TY - JOUR
T1 - The discontinuous Galerkin finite element method for solving the MEG and the combined MEG/EEG forward problem
AU - Piastra, Maria Carla
AU - Nüßing, Andreas
AU - Vorwerk, Johannes
AU - Bornfleth, Harald
AU - Oostenveld, Robert
AU - Engwer, Christian
AU - Wolters, Carsten H.
N1 - Funding Information:
We wish to thank Professor Marco M. Fato and Dr. Gabriele Arnufo (University of Genova) for their support This work was supported by EU project ChildBrain (Marie Curie Innovative Training Networks, grant agreement 641652), by the Deutsche Forschungsgemeinschaft (DFG), project WO1425/7-1, by the Priority Program 1665 of the DFG (WO1425/5-2), and partially by the Cluster of Excellence 1003 of the Deutsche Forschungsgemeinschaft (DFG EXC 1003 Cells in Motion)
Publisher Copyright:
© 2018 Piastra, Nüßing, Vorwerk, Bornfleth, Oostenveld, Engwer and Wolters.
PY - 2018/2/2
Y1 - 2018/2/2
N2 - 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.
AB - 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.
KW - Conservation properties
KW - Dipole
KW - Discontinous Galerkin
KW - Electroencephalography (EEG)
KW - Finite element methods
KW - Magnetoencephalography (MEG)
KW - Realistic head modeling
KW - Subtraction method
KW - UT-Gold-D
UR - http://www.scopus.com/inward/record.url?scp=85041863201&partnerID=8YFLogxK
U2 - 10.3389/fnins.2018.00030
DO - 10.3389/fnins.2018.00030
M3 - Article
AN - SCOPUS:85041863201
SN - 1662-4548
VL - 12
JO - Frontiers in Neuroscience
JF - Frontiers in Neuroscience
IS - FEB
M1 - 30
ER -