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
Full-text PDF Free Access
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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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1 B.N. Cuffin and D. Cohen, “Magnetic Fields of a Dipole in Special Volume Conductor Shapes”, IEEE Trans. Biomedical Eng., BME-24, pp. 372-381, 1997
2 G. Dassios and F. Kariotou, “On the Geselowitz Formula in Biomagnetics”, Quarterly of Applied Mathematics, 61 (2.2), 387-400, 2003
3 G. Dassios and F. Kariotou, “Magnetoencephalography in Ellispoidal Geometry”, J. Math. Phys., 44, pp. 220-241, 2003
4 G. Dassios and F. Kariotou, “On the Exterior Magnetic Field and Silent Sources in Magnetoencephalography”, Abstract and Applied Analysis, 2004, no. 4, 307–314.
5 A.S. Fokas, Y. Kurylev and V. Marinakis, “The Unique Determination of Neuronal Currents in the Brain via Magnetoencephalography”, Inverse Problems, 20, pp. 1067-1082, 2004
6 J.C. de Munck, “The Potential Distribution in a Layered Anisotropic Spheroidal Volume Conductor”, J. Appl. Phys., 64, pp. 464-470, 1988
7 D. B. Geselowitz, “On Bioelectric Potentials in an Inhomogeneous Volume Conductor”, Biophys. J., 7, pp. 1-11, 1967
8 D. B. Geselowitz, “On the Magnetic Field Generated Outside an Inhomogeneous Volume Conductor by Internal Current Sources”, IEEE Trans. Magn., MAG-6, pp. 346-347, 1970
9 E.W. Hobson, “The Theory of Spherical and Ellipsoidal Harmonics”, Chelsea, New York, 1955
10 R. J. Ilmoniemi, M. S. Hämäläinen and J. Knuutila, “The Forward and Inverse Problems in the Spherical model”, pp. 278-282, in Biomagnetism: Applications and Theory, edited by Harold Weinberg, Gerhard Stroink, and Toivo Katila, Pergamon Press, New York, 1985
11 Kamvyssas, G. and Kariotou, F., “Confocal Ellipsoidal Boundaries in EEG Modeling”, Bulletin of the Greek Mathematical Society (in press)
12 Kariotou, F., “Electroencephalography in Ellipsoidal Geometry”, Journal of Mathematical Analysis and Applications, 290, pp. 324-342, 2004
13 J. Malmivuo and R. Plonsey, “Bioelectromagnetism”, Oxford University Press, New York, 1995
14 G. Nolte, T. Fieseler and G. Curio, “Perturbative Analytical Solutions of the Magnetic Forward Problem for Realistic Volume Conductors”, J. Appl. Phys., 89, pp. 2360-2369, 2001
15 J. Sarvas, “Basic Mathematical and Electromagnetic Concepts of the Biomagnetic Inverse Problem”, Phys. Med. Biol., 32, pp. 11-22, 1987
16 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
MR Author ID:
54715
Fotini Kariotou
Affiliation:
Division of Applied Mathematics, Department of Chemical Engineering, University of Patras, and Hellenic Open University
Received by editor(s):
August 13, 2004
Published electronically:
July 26, 2005
Article copyright:
© Copyright 2005
Brown University
