  Solving the electroencephalography (EEG) forward problem is a fundamental
step in a wide range of applications including biomedical imaging techniques
based on inverse source localization. State-of-the-art electromagnetic solvers
resort to a computationally expensive volumetric discretization of the full
head to account for its complex and heterogeneous electric profile. The more
efficient, popular in biomedical imaging circles, but unfortunately
oversimplifying Boundary Element Method (BEM) relies instead on a
piecewise-uniform approximation that severely curbs its application in high
resolution EEGs. This contribution lifts the standard BEM contraints by
treating the local anisotropies with adequate wire and thin volume integral
equations that are tailored to specific structures of the fibrous white matter
and the inhomogeneous skull. The proposed hybrid integral equation formulation
thereby avoids the full volumetric discretization of the head medium and allows
for a realistic and efficient BEM-like solution of the anisotropic EEG forward
problem. The accuracy and flexibility of the proposed formulation is
demonstrated through numerical experiments involving both canonical and
realistic MRI-based head models.
