Analysis of the Inverse Electroencephalographic Problem for Volumetric Dipolar Sources Using a Simplification
Objective: To analyze the parameter identification problem for volumetric dipolar sources in the brain from measurement of the EEG on the scalp using a simplification which reduces the multilayer conductive medium problem to one homogeneous medium problem with a null Neumann boundary condition. Methodology: The minimum squares technique is used for parameter identification of the dipolar sources. The simple case in which the head is modelled by concentric circles is developed. This case was chosen because we were able to obtain the solution of the forward problem in exact form and for the simplicity of the exposition. Results: The parameter of the dipolar sources can be identified from the EEG on the scalp using the simplification. For the theoretical analysis the results developed for one homogeneous region are used. The numerical implementation is simpler than the multilayer case and the numerical computation requires minor computational cost. Conclusion: The feasibility for solving the parameter identification problem using the simplification is shown. These results can be extended to the case of concentric spheres and complex geometries but the solution cannot be found in exact form.
Upon acceptance of an article in the RMIB, corresponding authors will be asked to fulfill and sign the copyright and the journal publishing agreement, which will allow the RMIB authorization to publish this document in any media without limitations and without any cost. Authors may reuse parts of the paper in other documents and reproduce part or all of it for their personal use as long as a bibliographic reference is made to the RMIB and a copy of the reference is sent. However written permission of the Publisher is required for resale or distribution outside the corresponding author institution and for all other derivative works, including compilations and translations.