On the handling of brain tissue anisotropy in the forward EEG problem with a conformingly discretized surface integral method

This work presents a mixed discretized integral formulation for the EEG forward problem that can handle piecewise homogeneous anisotropic conductivities. Given that, in the presence of anisotropic conductivity profiles, an harmonic function for one profile is not necessarily harmonic for a different profile, standard methods to obtain surface integral equations cannot be used. For this reason, we have adopted here an indirect method strategy that allows to overcome this issue. In addition, the equation is discretized by using a mixed and conforming approach that is specifically designed to abide by the mapping properties of all integral operators involved. This results in a further enhancement of the accuracy, especially when dipolar sources are used to model the brain activity near a layer boundary. Numerical results confirms the accuracy of the approach and shows the applicability to real case scenario.