The Inverse Magnetoencephalography Problem and Its Flat Approximation

A. S. Demidov and M. A. Galchenkova
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A. S. Demidov: Lomonosov Moscow State University
M. A. Galchenkova: Moscow Institute of Physics and Technology (State University)

A chapter in Trends in Biomathematics: Modeling, Optimization and Computational Problems, 2018, pp 139-152 from Springer

Abstract: 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.

Keywords: Magnetoencephalography Inverse Problem; Flat Approximation; Current Dipole; Flat Model; Unique Solvability (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-91092-5_10

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DOI: 10.1007/978-3-319-91092-5_10

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