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The Inverse Magnetoencephalography Problem and Its Flat Approximation

  • A. S. Demidov
  • M. A. Galchenkova
Chapter

Abstract

Contrary to the prevailing opinion about the incorrectness of the inverse MEEG-problem, we prove its unique solvability in the framework of the system of Maxwell’s equations (Demidov, Unique solvability of the inverse MEEG-problem, 2017, to appear). The solution of this problem is the distribution of yq(y) current dipoles of brain neurons that occupies the region \(Y \subset \mathbb {R}^3 \). It is uniquely determined by the non-invasive measurements of the electric and magnetic fields induced by the current dipoles of neurons on the patient’s head. The solution can be represented in the form q = q0 + p0δ|∂Y, where q0 is the usual function defined in Y, and p0δ|∂Y is a δ-function on the boundary of the domain Y with a certain density p0. However, the components of the required 3-dimensional distribution q must turn out to be linearly dependent if only the magnetic field B is taken into account. This question is considered in detail in a flat model of the situation.

Notes

Acknowledgements

This work is partially supported by grants of Russian Foundation for Basic Research (15-01-03576, 16-01-00781 and 17-01-00809).

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • A. S. Demidov
    • 1
    • 2
  • M. A. Galchenkova
    • 2
  1. 1.Lomonosov Moscow State UniversityMoscowRussian Federation
  2. 2.Moscow Institute of Physics and Technology (State University)MoscowRussian Federation

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