Impact of uncertain head tissue conductivity in the optimization of transcranial direct current stimulation for an auditory target

Quasistatic approximation in neuromodulation

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuromodulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g. Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

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.

Are we really targeting and stimulating DLPFC by placing transcranial electrical stimulation (tES) electrodes over F3/F4?

In many clinical trials involving transcranial electrical stimulation (tES), target electrodes are typically placed over DLPFC with the assumption that this will primarily stimulate the underlying brain region. However, our study aimed to evaluate the electric fields (EF) that are actually delivered and identify prefrontal regions that may be inadvertently targeted in DLPFC tES. Head models were generated from the Human Connectome Project database's T1 + T2-weighted MRIs of 80 healthy adults. Two common DLPFC montages were simulated; symmetric-F4/F3, and asymmetric-F4/Fp1. Averaged EF was extracted from (1) the center of the target electrode (F4), and (2) the top 1% of voxels showing the strongest EF in individualized EF maps. Interindividual variabilities were quantified with the standard deviation of EF peak location/value. Similar steps were repeated with 66 participants with methamphetamine use disorder (MUDs) as an independent clinical population. In healthy adults, the group-level location of EF peaks was situated in the medial-frontopolar, and the individualized EF peaks were positioned in a cube with a volume of 29 cm3 /46 cm3 (symmetric/asymmetric montages). EFs in the frontopolar area were significantly higher than EF "under" the target electrode in both symmetric (peak: 0.41 ± 0.06, F4:0.22 ± 0.04) and asymmetric (peak: 0.38 ± 0.04, F4:0.2 ± 0.04) montages (Heges'g > 0.7). Similar results with slight between-group differences were found in MUDs. We highlighted that in common DLPFC tES montages, in addition to interindividual/intergroup variability, the frontopolar received the highest EFs rather than DLPFC as the main target. We specifically recommended considering the potential involvement of the frontopolar area as a mechanism underlying the effectiveness of DLPFC tES protocols.

Dose-response in modulating brain function with transcranial direct current stimulation: From local to network levels

Understanding the dose-response relationship is crucial in studying the effects of brain stimulation techniques, such as transcranial direct current stimulation (tDCS). The dose-response relationship refers to the relationship between the received stimulation dose and the resulting response, which can be described as a function of the dose at various levels, including single/multiple neurons, clusters, regions, or networks. Here, we are focused on the received stimulation dose obtained from computational head models and brain responses which are quantified by functional magnetic resonance imaging (fMRI) data. In this randomized, triple-blind, sham-controlled clinical trial, we recruited sixty participants with methamphetamine use disorders (MUDs) as a sample clinical population who were randomly assigned to receive either sham or active tDCS. Structural and functional MRI data, including high-resolution T1 and T2-weighted MRI, resting-state functional MRI, and a methamphetamine cue-reactivity task fMRI, were acquired before and after tDCS. Individual head models were generated using the T1 and T2-weighted MRI data to simulate electric fields. In a linear approach, we investigated the associations between electric fields (received dose) and changes in brain function (response) at four different levels: voxel level, regional level (using atlas-based parcellation), cluster level (identifying active clusters), and network level (task-based functional connectivity). At the voxel level, regional level, and cluster level, no FDR-corrected significant correlation was observed between changes in functional activity and electric fields. However, at the network level, a significant positive correlation was found between frontoparietal connectivity and the electric field at the frontopolar stimulation site (r = 0.42, p corrected = 0.02; medium effect size). Our proposed pipeline offers a methodological framework for analyzing tDCS effects by exploring dose-response relationships at different levels, enabling a direct link between electric field variability and the neural response to tDCS. The results indicate that network-based analysis provides valuable insights into the dependency of tDCS neuromodulatory effects on the individual's regional current dose. Integration of dose-response relationships can inform dose optimization, customization, or the extraction of predictive/treatment-response biomarkers in future brain stimulation studies.

Integrating electric field modeling and pre-tDCS behavioral performance to predict the individual tDCS effect on visual crowding

Objective.Transcranial direct current stimulation (tDCS) has been broadly used to modulate brain activity with both bipolar and high-definition montages. However, tDCS effects can be highly variable. In this work, we investigated whether the variability in the tDCS effects could be predicted by integrating individualized electric field modeling and individual pre-tDCS behavioral performance.Approach.Here, we first compared the effects of bipolar tDCS and 4 × 1 high-definition tDCS (HD-tDCS) with respect to the alleviation of visual crowding, which is the inability to identify targets in the presence of nearby flankers and considered to be an essential bottleneck of object recognition and visual awareness. We instructed subjects to perform an orientation discrimination task with both isolated and crowded targets in the periphery and measured their orientation discrimination thresholds before and after receiving 20 min of bipolar tDCS, 4 × 1 HD-tDCS, or sham stimulation over the visual cortex. Individual anatomically realistic head models were constructed to simulate tDCS-induced electric field distributions and quantify tDCS focality. Finally, a multiple linear regression model that used pre-tDCS behavioral performance and tDCS focality as factors was used to predict post-tDCS behavioral performance.Main results.We found that HD-tDCS, but not bipolar tDCS, could significantly alleviate visual crowding. Moreover, the variability in the tDCS effect could be reliably predicted by subjects' pre-tDCS behavioral performance and tDCS focality. This prediction model also performed well when generalized to other two tDCS protocols with a different electrode size or a different stimulation intensity.Significance.Our study links the variability in the tDCS-induced electric field and the pre-tDCS behavioral performance in a visual crowding task to the variability in post-tDCS performance. It provides a new approach to predicting individual tDCS effects and highlights the importance of understanding the factors that determine tDCS effectiveness while developing more robust protocols.

Comparison of EEG Source Localization Using Simplified and Anatomically Accurate Head Models in Younger and Older Adults

Accuracy of electroencephalography (EEG) source localization relies on the volume conduction head model. A previous analysis of young adults has shown that simplified head models have larger source localization errors when compared with head models based on magnetic resonance images (MRIs). As obtaining individual MRIs may not always be feasible, researchers often use generic head models based on template MRIs. It is unclear how much error would be introduced using template MRI head models in older adults that likely have differences in brain structure compared to young adults. The primary goal of this study was to determine the error caused by using simplified head models without individual-specific MRIs in both younger and older adults. We collected high-density EEG during uneven terrain walking and motor imagery for 15 younger (22±3 years) and 21 older adults (74±5 years) and obtained [Formula: see text]-weighted MRI for each individual. We performed equivalent dipole fitting after independent component analysis to obtain brain source locations using four forward modeling pipelines with increasing complexity. These pipelines included: 1) a generic head model with template electrode positions or 2) digitized electrode positions, 3) individual-specific head models with digitized electrode positions using simplified tissue segmentation, or 4) anatomically accurate segmentation. We found that when compared to the anatomically accurate individual-specific head models, performing dipole fitting with generic head models led to similar source localization discrepancies (up to 2 cm) for younger and older adults. Co-registering digitized electrode locations to the generic head models reduced source localization discrepancies by  ∼  6 mm. Additionally, we found that source depths generally increased with skull conductivity for the representative young adult but not as much for the older adult. Our results can help inform a more accurate interpretation of brain areas in EEG studies when individual MRIs are unavailable.

Review of individualized current flow modeling studies for transcranial electrical stimulation

There is substantial intersubject variability of behavioral and neurophysiological responses to transcranial electrical stimulation (tES), which represents one of the most important limitations of tES. Many tES protocols utilize a fixed experimental parameter set disregarding individual anatomical and physiological properties. This one-size-fits-all approach might be one reason for the observed interindividual response variability. Simulation of current flow applying head models based on available anatomical data can help to individualize stimulation parameters and contribute to the understanding of the causes of this response variability. Current flow modeling can be used to retrospectively investigate the characteristics of tES effectivity. Previous studies examined, for example, the impact of skull defects and lesions on the modulation of current flow and demonstrated effective stimulation intensities in different age groups. Furthermore, uncertainty analysis of electrical conductivities in current flow modeling indicated the most influential tissue compartments. Current flow modeling, when used in prospective study planning, can potentially guide stimulation configurations resulting in individually effective tES. Specifically, current flow modeling using individual or matched head models can be employed by clinicians and scientists to, for example, plan dosage in tES protocols for individuals or groups of participants. We review studies that show a relationship between the presence of behavioral/neurophysiological responses and features derived from individualized current flow models. We highlight the potential benefits of individualized current flow modeling.

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.

A computational study on the optimization of transcranial temporal interfering stimulation with high-definition electrodes using unsupervised neural networks

Transcranial temporal interfering stimulation (tTIS) can focally stimulate deep parts of the brain related to specific functions using beats at two high frequencies that do not individually affect the human brain. However, the complexity and nonlinearity of the simulation limit it in terms of calculation time and optimization precision. We propose a method to quickly optimize the interfering current value of high-definition electrodes, which can finely stimulate the deep part of the brain, using an unsupervised neural network (USNN) for tTIS. We linked a network that generates the values of electrode currents to another network, which is constructed to compute the interference exposure, for optimization by comparing the generated stimulus with the target stimulus. Further, a computational study was conducted using 16 realistic head models. We also compared tTIS with transcranial alternating current stimulation (tACS), in terms of performance and characteristics. The proposed method generated the strongest stimulation at the target, even when targeting deep areas or performing multi-target stimulation. The high-definition tTISl was less affected than tACS by target depth, and mis-stimulation was reduced compared with the case of using two-pair inferential stimulation in deep region. The optimization of the electrode currents for the target stimulus could be performed in 3 min. Using the proposed USNN for tTIS, we demonstrated that the electrode currents of tTIS can be optimized quickly and accurately. Moreover, we confirmed the possibility of precisely stimulating the deep parts of the brain via transcranial electrical stimulation.

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.

The influence of white matter lesions on the electric field in transcranial electric stimulation

•

Sensitivity analysis allows the simulation of tDCS with uncertain conductivities.

•

White matter lesions (WML) have no global influence on the electric field in tDCS.

•

In subjects with a high lesion load, a local influence can be observed.

•

In low to medium lesion load subjects, explicit modeling of WML is not required.

Background

Transcranial direct current stimulation (tDCS) is a promising tool to enhance therapeutic efforts, for instance, after a stroke. The achieved stimulation effects exhibit high inter-subject variability, primarily driven by perturbations of the induced electric field (EF). Differences are further elevated in the aging brain due to anatomical changes such as atrophy or lesions. Informing tDCS protocols by computer-based, individualized EF simulations is a suggested measure to mitigate this variability.

Objective

While brain anatomy in general and specifically atrophy as well as stroke lesions are deemed influential on the EF in simulation studies, the influence of the uncertainty in the change of the electrical properties of the white matter due to white matter lesions (WMLs) has not been quantified yet.

Methods

A group simulation study with 88 subjects assigned into four groups of increasing lesion load was conducted. Due to the lack of information about the electrical conductivity of WMLs, an uncertainty analysis was employed to quantify the variability in the simulation when choosing an arbitrary conductivity value for the lesioned tissue.

Results

The contribution of WMLs to the EF variance was on average only one tenth to one thousandth of the contribution of the other modeled tissues. While the contribution of the WMLs significantly increased (p≪.01) in subjects exhibiting a high lesion load compared to low lesion load subjects, typically by a factor of 10 and above, the total variance of the EF didnot change with the lesion load.

Conclusion

Our results suggest that WMLs do not perturb the EF globally and can thus be omitted when modeling subjects with low to medium lesion load. However, for high lesion load subjects, the omission of WMLs may yield less robust local EF estimations in the vicinity of the lesioned tissue. Our results contribute to the efforts of accurate modeling of tDCS for treatment planning.

Stimulation Montage Achieves Balanced Focality and Intensity

Transcranial direct current stimulation (tDCS) is a non-invasive neuromodulation technique to treat brain disorders by using a constant, low current to stimulate targeted cortex regions. Compared to the conventional tDCS that uses two large pad electrodes, multiple electrode tDCS has recently received more attention. It is able to achieve better stimulation performance in terms of stimulation intensity and focality. In this paper, we first establish a computational model of tDCS, and then propose a novel optimization algorithm using a regularization matrix λ to explore the balance between stimulation intensity and focality. The simulation study is designed such that the performance of state-of-the-art algorithms and the proposed algorithm can be compared via quantitative evaluation. The results show that the proposed algorithm not only achieves desired intensity, but also smaller target error and better focality. Robustness analysis indicates that the results are stable within the ranges of scalp and cerebrospinal fluid (CSF) conductivities, while the skull conductivity is most sensitive and should be carefully considered in real clinical applications.

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.

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.

Transcranial Direct Current Stimulation as a Treatment Tool for Mild Traumatic Brain Injury

Mild traumatic brain injury (mTBI) has been defined as a transient (<24 h) condition of confusion and/or loss of consciousness for less than 30 min after brain injury and can result in short- and long-term motor and cognitive impairments. Recent studies have documented the therapeutic potential of non-invasive neuromodulation techniques for the enhancement of cognitive and motor function in mTBI. Alongside repetitive transcranial magnetic stimulation (rTMS), the main technique used for this purpose is transcranial direct current stimulation (tDCS). The focus of this review was to provide a detailed, comprehensive (i.e., both cognitive and motor impairment) overview of the literature regarding therapeutic tDCS paradigms after mTBI. A publication search of the PubMed, Scopus, CINAHL, and PsycINFO databases was performed to identify records that applied tDCS in mTBI. The publication search yielded 14,422 records from all of the databases, however, only three met the inclusion criteria and were included in the final review. Based on the review, there is limited evidence of tDCS improving cognitive and motor performance. Surprisingly, there were only three studies that used tDCS in mTBI, which highlights an urgent need for more research to provide additional insights into ideal therapeutic brain targets and optimized stimulation parameters.

Does participant's age impact on tDCS induced fields? Insights from computational simulations

Objective: Understanding the induced current flow from transcranial direct current stimulation (tDCS) is essential for determining the optimal dose and treatment. Head tissue conductivities play a key role in the resulting electromagnetic fields. However, there exists a complicated relationship between skull conductivity and participant age, that remains unclear. We explored how variations in skull electrical conductivities, particularly as a suggested function of age, affected tDCS induced electric fields.Approach: Simulations were employed to compare tDCS outcomes for different intensities across head atlases of varying age. Three databases were chosen to demonstrate differing variability in skull conductivity with age and how this may affect induced fields. Differences in tDCS electric fields due to proposed age-dependent skull conductivity variation, as well as deviations in grey matter, white matter and scalp, were compared and the most influential tissues determined.Main results: tDCS induced peak electric fields significantly negatively correlated with age, exacerbated by employing proposed age-appropriate skull conductivity (according to all three datasets). Uncertainty in skull conductivity was the most sensitive to changes in peak fields with increasing age. These results were revealed to be directly due to changing skull conductivity, rather than head geometry alone. There was no correlation between tDCS focality and age.Significance: Accurate and individualised head anatomy andin vivoskull conductivity measurements are essential for modelling tDCS induced fields. In particular, age should be taken into account when considering stimulation dose to precisely predict outcomes.

Extended fMRI-Guided Anodal and Cathodal Transcranial Direct Current Stimulation Targeting Perilesional Areas in Post-Stroke Aphasia: A Pilot Randomized Clinical Trial

Transcranial direct current stimulation (tDCS) may enhance speech and language treatment (SLT) for stroke survivors with aphasia; however, to date, there is no standard protocol for the application of tDCS in post-stroke aphasia. We explored the safety and efficacy of fMRI-guided tDCS on functional language and cortical activity when delivered to the lesioned left hemisphere concurrently with SLT across an extended, six-week treatment period. Twelve persons with chronic, nonfluent aphasia following a single left-hemisphere stroke participated in the three-arm (anodal vs. cathodal vs. sham) single-blind, parallel, pilot trial. No serious adverse events occurred during 30 treatment sessions or in the following six weeks. All groups demonstrated functional language gains following intensive treatment; however, active tDCS resulted in greater gains in standardized, probe, and caregiver-reported measures of functional language than sham. Evidence declaring one polarity as superior for inducing language recovery was mixed. However, cathodal stimulation to the lesioned left hemisphere, expected to have a down-regulating effect, resulted in increased areas of cortical activation across both hemispheres, and specifically perilesionally. Generalization of these preliminary findings is limited; however, results are nevertheless compelling that tDCS combined with SLT can be safely applied across extended durations, with the potential to enhance functional language and cortical activation for persons with aphasia.

A novel method for calibrating head models to account for variability in conductivity and its evaluation in a sphere model

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.

Optimizing the electric field strength in multiple targets for multichannel transcranial electric stimulation

OBJECTIVE

Most approaches to optimize the electric field pattern generated by multichannel Transcranial Electric Stimulation (TES) require the definition of a preferred direction of the electric field in the target region(s). However, this requires knowledge about how the neural effects depend on the field direction, which is not always available. Thus, it can be preferential to optimize the field strength in the target(s), irrespective of the field direction. However, this results in a more complex optimization problem.

APPROACH

We introduce and validate a novel optimization algorithm that maximizes focality while controlling the electric field strength in the target to maintain a defined value. It obeys the safety constraints, allows limiting the number of active electrodes and allows also for multi-target optimization.

MAIN RESULTS

The optimization algorithm outperformed naïve search approaches in both quality of the solution and computational efficiency. Using the amygdala as test case, we show that it allows for reaching a reasonable trade-off between focality and field strength in the target. In contrast, simply maximizing the field strength in the target results in far more extended fields. In addition, by maintaining the pre-defined field strengths in the targets, the new algorithm allows for a balanced stimulation of two or more regions.

SIGNIFICANCE

The novel algorithm can be used to automatically obtain individualized, optimal montages for targeting regions without the need to define preferential directions. It will automatically select the field direction that achieves the desired field strength in the target(s) with the most focal stimulation pattern.

Localized Analysis of Normalized Distance from Scalp to Cortex and Personalized Evaluation (LANDSCAPE): Focusing on Age- and Dementia-Specific Changes

BACKGROUND

Scalp to cortex distance (SCD), as a key technological parameter, has been highlighted in the guidelines of non-invasive brain stimulation. However, in the context of age-related brain changes, the region-specific SCD and its impact on stimulation-induced electric field remain unclear.

OBJECTIVE

This study aimed to investigate the region-specific SCD and its relationship with morphometric features and cognitive function in age- and disease-specific populations.

METHODS

We analyzed the SCD and cortical thickness (CT) of left primary motor cortex (M1) and dorsolateral prefrontal cortex (DLPFC) in 214 cognitively normal adults and 43 dementia patients. CT-adjusted SCD was used to control the influence of CT on SCD. Head model was developed to simulate the impact of SCD on the electric field induced by transcranial electrical stimulation.

RESULTS

We found age-related increased SCD in the left DLPFC (p < 0.001), but not M1 (p = 0.134), and dementia-related increased SCD in both left DLPFC (p < 0.001) and M1 (p < 0.001). CT-adjusted SCD showed greater region-specific impact on left DLPFC rather than M1. The electric field induced by stimulation was consequently decreased with the increased SCD across normal aging and dementia groups.

CONCLUSIONS

Age and dementia have differential impacts on the SCDs of left DLPFC and M1. The findings suggest that it is important to be aware of region-specific distance measures when conducting neuromodulation in individuals with old age and dementia.

Imaging Transcranial Direct Current Stimulation (tDCS) with Positron Emission Tomography (PET)

Transcranial direct current stimulation (tDCS) is a form of non-invasive neuromodulation that is increasingly being utilized to examine and modify several cognitive and motor functions. Although tDCS holds great potential, it is difficult to determine optimal treatment procedures to accommodate configurations, the complex shapes, and dramatic conductivity differences among various tissues. Furthermore, recent demonstrations showed that up to 75% of the tDCS current applied to rodents and human cadavers was shunted by the scalp, subcutaneous tissue, and muscle, bringing the effects of tDCS on the cortex into question. Consequently, it is essential to combine tDCS with human neuroimaging to complement animal and cadaver studies and clarify if and how tDCS can affect neural function. One viable approach is positron emission tomography (PET) imaging. PET has unique potential for examining the effects of tDCS within the central nervous system in vivo, including cerebral metabolism, neuroreceptor occupancy, and neurotransmitter activity/binding. The focus of this review is the emerging role of PET and potential PET radiotracers for studying tDCS-induced functional changes in the human brain.

Impact of neuroanatomical variations and electrode orientation on stimulus current in a device for migraine: a computational study

OBJECTIVE

Conventional treatment methods for migraine often have side effects. One treatment involves a wearable neuromodulator targeting frontal nerves. Studies based on this technique have shown limited efficacy and the existing setting can cause pain. These may be associated with neuroanatomical variations which lead to high levels of required stimulus current. The aim of this paper is to study the effect of such variations on the activation currents of the Cefaly neuromodulator. Also, using a different electrode orientation, the possibility of reducing activation current levels to avoid painful side-effects and improve efficacy, is explored.

APPROACH

This paper investigates the effect of neuroanatomical variations and electrode orientation on the stimulus current thresholds using a computational hybrid model involving a volume conductor and an advanced nerve model. Ten human head models are developed considering statistical variations of key neuroanatomical features, to model a representative population.

MAIN RESULTS

By simulating the required stimulus current level in the head models, it is shown that neuroanatomical variations have a significant impact on the outcome, which is not solely a function of one specific neuroanatomical feature. The stimulus current thresholds based on the conventional Cefaly system vary from 4.4 mA to 25.1 mA across all head models. By altering the electrode orientation to align with the nerve branches, the stimulus current thresholds are substantially reduced to between 0.28 mA and 15 mA, reducing current density near pain-sensitive structures which may lead to a higher level of patient acceptance, further improving the efficacy.

SIGNIFICANCE

Computational modeling based on statistically valid neuroanatomical parameters, covering a representative adult population, offers a powerful tool for quantitative comparison of the effect of the position of stimulating electrodes which is otherwise not possible in clinical studies.

Electric field simulations for transcranial brain stimulation using FEM: an efficient implementation and error analysis

OBJECTIVE

Transcranial magnetic stimulation (TMS) and transcranial electric stimulation (TES) modulate brain activity non-invasively by generating electric fields either by electromagnetic induction or by injecting currents via skin electrodes. Numerical simulations based on anatomically detailed head models of the TMS and TES electric fields can help us to understand and optimize the spatial stimulation pattern in the brain. However, most realistic simulations are still slow, and the role of anatomical fidelity on simulation accuracy has not been evaluated in detail so far.

APPROACH

We present and validate a new implementation of the finite element method (FEM) for TMS and TES that is based on modern algorithms and libraries. We also evaluate the convergence of the simulations and estimate errors stemming from numerical and modelling aspects.

MAIN RESULTS

Comparisons with analytical solutions for spherical phantoms validate our new FEM implementation, which is three to six times faster than previous implementations. The convergence results suggest that accurately capturing the tissue geometry in addition to choosing a sufficiently accurate numerical method is of fundamental importance for accurate simulations.

SIGNIFICANCE

The new implementation allows for a substantial increase in computational efficiency of FEM TMS and TES simulations. This is especially relevant for applications such as the systematic assessment of model uncertainty and the optimization of multi-electrode TES montages. The results of our systematic error analysis allow the user to select the best tradeoff between model resolution and simulation speed for a specific application. The new FEM code is openly available as a part of our open-source software SimNIBS 3.0.

Transcranial Direct Current Stimulation Optimization - From Physics-Based Computer Simulations to High-Fidelity Head Phantom Fabrication and Measurements

Background

Transcranial direct current stimulation (tDCS) modulates neural networks. Computer simulations, while used to identify how currents behave within tissues of different conductivity properties, still need to be complemented by physical models.

Objective/Hypothesis

To better understand tDCS effects on biology-mimicking tissues by developing and testing the feasibility of a high-fidelity 3D head phantom model that has sensing capabilities at different compartmental levels.

Methods

Models obtained from MRI images generated 3D printed molds. Agar phantoms were fabricated, and 18 monitoring electrodes were placed on specific phantom brain areas.

Results

When using rectangular electrodes, the measured and simulated voltages at the monitoring electrodes agreed reasonably well, except at excitation locations. The electric field distribution in different phantom layers appeared better confined with circular electrodes compared to rectangular electrodes.

Conclusion

The high-fidelity 3D head model was found to be feasible and comparable with computer-based electrical simulations, with high correlation between simulated and measured brain voltages. This feasibility study supports testing to further assess the reliability of this model.

Scalp-to-cortex distance of left primary motor cortex and its computational head model: Implications for personalized neuromodulation

Background

Non‐invasive brain stimulation (NIBS) is increasingly used as a probe of function and therapeutics in experimental neuroscience and neurorehabilitation. Scalp‐to‐cortex distance (SCD), as a key parameter, has been shown to potentially impact on the electric field. This study aimed to examine the region‐specific SCD and its relationship with cognitive function in the context of age‐related brain atrophy.

Methods

We analyzed the SCD and cortical thickness (CT) of left primary motor cortex (M1) in 164 cognitively normal (CN) adults and 43 dementia patients drawn from the Open Access Series of Imaging Studies (OASIS). The degree of brain atrophy was measured by the volume of ventricular system. Computational head model was developed to simulate the impact of SCD on the electric field.

Results

Increased SCD of left M1 was only found in dementia patients (P < .001). When considering CT, the ratio of SCD to CT (F = 27.41, P < .001) showed better differential value than SCD. The SCD of left M1 was associated with worse global cognition (r = −.207, P = .011) and enlarged third ventricle (r = .241, P < .001). The electric field was consequently reduced with the increased SCD across cognitively normal elderly and dementia groups.

Conclusions

Scalable distance measures, including SCD and CT, are markedly correlated with reduced electric field in dementia patients. The findings suggest that it is important to be aware of region‐specific distance measures when conducting NIBS‐based rehabilitation in individuals with brain atrophy.

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.

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.

Establishment of a Numerical Model to Design an Electro-Stimulating System for a Porcine Mandibular Critical Size Defect

Electrical stimulation is a promising therapeutic approach for the regeneration of large bone defects. Innovative electrically stimulating implants for critical size defects in the lower jaw are under development and need to be optimized in silico and tested in vivo prior to application. In this context, numerical modelling and simulation are useful tools in the design process. In this study, a numerical model of an electrically stimulated minipig mandible was established to find optimal stimulation parameters that allow for a maximum area of beneficially stimulated tissue. Finite-element simulations were performed to determine the stimulation impact of the proposed implant design and to optimize the electric field distribution resulting from sinusoidal low-frequency ( f = 20 Hz ) electric stimulation. Optimal stimulation parameters of the electrode length h el = 25 m m and the stimulation potential φ stim = 0.5 V were determined. These parameter sets shall be applied in future in vivo validation studies. Furthermore, our results suggest that changing tissue properties during the course of the healing process might make a feedback-controlled stimulation system necessary.

Variation in Reported Human Head Tissue Electrical Conductivity Values

Electromagnetic source characterisation requires accurate volume conductor models representing head geometry and the electrical conductivity field. Head tissue conductivity is often assumed from previous literature, however, despite extensive research, measurements are inconsistent. A meta-analysis of reported human head electrical conductivity values was therefore conducted to determine significant variation and subsequent influential factors. Of 3121 identified publications spanning three databases, 56 papers were included in data extraction. Conductivity values were categorised according to tissue type, and recorded alongside methodology, measurement condition, current frequency, tissue temperature, participant pathology and age. We found variation in electrical conductivity of the whole-skull, the spongiform layer of the skull, isotropic, perpendicularly- and parallelly-oriented white matter (WM) and the brain-to-skull-conductivity ratio (BSCR) could be significantly attributed to a combination of differences in methodology and demographics. This large variation should be acknowledged, and care should be taken when creating volume conductor models, ideally constructing them on an individual basis, rather than assuming them from the literature. When personalised models are unavailable, it is suggested weighted average means from the current meta-analysis are used. Assigning conductivity as: 0.41 S/m for the scalp, 0.02 S/m for the whole skull, or when better modelled as a three-layer skull 0.048 S/m for the spongiform layer, 0.007 S/m for the inner compact and 0.005 S/m for the outer compact, as well as 1.71 S/m for the CSF, 0.47 S/m for the grey matter, 0.22 S/m for WM and 50.4 for the BSCR.

Cerebellar Lobules Optimal Stimulation (CLOS): A Computational Pipeline to Optimize Cerebellar Lobule-Specific Electric Field Distribution

OBJECTIVE

Cerebellar transcranial direct current stimulation (ctDCS) is challenging due to the complexity of the cerebellar structure which is reflected by the well-known variability in ctDCS effects. Therefore, our objective is to present a freely available computational modeling pipeline for cerebellar lobules' optimal stimulation (CLOS).

METHODS

CLOS can optimize lobule-specific electric field distribution following finite element analysis (FEA) using freely available computational modeling pipelines. We modeled published ctDCS montages with 5 cm × 5 cm anode placed 3 cm lateral to inion, and the same sized cathode was placed on the: (1) contralateral supra-orbital area (called Manto montage), and (2) buccinators muscle (called Celnik montage). Also, a published (3) 4×1 HD-ctDCS electrode montage was modeled. We also investigated the effects of the subject-specific head model versus Colin 27 average head model on lobule-specific electric field distribution. Three-way analysis of variance (ANOVA) was used to determine the effects of lobules, montage, and head model on the electric field distribution. The differences in lobule-specific electric field distribution across different freely available computational pipelines were also evaluated using subject-specific head model. We also presented an application of our computational pipeline to optimize a ctDCS electrode montage to deliver peak electric field at the cerebellar lobules VII-IX related to ankle function.

RESULTS

Eta-squared effect size after three-way ANOVA for electric field strength was 0.05 for lobule, 0.00 for montage, 0.04 for the head model, 0.01 for lobule∗montage interaction, 0.01 for lobule∗ head model interaction, and 0.00 for montage∗head model interaction. The electric field strength of both the Celnik and the Manto montages affected the lobules Crus I/II, VIIb, VIII, and IX of the targeted cerebellar hemisphere where Manto montage had a spillover to the contralateral cerebellar hemisphere. The 4×1 HD-ctDCS montage primarily affected the lobules Crus I/II of the targeted cerebellar hemisphere. All three published ctDCS montages were found to be not optimal for ankle function (lobules VII-IX), so we presented a novel HD-ctDCS electrode montage.

DISCUSSION

Our freely available CLOS pipeline can be leveraged to optimize electromagnetic stimulation to target cerebellar lobules related to different cognitive and motor functions.

A principled approach to conductivity uncertainty analysis in electric field calculations

Uncertainty surrounding ohmic tissue conductivity impedes accurate calculation of the electric fields generated by non-invasive brain stimulation. We present an efficient and generic technique for uncertainty and sensitivity analyses, which quantifies the reliability of field estimates and identifies the most influential parameters. For this purpose, we employ a non-intrusive generalized polynomial chaos expansion to compactly approximate the multidimensional dependency of the field on the conductivities. We demonstrate that the proposed pipeline yields detailed insight into the uncertainty of field estimates for transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS), identifies the most relevant tissue conductivities, and highlights characteristic differences between stimulation methods. Specifically, we test the influence of conductivity variations on (i) the magnitude of the electric field generated at each gray matter location, (ii) its normal component relative to the cortical sheet, (iii) its overall magnitude (indexed by the 98th percentile), and (iv) its overall spatial distribution. We show that TMS fields are generally less affected by conductivity variations than tDCS fields. For both TMS and tDCS, conductivity uncertainty causes much higher uncertainty in the magnitude as compared to the direction and overall spatial distribution of the electric field. Whereas the TMS fields were predominantly influenced by gray and white matter conductivity, the tDCS fields were additionally dependent on skull and scalp conductivities. Comprehensive uncertainty analyses of complex systems achieved by the proposed technique are not possible with classical methods, such as Monte Carlo sampling, without extreme computational effort. In addition, our method has the advantages of directly yielding interpretable and intuitive output metrics and of being easily adaptable to new problems.

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.

Evaluation of the electric field in the brain during transcranial direct current stimulation: A sensitivity analysis

The use of computational modeling studies accounts currently for the best approach to predict the electric field (E-field) distribution in transcranial direct current stimulation. As with any model, the values attributed to the physical properties, namely the electrical conductivity of the tissues, affect the predicted E-field distribution. A wide range of values for the conductivity of most tissues is reported in the literature. In this work, we used the finite element method to compute the E-field induced in a realistic human head model for two electrode montages targeting the left dorso-lateral prefrontal cortex (DLPFC). A systematic analysis of the effect of different isotropic conductivity profiles on the E-field distribution was performed for the standard bipolar 7×5 cm2 electrodes configuration and also for an optimized multielectrode montage. Average values of the E-field's magnitude, normal and tangential components were calculated in the target region in the left DLPFC. Results show that the field decreases with increasing scalp, cerebrospinal fluid (CSF) and grey matter (GM) conductivities, while the opposite is observed for the skull and white matter conductivities. The tissues whose conductivity most affects the E-field in the cortex are the scalp and the CSF, followed by the GM and the skull. Uncertainties in the conductivity of individual tissues may affect electric field values by up to about 80%.

Changing head model extent affects finite element predictions of transcranial direct current stimulation distributions

OBJECTIVE

In this study, we determined efficient head model sizes relative to predicted current densities in transcranial direct current stimulation (tDCS).

APPROACH

Efficiency measures were defined based on a finite element (FE) simulations performed using nine human head models derived from a single MRI data set, having extents varying from 60%-100% of the original axial range. Eleven tissue types, including anisotropic white matter, and three electrode montages (T7-T8, F3-right supraorbital, Cz-Oz) were used in the models.

MAIN RESULTS

Reducing head volume extent from 100% to 60%, that is, varying the model's axial range from between the apex and C3 vertebra to one encompassing only apex to the superior cerebellum, was found to decrease the total modeling time by up to half. Differences between current density predictions in each model were quantified by using a relative difference measure (RDM). Our simulation results showed that [Formula: see text] was the least affected (a maximum of 10% error) for head volumes modeled from the apex to the base of the skull (60%-75% volume).

SIGNIFICANCE

This finding suggested that the bone could act as a bioelectricity boundary and thus performing FE simulations of tDCS on the human head with models extending beyond the inferior skull may not be necessary in most cases to obtain reasonable precision in current density results.

Uncertainty Quantification of Oscillation Suppression During DBS in a Coupled Finite Element and Network Model

Models of the cortico-basal ganglia network and volume conductor models of the brain can provide insight into the mechanisms of action of deep brain stimulation (DBS). In this study, the coupling of a network model, under parkinsonian conditions, to the extracellular field distribution obtained from a three dimensional finite element model of a rodent's brain during DBS is presented. This coupled model is used to investigate the influence of uncertainty in the electrical properties of brain tissue and encapsulation tissue, formed around the electrode after implantation, on the suppression of oscillatory neural activity during DBS. The resulting uncertainty in this effect of DBS on the network activity is quantified using a computationally efficient and non-intrusive stochastic approach based on the generalized Polynomial Chaos. The results suggest that variations in the electrical properties of brain tissue may have a substantial influence on the level of suppression of oscillatory activity during DBS. Applying a global sensitivity analysis on the suppression of the simulated oscillatory activity showed that the influence of uncertainty in the electrical properties of the encapsulation tissue had only a minor influence, in agreement with previous experimental and computational studies investigating the mechanisms of current-controlled DBS in the literature.

A simple method for EEG guided transcranial electrical stimulation without models

OBJECTIVE

There is longstanding interest in using EEG measurements to inform transcranial Electrical Stimulation (tES) but adoption is lacking because users need a simple and adaptable recipe. The conventional approach is to use anatomical head-models for both source localization (the EEG inverse problem) and current flow modeling (the tES forward model), but this approach is computationally demanding, requires an anatomical MRI, and strict assumptions about the target brain regions. We evaluate techniques whereby tES dose is derived from EEG without the need for an anatomical head model, target assumptions, difficult case-by-case conjecture, or many stimulation electrodes.

APPROACH

We developed a simple two-step approach to EEG-guided tES that based on the topography of the EEG: (1) selects locations to be used for stimulation; (2) determines current applied to each electrode. Each step is performed based solely on the EEG with no need for head models or source localization. Cortical dipoles represent idealized brain targets. EEG-guided tES strategies are verified using a finite element method simulation of the EEG generated by a dipole, oriented either tangential or radial to the scalp surface, and then simulating the tES-generated electric field produced by each model-free technique. These model-free approaches are compared to a 'gold standard' numerically optimized dose of tES that assumes perfect understanding of the dipole location and head anatomy. We vary the number of electrodes from a few to over three hundred, with focality or intensity as optimization criterion.

MAIN RESULTS

Model-free approaches evaluated include (1) voltage-to-voltage, (2) voltage-to-current; (3) Laplacian; and two Ad-Hoc techniques (4) dipole sink-to-sink; and (5) sink to concentric. Our results demonstrate that simple ad hoc approaches can achieve reasonable targeting for the case of a cortical dipole, remarkably with only 2-8 electrodes and no need for a model of the head.

SIGNIFICANCE

Our approach is verified directly only for a theoretically localized source, but may be potentially applied to an arbitrary EEG topography. For its simplicity and linearity, our recipe for model-free EEG guided tES lends itself to broad adoption and can be applied to static (tDCS), time-variant (e.g., tACS, tRNS, tPCS), or closed-loop tES.

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

To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45° and a factor of 1.66, respectively.

Modeling sequence and quasi-uniform assumption in computational neurostimulation

Computational neurostimulation aims to develop mathematical constructs that link the application of neuromodulation with changes in behavior and cognition. This process is critical but daunting for technical challenges and scientific unknowns. The overarching goal of this review is to address how this complex task can be made tractable. We describe a framework of sequential modeling steps to achieve this: (1) current flow models, (2) cell polarization models, (3) network and information processing models, and (4) models of the neuroscientific correlates of behavior. Each step is explained with a specific emphasis on the assumptions underpinning underlying sequential implementation. We explain the further implementation of the quasi-uniform assumption to overcome technical limitations and unknowns. We specifically focus on examples in electrical stimulation, such as transcranial direct current stimulation. Our approach and conclusions are broadly applied to immediate and ongoing efforts to deploy computational neurostimulation.