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

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Yakhno Y. V., Molkov J. I., Muhin 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
Muhin Dmitrij 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. 

  1. Koronovskii AA, Kuznetsova GD, Midzyanovskaya IS, Sitnikova EY, Trubetskov DI, Hramov AE. Regularities of alternate behavior in spontaneous nonconvulsive seizure activity in rats. Doklady Biological Sciences. 2006;409(1):275–277. DOI: 10.1134/S0012496606040016.
  2. Stam СJ. Nonlinear dynamical analysis of EEG and MEG: Review of emerging field. Clinical Neurophysiology. 2005;116(10):2266–2301. DOI: 10.1016/j.clinph.2005.06.011.
  3. Sitnikova E. Thalamo-cortical mechanisms of sleep spindles and spike-wave discharges in rat model of absence epilepsy (a review). Epilepsy Res. 2010;89(1):17–26. DOI: 10.1016/j.eplepsyres.2009.09.005.
  4. Mukhin DN, Feigin AM, Loskutov EM, Molkov YI. Modified Bayesian approach for the reconstruction of dynamical systems from time series. Phys. Rev. E. 2006;73(3):036211. DOI: 10.1103/PhysRevE.73.036211.
  5. Molkov YI, Mukhin DN, Loskutov EM, Timushev RI, Feigin AM. Prognosis of qualitative behavior of a system by noisy chaotic time-series. Phys. Rev. E. 2011;84(3):036215. DOI: 10.1103/PhysRevE.84.036215.
  6. Molkov YI, Loskutov EM, Mukhin DN, Feigin AM. Random dynamical models from time series. Phys. Rev. E. 2012;85(3):036216. DOI: 10.1103/PhysRevE.85.036216.
  7. Engel J. A proposed diagnostic scheme for people with epileptic seizures and with epilepsy: report of the ILAE Task Force on Classification and Terminology. Epilepsia. 2001;42(6):796–803. DOI: 10.1046/j.1528-1157.2001.10401.x.
  8. van Luijtelaar EL, Coenen AM. Two types of electrocortical paroxysms in an inbred strain of rats. Neuroscience Letters. 1986;70(3):393–397. DOI: 10.1016/0304-3940(86)90586-0.
  9. Bosnyakova D, Gabova A, Zharikova A, Gnezditski V, Kuznetsova G, van Luijtelaar G. Some peculiarities of time-frequency dynamics of spike-wave discharges in humans and rats. Clinical Neurophysiology. 2007;118(8):1736–1743. DOI: 10.1016/j.clinph.2007.04.013.
  10. Abarbanel HDI. Analysis of Observed Chaotic Data. New York: Springer-Verlag; 1997. 272 p. DOI: 10.1007/978-1-4612-0763-4.
  11. Takens F. Detecting strange attractors in turbulence. In: Rand DA, Young LS, editors. Dynamical Systems and Turbulence. Lecture Notes in Mathematics. Vol. 898. Berlin: Srpinger; 1981. P. 366–381. DOI: 10.1007/BFb0091924.
  12. Bracewell R. The Fourier Transform and Its Applications. New York: McGraw-Hill; 1999. 381 p.
  13. Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A. 1998;454(1971):903–995. DOI: 10.1098/rspa.1998.0193.
  14. Inouye T, Toi S, Matsumoto Y. A new segmentation method of electroencephalograms by use of Akaike’s information criterion. Cognitive Brain Res. 1995;3(1):33–40. DOI: 10.1016/0926-6410(95)00016-x.
  15. Rechtschaffen A, Kales A, editors. A Manual of Standardized Terminology, Techniques and Scoring System for Sleep Stages of Human Subjects. Washington: Public Health Service, US Government Printing Office; 1968. 57 p.
  16. van Rijn CM, Gaetani S, Santolini I, Badura A, Gabova A, Fu J, Watanabe M, Cuomo V, van Luijtelaar G, Nicoletti F, Ngomba RT. WAG/Rij rats show a reduced expression of CB1 receptors in thalamic nuclei and respond to the CB1 receptor agonist, R(+)WIN55,212-2, with a reduced incidence of spike-wave discharges. Epilepsia. 2010;51(8):1511–1521. DOI: 10.1111/j.1528-1167.2009.02510.x.
  17. O’Mahony M. Sensory Evaluation of Food: Statistical Methods and Procedures. University of California, Davis, USA: CRC Press; 1986. 510 p.
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