Evaluation of boundary element methods for the EEG forward problem: effect of linear interpolation

Area of Science:

• Computational neuroscience
• Biophysics
• Medical imaging

Background:

• The electroencephalography (EEG) forward problem is crucial for understanding brain activity.
• Existing numerical methods often simplify electric potential assumptions within mesh elements.
• Accurate modeling is essential for interpreting EEG signals.

Purpose of the Study:

• To implement and evaluate a boundary integral equation approach for the EEG forward problem.
• To investigate the impact of linear potential variation across mesh elements compared to constant potential assumptions.
• To assess the influence of mesh resolution and dipole location on solution accuracy.

Main Methods:

• Implementation of the de Munck boundary integral equation method for the EEG forward problem.
• Utilizing a linear interpolation approximation for electric potential across plane triangle elements.
• Employing a three concentric sphere head model with a known analytic solution for validation.
• Systematic analysis of electric potential calculation with varying mesh choices and dipole positions.

Main Results:

• The linear interpolation approximation significantly reduces errors compared to constant potential assumptions.
• Errors were approximately halved when using the linear approximation with the same mesh.
• The method demonstrates reliability across different mesh configurations and dipole locations.
• Validation against an analytic solution confirms the accuracy of the implemented approach.

Conclusions:

• Linear interpolation of electric potential across mesh elements is a more accurate and reliable method for solving the EEG forward problem.
• This refined approach offers improved precision in EEG signal interpretation.
• The findings support the adoption of more sophisticated approximations in numerical modeling for EEG.