In the present study, 45 patients with schizophrenia syndromes and 39 healthy subjects are studied with electroencephalogram (EEG) signals. The study groups were of different genders. For each of the two groups, the signals were analyzed using 16 EEG channels. Multiscale entropy, Lempel-Ziv complexity and Lyapunov exponent were used to study the chaotic signals. The data were compared for two groups of subjects. Entropy was compared for each of the 16 channels for all subjects. As a result, topographic images of brain areas were obtained, illustrating the entropy and complexity of Lempel-Ziv. Lempel-Ziv complexity was found to be more representative of the classification problem. The results will be useful for further development of EEG signal classification algorithms for machine learning. This study shows that EEG signals can be an effective tool for classifying participants with symptoms of schizophrenia and control group. It is suggested that this analysis may be an additional tool to help psychiatrists diagnose patients with schizophrenia.
Schizophrenia is associated with disorders in the lobes and
areas of the brain, which are responsible for information
processing, temporary memory and executive functions [
However, quantifying and evaluating abnormalities in the
cerebral cortex can help to understand the mechanisms of such
psychotic disorders. Recent advances in the area of analysis of
complexity of time series provide insights into nonlinear
electroencephalogram (EEG) signals. [
with an increase of dynamic complexity. For example, randomized time series have a higher entropy than the original time series, since the process of generating of surrogate data reduces the correlation and worsens the information content of the original signal.
It is worth noting that many methods have been developed
for estimating the complexity of time series based on entropy
presented in the review [
Another common method for estimating of the complexity
of EEG signals is the Lempel – Ziv complexity - LZC. This
method
is non-parametric,
model-independent and
easily
calculated. In addition, it does not require long time series [
The oscillatory character by virtue of EEG is indicated of
the hypothesis that EEG signals originate from a nonlinear
dynamic system. Therefore, the unpredictability of the EEG can
be considered as a phenomenon characterized by randomness.
The essential property of chaotic dynamics is the so-called
sensitive dependence on the initial conditions. This property can
be quantified
by calculating the first positive
Lyapunov
exponent (L1) in the system [
The purpose of this study is to compare the signal complexity estimates obtained by the MSE, LZC methods and the Lyapunov senior exponent. It is suggested that nonlinear EEG analysis can be a useful tool in the analysis of EEG data for studying the neurodynamics of the brain of patients with schizophrenia.
Two EEG data archives were analyzed for two groups of subjects [http://brain.bio.msu.ru/eeg_schizophrenia.htm]. The subjects of the survey were adolescents who were tested by a psychiatrist and divided into two groups: healthy (n = 39) and with symptoms of schizophrenia (n = 45). Each file contains an EEG record for one subject. Each TXT file contains a column with EEG samples from 16 EEG channels, according to Fig.1. Signals were recorded by channels: 'F7', 'F3', 'F4', 'F8', 'T3', 'C3', 'Cz', 'C4', 'T4', 'T5', 'P3', ' Pz ',' P4 ',' T6 ',' O1 ',' O2 '. Each number in the column represented the EEG amplitude ( ) on a separate sample. The first 7680 samples represent 1 channel, then 7680 - channel 2, etc. The sampling rate is 128 Hz, so 7680 samples correspond to 1 minute of EEG recording.
The entropy calculation method MSE was presented in [
For a given discrete time series { 1, … , , … , } , the sequence is determined from the simplified time series { ( )} with respect to the scaling parameter . The original time series is divided into non-overlapping windows with a length , and then the values are averaged for each window. Thus, each element of the simplified time series is calculated by the formula ( ) = 1 =( −1) +1 , 1 ≤ ≤ / . cell size of the phase space (inaccuracy), ′ – the probability of repeating a sequence of data of a given length in the original data.
Lempel and Ziv proposed a measure of the complexity of
patterns for sequences of finite length [
= ( )/ ( ),
Lyapunov exponent give an estimate of the average exponential divergence or convergence of nearby trajectories in the phase space. Obtaining a positive value of the Lyapunov’s exponent is characterized by dependence on the initial conditions and shows that the system of interest is chaotic.
To calculate the Lyapunov senior exponent. L1, a modified
version of the Wulf algorithm was used [
For a comparative analysis of complexity (MSE, LZC, L1), the same EEG signals of two groups were studied. The average values for each of the EEG recording channels were calculated for the control group (norm) and patients with schizophrenia syndromes (sch). ). Statistical analysis based on P-value was used to compare methods of signal complexity. P-value is the probability that the criterion value will be not less than the critical value, provided that the null hypothesis about the absence of differences between groups is true. If the P-value was less than 0.05, the difference between the mean values was considered significant. Thus, the method that will show the largest number of channels with P<0.05 will be considered the most characteristic.
The results of calculation of MSE, LZC, L1 presented in EEG channels. Fig. 3 shows the visualization of the crosscorrelation function for both groups.
The proposed method of visual analysis of EEG allowed us to compare the interaction between the activity of brain regions. This approach makes it possible to evaluate the symmetry of activity on the basis of topographic images, to localize the activity centers and to correlate the activity of interaction between hemispheres by means of cross-correlation analysis.
The most characteristic EEG channels were selected for each method. Comparison of the methods for determining the signal complexity has shown that the most characteristic is LZC, because 5 significant channels were determined for this method.
The results will allow to implement the evaluation functionality with the use of machine learning for further research in medical diagnosis of schizophrenia. 5. Acknowledgements
This research was supported by the Ministry of Science and Higher Education of the Russian Federation, project No. 3.861.2017 / 4.6. 6. References