Comparison of spherical and realistically shaped boundary element head models for transcranial magnetic stimulation navigation

Pseudo-MRI Engine for MRI-Free Electromagnetic Source Imaging

Structural head MRIs are a crucial ingredient in MEG/EEG source imaging; they are used to define a realistically shaped volume conductor model, constrain the source space, and visualize the source estimates. However, individual MRIs are not always available, or they may be of insufficient quality for segmentation, leading to the use of a generic template MRI, matched MRI, or the application of a spherical conductor model. Such approaches deviate the model geometry from the true head structure and limit the accuracy of the forward solution. Here, we implemented an easy-to-use tool, pseudo-MRI engine, which utilizes the head-shape digitization acquired during a MEG/EEG measurement for warping an MRI template to fit the subject's head. To this end, the algorithm first removes outlier digitization points, densifies the point cloud by interpolation if needed, and finally warps the template MRI and its segmented surfaces to the individual head shape using the thin-plate-spline method. To validate the approach, we compared the geometry of segmented head surfaces, cortical surfaces, and canonical brain regions in the real and pseudo-MRIs of 25 subjects. We also tested the MEG source reconstruction accuracy with pseudo-MRIs against that obtained with the real MRIs from individual subjects with simulated and real MEG data. We found that the pseudo-MRI enables comparable source localization accuracy to the one obtained with the subject's real MRI. The study indicates that pseudo-MRI can replace the need for individual MRI scans in MEG/EEG source imaging for applications that do not require subcentimeter spatial accuracy.

Novel Volume Integral Equation Approach for Low-Frequency E-Field Dosimetry of Transcranial Magnetic Stimulation

A new volume integral equation (VIE) approach is introduced to study transcranial magnetic stimulation (TMS) and high-contrast media at low frequencies. This new integral equation offers a simple solution to the high-contrast breakdown observed in low-frequency electric field (E-field) dosimetry of conductive media. Specifically, we employ appropriate approximations that are valid for low frequencies and stabilize the VIE by introducing a basis expansion set that removes solutions associated with high eigenvalues in the equation. The new equation is devoid of high-contrast breakdown and does not require the use of auxiliary surface variables or projectors, providing a straightforward practical solution for the VIE analysis of TMS. Our results indicate that the novel VIE formulation matches boundary element, finite element, and analytical solutions. This new VIE represents a first step towards including anisotropy in integral equation E-field dosimetry for brain stimulation.

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.

Individual Prediction of Electric Field Induced by Deep-Brain Magnetic Stimulation With CNN-Transformer

Deep-brain Magnetic Stimulation (DMS) can improve the symptoms caused by Alzheimer's disease by inducing rhythmic electric field in the deep brain, and the induced electric field is rhythm-dependent. However, calculating the induced electric field requires building a voxel model of the brain for the stimulated object, which usually takes several hours. In order to obtain the rhythm-dependent electric field induced by DMS in real time, we adopt a CNN-Transformer model to predict it. A data set with a sample size of 7350 is established for the training and testing of the model. 10-fold cross validation is used to determine the optimal hyperparameters for training CNN-Transformer. The combination of 5-layer CNN and 6-layer Transformer is verified as the optimal combination of CNN-Transformer model. The experimental results show that the CNN-Transformer model can complete the prediction in 0.731s (CPU) or 0.042s (GPU), and the overall performance metrics of prediction can reach: MAE =0.0269, RMSE =0.0420, MAPE =4.61% and R2=0.9627. The prediction performance of the CNN-Transformer model for the hippocampal electric field is better than that of the brain grey matter electric field, and the stimulation rhythm has less influence on the model performance than the coil configuration. Taking the same dataset to train and test the separate CNN model and Transformer model, it is found that CNN-Transformer has better prediction performance than the separate CNN model and Transformer model in the task of predicting electric field induced by DMS.

A Closed Formalism for Anatomy-Independent Projection and Optimization of Magnetic Stimulation Coils on Arbitrarily Shaped Surfaces

INTRODUCTION

Transcranial magnetic stimulation (TMS) is a popular method for the noninvasive stimulation of neurons in the brain. It has become a standard instrument in experimental brain research and has been approved for a range of diagnostic and therapeutic applications. These applications require appropriately shaped coils. Various applications have been established or approved for specific coil designs with their corresponding spatial electric field distributions. However, the specific coil implementation may no longer be appropriate from the perspective of available material and manufacturing opportunities or considering the latest understanding of how to achieve induced electric fields in the head most efficiently. Furthermore, in some cases, field measurements of coils with unknown winding or a user-defined field are available and require an actual implementation. Similar applications exist for magnetic resonance imaging coils.

OBJECTIVE

This work aims at introducing a complete formalism free from heuristics, iterative optimization, and ad-hoc or manual steps to form practical stimulation coils with individual turns to either equivalently match an existing coil or produce a given field. The target coil can reside on practically any sufficiently large or closed surface adjacent to or around the head.

METHODS

The method derives an equivalent field through vector projection exploiting the well-known Huygens' and Love's equivalence principle. In contrast to other coil design or optimization approaches recently presented, the procedure is an explicit forward Hilbert-space vector projection or basis change. For demonstration, we map a commercial figure-of-eight coil as one of the most widely used devices and a more intricate coil recently approved clinically for addiction treatment (H4) onto a bent surface close to the head for highest efficiency and lowest field energy.

RESULTS

The resulting projections are within ≤4% of the target field and reduce the necessary pulse energy by more than 40%.

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 neuro-modulation 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.

Real-Time Computation of Brain E-Field for Enhanced Transcranial Magnetic Stimulation Neuronavigation and Optimization

Transcranial Magnetic Stimulation (TMS) coil placement and pulse waveform current are often chosen to achieve a specified E-field dose on targeted brain regions. TMS neuronavigation could be improved by including real-time accurate distributions of the E-field dose on the cortex. We introduce a method and develop software for computing brain E-field distributions in real-time enabling easy integration into neuronavigation and with the same accuracy as 1st -order finite element method (FEM) solvers. Initially, a spanning basis set (< 400) of E-fields generated by white noise magnetic currents on a surface separating the head and permissible coil placements are orthogonalized to generate the modes. Subsequently, Reciprocity and Huygens' principles are utilized to compute fields induced by the modes on a surface separating the head and coil by FEM, which are used in conjunction with online (real-time) computed primary fields on the separating surface to evaluate the mode expansion. We conducted a comparative analysis of E-fields computed by FEM and in real-time for eight subjects, utilizing two head model types (SimNIBS's 'headreco' and 'mri2mesh' pipeline), three coil types (circular, double-cone, and Figure-8), and 1000 coil placements (48,000 simulations). The real-time computation for any coil placement is within 4 milliseconds (ms), for 400 modes, and requires less than 4 GB of memory on a GPU. Our solver is capable of computing E-fields within 4 ms, making it a practical approach for integrating E-field information into the neuronavigation systems without imposing a significant overhead on frame generation (20 and 50 frames per second within 50 and 20 ms, respectively).

Targeted Modulation of Human Brain Interregional Effective Connectivity With Spike-Timing Dependent Plasticity

OBJECTIVE

The ability to selectively up- or downregulate interregional brain connectivity would be useful for research and clinical purposes. Toward this aim, cortico-cortical paired associative stimulation (ccPAS) protocols have been developed in which two areas are repeatedly stimulated with a millisecond-level asynchrony. However, ccPAS results in humans using bifocal transcranial magnetic stimulation (TMS) have been variable, and the mechanisms remain unproven. In this study, our goal was to test whether ccPAS mechanism is spike-timing-dependent plasticity (STDP).

MATERIALS AND METHODS

Eleven healthy participants received ccPAS to the left primary motor cortex (M1) → right M1 with three different asynchronies (5 milliseconds shorter, equal to, or 5 milliseconds longer than the 9-millisecond transcallosal conduction delay) in separate sessions. To observe the neurophysiological effects, single-pulse TMS was delivered to the left M1 before and after ccPAS while cortico-cortical evoked responses were extracted from the contralateral M1 using source-resolved electroencephalography.

RESULTS

Consistent with STDP mechanisms, the effects on synaptic strengths flipped depending on the asynchrony. Further implicating STDP, control experiments suggested that the effects were unidirectional and selective to the targeted connection.

CONCLUSION

The results support the idea that ccPAS induces STDP and may selectively up- or downregulate effective connectivity between targeted regions in the human brain.

Noninvasive Electrical Stimulation Neuromodulation and Digital Brain Technology: A Review

We review the research progress on noninvasive neural regulatory systems through system design and theoretical guidance. We provide an overview of the development history of noninvasive neuromodulation technology, focusing on system design. We also discuss typical cases of neuromodulation that use modern noninvasive electrical stimulation and the main limitations associated with this technology. In addition, we propose a closed-loop system design solution of the "time domain", "space domain", and "multi-electrode combination". For theoretical guidance, this paper provides an overview of the "digital brain" development process used for noninvasive electrical-stimulation-targeted modeling and the development of "digital human" programs in various countries. We also summarize the core problems of the existing "digital brain" used for noninvasive electrical-stimulation-targeted modeling according to the existing achievements and propose segmenting the tissue. For this, the tissue parameters of a multimodal image obtained from a fresh cadaver were considered as an index. The digital projection of the multimodal image of the brain of a living individual was implemented, following which the segmented tissues could be reconstructed to obtain a "digital twin brain" model with personalized tissue structure differences. The "closed-loop system" and "personalized digital twin brain" not only enable the noninvasive electrical stimulation of neuromodulation to achieve the visualization of the results and adaptive regulation of the stimulation parameters but also enable the system to have individual differences and more accurate stimulation.

TMS combined with EEG: Recommendations and open issues for data collection and analysis

Transcranial magnetic stimulation (TMS) evokes neuronal activity in the targeted cortex and connected brain regions. The evoked brain response can be measured with electroencephalography (EEG). TMS combined with simultaneous EEG (TMS-EEG) is widely used for studying cortical reactivity and connectivity at high spatiotemporal resolution. Methodologically, the combination of TMS with EEG is challenging, and there are many open questions in the field. Different TMS-EEG equipment and approaches for data collection and analysis are used. The lack of standardization may affect reproducibility and limit the comparability of results produced in different research laboratories. In addition, there is controversy about the extent to which auditory and somatosensory inputs contribute to transcranially evoked EEG. This review provides a guide for researchers who wish to use TMS-EEG to study the reactivity of the human cortex. A worldwide panel of experts working on TMS-EEG covered all aspects that should be considered in TMS-EEG experiments, providing methodological recommendations (when possible) for effective TMS-EEG recordings and analysis. The panel identified and discussed the challenges of the technique, particularly regarding recording procedures, artifact correction, analysis, and interpretation of the transcranial evoked potentials (TEPs). Therefore, this work offers an extensive overview of TMS-EEG methodology and thus may promote standardization of experimental and computational procedures across groups.

A Systematic Review and Large-Scale tES and TMS Electric Field Modeling Study Reveals How Outcome Measure Selection Alters Results in a Person- and Montage-Specific Manner

Background

Electric field (E-field) modeling is a potent tool to examine the cortical effects of transcranial magnetic and electrical stimulation (TMS and tES, respectively) and to address the high variability in efficacy observed in the literature. However, outcome measures used to report E-field magnitude vary considerably and have not yet been compared in detail.

Objectives

The goal of this two-part study, encompassing a systematic review and modeling experiment, was to provide an overview of the different outcome measures used to report the magnitude of tES and TMS E-fields, and to conduct a direct comparison of these measures across different stimulation montages.

Methods

Three electronic databases were searched for tES and/or TMS studies reporting E-field magnitude. We extracted and discussed outcome measures in studies meeting the inclusion criteria. Additionally, outcome measures were compared via models of four common tES and two TMS modalities in 100 healthy younger adults.

Results

In the systematic review, we included 118 studies using 151 outcome measures related to E-field magnitude. Structural and spherical regions of interest (ROI) analyses and percentile-based whole-brain analyses were used most often. In the modeling analyses, we found that there was an average of only 6% overlap between ROI and percentile-based whole-brain analyses in the investigated volumes within the same person. The overlap between ROI and whole-brain percentiles was montage- and person-specific, with more focal montages such as 4Ã-1 and APPS-tES, and figure-of-eight TMS showing up to 73%, 60%, and 52% overlap between ROI and percentile approaches respectively. However, even in these cases, 27% or more of the analyzed volume still differed between outcome measures in every analyses.

Conclusions

The choice of outcome measures meaningfully alters the interpretation of tES and TMS E-field models. Well-considered outcome measure selection is imperative for accurate interpretation of results, valid between-study comparisons, and depends on stimulation focality and study goals. We formulated four recommendations to increase the quality and rigor of E-field modeling outcome measures. With these data and recommendations, we hope to guide future studies towards informed outcome measure selection, and improve the comparability of studies.

Activation of MAP2K signaling by genetic engineering or HF-rTMS promotes corticospinal axon sprouting and functional regeneration

Facilitating axon regeneration in the injured central nervous system remains a challenging task. RAF-MAP2K signaling plays a key role in axon elongation during nervous system development. Here, we show that conditional expression of a constitutively kinase-activated BRAF in mature corticospinal neurons elicited the expression of a set of transcription factors previously implicated in the regeneration of zebrafish retinal ganglion cell axons and promoted regeneration and sprouting of corticospinal tract (CST) axons after spinal cord injury in mice. Newly sprouting axon collaterals formed synaptic connections with spinal interneurons, resulting in improved recovery of motor function. Noninvasive suprathreshold high-frequency repetitive transcranial magnetic stimulation (HF-rTMS) activated the BRAF canonical downstream effectors MAP2K1/2 and modulated the expression of a set of regeneration-related transcription factors in a pattern consistent with that induced by BRAF activation. HF-rTMS enabled CST axon regeneration and sprouting, which was abolished in MAP2K1/2 conditional null mice. These data collectively demonstrate a central role of MAP2K signaling in augmenting the growth capacity of mature corticospinal neurons and suggest that HF-rTMS might have potential for treating spinal cord injury by modulating MAP2K signaling.

Accuracy and precision of navigated transcranial magnetic stimulation

Objective.Transcranial magnetic stimulation (TMS) induces an electric field (E-field) in the cortex. To facilitate stimulation targeting, image-guided neuronavigation systems have been introduced. Such systems track the placement of the coil with respect to the head and visualize the estimated cortical stimulation location on an anatomical brain image in real time. The accuracy and precision of the neuronavigation is affected by multiple factors. Our aim was to analyze how different factors in TMS neuronavigation affect the accuracy and precision of the coil-head coregistration and the estimated E-field.Approach.By performing simulations, we estimated navigation errors due to distortions in magnetic resonance images (MRIs), head-to-MRI registration (landmark- and surface-based registrations), localization and movement of the head tracker, and localization of the coil tracker. We analyzed the effect of these errors on coil and head coregistration and on the induced E-field as determined with simplistic and realistic head models.Main results.Average total coregistration accuracies were in the range of 2.2-3.6 mm and 1°; precision values were about half of the accuracy values. The coregistration errors were mainly due to head-to-MRI registration with average accuracies 1.5-1.9 mm/0.2-0.4° and precisions 0.5-0.8 mm/0.1-0.2° better with surface-based registration. The other major source of error was the movement of the head tracker with average accuracy of 1.5 mm and precision of 1.1 mm. When assessed within an E-field method, the average accuracies of the peak E-field location, orientation, and magnitude ranged between 1.5 and 5.0 mm, 0.9 and 4.8°, and 4.4 and 8.5% across the E-field models studied. The largest errors were obtained with the landmark-based registration. When computing another accuracy measure with the most realistic E-field model as a reference, the accuracies tended to improve from about 10 mm/15°/25% to about 2 mm/2°/5% when increasing realism of the E-field model.Significance.The results of this comprehensive analysis help TMS operators to recognize the main sources of error in TMS navigation and that the coregistration errors and their effect in the E-field estimation depend on the methods applied. To ensure reliable TMS navigation, we recommend surface-based head-to-MRI registration and realistic models for E-field computations.

Angle-tuned coils: attractive building blocks for TMS with improved depth-spread performance

Objective.A novel angle-tuned ring coil is proposed for improving the depth-spread performance of transcranial magnetic stimulation (TMS) coils and serve as the building blocks for high-performance composite coils and multisite TMS systems.Approach.Improving depth-spread performance by reducing field divergence through creating a more elliptical emitted field distribution from the coil. To accomplish that, instead of enriching the Fourier components along the planarized (x-y) directions, which requires different arrays to occupy large brain surface areas, we worked along the radial (z) direction by using tilted coil angles and stacking coil numbers to reduce the divergence of the emitted near field without occupying large head surface areas. The emitted electric field distributions were theoretically simulated in spherical and real human head models to analyze the depth-spread performance of proposed coils and compare with existing figure-8 coils. The results were then experimentally validated with field probes andin-vivoanimal tests.Main results.The proposed 'angle-tuning' concept improves the depth-spread performance of individual coils with a significantly smaller footprint than existing and proposed coils. For composite structures, using the proposed coils as basic building blocks simplifies the design and manufacturing process and helps accomplish a leading depth-spread performance. In addition, the footprint of the proposed system is intrinsically small, making them suitable for multisite stimulations of inter and intra-hemispheric brain regions with an improved spread and less electric field divergence.Significance.Few brain functions are operated by isolated single brain regions but rather by coordinated networks involving multiple brain regions. Simultaneous or sequential multisite stimulations may provide tools for mechanistic studies of brain functions and the treatment of neuropsychiatric disorders. The proposed AT coil goes beyond the traditional depth-spread tradeoff rule of TMS coils, which provides the possibility of building new composite structures and new multisite TMS tools.

Electric Field Distribution Induced by TMS: Differences Due to Anatomical Variation

Transcranial magnetic stimulation (TMS) is a well-established technique for the diagnosis and treatment of neuropsychiatric diseases. The numerical calculation of the induced electric field (EF) distribution in the brain increases the efficacy of stimulation and improves clinical outcomes. However, unique anatomical features, which distinguish each subject, suggest that personalized models should be preferentially used. The objective of the present study was to assess how anatomy affects the EF distribution and to determine to what extent personalized models are useful for clinical studies. The head models of nineteen healthy volunteers were automatically segmented. Two versions of each head model, a homogeneous and a five-tissue anatomical, were stimulated by the model of a Hesed coil (H-coil), employing magnetic quasi-static simulations. The H-coil was placed at two standard stimulating positions per model, over the frontal and central areas. The results show small, but indisputable, variations in the EFs for the homogeneous and anatomical models. The interquartile ranges in the anatomical versions were higher compared to the homogeneous ones, indicating that individual anatomical features may affect the prediction of stimulation volumes. It is concluded that personalized models provide complementary information and should be preferably employed in the context of diagnostic and therapeutic TMS studies.

Rapid whole-brain electric field mapping in transcranial magnetic stimulation using deep learning

Transcranial magnetic stimulation (TMS) is a non-invasive neurostimulation technique that is increasingly used in the treatment of neuropsychiatric disorders and neuroscience research. Due to the complex structure of the brain and the electrical conductivity variation across subjects, identification of subject-specific brain regions for TMS is important to improve the treatment efficacy and understand the mechanism of treatment response. Numerical computations have been used to estimate the stimulated electric field (E-field) by TMS in brain tissue. But the relative long computation time limits the application of this approach. In this paper, we propose a deep-neural-network based approach to expedite the estimation of whole-brain E-field by using a neural network architecture, named 3D-MSResUnet and multimodal imaging data. The 3D-MSResUnet network integrates the 3D U-net architecture, residual modules and a mechanism to combine multi-scale feature maps. It is trained using a large dataset with finite element method (FEM) based E-field and diffusion magnetic resonance imaging (MRI) based anisotropic volume conductivity or anatomical images. The performance of 3D-MSResUnet is evaluated using several evaluation metrics and different combinations of imaging modalities and coils. The experimental results show that the output E-field of 3D-MSResUnet provides reliable estimation of the E-field estimated by the state-of-the-art FEM method with significant reduction in prediction time to about 0.24 second. Thus, this study demonstrates that neural networks are potentially useful tools to accelerate the prediction of E-field for TMS targeting.

Rapid computation of TMS-induced E-fields using a dipole-based magnetic stimulation profile approach

BACKGROUND

TMS neuronavigation with on-line display of the induced electric field (E-field) has the potential to improve quantitative targeting and dosing of stimulation, but present commercially available solutions are limited by simplified approximations.

OBJECTIVE

Developing a near real-time method for accurate approximation of TMS induced E-fields with subject-specific high-resolution surface-based head models that can be utilized for TMS navigation.

METHODS

Magnetic dipoles are placed on a closed surface enclosing an MRI-based head model of the subject to define a set of basis functions for the incident and total E-fields that define the subject's Magnetic Stimulation Profile (MSP). The near real-time speed is achieved by recognizing that the total E-field of the coil only depends on the incident E-field and the conductivity boundary geometry. The total E-field for any coil position can be obtained by matching the incident field of the stationary dipole basis set with the incident E-field of the moving coil and applying the same basis coefficients to the total E-field basis functions.

RESULTS

Comparison of the MSP-based approximation with an established TMS solver shows great agreement in the E-field amplitude (relative maximum error around 5%) and the spatial distribution patterns (correlation >98%). Computation of the E-field took ~100 ms on a cortical surface mesh with 120k facets.

CONCLUSION

The numerical accuracy and speed of the MSP approximation method make it well suited for a wide range of computational tasks including interactive planning, targeting, dosing, and visualization of the intracranial E-fields for near real-time guidance of coil positioning.

Effect of skin conductivity on the electric field induced by transcranial stimulation techniques in different head models

This study aims at quantifying the effect that using different skin conductivity values has on the estimation of the electric (E)-field distribution induced by transcranial magnetic stimulation (TMS) and transcranial direct current stimulation (tDCS) in the brain of two anatomical models. The induced E-field was calculated with numerical simulations inside MIDA and Duke models, assigning to the skin a conductivity value estimated from a multi-layered skin model and three values taken from literature. The effect of skin conductivity variations on the local E-field induced by tDCS in the brain was up to 70%. In TMS, minor local differences, in the order of 20%, were obtained in regions of interest for the onset of possible side effects. Results suggested that an accurate model of the skin is necessary in all numerical studies that aim at precisely estimating the E-field induced during TMS and tDCS applications. This also highlights the importance of further experimental studies on human skin characterization, especially at low frequencies.

Fast computational optimization of TMS coil placement for individualized electric field targeting

Background:

During transcranial magnetic stimulation (TMS) a coil placed on the scalp is used to non-invasively modulate activity of targeted brain networks via a magnetically induced electric field (E-field). Ideally, the E-field induced during TMS is concentrated on a targeted cortical region of interest (ROI). Determination of the coil position and orientation that best achieve this objective presently requires a large computational effort.

Objective:

To improve the accuracy of TMS we have developed a fast computational auxiliary dipole method (ADM) for determining the optimum coil position and orientation. The optimum coil placement maximizes the E-field along a predetermined direction or, alternatively, the overall E-field magnitude in the targeted ROI. Furthermore, ADM can assess E-field uncertainty resulting from precision limitations of TMS coil placement protocols.

Method:

ADM leverages the electromagnetic reciprocity principle to compute rapidly the TMS induced E-field in the ROI by using the E-field generated by a virtual constant current source residing in the ROI. The framework starts by solving for the conduction currents resulting from this ROI current source. Then, it rapidly determines the average E-field induced in the ROI for each coil position by using the conduction currents and a fast-multipole method. To further speed-up the computations, the coil is approximated using auxiliary dipoles enabling it to represent all coil orientations for a given coil position with less than 600 dipoles.

Results:

Using ADM, the E-fields generated in an MRI-derived head model when the coil is placed at 5900 different scalp positions and 360 coil orientations per position (over 2.1 million unique configurations) can be determined in under 15 min on a standard laptop computer. This enables rapid extraction of the optimum coil position and orientation as well as the E-field variation resulting from coil positioning uncertainty. ADM is implemented in SimNIBS 3.2.

Conclusion:

ADM enables the rapid determination of coil placement that maximizes E-field delivery to a specific brain target. This method can find the optimum coil placement in under 15 min enabling its routine use for TMS. Furthermore, it enables the fast quantification of uncertainty in the induced E-field due to limited precision of TMS coil placement protocols, enabling minimization and statistical analysis of the E-field dose variability.

Customizing TMS Applications in Traumatic Brain Injury Using Neuroimaging

Optimizing transcranial magnetic stimulation (TMS) treatments in traumatic brain injury (TBI) and co-occurring conditions may benefit from neuroimaging-based customization.

PARTICIPANTS

Our total sample (N = 97) included 58 individuals with TBI (49 mild, 8 moderate, and 1 severe in a state of disordered consciousness), of which 24 had co-occurring conditions (depression in 14 and alcohol use disorder in 10). Of those without TBI, 6 individuals had alcohol use disorder and 33 were healthy controls. Of our total sample, 54 were veterans and 43 were civilians.

DESIGN

Proof-of-concept study incorporating data from 5 analyses/studies that used multimodal approaches to integrate neuroimaging with TMS.

MAIN MEASURES

Multimodal neuroimaging methods including structural magnetic resonance imaging (MRI), MRI-guided TMS navigation, functional MRI, diffusion MRI, and TMS-induced electric fields. Outcomes included symptom scales, neuropsychological tests, and physiological measures.

RESULTS

It is feasible to use multimodal neuroimaging data to customize TMS targets and understand brain-based changes in targeted networks among people with TBI.

CONCLUSIONS

TBI is an anatomically heterogeneous disorder. Preliminary evidence from the 5 studies suggests that using multimodal neuroimaging approaches to customize TMS treatment is feasible. To test whether this will lead to increased clinical efficacy, studies that integrate neuroimaging and TMS targeting data with outcomes are needed.

Individual head models for estimating the TMS-induced electric field in rat brain

In transcranial magnetic stimulation (TMS), the initial cortical activation due to stimulation is determined by the state of the brain and the magnitude, waveform, and direction of the induced electric field (E-field) in the cortex. The E-field distribution depends on the conductivity geometry of the head. The effects of deviations from a spherically symmetric conductivity profile have been studied in detail in humans. In small mammals, such as rats, these effects are more pronounced due to their less spherical head, proportionally much thicker neck region, and overall much smaller size compared to the TMS coils. In this study, we describe a simple method for building individual realistically shaped head models for rats from high-resolution X-ray tomography images. We computed the TMS-induced E-field with the boundary element method and assessed the effect of head-model simplifications on the estimated E-field. The deviations from spherical symmetry have large, non-trivial effects on the E-field distribution: for some coil orientations, the strongest stimulation is in the brainstem even when the coil is over the motor cortex. With modelling prior to an experiment, such problematic coil orientations can be avoided for more accurate targeting.

Episodic memory improvements due to noninvasive stimulation targeting the cortical-hippocampal network: A replication and extension experiment

INTRODUCTION

The distributed cortical network of the human hippocampus is important for episodic memory. In a previous experiment, noninvasive stimulation of the hippocampal-cortical network applied for five consecutive days improved paired-associate learning measured after the stimulation regimen via cued recall (Wang et al., Science, 2014, 345, 1054). This finding has not yet been directly replicated. Furthermore, evidence for long-lasting effects of stimulation on paired-associate learning was obtained by analyzing relatively small subsamples (Wang & Voss, Hippocampus, 2015, 25, 877) and requires further evaluation.

METHODS

Sixteen healthy young adults participated in this replication study using the same experimental design as the original study. Participants received 1 week of active stimulation and 1 week of sham stimulation, with memory assessments occurring at the beginning (pre) and end (post) of each week. Assessments included the paired-associate task used in the original study, as well as a long-term episodic memory retention task in order to test the hypothesis that increased paired-associate learning could come at the cost of accelerated long-term forgetting. Change in memory scores was evaluated within (pre vs. post) and across (active vs. sham) weeks.

RESULTS

Similar to Wang et al., paired-associate learning was significantly improved after 1 week of active stimulation but not after 1 week of sham stimulation. We found no evidence that stimulation increased long-term forgetting for either week.

CONCLUSION

These findings confirm the beneficial effects of stimulation on episodic memory that were reported previously and indicate that stimulation-related gains in new learning ability do not come at the price of accelerated long-term forgetting.

The effect of coil placement and orientation on the assessment of focal excitability in motor mapping with navigated transcranial magnetic stimulation

BACKGROUND

Navigated transcranial magnetic stimulation (nTMS) is used for mapping muscle representations in the primary motor cortex. We used sulcus-aligned mapping and electric field (E-field) modeling to investigate the excitability of the motor hand area for further understanding the methodological limitations of nTMS.

NEW METHOD

We studied 10 healthy volunteers to locate the cortical target eliciting the largest responses (the hotspot) in the first dorsal interosseous (FDI) muscle. Six additional targets were placed along the central sulcus at 5-mm distances. Resting motor thresholds (rMTs) and optimal coil orientations were determined at all targets, and a conventional motor mapping was conducted. The cortical E-fields, induced by stimulating the targets with rMT intensities and optimal coil orientations, were modeled in a realistic head geometry to estimate the activated cortical sites.

RESULTS

The rMTs increased with increasing distance from the hotspot (p < 0.001). The greatest motor-evoked potential (MEP) amplitudes occurred with the coil perpendicular to the sulcus and with the coil pointing towards the hotspot or the center of gravity of the motor map. The E-field strengths at the hotspot (99±26 V/m) remained above previously estimated thresholds for activation.

COMPARISON WITH EXISTING METHODS

Depending on the target location, optimal coil orientations may deviate significantly from the conventional perpendicular-to-sulcus angle, which is often assumed optimal. These orientations seem to maintain the E-field stable in the hand knob, regardless of the sulcal shape near the stimulated target.

CONCLUSIONS

The coil orientation is crucial for the accuracy of motor mapping, and the apparent motor map may extend due to remote hotspot activation.

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.

Conditions for numerically accurate TMS electric field simulation

BACKGROUND

Computational simulations of the E-field induced by transcranial magnetic stimulation (TMS) are increasingly used to understand its mechanisms and to inform its administration. However, characterization of the accuracy of the simulation methods and the factors that affect it is lacking.

OBJECTIVE

To ensure the accuracy of TMS E-field simulations, we systematically quantify their numerical error and provide guidelines for their setup.

METHOD

We benchmark the accuracy of computational approaches that are commonly used for TMS E-field simulations, including the finite element method (FEM) with and without superconvergent patch recovery (SPR), boundary element method (BEM), finite difference method (FDM), and coil modeling methods.

RESULTS

To achieve cortical E-field error levels below 2%, the commonly used FDM and 1st order FEM require meshes with an average edge length below 0.4 mm, 1st order SPR-FEM requires edge lengths below 0.8 mm, and BEM and 2nd (or higher) order FEM require edge lengths below 2.9 mm. Coil models employing magnetic and current dipoles require at least 200 and 3000 dipoles, respectively. For thick solid-conductor coils and frequencies above 3 kHz, winding eddy currents may have to be modeled.

CONCLUSION

BEM, FDM, and FEM all converge to the same solution. Compared to the common FDM and 1st order FEM approaches, BEM and 2nd (or higher) order FEM require significantly lower mesh densities to achieve the same error level. In some cases, coil winding eddy-currents must be modeled. Both electric current dipole and magnetic dipole models of the coil current can be accurate with sufficiently fine discretization.

Real-time computation of the TMS-induced electric field in a realistic head model

Transcranial magnetic stimulation (TMS) is often targeted using a model of TMS-induced electric field (E). In such navigated TMS, the E-field models have been based on spherical approximation of the head. Such models omit the effects of cerebrospinal fluid (CSF) and gyral folding, leading to potentially large errors in the computed E-field. So far, realistic models have been too slow for interactive TMS navigation. We present computational methods that enable real-time solving of the E-field in a realistic five-compartment (5-C) head model that contains isotropic white matter, gray matter, CSF, skull and scalp. Using reciprocity and Geselowitz integral equation, we separate the computations to coil-dependent and -independent parts. For the Geselowitz integrals, we present a fast numerical quadrature. Further, we present a moment-matching approach for optimizing dipole-based coil models. We verified and benchmarked the new methods using simulations with over 100 coil locations. The new quadrature introduced a relative error (RE) of 0.3-0.6%. For a coil model with 42 dipoles, the total RE of the quadrature and coil model was 0.44-0.72%. Taking also other model errors into account, the contribution of the new approximations to the RE was 0.1%. For comparison, the RE due to omitting the separation of white and gray matter was >11%, and the RE due to omitting also the CSF was >23%. After the coil-independent part of the model has been built, E-fields can be computed very quickly: Using a standard PC and basic GPU, our solver computed the full E-field in a 5-C model in 9000 points on the cortex in 27 coil positions per second (cps). When the separation of white and gray matter was omitted, the speed was 43-65 cps. Solving only one component of the E-field tripled the speed. The presented methods enable real-time solving of the TMS-induced E-field in a realistic head model that contains the CSF and gyral folding. The new methodology allows more accurate targeting and precise adjustment of stimulation intensity during experimental or clinical TMS mapping.

Repetitive transcranial magnetic stimulation: Re-wiring the alcoholic human brain

Alcohol use disorders (AUDs) are one of the leading causes of mortality and morbidity worldwide. In spite of significant advances in understanding the neural underpinnings of AUDs, therapeutic options remain limited. Recent studies have highlighted the potential of repetitive transcranial magnetic stimulation (rTMS) as an innovative, safe, and cost-effective treatment for AUDs. Here, we summarize the fundamental principles of rTMS and its putative mechanisms of action via neurocircuitries related to alcohol addiction. We will also discuss advantages and limitations of rTMS, and argue that Hebbian plasticity and connectivity changes, as well as state-dependency, play a role in shaping some of the long-term effects of rTMS. Visual imaging studies will be linked to recent clinical pilot studies describing the effect of rTMS on alcohol craving and intake, pinpointing new advances, and highlighting conceptual gaps to be filled by future controlled studies.

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.

Prefrontal Cortex Stimulation Enhances Fear Extinction Memory in Humans

BACKGROUND

Animal fear conditioning studies have illuminated neuronal mechanisms of learned associations between sensory stimuli and fear responses. In rats, brief electrical stimulation of the infralimbic cortex has been shown to reduce conditioned freezing during recall of extinction memory. Here, we translated this finding to humans with magnetic resonance imaging-navigated transcranial magnetic stimulation (TMS).

METHODS

Subjects (N = 28) were aversively conditioned to two different cues (day 1). During extinction learning (day 2), TMS was paired with one of the conditioned cues but not the other. TMS parameters were similar to those used in rat infralimbic cortex: brief pulse trains (300 ms at 20 Hz) starting 100 ms after cue onset, total of four trains (28 TMS pulses). TMS was applied to one of two targets in the left frontal cortex, one functionally connected (target 1) and the other unconnected (target 2, control) with a human homologue of infralimbic cortex in the ventromedial prefrontal cortex. Skin conductance responses were used as an index of conditioned fear.

RESULTS

During extinction recall (day 3), the cue paired with TMS to target 1 showed significantly reduced skin conductance responses, whereas TMS to target 2 had no effect. Further, we built group-level maps that weighted TMS-induced electric fields and diffusion magnetic resonance imaging connectivity estimates with fear level. These maps revealed distinct cortical regions and large-scale networks associated with reduced versus increased fear.

CONCLUSIONS

The results showed that spatiotemporally focused TMS may enhance extinction learning and/or consolidation of extinction memory and suggested novel cortical areas and large-scale networks for targeting in future studies.

Transcranial magnetic stimulation for the treatment of cocaine addiction: evidence to date

There is a common consensus in considering substance-use disorders (SUDs) a devastating chronic illness with social and psychological impact. Despite significant progress in understanding the neurobiology of SUDs, therapeutic advances have proceeded at a slower pace, in particular for cocaine-use disorder (CUD). Transcranial magnetic stimulation (TMS) is gaining support as a safe and cost-effective tool in the treatment of SUDs. In this review, we consider human studies that have investigated the efficacy of TMS in achieving therapeutic benefits in treating CUD. All studies conducted to date that have evaluated the therapeutic effect of TMS in CUD are included. We focus on the protocol of stimulation applied, emphasizing the neurophysiological effects of coils employed related to outcomes. Moreover, we examine the subjective and objective measurements used to assess the therapeutic effects along the timeline considered. The revision of scientific literatures underscores the therapeutic potential of TMS in treating CUD. However, the variability in stimulation protocols applied and the lack of methodological control do not allow us to draw firm conclusions, and further studies are warranted to examine the interaction between TMS patterns of stimulation relative to clinical outcomes in depth.

A Quasi-Static Boundary Element Approach With Fast Multipole Acceleration for High-Resolution Bioelectromagnetic Models

OBJECTIVE

We develop a new accurate version of the boundary element fast multipole method for transcranial magnetic stimulation (TMS) related problems. This method is based on the surface-charge formulation and is using the highly efficient fast multipole accelerator along with analytical computations of neighbor surface integrals.

RESULTS

The method accuracy is demonstrated by comparison with the proven commercial finite-element method (FEM) software ANSYS Maxwell 18.2 2017 operating on unstructured grids and with adaptive mesh refinement. Five realistic high-definition head models from the Population Head Repository (IT'IS Foundation, Switzerland) have been acquired and augmented with a commercial TMS coil model (MRi-B91, MagVenture, Denmark). For each head model, simulations with our method and simulations with the FEM software ANSYS Maxwell 18.2 2017 have been performed. These simulations have been compared with each other and an excellent agreement was established in every case.

SIGNIFICANCE

At the same time, our new method runs approximately 500 times faster than the ANSYS FEM, finishes in about 200 s on a standard server, and naturally provides a submillimeter field resolution, which is justified using mesh refinement.

CONCLUSIONS

Our method can be applied to modeling of brain stimulation and recording technologies such as TMS and magnetoencephalography, and has the potential to become a real-time high-resolution simulation tool.

Noninvasive extraction of microsecond-scale dynamics from human motor cortex

State-of-the-art noninvasive electromagnetic recording techniques allow observing neuronal dynamics down to the millisecond scale. Direct measurement of faster events has been limited to in vitro or invasive recordings. To overcome this limitation, we introduce a new paradigm for transcranial magnetic stimulation. We adjusted the stimulation waveform on the microsecond scale, by varying the duration between the positive and negative phase of the induced electric field, and studied corresponding changes in the elicited motor responses. The magnitude of the electric field needed for given motor-evoked potential amplitude decreased exponentially as a function of this duration with a time constant of 17 µs. Our indirect noninvasive measurement paradigm allows studying neuronal kinetics on the microsecond scale in vivo.

A high-resolution computational localization method for transcranial magnetic stimulation mapping

BACKGROUND

Transcranial magnetic stimulation (TMS) is used for the mapping of brain motor functions. The complexity of the brain deters determining the exact localization of the stimulation site using simplified methods (e.g., the region below the center of the TMS coil) or conventional computational approaches.

OBJECTIVE

This study aimed to present a high-precision localization method for a specific motor area by synthesizing computed non-uniform current distributions in the brain for multiple sessions of TMS.

METHODS

Peritumoral mapping by TMS was conducted on patients who had intra-axial brain neoplasms located within or close to the motor speech area. The electric field induced by TMS was computed using realistic head models constructed from magnetic resonance images of patients. A post-processing method was implemented to determine a TMS hotspot by combining the computed electric fields for the coil orientations and positions that delivered high motor-evoked potentials during peritumoral mapping. The method was compared to the stimulation site localized via intraoperative direct brain stimulation and navigated TMS.

RESULTS

Four main results were obtained: 1) the dependence of the computed hotspot area on the number of peritumoral measurements was evaluated; 2) the estimated localization of the hand motor area in eight non-affected hemispheres was in good agreement with the position of a so-called "hand-knob"; 3) the estimated hotspot areas were not sensitive to variations in tissue conductivity; and 4) the hand motor areas estimated by this proposal and direct electric stimulation (DES) were in good agreement in the ipsilateral hemisphere of four glioma patients.

CONCLUSION(S)

The TMS localization method was validated by well-known positions of the "hand-knob" in brains for the non-affected hemisphere, and by a hotspot localized via DES during awake craniotomy for the tumor-containing hemisphere.

Multi-Scale Computational Models for Electrical Brain Stimulation

Electrical brain stimulation (EBS) is an appealing method to treat neurological disorders. To achieve optimal stimulation effects and a better understanding of the underlying brain mechanisms, neuroscientists have proposed computational modeling studies for a decade. Recently, multi-scale models that combine a volume conductor head model and multi-compartmental models of cortical neurons have been developed to predict stimulation effects on the macroscopic and microscopic levels more precisely. As the need for better computational models continues to increase, we overview here recent multi-scale modeling studies; we focused on approaches that coupled a simplified or high-resolution volume conductor head model and multi-compartmental models of cortical neurons, and constructed realistic fiber models using diffusion tensor imaging (DTI). Further implications for achieving better precision in estimating cellular responses are discussed.

Rehabilitating the addicted brain with transcranial magnetic stimulation

Substance use disorders (SUDs) are one of the leading causes of morbidity and mortality worldwide. In spite of considerable advances in understanding the neural underpinnings of SUDs, therapeutic options remain limited. Recent studies have highlighted the potential of transcranial magnetic stimulation (TMS) as an innovative, safe and cost-effective treatment for some SUDs. Repetitive TMS (rTMS) influences neural activity in the short and long term by mechanisms involving neuroplasticity both locally, under the stimulating coil, and at the network level, throughout the brain. The long-term neurophysiological changes induced by rTMS have the potential to affect behaviours relating to drug craving, intake and relapse. Here, we review TMS mechanisms and evidence that rTMS is opening new avenues in addiction treatments.

Minimum-Norm Estimation of Motor Representations in Navigated TMS Mappings

Navigated transcranial magnetic stimulation (nTMS) can be applied to locate and outline cortical motor representations. This may be important, e.g., when planning neurosurgery or focused nTMS therapy, or when assessing plastic changes during neurorehabilitation. Conventionally, a cortical location is considered to belong to the motor cortex if the maximum electric field (E-field) targeted there evokes a motor-evoked potential in a muscle. However, the cortex is affected by a broad E-field distribution, which tends to broaden estimates of representation areas by stimulating also the neighboring areas in addition to the maximum E-field location. Our aim was to improve the estimation of nTMS-based motor maps by taking into account the E-field distribution of the stimulation pulse. The effect of the E-field distribution was considered by calculating the minimum-norm estimate (MNE) of the motor representation area. We tested the method on simulated data and then applied it to recordings from six healthy volunteers and one stroke patient. We compared the motor representation areas obtained with the MNE method and a previously introduced interpolation method. The MNE hotspots and centers of gravity were close to those obtained with the interpolation method. The areas of the maps, however, depend on the thresholds used for outlining the areas. The MNE method may improve the definition of cortical motor areas, but its accuracy should be validated by comparing the results with maps obtained with direct cortical stimulation of the cortex where the E-field distribution can be better focused.

Virtual Human Models for Electromagnetic Studies and Their Applications

Numerical simulation of electromagnetic, thermal, and mechanical responses of the human body to different stimuli in magnetic resonance imaging safety, antenna research, electromagnetic tomography, and electromagnetic stimulation is currently limited by the availability of anatomically adequate and numerically efficient cross-platform computational models or "virtual humans." The objective of this study is to provide a comprehensive review of modern human models and body region models available in the field and their important features.

How much detail is needed in modeling a transcranial magnetic stimulation figure-8 coil: Measurements and brain simulations

Background

Despite TMS wide adoption, its spatial and temporal patterns of neuronal effects are not well understood. Although progress has been made in predicting induced currents in the brain using realistic finite element models (FEM), there is little consensus on how a magnetic field of a typical TMS coil should be modeled. Empirical validation of such models is limited and subject to several limitations.

Methods

We evaluate and empirically validate models of a figure-of-eight TMS coil that are commonly used in published modeling studies, of increasing complexity: simple circular coil model; coil with in-plane spiral winding turns; and finally one with stacked spiral winding turns. We will assess the electric fields induced by all 3 coil models in the motor cortex using a computer FEM model. Biot-Savart models of discretized wires were used to approximate the 3 coil models of increasing complexity. We use a tailored MR based phase mapping technique to get a full 3D validation of the incident magnetic field induced in a cylindrical phantom by our TMS coil. FEM based simulations on a meshed 3D brain model consisting of five tissues types were performed, using two orthogonal coil orientations.

Results

Substantial differences in the induced currents are observed, both theoretically and empirically, between highly idealized coils and coils with correctly modeled spiral winding turns. Thickness of the coil winding turns affect minimally the induced electric field, and it does not influence the predicted activation.

Conclusion

TMS coil models used in FEM simulations should include in-plane coil geometry in order to make reliable predictions of the incident field. Modeling the in-plane coil geometry is important to correctly simulate the induced electric field and to correctly make reliable predictions of neuronal activation

The development and modelling of devices and paradigms for transcranial magnetic stimulation

Magnetic stimulation is a non-invasive neurostimulation technique that can evoke action potentials and modulate neural circuits through induced electric fields. Biophysical models of magnetic stimulation have become a major driver for technological developments and the understanding of the mechanisms of magnetic neurostimulation and neuromodulation. Major technological developments involve stimulation coils with different spatial characteristics and pulse sources to control the pulse waveform. While early technological developments were the result of manual design and invention processes, there is a trend in both stimulation coil and pulse source design to mathematically optimize parameters with the help of computational models. To date, macroscopically highly realistic spatial models of the brain, as well as peripheral targets, and user-friendly software packages enable researchers and practitioners to simulate the treatment-specific and induced electric field distribution in the brains of individual subjects and patients. Neuron models further introduce the microscopic level of neural activation to understand the influence of activation dynamics in response to different pulse shapes. A number of models that were designed for online calibration to extract otherwise covert information and biomarkers from the neural system recently form a third branch of modelling.

Modeling fiber-like conductivity structures via the boundary element method using thin-wire approximation. I construction of basis functions

A set of one-dimensional basis functions is proposed and tested in order to model a thin homogeneous fiber of a higher conductivity within a medium with a lower conductivity. This set allows us to greatly speed up computations while keeping a good accuracy for the total fiber current and the resulting charge distribution averaged over the fiber cross-section.

MR-based measurements and simulations of the magnetic field created by a realistic transcranial magnetic stimulation (TMS) coil and stimulator

Transcranial magnetic stimulation (TMS) is an emerging technique that allows non-invasive neurostimulation. However, the correct validation of electromagnetic models of typical TMS coils and the correct assessment of the incident TMS field (B_TMS ) produced by standard TMS stimulators are still lacking. Such a validation can be performed by mapping B_TMS produced by a realistic TMS setup. In this study, we show that MRI can provide precise quantification of the magnetic field produced by a realistic TMS coil and a clinically used TMS stimulator in the region in which neurostimulation occurs. Measurements of the phase accumulation created by TMS pulses applied during a tailored MR sequence were performed in a phantom. Dedicated hardware was developed to synchronize a typical, clinically used, TMS setup with a 3-T MR scanner. For comparison purposes, electromagnetic simulations of B_TMS were performed. MR-based measurements allow the mapping and quantification of B_TMS starting 2.5 cm from the TMS coil. For closer regions, the intra-voxel dephasing induced by B_TMS prohibits TMS field measurements. For 1% TMS output, the maximum measured value was ~0.1 mT. Simulations reflect quantitatively the experimental data. These measurements can be used to validate electromagnetic models of TMS coils, to guide TMS coil positioning, and for dosimetry and quality assessment of concurrent TMS-MRI studies without the need for crude methods, such as motor threshold, for stimulation dose determination.

A multi-scale computational model of the effects of TMS on motor cortex

The detailed biophysical mechanisms through which transcranial magnetic stimulation (TMS) activates cortical circuits are still not fully understood. Here we present a multi-scale computational model to describe and explain the activation of different pyramidal cell types in motor cortex due to TMS. Our model determines precise electric fields based on an individual head model derived from magnetic resonance imaging and calculates how these electric fields activate morphologically detailed models of different neuron types. We predict neural activation patterns for different coil orientations consistent with experimental findings. Beyond this, our model allows us to calculate activation thresholds for individual neurons and precise initiation sites of individual action potentials on the neurons’ complex morphologies. Specifically, our model predicts that cortical layer 3 pyramidal neurons are generally easier to stimulate than layer 5 pyramidal neurons, thereby explaining the lower stimulation thresholds observed for I-waves compared to D-waves. It also shows differences in the regions of activated cortical layer 5 and layer 3 pyramidal cells depending on coil orientation. Finally, it predicts that under standard stimulation conditions, action potentials are mostly generated at the axon initial segment of cortical pyramidal cells, with a much less important activation site being the part of a layer 5 pyramidal cell axon where it crosses the boundary between grey matter and white matter. In conclusion, our computational model offers a detailed account of the mechanisms through which TMS activates different cortical pyramidal cell types, paving the way for more targeted application of TMS based on individual brain morphology in clinical and basic research settings.

Incorporating and Compensating Cerebrospinal Fluid in Surface-Based Forward Models of Magneto- and Electroencephalography

MEG/EEG source imaging is usually done using a three-shell (3-S) or a simpler head model. Such models omit cerebrospinal fluid (CSF) that strongly affects the volume currents. We present a four-compartment (4-C) boundary-element (BEM) model that incorporates the CSF and is computationally efficient and straightforward to build using freely available software. We propose a way for compensating the omission of CSF by decreasing the skull conductivity of the 3-S model, and study the robustness of the 4-C and 3-S models to errors in skull conductivity. We generated dense boundary meshes using MRI datasets and automated SimNIBS pipeline. Then, we built a dense 4-C reference model using Galerkin BEM, and 4-C and 3-S test models using coarser meshes and both Galerkin and collocation BEMs. We compared field topographies of cortical sources, applying various skull conductivities and fitting conductivities that minimized the relative error in 4-C and 3-S models. When the CSF was left out from the EEG model, our compensated, unbiased approach improved the accuracy of the 3-S model considerably compared to the conventional approach, where CSF is neglected without any compensation (mean relative error < 20% vs. > 40%). The error due to the omission of CSF was of the same order in MEG and compensated EEG. EEG has, however, large overall error due to uncertain skull conductivity. Our results show that a realistic 4-C MEG/EEG model can be implemented using standard tools and basic BEM, without excessive workload or computational burden. If the CSF is omitted, compensated skull conductivity should be used in EEG.

Effect of Anatomically Realistic Full-Head Model on Activation of Cortical Neurons in Subdural Cortical Stimulation-A Computational Study

Electrical brain stimulation (EBS) is an emerging therapy for the treatment of neurological disorders, and computational modeling studies of EBS have been used to determine the optimal parameters for highly cost-effective electrotherapy. Recent notable growth in computing capability has enabled researchers to consider an anatomically realistic head model that represents the full head and complex geometry of the brain rather than the previous simplified partial head model (extruded slab) that represents only the precentral gyrus. In this work, subdural cortical stimulation (SuCS) was found to offer a better understanding of the differential activation of cortical neurons in the anatomically realistic full-head model than in the simplified partial-head models. We observed that layer 3 pyramidal neurons had comparable stimulation thresholds in both head models, while layer 5 pyramidal neurons showed a notable discrepancy between the models; in particular, layer 5 pyramidal neurons demonstrated asymmetry in the thresholds and action potential initiation sites in the anatomically realistic full-head model. Overall, the anatomically realistic full-head model may offer a better understanding of layer 5 pyramidal neuronal responses. Accordingly, the effects of using the realistic full-head model in SuCS are compelling in computational modeling studies, even though this modeling requires substantially more effort.