=Paper=
{{Paper
|id=Vol-2525/paper4
|storemode=property
|title=A structural approach to computer analysis of brain signals and its implementation in the decision support system
|pdfUrl=https://ceur-ws.org/Vol-2525/ITTCS-19_paper_10.pdf
|volume=Vol-2525
|authors=Yakov Furman,Viktor Sevastyanov,Konstantin Ivanov,Nataliya Glazunova
|dblpUrl=https://dblp.org/rec/conf/ittcs/FurmanSIG19
}}
==A structural approach to computer analysis of brain signals and its implementation in the decision support system==
https://ceur-ws.org/Vol-2525/ITTCS-19_paper_10.pdf
A Structural Approach to Computer Analysis of Brain Signals and Its
Implementation in the Decision Support System
Yakov A. Furman Viktor V. Sevastyanov Konstantin O. Ivanov
Volga State University of Volga State University of Technology Volga State University of
Technology Yoshkar-Ola, Russia Technology
Yoshkar-Ola, Russia SevastyanovVV@volgatech.net Yoshkar-Ola, Russia
FurmanYA@volgatech.net konstantin4002000@gmail.com
Nataliya U. Glazunova
Volga State University of Technology
Yoshkar-Ola, Russia
GlazunovaNU@volgatech.net
Abstract
The paper considers a number of issues related to modern quantitative
electroencephalography (EEG): the non-stationarity of the processed signal,
which reduces the accuracy of results due to the averaging effect of spectral
analysis methods used in computer EEG, and the unfeasibility of pattern
detection in the EEG composition without involving a clinician in the
analysis. The authors propose a structural (syntactic) approach to mitigate the
negative effects of these problems, as well as a mathematical apparatus for its
implementation. The paper discusses the results of using the proposed
approach for analyzing real EEG data.
1 Introduction
EEG signals serve as an objective and common source of information about a patient’s cerebral functioning in normal and
pathological conditions. An EEG test can show if there are such disorders as diffuse brain damage, traumatic brain injuries,
tumors, epilepsy, vascular diseases and mental, etc [1].
Despite the long-standing experience in the clinical use of EEG, the problem of its correct interpretation remains highly
relevant. At present, the main method of EEG interpretation is its visual analysis, which is rather time-consuming and
subjective as its results depend largely on the professional expertise of the clinician reading the EEG. The use of quantitative
methods for EEG analysis allows a greater degree of objectivity in the work of a neurophysiologist. Currently, these
methods are based on the spectral and correlation analyses [2]. Due to their frequency resolution, the methods allow us to
find out how detailed the signal spectrum is. However, weighted averaging of all signal counts causes loss of data on
heterogeneous patterns in the signal composition thus making their automatic classification impossible.
Frequency and time characteristics of the EEG signal can be obtained using the wavelet transform. One of the areas of
contemporary research into computer electroencephalography focuses on interpreting the wavelet transform coefficients in
terms of the functional state of the human central nervous system [3]. To date, studies in this area have been confined to
Copyright © 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0
International (CC BY 4.0).
either a verbal description of the EEG wavelet spectrum, or a description of a limited number of EEG patterns, such as
epiphenomena and sleep spindles, which is insufficient for making an informed decision on the nature of the entire EEG
record as a whole. Studies on the automatic classification of abnormal EEGs featuring non-epileptic kinds of deviation
from the norm are, in fact, unavailable.
Another feasible approach to EEG classification is the use of deep learning methods, in particular, the application of
convolutional neural networks to the entire EEG record without preliminary processing. The use of such approaches
requires the availability of extensive EEG databases, which would take into account all possible combinations of patterns,
at least for a specific pathology, as well as the access to significant computational resources [4]. For the moment, these
preconditions significantly hinder a comprehensive analysis of EEG using the methods of deep learning.
Therefore, irrespective of the widespread use of the EEG for monitoring the brain functional activity, there are still
major challenges associated with increasing its effectiveness. One of these problems is automatic classification
(recognition) of the EEG [5].
2 A structural approach to the analysis of the EEG
The problem of the automatic EEG classification may be addressed on the basis of a structural approach suggesting that a
recognizable pattern (EEG) is made up by linking together simple sub-patterns [6]. The brain’s bioelectrical activity is the
generation of oscillations in the frequency domain of 0.3÷50 Hz, which are divided into frequency bands of particular
activity types: delta, theta, alpha, beta, and gamma. In visual analysis, each frequency domain component is estimated by
determining the frequency and the amplitude of an individual oscillation [7]. Therefore, it is expedient that an individual
wave represented as a signal fragment between two consecutive global minima, should be taken as a primitive element.
To implement the structural approach, we have developed an EEG segmentation algorithm [8] which allows us to
represent the signal as an ordered sequence of segments, as well as algorithms for classifying EEG segments [9].
Classification of EEG segments is performed by calculating the informative features of their shapes used in visual analysis.
To obtain the quantitative characteristics of the segment shapes, a new contour model of EEG has been developed [10].
Thus, the approach proposed in this study is the computer-assisted equivalent of the visual analysis of EEG. Classification
of the entire EEG can be accomplished relying on the positioning of the previously classified EEG waves in relation to
each other. The software implementation of the proposed approaches to the EEG analysis is offered as a decision support
system (DSS) which forms a draft medical report containing results of the EEG segment classification. The study revealed
that the use of the DSS information on the signal by a neurologist increases the reliability of his clinical conclusions.
2.1 Contour model of the EEG
The theory of contour analysis has been developed over the past decade and is successfully applied for signal processing.
Based on the theory, it is possible to quantify the shapes of various images, determine the degree of their similarity
(difference) with regard to the images of two objects regardless of their scale and angular orientation [11]. Interpreting
EEG, in line with this area of mathematics, as a boundary of a particular image, we developed a novel mathematical model
of EEG, called the contour model of the electroencephalogram (Figure 1). To obtain the model, the consecutive digital
counts of the signal are connected by complex vectors ( n ) , n = 0, 1,..., K − 1, set in unitary space Ck :
( n ) = ts + iu ( n ) = ( n ) exp i ( n ) , n = 0, 1,..., k − 1, (1)
where t s - EEG sampling period, Δu(n) = u(n + 1) - u(n) is the first order difference of the digital samples U from the
output of the electroencephalograph, |γ(n)| and ψ(n) are, respectively, the module and argument of the elementary vector
(EV) γ(n). By analyzing the resulting contour model, it is possible to get information about the shape of each pulse of the
EEG fine structure [12].
Compared with the EEG model applied in practice as a sequence of real samples, the model (1) is more informative
since it takes into account the sampling interval of the signal, as well as due to the greater informativeness of the scalar
product (SP) operation in the space Ck . The greater SP informativeness in the space Ck in comparison with the real space
Rk is expressed in the presence of the imaginary component in the SP result, which allows us to find the degree of similarity
between two fragments of the EEG signal irrespective of their relative angular orientation.
U, μV u(2) u(9) U, μV γ(2)
u(3)
60 60 γ(1) γ(8)
u(1) γ(0) γ(3)
40 u(8) 40
u(4)
20 ts 20 ts γ(7)
7
0 0
1 2 3 4 5 6 8 -2 1 2 3 4 5 6 8 t×10-2, sec
-20 u(7) t×10 , sec -20
u(6) γ(4) γ(6)
-40 u(5) -40 γ(5)
a) b)
Figure 1: Towards the discrete contour model of EEG. a) continuous signal u = f (t), t = 0, 1, ..., 9;
b) vector sequence Г={γ(n)}𝑘0 approximating the EEG
2.2 Segmentation of the EEG
An algorithm has been developed for the EEG contour model decomposition into fragments limited by the points of global
minima. The segmentation algorithm can be represented as a sequence of the following steps:
Step 1: suppression of high-frequency signal components (up to 10 Hz) and the search for the boundaries between the
pulses in the form of local minima (Figure 2b)
Step 2: gradual expansion of the filter passband and search for the points of local minima in the vicinity of the
boundaries between the pulses found in the previous iteration.
Step 2 of the algorithm is performed until the filter passband reaches the value of 75 Hz (Figure 2d). Almost all the
energy of the EEG signal is concentrated in this frequency band; therefore, the shapes of the segments virtually do not
differ from their shapes in the original signal. The filter bandwidth is increased by 1 Hz at each iteration of the algorithm.
Figure 2: Changes in the oscillation pulse shapes occurring with variations of the bandpass f of the bandpass filter.
a) original oscillation; b) f = ( 0 8) Hz; c) f = ( 0 32) Hz; d) f = ( 0 75) Hz
To test the algorithm reliability, we obtained the probability estimates of correct segmentation of EEG waves in the
main frequency bands. For this, 42 EEG epochs with predominant activity in the delta range and 43 EEG epochs containing
oscillations in the theta range were selected from the open EEG database available at https://physionet.org/pn4/sleep-edfx/.
51 epochs containing oscillations in the alpha range and 28 epochs with activity in the beta range were acquired from the
database of the Republican Clinical Hospital (Yoshkar-Ola). The selected epochs were segmented; the segmentation
accuracy was tested by three neurological specialists. The segmented EEG epochs contained 650 delta waves, 554 theta
waves, 740 alpha waves, and 588 beta waves, of which 592, 520, 722 and 576 waves, respectively, had been segmented
correctly. Thus, the estimates of the correct EEG wave segmentation were 0.91, 0.94, 0.98, and 0.98 for
electroencephalograms in the δ, θ, α and β frequency bands, respectively [13].
2.3 Informative features for EEG segment classification that were obtained using the contour model
Based on the visual methodology of the EEG analysis, the following set of informative features is proposed for conducting
classification of each segment of the EEG (wave): 1) features of the segment shape: parameters of the segment extreme
points, the degree of pulse symmetry and angle values at each vertex of the pulse; 2) features of a segment envelope:
dimensionality of the segment contour, the signal amplitude, its minimum and maximum values; 3) time features: pulse
duration at the level of 0.707 of the range, at the level of the zero line, and at the base level; 4) frequency features - the
distribution of the signal energy across the EEG frequency bands (δ, θ, α, β1, β2, γ) (Figure 3) [9].
Figure 3: Informative features of the shape of a segmented EEG pulse
To evaluate the frequency properties of the EEG segment specified by the contour model, we obtained the analytical
relationships establishing the relation between the result of the Discrete Fourier transform (DFT) of the real samples and
the DFT of the contour model. In particular, the spectrum of a real signal can be obtained from the contour model spectrum
by using the expression:
Г ( m )
U ( 0 ) = 0, U ( m ) = , m = 1, 2,..., k − 1,
i ( 1 ( m ) − 0 ( m ) )
(2)
where Г ( m ) is the Discrete Fourier transform (DFT) of the EEG contour model, 0 ( m ) and 1 ( m ) are the elementary
contours of the zero and first order, which are determined by the expression:
k −1
2
m ( m )0
k −1
= exp i mn , m = 0, 1,..., k − 1.
k 0
Using the expression (2) for each segment, energy fractions of its spectrum are found in the main EEG frequency bands:
δ, θ, α, β1, β2, and γ.
Before calculating the remaining features, each segment undergoes the equalization procedure, which consists in
approximating the EEG curve by vectors of the same length; this helps to eliminate the influence of the vector length
variations on the results of computing the informative features of shapes.
As a rule, the shape of an EEG signal is distorted by random fluctuations, which does not allow us to estimate the
positions of the extreme points by reversing the sign of the EV imaginary components. To determine the positions of the
peaks (troughs) of an EEG segment, the use of a cross-correlation device (CCD) is proposed, the operation of which is
described by the expression:
m = (E( m, r ) , V ) / (|| E( m, r ) || || V ||) , m = 0, 1,..., k − r − 1, (3)
where E( = ( n )n = m is the filtered fragment of the contour E, V = v ( n )0 = il , 02 , − il is the reference pulse.
m, r ) m + r −1 r
The position of vertices is determined with
s = max (m | m thold ) + r 2 − 1, m = 0, 1,..., k − r − 1,
m
where r is the dimensionality of the reference pulse V, ηthold = 0.5 is the threshold value, which allows excluding the
influence of random fluctuations on the determination of the positions of vertices.
The expression (3) determines the degree of similarity between the shapes of the signal sections with the reference pulse
V. Representation of the signals E and V in the unitary space Ck allows one to find a higher value of the degree of similarity
compared to the real space, since ηm is invariant to the mutual rotation angle of E and V. The shape of the reference pulse
V provides the maximum CCD response when the position of its window coincides with the peak of the pulse due to the
sign change of the imaginary component of the vectors of one of the pulse segments edges (Figure 4). The calculation of
the degree of similarity is performed several times, and at each iteration, the dimension of the filter window (value l)
increases until η decreases, which provides a more accurate determination of the maxima positions due to the summation
of a larger number of EVs. The application of CCD allows a reliable determination of the positions of vertices (troughs) of
the EEG segments without changing their shape, in contrast to approaches based on preliminary filtering of the signal and
search for its derivative.
CCD can produce false values of the positions of extrema due to the difference in the values of lengths of the EVs of
the leading and trailing edges of the pulse, as is shown in Figure 4. To eliminate this effect, an equalization procedure is
preliminarily applied to each pulse, while keeping the number of its EVs unchanged.
γ( 10) γ(11) γ(21) γ(22)
γ(9) γ(12) γ(20) γ(23)
U, μV true position of U, μV
false pulse peak
position of 8 γ(7) 8
pulse peak Г Е
6 γ(6) 6
4 4
2 2
0 0
0 0.02 0.04 0.06 0.08 t, sec 0 0.02 0.04 0.06 0.08 t, sec
9 12
V={i , i , -i , -i} Г1={γ(n) }6 Г2={γ(n )}9 16
E1= {ε (n) }13
η1 = (Г1,V) = (γ(6), i) + ( γ(7), i) + (γ(10), i) ( γ(11), -i ) η3 = ( E1,V) = ( ε(20), i) + ( ε(21), i) +
+ (γ(8), -i) + ( γ(9), -i ) + (ε(22), -i ) + (ε( 23), -i )
( γ(9), i) (γ(12), -i )
( ε(23), -i )
(γ(9), -i ) (ε (20), i)
(γ(6), i) ( γ(7), i) η2 = (Г2,V) = (γ(9), i) + (γ(10), i ) +
(γ(8), -i ) + (γ(11), i) + ( γ(12), i) (ε( 21), i ) (ε(22), -i )
Re(η1) > Re(η2)
Figure 4: Illustration of the effect of a variation in changing the potential and erroneous determining of
positions of vertices by the CCD
The inevitable fluctuations of the EEG potentials in the region of the edges and the roof of the segment pulse are
represented as additional random vertices. Therefore, it becomes necessary to give a quantitative characterization of the
significance of each local extreme point of the EEG segment contour. For this purpose, the concept of the vertex status has
been introduced. Suppose a = {an} is a set of vertices of the EEG pulse, and b = {bn} is a set of points of global minima.
The status λ(an) quantitatively characterizes the position of an relative to the point bn (absolute status λ(an | bn) or relative
to the neighboring vertex an (relative status λ(an | an+1), n = 0, 1,…):
h ( an ) − h ( bn ) h ( an ) − h ( bn )
( an | bn ) = ; ( an | an +1 ) = , n = 1, 2,..., (4)
h ( an ) h ( an +1 )
where h(an) = Imβ(n), h(bl) = Imβ(l). If at least one of the statuses of the vertex an is lower than the threshold value of 0.15,
it is considered to be a slight fluctuation and is not taken into account in the classification of the entire segment.
In significant vertices of the pulse, the angles are determined:
s −1
t
an = − arccos ( n − l ), (n + r ), (5)
l = 0 n = 1
where s and t are the numbers of EVs to the left and to the right of the vertex an, respectively.
To assess the sinusoidality of the segment shape, it is necessary to determine the value of its normalized SP with a
contour of the same dimensionality that envelopes one period of a sinusoid with a phase shift of 3π/2.
To calculate the magnitude of the potential and the pulse duration values at given levels, a transition is made towards
the integral representation (IR) of the segment contour:
( n) = ( m −1) + ( m) , m = 0, 1,..., k −1, u (m) = Im (m).
m
( m) =
n =0
The pulse amplitude is calculated as the difference between the maximum and minimum values of the imaginary
components of its IR. The duration τ of an EEG pulse means the length of the horizontal segment, which is expressed in
time units and connects two points, one of which is located on the line of the leading edge of the pulse, and the other on
the line of its trailing edge. To estimate the pulse duration at a given level un, a search is performed in the contour IR to
identify the vectors β(l) and β(m), located on the left and right edges of the pulses, whose the imaginary parts are at a
smaller distance from the value un. In accordance with the value notations introduced, the pulse duration at the level un is
um = Im ( m ) = Re ( l ) − Re ( m ) , u 0, Im ( l ) − Im ( m) 0.
n
(6)
2.4 Classification of EEG segments based on quantitative features of shapes obtained using the contour model
The block diagram of the EEG segment classification algorithm is presented in Figure 5. In compliance with the
recommendations for the visual analysis methodology, each EEG segment is automatically classified according to the
degree of pathology significance as “normal”, “element of borderline EEG”, or “element of the pathology EEG”. The
segments are also classified according to the type of the EEG phenomena: a delta wave, a theta wave, an alpha wave, a
beta wave, a gamma wave, a spike, a sharp wave, a helmet-like wave, peak. EEG segments are classified by calculating
their informative feature and by comparing the features with the ranges of values for the classes considered [14].
The value ranges for the substantiated informative features were found for carrying out classification of the EEG
segments. The value ranges of the informative features intended for the phenomenological classification have been found
out using a sample containing 50 segments of delta waves, theta waves, alpha waves, beta waves, gamma waves, spikes,
sharp waves, helmet-like waves, and peaks. To classify the EEG segments according to the degree of their pathology
significance, the value ranges of their informative features were determined on a sample consisting of about 150 previously
classified EEG segments, in particular, for the normal EEG: 170 waves with predominant activity in the alpha range, 156
waves with activity in beta range, 149 delta waves, 151 theta waves; for the borderline EEG: 175 alpha waves, 186 waves
with activity in the beta1- and beta2-frequency band; for the pathology EEG: 146 theta waves, 166 delta waves, 175 spikes,
116 peaks, 191 sharp waves and 75 helmet-like waves. In both cases, we used EEG records obtained from the State
budgetary institution of the Republic of Mari El "Medical and Sanitary Unit №1". Three neurologists were engaged in the
classification of the EEG segments [13].
Calculation of shape Database of EEG
Pre-processing of features of the element parametres
the EEG segment Wr
Calculation of time
Classification of the
features of the
segment Wr according
segment Wr
Selection of EEG to its phenomenological
epoch description and degree
Calculation of features of pathology
of the segment Wr significance
kэп - 1
Гэп = {γ(n)}0 envelope
Calculation of
Formation of the
Segmentation frequency features of
R-1 medical report project
W = {Wr}0 the segment Wr
Figure 5: Block diagram of the EEG preprocessing algorithm for classification of EEG elements
3 Decision support system for EEG tests
The classification algorithms for EEG elements have been implemented in the decision support system (DSS) based on the
results of EEG tests. DSS was developed in C ++ using the Qt, OpenCV, and OpenGL libraries. The DSS interface is
shown in Figure 6.
Figure 6: Appearance of DSS based on EEG test results
The results of the analysis are presented to the doctor as a draft medical report containing information on the types of
the EEG phenomena occurring in the epoch, as well as on the degree of the pathology significance of the EEG elements,
with the parameters outside the norm being indicated. Based on the totality of classes of the EEG elements, the doctor
makes a decision on the class of the entire recording as a whole.
A comparative assessment of the results of EEG epoch classification was performed by a clinician with and without
using the proposed DSS. To this end, two samples of records of the EEG epochs were formed using the regulatory EEG
record databases placed in the public domain of the Internet at:
www.isip.piconepress.com/projects/tuh_eeg/downloads/tuh_eeg_abnormal/v1.1.2/, www.physionet.org/physiobank/data-
base/chbmit.
Each of the two samples contained 147, 140, and 160 epochs of the normal, borderline, and pathology EEGs,
respectively. Three clinicians participated in the assessment. Each of the doctors worked with the first sample without using
the DSS, and dealt with the second using the DSS. The comparative probability estimates of correct EEG classification for
both cases are presented in Figure 7.
Figure 7: Probability estimates for correct classification of EEG using and without using the proposed
DSS by three neurologists
The tests showed that the use of the EEG processing algorithms for providing the doctor with the information on the
types of EEG patterns can lead to an average increase in the accuracy of diagnosis from 0.86 to 0.92 for normal EEGs,
from 0.81 to 0.88 for borderline EEGs, and from 0.9 to 0.98 for EEGs indicating some pathology [13].
4 Conclusion
Algorithms for the classification of human EEG elements have been proposed on the basis of the quantitative characteristics
of the element shapes. In contrast to the spectral and correlation methods applied in practice, the proposed approach allows
the determination of the location of the EEG elements in time while keeping the information on the heterogeneous elements
of the EEG signal. Due to the use of the quantitative characteristics of the shapes of EEG elements, the proposed approach
simplifies the interpretation of the quantitative data obtained, and serves as a direct equivalent to the visual technique of
EEG analysis. The studies have shown that the proposed approach can increase the reliability of the clinical report made
by a neurologist. Further research will aim to develop structural methods for EEG analysis, which perform EEG
classification based on the relative positioning of the classified patterns in different EEG channels.
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