Three-Dimensional Electrode Model for EEG Forward Problem

Objective: This study aims to address inaccuracies in model description and boundary representation due to dimension-ality loss in the commonly-used point electrode model (PEM) and complete electrode model (CEM) for EEG forward problem (FP). Methods: To overcome these limitations, this paper proposes a three-dimensional electrode model (TEM). Firstly, we devise an extension-constraint framework to generate an electrode mesh based on the structural priors and seamlessly integrate it into the MRI-based head mesh through two modules: (1) an extension module designed to extend a cuboid mesh containing both head and electrode meshes to avoid the challenges in fusing two irregular stepped surface mesh, and (2) loosely coupled constraints formulated in the constraint module to describe the electrode structure and enhance the flexibility and extensibility. Secondly, an accurate boundary representation is achieved by setting a local equipotential on the metal surface of the electrodes. Results: Experimental results indicate that, compared with PEM and CEM, TEM exhibits significant differences in FP and inverse problem. Further explorations reveal that alterations in electrode height, structure, and contact area exert a more profound impact than conductivity, whereas the impact of air bubbles, hair, and gel bridges is structure-dependent. Conclusion: The proposed TEM has the potential to enhance the solution accuracy of FP and inverse problem. Significance: This paper introduces an ingenious method for incorporating the 3D structure of electrodes into FP solution to improve the accuracy and explore the effect of electrode structure.