One Definition to Join Them All: The N-Spherical Solution for the EEG Lead Field.

Area of Science:

• Biophysics
• Computational Neuroscience
• Medical Imaging

Background:

• The concentric spheres head model is widely used in electroencephalography (EEG) due to its computational efficiency.
• Existing formulations for the electrical lead field in this model present contradictory results in the literature.
• These discrepancies hinder accurate EEG source localization and interpretation.

Purpose of the Study:

• To investigate and resolve contradictory formulations of the electrical lead field for the concentric spheres head model.
• To identify mathematical errors in existing lead field calculations.
• To develop a generalized formulation for arbitrary multi-sphere head models.

Main Methods:

• Mathematical analysis of different lead field formulations for a four-concentric-sphere model.
• Identification and correction of errors in previously published formulae.
• Development of a novel, iterative formulation for generalized multi-sphere head models.

Main Results:

• Contradictory results from different lead field formulations were confirmed.
• Specific mathematical errors in existing formulae were identified as the cause of discrepancies.
• A new, accurate formulation for calculating lead fields in multi-sphere head models was successfully developed.

Conclusions:

• The study clarifies errors in the concentric spheres head model, improving its reliability for EEG.
• The newly developed formulation enables accurate lead field computation for complex, multi-layered head models.
• This work provides a foundation for more precise EEG source localization and brain activity analysis.