Electroencephalography records brain electrical activity arising from synchronized synaptic activity of neurons in the cerebral cortex, as measured at the scalp surface. In this work, neural activity is modeled as an equivalent current dipole with arbitrary orientation located within the innermost conductive layer. To represent the head anatomy, the volume conductor is modeled as a central brain compartment enclosed by concentric spherical shells representing the cerebrospinal fluid (CSF), skull, and scalp, with different conductivity values. The present study incorporates anisotropic conductivity with distinct radial and tangential components within a multilayer spherical head model by extending existing analytical formulations. While analytical solutions for isotropic spherical models are well established, anisotropic formulations are typically addressed using numerical or approximate methods. By applying spherical harmonics to the Poisson equation in layered anisotropic media, analytical expressions are derived for the electric potential generated by dipole sources. The forward model is evaluated using electrode positions (θ, φ) defined according to the EEGLAB layout, for a representative configuration with a head radius of 9.2 cm. Quantitative comparisons are performed using MAG and RDM metrics for homogeneous and inhomogeneous anisotropic conductivity models. The results indicate that conductivity anisotropy significantly influences both the magnitude and spatial distribution of scalp potentials, particularly due to attenuation and spatial smoothing effects introduced by the skull layer. The analytical expressions derived contribute to the theoretical study of EEG forward modeling in anisotropic layered media and may serve as reference solutions for the assessment of numerical formulations.
Bampali et al. (Sat,) studied this question.