Abstract
In Electro- (EEG) and Magnetoencephalography (MEG), one important requirement of source reconstruction is the forward model. The continuous Galerkin finite element method (CG-FEM) has become one of the dominant approaches for solving the forward problem over the last decades. Recently, a discontinuous Galerkin FEM (DG-FEM) EEG forward approach has been proposed as an alternative to CG-FEM (Engwer et al., 2017). It was shown that DG-FEM preserves the property of conservation of charge and that it can, in certain situations such as the so-called skull leakages, be superior to the standard CG-FEM approach. In this paper, we developed, implemented, and evaluated two DG-FEM approaches for the MEG forward problem, namely a conservative and a non-conservative one. The subtraction approach was used as source model. The validation and evaluation work was done in statistical investigations in multi-layer homogeneous sphere models, where an analytic solution exists, and in a six-compartment realistically shaped head volume conductor model. In agreement with the theory, the conservative DG-FEM approach was found to be superior to the non-conservative DG-FEM implementation. This approach also showed convergence with increasing resolution of the hexahedral meshes. While in the EEG case, in presence of skull leakages, DG-FEM outperformed CG-FEM, in MEG, DG-FEM achieved similar numerical errors as the CG-FEM approach, i.e., skull leakages do not play a role for the MEG modality. In particular, for the finest mesh resolution of 1 mm sources with a distance of 1.59 mm from the brain-CSF surface, DG-FEM yielded mean topographical errors (relative difference measure, RDM%) of 1.5% and mean magnitude errors (MAG%) of 0.1% for the magnetic field. However, if the goal is a combined source analysis of EEG and MEG data, then it is highly desirable to employ the same forward model for both EEG and MEG data. Based on these results, we conclude that the newly presented conservative DG-FEM can at least complement and in some scenarios even outperform the established CG-FEM approaches in EEG or combined MEG/EEG source analysis scenarios, which motivates a further evaluation of DG-FEM for applications in bioelectromagnetism.
Highlights
Together with electroencephalography (EEG), magnetoencephalography (MEG) is a technique used to investigate brain activity
We introduce the first application of discontinuous Galerkin finite element method (FEM) (DG-FEM) for solving the MEG forward problem
We studied the behavior of the RDM% and MAG% errors for 8,000 tangentially oriented and randomly distributed dipoles at different eccentricities
Summary
Together with electroencephalography (EEG), magnetoencephalography (MEG) is a technique used to investigate brain activity. EEG and MEG are devoted to detect the electric potential distribution and the magnetic field generated by the brain, respectively, with a unique time resolution (Brette and Destexhe, 2012). An important topic in many applications of EEG and MEG is the source reconstruction, i.e., the identification of the sources in the brain responsible for the signals recorded at the head surface (EEG) or in a small distance from the head surface (MEG). Following Hämäläinen et al (1993) and Brette and Destexhe (2012), the electric potential distribution and the resulting magnetic induction generated in the brain can be modeled through the quasistatic approximation of Maxwell’s equations, when assuming that the permeability of the tissue in the head is that of the free space, i.e., μ = μ0, ∇ × E = 0, (1a) ∇·E= ρ,.
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