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 method 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 conductivity of the compartment model is described, which can reduce errors in estimated dipole location caused by incorrect head geometry. The concept of reciprocity is explained, which is applied to understanding a relation between the electrode configuration and its sensitivity for various source conditions. Typical techniques for solving the inverse problem are reviewed for discrete source models. Methods of estimating accuracy of the dipole location in the presence of noise are discussed, together with some numerical examples. 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 model parameters is given in terms of AIC (Akaike Information Criterion), which is applied to decide the most probable number of equivalent dipoles.