Rapidly recomputable EEG forward models for realistic head shapes

With the increasing availability of surface extraction techniques for magne tic resonance and x-ray computed tomography images, realistic head models c an be readily generated as forward models in the analysis of electroencepha lography (EEG) and magnetoencephalography (MEG) data. Inverse analysis of t his data, however, requires that the forward model be computationally effic ient. We propose two methods for approximating the EEG forward model using realistic head shapes. The 'sensor-fitted sphere' approach fits a multilaye r sphere individually to each sensor, and the 'three-dimensional interpolat ion' scheme interpolates using a grid on which a numerical boundary element method (BEM) solution has been precomputed. We have characterized the perf ormance of each method in terms of magnitude and subspace error metrics, as well as computational and memory requirements. We have also made direct pe rformance comparisons with traditional spherical models. The approximation provided by the interpolative scheme had an accuracy nearly identical to fu ll BEM, even within 3 mm of the inner skull surface. Forward model computat ion during inverse procedures was approximately 30 times faster than for a traditional three-shell spherical model. Cast in this framework, high-fidel ity numerical solutions currently viewed as computationally prohibitive for solving the inverse problem (e.g. linear Galerkin BEM) can be rapidly reco mputed in a highly efficient manner. The sensor-fitting method has a simila r one-time cost to the BEM method, and while it produces some improvement o ver a standard three-shell sphere, its performance does not approach that o f the interpolation method. In both methods, there is a one-time cost assoc iated with precomputing the forward solution over a set of grid points.