Abstract and Applied Analysis
Volume 2004 (2004), Issue 4, Pages 307-314

On the exterior magnetic field and silent sources in magnetoencephalography

George Dassios1 and Fotini Kariotou2

1Division of Applied Mathematics, Department of Chemical Engineering, University of Patras, Patras 26504, Greece
2Institute of Chemical Engineering and High Temperature Chemical Processes (ICE/HT), Foundation for Research Technology-Hellas (FORTH), Patras 26504, Greece

Received 27 September 2002

Copyright © 2004 George Dassios and Fotini Kariotou. 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.


Two main results are included in this paper. The first one deals with the leading asymptotic term of the magnetic field outside any conductive medium. In accord with physical reality, it is proved mathematically that the leading approximation is a quadrupole term which means that the conductive brain tissue weakens the intensity of the magnetic field outside the head. The second one concerns the orientation of the silent sources when the geometry of the brain model is not a sphere but an ellipsoid which provides the best possible mathematical approximation of the human brain. It is shown that what characterizes a dipole source as “silent” is not the collinearity of the dipole moment with its position vector, but the fact that the dipole moment lives in the Gaussian image space at the point where the position vector meets the surface of the ellipsoid. The appropriate representation for the spheroidal case is also included.