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Investigating classical models of magneto- and electroencephalography by means of integral equations

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Abstract

Two basic methods for recording the activity of neural sources of the human brain are considered: magnetoencephalography (MEG) and electroencephalography (EEG). Homogeneous and spherical models of a head are used. Boundary integral equations for the direct MEG/EEG problem are obtained and analytical solutions of these equations in both cases are presented. The dependence of these solutions on their initial data (the position and the orientation of a source) is shown.

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References

  1. G. A. Grinberg, Selected Issues of the Mathematical Theory of Electric and Magnetic Phenomena (Akad. Nauk SSSR, Moscow, 1948) [in Russian].

    Google Scholar 

  2. L. D. Landau, E. M. Livshits, and L. P. Pitaevskii, Electrodynamics of Continuous Media (Fizmatlit, Moscow, 2005) [in Russian].

    Google Scholar 

  3. A. M. Popov, “Solution of an EEG inverse problem with the help of stochastic methods of pattern recognition,” Vestn. Mosk. Univ., Ser. 15: Vychisl. Mat. Kibern., No. 3, 91–100 (2006).

    Google Scholar 

  4. M. Hamalainen, R. Hari, R. J. Ilmoniemi, et al., “Magnetoencephalography - theory, instrumentation, and applications to noninvasive studies of the working human brain,” Rev. Mod. Phys. 65, 413–497 (1993).

    Article  Google Scholar 

  5. J. C. Mosher, R. M. Leahy, and P. S. Lewis, “EEG and MEG: Forward solutions for inverse methods,” IEEE Trans. on Biomed. Eng. 46, 245–259 (1999).

    Article  Google Scholar 

  6. V. V. Gnezditskii, Inverse Problem of EEG and Clinical Electroencephalography (Mapping and Locating of the Sources of Electrical Activity of Brain) (MEDPress Inform, Moscow, 2004) [in Russian].

    Google Scholar 

  7. E. V. Zakharov, R. E. Zimozdra, “Limits of applicability of a spherical model for solving Problems of electroencephalography,” Moscow Univ. Comput. Math. Cybernet. 38, 100–104 (2014).

    Article  MATH  Google Scholar 

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Correspondence to E. V. Zakharov.

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Original Russian Text © E.V. Zakharov, R.E. Zimozdra, 2015, published in Vestnik Moskovskogo Universiteta. Vychislitel’naya Matematika i Kibernetika, 2015, No. 2, pp. 11–15.

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Zakharov, E.V., Zimozdra, R.E. Investigating classical models of magneto- and electroencephalography by means of integral equations. MoscowUniv.Comput.Math.Cybern. 39, 58–62 (2015). https://doi.org/10.3103/S0278641915020090

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  • DOI: https://doi.org/10.3103/S0278641915020090

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