Complexity of EEG Signals in Schizophrenia Syndromes I.E. Kutepov1, V.A. Krysko1, A.V. Krysko1, S.P. Pavlov1, M.V. Zigalov1, I.V. Papkova1, O.A. Saltykova1, T.Y. Yaroshenko1, E.Y. Krylova2, T.V. Yakovleva1, V.V. Dobriyan1, N.P. Erofeev1 ilyakutepov@yandex.ru 1 Yuri Gagarin State Technical University of Saratov, Saratov, Russia; 2 Saratov State University, Saratov, Russia 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. Keywords: entropy, chaos, EEG classification, schizophrenia, Lyapunov exponent. 1. Introduction Schizophrenia is associated with disorders in the lobes and The oscillatory character by virtue of EEG is indicated of areas of the brain, which are responsible for information the hypothesis that EEG signals originate from a nonlinear processing, temporary memory and executive functions [3]. The dynamic system. Therefore, the unpredictability of the EEG can diagnosis of schizophrenic spectrum disorders and other be considered as a phenomenon characterized by randomness. psychotic disorders is challenging. The scientific community is The essential property of chaotic dynamics is the so-called constantly working to integrate the latest clinical and scientific sensitive dependence on the initial conditions. This property can advances in the field of psychiatry into diagnostic and statistical be quantified by calculating the first positive Lyapunov manuals. [5] exponent (L1) in the system [8]. Studies [10] showed that However, quantifying and evaluating abnormalities in the patients with schizophrenia, the values of Lyapunov's senior cerebral cortex can help to understand the mechanisms of such exponent were lower in the left lower frontal and anterior psychotic disorders. Recent advances in the area of analysis of temporal areas compared with the control group. complexity of time series provide insights into nonlinear The purpose of this study is to compare the signal electroencephalogram (EEG) signals. [1]. The complexity of complexity estimates obtained by the MSE, LZC methods and time series can be investigated by using several measures, for the Lyapunov senior exponent. It is suggested that nonlinear instance, Approximate Entropy or Sample Entropy - SampEn. EEG analysis can be a useful tool in the analysis of EEG data Traditional entropy-based algorithms quantitatively determine for studying the neurodynamics of the brain of patients with the regularity (ordering) of a time series. Entropy rises as the schizophrenia. degree of irregularity increases and is maximum for completely random systems. However, an increase of entropy is not always associated with an increase of dynamic complexity. For 2. Methods. example, randomized time series have a higher entropy than the original time series, since the process of generating of surrogate 2.1. Subject of research. data reduces the correlation and worsens the information content Two EEG data archives were analyzed for two groups of of the original signal. subjects [http://brain.bio.msu.ru/eeg_schizophrenia.htm]. The It is worth noting that many methods have been developed subjects of the survey were adolescents who were tested by a for estimating the complexity of time series based on entropy psychiatrist and divided into two groups: healthy (n = 39) and presented in the review [6], but preference is given to Multiscale with symptoms of schizophrenia (n = 45). Each file contains an Entropy - MSE. Multiscale entropy relies on sample entropy EEG record for one subject. Each TXT file contains a column calculations at different scales: the MSE algorithm uses the with EEG samples from 16 EEG channels, according to Fig.1. SampEn algorithm to analyze time series that represent the Signals were recorded by channels: 'F7', 'F3', 'F4', 'F8', 'T3', 'C3', system dynamics at various levels. Multiscale entropy has 'Cz', 'C4', 'T4', 'T5', 'P3', ' Pz ',' P4 ',' T6 ',' O1 ',' O2 '. Each become the predominant method for quantifying the complexity number in the column represented the EEG amplitude (πœ‡π‘‰) on a of signals. This method has been successfully used in various separate sample. The first 7680 samples represent 1 channel, fields of research, including biomedical time series [2]. The then 7680 - channel 2, etc. The sampling rate is 128 Hz, so 7680 disadvantages of this method include: a discrete representation samples correspond to 1 minute of EEG recording. of a signal of continuous nature (significantly affects on the 2.2. Multiscale Entropy entropy estimate), signal length, presence of noise, selection of The entropy calculation method MSE was presented in [2]. parameters (length of the analyzed sequence, cell size of the For a given discrete time series {π‘₯1 , … , π‘₯𝑖 , … , π‘₯𝑁 } , the phase space). sequence is determined from the simplified time series {𝑦 (𝜏) } Another common method for estimating of the complexity with respect to the scaling parameter𝜏. The original time series of EEG signals is the Lempel – Ziv complexity - LZC. This is divided into non-overlapping windows with a length 𝜏, and method is non-parametric, model-independent and easily then the values are averaged for each window. Thus, each calculated. In addition, it does not require long time series [12]. element of the simplified time series is calculated by the formula The LZC algorithm provides more reliable results for short π‘—πœ (𝜏) 1 signal segments, which is important in most experimental and 𝑦𝑗 = βˆ‘ π‘₯𝑖 , 1 ≀ 𝑗 ≀ 𝑁/𝜏. clinical studies [4]. 𝜏 𝑖=(π‘—βˆ’1)𝜏+1 Copyright Β© 2019 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). 3. Results 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 Tables 1-3 are consistent with the majority of previous works, showing that patients with schizophrenia are characterized by Fig. 1. Configuration diagram of electrodes on the surface of less complex neuropsychological measurements. The analysis head showed that the most characteristic channels for MSE entropy For the first scale, the time series {𝑦 (1) } is equivalent to the assessment are: F3', 'F4', 'T6'. Table 1 Average MSE original time series. The length of each time series corresponds to the length of the original time series divided by the scaling parameter 𝜏. Control group Sch group P- Channel (Average + SD) (Average + SD) value The calculation of the quantitative measure of entropy 𝑆𝐸 for each simplified time series is made by the formula 'F7' 0,9296 Β± 0,1154 0,8859 Β± 0,1495 0,1568 π‘βˆ’π‘š β€²π‘š 'F3' 0,9524 Β± 0,1306 0,8867 Β± 0,1267 0,0296 βˆ‘ 𝑖=1 𝑛𝑖 'F4' 0,9655 Β± 0,1230 0,8866 Β± 0,1221 0,0042 𝑆𝐸 (π‘š, π‘Ÿ, 𝑁) = 𝑙𝑛 π‘βˆ’π‘š β€²π‘š+1 , 'F8' 0,9629 Β± 0,1563 0,9035 Β± 0,1385 0,1075 βˆ‘ 𝑖=1 𝑛𝑖 'T3' 0,9670 Β± 0,1363 0,926 Β± 0,1386 0,1705 where π‘š – the increment of the length of the data vector, π‘Ÿ – the 'C3' 0,9604 Β± 0,1047 0,9309 Β± 0,1043 0,2085 cell size of the phase space (inaccuracy), π‘›β€²π‘š 𝑖 – the probability 'Cz' 0,9454 Β± 0,1087 0,9165 Β± 0,0866 0,2180 of repeating a sequence of data of a given length in the original 'C4' 0,9412 Β± 0,1026 0,9212 Β± 0,1025 0,4021 data. 'T4' 0,9737 Β± 0,1329 0,9346 Β± 0,1256 0,1587 'T5' 0,9891 Β± 0,1586 0,9608 Β± 0,1354 0,3733 2.3. Lempel – Ziv complexity 'P3' 0,9267 Β± 0,1063 0,9151 Β± 0,1117 0,6317 Lempel and Ziv proposed a measure of the complexity of 'Pz' 0,9044 Β± 0,1029 0,8907 Β± 0,1031 0,5801 patterns for sequences of finite length [9]. Later, Kaspar and 'P4' 0,9161 Β± 0,1090 0,8955 Β± 0,1091 0,4415 Shuster developed an algorithm for computing the LZC on a 'T6' 0,9922 Β± 0,1446 0,9112 Β± 0,1323 0,0094 computer that determined the measure of complexity [7]. LZC 'O1' 0,8822 Β± 0,1130 0,9007 Β± 0,1271 0,4969 calculates the number of new images, i.e. segments that are not 'O2' 0,8747 Β± 0,1086 0,8843 Β± 0,1332 0,7071 consistently represented in all previous data. In this algorithm, The analysis of the data presented in Table 2 shows that the the EEG signal {π‘₯(𝑛)} is converted into a binary sequence objects in the control group are characterized by a lower average {𝑠(𝑛)} by comparing with the average value of the signal π‘š. value of LZC compared to objects with schizophrenia After receiving a binary sequence, the corresponding measure syndromes. The most indicative channels for LZC estimation of complexity 𝑐(𝑛) is increased by one until a new sequence is are: F4', 'Cz', 'P3', 'O1', 'O2'. detected. The process of searching for sequences is repeated It should be noted that the complexity of the Lampell-Ziva until the last character of the time series is read. LZC is defined characterizes the chaotic nature of the signal with an inverse as value in relation to the entropy and Lyapunov exponent, i.e. the 𝐿𝑍𝐢 = 𝑐(𝑛)/𝑏(𝑛), higher the value of LZC the more regular the time series. Π³Π΄Π΅ 𝑏(𝑛) = 𝑛/π‘™π‘œπ‘”2 (𝑛). Table 3 presents average values of Lyapunov exponent L1 for two groups of research objects. The analysis of the average 2.4. Lyapunov exponent. values of Lyapunov senior exponent for all study objects Lyapunov exponent give an estimate of the average showed that the most typical results were obtained through the exponential divergence or convergence of nearby trajectories in channel 'O1'. the phase space. Obtaining a positive value of the Lyapunov’s Visualization of the data which was obtained in the Matlab exponent is characterized by dependence on the initial software package, algorithms for constructing topographic conditions and shows that the system of interest is chaotic. images of the EEG signal spectra shown in Fig.2. Topographic To calculate the Lyapunov senior exponent. L1, a modified images are constructed in accordance with the layout of the version of the Wulf algorithm was used [11]. Essentially, the electrodes in Fig. 1. The channels used in the research are tangent vectors to points on the reference path are approximated marked with dots. Values at intermediate points were by difference vectors in the phase space. The Wulf algorithm is interpolated by using a spherical spline. based on the fact that the time series is normalized to match the Table 2 Average LZC equilibrium state to zero. Next is the reconstruction of the trajectory in the phase space. After that, with some step for the Control group Sch group P- coordinate vector of the reconstructed phase space, the indicator Channel (Average + SD) (Average + SD) value component is calculated. For each component calculation, the series is renormalized so that the initial discrepancy coincides 'F7' 0,0128 Β± 0,0592 0,0284 Β± 0,0813 0,3514 for each next component. Then the procedure is repeated. 'F3' 0,1418 Β± 0,0261 0,1542 Β± 0,0365 0,0793 'F4' 0,1415 Β± 0,0294 0,1597 Β± 0,0406 0,0239 EEG channels. Fig. 3 shows the visualization of the cross- 'F8' 0,1667 Β± 0,0413 0,1862 Β± 0,0459 0,0631 correlation function for both groups. 'T3' 0,1707 Β± 0,0371 0,1766 Β± 0,0540 0,5992 'C3' 0,1382 Β± 0,0298 0,1517 Β± 0,0391 0,1282 'Cz' 0,1317 Β± 0,0292 0,1469 Β± 0,0362 0,0497 'C4' 0,1370 Β± 0,0306 0,1524 Β± 0,0377 0,0576 'T4' 0,1722 Β± 0,0544 0,1765 Β± 0,0490 0,7377 'T5' 0,1668 Β± 0,0433 0,1762 Β± 0,0434 0,3813 'P3' 0,1261 Β± 0,0322 0,1487 Β± 0,0402 0,0085 'Pz' 0,1197 Β± 0,0291 0,1353 Β± 0,0387 0,0626 'P4' 0,1251 Β± 0,0338 0,1427 Β± 0,0395 0,0536 'T6' 0,1619 Β± 0,0471 0,1601 Β± 0,0464 0,8733 'O1' 0,1057 Β± 0,0332 0,1338 Β± 0,0412 0,0025 'O2' 0,1032 Β± 0,0324 0,1280 Β± 0,0416 0,0083 Fig. 3. Cross-correlation of LZC for a) control group and b) schizophrenia syndrome group The following pairs of electrodes with the lowest value were identified: for the control group - O2-F8, O2-T3, O2-C4, O2- T4, O2-T5, O2-P3, O2-Pz, O2-P4; for the group with schizophrenia syndromes - C3-F8, C3-T3, Cz-T3, Cz-C3, C4- Fig. 2. Topographical representations of MSE(a), LZC(b) and C3, C4-Cz, T4-C3, T4-Cz. Thus, a decrease in cross-correlation L1(c) values in patients with schizophrenia was found for LZC in the left hemisphere compared to the right hemisphere, mainly in the Table 3 Average L1 parietal zone. The control group is characterized by weak cross- correlation, predominant right occipital zone with parietal zone. Control group Sch group P- These results support the assumption that schizophrenia may be Channel (Average + SD) (Average + SD) value a disruption of the activity ratio in different brain regions. 'F7' 0,4213 Β± 0,1196 0,4251 Β± 0,1558 0,9173 4. Conclusion 'F3' 0,5704 Β± 0,1467 0,5716 Β± 0,1245 0,9722 'F4' 0,5683 Β± 0,1556 0,5571 Β± 0,1914 0,7964 The proposed method of visual analysis of EEG allowed us 'F8' 0,5554 Β± 0,1540 0,5483 Β± 0,1567 0,8395 to compare the interaction between the activity of brain regions. 'T3' 0,5064 Β± 0,1887 0,5207 Β± 0,2236 0,7638 This approach makes it possible to evaluate the symmetry of 'C3' 0,5557 Β± 0,1501 0,5650 Β± 0,1881 0,8122 activity on the basis of topographic images, to localize the 'Cz' 0,5758 Β± 0,1808 0,6015 Β± 0,1436 0,5063 activity centers and to correlate the activity of interaction 'C4' 0,5891 Β± 0,1263 0,5781 Β± 0,1811 0,7574 between hemispheres by means of cross-correlation analysis. 'T4' 0,5308 Β± 0,1544 0,5098 Β± 0,2154 0,6383 The most characteristic EEG channels were selected for 'T5' 0,5121 Β± 0,1944 0,4800 Β± 0,2267 0,5302 each method. Comparison of the methods for determining the 'P3' 0,5853 Β± 0,1919 0,5511 Β± 0,2116 0,4797 signal complexity has shown that the most characteristic is LZC, 'Pz' 0,6177 Β± 0,1463 0,6163 Β± 0,1340 0,9665 because 5 significant channels were determined for this method. 'P4' 0,6021 Β± 0,1981 0,6061 Β± 0,1302 0,9145 The results will allow to implement the evaluation 'T6' 0,5504 Β± 0,1525 0,5912 Β± 0,0968 0,1977 functionality with the use of machine learning for further 'O1' 0,6908 Β± 0,1045 0,5861 Β± 0,1990 0,0106 research in medical diagnosis of schizophrenia. 'O2' 0,5971 Β± 0,2503 0,6602 Β± 0,1062 0,1958 Comparison of topographic images of EEG signal 5. 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