Journal of Applied Mathematics and Physics, 2014, 2, 771-782 Published Online July 2014 in SciRes. http://www.scirp.org/journal/jamp http://dx.doi.org/10.4236/jamp.2014.28085 How to cite this paper: Dassios, G. and Satrazemi, K. (2014) Inversion of Meg Data for a 2-D Current Distribution. Journal of Applied Mathematics and Physics, 2, 771-782. http://dx.doi.org/10.4236/jamp.2014.28085 Inversion of Meg Data for a 2-D Current Distribution George Dassios, Konstantia Satrazemi Department of Chemical Engineering, University of Patras and ICE/HT-FORTH, Patras, Greece Email: gdassios@otenet.gr Received 4 May 2014; revised 2 June 2014; accepted 12 June 2014 Copyright © 2014 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract The support of a localized three-dimensional neuronal current distribution, within a conducting medium, is not identifiable from knowledge of the exterior magnetic flux density, obtained via Magnetoencephalographic (MEG) measurements. However, this is not true if the neuronal current is supported on a set with dimensionality less than three. That is, the support of a dipolar current distribution can be recovered if it is a set of isolated points, a segment of a curve, or a surface patch. In this work we provide an analytic algorithm for this inverse MEG problem and apply it to the case where the current is supported on a localized disk having arbitrary position and size within the brain tissue. The proposed recovery algorithm reduces the identification of the charac- teristics of the current to the solution of a nonlinear algebraic system, which can be handled nu- merically. Keywords Magnetoencephalography, Inversion of Current 1. Introduction Magnetoencephalography associates a neuronal current within the functional brain with the magnetic flux den- sity and it creates outside the head. In particular, the direct problem consists of the calculation of the exterior magnetic field when the primary neuronal current is given, and the inverse problem seeks to identify the current that generates a given exterior magnetic field. The main difficulty with the inverse problem of Magnetoence- phalography is due to the fact that, besides the excitation of the neuronal current within the conductive brain tis- sue, a secondary induction current is generated which, in a sense, makes the primary neuronal current less “visi- ble” by the exterior magnetic field. The induction current is supported on the conductive brain tissue and there- fore it depends on the geometry of the brain-head system. Even for relatively simple geometrical models such as