ArticleJournal of neural engineering2019
Comparative performance of the finite element method and the boundary element fast multipole method for problems mimicking transcranial magnetic stimulation (TMS).
Article in Journal of neural engineering, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 19 papers.
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Who cites it
19 citing papers in PubMed, 54 citations in OpenAlex.
- Charge based boundary element method with residual driven adaptive mesh refinement for high resolution electrical stimulation modeling.Scientific reports · 2026Article
- Involvement of aSPOC in the Online Updating of Reach-to-Grasp to Mechanical Perturbations of Hand Transport.The Journal of neuroscience : the official journal of the Society for Neuroscience · 2025Article
- Novel Volume Integral Equation Approach for Low-Frequency E-Field Dosimetry of Transcranial Magnetic Stimulation.IEEE transactions on magnetics · 2024Article
- A survey on integral equations for bioelectric modeling.Physics in medicine and biology · 2024Review
- A review of algorithms and software for real-time electric field modeling techniques for transcranial magnetic stimulation.Biomedical engineering letters · 2024Review
- A fast direct solver for surface-based whole-head modeling of transcranial magnetic stimulation.Scientific reports · 2023Article
- A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields.Brain sciences · 2023Review
- Pinpointing the precise stimulation targets for brain rehabilitation in early-stage Parkinson's disease.BMC neuroscience · 2023Article
- Bioelectromagnetism in Human Brain Research: New Applications, New Questions.The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry · 2023Review
- Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning.NeuroImage · 2022Article
- Devices and Technology in Transcranial Magnetic Stimulation: A Systematic Review.Brain sciences · 2022Review
- Precise Modulation Strategies for Transcranial Magnetic Stimulation: Advances and Future Directions.Neuroscience bulletin · 2021Review
- Boundary element fast multipole method for modeling electrical brain stimulation with voltage and current electrodes.Journal of neural engineering · 2021Article
- Rapid computation of TMS-induced E-fields using a dipole-based magnetic stimulation profile approach.NeuroImage · 2021Article
- Boundary Element Fast Multipole Method for Enhanced Modeling of Neurophysiological Recordings.IEEE transactions on bio-medical engineering · 2021Article
- Article
- A 3-axis coil design for multichannel TMS arrays.NeuroImage · 2021Article
- How conductivity boundaries influence the electric field induced by transcranial magnetic stimulation in in vitro experiments.Brain stimulationArticle
- Conditions for numerically accurate TMS electric field simulation.Brain stimulationArticle
Corrections and comments
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Authors and funding
6 authors at 3 institutions in 2 countries.
Funding
Abstract
objectiveA study pertinent to the numerical modeling of cortical neurostimulation is conducted in an effort to compare the performance of the finite element method (FEM) and an original formulation of the boundary element fast multipole method (BEM-FMM) at matched computational performance metrics. APPROACH: We consider two problems: (i) a canonic multi-sphere geometry and an external magnetic-dipole excitation where the analytical solution is available and; (ii) a problem with realistic head models excited by a realistic coil geometry. In the first case, the FEM algorithm tested is a fast open-source getDP solver running within the SimNIBS 2.1.1 environment. In the second case, a high-end commercial FEM software package ANSYS Maxwell 3D is used. The BEM-FMM method runs in the MATLAB MAIN
resultsIn the first case, we observe that the BEM-FMM algorithm gives a smaller solution error for all mesh resolutions and runs significantly faster for high-resolution meshes when the number of triangular facets exceeds approximately 0.25 M. We present other relevant simulation results such as volumetric mesh generation times for the FEM, time necessary to compute the potential integrals for the BEM-FMM, and solution performance metrics for different hardware/operating system combinations. In the second case, we observe an excellent agreement for electric field distribution across different cranium compartments and, at the same time, a speed improvement of three orders of magnitude when the BEM-FMM algorithm used. SIGNIFICANCE: This study may provide a justification for anticipated use of the BEM-FMM algorithm for high-resolution realistic transcranial magnetic stimulation scenarios.
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Registered trials
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.