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Research of native electroencephalograms of patients with multiple sclerosis by means of methods of the theory of nonlinear dynamical systems


I.O. Mihalchich - Assistant, Department of Medical and Biological Physics, Rostov State Medical University of Ministry of Health of the Russian Federation, Rostov-on-Don. E-mail: V.P. Omelchenko - Dr.Sc. (Biol.), Professor, Head of the Department of Medical and Biological Physics, Rostov State Medical University of Ministry of Health of the Russian Federation, Rostov-on-Don. E-mail:

The main results of research of bioelectric activity of a brain of the person by methods of the theory of nonlinear dynamic systems are reflected in article. Theoretical prerequisites of use of provisions of this theory for researching of the electroencephalogram (EEG) of the person are stated. The technique of definition of the main nonlinear dynamic characteristics of an EEG signal applied during work is described in detail. For practical application of this technique two groups of examinees are chosen: the studied group – patients with the multiple sclerosis (MS) with clinically confirmed diagnosis and control group – healthy volunteers. All examinee carried out standard procedure of electroencephalography. The received temporary sequences of amplitudes of EEG were investigated by methods of the deterministic chaos theory. Results of processing of EEG of the surveyed both groups by means of this technique are presented. Values of the main nonlinear indicators of EEG are defined: dimensions of introduction (n), correlation dimension (DC), Hurst\'s exponents (H), correlation entropy (K2) and fractal dimension (DF). It is proved that values of these indicators change at sick MS in comparison with healthy examinees. The assessment of the found changes from a position of the theory of dynamic chaos is given. The view of probable mechanisms and the reasons of formation of such distinctions is reflected. It became clear that the main nonlinear characteristics which distinguish EEG at MS from EEG healthy, correlation and fractal dimensions, and also Hurst exponent are. Significant distinctions of values of these indicators are observed in bigger number of assignments of EEG. At MS significant decrease in DC and H and increase of DF is noted. Reduction of values of correlation dimension of EEG at MS probably is connected with «simplification» of the processes proceeding in hypermarket in connection with violation of carrying out nervous impulses in the struck areas of bark of hypermarket. Significant decrease Hurst\'s exponents and a distance of its value from H=0,5 can testify to decrease in stochastic of the EEG-signal and growth of effects of «short-term memory». That is EEG healthy is more changeable, that is adapts for changes allegedly easier and quicker to them reacts. It, perhaps, is the evidence of loss of plasticity of a brain at the studied disease. The importance of observed distinctions of nonlinear characteristics of EEG in the studied and control groups confirmed statistically testifies to prospects of further application of receptions of the theory of nonlinear dynamic systems in diagnostics and research of multiple sclerosis. Possible further prospects of application of the methods called above in research of bioelectric activity of a brain of the person in norm are also outlined at various pathologies.


  1. Semenova N.JU., Zakharov, V.S.Analiz korreljacionnojj razmernosti dannykh EHEHG pri ehpilepsii udetejj //Nelinejjnyjj mir. 2010. № 3. S. 180–188.
  2. Starchenko I.B., Reznichenko A.A., Budko R.JU.  Modelirovanie ehlektricheskikh processov v mozge cheloveka metodami nelinejjnojj dinamiki // Prikaspijjskijj zhurnal: upravlenie i vysokie tekhnologii. 2013. T. 22. № 2. S. 80-90.
  3. Mihalchich I.O., Omelchenko V.P. The characteristics of the non-linear dynamics of the electroencephalograms of patients with trigeminal neuralgia// Modeling of Artificial Intelligence. 2014.№ 2 (2). R. 77-84.
  4. Poverennova I.E., Vlasov JA.V., Dolgikh G.T., Kacnel-son V.M., Zemskov S.G., Golub JU.V. Statisticheskijj obzor. Problemy rassejannogo skleroza v Samarskojj oblasti [EHlektronnyjj resurs]. Obshherossijjskaja obshhestvennaja organizacija invalidov-bolnykh rassejannym sklerozom. Samara 12.04.2005. URL: /index.php?Itemid= 1&id=1620&option=com_content&task=view (dataobrashhenija: 15.10.2015).
  5. Sychyov V.V. Fractan 4.4. Programma dlja vychislenija korreljacionnojj razmernosti i korreljacionnojj ehntropii povremennomu rjadu dannykh, DataProcessingLab., IMPBRAS, Pushchino, Russia. magbase/RESULT/ APPENDIX/ 15.06.2015 19:02.
  6. Takens F. Detecting strange attractors in turbulence. In: Dynamical Systems and Turbulence. Lecture Notes in Mathematics, edited by D.A. Rand, L.S. Young. Heidelberg: Springer-Verlag. 1981. P. 366-381.
  7. Mekler A.A. Primenenie apparata nelinejjnogo analiza dinamicheskikh sistem dlja obrabotki signalov EHEHG / red. prof. E.V. Kalashnikov // V: sb. Aktualnye problemy sovremennojj matematiki: uchjonye zapiski. SPb.: Izd-vo LGU im. A.S. Pushkina. 2004. T. 13 (vyp. 2). S. 112-140.
  8. Majjorov O.JU., Fenchenko V.N.Povyshenie nadezhnosti issledovanijj determinirovannogo khaosa v bioehlektricheskojj aktivnosti (EHEHG, EHKG i variabelnosti serdechnogo ritma) metodami nelinejjnogo analiza // Klinicheskaja informatika i telemedicina. 2009. T. 5. № 6. S. 10-17.
  9. Fraser A.M., Swinney H.L.Independent coordinates for strange attractors from mutual information // Phys. Rev. A. 1986. V. 33. P. 1134-1140.
  10. Grassberger P., Procaccia I. Estimation of the Kolmogorov entropy from a chaotic signal // Phys. Rev.A. 1983. V. 28. P. 2591-2593.


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