
Coherence is defined as a normalized cross-spectrum [2]:
ππππππ (ππ)
πΆπΆππππ (ππ) = (2)
(ππππππ (ππ)ππππππ (ππ))1 β2
and the connectivity is defined as the absolute value of the coherence:
πΆπΆπΆπΆβππππ (ππ) = οΏ½πΆπΆππππ (ππ)οΏ½ (3)
The phase connectivity is calculated using the phases of the signals i and j. If π₯π₯ππ = ππππ expβ‘ (ππΠ€ππ ) and
π₯π₯ππ = ππππ exp(ππΠ€ππ ) are Fourier transforms of the signals, then the cross-spectrum is calculated as [2]:
ππππππ (ππ) = β©ππππ ππππ expβ‘ (ππβΞ¦)βͺ (4)
where βΠ€ = Π€ππ β Π€ππ is the phase difference of signals in channels i and j at a certain frequency.
In order to calculate the phase connectivity, the cross-spectrum is normalized to the 'global'
amplitudes β©ππππ2 βͺ1/2 and β©ππππ2 βͺ1/2. If the signals in the two channels are independent, then βΠ€ is a random
number and the connectivity is equal zero. Phase connectivity or phase synchronization is defined as
an unweighted average:
ππ = β©expβ‘(ππβΞ¦)βͺ (5)
Further, the phase difference is averaged over a certain frequency range predetermined from the
neurophysiological considerations. Usually these are the ranges corresponding to the EEG rhythms,
such as delta, theta, alpha, etc. rhythms. Phase-coupled pairs of brain regions are received by
IV International Conference on "Information Technology and Nanotechnology" (ITNT-2018)
Data Science
Y V Obukhov, R A Tolmacheva, A F Polupanov and L A Zhavoronkova
calculating the averaged phase difference between all pairs of signals and selecting the cut-off
threshold.
The averaging of the coherence or the phase difference for different time periods and in the
frequency range predetermined on the basis of neurophysiological experience is done in the coherent
analysis. Shortcomings of this approach are considered in [4]. In this regard, the actual task is the
development of the method for determining the phase-coupled pairs of signals from single trial data
and for a more sustainable choice of the phase coherency threshold.
We consider a new approach to the evaluation of phase synchrony of non-stationary EEG signals in
cognitive tests. As a criterion of phase synchronization of two signals the following condition [5] is
considered:
Ο i , j (t ) β€ const (6)
where Ο i=
, j (t ) nΟ i (t ) β mΟ j (t ) , Ο is the phase of the signal, n, m are integers.
We consider the case n = m = 1, which can easily be generalized to the case of any ππ β ππ.
2. Method description
A method of evaluation of the inter-channel phase coherence of EEG signals is based on the
calculation and comparison of definite phase characteristics of signals in different channels at the
points of the ridges of their wavelet spectrograms. In case the signal satisfies asymptotic properties,
the wavelet transform can be approximated in the stationary phase approximation, the points of ridges
are the points of the stationary phase where the instantaneous frequency of the signal is equal to the
wavelet frequency [6, 7].
At first we find a ridge with the maximum value of |W| at each reference point of the Morlet
wavelet spectrogram:
1  t βΟ ο£Ά
W( Ο ,T) =
T β« x(t)Ο ο£¬
ο£ T ο£Έ
ο£·dt , (7)
Ξ·2
1 β
Ο (Ξ· ) = e 2 iΟ FcΞ· e Fb , (8)
Ο Fb
where we accept Fb = Fc = 1 [8].
Further, at the points of the ridge we calculatethe phase characteristic of
the signal which is defined as a product of the instantaneous frequency of the signal at the time ti and
time: and the difference for two signals.
In this case points beyond the ridge of the wavelet spectrogram are not taken into account in the
evaluation of the phase coherency. Some points of the ridges may not satisfy the asymptotic
conditions, which will lead to errors in the calculation of the phase. However, this error seems to be
substantially less than errors associated with averaging the phase difference in a wide frequency range.
By removing the frequency range of the processed ridge in the wavelet-spectrogram, we can further
apply the described algorithm to distinguish another ridge (in another frequency range, etc.).
3. Results
Histograms of the values of portions , where is number of reference points of ridges
with , and N is a summary number of EEG signal reference points during the test, are
represented in Figure 1. The first pair of leads (Figure 1a) can be referred to a phase-coupled pair.
Another pair (Figure 1b) can be referred to a phase-unconnected pair. Figure 1a shows, that , less
than 0.1, can be considered as a background. We consider the threshold equal to 0.15 and we
will assume that above this value of the points portions the ridge correspond to the phase-coupled pairs
of leads.
EEG of healthy subjects were analyzed, which performed cognitive tasks in isolation. Below, for
example, the results of the phase connectivity analysis are presented for two cognitive tests. Some
items that belong to the category "clothes" or "food" were randomly listed to the subject during the
cognitive test (CT1). During the test, he counts in his mind the quantity of items belonging to one of
these categories, and at the end of the test declares the result. When performing a cognitive test (CT2),
IV International Conference on "Information Technology and Nanotechnology" (ITNT-2018) 85
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Y V Obukhov, R A Tolmacheva, A F Polupanov and L A Zhavoronkova
the doctor randomly called the time.The test subject must imagine in his mind the dial of the clock and
the position of the clock hands on it in accordance with the time mentioned. If both clock hands are in
the same half of the dial, he says "yes," and if they are in different halves, he keeps silent. All tests
were performed for 60 seconds.
Distribution graphs of the portions of the reference points for pairs of EEG leads, based on the
histograms obtained, were built and they were sorted in order of increasing with EEG records
without tests, with cognitive tests. These distributions are shown in Figure 2 for a healthy subject and
for a patient after a traumatic brain injury.
The distribution of the portions of the reference points by pairs of EEG leads, sorted in ascending
order for certain tests correspond to lines of a certain color (blue line: recording EEG without test;
red line: record EEG with cognitive test CT1; lilac line: recording of EEG with cognitive test CT2).
The abscissa axis shows the number of pairs of EEG leads. In the article records of 19-channel EEG
were analyzed, therefore the number of pairs of leads is 171. Figure 2 represent that for a certain value
on the abscissa axis for each test corresponds, possibly, a different pair of EEG leads. Based on the
obtained pairs of EEG leads, it is calculate the number of pairs of leads for each test above the
threshold and it can be concluded that for a healthy subject the number of such pairs is higher
with cognitive tests than when record is without a test (CT1: = 131, number of coupled pairs of
EEG leads: 171-131=40; CT2: =130, number of coupled pairs of EEG leads: 171-130=41; record is
without test: =150, number of coupled pairs of EEG leads: 171-150=21 (figure 4). As well as,
according to figure 3, it is possible to =144, number of coupled pairs of EEG leads: 171-144=27).
Pairs of EEG leads in a healthy subject with a cognitive test CT1 are given as an example on the
figure 3a. These pairs of leads are absent when EEG record is without test. Pairs of EEG leads in a
healthy subject with a cognitive test CT2 are given as an example on the figure 3b. These pairs of
leads are absent when EEG record is without test. Pairs of EEG leads in a patient with craniocerebral
trauma with a cognitive test CT1 are given as an example on the figure 3Ρ.
a) b)
Figure 1. Wavelet spectrogram of the Morlet signal in a pair of EEG leads with a cognitive test with
aselected ridge: a)For one lead. b) For the second lead. The abscissa axis is the time in seconds, the
ordinate axis is the frequency in Hz, the color isproportinal to the power spectral density (red - max).
a) b)
Figure 2. The distribution of the portions of the reference points for pairs of EEG leads, sorted in
ascending order ππππ,ππ . The abscissa is the number of the pair of EEG leads that correspond to different
pairs of EEG leads. Π°) healthy subject; Π±) patient with craniocerebral trauma.
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Y V Obukhov, R A Tolmacheva, A F Polupanov and L A Zhavoronkova
Π°) b)
c) d)
Figure 3. Distinctive pairs of EEG leads in cognitive tests CT1 and CT2 in a 4 healthy subjects: (Π°) β
CT1, (b) β CT2; 2 patients with craniocerebral trauma: (Ρ) β CT1, (d) β CT2.
These pairs of leads are absent when EEG record is without test. Pairs of EEG leads in a patients
with craniocerebral trauma with a cognitive test CT2 are given as an example on the figure 3d. These
pairs of leads are absent when EEG record is without test.
According to [9] the test CT1 is accompanied by a predominant activation of the prefrontal areas of
the left hemisphere and the test CT2 is accompanied by a predominant activation of the prefrontal
areas of the right hemisphere.
The distinctive phase-coupled pairs of leads demonstrate this (figure 3a and figure 3b).
4. Conclusion
The proposed approach improves the calculation of phase synchronization of EEG signals in order to
get rid of the shortcomings of the existing estimates of coherence, related to the necessity of averaging
the estimates over a wide range of frequencies. The method is tested in the problem of analysis of
inter-channel phase synchronization in cognitive tests by healthy subjects and patients after
craniocerebral injuries. The number of phase-coupled of the EEG leads is about the same as with
cognitive tests for patients after craniocerebral injuries than when record is without a test.
5. References
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connectivity: a model-based evaluation of interdependence measures J of Neuroscience Methods
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Y V Obukhov, R A Tolmacheva, A F Polupanov and L A Zhavoronkova
[2] Nolte G, Bai O, Wheaton L, Mari Z, Vorbach S and Hallet M 2004 Identifying true brain
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[6] Mallat S A 2009 Wavelet Tour of Signal Processing (Elsevier Inc.)
[7] Guilleemain P and Kronland-Martinet R 1996 Characterization of Acoustic Signals Through
Continuous Linear Time-Frequency Representations Proceedings of the IEEE 84(4) 561-585
[8] Daubechies I 1992 Ten lectures on Wavelets (SIAM) p 194
[9] Zhavoronkova L, Shevtsova T and Maksakova O 2017 How the human brain simultaneously
solves two problems (SaarbrΓΌcken: LAP LAMBERT Academic Publishing) p 68 (in Russian)
Acknowledgments
The reported study was funded by RFBR according to the research project β 18-07-00609.
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