Anisotropic spherical head model and its application to imaging electric activity of the brain

This study reports on a solution to Poisson's equation describing an electric potential and field generated by a dipolar current source positioned inside a set of concentric spherical shells characterized by a homogeneous anisotropic conductivity inside each shell. Formulas giving a unique continuation of potentials and fields between the shells are derived. The formulas are applied to a spherical model of the human head to show that (i) real human skulls comprising isotropic compact and cancellous bone layers can be closely approximated by a single shell with radial-tangential conductivity anisotropy ~1:2 and radial conductivity equal to 1/30 of the brain/scalp conductivity; (ii) errors due to the spherical approximation of the head shape are of the same magnitude as errors due to poorly known electrical properties of the modeled head tissues; (iii) commonly used electroencephalography (EEG) average reference contributes 15% of the signal (on the average) and, therefore, makes EEG measurements significantly nonlocal; and (iv) the surface Laplacian of EEG measurements closely approximates electric currents at the skull-scalp interface, providing a parameter-free (up to a constant factor) deblurring and dereferencing of EEG data. These results can be useful for localization of sources underlying electric activity of the brain.