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Objective: The purpose of this study is to introduce and evaluate theunfitted discontinuous Galerkin finite element method (UDG-FEM) for solving theelectroencephalography (EEG) forward problem. Methods: This new approach forsource analysis does not use a geometry conforming volume triangulation, butinstead uses a structured mesh that does not resolve the geometry. The geometryis described using level set functions and is incorporated implicitly in itsmathematical formulation. As no triangulation is necessary, the complexity of asimulation pipeline and the need for manual interaction for patient specificsimulations can be reduced and is comparable with that of the FEM forhexahedral meshes. In addition, it maintains conservation laws on a discretelevel. Here, we present the theory for UDG-FEM forward modeling, itsverification using quasi-analytical solutions in multi-layer sphere models andan evaluation in a comparison with a discontinuous Galerkin (DG-FEM) method onhexahedral and on conforming tetrahedral meshes. We furthermore apply theUDG-FEM forward approach in a realistic head model simulation study. Results:The given results show convergence and indicate a good overall accuracy of theUDG-FEM approach. UDG-FEM performs comparable or even better than DG-FEM on aconforming tetrahedral mesh while providing a less complex simulation pipeline.When compared to DG-FEM on hexahedral meshes, an overall better accuracy isachieved. Conclusion: The UDG-FEM approach is an accurate, flexible andpromising method to solve the EEG forward problem. Significance: This studyshows the first application of the UDG-FEM approach to the EEG forward problem.

The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem