The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem.

Area of Science:

• Computational neuroscience
• Medical physics
• Numerical analysis

Background:

• The electroencephalography (EEG) forward problem is crucial for understanding brain activity.
• Traditional methods for solving the EEG forward problem often involve complex, geometry-conforming meshes, increasing computational cost and requiring manual intervention.
• Developing efficient and accurate numerical methods is essential for advancing EEG source analysis.

Purpose of the Study:

• To introduce and evaluate the unfitted discontinuous Galerkin finite element method (UDG-FEM) for solving the EEG forward problem.
• To assess the accuracy and efficiency of UDG-FEM compared to existing methods.
• To demonstrate the applicability of UDG-FEM in realistic head models.

Main Methods:

• The study employs the unfitted discontinuous Galerkin finite element method (UDG-FEM), which utilizes a structured mesh without requiring geometry-conforming triangulation.
• Level set functions are used to implicitly incorporate complex geometries.
• The method was verified using quasi-analytical solutions in multilayer sphere models and compared against the discontinuous Galerkin finite element method (DG-FEM) on hexahedral and tetrahedral meshes.

Main Results:

• UDG-FEM demonstrated convergence to quasi-analytical solutions, indicating good accuracy.
• The method achieved comparable or superior accuracy to DG-FEM on conforming tetrahedral meshes.
• UDG-FEM provided better accuracy than DG-FEM on hexahedral meshes and resulted in a less complex simulation pipeline.

Conclusions:

• The unfitted discontinuous Galerkin finite element method (UDG-FEM) is an accurate, flexible, and promising approach for the EEG forward problem.
• UDG-FEM offers a simplified simulation pipeline, reducing the need for manual interaction in patient-specific simulations.
• This study represents the first application of UDG-FEM to the EEG forward problem, highlighting its potential for advancing EEG source analysis.