Improved EEG source localization with Bayesian uncertainty modelling of unknown skull conductivity

Electroencephalography (EEG) source imaging is an ill-posed inverse problem that requires accurate conductivity modelling of the head tissues, especially the skull. Unfortunately, the conductivity values are difficult to determine in vivo. In this paper, we show that the exact knowledge of the skull conductivity is not always necessary when the Bayesian approximation error (BAE) approach is exploited. In BAE, we first postulate a probability

The Effect of Head Model Simplification on Beamformer Source Localization

Beamformers are a widely-used tool in brain analysis with magnetoencephalography (MEG) and electroencephalography (EEG). For the construction of the beamformer filters realistic head volume conductor modeling is necessary for accurately computing the EEG and MEG leadfields, i.e., for solving the EEG and MEG forward problem. In this work, we investigate the influence of including realistic head tissue compartments into a finite element method (FEM) model on the beamformer's localization ability. Specifically, we investigate the effect of including cerebrospinal fluid, gray matter, and white matter distinction, as well as segmenting the skull bone into compacta and spongiosa, and modeling white matter anisotropy. We simulate an interictal epileptic measurement with white sensor noise. Beamformer filters are constructed with unit gain, unit array gain, and unit noise gain constraint. Beamformer source positions are determined by evaluating power and excess sample kurtosis (g2) of the source-waveforms at all source space nodes. For both modalities, we see a strong effect of modeling the cerebrospinal fluid and white and gray matter. Depending on the source position, both effects can each be in the magnitude of centimeters, rendering their modeling necessary for successful localization. Precise skull modeling mainly effected the EEG up to a few millimeters, while both modalities could profit from modeling white matter anisotropy to a smaller extent of 5–10 mm. The unit noise gain or neural activity index beamformer behaves similarly to the array gain beamformer when noise strength is sufficiently high. Variance localization seems more robust against modeling errors than kurtosis

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

Can individually targeted and optimized multi-channel tDCS outperform standard bipolar tDCS in stimulating the primary somatosensory cortex?

Background: Transcranial direct current stimulation (tDCS) has emerged as a non-invasive neuro-modulation technique. Most studies show that anodal tDCS increases cortical excitability, however, withvariable outcomes. Previously, we have shown in computer simulations that our multi-channel tDCS (mc-tDCS) approach, the distributed constrained maximum intensity (D-CMI) method can potentially lead to better controlled tDCS results due to the improved directionality of the injected current at the target side for individually optimized D-CMI montages. Objective: In this study, we test the application of the D-CMI approach in an experimental study to stimulate the somatosensory P20/N20 target source in Brodmann area 3b and compare it with standard bipolar tDCS and sham onditions. Methods: We applied anodal D-CMI, the standard bipolar and D-CMI based Sham tDCS for 10 min to target the 20 ms post-stimulus somatosensory P20/N20 target brain source in Brodmann area 3b reconstructed using combined magnetoencephalography (MEG) and electroencephalography (EEG) source analysis in realistic head models with calibrated skull conductivity in a group-study with 13 subjects. Finger-stimulated somatosensory evoked fields (SEF) were recorded and the component at 20 ms post-stimulus (M20) was analyzed before and after the application of the three tDCS conditions in order to read out the stimulation effect on Brodmann area 3b. Results: Analysis of the finger stimulated SEF M20 peak before (baseline) and after tDCS shows a significant increase in source amplitude in Brodmann area 3b for D-CMI (6-16 min after tDCS), while no significant effects are found for standard bipolar (6-16 min after tDCS) and sham (6-16 min after tDCS) stimulation conditions. For the later time courses (16-26 and 27-37 min post-stimulation), we found a significant decrease in M20 peak source amplitude for standard bipolar and sham tDCS, while there was no effect for D-CMI. Conclusion: Our results indicate that targeted and optimized, and thereby highly individualized, mc-tDCS can outperform standard bipolar stimulation and lead to better control over stimulation outcomes with, however, a considerable amount of additional work compared to standard bipolar tDCS

DUNEuro—A software toolbox for forward modeling in bioelectromagnetism

Accurate and efficient source analysis in electro- and magnetoencephalography using sophisticated realistic head geometries requires advanced numerical approaches. This paper presents DUNEuro, a free and open-source C++ software toolbox for the numerical computation of forward solutions in bioelectromagnetism. Building upon the DUNE framework, it provides implementations of modern fitted and unfitted finite element methods to efficiently solve the forward problems of electro- and magnetoencephalography. The user can choose between a variety of different source models that are implemented. The software’s aim is to provide interfaces that are extendable and easy-to-use. In order to enable a closer integration into existing analysis pipelines, interfaces to Python and MATLAB are provided. The practical use is demonstrated by a source analysis example of somatosensory evoked potentials using a realistic six-compartment head model. Detailed installation instructions and example scripts using spherical and realistic head models are appended