Perspectives on Optimized Transcranial Electrical Stimulation Based on Spatial Electric Field Modeling in Humans

Background: Transcranial electrical stimulation (tES) generates an electric field (or current density) in the brain through surface electrodes attached to the scalp. Clinical significance has been demonstrated, although with moderate and heterogeneous results partly due to a lack of control of the delivered electric currents. In the last decade, computational electric field analysis has allowed the estimation and optimization of the electric field using accurate anatomical head models. This review examines recent tES computational studies, providing a comprehensive background on the technical aspects of adopting computational electric field analysis as a standardized procedure in medical applications. Methods: Specific search strategies were designed to retrieve papers from the Web of Science database. The papers were initially screened based on the soundness of the title and abstract and then on their full contents, resulting in a total of 57 studies. Results: Recent trends were identified in individual- and population-level analysis of the electric field, including head models from non-neurotypical individuals. Advanced optimization techniques that allow a high degree of control with the required focality and direction of the electric field were also summarized. There is also growing evidence of a correlation between the computationally estimated electric field and the observed responses in real experiments. Conclusions: Computational pipelines and optimization algorithms have reached a degree of maturity that provides a rationale to improve tES experimental design and a posteriori analysis of the responses for supporting clinical studies.

Lattice layout and optimizer effect analysis for generating optimal transcranial electrical stimulation (tES) montages through the metaheuristic L1L1 method

Introduction

This study focuses on broadening the applicability of the metaheuristic L1-norm fitted and penalized (L1L1) optimization method in finding a current pattern for multichannel transcranial electrical stimulation (tES). The metaheuristic L1L1 optimization framework defines the tES montage via linear programming by maximizing or minimizing an objective function with respect to a pair of hyperparameters.

Methods

In this study, we explore the computational performance and reliability of different optimization packages, algorithms, and search methods in combination with the L1L1 method. The solvers from Matlab R2020b, MOSEK 9.0, Gurobi Optimizer, CVX's SeDuMi 1.3.5, and SDPT3 4.0 were employed to produce feasible results through different linear programming techniques, including Interior-Point (IP), Primal-Simplex (PS), and Dual-Simplex (DS) methods. To solve the metaheuristic optimization task of L1L1, we implement an exhaustive and recursive search along with a well-known heuristic direct search as a reference algorithm.

Results

Based on our results, and the given optimization task, Gurobi's IP was, overall, the preferable choice among Interior-Point while MOSEK's PS and DS packages were in the case of Simplex methods. These methods provided substantial computational time efficiency for solving the L1L1 method regardless of the applied search method.

Discussion

While the best-performing solvers show that the L1L1 method is suitable for maximizing either focality and intensity, a few of these solvers could not find a bipolar configuration. Part of the discrepancies between these methods can be explained by a different sensitivity with respect to parameter variation or the resolution of the lattice provided.

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.

Personalized alpha-tACS targeting left posterior parietal cortex modulates visuo-spatial attention and posterior evoked EEG activity

BACKGROUND

Covert visuo-spatial attention is marked by the anticipatory lateralization of neuronal alpha activity in the posterior parietal cortex. Previous applications of transcranial alternating current stimulation (tACS) at the alpha frequency, however, were inconclusive regarding the causal contribution of oscillatory activity during visuo-spatial attention.

OBJECTIVE

Attentional shifts of behavior and electroencephalography (EEG) after-effects were assessed in a cued visuo-spatial attention paradigm. We hypothesized that parietal alpha-tACS shifts attention relative to the ipsilateral visual hemifield. Furthermore, we assumed that modulations of behavior and neurophysiology are related to individual electric field simulations.

METHODS

We applied personalized tACS at alpha and gamma frequencies to elucidate the role of oscillatory neuronal activity for visuo-spatial attention. Personalized tACS montages were algorithmically optimized to target individual left and right parietal regions that were defined by an EEG localizer.

RESULTS

Behavioral performance in the left hemifield was specifically increased by alpha-tACS compared to gamma-tACS targeting the left parietal cortex. This hemisphere-specific effect was observed despite the symmetry of simulated electric fields. In addition, visual event-related potential (ERP) amplitudes showed a reduced lateralization over posterior sites induced by left alpha-tACS. Neuronal sources of this effect were localized in the left premotor cortex. Interestingly, accuracy modulations induced by left parietal alpha-tACS were directly related to electric field magnitudes in the left premotor cortex.

CONCLUSION

Overall, results corroborate the notion that alpha lateralization plays a causal role in covert visuo-spatial attention and indicate an increased susceptibility of parietal and premotor brain regions of the left dorsal attention network to subtle tACS-neuromodulation.

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, with variable 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 conditions.

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.

L1-norm vs. L2-norm fitting in optimizing focal multi-channel tES stimulation: linear and semidefinite programming vs. weighted least squares

BACKGROUND AND OBJECTIVE

This study focuses on Multi-Channel Transcranial Electrical Stimulation, a non-invasive brain method for stimulating neuronal activity under the influence of low-intensity currents. We introduce a mathematical formulation for finding a current pattern that optimizes an L1-norm fit between a given focal target distribution and volumetric current density inside the brain. L1-norm is well-known to favor well-localized or sparse distributions compared to L2-norm (least-squares) fitted estimates.

METHODS

We present a linear programming approach that performs L1-norm fitting and penalization of the current pattern (L1L1) to control the number of non-zero currents. The optimizer filters a large set of candidate solutions using a two-stage metaheuristic search from a pre-filtered set of candidates.

RESULTS

The numerical simulation results obtained with both 8- and 20-channel electrode montages suggest that our hypothesis on the benefits of L1-norm data fitting is valid. Compared to an L1-norm regularized L2-norm fitting (L1L2) via semidefinite programming and weighted Tikhonov least-squares method (TLS), the L1L1 results were overall preferable for maximizing the focused current density at the target position, and the ratio between focused and nuisance current magnitudes.

CONCLUSIONS

We propose the metaheuristic L1L1 optimization approach as a potential technique to obtain a well-localized stimulus with a controllable magnitude at a given target position. L1L1 finds a current pattern with a steep contrast between the anodal and cathodal electrodes while suppressing the nuisance currents in the brain, hence, providing a potential alternative to modulate the effects of the stimulation, e.g., the sensation experienced by the subject.

Individually optimized multi-channel tDCS for targeting somatosensory cortex

OBJECTIVE

Transcranial direct current stimulation (tDCS) is a non-invasive neuro-modulation technique that delivers current through the scalp by a pair of patch electrodes (2-Patch). This study proposes a new multi-channel tDCS (mc-tDCS) optimization method, the distributed constrained maximum intensity (D-CMI) approach. For targeting the P20/N20 somatosensory source at Brodmann area 3b, an integrated combined magnetoencephalography (MEG) and electroencephalography (EEG) source analysis is used with individualized skull conductivity calibrated realistic head modeling.

METHODS

Simulated electric fields (EF) for our new D-CMI method and the already known maximum intensity (MI), alternating direction method of multipliers (ADMM) and 2-Patch methods were produced and compared for the individualized P20/N20 somatosensory target for 10 subjects.

RESULTS

D-CMI and MI showed highest intensities parallel to the P20/N20 target compared to ADMM and 2-Patch, with ADMM achieving highest focality. D-CMI showed a slight reduction in intensity compared to MI while reducing side effects and skin level sensations by current distribution over multiple stimulation electrodes.

CONCLUSION

Individualized D-CMI montages are preferred for our follow up somatosensory experiment to provide a good balance between high current intensities at the target and reduced side effects and skin sensations.

SIGNIFICANCE

An integrated combined MEG and EEG source analysis with D-CMI montages for mc-tDCS stimulation potentially can improve control, reproducibility and reduce sensitivity differences between sham and real stimulations.

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.

Influence of Head Tissue Conductivity Uncertainties on EEG Dipole Reconstruction

Reliable EEG source analysis depends on sufficiently detailed and accurate head models. In this study, we investigate how uncertainties inherent to the experimentally determined conductivity values of the different conductive compartments influence the results of EEG source analysis. In a single source scenario, the superficial and focal somatosensory P20/N20 component, we analyze the influence of varying conductivities on dipole reconstructions using a generalized polynomial chaos (gPC) approach. We find that in particular the conductivity uncertainties for skin and skull have a significant influence on the EEG inverse solution, leading to variations in source localization by several centimeters. The conductivity uncertainties for gray and white matter were found to have little influence on the source localization, but a strong influence on the strength and orientation of the reconstructed source, respectively. As the CSF conductivity is most accurately determined of all conductivities in a realistic head model, CSF conductivity uncertainties had a negligible influence on the source reconstruction. This small uncertainty is a further benefit of distinguishing the CSF in realistic volume conductor models.

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 distribution for the skull conductivity that describes our (lack of) knowledge on its value, and model the effects of this uncertainty on EEG recordings with the help of an additive error term in the observation model. Before the Bayesian inference, the likelihood is marginalized over this error term. Thus, in the inversion we estimate only our primary unknown, the source distribution. We quantified the improvements in the source localization when the proposed Bayesian modelling was used in the presence of different skull conductivity errors and levels of measurement noise. Based on the results, BAE was able to improve the source localization accuracy, particularly when the unknown (true) skull conductivity was much lower than the expected standard conductivity value. The source locations that gained the highest improvements were shallow and originally exhibited the largest localization errors. In our case study, the benefits of BAE became negligible when the signal-to-noise ratio dropped to 20 dB.

Computationally optimized ECoG stimulation with local safety constraints

Direct stimulation of the cortical surface is used clinically for cortical mapping and modulation of local activity. Future applications of cortical modulation and brain-computer interfaces may also use cortical stimulation methods. One common method to deliver current is through electrocorticography (ECoG) stimulation in which a dense array of electrodes are placed subdurally or epidurally to stimulate the cortex. However, proximity to cortical tissue limits the amount of current that can be delivered safely. It may be desirable to deliver higher current to a specific local region of interest (ROI) while limiting current to other local areas more stringently than is guaranteed by global safety limits. Two commonly used global safety constraints bound the total injected current and individual electrode currents. However, these two sets of constraints may not be sufficient to prevent high current density locally (hot-spots). In this work, we propose an efficient approach that prevents current density hot-spots in the entire brain while optimizing ECoG stimulus patterns for targeted stimulation. Specifically, we maximize the current along a particular desired directional field in the ROI while respecting three safety constraints: one on the total injected current, one on individual electrode currents, and the third on the local current density magnitude in the brain. This third set of constraints creates a computational barrier due to the huge number of constraints needed to bound the current density at every point in the entire brain. We overcome this barrier by adopting an efficient two-step approach. In the first step, the proposed method identifies the safe brain region, which cannot contain any hot-spots solely based on the global bounds on total injected current and individual electrode currents. In the second step, the proposed algorithm iteratively adjusts the stimulus pattern to arrive at a solution that exhibits no hot-spots in the remaining brain. We report on simulations on a realistic finite element (FE) head model with five anatomical ROIs and two desired directional fields. We also report on the effect of ROI depth and desired directional field on the focality of the stimulation. Finally, we provide an analysis of optimization runtime as a function of different safety and modeling parameters. Our results suggest that optimized stimulus patterns tend to differ from those used in clinical practice.