A preliminary study on the application of the two-space nonperiodic asymptotic homogenization method to the EEG forward problem with continuously differentiable coefficient

The knowledge on the Electroencephalogram (EEG) forward problem is important to improve the imaging of the neural activity, that is an inverse problem. This paper introduces the study of the EEG forward problem via a nonperiodic homogenization technique: the two-space method. Considering a concentric spheres head model for the brain-skull-scalp medium as an micro-heterogeneous medium, a simplification consisting of a 1D problem in spherical coordinates with continuously differentiable coefficient is considered. The two-space method is applied successfully, and a numerical example shows the convergence of the micro-heterogeneous solution to the one obtained by the two-space method, as was expected. The preliminary conclusion is that this approach for the EEG forward problem with homogenization techniques shows itself as very promising. More experiments should be executed, considering more realistic models for the head.