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Journal of Applied Mathematics
Volume 2014, Article ID 232747, 8 pages
http://dx.doi.org/10.1155/2014/232747
Research Article

Localizing Brain Activity from Multiple Distinct Sources via EEG

Division of Applied Mathematics, Department of Chemical Engineering, University of Patras and FORTH/ICE-HT, 26504 Patras, Greece

Received 25 June 2014; Accepted 31 October 2014; Published 23 November 2014

Academic Editor: Urmila Diwekar

Copyright © 2014 George Dassios et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

An important question arousing in the framework of electroencephalography (EEG) is the possibility to recognize, by means of a recorded surface potential, the number of activated areas in the brain. In the present paper, employing a homogeneous spherical conductor serving as an approximation of the brain, we provide a criterion which determines whether the measured surface potential is evoked by a single or multiple localized neuronal excitations. We show that the uniqueness of the inverse problem for a single dipole is closely connected with attaining certain relations connecting the measured data. Further, we present the necessary and sufficient conditions which decide whether the collected data originates from a single dipole or from numerous dipoles. In the case where the EEG data arouses from multiple parallel dipoles, an isolation of the source is, in general, not possible.