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Journal of Mathematical Sciences

, Volume 237, Issue 6, pp 858–864 | Cite as

Magnetoencephalography Inverse Problem for Spherical and Spheroid Models

  • T. V. ZakharovaEmail author
  • M. A. Dranitsyna
  • P. I. Karpov
Article
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Magnetoencephalography produces big data. The processing of these data in order to reconstruct signal sources with a given accuracy is an extremely ill-posed problem. The main purpose of this work is an extension of our previous results to spheroid model providing a more accurate solution. In certain models of a human head (spherical and spheroid), the Biot–Savart law and IC analysis give a background for the detailed investigation in order to develop an algorithm for primary motor cortex localization. For a general case of the spheroid model, it is possible to approximately solve the inverse problem, neglecting volume magnetic field near the points of maxima of the magnetic field and taking into account only primary magnetic field. This paper presents a stepwise algorithm to obtain MEG inverse problem solution under the assumptions of discreteness of signal sources, originating from distinct functional brain areas and superficial location of the signal sources.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • T. V. Zakharova
    • 1
    Email author
  • M. A. Dranitsyna
    • 2
  • P. I. Karpov
    • 3
  1. 1.Faculty of Computational Mathematics and CyberneticsM.V. Lomonosov Moscow State UniversityMoscowRussia
  2. 2.Faculty of Computational Mathematics and CyberneticsM.V. Lomonosov Moscow State UniversityMoscowRussia
  3. 3.National University of Science and Technology “MISiS,” Department of Theoretical Physics and Quantum TechnologiesMoscowRussia

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