A highly accurate full subtraction approach for dipole modelling in EEG source analysis using the finite element method
Florian Drechsler, Carsten H. Wolters, Thomas Dierkes, Hang Si,and Lars Grasedyck
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Submission date: 25. Oct. 2007
published in: NeuroImage, 46 (2009) 4, p. 1055-1065
DOI number (of the published article): 10.1016/j.neuroimage.2009.02.024
with the following different title: A full subtraction approach for finite element method based source analysis using constrained Delaunay tetrahedralisation
Keywords and phrases: source reconstruction, electroencephalography, full subtraction approach, finite element method, constrained Delaunay tetrahedralisation, projected subtraction approach, transfer matrices, validation in four-layer sphere models, electronencephalography, dipole, validateion in four-layer sphere models
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A mathematical dipole is widely used as a model for the primary current source in electroencephalography (EEG) source analysis. In the governing Poisson-type dif- ferential equation, the dipole leads to a singularity on the right-hand side, which has to be treated speciﬁcally. In this paper, we will present a full subtraction approach where the total potential is divided into a singularity and a correction potential. The singularity potential is due to a dipole in an inﬁnite region of homogeneous conductivity. The correction potential is computed using the ﬁnite element (FE) method. Special care is taken to appropriately evaluate the right-hand side integral with the objective of achieving highest possible convergence order for linear basis functions. Our new approach allows the construction of transfer matrices for fast computation of the inverse problem for volume conductors with arbitrary local and remote conductivity anisotropy. A constrained Delaunay tetrahedralisation (CDT) approach is used for the generation of high-quality FE meshes. We validate the new approach in a four-layer sphere model with anisotropic skull compartment. For ra- dial and tangential sources with eccentricities up to 1mm below the cerebrospinal ﬂuid compartment, we achieve a maximal relative error of 0.71% in a tetrahedra model with 360K nodes which is not locally reﬁned around the source singularity. The combination of the full subtraction approach with the high quality CDT meshes leads to accuracies that, to the best of the authors knowledge, have not yet been presented before.