Fast realistic modeling in bioelectromagnetism using lead-field interpolation

The practical use of realistic models in bioelectromagnetism is limited by the time-consuming amount of numerical calculations. We propose a method le ading to much higher speed than currently available, and compatible with an y kind of numerical methods (boundary elements (BEM), finite elements, fini te differences). Illustrated with the BEM for EEG and MEG, it applies to EC G and MCG as well. The principle is two-fold. First, a Lead-Field matrix is calculated (once for all) for a grid of dipoles covering the brain volume. Second, any forward solution is interpolated from the pre-calculated Lead- Fields corresponding to grid dipoles near the source. Extrapolation is used for shallow sources falling outside the grid. Three interpolation techniqu es were tested: trilinear, second-order Bezier (Bernstein polynomials), and 3D spline. The trilinear interpolation yielded the highest speed gain, wit h factors better than x 10,000 for a 9,000-triangle BEM model. More accurat e results could be obtained with the Bezier interpolation (speed gain simil ar to1,000), which, combined with a 8-mm step grid, lead to intrinsic local ization and orientation errors of only 0.2 mm and 0.2 degrees. Further impr ovements in MEG could be obtained by interpolating only the contribution of secondary currents. Cropping grids by removing shallow points lead to a mu ch better estimation of the dipole orientation in EEG than when solving the forward problem classically, providing an efficient alternative to locally refined models. This method would show special usefulness when combining r ealistic models with stochastic inverse procedures (simulated annealing, ge netic algorithms) requiring many forward calculations. Hum, Brain Mapping 1 4:48-63, 2001. (C) 2001 Wiley-Liss, Inc.