ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Yakhno Y. V., Molkov J. I., Mukhin D. N., Loskutov E. M., Feigin A. M. Reconstruction of an evolution operator as a technique of analysis of epileptiform electric brain activity. Izvestiya VUZ. Applied Nonlinear Dynamics, 2011, vol. 19, iss. 6, pp. 156-172. DOI: 10.18500/0869-6632-2011-19-6-156-172

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Reconstruction of an evolution operator as a technique of analysis of epileptiform electric brain activity

Yakhno Yuri Vladimirovich, Institute of Applied Physics of the Russian Academy of Sciences
Molkov Jaroslav Igorevich, Institute of Applied Physics of the Russian Academy of Sciences
Mukhin Dmitry Nikolaevich, Institute of Applied Physics of the Russian Academy of Sciences
Loskutov Evgenij Mihajlovich, Institute of Applied Physics of the Russian Academy of Sciences
Feigin Aleksandr Markovich, Institute of Applied Physics of the Russian Academy of Sciences

We propose a new method for analysis of electroencephalograms. It is based on construction of a parameterized stochastic model of the observed process (evolution operator). A certain functional form of the evolution operator is proposed. This form describes deterministic properties of the investigated process, as well as stochastic ones. The parameters of the evolution operator are reconstructed from the experimental data by using the Bayesian approach. New («fast») dynamical variables, which allow for the peculiar features of electroencephalogram, are found. They make it possible to construct the evolution operator, which describes electroencephalogram on few-second intervals. The time-varying parameters of this operator and the amplitude of oscillations in electroencephalogram form «slow» variables, which describe changes in the oscillation properties during the entire recording period. It is possible to single out individual brain states with these variables and to present a result in an obvious diagram. Moreover, changes in the singled-out brain states can be revealed. The proposed method was successfully applied to a specific physiological problem. 

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