Forward and inverse problems of EEG dipole localization

Mathematical procedures are discussed in detail of numerical solutions for obtaining scalp potentials from the electric sources. The finite-element me thod for an inhomogeneous volume conductor, the boundary-element method for a compartment model, and their hybrid for more general cases are discussed . Construction of the head model and typical estimation of electric conduct ivity of the compartment model is described, which can reduce errors in est imated dipole location caused by incorrect head geometry. The concept of re ciprocity is explained, which is applied to understanding a relation betwee n the electrode configuration and its sensitivity for various source condit ions. Typical techniques for solving the inverse problem are reviewed for d iscrete source models. Methods of estimating accuracy of the dipole locatio n in the presence of noise are discussed, together with some numerical exam ples. The dipolarity is a goodness-of-fit of the dipole approximation, and lowering of the dipolarity is related to inhomogeneous neuronal activity in the cortex. Finally, a criterion of determining the optimal number of mode l parameters is given in terms of AIC (Akaike Information Criterion), which is applied to decide the most probable number of equivalent dipoles.