ArticleBrain stimulation
Conditions for numerically accurate TMS electric field simulation.
Article in Brain stimulation. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 49 papers, 1 of them a synthesis that pooled it.
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Who cites it
49 citing papers in PubMed, 1 synthesis or guideline pooled it.
- Outcome measures for electric field modeling in tES and TMS: A systematic review and large-scale modeling study.NeuroImage · 2023Pooled it
- Precision in Delivery, Variability in Response: A Multiscale Mechanistic Framework for Neuronavigated Transcranial Magnetic Stimulation.Brain sciences · 2026Review
- Charge based boundary element method with residual driven adaptive mesh refinement for high resolution electrical stimulation modeling.Scientific reports · 2026Article
- How Standardized Is Transcranial Magnetic Stimulation Treatment for Depression? Large-Cohort Modeling Reveals Systematic Dosimetric Variability.Psychotherapy and psychosomatics · 2026Article
- Standardizing TMS Intensity Across Different Coils Using Individualized Electric Field Modeling.Human brain mapping · 2026Article
- High-Resolution EEG Source Reconstruction from PCA-Corrected BEM-FMM Reciprocal Basis Funcions: A Study with Visual Evoked Potentials from Intermittent Photic Stimulation.bioRxiv : the preprint server for biology · 2025Article
- Comprehensive evaluation of U-Net based transcranial magnetic stimulation electric field estimations.Scientific reports · 2025Article
- Real-time computation of brain E-field for enhanced transcranial magnetic stimulation neuronavigation and optimization.Imaging neuroscience (Cambridge, Mass.) · 2025Article
- Highly accurate calculation of electric field for transcranial magnetic stimulation using hybridizable discontinuous galerkin method.Scientific reports · 2024Article
- Novel Volume Integral Equation Approach for Low-Frequency E-Field Dosimetry of Transcranial Magnetic Stimulation.IEEE transactions on magnetics · 2024Article
- Improving EEG Forward Modeling Using High-Resolution Five-Layer BEM-FMM Head Models: Effect on Source Reconstruction Accuracy.Bioengineering (Basel, Switzerland) · 2024Article
- A survey on integral equations for bioelectric modeling.Physics in medicine and biology · 2024Review
- A semi-automated pipeline for finite element modeling of electric field induced in nonhuman primates by transcranial magnetic stimulation.Journal of neuroscience methods · 2024Article
- Quasistatic approximation in neuromodulation.Journal of neural engineering · 2024Review
- Model-based analysis of the acute effects of transcutaneous magnetic spinal cord stimulation on micturition after spinal cord injury in humans.PLoS computational biology · 2024Article
- A review of algorithms and software for real-time electric field modeling techniques for transcranial magnetic stimulation.Biomedical engineering letters · 2024Review
- Electric Field Modeling in Personalizing Transcranial Magnetic Stimulation Interventions.Biological psychiatry · 2024Review
- An adaptive h-refinement method for the boundary element fast multipole method for quasi-static electromagnetic modeling.Physics in medicine and biology · 2024Article
- Efficacy of transcranial magnetic stimulation treatment in reducing neuropsychiatric symptomatology after traumatic brain injury.Frontiers in neurology · 2024Article
- Fast and accurate computational E-field dosimetry for group-level transcranial magnetic stimulation targeting.Computers in biology and medicine · 2023Article
Corrections and comments
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Authors and funding
4 authors.
Funding
Abstract
backgroundComputational simulations of the E-field induced by transcranial magnetic stimulation (TMS) are increasingly used to understand its mechanisms and to inform its administration. However, characterization of the accuracy of the simulation methods and the factors that affect it is lacking.
objectiveTo ensure the accuracy of TMS E-field simulations, we systematically quantify their numerical error and provide guidelines for their setup.
methodWe benchmark the accuracy of computational approaches that are commonly used for TMS E-field simulations, including the finite element method (FEM) with and without superconvergent patch recovery (SPR), boundary element method (BEM), finite difference method (FDM), and coil modeling methods.
resultsTo achieve cortical E-field error levels below 2%, the commonly used FDM and 1st order FEM require meshes with an average edge length below 0.4 mm, 1st order SPR-FEM requires edge lengths below 0.8 mm, and BEM and 2nd (or higher) order FEM require edge lengths below 2.9 mm. Coil models employing magnetic and current dipoles require at least 200 and 3000 dipoles, respectively. For thick solid-conductor coils and frequencies above 3 kHz, winding eddy currents may have to be modeled.
conclusionBEM, FDM, and FEM all converge to the same solution. Compared to the common FDM and 1st order FEM approaches, BEM and 2nd (or higher) order FEM require significantly lower mesh densities to achieve the same error level. In some cases, coil winding eddy-currents must be modeled. Both electric current dipole and magnetic dipole models of the coil current can be accurate with sufficiently fine discretization.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.