COMPUTATIONAL ASPECTS OF FINITE-ELEMENT MODELING IN EEG SOURCE LOCALIZATION

A comparison is made of two different implementations of the finite el ement method (FEM) for calculating the potential due to dipole sources in electroencephalography (EEG), In one Formulation (the direct metho d) the total potential is the unknown that is solved for and the dipol e source is directly incorporated into the model, In the second formul ation (the subtraction method) the unknown is the difference between t he total potential and the potential due to the same dipole in an infi nite region of homogeneous conductivity, corresponding to the region w here the dipole is located, Both methods have the same FEM system matr ix, However, the subtraction method requires an additional calculation of flux integrations along the edges of I-he elements in the computat ion of the right-hand side (RHS) vector, It is shown that: the subtrac tion method is usually more accurate in the forward modeling, provided the flux integrations are computed accurately, Errors in calculating the flux integrations may result in large errors in the forward soluti on due to the ill-conditioned nature of the FEM system matrix caused b y the Neumann boundary condition, To minimize the errors, closed-form expressions for the flux integrations are used for both linear and qua dratic triangular elements, It is also Found that FEM forward modeling errors mag cause false extrema in the least-square objective function obtained from the boundary potential, near boundaries between media o f differing conductivity. Multiple initial guesses help eliminate the possibility of the solution getting trapped in these false extrema.