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

**2016-01-28**

1601.07810 | cs.CE

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

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