# Handling Anisotropic Conductivities in the EEG Forward Problem with a Symmetric Formulation

## TL;DR

This paper introduces a modified symmetric surface integral formulation for the EEG forward problem that effectively models anisotropic conductivities in the skull and white matter, improving accuracy in source analysis.

## Contribution

It presents a novel surface integral equation approach that incorporates anisotropic conductivity profiles using an anisotropic fundamental solution.

## Key findings

- The proposed method accurately models anisotropic conductivities.
- Numerical results demonstrate improved forward problem solutions.
- Impact shown on both canonical and real EEG scenarios.

## Abstract

The electroencephalography (EEG) forward problem, the computation of the electric potential generated by a known electric current source configuration in the brain, is a key step of EEG source analysis. In this problem, it is often desired to model the anisotropic conductivity profiles of the skull and of the white matter. These profiles, however, cannot be handled by standard surface integral formulations and the use of volume finite elements is required. Leveraging on the representation theorem using an anisotropic fundamental solution, this paper proposes a modified symmetric formulation for solving the EEG forward problem by a surface integral equation which can take into account anisotropic conductivity profiles. A set of numerical results is presented to corroborate theoretical treatments and to show the impact of the proposed approach on both canonical and real case scenarios.