A comprehensive study on electroencephalography and magnetoencephalography sensitivity to cortical and subcortical sources.

Signal-to-noise ratio (SNR) maps are a good way to visualize electroencephalography (EEG) and magnetoencephalography (MEG) sensitivity. SNR maps extend the knowledge about the modulation of EEG and MEG signals by source locations and orientations and can therefore help to better understand and interpret measured signals as well as source reconstruction results thereof. Our work has two main objectives. First, we investigated the accuracy and reliability of EEG and MEG finite element method (FEM)-based sensitivity maps for three different head models, namely an isotropic three and four-compartment and an anisotropic six-compartment head model. As a result, we found that ignoring the cerebrospinal fluid leads to an overestimation of EEG SNR values. Second, we examined and compared EEG and MEG SNR mappings for both cortical and subcortical sources and their modulation by source location and orientation. Our results for cortical sources show that EEG sensitivity is higher for radial and deep sources and MEG for tangential ones, which are the majority of sources. As to the subcortical sources, we found that deep sources with sufficient tangential source orientation are recordable by the MEG. Our work, which represents the first comprehensive study where cortical and subcortical sources are considered in highly detailed FEM-based EEG and MEG SNR mappings, sheds a new light on the sensitivity of EEG and MEG and might influence the decision of brain researchers or clinicians in their choice of the best modality for their experiment or diagnostics, respectively.

A realistic, accurate and fast source modeling approach for the EEG forward problem.

The aim of this paper is to advance electroencephalography (EEG) source analysis using finite element method (FEM) head volume conductor models that go beyond the standard three compartment (skin, skull, brain) approach and take brain tissue inhomogeneity (gray and white matter and cerebrospinal fluid) into account. The new approach should enable accurate EEG forward modeling in the thin human cortical structures and, more specifically, in the especially thin cortices in children brain research or in pathological applications. The source model should thus be focal enough to be usable in the thin cortices, but should on the other side be more realistic than the current standard mathematical point dipole. Furthermore, it should be numerically accurate and computationally fast. We propose to achieve the best balance between these demands with a current preserving (divergence conforming) dipolar source model. We develop and investigate a varying number of current preserving source basis elements n (n=1,…,n=5). For validation, we conducted numerical experiments within a multi-layered spherical domain, where an analytical solution exists. We show that the accuracy increases along with the number of basis elements, while focality decreases. The results suggest that the best balance between accuracy and focality in thin cortices is achieved with n=4 (or in extreme cases even n=3) basis functions, while in thicker cortices n=5 is recommended to obtain the highest accuracy. We also compare the current preserving approach to two further FEM source modeling techniques, namely partial integration and St. Venant, and show that the best current preserving source model outperforms the competing methods with regard to overall balance. For all tested approaches, FEM transfer matrices enable high computational speed. We implemented the new EEG forward modeling approaches into the open source duneuro library for forward modeling in bioelectromagnetism to enable its broader use by the brain research community. This library is build upon the DUNE framework for parallel finite elements simulations and integrates with high-level toolboxes like FieldTrip. Additionally, an inversion test has been implemented using the realistic head model to demonstrate and compare the differences between the aforementioned source models.

The Discontinuous Galerkin Finite Element Method for Solving the MEG and the Combined MEG/EEG Forward Problem.

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.