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Human brain activity generates scalp potentials (electroencephalography - EEG), intracranial potentials (iEEG), and external magnetic fields (magnetoencephalography - MEG). These electrophysiology (e-phys) signals can often be measured simultaneously for research and clinical applications. The forward problem involves modeling these signals at their sensors for a given equivalent current dipole configuration within the brain. While earlier researchers modeled the head as a simple set of isotropic spheres, today's magnetic resonance imaging (MRI) data allow for a detailed anatomic description of brain structures and anisotropic characterization of tissue conductivities. We present a complete pipeline, integrated into the Brainstorm software, that allows users to automatically generate an individual and accurate head model based on the subject's MRI and calculate the electromagnetic forward solution using the finite element method (FEM). The head model generation is performed by integrating the latest tools for MRI segmentation and FEM mesh generation. The final head model comprises the five main compartments: white-matter, gray-matter, CSF, skull, and scalp. The anisotropic brain conductivity model is based on the effective medium approach (EMA), which estimates anisotropic conductivity tensors from diffusion-weighted imaging (DWI) data. The FEM electromagnetic forward solution is obtained through the DUNEuro library, integrated into Brainstorm, and accessible with either a user-friendly graphical interface or scripting. With tutorials and example data sets available in an open-source format on the Brainstorm website, this integrated pipeline provides access to advanced FEM tools for electromagnetic modeling to a broader neuroscience community., Competing Interests: Declaration of Competing Interest The authors declare that they have no known financial interests or personal relationships that could have influenced the work reported in this paper., (Copyright © 2022. Published by Elsevier Inc.)

The accuracy in electroencephalography (EEG) and combined EEG and magnetoencephalography (MEG) source reconstructions as well as in optimized transcranial electric stimulation (TES) depends on the conductive properties assigned to the head model, and most importantly on individual skull conductivity. In this study, we present an automatic pipeline to calibrate head models with respect to skull conductivity based on the reconstruction of the P20/N20 response using somatosensory evoked potentials and fields. In order to validate in a well-controlled setup without interplay with numerical errors, we evaluate the accuracy of this algorithm in a 4-layer spherical head model using realistic noise levels as well as dipole sources at different eccentricities with strengths and orientations related to somatosensory experiments. Our results show that the reference skull conductivity can be reliably reconstructed for sources resembling the generator of the P20/N20 response. In case of erroneous assumptions on scalp conductivity, the resulting skull conductivity parameter counterbalances this effect, so that EEG source reconstructions using the fitted skull conductivity parameter result in lower errors than when using the standard value. We propose an automatized procedure to calibrate head models which only relies on non-invasive modalities that are available in a standard MEG laboratory, measures under in vivo conditions and in the low frequency range of interest. Calibrated head modeling can improve EEG and combined EEG/MEG source analysis as well as optimized TES.

For accurate EEG forward solutions, it is necessary to apply numerical methods that allow to take into account the realistic geometry of the subject's head. A commonly used method to solve this task is the finite element method (FEM). Different approaches have been developed to obtain EEG forward solutions for dipolar sources with the FEM. The St. Venant approach is frequently applied, since its high numerical accuracy and stability as well as its computational efficiency was demonstrated in multiple comparison studies. In this manuscript, we propose a variation of the St. Venant approach, the multipole approach, to improve the numerical accuracy of the St. Venant approach even further and to allow for the simulation of additional source scenarios, such as quadrupolar sources. Exploiting the multipole expansion of electric fields, we demonstrate that the newly proposed multipole approach achieves even higher numerical accuracies than the St. Venant approach in both multi-layer sphere and realistic head models. Additionally, we exemplarily show that the multipole approach allows to not only simulate dipolar but also quadrupolar sources., (Copyright © 2019 Elsevier Inc. All rights reserved.)

This paper investigates finite element method-based modeling in the context of neonatal electroencephalography (EEG). In particular, the focus lies on electrode boundary conditions. We compare the complete electrode model (CEM) with the point electrode model (PEM), which is the current standard in EEG. In the CEM, the voltage experienced by an electrode is modeled more realistically as the integral average of the potential distribution over its contact surface, whereas the PEM relies on a point value. Consequently, the CEM takes into account the subelectrode shunting currents, which are absent in the PEM. In this study, we aim to find out how the electrode voltage predicted by these two models differ, if standard size electrodes are attached to a head of a neonate. Additionally, we study voltages and voltage variation on electrode surfaces with two source locations: 1 ) next to the C6 electrode and 2 ) directly under the Fz electrode and the frontal fontanel. A realistic model of a neonatal head, including a skull with fontanels and sutures, is used. Based on the results, the forward simulation differences between CEM and PEM are in general small, but significant outliers can occur in the vicinity of the electrodes. The CEM can be considered as an integral part of the outer head model. The outcome of this study helps understanding volume conduction of neonatal EEG, since it enlightens the role of advanced skull and electrode modeling in forward and inverse computations. NEW & NOTEWORTHY The effect of the complete electrode model on electroencephalography forward and inverse computations is explored. A realistic neonatal head model, including a skull structure with fontanels and sutures, is used. The electrode and skull modeling differences are analyzed and compared with each other. The results suggest that the complete electrode model can be considered as an integral part of the outer head model. To achieve optimal source localization results, accurate electrode modeling might be necessary., (Copyright © 2017 the American Physiological Society.)

Objective: Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation technique to modify neural excitability. Using multi-array tDCS, we investigate the influence of inter-individually varying head tissue conductivity profiles on optimal electrode configurations for an auditory cortex stimulation., Approach: In order to quantify the uncertainty of the optimal electrode configurations, multi-variate generalized polynomial chaos expansions of the model solutions are used based on uncertain conductivity profiles of the compartments skin, skull, gray matter, and white matter. Stochastic measures, probability density functions, and sensitivity of the quantities of interest are investigated for each electrode and the current density at the target with the resulting stimulation protocols visualized on the head surface., Main Results: We demonstrate that the optimized stimulation protocols are only comprised of a few active electrodes, with tolerable deviations in the stimulation amplitude of the anode. However, large deviations in the order of the uncertainty in the conductivity profiles could be noted in the stimulation protocol of the compensating cathodes. Regarding these main stimulation electrodes, the stimulation protocol was most sensitive to uncertainty in skull conductivity. Finally, the probability that the current density amplitude in the auditory cortex target region is supra-threshold was below 50%., Significance: The results suggest that an uncertain conductivity profile in computational models of tDCS can have a substantial influence on the prediction of optimal stimulation protocols for stimulation of the auditory cortex. The investigations carried out in this study present a possibility to predict the probability of providing a therapeutic effect with an optimized electrode system for future auditory clinical and experimental procedures of tDCS applications.

The results of brain connectivity analysis using reconstructed source time courses derived from EEG and MEG data depend on a number of algorithmic choices. While previous studies have investigated the influence of the choice of source estimation method or connectivity measure, the effects of the head modeling errors or simplifications have not been studied sufficiently. In the present simulation study, we investigated the influence of particular properties of the head model on the reconstructed source time courses as well as on source connectivity analysis in EEG and MEG. Therefore, we constructed a realistic head model and applied the finite element method to solve the EEG and MEG forward problems. We considered the distinction between white and gray matter, the distinction between compact and spongy bone, the inclusion of a cerebrospinal fluid (CSF) compartment, and the reduction to a simple 3-layer model comprising only the skin, skull, and brain. Source time courses were reconstructed using a beamforming approach and the source connectivity was estimated by the imaginary coherence (ICoh) and the generalized partial directed coherence (GPDC). Our results show that in both EEG and MEG, neglecting the white and gray matter distinction or the CSF causes considerable errors in reconstructed source time courses and connectivity analysis, while the distinction between spongy and compact bone is just of minor relevance, provided that an adequate skull conductivity value is used. Large inverse and connectivity errors are found in the same regions that show large topography errors in the forward solution. Moreover, we demonstrate that the very conservative ICoh is relatively safe from the crosstalk effects caused by imperfect head models, as opposed to the GPDC., (Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.)

Transcranial direct current stimulation (tDCS) is a noninvasive brain stimulation technique able to induce long-lasting changes in cortical excitability that can benefit cognitive functioning and clinical treatment. In order to both better understand the mechanisms behind tDCS and possibly improve the technique, finite element models are used to simulate tDCS of the human brain. With the detailed anisotropic head model presented in this study, we provide accurate predictions of tDCS in the human brain for six of the practically most-used setups in clinical and cognitive research, targeting the primary motor cortex, dorsolateral prefrontal cortex, inferior frontal gyrus, occipital cortex, and cerebellum. We present the resulting electric field strengths in the complete brain and introduce new methods to evaluate the effectivity in the target area specifically, where we have analyzed both the strength and direction of the field. For all cerebral targets studied, the currently accepted configurations produced sub-optimal field strengths. The configuration for cerebellum stimulation produced relatively high field strengths in its target area, but it needs higher input currents than cerebral stimulation does. This study suggests that improvements in the effects of transcranial direct current stimulation are achievable.

We used computer simulations to investigate finite element models of the layered structure of the human skull in EEG source analysis. Local models, where each skull location was modeled differently, and global models, where the skull was assumed to be homogeneous, were compared to a reference model, in which spongy and compact bone were explicitly accounted for. In both cases, isotropic and anisotropic conductivity assumptions were taken into account. We considered sources in the entire brain and determined errors both in the forward calculation and the reconstructed dipole position. Our results show that accounting for the local variations over the skull surface is important, whereas assuming isotropic or anisotropic skull conductivity has little influence. Moreover, we showed that, if using an isotropic and homogeneous skull model, the ratio between skin/brain and skull conductivities should be considerably lower than the commonly used 80:1. For skull modeling, we recommend (1) Local models: if compact and spongy bone can be identified with sufficient accuracy (e.g., from MRI) and their conductivities can be assumed to be known (e.g., from measurements), one should model these explicitly by assigning each voxel to one of the two conductivities, (2) Global models: if the conditions of (1) are not met, one should model the skull as either homogeneous and isotropic, but with considerably higher skull conductivity than the usual 0.0042 S/m, or as homogeneous and anisotropic, but with higher radial skull conductivity than the usual 0.0042 S/m and a considerably lower radial:tangential conductivity anisotropy than the usual 1:10., (Copyright © 2010 Wiley-Liss, Inc.)

Bioelectric source analysis in the human brain from scalp electroencephalography (EEG) signals is sensitive to geometry and conductivity properties of the different head tissues. We propose a low-resolution conductivity estimation (LRCE) method using simulated annealing optimization on high-resolution finite element models that individually optimizes a realistically shaped four-layer volume conductor with regard to the brain and skull compartment conductivities. As input data, the method needs T1- and PD-weighted magnetic resonance images for an improved modeling of the skull and the cerebrospinal fluid compartment and evoked potential data with high signal-to-noise ratio (SNR). Our simulation studies showed that for EEG data with realistic SNR, the LRCE method was able to simultaneously reconstruct both the brain and the skull conductivity together with the underlying dipole source and provided an improved source analysis result. We have also demonstrated the feasibility and applicability of the new method to simultaneously estimate brain and skull conductivity and a somatosensory source from measured tactile somatosensory-evoked potentials of a human subject. Our results show the viability of an approach that computes its own conductivity values and thus reduces the dependence on assigning values from the literature and likely produces a more robust estimate of current sources. Using the LRCE method, the individually optimized four-compartment volume conductor model can, in a second step, be used for the analysis of clinical or cognitive data acquired from the same subject., (2008 Wiley-Liss, Inc.)