Rapidly re-computable EEG (electroencephalography) forward models for realistic head shapes

Solution of the EEG source localization (inverse) problem utilizing model-based methods typically requires a significant number of forward model evaluations. For subspace based inverse methods like MUSIC (6), the total number of forward model evaluations can often approach an order of 103 or 104. Techniques based on least-squares minimization may require significantly more evaluations. The observed set of measurements over an M-sensor array is often expressed as a linear forward spatio-temporal model of the form: F = GQ + N (1) where the observed forward field F (M-sensors x N-time samples) can be expressed in terms of the forward model G, a set of dipole moment(s) Q (3xP-dipoles x N-time samples) and additive noise N. Because of their simplicity, ease of computation, and relatively good accuracy, multi-layer spherical models (7) (or fast approximations described in (1), (7)) have traditionally been the 'forward model of choice' for approximating the human head. However, approximation of the human head via a spherical model does have several key drawbacks. By its very shape, the use of a spherical model distorts the true distribution of passive currents in the skull cavity. Spherical models also require that the sensor positions be projected onto the fitted sphere (Fig. 1), resulting in a distortion of the true sensor-dipole spatial geometry (and ultimately the computed surface potential). The use of a single 'best-fitted' sphere has the added drawback of incomplete coverage of the inner skull region, often ignoring areas such as the frontal cortex. In practice, this problem is typically countered by fitting additional sphere(s) to those region(s) not covered by the primary sphere. The use of these additional spheres results in added complication to the forward model. Using high-resolution spatial information obtained via X-ray CT or MR imaging, a realistic head model can be formed by tessellating the head into a set of contiguous regions (typically the scalp, outer skull, and inner skull surfaces). Since accurate in vivo determination of internal conductivities is currently not currently possible, the head is typically assumed to consist of a set of contiguous isotropic regions, each with constant conductivity.