Computing the forward EEG solution of the multishell spherical head model for localizing electrical activity in the brain

Localization of electrical activity in the brain based on multichannel EEG measurement has been a problem of major interest in computational neuroscience. To compute the current dipole source within the brain a head volume conductor model is required which relates the EEG potentials to the underlying source. The most commonly used head model is a multishell conducting sphere whose forward solution requires a costly evaluation of an infinite sum of the Legendre polynomials. This paper presents a new algorithm which is a closed-form approximation to the exact solution. The resulting computation is accelerated by as much as sixteen times, and the approximation error is very small. A complete C-source code is provided to facilitate the application of this algorithm