On the Inverse EEG Problem for a 1D Current Distribution

George Dassios, George Fragoyiannis and Konstantia Satrazemi

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

Abstract: Albanese and Monk (2006) have shown that, it is impossible to recover the support of a three‐dimensional current distribution within a conducting medium from the knowledge of the electric potential outside the conductor. On the other hand, it is possible to obtain the support of a current which lives in a subspace of dimension lower than three. In the present work, we actually demonstrate this possibility by assuming a one‐dimensional current distribution supported on a small line segment having arbitrary location and orientation within a uniform spherical conductor. The immediate representation of this problem refers to the inverse problem of electroencephalography (EEG) with a linear current distribution and the spherical model of the brain‐head system. It is shown that the support is identified through the solution of a nonlinear algebraic system which is investigated thoroughly. Numerical tests show that this system has exactly one real solution. Exact solutions are analytically obtained for a couple of special cases.

Date: 2014
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https://doi.org/10.1155/2014/715785

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:715785

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