2015/11/16 by Christian Engwer, Johannes Vorwerk, Engwer, Christian +5
Engineering · Neuroscience · #35J25 #35J75 #35Q90 #65N12 #65N30 #68U20 #92C50 #Computational Engineering #Electrical and Bioimpedance Tomography #FOS: Biological sciences #FOS: Computer and information sciences #FOS: Mathematics #Finance #G.1.10 #G.1.8 #I.6.0 #J.3 #Neural dynamics and brain function #Neurons and Cognition (q-bio.NC) #Numerical Analysis (math.NA) #Sparse and Compressive Sensing Techniques #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.1511.04892
openalex publication_date 2015/11/16 · openalex created_date 2022/10/04 · openalex updated_date 2026/08/01
In order to perform electroencephalography (EEG) source reconstruction, i.e.,\nto localize the sources underlying a measured EEG, the electric potential\ndistribution at the electrodes generated by a dipolar current source in the\nbrain has to be simulated, which is the so-called EEG forward problem. To solve\nit accurately, it is necessary to apply numerical methods that are able to take\nthe individual geometry and conductivity distribution of the subject's head\ninto account. In this context, the finite element method (FEM) has shown high\nnumerical accuracy with the possibility to model complex geometries and\nconductive features, e.g., white matter conductivity anisotropy. In this\narticle, we introduce and analyze the application of a discontinuous Galerkin\n(DG) method, a finite element method that includes features of the finite\nvolume framework, to the EEG forward problem. The DG-FEM approach fulfills the\nconservation property of electric charge also in the discrete case, making it\nattractive for a variety of applications. Furthermore, as we show, this\napproach can alleviate modeling inaccuracies that might occur in head\ngeometries when using classical FE methods, e.g., so-called "skull leakage\neffects", which may occur in areas where the thickness of the skull is in the\nrange of the mesh resolution. Therefore, we derive a DG formulation of the FEM\nsubtraction approach for the EEG forward problem and present numerical results\nthat highlight the advantageous features and the potential benefits of the\nproposed approach.\n