The Unfitted Discontinuous Galerkin Method for Solving the EEG Forward Problem
| Autor: | Andreas Nüßing, Christian Engwer, Carsten H. Wolters, Heinrich Brinck |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Adult
Male FOS: Computer and information sciences J.3 Computer science Pipeline (computing) Finite Element Analysis Biomedical Engineering G.1.8 010103 numerical & computational mathematics 35J25 35J75 35Q92 65N30 68U20 92C50 01 natural sciences Models Biological Computational Engineering Finance and Science (cs.CE) 03 medical and health sciences 0302 clinical medicine Level set G.1.10 Discontinuous Galerkin method FOS: Mathematics Humans Polygon mesh I.6.0 Mathematics - Numerical Analysis 0101 mathematics Computer Science - Computational Engineering Finance and Science ComputingMethodologies_COMPUTERGRAPHICS Conservation law Models Statistical Triangulation (social science) Brain Electroencephalography Numerical Analysis (math.NA) Finite element method Quantitative Biology - Neurons and Cognition FOS: Biological sciences Neurons and Cognition (q-bio.NC) Hexahedron Algorithm Head 030217 neurology & neurosurgery |
| Zdroj: | IEEE Transactions on Biomedical Engineering |
| DOI: | 10.48550/arxiv.1601.07810 |
| Popis: | 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. Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible |
| Databáze: | OpenAIRE |
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