Source reconstruction is used to improve the interpretation of surface-level electroencephalography (EEG) and magnetoencephalography (MEG) measurements. It has been shown that combined EEG/MEG provides source reconstructions that outperform the ones provided by single modalities. To compute the EEG/MEG source reconstruction, which is an inverse problem, the forward problem has to be solved. When computing the EEG/MEG forward problem in realistically shaped head models, numerical methods have to be adopted. In this work, we deal with finite element methods (FEMs), focusing on fulfilling the conservation of charge law. Specific consequences of the conservation law have been observed in an EEG study, where the unwanted phenomenon of “skull leakages” was overcome by using a discontinuous Galerkin FEM (DG-­FEM) instead of a classical, continuous Galerkin FEM (CG­-FEM). As a consequence of the conservation law fulfillment, in “leaky scenarios” the accuracy of EEG results is increased by the DG­-FEM scheme. In the same scenarios, it can be desirable to proceed with MEG investigations without changing the discretization underneath. When implementing the standard formulation of the MEG solution, the accuracy of the results is compromised by a non-­conservative current reconstruction. Here, we present an improved approach that exploits the conservation law, thus providing a conservative current reconstruction and leading to results in the same range of accuracy of the ones of a CG-­FEM implementation for MEG. Finally, DG­-FEM makes it possible to perform combined EEG and MEG forward computations using the same discretization in those scenarios where DG-­FEM leads to advantages.

Beamformers are often applied in estimating locations and strengths of neuronal sources underlying the measured MEG/EEG signals. Several MEG analysis toolboxes have implemented linearly constrained minimum variance (LCMV) beamformers, but there are still remaining issues such as the effects of novel interference suppression methods such as signal-space separation (SSS) and its variants. Differences in implementations and processing pipelines in the packages complicates the application of beamformers and may hinder their wider adoption in research and clinical uses.

In this study, we compared event-related beamformer results obtained with four software packages (Fieldtrip, SPM12, Elekta Beamformer and MNE Python) with different noise covariance matrices applied to raw and SSS-preprocessed data from a 306-channel Elekta MEG system.

First, we applied the packages on phantom data where location and strength of sources are known. There were substantial source localization differences (up to 10 mm) between results obtained from the different packages and SSS effected the results.

Next, we utilized somatosensory evoked responses acquired with the Elekta MEG device from a healthy subject. Electrical stimulation was delivered separately to the tip of four fingers of right hand, resulting in relatively weak SEF responses (~10 nAm). We computed the event-related beamformer power normalized by projected noise (Z2) images. The obtained sources from the packages were mostly localized in hand somatosensory area but there were 5-15 mm differences across the packages.

These implementation-dependent differences in results should be understood thoroughly, and guidelines for comparable use of different packages should be established to obtain reliable clinical results.

Combined magnetoencephalography and electroencephalography recordings were collected to investigate the differences in source reconstruction of the primary somatosensory cortex following electrical wrist stimulation of the median nerve (EW) and hapto-tactile (HT) and pneumato-tactile (PT) stimulation of the index finger. The functional data (275 gradiometers and 80 electrodes) were preprocessed for artifact elimination. Magnetic resonance images (T1w- and T2w-MRI scans) were collected and segmented into six compartments (skin, compacta, spongiosa, cerebrospinal fluid, grey and white matter). Furthermore, diffusion weighted MRI was measured allowing to model white matter conductivity anisotropy to investigate its influence on especially source orientation. A six-compartment anisotropic finite element head model was constructed with individually calibrated skull conductivity. With regard to the reconstruction of the P20 component, only small differences in source locations (7mm) among the three stimulations, while significant source orientation changes between EW and PT (53o degrees) and between EW and HT (40o degrees) and also significantly higher EW source amplitude (37.6 μAmm) than for HT (6.37 μAmm) and PT (7.83 μAmm) were found. Our results might be interpreted in the way that EW causes a higher number of pyramidal cells in somatosensory area 3b to synchronize leading then to better SNR. EW might thus be called the most robust type of somatosensory stimulation. However, compared to PT and HT stimulation, EW might be less acceptable because of slightly painly kind of stimulation, especially for long – lasting stimulations or application in children. Alternatively, HT might be used instead of EW avoiding any kind of discomfort.

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to the conductivity of the different head tissues. Conductivity values are time and subject dependent, so non-invasive methods of conductivity estimation are necessary to fine tune the EEG models. In this work, we aim at estimating conductivity while solving the EEG source localization problem. To do this, we need to compute a forward EEG problem solution (so-called lead field matrix) for a large number of conductivity configurations.

Computing one lead field requires a matrix inversion which is computationally intensive for realistic head models. Thus, the required time for computing of a large number of solutions quickly becomes impractical. In this work, we propose a method which allows us to approximate the lead field matrix for a set of conductivity configurations, using only the exact solution for a small set of basis points from the conductivity space. Our approach accelerates the computing time, while the approximation error remains controlled.

Our method is tested for brain and skull conductivity estimation, with simulated and real EEG data. In the case of real data, we process EEG evoked potentials of median nerve stimulation. We used a single-dipole model to estimate both source location and conductivities of brain and skull. Our approximation method offers a performance similar to using exact lead field matrices, but with a remarkable gain of time.

High density scalp EEG data is routinely collected with a sampling rate of 1 KHz. However, higher sampling rates of up to 16 KHz/channel are available. We examined what additional information can be derived from EEG data sampled at a higher rate. We compared power spectral densities (PSD) and phase clustering behavior of EEG data sampled at 16.384 KHz and at 1.024 KHz. The PSD plots were similar at both sampling frequencies. However, there were significant differences in the spatiotemporal analysis of EEG phase cone formations. The data of an adult subject was collected with an ANT Neuro 256-channel system (eego mylab) with 16.384 KHz/channel sampling frequency. This data set was down sampled at 1.024 KHz/channel for a comparative analysis. The PSD was calculated by use of Fourier transform in alpha, beta and gamma bands. The phase was calculated and unwrapped after taking Hilbert transform of the data in the gamma band. The spatiotemporal plots of the phase were made by using a montage layout of 256 equidistant electrode positions and stable phase cone structures and their clusters were extracted. The spatiotemporal plots of phase and instantaneous power both had detailed additional spatial features at higher sampling frequency which were missing or smoothed out at lower sampling frequency. The phase cluster rate was higher at higher sampling frequency. These results indicate that additional information about the formation of phase clusters and related cortical phase transitions can be derived from EEG data collected at a higher sampling rate.

Functional connectivity can be measured with electroencephalography (EEG) data using a variety of metrics that emphasize different aspects of brain dynamics. Coherence, which measures the consistency of relative phase between channels, is a widely used measure of synchronization in different frequency bands and describes marginal dependence between channels. The interpretation of coherence as reflecting a functional connection in the brain is confounded by volume conduction of current and by common inputs to both channels. Spatial filtering (e.g., surface Laplacians) is often used to minimize volume conduction effects, but removes variance from the data providing only a partial view of the underlying network. Other approaches such as imaginary coherence introduce new distortions to coherence estimates. In this paper we assume that EEG data in a frequency band are generated by a complex multivariate normal (CMVN) in order to define a complex-Gaussian Graphical Model of the data. Conditional dependence between channels is reflected in the precision values of the model. Compared to coherence, precision estimates suppress volume conduction and common input effects, while providing, by way of the graphical lasso, a sparse estimate of the underlying network. We show through simulation that this model outperforms coherence as an estimate of connectivity and captures the most important features of the network. Examples provided demonstrate that Complex-Gaussian graphical models can be applied to either EEG time series (channel space) or reconstructed source time series (source space), to suppress the effects of volume conduction and common inputs, thereby obtaining genuine estimates of brain networks.