Electro-magneto-encephalography and fundamental solutions

Dassios, G.; Fokas, A.

doi:10.1090/S0033-569X-09-01144-7

Authors: G. Dassios and A. S. Fokas
Journal: Quart. Appl. Math. 67 (2009), 771-780
MSC (2000): Primary 35J25, 35J55, 92B05, 92C55
DOI: https://doi.org/10.1090/S0033-569X-09-01144-7
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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