Four-Sphere Head Model For EEG Signals Revisited

Abstract

Electric potential recorded at the scalp (EEG) is dominated by contributions from current dipoles set by active neurons in the cortex. Estimation of these currents, called inverse modeling, requires a forward model, which gives the potential when the positions, sizes, and directions of the current dipoles are known. Di[ff]erent models of varying complexity and realism are used in the field. An important analytical example is the four-sphere model which assumes a four-layered spherical head where the layers represent brain tissue, cerebrospinal fluid (CSF), skull, and scalp, respectively. This model has been used extensively in the analysis of EEG recordings. Since it is analytical, it can also serve as a benchmark against which numerical schemes, such as the Finite Element Method (FEM), can be tested. While conceptually clear, the mathematical expression for the scalp potentials in the four-sphere model is quite cumbersome, and we observed the formulas presented in the literature to contain errors. We here derive and present the correct analytical formulas for future reference. They are compared with the results of FEM simulations of four-sphere model. We also provide scripts for computing EEG potentials in this model with the correct analytical formula and using FEM.