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The Inverse Magnetoencephalography Problem and Its Flat Approximation

In: Trends in Biomathematics: Modeling, Optimization and Computational Problems

Author

Listed:
  • A. S. Demidov

    (Lomonosov Moscow State University
    Moscow Institute of Physics and Technology (State University))

  • M. A. Galchenkova

    (Moscow Institute of Physics and Technology (State University))

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 y↦q(y) current dipoles of brain neurons that occupies the region Y ⊂ ℝ 3 $$Y \subset \mathbb {R}^3 $$ . 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 = q 0 + p 0 δ|∂Y, where q 0 is the usual function defined in Y, and p 0 δ|∂Y is a δ-function on the boundary of the domain Y with a certain density p 0. 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.

Suggested Citation

  • A. S. Demidov & M. A. Galchenkova, 2018. "The Inverse Magnetoencephalography Problem and Its Flat Approximation," Springer Books, in: Rubem P. Mondaini (ed.), Trends in Biomathematics: Modeling, Optimization and Computational Problems, pages 139-152, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-91092-5_10
    DOI: 10.1007/978-3-319-91092-5_10
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