The influence of sulcus width on simulated electric fields induced by transcranial magnetic stimulation

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.

Electric Field Modeling in Personalizing Transcranial Magnetic Stimulation Interventions

The modeling of transcranial magnetic stimulation (TMS)-induced electric fields (E-fields) is a versatile technique for evaluating and refining brain targeting and dosing strategies, while also providing insights into dose-response relationships in the brain. This review outlines the methodologies employed to derive E-field estimations, covering TMS physics, modeling assumptions, and aspects of subject-specific head tissue and coil modeling. We also summarize various numerical methods for solving the E-field and their suitability for various applications. Modeling methodologies have been optimized to efficiently execute numerous TMS simulations across diverse scalp coil configurations, facilitating the identification of optimal setups or rapid cortical E-field visualization for specific brain targets. These brain targets are extrapolated from neurophysiological measurements and neuroimaging, enabling precise and individualized E-field dosing in experimental and clinical applications. This necessitates the quantification of E-field estimates using metrics that enable the comparison of brain target engagement, functional localization, and TMS intensity adjustments across subjects. The integration of E-field modeling with empirical data has the potential to uncover pivotal insights into the aspects of E-fields responsible for stimulating and modulating brain function and states, enhancing behavioral task performance, and impacting the clinical outcomes of personalized TMS interventions.

Single-pulse transcranial magnetic stimulation for assessment of motor development in infants with early brain injury

INTRODUCTION

Single-pulse transcranial magnetic stimulation (TMS) has many applications for pediatric clinical populations, including infants with perinatal brain injury. As a noninvasive neuromodulation tool, single-pulse TMS has been used safely in infants and children to assess corticospinal integrity and circuitry patterns. TMS may have important applications in early detection of atypical motor development or cerebral palsy.

AREAS COVERED

The authors identified and summarized relevant studies incorporating TMS in infants, including findings related to corticospinal development and circuitry, motor cortex localization and mapping, and safety. This special report also describes methodologies and safety considerations related to TMS assessment in infants, and discusses potential applications related to diagnosis of cerebral palsy and early intervention.

EXPERT OPINION

Single-pulse TMS has demonstrated safety and feasibility in infants with perinatal brain injury and may provide insight into neuromotor development and potential cerebral palsy diagnosis. Additional research in larger sample sizes will more fully evaluate the utility of TMS biomarkers in early diagnosis and intervention. Methodological challenges to performing TMS in infants and technical/equipment limitations require additional consideration and innovation toward clinical implementation. Future research may explore use of noninvasive neuromodulation techniques as an intervention in younger children with perinatal brain injury to improve motor outcomes.

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

Introduction

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

Methods

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

Results

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

Discussion

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

Outcome measures for electric field modeling in tES and TMS: A systematic review and large-scale modeling study

BACKGROUND

Electric field (E-field) modeling is a potent tool to estimate the amount of transcranial magnetic and electrical stimulation (TMS and tES, respectively) that reaches the cortex and to address the variable behavioral effects observed in the field. However, outcome measures used to quantify E-fields vary considerably and a thorough comparison is missing.

OBJECTIVES

This two-part study aimed to examine the different outcome measures used to report on tES and TMS induced E-fields, including volume- and surface-level gray matter, region of interest (ROI), whole brain, geometrical, structural, and percentile-based approaches. The study aimed to guide future research in informed selection of appropriate outcome measures.

METHODS

Three electronic databases were searched for tES and/or TMS studies quantifying E-fields. The identified outcome measures were compared across volume- and surface-level E-field data in ten tES and TMS modalities targeting two common targets in 100 healthy individuals.

RESULTS

In the systematic review, we extracted 308 outcome measures from 202 studies that adopted either a gray matter volume-level (n = 197) or surface-level (n = 111) approach. Volume-level results focused on E-field magnitude, while surface-level data encompassed E-field magnitude (n = 64) and normal/tangential E-field components (n = 47). E-fields were extracted in ROIs, such as brain structures and shapes (spheres, hexahedra and cylinders), or the whole brain. Percentiles or mean values were mostly used to quantify E-fields. Our modeling study, which involved 1,000 E-field models and > 1,000,000 extracted E-field values, revealed that different outcome measures yielded distinct E-field values, analyzed different brain regions, and did not always exhibit strong correlations in the same within-subject E-field model.

CONCLUSIONS

Outcome measure selection significantly impacts the locations and intensities of extracted E-field data in both tES and TMS E-field models. The suitability of different outcome measures depends on the target region, TMS/tES modality, individual anatomy, the analyzed E-field component and the research question. To enhance the quality, rigor, and reproducibility in the E-field modeling domain, we suggest standard reporting practices across studies and provide four recommendations.

A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields

Since the inception of the transcranial magnetic stimulation (TMS) technique, it has become imperative to numerically compute the distribution of the electric field induced in the brain. Various models of the coil-brain system have been proposed for this purpose. These models yield a set of formulations and boundary conditions that can be employed to calculate the induced electric field. However, the literature on TMS simulation presents several of these formulations, leading to potential confusion regarding the interpretation and contribution of each source of electric field. The present study undertakes an extensive compilation of widely utilized formulations, boundary value problems and numerical solutions employed in TMS fields simulations, analyzing the advantages and disadvantages associated with each used formulation and numerical method. Additionally, it explores the implementation strategies employed for their numerical computation. Furthermore, this work provides numerical expressions that can be utilized for the numerical computation of TMS fields using the finite difference and finite element methods. Notably, some of these expressions are deduced within the present study. Finally, an overview of some of the most significant results obtained from numerical computation of TMS fields is presented. The aim of this work is to serve as a guide for future research endeavors concerning the numerical simulation of TMS.

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.

UncertainSCI: Uncertainty quantification for computational models in biomedicine and bioengineering

BACKGROUND

Computational biomedical simulations frequently contain parameters that model physical features, material coefficients, and physiological effects, whose values are typically assumed known a priori. Understanding the effect of variability in those assumed values is currently a topic of great interest. A general-purpose software tool that quantifies how variation in these parameters affects model outputs is not broadly available in biomedicine. For this reason, we developed the 'UncertainSCI' uncertainty quantification software suite to facilitate analysis of uncertainty due to parametric variability.

METHODS

We developed and distributed a new open-source Python-based software tool, UncertainSCI, which employs advanced parameter sampling techniques to build polynomial chaos (PC) emulators that can be used to predict model outputs for general parameter values. Uncertainty of model outputs is studied by modeling parameters as random variables, and model output statistics and sensitivities are then easily computed from the emulator. Our approaches utilize modern, near-optimal techniques for sampling and PC construction based on weighted Fekete points constructed by subsampling from a suitably randomized candidate set.

RESULTS

Concentrating on two test cases-modeling bioelectric potentials in the heart and electric stimulation in the brain-we illustrate the use of UncertainSCI to estimate variability, statistics, and sensitivities associated with multiple parameters in these models.

CONCLUSION

UncertainSCI is a powerful yet lightweight tool enabling sophisticated probing of parametric variability and uncertainty in biomedical simulations. Its non-intrusive pipeline allows users to leverage existing software libraries and suites to accurately ascertain parametric uncertainty in a variety of applications.

Uncertainty quantification of TMS simulations considering MRI segmentation errors

OBJECTIVE

Transcranial Magnetic Stimulation (TMS) is a non-invasive brain stimulation method that is used to study brain function and conduct neuropsychiatric therapy. Computational methods that are commonly used for electric field (E-field) dosimetry of TMS are limited in accuracy and precision because of possible geometric errors introduced in the generation of head models by segmenting medical images into tissue types. This paper studies E-field prediction fidelity as a function of segmentation accuracy.

APPROACH

The errors in the segmentation of medical images into tissue types are modeled as geometric uncertainty in the shape of the boundary between tissue types. For each tissue boundary realization, we then use an in-house boundary element method to perform a forward propagation analysis and quantify the impact of tissue boundary uncertainties on the induced cortical E-field.

MAIN RESULTS

Our results indicate that predictions of E-field induced in the brain are negligibly sensitive to segmentation errors in scalp, skull and white matter, compartments. In contrast, E-field predictions are highly sensitive to possible CSF segmentation errors. Specifically, the segmentation errors on the CSF and gray matter interface lead to higher E-field uncertainties in the gyral crowns, and the segmentation errors on CSF and white matter interface lead to higher uncertainties in the sulci. Furthermore, the uncertainty of the average cortical E-fields over a region exhibits lower uncertainty relative to point-wise estimates.

SIGNIFICANCE

The accuracy of current cortical E-field simulations is limited by the accuracy of CSF segmentation accuracy. Other quantities of interest like the average of the E-field over a cortical region could provide a dose quantity that is robust to possible segmentation errors.

Uncertainty quantification of TMS simulations considering MRI segmentation errors

OBJECTIVE

Transcranial Magnetic Stimulation (TMS) is a non-invasive brain stimulation method that is used to study brain function and conduct neuropsychiatric therapy. Computational methods that are commonly used for electric field (E-field) dosimetry of TMS are limited in accuracy and precision because of possible geometric errors introduced in the generation of head models by segmenting medical images into tissue types. This paper studies E-field prediction fidelity as a function of segmentation accuracy.

APPROACH

The errors in the segmentation of medical images into tissue types are modeled as geometric uncertainty in the shape of the boundary between tissue types. For each tissue boundary realization, we then use an in-house boundary element method to perform a forward propagation analysis and quantify the impact of tissue boundary uncertainties on the induced cortical E-field.

MAIN RESULTS

Our results indicate that predictions of E-field induced in the brain are negligibly sensitive to segmentation errors in scalp, skull and white matter, compartments. In contrast, E-field predictions are highly sensitive to possible CSF segmentation errors. Specifically, the segmentation errors on the CSF and gray matter interface lead to higher E-field uncertainties in the gyral crowns, and the segmentation errors on CSF and white matter interface lead to higher uncertainties in the sulci. Furthermore, the uncertainty of the average cortical E-fields over a region exhibits lower uncertainty relative to point-wise estimates.

SIGNIFICANCE

The accuracy of current cortical E-field simulations is limited by the accuracy of CSF segmentation accuracy. Other quantities of interest like the average of the E-field over a cortical region could provide a dose quantity that is robust to possible segmentation errors.

DUNEuro-A software toolbox for forward modeling in bioelectromagnetism

Accurate and efficient source analysis in electro- and magnetoencephalography using sophisticated realistic head geometries requires advanced numerical approaches. This paper presents DUNEuro, a free and open-source C++ software toolbox for the numerical computation of forward solutions in bioelectromagnetism. Building upon the DUNE framework, it provides implementations of modern fitted and unfitted finite element methods to efficiently solve the forward problems of electro- and magnetoencephalography. The user can choose between a variety of different source models that are implemented. The software's aim is to provide interfaces that are extendable and easy-to-use. In order to enable a closer integration into existing analysis pipelines, interfaces to Python and MATLAB are provided. The practical use is demonstrated by a source analysis example of somatosensory evoked potentials using a realistic six-compartment head model. Detailed installation instructions and example scripts using spherical and realistic head models are appended.

Transcranial direct current stimulation in attention-deficit/hyperactivity disorder: A meta-analysis of clinical efficacy outcomes

BACKGROUND

Evidence for the application of transcranial direct current stimulation (tDCS) in the clinical care of attention-deficit/hyperactivity disorder (ADHD) is limited. Therefore, we aimed to summarize study results using meta-analyses of measures of the cardinal symptoms of ADHD.

METHODS

We conducted a systematic literature search (PubMed/pubpsych/PsychInfo/WOS) until 01/05/2020 for randomized controlled trials (RCTs) evaluating tDCS vs. control condition in patients with ADHD. A random effects meta-analysis of symptom-related outcomes was performed separately for data on the immediate effect and follow-up. Subgroup- and metaregression analyses for patient characteristics and tDCS parameters were included.

RESULTS

Meta-analyzing 13 studies (n=308, age=23.7±13.3), including 20 study arms, tDCS had an immediate effect on overall symptom severity, inattention, and impulsivity, but not on hyperactivity. Results were significant in children and adolescents (8 studies, n=133, age=12.4±3.0). Follow-up data (3 days-4 weeks after stimulation) suggested an ongoing beneficial effect regarding overall symptom severity and a delayed effect on hyperactivity.

DISCUSSION

TDCS seems to be a promising method to treat clinical symptoms in ADHD with long-lasting effects. Still, more research considering the individual neuropsychological and anatomical dispositions of the subjects is needed to optimize tDCS protocols and efficacy. Safety issues of tDCS treatment in children and adolescents are addressed.

Influence of segmentation accuracy in structural MR head scans on electric field computation for TMS and tES

In several diagnosis and therapy procedures based on electrostimulation effect, the internal physical quantity related to the stimulation is the induced electric field. To estimate the induced electric field in an individual human model, the segmentation of anatomical imaging, such as magnetic resonance image (MRI) scans, of the corresponding body parts into tissues is required. Then, electrical properties associated with different annotated tissues are assigned to the digital model to generate a volume conductor. However, the segmentation of different tissues is a tedious task with several associated challenges specially with tissues appear in limited regions and/or low-contrast in anatomical images. An open question is how segmentation accuracy of different tissues would influence the distribution of the induced electric field. In this study, we applied parametric segmentation of different tissues to exploit the segmentation of available MRI to generate different quality of head models using deep learning neural network architecture, named ForkNet. Then, the induced electric field are compared to assess the effect of model segmentation variations. Computational results indicate that the influence of segmentation error is tissue-dependent. In brain, sensitivity to segmentation accuracy is relatively high in cerebrospinal fluid (CSF), moderate in gray matter (GM) and low in white matter for transcranial magnetic stimulation (TMS) and transcranial electrical stimulation (tES). A CSF segmentation accuracy reduction of 10% in terms of Dice coefficient (DC) lead to decrease up to 4% in normalized induced electric field in both applications. However, a GM segmentation accuracy reduction of 5.6% DC leads to increase of normalized induced electric field up to 6%. Opposite trend of electric field variation was found between CSF and GM for both TMS and tES. The finding obtained here would be useful to quantify potential uncertainty of computational results.

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.

Inter-individual variations in electric fields induced in the brain by exposure to uniform magnetic fields at 50 Hz

The International Commission on Non-Ionizing Radiation Protection (ICNIRP) guidelines and the Institute of Electrical and Electronics Engineers (IEEE) standard establish safety limits for human exposure to electromagnetic fields. At low frequencies, only a limited number of computational body models or simplified geometrical shapes are used to relate the internal induced electric fields and the external magnetic fields. As a consequence, both standard/guidelines derive the exposure reference levels for the external magnetic field without considering the variability between individuals. Here we provide quantitative data on the variation of the maximum electric field strengths induced in the brain of 118 individuals when exposed to uniform magnetic fields at 50 Hz. We found that individual characteristics, such as age and skull volume, as well as incident magnetic field direction, have a systematic effect on the peak electric field values. Older individuals show higher induced electric field strengths, possibly due to age-related anatomical changes in brain. Peak electric field strengths are found to increase for larger skull volumes, as well as for incident magnetic fields directed along the lateral direction. Moreover, the maximum electric fields provided by the anatomical models used by ICNIRP for deriving exposure limits are considerably higher than those obtained here. On the contrary, the IEEE elliptical exposure model produces a weaker peak electric field strength. Our findings are useful for the revision and harmonization of the current exposure standard and guidelines. The present investigation reduces the dosimetric uncertainty of the induced electric field among different anatomical induction models. The obtained results can be used as a basis for the selection of appropriate reduction factors when deriving exposure reference levels for human protection to low-frequency electromagnetic exposure.

Effect of structural complexities in head modeling on the accuracy of EEG source localization in neonates

OBJECTIVE

Neonatal electroencephalography (EEG) source localization is highly prone to errors due to head modeling deficiencies. In this study, we investigated the effect of head model complexities on the accuracy of EEG source localization in full term neonates using a realistic volume conductor head model.

APPROACH

We performed numerical simulations to investigate source localization errors caused by cerebrospinal fluid (CSF) and fontanel exclusion and gray matter (GM)/white matter (WM) distinction using the finite element method.

MAIN RESULTS

Our results showed that the exclusion of CSF from the head model could cause significant localization errors mostly for sources closer to the inner surface of the skull. With a less pronounced effect compared to the CSF exclusion, the discrimination between GM and WM also widely affected all sources, especially those located in deeper structures. The exclusion of the fontanels from the head model led to source localization errors for sources located in areas beneath the fontanels. Our finding clearly shows that the CSF inclusion and GM/WM distinction in EEG inverse modeling can substantially reduce EEG source localization errors. Moreover, fontanels should be included in neonatal head models, particularly in source localization applications, in which sources of interest are located beneath or in vicinity of fontanels.

SIGNIFICANCE

Our findings have practical implications for a better understanding of the impact of head model complexities on the accuracy of EEG source localization in neonates.

Obtaining accurate and calibrated coil models for transcranial magnetic stimulation using magnetic field measurements

Currently, simulations of the induced currents in the brain produced by transcranial magnetic stimulation (TMS) are used to elucidate the regions reached by stimuli. However, models commonly found in the literature are too general and neglect imperfections in the windings. Aiming to predict the stimulation sites in patients requires precise modeling of the electric field (E-field), and a proper calibration to adequate to the empirical data of the particular coil employed. Furthermore, most fabricators do not provide precise information about the coil geometries, and even using X-ray images may lead to subjective interpretations. We measured the three components of the vector magnetic field induced by a TMS figure-8 coil with spatial resolutions of up to 1 mm. Starting from a computerized tomography-based coil model, we applied a multivariate optimization algorithm to automatically modify the original model and obtain one that optimally fits the measurements. Differences between models were assessed in a human brain mesh using the finite-elements method showing up to 6% variations in the E-field magnitude. Our calibrated model could increase the precision of the estimated E-field induced in the brain during TMS, enhance the accuracy of delivered stimulation during functional brain mapping, and improve dosimetry for repetitive TMS. Graphical Abstract Geometrical model of TMS coil based on TAC images is optimally deformed to match magnetic field measurements. The calibrated model's induced electric field in the brain differs from the original.

Particle Swarm Optimization for Positioning the Coil of Transcranial Magnetic Stimulation

The distribution of the induced electric field (E-field) during transcranial magnetic stimulation (TMS) depends on the individual anatomical structure of the brain as well as coil positioning. Inappropriate stimulation may degrade the efficacy of TMS or even induce adverse effects. Therefore, optimizing the E-field according to individual anatomy and clinical need has become a research focus. In this paper, particle swarm optimization (PSO) was applied for the first time to the positioning of TMS coils with anatomical head models. We discuss the parameters of the PSO algorithm, which were optimized to achieve a reasonable convergence time suitable for in-time treatment planning. The optimizer improved the distribution of the induced E-field strength at the dedicated cortical region, with a mean value of 48.31% compared with that from the conventional treatment position. The optimization terminated after 4–11 iterations for 13 head models. The applicability and performance of the optimizer for a large population are discussed in terms of cortical complexity. This study could benefit not only clinics but also research on brain modulation.

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.

Modulation of Resting Connectivity Between the Mesial Frontal Cortex and Basal Ganglia

Background: The mesial prefrontal cortex, cingulate cortex, and the ventral striatum are key nodes of the human mesial fronto-striatal circuit involved in decision-making and executive function and pathological disorders. Here we ask whether deep wide-field repetitive transcranial magnetic stimulation (rTMS) targeting the mesial prefrontal cortex (MPFC) influences resting state functional connectivity. Methods: In Study 1, we examined functional connectivity using resting state multi-echo and independent components analysis in 154 healthy subjects to characterize default connectivity in the MPFC and mid-cingulate cortex (MCC). In Study 2, we used inhibitory, 1 Hz deep rTMS with the H7-coil targeting MPFC and dorsal anterior cingulate (dACC) in a separate group of 20 healthy volunteers and examined pre- and post-TMS functional connectivity using seed-based and independent components analysis. Results: In Study 1, we show that MPFC and MCC have distinct patterns of functional connectivity with MPFC-ventral striatum showing negative, whereas MCC-ventral striatum showing positive functional connectivity. Low-frequency rTMS decreased functional connectivity of MPFC and dACC with the ventral striatum. We further showed enhanced connectivity between MCC and ventral striatum. Conclusions: These findings emphasize how deep inhibitory rTMS using the H7-coil can influence underlying network functional connectivity by decreasing connectivity of the targeted MPFC regions, thus potentially enhancing response inhibition and decreasing drug-cue reactivity processes relevant to addictions. The unexpected finding of enhanced default connectivity between MCC and ventral striatum may be related to the decreased influence and connectivity between the MPFC and MCC. These findings are highly relevant to the treatment of disorders relying on the mesio-prefrontal-cingulo-striatal circuit.

Impact of non-brain anatomy and coil orientation on inter- and intra-subject variability in TMS at midline

OBJECTIVE

To investigate inter-subject variability with respect to cerebrospinal fluid thickness and brain-scalp distance, and to investigate intra-subject variability with different coil orientations.

METHODS

Simulations of the induced electric field (E-Field) using a figure-8 coil over the vertex were conducted on 50 unique head models and varying orientations on 25 models. Metrics exploring stimulation intensity, spread, and localization were used to describe inter-subject variability and effects of non-brain anatomy.

RESULTS

Both brain-scalp distance and CSF thickness were correlated with weaker stimulation intensity and greater spread. Coil rotations show that for the dorsal portion of the stimulated brain, E-Field intensities are highest when the anterior-posterior axis of the coil is perpendicular to the longitudinal fissure, but highest for the medial portion of the stimulated brain when the coil is oriented parallel to the longitudinal fissure.

CONCLUSIONS

Normal anatomical variation in healthy individuals leads to significant differences in the site of TMS, the intensity, and the spread. These variables are generally neglected but could explain significant variability in basic and clinical studies.

SIGNIFICANCE

This is the first work to show how brain-scalp distance and cerebrospinal fluid thickness influence focality, and to show the disassociation between dorsal and medial TMS.

Computationally optimized ECoG stimulation with local safety constraints

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

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.

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.

Functional and structural cortical characteristics after restricted focal motor cortical infarction evaluated at chronic stage - Indications from a preliminary study

OBJECTIVE

To assess the inter-hemispheric differences in neuronal function and structure of the motor cortex in a small group of chronic stroke patients having suffered a restricted ischemic lesion affecting hand motor representation. GABAergic intracortical inhibition, known to be affected by stroke lesion, was also investigated.

METHODS

Eight patients exhibiting little or no motor impairment were studied using transcranial magnetic stimulation (TMS) and diffusion weighted imaging (DWI) >15months from diagnosis. Resting motor threshold (MT) for 50μV and 2mV motor evoked potentials, and short-interval intracortical inhibition (SICI) were measured from hand muscles. Apparent diffusion coefficients (ADCs) were analyzed from the DWI for the primary motor cortex (M1), the supplementary motor area (SMA) and thalamus for reflecting changes in neuronal organization.

RESULTS

The MTs did not differ between the affected (AH) and unaffected hemisphere (UH) in 50μV responses, while the MTs for 2mV responses were higher (p=0.018) in AH. SICI was weakened in AH (p=0.008). ADCs were higher in the affected M1 compared to the unaffected M1 (p=0.018) while there were no inter-hemispheric differences in SMA or thalamus.

CONCLUSIONS

Inter-hemispheric asymmetry and neuronal organization demonstrated abnormalities in the M1. However, no confident inference can be made whether the observed alterations in neurophysiological and imaging measures have causal role for motor rehabilitation in these patients.

SIGNIFICANCE

Neurophysiological changes persist and are detectable using TMS years after stroke even though clinical symptoms have normalized.

Modeling transcranial magnetic stimulation from the induced electric fields to the membrane potentials along tractography-based white matter fiber tracts

OBJECTIVE

Transcranial magnetic stimulation (TMS) is a promising non-invasive tool for modulating the brain activity. Despite the widespread therapeutic and diagnostic use of TMS in neurology and psychiatry, its observed response remains hard to predict, limiting its further development and applications. Although the stimulation intensity is always maximum at the cortical surface near the coil, experiments reveal that TMS can affect deeper brain regions as well.

APPROACH

The explanation of this spread might be found in the white matter fiber tracts, connecting cortical and subcortical structures. When applying an electric field on neurons, their membrane potential is altered. If this change is significant, more likely near the TMS coil, action potentials might be initiated and propagated along the fiber tracts towards deeper regions. In order to understand and apply TMS more effectively, it is important to capture and account for this interaction as accurately as possible. Therefore, we compute, next to the induced electric fields in the brain, the spatial distribution of the membrane potentials along the fiber tracts and its temporal dynamics.

MAIN RESULTS

This paper introduces a computational TMS model in which electromagnetism and neurophysiology are combined. Realistic geometry and tissue anisotropy are included using magnetic resonance imaging and targeted white matter fiber tracts are traced using tractography based on diffusion tensor imaging. The position and orientation of the coil can directly be retrieved from the neuronavigation system. Incorporating these features warrants both patient- and case-specific results.

SIGNIFICANCE

The presented model gives insight in the activity propagation through the brain and can therefore explain the observed clinical responses to TMS and their inter- and/or intra-subject variability. We aspire to advance towards an accurate, flexible and personalized TMS model that helps to understand stimulation in the connected brain and to target more focused and deeper brain regions.

The coil orientation dependency of the electric field induced by TMS for M1 and other brain areas

Background

The effectiveness of transcranial magnetic stimulation (TMS) depends highly on the coil orientation relative to the subject’s head. This implies that the direction of the induced electric field has a large effect on the efficiency of TMS. To improve future protocols, knowledge about the relationship between the coil orientation and the direction of the induced electric field on the one hand, and the head and brain anatomy on the other hand, seems crucial. Therefore, the induced electric field in the cortex as a function of the coil orientation has been examined in this study.

Methods

The effect of changing the coil orientation on the induced electric field was evaluated for fourteen cortical targets. We used a finite element model to calculate the induced electric fields for thirty-six coil orientations (10 degrees resolution) per target location. The effects on the electric field due to coil rotation, in combination with target site anatomy, have been quantified.

Results

The results confirm that the electric field perpendicular to the anterior sulcal wall of the central sulcus is highly susceptible to coil orientation changes and has to be maximized for an optimal stimulation effect of the motor cortex. In order to obtain maximum stimulation effect in areas other than the motor cortex, the electric field perpendicular to the cortical surface in those areas has to be maximized as well. Small orientation changes (10 degrees) do not alter the induced electric field drastically.

Conclusions

The results suggest that for all cortical targets, maximizing the strength of the electric field perpendicular to the targeted cortical surface area (and inward directed) optimizes the effect of TMS. Orienting the TMS coil based on anatomical information (anatomical magnetic resonance imaging data) about the targeted brain area can improve future results. The standard coil orientations, used in cognitive and clinical neuroscience, induce (near) optimal electric fields in the subject-specific head model in most cases.

Electronic supplementary material

The online version of this article (doi:10.1186/s12984-015-0036-2) contains supplementary material, which is available to authorized users.

Effective electric fields along realistic DTI-based neural trajectories for modelling the stimulation mechanisms of TMS

In transcranial magnetic stimulation (TMS), an applied alternating magnetic field induces an electric field in the brain that can interact with the neural system. It is generally assumed that this induced electric field is the crucial effect exciting a certain region of the brain. More specifically, it is the component of this field parallel to the neuron's local orientation, the so-called effective electric field, that can initiate neuronal stimulation. Deeper insights on the stimulation mechanisms can be acquired through extensive TMS modelling. Most models study simple representations of neurons with assumed geometries, whereas we embed realistic neural trajectories computed using tractography based on diffusion tensor images. This way of modelling ensures a more accurate spatial distribution of the effective electric field that is in addition patient and case specific. The case study of this paper focuses on the single pulse stimulation of the left primary motor cortex with a standard figure-of-eight coil. Including realistic neural geometry in the model demonstrates the strong and localized variations of the effective electric field between the tracts themselves and along them due to the interplay of factors such as the tract's position and orientation in relation to the TMS coil, the neural trajectory and its course along the white and grey matter interface. Furthermore, the influence of changes in the coil orientation is studied. Investigating the impact of tissue anisotropy confirms that its contribution is not negligible. Moreover, assuming isotropic tissues lead to errors of the same size as rotating or tilting the coil with 10 degrees. In contrast, the model proves to be less sensitive towards the not well-known tissue conductivity values.

Hypothesis-driven methods to augment human cognition by optimizing cortical oscillations

Cortical oscillations have been shown to represent fundamental functions of a working brain, e.g., communication, stimulus binding, error monitoring, and inhibition, and are directly linked to behavior. Recent studies intervening with these oscillations have demonstrated effective modulation of both the oscillations and behavior. In this review, we collect evidence in favor of how hypothesis-driven methods can be used to augment cognition by optimizing cortical oscillations. We elaborate their potential usefulness for three target groups: healthy elderly, patients with attention deficit/hyperactivity disorder, and healthy young adults. We discuss the relevance of neuronal oscillations in each group and show how each of them can benefit from the manipulation of functionally-related oscillations. Further, we describe methods for manipulation of neuronal oscillations including direct brain stimulation as well as indirect task alterations. We also discuss practical considerations about the proposed techniques. In conclusion, we propose that insights from neuroscience should guide techniques to augment human cognition, which in turn can provide a better understanding of how the human brain works.