The direct MEG problem in the presence of an ellipsoidal shell inhomogeneity
Authors:
George Dassios and Fotini Kariotou
Journal:
Quart. Appl. Math. 63 (2005), 601618
MSC (2000):
Primary 78M99, 35QXX
Published electronically:
July 26, 2005
MathSciNet review:
2187922
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Abstract: The forward problem of Magnetoencephalography for an ellipsoidal inhomogeneous shellmodel 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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 J.C. de Munck, ``The Potential Distribution in a Layered Anisotropic Spheroidal Volume Conductor'', J. Appl. Phys., 64, pp. 464470, 1988
 7.
 D. B. Geselowitz, ``On Bioelectric Potentials in an Inhomogeneous Volume Conductor'', Biophys. J., 7, pp. 111, 1967
 8.
 D. B. Geselowitz, ``On the Magnetic Field Generated Outside an Inhomogeneous Volume Conductor by Internal Current Sources'', IEEE Trans. Magn., MAG6, pp. 346347, 1970
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 E.W. Hobson, ``The Theory of Spherical and Ellipsoidal Harmonics'', Chelsea, New York, 1955 MR 0064922 (16:356i)
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 R. J. Ilmoniemi, M. S. Hämäläinen and J. Knuutila, ``The Forward and Inverse Problems in the Spherical model'', pp. 278282, in Biomagnetism: Applications and Theory, edited by Harold Weinberg, Gerhard Stroink, and Toivo Katila, Pergamon Press, New York, 1985
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 Kamvyssas, G. and Kariotou, F., ``Confocal Ellipsoidal Boundaries in EEG Modeling'', Bulletin of the Greek Mathematical Society (in press)
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 Kariotou, F., ``Electroencephalography in Ellipsoidal Geometry'', Journal of Mathematical Analysis and Applications, 290, pp. 324342, 2004 MR 2032245 (2004j:92033)
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 J. Malmivuo and R. Plonsey, ``Bioelectromagnetism'', Oxford University Press, New York, 1995
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 G. Nolte, T. Fieseler and G. Curio, ``Perturbative Analytical Solutions of the Magnetic Forward Problem for Realistic Volume Conductors'', J. Appl. Phys., 89, pp. 23602369, 2001
 15.
 J. Sarvas, ``Basic Mathematical and Electromagnetic Concepts of the Biomagnetic Inverse Problem'', Phys. Med. Biol., 32, pp. 1122, 1987
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 W.S. Snyder, M.R. Ford, G.G. Warner and H.L. Fisher, Jr., ``Estimates of Absorbed Fractions for Monoenergetic Photon Sources Uniformly Distributed in Various Organs of a Heterogeneous Phantom'', Journal of Nuclear Medicine, Supplement Number 3, August 1969, Volume 10, Pamphlet No. 5, Revised 1978
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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:
http://dx.doi.org/10.1090/S0033569X05009712
PII:
S 0033569X(05)009712
Received by editor(s):
August 13, 2004
Published electronically:
July 26, 2005
Article copyright:
© Copyright 2005 Brown University
