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.

Accurate TMS Head Modeling: Interfacing SimNIBS and BEM-FMM in a MATLAB-Based Module.

We interface the head modelling, coil models, Graphical User Interface (GUI), and post-processing capabilities of the SimNIBS package with the boundary element fast multipole method (BEM-FMM), implemented in a MATLAB-based module. The resulting pipeline combines the best of both worlds: the individualized head modelling and ease-of-use of SimNIBS with the numerical accuracy of BEM-FMM. The corresponding TMS (transcranial magnetic stimulation) modeling package is developed and made available online. It imports a SimNIBS surface segmentation and a coil field, and then exports electric-field values in selected surfaces or volumes. Additional information is also made available, such as discontinuous compartment surface electric fields and associated surface electric charge distributions.

Accurate and robust whole-head segmentation from magnetic resonance images for individualized head modeling.

Transcranial brain stimulation (TBS) has been established as a method for modulating and mapping the function of the human brain, and as a potential treatment tool in several brain disorders. Typically, the stimulation is applied using a one-size-fits-all approach with predetermined locations for the electrodes, in electric stimulation (TES), or the coil, in magnetic stimulation (TMS), which disregards anatomical variability between individuals. However, the induced electric field distribution in the head largely depends on anatomical features implying the need for individually tailored stimulation protocols for focal dosing. This requires detailed models of the individual head anatomy, combined with electric field simulations, to find an optimal stimulation protocol for a given cortical target. Considering the anatomical and functional complexity of different brain disorders and pathologies, it is crucial to account for the anatomical variability in order to translate TBS from a research tool into a viable option for treatment. In this article we present a new method, called CHARM, for automated segmentation of fifteen different head tissues from magnetic resonance (MR) scans. The new method compares favorably to two freely available software tools on a five-tissue segmentation task, while obtaining reasonable segmentation accuracy over all fifteen tissues. The method automatically adapts to variability in the input scans and can thus be directly applied to clinical or research scans acquired with different scanners, sequences or settings. We show that an increase in automated segmentation accuracy results in a lower relative error in electric field simulations when compared to anatomical head models constructed from reference segmentations. However, also the improved segmentations and, by implication, the electric field simulations are affected by systematic artifacts in the input MR scans. As long as the artifacts are unaccounted for, this can lead to local simulation differences up to 30% of the peak field strength on reference simulations. Finally, we exemplarily demonstrate the effect of including all fifteen tissue classes in the field simulations against the standard approach of using only five tissue classes and show that for specific stimulation configurations the local differences can reach 10% of the peak field strength.

Probing EEG activity in the targeted cortex after focal transcranial electrical stimulation.

BACKGROUND: Recording electroencephalography (EEG) from the targeted cortex immediately before and after focal transcranial electrical stimulation (TES) remains a challenge. METHODS: We introduce a hybrid stimulation-recording approach where a single EEG electrode is inserted into the inner electrode of a double-ring montage for focal TES. The new combined electrode was placed at the C3 position of the EEG 10-20 system. Neuronal activity was recorded in two volunteers before and after 20 Hz alternating-current TES at peak-to-peak intensities of 1 and 2 mA. TES-induced electric field distributions were simulated with SIMNIBS software. RESULTS: Using the hybrid stimulation-recording set-up, EEG activity was successfully recorded directly before and after TES. Simulations revealed comparable electrical fields in the stimulated cortex for the pseudomonopolar montage with and without embedded EEG electrode. CONCLUSION: The hybrid TES-EEG approach can be used to probe after-effects of focal TES on neuronal activity in the targeted cortex.

Value and limitations of intracranial recordings for validating electric field modeling for transcranial brain stimulation.

Comparing electric field simulations from individualized head models against in-vivo intra-cranial recordings is considered the gold standard for direct validation of computational field modeling for transcranial brain stimulation and brain mapping techniques such as electro- and magnetoencephalography. The measurements also help to improve simulation accuracy by pinning down the factors having the largest influence on the simulations. Here we compare field simulations from four different automated pipelines against intracranial voltage recordings in an existing dataset of 14 epilepsy patients. We show that modeling differences in the pipelines lead to notable differences in the simulated electric field distributions that are often large enough to change the conclusions regarding the dose distribution and strength in the brain. Specifically, differences in the automatic segmentations of the head anatomy from structural magnetic resonance images are a major factor contributing to the observed field differences. However, the differences in the simulated fields are not reflected in the comparison between the simulations and intra-cranial measurements. This apparent mismatch is partly explained by the noisiness of the intra-cranial measurements, which renders comparisons between the methods inconclusive. We further demonstrate that a standard regression analysis, which ignores uncertainties in the simulations, leads to a strong bias in the estimated linear relationship between simulated and measured fields. Ignoring this bias leads to the incorrect conclusion that the models systematically misestimate the field strength in the brain. We propose a new Bayesian regression analysis of the data that yields unbiased parameter estimates, along with their uncertainties, and gives further insights to the fit between simulations and measurements. Specifically, the unbiased results give only weak support for systematic misestimations of the fields by the models.

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.

Comparative performance of the finite element method and the boundary element fast multipole method for problems mimicking transcranial magnetic stimulation (TMS).

OBJECTIVE: A study pertinent to the numerical modeling of cortical neurostimulation is conducted in an effort to compare the performance of the finite element method (FEM) and an original formulation of the boundary element fast multipole method (BEM-FMM) at matched computational performance metrics. APPROACH: We consider two problems: (i) a canonic multi-sphere geometry and an external magnetic-dipole excitation where the analytical solution is available and; (ii) a problem with realistic head models excited by a realistic coil geometry. In the first case, the FEM algorithm tested is a fast open-source getDP solver running within the SimNIBS 2.1.1 environment. In the second case, a high-end commercial FEM software package ANSYS Maxwell 3D is used. The BEM-FMM method runs in the MATLAB® 2018a environment. MAIN RESULTS: In the first case, we observe that the BEM-FMM algorithm gives a smaller solution error for all mesh resolutions and runs significantly faster for high-resolution meshes when the number of triangular facets exceeds approximately 0.25 M. We present other relevant simulation results such as volumetric mesh generation times for the FEM, time necessary to compute the potential integrals for the BEM-FMM, and solution performance metrics for different hardware/operating system combinations. In the second case, we observe an excellent agreement for electric field distribution across different cranium compartments and, at the same time, a speed improvement of three orders of magnitude when the BEM-FMM algorithm used. SIGNIFICANCE: This study may provide a justification for anticipated use of the BEM-FMM algorithm for high-resolution realistic transcranial magnetic stimulation scenarios.

The non-transcranial TMS-evoked potential is an inherent source of ambiguity in TMS-EEG studies.

Transcranial Magnetic Stimulation (TMS) excites populations of neurons in the stimulated cortex, and the resulting activation may spread to connected brain regions. The distributed cortical response can be recorded with electroencephalography (EEG). Since TMS also stimulates peripheral sensory and motor axons and generates a loud "click" sound, the TMS-evoked EEG potentials (TEPs) reflect not only neural activity induced by transcranial neuronal excitation but also neural activity due to somatosensory and auditory processing. In 17 healthy young individuals, we systematically assessed the contribution of multisensory peripheral stimulation to TEPs using a TMS-compatible EEG system. Real TMS was delivered with a figure-of-eight coil over the left para-median posterior parietal cortex or superior frontal gyrus with the coil being oriented perpendicularly or in parallel to the target gyrus. We also recorded the EEG responses evoked by realistic sham stimulation over the posterior parietal and superior frontal cortex, mimicking the auditory and somatosensory sensations evoked by real TMS. We applied state-of-the-art procedures to attenuate somatosensory and auditory confounds during real TMS, including the placement of a foam layer underneath the coil and auditory noise masking. Despite these precautions, the temporal and spatial features of the cortical potentials evoked by real TMS at the prefrontal and parietal site closely resembled the cortical potentials evoked by realistic sham TMS, both for early and late TEP components. Our findings stress the need to include a peripheral multisensory control stimulation in the design of TMS-EEG studies to enable a dissociation between truly transcranial and non-transcranial components of TEPs.

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.

Accurate anatomical head segmentations: a data set for biomedical simulations.

Detailed computational anatomical models of the entire head are needed for accurate in silico modeling in a variety of transcranial stimulation applications. Models from different subjects help to understand and account for population variability. To this end, we have developed a new library of head models of 20 individuals, segmented from co-aligned multi-modal medical image data. The acquired image modalities allow to accurately model tissues with different material properties, such as electrical conductivity or spatially varying acoustic properties. The usefulness of the models is illustrated for two example applications.

Enhancing Tumor Treating Fields Therapy with Skull-Remodeling Surgery. The Role of Finite Element Methods in Surgery Planning.

Skull-remodeling surgery has been proposed to enhance the dose of tumor treating fields in glioblastoma treatment. This abstract describes the finite element methods used to plan the surgery and evaluate the treatment efficacy.

Automatic skull segmentation from MR images for realistic volume conductor models of the head: Assessment of the state-of-the-art.

Anatomically realistic volume conductor models of the human head are important for accurate forward modeling of the electric field during transcranial brain stimulation (TBS), electro- (EEG) and magnetoencephalography (MEG). In particular, the skull compartment exerts a strong influence on the field distribution due to its low conductivity, suggesting the need to represent its geometry accurately. However, automatic skull reconstruction from structural magnetic resonance (MR) images is difficult, as compact bone has a very low signal in magnetic resonance imaging (MRI). Here, we evaluate three methods for skull segmentation, namely FSL BET2, the unified segmentation routine of SPM12 with extended spatial tissue priors, and the skullfinder tool of BrainSuite. To our knowledge, this study is the first to rigorously assess the accuracy of these state-of-the-art tools by comparison with CT-based skull segmentations on a group of ten subjects. We demonstrate several key factors that improve the segmentation quality, including the use of multi-contrast MRI data, the optimization of the MR sequences and the adaptation of the parameters of the segmentation methods. We conclude that FSL and SPM12 achieve better skull segmentations than BrainSuite. The former methods obtain reasonable results for the upper part of the skull when a combination of T1- and T2-weighted images is used as input. The SPM12-based results can be improved slightly further by means of simple morphological operations to fix local defects. In contrast to FSL BET2, the SPM12-based segmentation with extended spatial tissue priors and the BrainSuite-based segmentation provide coarse reconstructions of the vertebrae, enabling the construction of volume conductor models that include the neck. We exemplarily demonstrate that the extended models enable a more accurate estimation of the electric field distribution during transcranial direct current stimulation (tDCS) for montages that involve extraencephalic electrodes. The methods provided by FSL and SPM12 are integrated into pipelines for the automatic generation of realistic head models based on tetrahedral meshes, which are distributed as part of the open-source software package SimNIBS for field calculations for transcranial brain stimulation.

The impact of large structural brain changes in chronic stroke patients on the electric field caused by transcranial brain stimulation.

Transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (TDCS) are two types of non-invasive transcranial brain stimulation (TBS). They are useful tools for stroke research and may be potential adjunct therapies for functional recovery. However, stroke often causes large cerebral lesions, which are commonly accompanied by a secondary enlargement of the ventricles and atrophy. These structural alterations substantially change the conductivity distribution inside the head, which may have potentially important consequences for both brain stimulation methods. We therefore aimed to characterize the impact of these changes on the spatial distribution of the electric field generated by both TBS methods. In addition to confirming the safety of TBS in the presence of large stroke-related structural changes, our aim was to clarify whether targeted stimulation is still possible. Realistic head models containing large cortical and subcortical stroke lesions in the right parietal cortex were created using MR images of two patients. For TMS, the electric field of a double coil was simulated using the finite-element method. Systematic variations of the coil position relative to the lesion were tested. For TDCS, the finite-element method was used to simulate a standard approach with two electrode pads, and the position of one electrode was systematically varied. For both TMS and TDCS, the lesion caused electric field "hot spots" in the cortex. However, these maxima were not substantially stronger than those seen in a healthy control. The electric field pattern induced by TMS was not substantially changed by the lesions. However, the average field strength generated by TDCS was substantially decreased. This effect occurred for both head models and even when both electrodes were distant to the lesion, caused by increased current shunting through the lesion and enlarged ventricles. Judging from the similar peak field strengths compared to the healthy control, both TBS methods are safe in patients with large brain lesions (in practice, however, additional factors such as potentially lowered thresholds for seizure-induction have to be considered). Focused stimulation by TMS seems to be possible, but standard tDCS protocols appear to be less efficient than they are in healthy subjects, strongly suggesting that tDCS studies in this population might benefit from individualized treatment planning based on realistic field calculations.

On the importance of electrode parameters for shaping electric field patterns generated by tDCS.

Transcranial direct current stimulation (tDCS) uses electrode pads placed on the head to deliver weak direct current to the brain and modulate neuronal excitability. The effects depend on the intensity and spatial distribution of the electric field. This in turn depends on the geometry and electric properties of the head tissues and electrode pads. Previous numerical studies focused on providing a reasonable level of detail of the head anatomy, often using simplified electrode models. Here, we explore via finite element method (FEM) simulations based on a high-resolution head model how detailed electrode modeling influences the calculated electric field in the brain. We take into account electrode shape, size, connector position and conductivities of different electrode materials (including saline solutions and electrode gels). These factors are systematically characterized to demonstrate their impact on the field distribution in the brain. The goals are to assess the effect of simplified electrode models; and to develop practical rules-of-thumb to achieve a stronger stimulation of the targeted brain regions underneath the electrode pads. We show that for standard rectangular electrode pads, lower saline and gel conductivities result in more homogeneous fields in the region of interest (ROI). Placing the connector at the center of the electrode pad or farthest from the second electrode substantially increases the field strength in the ROI. Our results highlight the importance of detailed electrode modeling and of having an adequate selection of electrode pads/gels in experiments. We also advise for a more detailed reporting of the electrode montages when conducting tDCS experiments, as different configurations significantly affect the results.

Field modeling for transcranial magnetic stimulation: A useful tool to understand the physiological effects of TMS?

Electric field calculations based on numerical methods and increasingly realistic head models are more and more used in research on Transcranial Magnetic Stimulation (TMS). However, they are still far from being established as standard tools for the planning and analysis in practical applications of TMS. Here, we start by delineating three main challenges that need to be addressed to unravel their full potential. This comprises (i) identifying and dealing with the model uncertainties, (ii) establishing a clear link between the induced fields and the physiological stimulation effects, and (iii) improving the usability of the tools for field calculation to the level that they can be easily used by non-experts. We then introduce a new version of our pipeline for field calculations (www.simnibs.org) that substantially simplifies setting up and running TMS and tDCS simulations based on Finite-Element Methods (FEM). We conclude with a brief outlook on how the new version of SimNIBS can help to target the above identified challenges.