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Title: On the complementarity of electroencephalography and magnetoencephalography
Authors: Dassios, George
Fokas, Athanassios S.
Hadjiloizi, Demetra 
Keywords: Electroencephalography;Electric fields;Magnetoencephalography;Data reduction;Brain
Issue Date: 2007
Publisher: IOP
Source: Inverse Problems, 2007, Volume 23, Issue 6, Pages 2541-2549
Abstract: We show that for the spherical model of the brain, the part of the neuronal current that generates the electric potential (and therefore the electric field) lives in the orthogonal complement of the part of the current that generates the magnetic potential (and therefore the magnetic induction field). This means that for a continuously distributed neuronal current, information missing in the electroencephalographic data is precisely information that is available in the magnetoencephalographic data, and vice versa. In this way, the notion of complementarity between the imaging techniques of electroencephalography and magnetoencephalography is mathematically defined. Using this notion of complementarity and expanding the neuronal current in terms of vector spherical harmonics, which by definition provide the angular dependence of the current, we show that if the electric and the magnetic potentials in the exterior of the head are given, then we can determine certain moments of the functions which provide the radial dependence of the neuronal current. In addition to the above notion of complementarity, we also present a notion of unification of electroencephalography and magnetoencephalography by showing that they are governed respectively by the scalar and the vector invariants of a unified dyadic field describing electromagnetoencephalography.
ISSN: 02665611
DOI: 10.1088/0266-5611/23/6/016
Rights: © 2007 IOP Publishing Ltd
Type: Article
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