  The surface Boundary Element Method (BEM) is one of the most commonly
employed formulations to solve the forward problem in electroencephalography,
but the applicability of its classical incarnations is lamentably limited to
piece-wise homogeneous media. Several head tissues, however, are strongly
anisotropic due to their complex underlying micro-structure. This implies that
standard boundary integral formulations oversimplify the electrical properties
of the head and produce unrealistic solutions, something that drastically
limits the suitability and impact of BEM technologies to brain imaging. This
contribution addresses this issue by observing that the brain anisotropy in the
white matter is due to the presence of neuronal wire-like structures. We then
extend the well known wire integral equations used for high frequency problems
to the imperfectly conducting quasi-static case and we propose a new hybrid
wire/surface/volume integral equation. When applied on multimodal magnetic
resonance images combined with tractography, this new approach can flexibly and
realistically handle the conductivity anisotropy in any head compartment
providing high level of accuracy and efficiency. The beneficial properties of
the new formulation together with its impact on brain imaging is demonstrated
via numerical results on both canonical and realistic case scenarios.
