Inverse calculations in EEG source analysis applying the finite difference method, reciprocity and lead fields

The advances in computer power and memory make the finite difference method (FDM) attractive to solve the Poison differential equation. To reduce the calculation time of the inverse procedure in EEG source analysis, the concept of lead fields in combination with the reciprocity theorem are utilized. First the accuracy of the finite difference method is evaluated in a three-shell spherical head model. The potentials at the 27 EEG scalp electrodes are obtained using the FDM in a cubic grid with node spacing of 2.5 mm. The inverse problem is solved applying the analytical expression. The mean localization error is 2 mm (ranging from 0.3 to 4.5 mm for 18 dipoles). Next, the potentials at the electrodes are given by the analytical expression. The inverse fit is then done utilizing 26 lead fields calculated numerically in a cubic grid with node spacing of 4 mm. The mean localization error is 4.1 mm (ranging from 1.2 mm to 7 mm for 18 dipoles). Finally a realistic head model is used. The potentials at the electrodes, obtained numerically in a grid with node spacing of 2.5 mm, are brought in the inverse procedure. 26 lead fields calculated numerically in a grid with node spacing of 4 mm, are then applied to perform the inverse calculations. The mean localization error is 4 mm (ranging from 0.9 to 7.2 mm for 12 dipoles). These result suggest that the FDM in combination with the lead field concept can be used for EEG source analysis