Quarterly of Applied Mathematics

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Electro-magneto-encephalography and fundamental solutions

Authors: G. Dassios and A. S. Fokas
Journal: Quart. Appl. Math. 67 (2009), 771-780
MSC (2000): Primary 35J25, 35J55, 92B05, 92C55
Published electronically: May 27, 2009
MathSciNet review: 2588236
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Abstract: Electroencephalography (EEG) and Magnetoencephalography (MEG) are two important methods for the functional imaging of the brain. For the case of the spherical homogeneous model, we elucidate the mathematical relations of these two methods. In particular, we derive and analyse three different representations for the electric and magnetic potentials, as well as the corresponding electric and magnetic induction fields, namely: integral representations involving the Green and the Neumann kernels, representations in terms of eigenfunction expansions, and closed form expressions. We show that the parts of the EEG and MEG fields in the interior of the brain that are due to the induction current are related via Kelvin's inversion transformation. We also derive closed form expressions for the interior and exterior vector potentials of the corresponding magnetic induction fields.

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Additional Information

G. Dassios
Affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom

A. S. Fokas
Affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom

DOI: http://dx.doi.org/10.1090/S0033-569X-09-01144-7
Received by editor(s): September 4, 2008
Published electronically: May 27, 2009
Additional Notes: The first author is on leave from the University of Patras and ICEHT/FORTH, Greece.
Article copyright: © Copyright 2009 Brown University

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