From measurements by electrodes of the electric potential on the scalp, the problem is to recover a distribution of pointwise dipolar current
sources with moments located in the brain (modeling the presence of epileptic foci). The head is modeled as a set of three spherical nested regions (brain, skull, scalp) and in each region constant conductivities are assumed. A macroscopic model and quasi-static approximation of Maxwell-equations are used to describe the spacial behavior of the potential.
The inverse problem can be approached in two steps:
- get the anti-harmonic part of the potential from the data using propagation techniques
- recover the localizations and the moments of the sources by rational approximation on planar sections (RARL2)
The singularities (green) of the potential are aligned and the sources (black) correspond to the maximum modulus. The rational approximations (pink) accumulate to these singularities:
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One of the advantages of this method is that it does not require the a priori knowledge of the exact number of sources. If the order of the approximation is larger than the number of sources, the extra poles accumulate to the boundary of he disks. For this application, the software RARL2 has been modified to impose triple poles for the approximant. The whole process is handled by the software FindSources3d .
