The direct MEG problem in the presence of an ellipsoidal shell inhomogeneity

Authors:
George Dassios and Fotini Kariotou

Journal:
Quart. Appl. Math. **63** (2005), 601-618

MSC (2000):
Primary 78M99, 35QXX

DOI:
https://doi.org/10.1090/S0033-569X-05-00971-2

Published electronically:
July 26, 2005

MathSciNet review:
2187922

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Abstract: The forward problem of Magnetoencephalography for an ellipsoidal inhomogeneous shell-model of the brain is considered. The inhomogeneity enters through a confocal ellipsoidal shell exhibiting different conductivity than the one of the brain tissue. It is shown that, as far as the leading quadrupolic moment of the exterior magnetic field is concerned, the complicated expression associated with the field itself is the same as in the homogeneous case, while the effect of the shell is focused on the form of the generalized dipole moment. In contrast to the spherical case, where no shell inhomogeneities are ``readable'' outside the skull, the ellipsoidal shells establish their existence on the exterior magnetic induction field in a way that depends not only on the geometry but also on the conductivity of the shell. The degenerated spherical results are fully recovered.

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Additional Information

**George Dassios**

Affiliation:
Division of Applied Mathematics, Department of Chemical Engineering, University of Patras, and ICEHT/FORTH

**Fotini Kariotou**

Affiliation:
Division of Applied Mathematics, Department of Chemical Engineering, University of Patras, and Hellenic Open University

DOI:
https://doi.org/10.1090/S0033-569X-05-00971-2

Received by editor(s):
August 13, 2004

Published electronically:
July 26, 2005

Article copyright:
© Copyright 2005
Brown University