G Dassios and D Hadjiloizi 2009 Inverse Problems 25 115012 doi:10.1088/0266-5611/25/11/115012
On the non-uniqueness of the inverse problem associated with electroencephalography
G Dassios and D Hadjiloizi1
Show affiliationsWe present here a quantitative characterization of the non-uniqueness for the inverse problem of electroencephalography (EEG). First, we identify the singular support of the electric potential generated by a dipolar current which is fired inside the spherical model of the brain. Next, we extend this result to a continuously distributed neuronal current and we derive the equivalent Green's integral representation. Then, using the Hansen representation of the current, we show that among the three scalar representation functions, only two are needed to represent the observed electric potential on the surface or outside the head. The scalar function that is missed by the EEG recordings is exactly the one that is recorded by magnetoencephalography (MEG). Finally, the solution of the inverse EEG problem is reduced to a specific moment problem, which is exactly solved under the minimum-current assumption.
- PACS
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87.19.R- Mechanical and electrical properties of tissues and organs
- MSC
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26B20 Integral formulas (Stokes, Gauss, Green, etc.)
92B05 General biology and biomathematics
35R30 Inverse problems (undetermined coefficients, etc.) for PDE
- Subjects
- Dates
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Issue 11 (November 2009)
Received 22 September 2008, in final form 9 September 2009
Published 29 October 2009
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On the non-uniqueness of the inverse problem associated with electroencephalography
G Dassios and D Hadjiloizi 2009 Inverse Problems 25 115012
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