Conditions for numerically accurate TMS electric field simulation

Anatomical measurements and field modeling to assess transcranial magnetic stimulation motor and non-motor effects

OBJECTIVE

Explore how anatomical measurements and field modeling can be leveraged to improve investigations of transcranial magnetic stimulation (TMS) effects on both motor and non-motor TMS targets.

METHODS

TMS motor effects (targeting the primary motor cortex [M1]) were evaluated using the resting motor threshold (rMT), while TMS non-motor effects (targeting the superior temporal gyrus [STG]) were assessed using a pain memory task. Anatomical measurements included scalp-cortex distance (SCD) and cortical thickness (CT), whereas field modeling encompassed the magnitude of the electric field (E) induced by TMS.

RESULTS

Anatomical measurements and field modeling values differed significantly between M1 and STG. For TMS motor effects, rMT was correlated with SCD, CT, and E values at M1 (p < 0.05). No correlations were found between these metrics for the STG and TMS non-motor effects (pain memory; all p-values > 0.05).

CONCLUSION

Although anatomical measurements and field modeling are closely related to TMS motor effects, their relationship to non-motor effects - such as pain memory - appear to be much more tenuous and complex, highlighting the need for further advancement in our use of TMS and virtual lesion paradigms.

Dosimetry for repetitive transcranial magnetic stimulation: a translational study from Alzheimer's disease patients to controlledin vitroinvestigations

Objective.Recent studies have indicated that repetitive transcranial magnetic stimulation (rTMS) could enhance cognition in Alzheimer's Disease (AD) patients, but to now the molecular-level interaction mechanisms driving this effect remain poorly understood. While cognitive scores have been the primary measure of rTMS effectiveness, employing molecular-based approaches could offer more precise treatment predictions and prognoses. To reach this goal, it is fundamental to assess the electric field (E-field) and the induced current densities (J) within the stimulated brain areas and to translate these values toin vitrosystems specifically devoted in investigating molecular-based interactions of this stimulation.Approach.This paper offers a methodological procedure to guide dosimetric assessment to translate the E-field induced in humans (in a specific pilot study) intoin vitrosettings. Electromagnetic simulations on patients' head models and cellular holders were conducted to characterize exposure conditions and determine necessary adjustments forin vitroreplication of the same dose delivered in humans using the same stimulating coil.Main results.Our study highlighted the levels of E-field andJinduced in the target brain region and showed that the computed E-field andJwere different among patients that underwent the treatment, so to replicate the exposure to thein vitrosystem, we have to consider a range of electric quantities as reference. To match the E-field to the levels calculated in patients' brains, an increase of at least the 25% in the coil feeding current is necessary whenin vitrostimulations are performed. Conversely, to equalize current densities, modifications in the cells culture medium conductivity have to be implemented reducing it to one fifth of its value.Significance.This dosimetric assessment and subsequent experimental adjustments are essential to achieve controlledin vitroexperiments to better understand rTMS effects on AD cognition. Dosimetry is a fundamental step for comparing the cognitive effects with those obtained by stimulating a cellular model at an equal dose rigorously evaluated.

A survey on integral equations for bioelectric modeling

Bioelectric modeling problems, such as electroencephalography, magnetoencephalography, transcranial electrical stimulation, deep brain stimulation, and transcranial magnetic stimulation, among others, can be approached through the formulation and resolution of integral equations of theboundary element method(BEM). Recently, it has been realized that thecharge-based formulationof the BEM is naturally well-suited for the application of thefast multipole method(FMM). The FMM is a powerful algorithm for the computation of many-body interactions and is widely applied in electromagnetic modeling problems. With the introduction of BEM-FMM in the context of bioelectromagnetism, the BEM can now compete with thefinite element method(FEM) in a number of application cases. This survey has two goals: first, to give a modern account of the main BEM formulations in the literature and their integration with FMM, directed to general researchers involved in development of BEM software for bioelectromagnetic applications. Second, to survey different techniques and available software, and to contrast different BEM and FEM approaches. As a new contribution, we showcase that the charge-based formulation is dual to the more common surface potential formulation.

How conductivity boundaries influence the electric field induced by transcranial magnetic stimulation in in vitro experiments

BACKGROUND

Although transcranial magnetic stimulation (TMS) has become a valuable method for non-invasive brain stimulation, the cellular basis of TMS activation of neurons is still not fully understood. In vitro preparations have been used to understand the biophysical mechanisms of TMS, but in many cases these studies have encountered substantial difficulties in activating neurons.

OBJECTIVE/HYPOTHESIS

The hypothesis of this work is that conductivity boundaries can have large effects on the electric field in commonly used in vitro preparations. Our goal was to analyze the resulting difficulties in in vitro TMS using a simulation study, using a charge-based boundary element model.

METHODS

We decomposed the total electric field into the sum of the primary electric field, which only depends on coil geometry and current, and the secondary electric field arising from conductivity boundaries, which strongly depends on tissue and chamber geometry. We investigated the effect of the conductivity boundaries on the electric field strength for a variety of in vitro experimental settings to determine the sources of difficulty.

RESULTS

We showed that conductivity boundaries can have large effects on the electric field in in vitro preparations. Depending on the geometry of the air-saline and the saline-tissue interfaces, the secondary electric field can significantly enhance, or attenuate the primary electric field, resulting in a much stronger or weaker total electric field inside the tissue; we showed this using a realistic preparation. Submerged chambers are generally much more efficient than interface chambers since the secondary field due to the thin film of saline covering the tissue in the interface chamber opposes the primary field and significantly reduces the total field in the tissue placed in the interface chamber. The relative dimensions of the chamber and the TMS coil critically determine the total field; the popular setup with a large coil and a small chamber is particularly sub-optimal because the secondary field due to the air-chamber boundary opposes the primary field, thereby attenuating the total field. The form factor (length vs width) of the tissue in the direction of the induced field can be important since a relatively narrow tissue enhances the total field at the saline-tissue boundary.

CONCLUSIONS

Overall, we found that the total electric field in the tissue is higher in submerged chambers, higher if the chamber size is larger than the coil and if the shorter tissue dimension is in the direction of the electric field. Decomposing the total field into the primary and secondary fields is useful for designing in vitro experiments and interpreting the results.

A semi-automated pipeline for finite element modeling of electric field induced in nonhuman primates by transcranial magnetic stimulation

BACKGROUND

Transcranial magnetic stimulation (TMS) is used to treat a range of brain disorders by inducing an electric field (E-field) in the brain. However, the precise neural effects of TMS are not well understood. Nonhuman primates (NHPs) are used to model the impact of TMS on neural activity, but a systematic method of quantifying the induced E-field in the cortex of NHPs has not been developed.

NEW METHOD

The pipeline uses statistical parametric mapping (SPM) to automatically segment a structural MRI image of a rhesus macaque into five tissue compartments. Manual corrections are necessary around implants. The segmented tissues are tessellated into 3D meshes used in finite element method (FEM) software to compute the TMS induced E-field in the brain. The gray matter can be further segmented into cortical laminae using a volume preserving method for defining layers.

RESULTS

Models of three NHPs were generated with TMS coils placed over the precentral gyrus. Two coil configurations, active and sham, were simulated and compared. The results demonstrated a large difference in E-fields at the target. Additionally, the simulations were calculated using two different E-field solvers and were found to not significantly differ.

COMPARISON WITH EXISTING METHODS

Current methods segment NHP tissues manually or use automated methods for only the brain tissue. Existing methods also do not stratify the gray matter into layers.

CONCLUSION

The pipeline calculates the induced E-field in NHP models by TMS and can be used to plan implant surgeries and determine approximate E-field values around neuron recording sites.

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.

Addressing the sources of inter-subject variability in E-field parameters in anodal tDCS stimulation over motor cortical network

Objetive: .Although transcranial direct current stimulation constitutes a non-invasive neuromodulation technique with promising results in a great variety of applications, its clinical implementation is compromised by the high inter-subject variability reported. This study aims to analyze the inter-subject variability in electric fields (E-fields) over regions of the cortical motor network under two electrode montages: the classical C3Fp2 and an alternative P3F3, which confines more the E-field over this region.Approach.Computational models of the head of 98 healthy subjects were developed to simulate the E-field under both montages. E-field parameters such as magnitude, focality and orientation were calculated over three regions of interest (ROI): M1S1, supplementary motor area (SMA) and preSMA. The role of anatomical characteristics as a source of inter-subject variability on E-field parameters and individualized stimulation intensity were addressed using linear mixed-effect models.Main results.P3F3 showed a more confined E-field distribution over M1S1 than C3Fp2; the latter elicited higher E-fields over supplementary motor areas. Both montages showed high inter-subject variability, especially for the normal component over C3Fp2. Skin, bone and CSF ROI volumes showed a negative association with E-field magnitude irrespective of montage. Grey matter volume and montage were the main sources of variability for focality. The curvature of gyri was found to be significantly associated with the variability of normal E-fields.Significance.Computational modeling proves useful in the assessment of E-field variability. Our simulations predict significant differences in E-field magnitude and focality for C3Fp2 and P3F3. However, anatomical characteristics were also found to be significant sources of E-field variability irrespective of electrode montage. The normal E-field component better captured the individual variability and low rate of responder subjects observed in experimental studies.

Model-based analysis of the acute effects of transcutaneous magnetic spinal cord stimulation on micturition after spinal cord injury in humans

AIM

After spinal cord injuries (SCIs), patients may develop either detrusor-sphincter dyssynergia (DSD) or urinary incontinence, depending on the level of the spinal injury. DSD and incontinence reflect the loss of coordinated neural control among the detrusor muscle, which increases bladder pressure to facilitate urination, and urethral sphincters and pelvic floor muscles, which control the bladder outlet to restrict or permit bladder emptying. Transcutaneous magnetic stimulation (TMS) applied to the spinal cord after SCI reduced DSD and incontinence. We defined, within a mathematical model, the minimum neuronal elements necessary to replicate neurogenic dysfunction of the bladder after a SCI and incorporated into this model the minimum additional neurophysiological features sufficient to replicate the improvements in bladder function associated with lumbar TMS of the spine in patients with SCI.

METHODS

We created a computational model of the neural circuit of micturition based on Hodgkin-Huxley equations that replicated normal bladder function. We added interneurons and increased network complexity to reproduce dysfunctional micturition after SCI, and we increased the density and complexity of interactions of both inhibitory and excitatory lumbar spinal interneurons responsive to TMS to provide a more diverse set of spinal responses to intrinsic and extrinsic activation of spinal interneurons that remains after SCI.

RESULTS

The model reproduced the re-emergence of a spinal voiding reflex after SCI. When we investigated the effect of monophasic and biphasic TMS at two frequencies applied at or below T10, the model replicated the improved coordination between detrusor and external urethral sphincter activity that has been observed clinically: low-frequency TMS (1 Hz) within the model normalized control of voiding after SCI, whereas high-frequency TMS (30 Hz) enhanced urine storage.

CONCLUSION

Neuroplasticity and increased complexity of interactions among lumbar interneurons, beyond what is necessary to simulate normal bladder function, must be present in order to replicate the effects of SCI on control of micturition, and both neuronal and network modifications of lumbar interneurons are essential to understand the mechanisms whereby TMS reduced bladder dysfunction after SCI.

A boundary element method of bidomain modeling for predicting cellular responses to electromagnetic fields

Objective.Commonly used cable equation approaches for simulating the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or 'whole' finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.Approach.Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.Main Results.Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is simplified, and the relative placement of devices and cells can be varied without the need to generate a new mesh.Significance.Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

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%.

A review of algorithms and software for real-time electric field modeling techniques for transcranial magnetic stimulation

Transcranial magnetic stimulation (TMS) is a device-based neuromodulation technique increasingly used to treat brain diseases. Electric field (E-field) modeling is an important technique in several TMS clinical applications, including the precision stimulation of brain targets with accurate stimulation density for the treatment of mental disorders and the localization of brain function areas for neurosurgical planning. Classical methods for E-field modeling usually take a long computation time. Fast algorithms are usually developed with significantly lower spatial resolutions that reduce the prediction accuracy and limit their usage in real-time or near real-time TMS applications. This review paper discusses several modern algorithms for real-time or near real-time TMS E-field modeling and their advantages and limitations. The reviewed methods include techniques such as basis representation techniques and deep neural-network-based methods. This paper also provides a review of software tools that can integrate E-field modeling with navigated TMS, including a recent software for real-time navigated E-field mapping based on deep neural-network models.

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.

Verification of neuronavigated TMS accuracy using structured-light 3D scans

Objective.To investigate the reliability and accuracy of the manual three-point co-registration in neuronavigated transcranial magnetic stimulation (TMS). The effect of the error in landmark pointing on the coil placement and on the induced electric and magnetic fields was examined.Approach.The position of the TMS coil on the head was recorded by the neuronavigation system and by 3D scanning for ten healthy participants. The differences in the coil locations and orientations and the theoretical error values for electric and magnetic fields between the neuronavigated and 3D scanned coil positions were calculated. In addition, the sensitivity of the coil location on landmark accuracy was calculated.Main results.The measured distances between the neuronavigated and 3D scanned coil locations were on average 10.2 mm, ranging from 3.1 to 18.7 mm. The error in angles were on average from two to three degrees. The coil misplacement caused on average a 29% relative error in the electric field with a range from 9% to 51%. In the magnetic field, the same error was on average 33%, ranging from 10% to 58%. The misplacement of landmark points could cause a 1.8-fold error for the coil location.Significance.TMS neuronavigation with three landmark points can cause a significant error in the coil position, hampering research using highly accurate electric field calculations. Including 3D scanning to the process provides an efficient method to achieve a more accurate coil position.

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.

An adaptive h-refinement method for the boundary element fast multipole method for quasi-static electromagnetic modeling

Objective.In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems.Approach.We propose, describe, and systematically investigate an AMR method using the boundary element method with fast multipole acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy. The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a 'silver-standard' solution found by subsequent 4:1 global refinement of the adaptively-refined model.Main results.Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models.Significance.This error has especially important implications for TES dosing prediction-where the stimulation strength plays a central role-and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

A Boundary Element Method of Bidomain Modeling for Predicting Cellular Responses to Electromagnetic Fields

Objective

Commonly used cable equation-based approaches for determining the effects of electromagnetic fields on excitable cells make several simplifying assumptions that could limit their predictive power. Bidomain or "whole" finite element methods have been developed to fully couple cells and electric fields for more realistic neuron modeling. Here, we introduce a novel bidomain integral equation designed for determining the full electromagnetic coupling between stimulation devices and the intracellular, membrane, and extracellular regions of neurons.

Methods

Our proposed boundary element formulation offers a solution to an integral equation that connects the device, tissue inhomogeneity, and cell membrane-induced E-fields. We solve this integral equation using first-order nodal elements and an unconditionally stable Crank-Nicholson time-stepping scheme. To validate and demonstrate our approach, we simulated cylindrical Hodgkin-Huxley axons and spherical cells in multiple brain stimulation scenarios.

Main Results

Comparison studies show that a boundary element approach produces accurate results for both electric and magnetic stimulation. Unlike bidomain finite element methods, the bidomain boundary element method does not require volume meshes containing features at multiple scales. As a result, modeling cells, or tightly packed populations of cells, with microscale features embedded in a macroscale head model, is made computationally tractable, and the relative placement of devices and cells can be varied without the need to generate a new mesh.

Significance

Device-induced electromagnetic fields are commonly used to modulate brain activity for research and therapeutic applications. Bidomain solvers allow for the full incorporation of realistic cell geometries, device E-fields, and neuron populations. Thus, multi-cell studies of advanced neuronal mechanisms would greatly benefit from the development of fast-bidomain solvers to ensure scalability and the practical execution of neural network simulations with realistic neuron morphologies.

Astrocyte Responses Influence Local Effects of Whole-Brain Magnetic Stimulation in Parkinsonian Rats

BACKGROUND

Excessive glutamatergic transmission in the striatum is implicated in Parkinson's disease (PD) progression. Astrocytes maintain glutamate homeostasis, protecting from excitotoxicity through the glutamate-aspartate transporter (GLAST), whose alterations have been reported in PD. Noninvasive brain stimulation using intermittent theta-burst stimulation (iTBS) acts on striatal neurons and glia, inducing neuromodulatory effects and functional recovery in experimental parkinsonism.

OBJECTIVE

Because PD is associated with altered astrocyte function, we hypothesized that acute iTBS, known to rescue striatal glutamatergic transmission, exerts regional- and cell-specific effects through modulation of glial functions.

METHODS

6-Hydroxydopamine-lesioned rats were exposed to acute iTBS, and the areas predicted to be more responsive by a biophysical, hyper-realistic computational model that faithfully reconstructs the experimental setting were analyzed. The effects of iTBS on glial cells and motor behavior were evaluated by molecular and morphological analyses, and CatWalk and Stepping test, respectively.

RESULTS

As predicted by the model, the hippocampus, cerebellum, and striatum displayed a marked c-FOS activation after iTBS, with the striatum showing specific morphological and molecular changes in the astrocytes, decreased phospho-CREB levels, and recovery of GLAST. Striatal-dependent motor performances were also significantly improved.

CONCLUSION

These data uncover an unknown iTBS effect on astrocytes, advancing the understanding of the complex mechanisms involved in TMS-mediated functional recovery. Data on numerical dosimetry, obtained with a degree of anatomical details never before considered and validated by the biological findings, provide a framework to predict the electric-field induced in different specific brain areas and associate it with functional and molecular changes. © 2023 The Authors. Movement Disorders published by Wiley Periodicals LLC on behalf of International Parkinson and Movement Disorder Society.

Fast and accurate computational E-field dosimetry for group-level transcranial magnetic stimulation targeting

Transcranial magnetic stimulation (TMS) is used to study brain function and treat mental health disorders. During TMS, a coil placed on the scalp induces an E-field in the brain that modulates its activity. TMS is known to stimulate regions that are exposed to a large E-field. Clinical TMS protocols prescribe a coil placement based on scalp landmarks. There are inter-individual variations in brain anatomy that result in variations in the TMS-induced E-field at the targeted region and its outcome. These variations across individuals could in principle be minimized by developing a large database of head subjects and determining scalp landmarks that maximize E-field at the targeted brain region while minimizing its variation using computational methods. However, this approach requires repeated execution of a computational method to determine the E-field induced in the brain for a large number of subjects and coil placements. We developed a probabilistic matrix decomposition-based approach for rapidly evaluating the E-field induced during TMS for a large number of coil placements due to a pre-defined coil model. Our approach can determine the E-field induced in over 1 Million coil placements in 9.5 h, in contrast, to over 5 years using a brute-force approach. After the initial set-up stage, the E-field can be predicted over the whole brain within 2-3 ms and to 2% accuracy. We tested our approach in over 200 subjects and achieved an error of <2% in most and <3.5% in all subjects. We will present several examples of bench-marking analysis for our tool in terms of accuracy and speed. Furthermore, we will show the methods' applicability for group-level optimization of coil placement for illustration purposes only. The software implementation link is provided in the appendix.

Detailed high quality surface-based mouse CAD model suitable for electromagnetic simulations

Transcranial magnetic stimulation (TMS) studies with small animals can provide useful knowledge of activating regions and mechanisms. Along with this, functional magnetic resonance imaging (fMRI) in mice and rats is increasingly often used to draw important conclusions about brain connectivity and functionality. For cases of both low- and high-frequency TMS studies, a high-quality computational surface-based rodent model may be useful as a tool for performing supporting modeling and optimization tasks. This work presents the development and usage of an accurate CAD model of a mouse that has been optimized for use in computational electromagnetic modeling in any frequency range. It is based on the labeled atlas data of the Digimouse archive. The model includes a relatively accurate four-compartment brain representation (the 'whole brain' according to the original terminology, external cerebrum, cerebellum, and striatum [9]) and contains 21 distinct compartments in total. Four examples of low- and high frequency modeling have been considered to demonstrate the utility and applicability of the model.

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.

Multi-scale model of axonal and dendritic polarization by transcranial direct current stimulation in realistic head geometry

BACKGROUND

Transcranial direct current stimulation (tDCS) is a non-invasive brain stimulation modality that can alter cortical excitability. However, it remains unclear how the subcellular elements of different neuron types are polarized by specific electric field (E-field) distributions.

OBJECTIVE

To quantify neuronal polarization generated by tDCS in a multi-scale computational model.

METHODS

We embedded layer-specific, morphologically-realistic cortical neuron models in a finite element model of the E-field in a human head and simulated steady-state polarization generated by conventional primary-motor-cortex-supraorbital (M1-SO) and 4 × 1 high-definition (HD) tDCS. We quantified somatic, axonal, and dendritic polarization of excitatory pyramidal cells in layers 2/3, 5, and 6, as well as inhibitory interneurons in layers 1 and 4 of the hand knob.

RESULTS

Axonal and dendritic terminals were polarized more than the soma in all neurons, with peak axonal and dendritic polarization of 0.92 mV and 0.21 mV, respectively, compared to peak somatic polarization of 0.07 mV for 1.8 mA M1-SO stimulation. Both montages generated regions of depolarization and hyperpolarization beneath the M1 anode; M1-SO produced slightly stronger, more diffuse polarization peaking in the central sulcus, while 4 × 1 HD produced higher peak polarization in the gyral crown. The E-field component normal to the cortical surface correlated strongly with pyramidal neuron somatic polarization (R2>0.9), but exhibited weaker correlations with peak pyramidal axonal and dendritic polarization (R2:0.5-0.9) and peak polarization in all subcellular regions of interneurons (R2:0.3-0.6). Simulating polarization by uniform local E-field extracted at the soma approximated the spatial distribution of tDCS polarization but produced large errors in some regions (median absolute percent error: 7.9 %).

CONCLUSIONS

Polarization of pre- and postsynaptic compartments of excitatory and inhibitory cortical neurons may play a significant role in tDCS neuromodulation. These effects cannot be predicted from the E-field distribution alone but rather require calculation of the neuronal response.

A fast direct solver for surface-based whole-head modeling of transcranial magnetic stimulation

When modeling transcranial magnetic stimulation (TMS) in the brain, a fast and accurate electric field solver can support interactive neuronavigation tasks as well as comprehensive biophysical modeling. We formulate, test, and disseminate a direct (i.e., non-iterative) TMS solver that can accurately determine global TMS fields for any coil type everywhere in a high-resolution MRI-based surface model with ~ 200,000 or more arbitrarily selected observation points within approximately 5 s, with the solution time itself of 3 s. The solver is based on the boundary element fast multipole method (BEM-FMM), which incorporates the latest mathematical advancement in the theory of fast multipole methods-an FMM-based LU decomposition. This decomposition is specific to the head model and needs to be computed only once per subject. Moreover, the solver offers unlimited spatial numerical resolution. Despite the fast execution times, the present direct solution is numerically accurate for the default model resolution. In contrast, the widely used brain modeling software SimNIBS employs a first-order finite element method that necessitates additional mesh refinement, resulting in increased computational cost. However, excellent agreement between the two methods is observed for various practical test cases following mesh refinement, including a biophysical modeling task. The method can be readily applied to a wide range of TMS analyses involving multiple coil positions and orientations, including image-guided neuronavigation. It can even accommodate continuous variations in coil geometry, such as flexible H-type TMS coils. The FMM-LU direct solver is freely available to academic users.

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).

Anatomical details affect electric field predictions for non-invasive brain stimulation in non-human primates

Non-human primates (NHPs) have become key for translational research in noninvasive brain stimulation (NIBS). However, in order to create comparable stimulation conditions for humans it is vital to study the accuracy of current modeling practices across species. Numerical models to simulate electric fields are an important tool for experimental planning in NHPs and translation to human studies. It is thus essential whether and to what extent the anatomical details of NHP models agree with current modeling practices when calculating NIBS electric fields. Here, we create highly accurate head models of two non-human primates (NHP) MR data. We evaluate how muscle tissue and head field of view (depending on MRI parameters) affect simulation results in transcranial electric and magnetic stimulation (TES and TMS). Our findings indicate that the inclusion of anisotropic muscle can affect TES electric field strength up to 22% while TMS is largely unaffected. Additionally, comparing a full head model to a cropped head model illustrates the impact of head field of view on electric fields for both TES and TMS. We find opposing effects between TES and TMS with an increase up to 24.8% for TES and a decrease up to 24.6% for TMS for the cropped head model compared to the full head model. Our results provide important insights into the level of anatomical detail needed for NHP head models and can inform future translational efforts for NIBS studies.

Optimizing TMS Coil Placement Approaches for Targeting the Dorsolateral Prefrontal Cortex in Depressed Adolescents: An Electric Field Modeling Study

High-frequency repetitive transcranial magnetic stimulation (rTMS) to the left dorsolateral prefrontal cortex (L-DLPFC) shows promise as a treatment for treatment-resistant depression in adolescents. Conventional rTMS coil placement strategies include the 5 cm, the Beam F3, and the magnetic resonance imaging (MRI) neuronavigation methods. The purpose of this study was to use electric field (E-field) models to compare the three targeting approaches to a computational E-field optimization coil placement method in depressed adolescents. Ten depressed adolescents (4 females, age: 15.9±1.1) participated in an open-label rTMS treatment study and were offered MRI-guided rTMS five times per week over 6-8 weeks. Head models were generated based on individual MRI images, and E-fields were simulated for the four targeting approaches. Results showed a significant difference in the induced E-fields at the L-DLPFC between the four targeting methods (χ2=24.7, p<0.001). Post hoc pairwise comparisons showed that there was a significant difference between any two of the targeting methods (Holm adjusted p<0.05), with the 5 cm rule producing the weakest E-field (46.0±17.4V/m), followed by the F3 method (87.4±35.4V/m), followed by MRI-guided (112.1±14.6V/m), and followed by the computational approach (130.1±18.1V/m). Variance analysis showed that there was a significant difference in sample variance between the groups (K2=8.0, p<0.05), with F3 having the largest variance. Participants who completed the full course of treatment had median E-fields correlated with depression symptom improvement (r=-0.77, p<0.05). E-field models revealed limitations of scalp-based methods compared to MRI guidance, suggesting computational optimization could enhance dose delivery to the target.

An Adaptive H-Refinement Method for the Boundary Element Fast Multipole Method for Quasi-static Electromagnetic Modeling

Objective

In our recent work pertinent to modeling of brain stimulation and neurophysiological recordings, substantial modeling errors in the computed electric field and potential have sometimes been observed for standard multi-compartment head models. The goal of this study is to quantify those errors and, further, eliminate them through an adaptive mesh refinement (AMR) algorithm. The study concentrates on transcranial magnetic stimulation (TMS), transcranial electrical stimulation (TES), and electroencephalography (EEG) forward problems.

Approach

We propose, describe, and systematically investigate an AMR method using the Boundary Element Method with Fast Multipole Acceleration (BEM-FMM) as the base numerical solver. The goal is to efficiently allocate additional unknowns to critical areas of the model, where they will best improve solution accuracy.The implemented AMR method's accuracy improvement is measured on head models constructed from 16 Human Connectome Project subjects under problem classes of TES, TMS, and EEG. Errors are computed between three solutions: an initial non-adaptive solution, a solution found after applying AMR with a conservative refinement rate, and a "silver-standard" solution found by subsequent 4:1 global refinement of the adaptively-refined model.

Main Results

Excellent agreement is shown between the adaptively-refined and silver-standard solutions for standard head models. AMR is found to be vital for accurate modeling of TES and EEG forward problems for standard models: an increase of less than 25% (on average) in number of mesh elements for these problems, efficiently allocated by AMR, exposes electric field/potential errors exceeding 60% (on average) in the solution for the unrefined models.

Significance

This error has especially important implications for TES dosing prediction - where the stimulation strength plays a central role - and for EEG lead fields. Though the specific form of the AMR method described here is implemented for the BEM-FMM, we expect that AMR is applicable and even required for accurate electromagnetic simulations by other numerical modeling packages as well.

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 fast direct solver for surface-based whole-head modeling of transcranial magnetic stimulation

Background

When modeling transcranial magnetic stimulation (TMS) in the brain, a fast and accurate electric field solver can support interactive neuronavigation tasks as well as comprehensive biophysical modeling.

Objective

We formulate, test, and disseminate a direct (i.e., non-iterative) TMS solver that can accurately determine global TMS fields for any coil type everywhere in a high-resolution MRI-based surface model with ~200,000 or more arbitrarily selected observation points within approximately 5 sec, with the solution time itself of 3 sec.

Method

The solver is based on the boundary element fast multipole method (BEM-FMM), which incorporates the latest mathematical advancement in the theory of fast multipole methods - an FMM-based LU decomposition. This decomposition is specific to the head model and needs to be computed only once per subject. Moreover, the solver offers unlimited spatial numerical resolution.

Results

Despite the fast execution times, the present direct solution is numerically accurate for the default model resolution. In contrast, the widely used brain modeling software SimNIBS employs a first-order finite element method that necessitates additional mesh refinement, resulting in increased computational cost. However, excellent agreement between the two methods is observed for various practical test cases following mesh refinement, including a biophysical modeling task.

Conclusion

The method can be readily applied to a wide range of TMS analyses involving multiple coil positions and orientations, including image-guided neuronavigation. It can even accommodate continuous variations in coil geometry, such as flexible H-type TMS coils. The FMM-LU direct solver is freely available to academic users.

Pinpointing the precise stimulation targets for brain rehabilitation in early-stage Parkinson's disease

BACKGROUND

Transcranial magnetic stimulation (TMS) is increasingly used as a promising non-pharmacological treatment for Parkinson's disease (PD). Scalp-to-cortex distance (SCD), as a key technical parameter of TMS, plays a critical role in determining the locations of treatment targets and corresponding dosage. Due to the discrepancies in TMS protocols, the optimal targets and head models have yet to be established in PD patients.

OBJECTIVE

To investigate the SCDs of the most popular used targets in left dorsolateral prefrontal cortex (DLPFC) and quantify its impact on the TMS-induced electric fields (E-fields) in early-stage PD patients.

METHODS

Structural magnetic resonance imaging scans from PD patients (n = 47) and normal controls (n = 36) were drawn from the NEUROCON and Tao Wu datasets. SCD of left DLPFC was measured by Euclidean Distance in TMS Navigation system. The intensity and focality of SCD-dependent E-fields were examined and quantified using Finite Element Method.

RESULTS

Early-stage PD patients showed an increased SCDs, higher variances in the SCDs and SCD-dependent E-fields across the seven targets of left DLPFC than normal controls. The stimulation targets located on gyral crown had more focal and homogeneous E-fields. The SCD of left DLPFC had a better performance in differentiating early-stage PD patients than global cognition and other brain measures.

CONCLUSION

SCD and SCD-dependent E-fields could determine the optimal TMS treatment targets and may also be used as a novel marker to differentiate early-stage PD patients. Our findings have important implications for developing optimal TMS protocols and personalized dosimetry in real-world clinical practice.

Modelling the differential effects of age on transcranial magnetic stimulation induced electric fields

Objective. The therapeutic application of noninvasive brain stimulation modalities such as transcranial magnetic stimulation (TMS) has expanded in terms of indications and patient populations. Often neurodevelopmental and neurodegenerative changes are not considered in research studies and clinical applications. This study sought to examine TMS dosing across time points in the life cycle.Approach. TMS induced electric fields with a figure-of-eight coil was simulated at left dorsolateral prefrontal cortex regions and taken in vertex as a control region. Realistic magnetic resonance imaging-based head models (N= 48) were concurrently examined in a cross-sectional study of three different age groups (children, adults, and elderlies).Main results. Age had a negative correlation with electric field peaks in white matter, grey matter and cerebrospinal fluid (P< 0.001). Notably, the electric field map in children displayed the widest cortical surface spread of TMS induced electric fields.Significance. Age-related anatomical geometry beneath the coil stimulation site had a significant impact on the TMS induced electric fields for different age groups. Safety considerations for TMS applications and protocols in children are warranted based on the present electric field findings.

Transcranial magnetic stimulation to frontal but not occipital cortex disrupts endogenous attention

Covert endogenous (voluntary) attention improves visual performance. Human neuroimaging studies suggest that the putative human homolog of macaque frontal eye fields (FEF+) is critical for this improvement, whereas early visual areas are not. Yet, correlational MRI methods do not manipulate brain function. We investigated whether rFEF+ or V1/V2 plays a causal role in endogenous attention. We used transcranial magnetic stimulation (TMS) to alter activity in the visual cortex or rFEF+ when observers performed an orientation discrimination task while attention was manipulated. On every trial, they received double-pulse TMS at a predetermined site (stimulated region) around V1/V2 or rFEF+. Two cortically magnified gratings were presented, one in the stimulated region (contralateral to the stimulated area) and another in the symmetric (ipsilateral) nonstimulated region. Grating contrast was varied to measure contrast response functions (CRFs) for all attention and stimulation combinations. In experiment 1, the CRFs were similar at the stimulated and nonstimulated regions, indicating that early visual areas do not modulate endogenous attention during stimulus presentation. In contrast, occipital TMS eliminates exogenous (involuntary) attention effects on performance [A. Fernández, M. Carrasco,Curr. Biol. 30, 4078-4084 (2020)]. In experiment 2, rFEF+ stimulation decreased the overall attentional effect; neither benefits at the attended location nor costs at the unattended location were significant. The frequency and directionality of microsaccades mimicked this pattern: Whereas occipital stimulation did not affect microsaccades, rFEF+ stimulation caused a higher microsaccade rate directed toward the stimulated hemifield. These results provide causal evidence of the role of this frontal region for endogenous attention.

Fast computational E-field dosimetry for transcranial magnetic stimulation using adaptive cross approximation and auxiliary dipole method (ACA-ADM)

Transcranial Magnetic Stimulation (TMS) is a non-invasive brain stimulation technique that uses a coil to induce an electric field (E-field) in the brain and modulate its activity. Many applications of TMS call for the repeated execution of E-field solvers to determine the E-field induced in the brain for different coil placements. However, the usage of solvers for these applications remains impractical because each coil placement requires the solution of a large linear system of equations. We develop a fast E-field solver that enables the rapid evaluation of the E-field distribution for a brain region of interest (ROI) for a large number of coil placements, which is achieved in two stages. First, during the pre-processing stage, the mapping between coil placement and brain ROI E-field distribution is approximated from E-field results for a few coil placements. Specifically, we discretize the mapping into a matrix with each column having the ROI E-field samples for a fixed coil placement. This matrix is approximated from a few of its rows and columns using adaptive cross approximation (ACA). The accuracy, efficiency, and applicability of the new ACA approach are determined by comparing its E-field predictions with analytical and standard solvers in spherical and MRI-derived head models. During the second stage, the E-field distribution in the brain ROI from a specific coil placement is determined by the obtained rows and columns in milliseconds. For many applications, only the E-field distribution for a comparatively small ROI is required. For example, the solver can complete the pre-processing stage in approximately 4 hours and determine the ROI E-field in approximately 40 ms for a 100 mm diameter ROI with less than 2% error enabling its use for neuro-navigation and other applications. Highlight: We developed a fast solver for TMS computational E-field dosimetry, which can determine the ROI E-field in approximately 40 ms for a 100 mm diameter ROI with less than 2% error.

Fast And Accurate Population Level Transcranial Magnetic Stimulation via Low-Rank Probabilistic Matrix Decomposition (PMD)

Transcranial magnetic stimulation (TMS) is used to study brain function and treat mental health disorders. During TMS, a coil placed on the scalp induces an E-field in the brain that modulates its activity. TMS is known to stimulate regions that are exposed to a large E-field. Clinical TMS protocols prescribe a coil placement based on scalp landmarks. There are inter-individual variations in brain anatomy that result in variations in the TMS-induced E-field at the targeted region and its outcome. These variations across individuals could in principle be minimized by developing a large database of head subjects and determining scalp landmarks that maximize E-field at the targeted brain region while minimizing its variation using computational methods. However, this approach requires repeated execution of a computational method to determine the E-field induced in the brain for a large number of subjects and coil placements. We developed a probabilistic matrix decomposition-based approach for rapidly evaluating the E-field induced during TMS for a large number of coil placements. Our approach can determine the E-field induced in over 1 Million coil placements in 9.5 hours, in contrast, to over 5 years using a bruteforce approach. After the initial set-up stage, the E-field can be predicted over the whole brain within 2-3 milliseconds and to 2% accuracy. We tested our approach in over 200 subjects and achieved an error of < 2% in most and < 3.5% in all subjects. We will present several examples of bench-marking analysis for our tool in terms of accuracy and speed across and its applicability for population level optimization of coil placement.

Highlights

A method for practical E-field informed population-level TMS coil placement strategies is developed.This algorithm enables the determination of E-field informed optimal coil placement in seconds enabling it’s use for close-loop and on-the-fly reconfiguration of TMS.After the initial set-up stage of less than 10 hours, the E-field can be predicted for any coil placement across the whole brain within in 2-3 milliseconds.

Effects of neuromodulation on cognitive and emotional responses to psychosocial stressors in healthy humans

Physiological and psychological stressors can exert wide-ranging effects on the human brain and behavior. Research has improved understanding of how the sympatho-adreno-medullary (SAM) and hypothalamic-pituitary-adrenocortical (HPA) axes respond to stressors and the differential responses that occur depending on stressor type. Although the physiological function of SAM and HPA responses is to promote survival and safety, exaggerated psychobiological reactivity can occur in psychiatric disorders. Exaggerated reactivity may occur more for certain types of stressors, specifically, psychosocial stressors. Understanding stressor effects and how the body regulates these responses can provide insight into ways that psychobiological reactivity can be modulated. Non-invasive neuromodulation is one way that responding to stressors may be altered; research into these interventions may provide further insights into the brain circuits that modulate stress reactivity. This review focuses on the effects of acute psychosocial stressors and how neuromodulation might be effective in altering stress reactivity. Although considerable research into stress interventions focuses on treating pathology, it is imperative to first understand these mechanisms in non-clinical populations; therefore, this review will emphasize populations with no known pathology and consider how these results may translate to those with psychiatric pathologies.

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.

Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning

Electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) can be modeled using partial differential equations (PDEs). Using state-of-the-art finite-element methods (FEM), it often takes tens of seconds to solve the PDEs for computing a high-resolution E-field, hampering the wide application of the E-field modeling in practice and research. To improve the E-field modeling's computational efficiency, we developed a self-supervised deep learning (DL) method to compute precise TMS E-fields. Given a head model and the primary E-field generated by TMS coils, a DL model was built to generate a E-field by minimizing a loss function that measures how well the generated E-field fits the governing PDE. The DL model was trained in a self-supervised manner, which does not require any external supervision. We evaluated the DL model using both a simulated sphere head model and realistic head models of 125 individuals and compared the accuracy and computational speed of the DL model with a state-of-the-art FEM. In realistic head models, the DL model obtained accurate E-fields that were significantly correlated with the FEM solutions. The DL model could obtain precise E-fields within seconds for whole head models at a high spatial resolution, faster than the FEM. The DL model built for the simulated sphere head model also obtained an accurate E-field whose average difference from the analytical E-fields was 0.0054, comparable to the FEM solution. These results demonstrated that the self-supervised DL method could obtain precise E-fields comparable to the FEM solutions with improved computational speed.

Devices and Technology in Transcranial Magnetic Stimulation: A Systematic Review

The technology for transcranial magnetic stimulation (TMS) has significantly changed over the years, with important improvements in the signal generators, the coils, the positioning systems, and the software for modeling, optimization, and therapy planning. In this systematic literature review (SLR), the evolution of each component of TMS technology is presented and analyzed to assess the limitations to overcome. This SLR was carried out following the PRISMA 2020 statement. Published articles of TMS were searched for in four databases (Web of Science, PubMed, Scopus, IEEE). Conference papers and other reviews were excluded. Records were filtered using terms about TMS technology with a semi-automatic software; articles that did not present new technology developments were excluded manually. After this screening, 101 records were included, with 19 articles proposing new stimulator designs (18.8%), 46 presenting or adapting coils (45.5%), 18 proposing systems for coil placement (17.8%), and 43 implementing algorithms for coil optimization (42.6%). The articles were blindly classified by the authors to reduce the risk of bias. However, our results could have been influenced by our research interests, which would affect conclusions for applications in psychiatric and neurological diseases. Our analysis indicates that more emphasis should be placed on optimizing the current technology with a special focus on the experimental validation of models. With this review, we expect to establish the base for future TMS technological developments.

EMvelop stimulation: minimally invasive deep brain stimulation using temporally interfering electromagnetic waves

OBJECTIVE

Recently, the temporal interference stimulation (TIS) technique for focal noninvasive deep brain stimulation (DBS) was reported. However, subsequent computational modeling studies on the human brain have shown that while TIS achieves higher focality of electric fields than state-of-the-art methods, further work is needed to improve the stimulation strength. Here, we investigate the idea of EMvelop stimulation, a minimally invasive DBS setup using temporally interfering gigahertz (GHz) electromagnetic (EM) waves. At GHz frequencies, we can create antenna arrays at the scale of a few centimeters or less that can be endocranially implanted to enable longitudinal stimulation and circumvent signal attenuation due to the scalp and skull. Furthermore, owing to the small wavelength of GHz EM waves, we can optimize both amplitudes and phases of the EM waves to achieve high intensity and focal stimulation at targeted regions within the safety limit for exposure to EM waves.

APPROACH

We develop a simulation framework investigating the propagation of GHz EM waves generated by line current antenna elements and the corresponding heat generated in the brain tissue. We propose two optimization flows to identify antenna current amplitudes and phases for either maximal intensity or maximal focality transmission of the interfering electric fields with EM waves safety constraint.

MAIN RESULTS

A representative result of our study is that with two endocranially implanted arrays of size 4.2 cm × 4.7 cm each, we can achieve an intensity of 12 V/m with a focality of 3.6 cm at a target deep in the brain tissue.

SIGNIFICANCE

In this proof-of-principle study, we show that the idea of EMvelop stimulation merits further investigation as it can be a minimally invasive way of stimulating deep brain targets and offers benefits not shared by prior methodologies of electrical or magnetic stimulation.

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.

TAP: targeting and analysis pipeline for optimization and verification of coil placement in transcranial magnetic stimulation

Objective.Transcranial magnetic stimulation (TMS) can modulate brain function via an electric field (E-field) induced in a brain region of interest (ROI). The ROI E-field can be computationally maximized and set to match a specific reference using individualized head models to find the optimal coil placement and stimulus intensity. However, the available software lacks many practical features for prospective planning of TMS interventions and retrospective evaluation of the experimental targeting accuracy.Approach.The TMS targeting and analysis pipeline (TAP) software uses an MRI/fMRI-derived brain target to optimize coil placement considering experimental parameters such as the subject's hair thickness and coil placement restrictions. The coil placement optimization is implemented in SimNIBS 3.2, for which an additional graphical user interface (TargetingNavigator) is provided to visualize/adjust procedural parameters. The coil optimization process also computes the E-field at the target, allowing the selection of the TMS device intensity setting to achieve specific E-field strengths. The optimized coil placement information is prepared for neuronavigation software, which supports targeting during the TMS procedure. The neuronavigation system can record the coil placement during the experiment, and these data can be processed in TAP to quantify the accuracy of the experimental TMS coil placement and induced E-field.Main results.TAP was demonstrated in a study consisting of three repetitive TMS sessions in five subjects. TMS was delivered by an experienced operator under neuronavigation with the computationally optimized coil placement. Analysis of the experimental accuracy from the recorded neuronavigation data indicated coil location and orientation deviations up to about 2 mm and 2°, respectively, resulting in an 8% median decrease in the target E-field magnitude compared to the optimal placement.Significance.TAP supports navigated TMS with a variety of features for rigorous and reproducible stimulation delivery, including planning and evaluation of coil placement and intensity selection for E-field-based dosing.

The effect of meninges on the electric fields in TES and TMS. Numerical modeling with adaptive mesh refinement

BACKGROUND

When modeling transcranial electrical stimulation (TES) and transcranial magnetic stimulation (TMS) in the brain, the meninges - dura, arachnoid, and pia mater - are often neglected due to high computational costs.

OBJECTIVE

We investigate the impact of the meningeal layers on the cortical electric field in TES and TMS while considering the headreco segmentation as the base model.

METHOD

We use T1/T2 MRI data from 16 subjects and apply the boundary element fast multipole method with adaptive mesh refinement, which enables us to accurately solve this problem and establish method convergence at reasonable computational cost. We compare electric fields in the presence and absence of various meninges for two brain areas (M1_HAND and DLPFC) and for several distinct TES and TMS setups.

RESULTS

Maximum electric fields in the cortex for focal TES consistently increase by approximately 30% on average when the meninges are present in the CSF volume. Their effect on the maximum field can be emulated by reducing the CSF conductivity from 1.65 S/m to approximately 0.85 S/m. In stark contrast to that, the TMS electric fields in the cortex are only weakly affected by the meningeal layers and slightly (∼6%) decrease on average when the meninges are included.

CONCLUSION

Our results quantify the influence of the meninges on the cortical TES and TMS electric fields. Both focal TES and TMS results are very consistent. The focal TES results are also in a good agreement with a prior relevant study. The solver and the mesh generator for the meningeal layers (compatible with SimNIBS) are available online.

Optimal Design of Transcranial Magnetic Stimulation Coil with Iron Core

OBJECTIVE

Iron core coils offer a passive way to increase the induced electric field intensity during transcranial magnetic stimulation (TMS), but the influences of core position and dimensions on coil performance have not been elaborately discussed before.

APPROACH

In this study, with the basic figure-of-eight (Fo8) and slinky coil structures, iron core coil optimization is performed with the finite element method considering core position and dimensions. A performance factor combining performance parameters, including the maximum induced electric field, stimulation depth, focus, and heat loss, is utilized to evaluate the comprehensive coil performance.

MAIN RESULTS

According to the performance factor, both iron core coils obtain the best overall performance with a fill factor 0.4 and the two legs of the iron core close to the inner sides of the coil. Finally, three prototypes are constructed-the basic, optimized, and full-size slinky iron core coil-and magnetic field detection demonstrates a good agreement with the simulation results.

SIGNIFICANCE

The proposed systematic optimization approach for iron core coil based on Fo8 and slinky basic structure can be applied to improve TMS coil performance, reduce power requirements, and guide the design of other iron core TMS coils.

Systematic numerical assessment of occupational exposure to electromagnetic fields of Transcranial Magnetic Stimulation

Purpose

This study aims to perform a classification and rigorous numerical evaluation of the risks of occupational exposure in the health environment related to the administration of transcranial magnetic stimulation (TMS) treatment. The study investigates the numerically estimated induced electric field that occurs in the human tissues of an operator caused by exposure to the variable magnetic field produced by TMS during treatments. This could be a useful starting point for future risk assessment studies and safety indications in this context.

Methods

We performed a review of the actual positions assumed by clinicians during TMS treatments. Three different TMS coils (two circular and one figure‐of‐eight) were modeled and characterized numerically. Different orientations and positions of each coil with respect to the body of the operator were investigated to evaluate the induced electric (‐E) field in the body tissues. The collected data were processed to allow comparison with the safety standards for occupational exposure, as suggested by the International Commission on Non‐Ionizing Radiation Protection (ICNIRP) 2010 guidelines.

Results

Under the investigated conditions, exposure to TMS shows some criticalities for the operator performing the treatment. Depending on the model of the TMS coil and its relative position with respect to the operator's body, the numerically estimated E‐field could exceed the limits suggested by the ICNIRP 2010 guidelines. We established that the worst‐case scenario for the three coils occurs when they are placed in correspondence of the abdomen, with the handle oriented parallel to the body (II orientation). Working at a maximum TMS stimulator output (MSO), the induced E‐field is up to 7.32 V/m (circular coil) and up to 1.34 V/m (figure‐of‐eight coil). The induced E‐field can be modulated by the TMS percentage of MSO (%MSO) and by the distance between the source and the operator. At %MSO equal to or below 80%, the figure‐of‐eight coil was compliant with the ICNIRP limit (1.13 V/m). Conversely, the circular coil causes an induced E‐field above the limits, even when powered at a %MSO of 30%. Thus, in the investigated worst‐case conditions, an operator working with a circular coil should keep a distance from its edge to be compliant with the guidelines limit, which depends on the selected %MSO: 38 cm at 100%, 32 cm at 80%, 26.8 cm at 50%, and 19.8 cm at 30%. Furthermore, attention should be paid to the induced E‐field reached in the operator's hand as the operator typically holds the coil by hand. In fact in the hand, we estimated an induced E‐field up to 10 times higher than the limits.

Conclusions

Our numerical results indicate that coil positions, orientations, and distances with respect to the operator's body can determine the levels of induced E‐field that exceed the ICNIRP limits. The induced E‐field is also modulated by the choice of %MSO, which is related to the TMS application. Even under the best exposure conditions, attention should be paid to the exposure of the hand. These findings highlight the need for future risk assessment studies to provide more safety information for the correct and safe use of TMS devices.

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.

Multi-scale modeling toolbox for single neuron and subcellular activity under Transcranial Magnetic Stimulation

BACKGROUND

Transcranial Magnetic Stimulation (TMS) is a widely used non-invasive brain stimulation method. However, its mechanism of action and the neural response to TMS are still poorly understood. Multi-scale modeling can complement experimental research to study the subcellular neural effects of TMS. At the macroscopic level, sophisticated numerical models exist to estimate the induced electric fields. However, multi-scale computational modeling approaches to predict TMS cellular and subcellular responses, crucial to understanding TMS plasticity inducing protocols, are not available so far.

OBJECTIVE

We develop an open-source multi-scale toolbox Neuron Modeling for TMS (NeMo-TMS) to address this problem.

METHODS

NeMo-TMS generates accurate neuron models from morphological reconstructions, couples them to the external electric fields induced by TMS, and simulates the cellular and subcellular responses of single-pulse and repetitive TMS.

RESULTS

We provide examples showing some of the capabilities of the toolbox.

CONCLUSION

NeMo-TMS toolbox allows researchers a previously not available level of detail and precision in realistically modeling the physical and physiological effects of TMS.

Precise Modulation Strategies for Transcranial Magnetic Stimulation: Advances and Future Directions

Transcranial magnetic stimulation (TMS) is a popular modulatory technique for the noninvasive diagnosis and therapy of neurological and psychiatric diseases. Unfortunately, current modulation strategies are only modestly effective. The literature provides strong evidence that the modulatory effects of TMS vary depending on device components and stimulation protocols. These differential effects are important when designing precise modulatory strategies for clinical or research applications. Developments in TMS have been accompanied by advances in combining TMS with neuroimaging techniques, including electroencephalography, functional near-infrared spectroscopy, functional magnetic resonance imaging, and positron emission tomography. Such studies appear particularly promising as they may not only allow us to probe affected brain areas during TMS but also seem to predict underlying research directions that may enable us to precisely target and remodel impaired cortices or circuits. However, few precise modulation strategies are available, and the long-term safety and efficacy of these strategies need to be confirmed. Here, we review the literature on possible technologies for precise modulation to highlight progress along with limitations with the goal of suggesting future directions for this field.

Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes

Objective. To formulate, validate, and apply an alternative to the finite element method (FEM) high-resolution modeling technique for electrical brain stimulation-the boundary element fast multipole method (BEM-FMM). To include practical electrode models for both surface and embedded electrodes.Approach. Integral equations of the boundary element method in terms of surface charge density are combined with a general-purpose fast multipole method and are expanded for voltage, shunt, current, and floating electrodes. The solution of coupled and properly weighted/preconditioned integral equations is accompanied by enforcing global conservation laws: charge conservation law and Kirchhoff's current law.Main results.A sub-percent accuracy is reported as compared to the analytical solutions and simple validation geometries. Comparison to FEM considering realistic head models resulted in relative differences of the electric field magnitude in the range of 3%-6% or less. Quantities that contain higher order spatial derivatives, such as the activating function, are determined with a higher accuracy and a faster speed as compared to the FEM. The method can be easily combined with existing head modeling pipelines such as headreco or mri2mesh.Significance.The BEM-FMM does not rely on a volumetric mesh and is therefore particularly suitable for modeling some mesoscale problems with submillimeter (and possibly finer) resolution with high accuracy at moderate computational cost. Utilizing Helmholtz reciprocity principle makes it possible to expand the method to a solution of EEG forward problems with a very large number of cortical dipoles.

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.