Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem

A survey on integral equations for bioelectric modeling

Bioelectric modeling problems, such as electroencephalography, magnetoencephalography, transcranial electrical stimulation, deep brain stimulation, and transcranial magnetic stimulation, among others, can be approached through the formulation and resolution of integral equations of theboundary element method(BEM). Recently, it has been realized that thecharge-based formulationof the BEM is naturally well-suited for the application of thefast multipole method(FMM). The FMM is a powerful algorithm for the computation of many-body interactions and is widely applied in electromagnetic modeling problems. With the introduction of BEM-FMM in the context of bioelectromagnetism, the BEM can now compete with thefinite element method(FEM) in a number of application cases. This survey has two goals: first, to give a modern account of the main BEM formulations in the literature and their integration with FMM, directed to general researchers involved in development of BEM software for bioelectromagnetic applications. Second, to survey different techniques and available software, and to contrast different BEM and FEM approaches. As a new contribution, we showcase that the charge-based formulation is dual to the more common surface potential formulation.

A hybrid boundary element-finite element approach for solving the EEG forward problem in brain modeling

This article introduces a hybrid BE-FE method for solving the EEG forward problem, leveraging the strengths of both the Boundary Element Method (BEM) and Finite Element Method (FEM). FEM accurately models complex and anisotropic tissue properties for realistic head geometries, while BEM excels in handling isotropic tissue regions and dipolar sources efficiently. The proposed hybrid method divides regions into homogeneous boundary element (BE) regions that include sources and heterogeneous anisotropic finite element (FE) regions. So, BEM models the brain, including dipole sources, and FEM models other head layers. Validation includes inhomogeneous isotropic/anisotropic three- and four-layer spherical head models, and a four-layer MRI-based realistic head model. Results for six dipole eccentricities and two orientations are computed using BEM, FEM, and hybrid BE-FE method. Statistical analysis, comparing error criteria of RDM and MAG, reveals notable improvements using the hybrid FE-BE method. In the spherical head model, the hybrid BE-FE method compared with FEM demonstrates enhancements of at least 1.05 and 38.31% in RDM and MAG criteria, respectively. Notably, in the anisotropic four-layer head model, improvements reach a maximum of 88.3% for RDM and 93.27% for MAG over FEM. Moreover, in the anisotropic four-layer realistic head model, the proposed hybrid method exhibits 55.4% improvement in RDM and 89.3% improvement in MAG compared to FEM. These findings underscore the proposed method is a promising approach for solving the realistic EEG forward problems, advancing neuroimaging techniques and enhancing understanding of brain function.

How to assess the accuracy of volume conduction models? A validation study with stereotactic EEG data

Introduction

Volume conduction models of the human head are used in various neuroscience fields, such as for source reconstruction in EEG and MEG, and for modeling the effects of brain stimulation. Numerous studies have quantified the accuracy and sensitivity of volume conduction models by analyzing the effects of the geometrical and electrical features of the head model, the sensor model, the source model, and the numerical method. Most studies are based on simulations as it is hard to obtain sufficiently detailed measurements to compare to models. The recording of stereotactic EEG during electric stimulation mapping provides an opportunity for such empirical validation.

Methods

In the study presented here, we used the potential distribution of volume-conducted artifacts that are due to cortical stimulation to evaluate the accuracy of finite element method (FEM) volume conduction models. We adopted a widely used strategy for numerical comparison, i.e., we fixed the geometrical description of the head model and the mathematical method to perform simulations, and we gradually altered the head models, by increasing the level of detail of the conductivity profile. We compared the simulated potentials at different levels of refinement with the measured potentials in three epilepsy patients.

Results

Our results show that increasing the level of detail of the volume conduction head model only marginally improves the accuracy of the simulated potentials when compared to in-vivo sEEG measurements. The mismatch between measured and simulated potentials is, throughout all patients and models, maximally 40 microvolts (i.e., 10% relative error) in 80% of the stimulation-recording combination pairs and it is modulated by the distance between recording and stimulating electrodes.

Discussion

Our study suggests that commonly used strategies used to validate volume conduction models based solely on simulations might give an overly optimistic idea about volume conduction model accuracy. We recommend more empirical validations to be performed to identify those factors in volume conduction models that have the highest impact on the accuracy of simulated potentials. We share the dataset to allow researchers to further investigate the mismatch between measurements and FEM models and to contribute to improving volume conduction models.

Normative tDCS over V5 and FEF reveals practice-induced modulation of extraretinal smooth pursuit mechanisms, but no specific stimulation effect

The neural networks subserving smooth pursuit eye movements (SPEM) provide an ideal model for investigating the interaction of sensory processing and motor control during ongoing movements. To better understand core plasticity aspects of sensorimotor processing for SPEM, normative sham, anodal or cathodal transcranial direct current stimulation (tDCS) was applied over visual area V5 and frontal eye fields (FEF) in sixty healthy participants. The identical within-subject paradigm was used to assess SPEM modulations by practice. While no specific tDCS effects were revealed, within- and between-session practice effects indicate plasticity of top-down extraretinal mechanisms that mainly affect SPEM in the absence of visual input and during SPEM initiation. To explore the potential of tDCS effects, individual electric field simulations were computed based on calibrated finite element head models and individual functional localization of V5 and FEF location (using functional MRI) and orientation (using combined EEG/MEG) was conducted. Simulations revealed only limited electric field target intensities induced by the applied normative tDCS montages but indicate the potential efficacy of personalized tDCS for the modulation of SPEM. In sum, results indicate the potential susceptibility of extraretinal SPEM control to targeted external neuromodulation (e.g., personalized tDCS) and intrinsic learning protocols.

Bioelectromagnetism in Human Brain Research: New Applications, New Questions

Bioelectromagnetism has contributed some of the most commonly used techniques to human neuroscience such as magnetoencephalography (MEG), electroencephalography (EEG), transcranial magnetic stimulation (TMS), and transcranial electric stimulation (TES). The considerable differences in their technical design and practical use give rise to the impression that these are quite different techniques altogether. Here, we review, discuss and illustrate the fundamental principle of Helmholtz reciprocity that provides a common ground for all four techniques. We show that, more than 150 years after its discovery by Helmholtz in 1853, reciprocity is important to appreciate the strengths and limitations of these four classical tools in neuroscience. We build this case by explaining the concept of Helmholtz reciprocity, presenting a methodological account of this principle for all four methods and, finally, by illustrating its application in practical clinical studies.

Estimating the influence of stroke lesions on MEG source reconstruction

Source reconstruction of magnetoencephalography (MEG) has been used to assess brain reorganization after brain damage, such as stroke. Lesions result in parts of the brain having an electrical conductivity that differs from the normal values. The effect this has on the forward solutions (i.e., the propagation of electric currents and magnetic fields generated by cortical activity) is well predictable. However, their influence on source localization results is not well characterized and understood. This is specifically a concern for patient studies with asymmetric (i.e., within one hemisphere) lesions focusing on asymmetric and lateralized brain activity, such as language. In particular, it is good practice to consider the level of geometrical detail that is necessary to compute and interpret reliable source reconstruction results. To understand the effect of lesions on source estimates and propose recommendations to researchers working with clinical data, in this study we consider the trade off between improved accuracy and the additional effort to compute more realistic head models, with the aim to answer the question whether the additional effort is worth it. We simulated and analyzed the effects of a stroke lesion (i.e., an asymmetrically distributed CSF-filled cavity) in the head model with three different sizes and locations when performing MEG source reconstruction using a finite element method (FEM). We compared the effect of the lesion with a homogeneous head model that neglects the lesion. We computed displacement and attenuation/amplification maps to quantify the localization errors and signal magnitude modulation. We conclude that brain lesions leading to asymmetrically distributed CSF-filled cavities should be modeled when performing MEG source reconstruction, especially when investigating deep sources or post-stroke hemispheric lateralization of functions. The strongest effects are not only visible in perilesional areas, but can extend up to 20 mm from the lesion. Bigger lesions lead to stronger effects impacting larger areas, independently from the lesion location. Lastly, we conclude that more priority should be given to usability and accessibility of the required computational tools, to allow researchers with less technical expertise to use the improved methods that are available but currently not widely adopted yet.

Using non-invasive transcranial direct current stimulation for neglect and associated attentional deficits following stroke

Neglect is a disabling neuropsychological syndrome that is frequently observed following right-hemispheric stroke. Affected individuals often present with multiple attentional deficits, ranging from reduced orienting towards contralesional space to a generalized impairment in maintaining attention over time. Although a degree of spontaneous recovery occurs in most patients, in some individuals this condition can be treatment-resistant with prominent ongoing non-spatial deficits. Further, there is a large inter-individual variability in response to different therapeutic approaches. Given its potential to alter neuronal excitability and affect neuroplasticity, non-invasive brain stimulation is a promising tool that could potentially be utilized to facilitate recovery. However, there are many outstanding questions regarding its implementation in this heterogeneous patient group. Here we provide a critical overview of the available evidence on the use of non-invasive electrical brain stimulation, focussing on transcranial direct current stimulation (tDCS), to improve neglect and associated attentional deficits after right-hemispheric stroke. At present, there is insufficient robust evidence supporting the clinical use of tDCS to alleviate symptoms of neglect. Future research would benefit from careful study design, enhanced precision of electrical montages, multi-modal approaches exploring predictors of response, tailored dose-control applications and increased efforts to evaluate standalone tDCS versus its incorporation into combination therapy.

Directionality of the injected current targeting the P20/N20 source determines the efficacy of 140 Hz transcranial alternating current stimulation (tACS)-induced aftereffects in the somatosensory cortex

Interindividual anatomical differences in the human cortex can lead to suboptimal current directions and may result in response variability of transcranial electrical stimulation methods. These differences in brain anatomy require individualized electrode stimulation montages to induce an optimal current density in the targeted area of each individual subject. We aimed to explore the possible modulatory effects of 140 Hz transcranial alternating current stimulation (tACS) on the somatosensory cortex using personalized multi-electrode stimulation montages. In two randomized experiments using either tactile finger or median nerve stimulation, we measured by evoked potentials the plasticity aftereffects and oscillatory power changes after 140 Hz tACS at 1.0 mA as compared to sham stimulation (n = 17, male = 9). We found a decrease in the power of oscillatory mu-rhythms during and immediately after tactile discrimination tasks, indicating an engagement of the somatosensory system during stimulus encoding. On a group level both the oscillatory power and the evoked potential amplitudes were not modulated by tACS neither after tactile finger stimulation nor after median nerve stimulation as compared to sham stimulation. On an individual level we could however demonstrate that lower angular difference (i.e., differences between the injected current vector in the target region and the source orientation vector) is associated with significantly higher changes in both P20/N20 and N30/P30 source activities. Our findings suggest that the higher the directionality of the injected current correlates to the dipole orientation the greater the tACS-induced aftereffects are.

Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes

Objective. To formulate, validate, and apply an alternative to the finite element method (FEM) high-resolution modeling technique for electrical brain stimulation-the boundary element fast multipole method (BEM-FMM). To include practical electrode models for both surface and embedded electrodes.Approach. Integral equations of the boundary element method in terms of surface charge density are combined with a general-purpose fast multipole method and are expanded for voltage, shunt, current, and floating electrodes. The solution of coupled and properly weighted/preconditioned integral equations is accompanied by enforcing global conservation laws: charge conservation law and Kirchhoff's current law.Main results.A sub-percent accuracy is reported as compared to the analytical solutions and simple validation geometries. Comparison to FEM considering realistic head models resulted in relative differences of the electric field magnitude in the range of 3%-6% or less. Quantities that contain higher order spatial derivatives, such as the activating function, are determined with a higher accuracy and a faster speed as compared to the FEM. The method can be easily combined with existing head modeling pipelines such as headreco or mri2mesh.Significance.The BEM-FMM does not rely on a volumetric mesh and is therefore particularly suitable for modeling some mesoscale problems with submillimeter (and possibly finer) resolution with high accuracy at moderate computational cost. Utilizing Helmholtz reciprocity principle makes it possible to expand the method to a solution of EEG forward problems with a very large number of cortical dipoles.

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.

Sustained neural rhythms reveal endogenous oscillations supporting speech perception

Rhythmic sensory or electrical stimulation will produce rhythmic brain responses. These rhythmic responses are often interpreted as endogenous neural oscillations aligned (or "entrained") to the stimulus rhythm. However, stimulus-aligned brain responses can also be explained as a sequence of evoked responses, which only appear regular due to the rhythmicity of the stimulus, without necessarily involving underlying neural oscillations. To distinguish evoked responses from true oscillatory activity, we tested whether rhythmic stimulation produces oscillatory responses which continue after the end of the stimulus. Such sustained effects provide evidence for true involvement of neural oscillations. In Experiment 1, we found that rhythmic intelligible, but not unintelligible speech produces oscillatory responses in magnetoencephalography (MEG) which outlast the stimulus at parietal sensors. In Experiment 2, we found that transcranial alternating current stimulation (tACS) leads to rhythmic fluctuations in speech perception outcomes after the end of electrical stimulation. We further report that the phase relation between electroencephalography (EEG) responses and rhythmic intelligible speech can predict the tACS phase that leads to most accurate speech perception. Together, we provide fundamental results for several lines of research-including neural entrainment and tACS-and reveal endogenous neural oscillations as a key underlying principle for speech perception.

A flexible workflow for simulating transcranial electric stimulation in healthy and lesioned brains

Simulating transcranial electric stimulation is actively researched as knowledge about the distribution of the electrical field is decisive for understanding the variability in the elicited stimulation effect. Several software pipelines comprehensively solve this task in an automated manner for standard use-cases. However, simulations for non-standard applications such as uncommon electrode shapes or the creation of head models from non-optimized T1-weighted imaging data and the inclusion of irregular structures are more difficult to accomplish. We address these limitations and suggest a comprehensive workflow to simulate transcranial electric stimulation based on open-source tools. The workflow covers the head model creation from MRI data, the electrode modeling, the modeling of anisotropic conductivity behavior of the white matter, the numerical simulation and visualization. Skin, skull, air cavities, cerebrospinal fluid, white matter, and gray matter are segmented semi-automatically from T1-weighted MR images. Electrodes of arbitrary number and shape can be modeled. The meshing of the head model is implemented in a way to preserve the feature edges of the electrodes and is free of topological restrictions of the considered structures of the head model. White matter anisotropy can be computed from diffusion-tensor imaging data. Our solver application was verified analytically and by contrasting the tDCS simulation results with that of other simulation pipelines (SimNIBS 3.0, ROAST 3.0). An agreement in both cases underlines the validity of our workflow. Our suggested solutions facilitate investigations of irregular structures in patients (e.g. lesions, implants) or new electrode types. For a coupled use of the described workflow, we provide documentation and disclose the full source code of the developed tools.

Unification of optimal targeting methods in transcranial electrical stimulation

One of the major questions in high-density transcranial electrical stimulation (TES) is: given a region of interest (ROI) and electric current limits for safety, how much current should be delivered by each electrode for optimal targeting of the ROI? Several solutions, apparently unrelated, have been independently proposed depending on how "optimality" is defined and on how this optimization problem is stated mathematically. The least squares (LS), weighted LS (WLS), or reciprocity-based approaches are the simplest ones and have closed-form solutions. An extended optimization problem can be stated as follows: maximize the directional intensity at the ROI, limit the electric fields at the non-ROI, and constrain total injected current and current per electrode for safety. This problem requires iterative convex or linear optimization solvers. We theoretically prove in this work that the LS, WLS and reciprocity-based closed-form solutions are specific solutions to the extended directional maximization optimization problem. Moreover, the LS/WLS and reciprocity-based solutions are the two extreme cases of the intensity-focality trade-off, emerging under variation of a unique parameter of the extended directional maximization problem, the imposed constraint to the electric fields at the non-ROI. We validate and illustrate these findings with simulations on an atlas head model. The unified approach we present here allows a better understanding of the nature of the TES optimization problem and helps in the development of advanced and more effective targeting strategies.

The effect of stimulation type, head modeling, and combined EEG and MEG on the source reconstruction of the somatosensory P20/N20 component

Modeling and experimental parameters influence the Electro- (EEG) and Magnetoencephalography (MEG) source analysis of the somatosensory P20/N20 component. In a sensitivity group study, we compare P20/N20 source analysis due to different stimulation type (Electric-Wrist [EW], Braille-Tactile [BT], or Pneumato-Tactile [PT]), measurement modality (combined EEG/MEG - EMEG, EEG, or MEG) and head model (standard or individually skull-conductivity calibrated including brain anisotropic conductivity). Considerable differences between pairs of stimulation types occurred (EW-BT: 8.7 ± 3.3 mm/27.1° ± 16.4°, BT-PT: 9 ± 5 mm/29.9° ± 17.3°, and EW-PT: 9.8 ± 7.4 mm/15.9° ± 16.5° and 75% strength reduction of BT or PT when compared to EW) regardless of the head model used. EMEG has nearly no localization differences to MEG, but large ones to EEG (16.1 ± 4.9 mm), while source orientation differences are non-negligible to both EEG (14° ± 3.7°) and MEG (12.5° ± 10.9°). Our calibration results show a considerable inter-subject variability (3.1-14 mS/m) for skull conductivity. The comparison due to different head model show localization differences smaller for EMEG (EW: 3.4 ± 2.4 mm, BT: 3.7 ± 3.4 mm, and PT: 5.9 ± 6.8 mm) than for EEG (EW: 8.6 ± 8.3 mm, BT: 11.8 ± 6.2 mm, and PT: 10.5 ± 5.3 mm), while source orientation differences for EMEG (EW: 15.4° ± 6.3°, BT: 25.7° ± 15.2° and PT: 14° ± 11.5°) and EEG (EW: 14.6° ± 9.5°, BT: 16.3° ± 11.1° and PT: 12.9° ± 8.9°) are in the same range. Our results show that stimulation type, modality and head modeling all have a non-negligible influence on the source reconstruction of the P20/N20 component. The complementary information of both modalities in EMEG can be exploited on the basis of detailed and individualized head models.

Benchmarking transcranial electrical stimulation finite element models: a comparison study

OBJECTIVE

To compare field measure differences in simulations of transcranial electrical stimulation (tES) generated by variations in finite element (FE) models due to boundary condition specification, use of tissue compartment smoothing filters, and use of free or structured tetrahedral meshes based on magnetic resonance imaging (MRI) data.

APPROACH

A structural MRI head volume was acquired at 1 mm³ resolution and segmented into ten tissue compartments. Predicted current densities and electric fields were computed in segmented models using modeling pipelines involving either an in-house (block) or a commercial platform commonly used in previous FE tES studies involving smoothed compartments and free meshing procedures (smooth). The same boundary conditions were used for both block and smooth pipelines. Differences caused by varying boundary conditions were examined using a simple geometry. Percentage differences of median current density values in five cortical structures were compared between the two pipelines for three electrode montages (F3-right supraorbital, T7-T8 and Cz-Oz).

MAIN RESULTS

Use of boundary conditions commonly used in previous tES FE studies produced asymmetric current density profiles in the simple geometry. In head models, median current density differences produced by the two pipelines, using the same boundary conditions, were up to 6% (isotropic) and 18% (anisotropic) in structures targeted by each montage. Tangential electric field measures calculated via either pipeline were within the range of values reported in the literature, when averaged over cortical surface patches.

SIGNIFICANCE

Apparently equivalent boundary settings may affect predicted current density outcomes and care must be taken in their specification. Smoothing FE model compartments may not be necessary, and directly translated, voxellated tissue boundaries at 1 mm³ resolution may be sufficient for use in tES FE studies, greatly reducing processing times. The findings here may be used to inform future current density modeling studies.

Head phantoms for electroencephalography and transcranial electric stimulation: a skull material study

Physical head phantoms allow the assessment of source reconstruction procedures in electroencephalography and electrical stimulation profiles during transcranial electric stimulation. Volume conduction in the head is strongly influenced by the skull, which represents the main conductivity barrier. Realistic modeling of its characteristics is thus important for phantom development. In the present study, we proposed plastic clay as a material for modeling the skull in phantoms. We analyzed five clay types varying in granularity and fractions of fire clay, each with firing temperatures from 550°C to 950°C. We investigated the conductivity of standardized clay samples when immersed in a 0.9% sodium chloride solution with time-resolved four-point impedance measurements. To test the reusability of the clay model, these measurements were repeated after cleaning the samples by rinsing in deionized water for 5 h. We found time-dependent impedance changes for approximately 5 min after immersion in the solution. Thereafter, the conductivities stabilized between 0.0716 S/m and 0.0224 S/m depending on clay type and firing temperatures. The reproducibility of the measurement results proved the effectiveness of the rinsing procedure. Clay provides formability, is permeable to ions, can be adjusted in conductivity value and is thus suitable for the skull modeling in phantoms.

Inherent physiological artifacts in EEG during tDCS

Online imaging and neuromodulation is invalid if stimulation distorts measurements beyond the point of accurate measurement. In theory, combining transcranial Direct Current Stimulation (tDCS) with electroencephalography (EEG) is compelling, as both use non-invasive electrodes and image-guided dose can be informed by the reciprocity principle. To distinguish real changes in EEG from stimulation artifacts, prior studies applied conventional signal processing techniques (e.g. high-pass filtering, ICA). Here, we address the assumptions underlying the suitability of these approaches. We distinguish physiological artifacts - defined as artifacts resulting from interactions between the stimulation induced voltage and the body and so inherent regardless of tDCS or EEG hardware performance - from methodology-related artifacts - arising from non-ideal experimental conditions or non-ideal stimulation and recording equipment performance. Critically, we identify inherent physiological artifacts which are present in all online EEG-tDCS: 1) cardiac distortion and 2) ocular motor distortion. In conjunction, non-inherent physiological artifacts which can be minimized in most experimental conditions include: 1) motion and 2) myogenic distortion. Artifact dynamics were analyzed for varying stimulation parameters (montage, polarity, current) and stimulation hardware. Together with concurrent physiological monitoring (ECG, respiration, ocular, EMG, head motion), and current flow modeling, each physiological artifact was explained by biological source-specific body impedance changes, leading to incremental changes in scalp DC voltage that are significantly larger than real neural signals. Because these artifacts modulate the DC voltage and scale with applied current, they are dose specific such that their contamination cannot be accounted for by conventional experimental controls (e.g. differing stimulation montage or current as a control). Moreover, because the EEG artifacts introduced by physiologic processes during tDCS are high dimensional (as indicated by Generalized Singular Value Decomposition- GSVD), non-stationary, and overlap highly with neurogenic frequencies, these artifacts cannot be easily removed with conventional signal processing techniques. Spatial filtering techniques (GSVD) suggest that the removal of physiological artifacts would significantly degrade signal integrity. Physiological artifacts, as defined here, would emerge only during tDCS, thus processing techniques typically applied to EEG in the absence of tDCS would not be suitable for artifact removal during tDCS. All concurrent EEG-tDCS must account for physiological artifacts that are a) present regardless of equipment used, and b) broadband and confound a broad range of experiments (e.g. oscillatory activity and event related potentials). Removal of these artifacts requires the recognition of their non-stationary, physiology-specific dynamics, and individualized nature. We present a broad taxonomy of artifacts (non/stimulation related), and suggest possible approaches and challenges to denoising online EEG-tDCS stimulation artifacts.

Physics of Transcranial Direct Current Stimulation Devices and Their History

Transcranial direct current stimulation (tDCS) devices apply direct current through electrodes on the scalp with the intention to modulate brain function for experimental or clinical purposes. All tDCS devices include a current controlled stimulator, electrodes that include a disposable electrolyte, and headgear to position the electrodes on the scalp. Transcranial direct current stimulation dose can be defined by the size and position of electrodes and the duration and intensity of current applied across electrodes. Electrode design and preparation are important for reproducibility and tolerability. High-definition tDCS uses smaller electrodes that can be arranged in arrays to optimize brain current flow. When intended to be used at home, tDCS devices require specific device design considerations. Computational models of current flow have been validated and support optimization and hypothesis testing. Consensus on the safety and tolerability of tDCS is protocol specific, but medical-grade tDCS devices minimize risk.

Transcranial alternating current stimulation modulates auditory temporal resolution in elderly people

Recent research provides evidence for a functional role of brain oscillations for perception. For example, auditory temporal resolution seems to be linked to individual gamma frequency of auditory cortex. Individual gamma frequency not only correlates with performance in between-channel gap detection tasks but can be modulated via auditory transcranial alternating current stimulation. Modulation of individual gamma frequency is accompanied by an improvement in gap detection performance. Aging changes electrophysiological frequency components and sensory processing mechanisms. Therefore, we conducted a study to investigate the link between individual gamma frequency and gap detection performance in elderly people using auditory transcranial alternating current stimulation. In a within-subject design, twelve participants were electrically stimulated with two individualized transcranial alternating current stimulation frequencies: 3 Hz above their individual gamma frequency (experimental condition) and 4 Hz below their individual gamma frequency (control condition), while they were performing a between-channel gap detection task. As expected, individual gamma frequencies correlated significantly with gap detection performance at baseline and in the experimental condition, transcranial alternating current stimulation modulated gap detection performance. In the control condition, stimulation did not modulate gap detection performance. In addition, in elderly, the effect of transcranial alternating current stimulation on auditory temporal resolution seems to be dependent on endogenous frequencies in auditory cortex: Elderlies with slower individual gamma frequencies and lower auditory temporal resolution profit from auditory transcranial alternating current stimulation and show increased gap detection performance during stimulation. Our results strongly suggest individualized transcranial alternating current stimulation protocols for successful modulation of performance.

Noninvasive stimulation of the ventromedial prefrontal cortex modulates emotional face processing

The ventromedial prefrontal cortex (vmPFC) is associated with emotional states that can be characterized as positive affect. Moreover, a variety of psychiatric disorders that are associated with disturbed reactions toward reward- or safety-signaling stimuli reveal functional or structural anomalies within this area. Thus, neuromodulation of this region via transcranial direct current stimulation (tDCS) offers an attractive opportunity to noninvasively influence pleasant emotional and reward processing. Recent experiments revealed hemodynamic and electrophysiological evidence for valence specific modulations of emotional scene processing after excitatory and inhibitory tDCS of the vmPFC. Here, we identified that tDCS modulation of vmPFC during emotional face processing results in effects convergent with scene processing, in that excitatory tDCS increased neural reactivity during happy compared to fearful face perception, whereas inhibitory stimulation led to a converse effect. In addition, behavioral data (affect identification of ambiguous expressive faces) revealed a bias toward preferential processing of happy compared to fearful faces after excitatory compared to after inhibitory stimulation. These results further support the vmPFC as an appropriate target for noninvasive neuromodulation of an appetitive processing network in patients suffering from disturbed cognition of reward- and safety-signaling stimuli. It should however be noted that electrophysiological pre-tDCS differences at earlier time intervals of emotional face and scene processing appeared amplified by tDCS, which remains to be investigated.

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.

Transcranial electric stimulation (tES) and NeuroImaging: the state-of-the-art, new insights and prospects in basic and clinical neuroscience

Transcranial electric stimulation (tES) of the brain has attracted an increased interest in recent years. Yet, despite remarkable research efforts to date, the underlying neurobiological mechanisms of tES' effects are still incompletely understood. This Special Issue aims to provide a comprehensive and up-to-date overview of the state-of-the-art in studies combining tES and neuroimaging, while introducing most recent insights and outlining future prospects related to this new and rapidly growing field. The findings reported here combine methodological advancements with insights into the underlying mechanisms of tES itself. At the same time, they also point to the many caveats and specific challenges associated with such studies, which can arise from both technical and biological sources. Besides promising to advance basic neuroscience, combined tES and neuroimaging studies may also substantially change previous conceptions about the methods of action of electric or magnetic stimulation on the brain.

Optimal use of EEG recordings to target active brain areas with transcranial electrical stimulation

To demonstrate causal relationships between brain and behavior, investigators would like to guide brain stimulation using measurements of neural activity. Particularly promising in this context are electroencephalography (EEG) and transcranial electrical stimulation (TES), as they are linked by a reciprocity principle which, despite being known for decades, has not led to a formalism for relating EEG recordings to optimal stimulation parameters. Here we derive a closed-form expression for the TES configuration that optimally stimulates (i.e., targets) the sources of recorded EEG, without making assumptions about source location or distribution. We also derive a duality between TES targeting and EEG source localization, and demonstrate that in cases where source localization fails, so does the proposed targeting. Numerical simulations with multiple head models confirm these theoretical predictions and quantify the achieved stimulation in terms of focality and intensity. We show that constraining the stimulation currents automatically selects optimal montages that involve only a few (4-7) electrodes, with only incremental loss in performance when targeting focal activations. The proposed technique allows brain scientists and clinicians to rationally target the sources of observed EEG and thus overcomes a major obstacle to the realization of individualized or closed-loop brain stimulation.

Zoomed MRI Guided by Combined EEG/MEG Source Analysis: A Multimodal Approach for Optimizing Presurgical Epilepsy Work-up and its Application in a Multi-focal Epilepsy Patient Case Study

In recent years, the use of source analysis based on electroencephalography (EEG) and magnetoencephalography (MEG) has gained considerable attention in presurgical epilepsy diagnosis. However, in many cases the source analysis alone is not used to tailor surgery unless the findings are confirmed by lesions, such as, e.g., cortical malformations in MRI. For many patients, the histology of tissue resected from MRI negative epilepsy shows small lesions, which indicates the need for more sensitive MR sequences. In this paper, we describe a technique to maximize the synergy between combined EEG/MEG (EMEG) source analysis and high resolution MRI. The procedure has three main steps: (1) construction of a detailed and calibrated finite element head model that considers the variation of individual skull conductivities and white matter anisotropy, (2) EMEG source analysis performed on averaged interictal epileptic discharges (IED), (3) high resolution (0.5 mm) zoomed MR imaging, limited to small areas centered at the EMEG source locations. The proposed new diagnosis procedure was then applied in a particularly challenging case of an epilepsy patient: EMEG analysis at the peak of the IED coincided with a right frontal focal cortical dysplasia (FCD), which had been detected at standard 1 mm resolution MRI. Of higher interest, zoomed MR imaging (applying parallel transmission, 'ZOOMit') guided by EMEG at the spike onset revealed a second, fairly subtle, FCD in the left fronto-central region. The evaluation revealed that this second FCD, which had not been detectable with standard 1 mm resolution, was the trigger of the seizures.

A Mixed Finite Element Method to Solve the EEG Forward Problem

Finite element methods have been shown to achieve high accuracies in numerically solving the EEG forward problem and they enable the realistic modeling of complex geometries and important conductive features such as anisotropic conductivities. To date, most of the presented approaches rely on the same underlying formulation, the continuous Galerkin (CG)-FEM. In this article, a novel approach to solve the EEG forward problem based on a mixed finite element method (Mixed-FEM) is introduced. To obtain the Mixed-FEM formulation, the electric current is introduced as an additional unknown besides the electric potential. As a consequence of this derivation, the Mixed-FEM is, by construction, current preserving, in contrast to the CG-FEM. Consequently, a higher simulation accuracy can be achieved in certain scenarios, e.g., when the diameter of thin insulating structures, such as the skull, is in the range of the mesh resolution. A theoretical derivation of the Mixed-FEM approach for EEG forward simulations is presented, and the algorithms implemented for solving the resulting equation systems are described. Subsequently, first evaluations in both sphere and realistic head models are presented, and the results are compared to previously introduced CG-FEM approaches. Additional visualizations are shown to illustrate the current preserving property of the Mixed-FEM. Based on these results, it is concluded that the newly presented Mixed-FEM can at least complement and in some scenarios even outperform the established CG-FEM approaches, which motivates a further evaluation of the Mixed-FEM for applications in bioelectromagnetism.