Electroencephalography (EEG) Forward Modeling via H(div) Finite Element Sources with Focal Interpolation

TL;DR

This paper introduces a divergence-conforming finite element method for EEG forward modeling that accurately predicts surface potentials from complex source configurations, improving upon classical methods.

Contribution

It develops a mathematically rigorous H(div) finite element approach with novel dipolar source interpolation techniques for EEG forward modeling.

Findings

Dipolar approach matches or exceeds classical methods in accuracy.

Focal and robust source placement improves EEG potential predictions.

New interpolation methods enhance modeling of complex source configurations.

Abstract

The goal of this study is to develop focal, accurate and robust finite element method (FEM) based approaches which can predict the electric potential on the surface of the computational domain given its structure and internal primary source current distribution. While conducting an EEG evaluation, the placement of source currents to the geometrically complex grey matter compartment is a challenging but necessary task to avoid forward errors attributable to tissue conductivity jumps. Here, this task is approached via a mathematically rigorous formulation, in which the current field is modeled via divergence conforming H(div) basis functions. Both linear and quadratic functions are used while the potential field is discretized via the standard linear Lagrangian (nodal) basis. The resulting model includes dipolar sources which are interpolated into a random set of positions and orientations utilizing two alternative approaches: the position based optimization (PBO) and the mean position/orientation (MPO) method. These results demonstrate that the present dipolar approach can reach or even surpass, at least in some respects, the accuracy of two classical reference methods, the partial integration (PI) and St. Venant (SV) approach which utilize monopolar loads instead of dipolar currents.