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Localization of the Activity Source in the Inverse Problem of Magnetoencephalography

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The article discusses the development of noninvasive preoperative methods for the localization of eloquent areas in the human brain. The accuracy with which such areas are localized directly determines the outcome of surgery. An analytical formula is derived for the solution of the forward problem that computes the magnetic field on the surface of the head from the known location and orientation of a current dipole in the low-frequency approximation in the spherical model. The inverse problem is also solved, reconstructing the location and orientation of the source given the magnetic field on the surface of the head. Qualitative analysis of the ellipsoidal model is carried out.

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References

  1. M. Hamalainen, R. Hari, R. Ilmoniemi, J. Knuutila, and O. V. Lounasmaa, “Magnetoencephalography — theory, instrumentation, and applications to noninvasive studies of the working human brain,” Reviews of Modern Physics, 65, 413–497 (1993).

    Article  Google Scholar 

  2. T. V. Zakharova, S. Yu. Nikiforov, M. B. Goncharenko, M. A. Dranitsyna, G. A. Klimov, M. S. Khaziakhmetov, and N. V. Chayanov, “Signal processing method for localization of eloquent regions of the human brain,” Sist. Sred. Inform., 22, No. 2, 157–176 (2013).

    Google Scholar 

  3. M. Sh. Khaziakhmetov and T. V. Zakharova, “On algorithms to find support points in a myogram for the localization of eloquent regions of the human brain,” in: Statistical Estimation and Hypothesis Testing Methods: Inter-University Collection of Papers [in Russian], Vol. 25, PGNIU, Perm’ (2013), pp. 56–63.

  4. T. V. Zakharova, M. B. Goncharenko, and S. Yu. Nikiforov, “A method for the inverse problem of magnetoencephalography based on brain surface clustering,” in: Statistical Estimation and Hypothesis Testing Methods: Inter-University Collection of Papers [in Russian], Vol. 25, PGNIU, Perm’ (2013), pp. 120–125.

  5. M. Dranitsyna, T. Aakharova, V. Allakhverdiyeva, and E. Chshenyavskaya, “Probability density function of myogram noise and its role in localization of grain activity,” in: XXXII International Sem. on Stability Problems for Stochastic Models, Trondheim, Norway (2014), pp. 25–26.

  6. V. E. Bening, M. A. Dranitsyna, T. V. Zakharova, and P. I. Karpov, “Solution of the inverse problem in multi-dipole model of magnetoencephalogram sources by independent component method,” Inform. Prim., 8, No. 2, 79–87 (2014).

    Google Scholar 

  7. V. M. Allakhverdieva, E. V. Chshenyavskaya, M. Dranitsyna, P. I. Karpov, and T. V. Zakharova, “Approach for inverse problem solving, assuming gamma distribution of myogram noise within rest intervals and utilizing independent component analysis,” J. Math. Sci., 214, No. 1, 3–11 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  8. S. Babillet, J. C. Mosher, and R. M. Leahy, “Electromagnetic brain mapping,” IEEE Sign. Proces. Magaz., 18, No. 6, 14–30 (2001).

    Article  Google Scholar 

  9. J. Sarvas, “Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem,” Physics of Medicine and Biology, 32, 22–11 (1987).

    Article  Google Scholar 

  10. R. Uitert, D. Weinstein, and C. Johnson, “Can a spherical model substitute for a realistic head model in forward and inverse MEG simulations?,” in: Proc. 13th Int. Conf. on Biomagnetism, Jena, Germany (2002), pp. 798–800.

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

    Google Scholar 

  12. J. A. Stratton, Electromagnetic Theory [Russian translation], OGIZ (1948).

  13. P. A. Hasgall, F. Di Gennaro, C. Baumgartner, E. Neufeld, M. C. Gosselin, D. Payne, A. Klingenbock, and N. Kuster, IT’IS Database for Thermal and Electromagnetic Parameters of Biological Tissues, Version 3.0, (September 01, 2015). DOI: 10.13099/VIP21000-03-0. www.itis.ethz.ch/database

  14. R. J. Ilmoniemi, M. S. Hamalainen, and J. Knuutila, “The forward and inverse problems in the spherical model,” in: H. Geinberg, G. Stroink, and T. Katila (editors), Biomagnetism: Applications and Theory, Pergamon, New York (1985), pp. 278–282.

    Google Scholar 

  15. G. Dassios, “The magnetic potential of the ellipsoidal MEG problem,” J. Comp. Math., 25, 145–156 (2007).

    MathSciNet  Google Scholar 

  16. B. Cuffin and D. Cohen, “Magnetic fields of a dipole in special volume conductor shapes,” IEEE Trans. Biome. Eng., BMS-24, 372–381 (1977).

    Article  Google Scholar 

  17. J. C. de Munck, “The potential distribution of a layered anisotropic spheroidal volume conductor,” J. Appl. Phys., 64, 464–470 (1988).

    Article  Google Scholar 

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    T. V. Zakharova & V. M. Bugaevskii

  2. National University of Science and Technology MISiS (Karpov), Moscow, Russia

    P. I. Karpov

Authors
  1. T. V. Zakharova
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  2. P. I. Karpov
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  3. V. M. Bugaevskii
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Corresponding author

Correspondence to T. V. Zakharova.

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Translated from Prikladnaya Matematika i Informatika, No. 52, 2016, pp. 12–25.

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Zakharova, T.V., Karpov, P.I. & Bugaevskii, V.M. Localization of the Activity Source in the Inverse Problem of Magnetoencephalography. Comput Math Model 28, 148–157 (2017). https://doi.org/10.1007/s10598-017-9353-6

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  • DOI: https://doi.org/10.1007/s10598-017-9353-6

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