ArticleBiophysical journal2018
Coupling Magnetically Induced Electric Fields to Neurons: Longitudinal and Transverse Activation.
Article in Biophysical journal, 2018. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 31 papers.
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Who cites it
31 citing papers in PubMed.
- Mechanisms of transcranial magnetic brain stimulation.Physiological reviews · 2026Review
- Histologically Informed Multiscale Modeling of the Neuronal Elements Activated by TMS.bioRxiv : the preprint server for biology · 2026Article
- Magnetoelectric Nanoparticle-Based Wireless Brain-Computer Interface: Underlying Physics and Projected Technology Pathway.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2026Article
- A coupling model of transcranial magnetic stimulation induced electric fields to neural state variables.PLoS computational biology · 2026Article
- Effects of transcranial alternating current stimulation on Spike train correlation in two-compartment model neurons.Biological cybernetics · 2025Article
- Simulation of evoked responses to transcranial magnetic stimulation using a multiscale cortical circuit model.bioRxiv : the preprint server for biology · 2025Article
- A survey on integral equations for bioelectric modeling.Physics in medicine and biology · 2024Review
- Quasistatic approximation in neuromodulation.Journal of neural engineering · 2024Review
- Transparent and Conformal Microcoil Arrays for Spatially Selective Neuronal Activation.Device · 2024Article
- Cellular mechanisms underlying carry-over effects after magnetic stimulation.Scientific reports · 2024Article
- Estimations of Charge Deposition Onto Convoluted Axon Surfaces Within Extracellular Electric Fields.IEEE transactions on bio-medical engineering · 2024Article
- A Review of Formulations, Boundary Value Problems and Solutions for Numerical Computation of Transcranial Magnetic Stimulation Fields.Brain sciences · 2023Review
- Rapid estimation of cortical neuron activation thresholds by transcranial magnetic stimulation using convolutional neural networks.NeuroImage · 2023Article
- Intensity- and frequency-specific effects of transcranial alternating current stimulation are explained by network dynamics.bioRxiv : the preprint server for biology · 2023Article
- Microglial Cytokines Mediate Plasticity Induced by 10 Hz Repetitive Magnetic Stimulation.The Journal of neuroscience : the official journal of the Society for Neuroscience · 2023Article
- A C-shaped miniaturized coil for transcranial magnetic stimulation in rodents.Journal of neural engineering · 2023Article
- Directional sensitivity of cortical neurons towards TMS-induced electric fields.Imaging neuroscience (Cambridge, Mass.) · 2023Article
- Transcranial magnetic stimulation of the brain: What is stimulated? - A consensus and critical position paper.Clinical neurophysiology : official journal of the International Federation of Clinical Neurophysiology · 2022Review
- Effects of transcranial alternating current stimulation on spiking activity in computational models of single neocortical neurons.NeuroImage · 2022Article
- Finding the Location of Axonal Activation by a Miniature Magnetic Coil.Frontiers in computational neuroscience · 2022Article
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3 authors.
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Abstract
We present a theory and computational models to couple the electric field induced by magnetic stimulation to neuronal membranes. Based on the characteristics of magnetically induced electric fields and the modified cable equation that we developed previously, quasipotentials are derived as a simple and accurate approximation for coupling of the electric fields to neurons. The conventional and modified cable equations are used to simulate magnetic stimulation of long peripheral nerves by circular and figure-8 coils. Activation thresholds are obtained over a range of lateral and vertical coil positions for two nonlinear membrane models representing unmyelinated and myelinated straight axons and also for undulating myelinated axons. For unmyelinated straight axons, the thresholds obtained with the modified cable equation are significantly lower due to transverse polarization, and the spatial distributions of thresholds as a function of coil position differ significantly from predictions by the activating function. However, the activation thresholds of unmyelinated axons obtained with either cable equation are very high and beyond the output capabilities of conventional magnetic stimulators. For myelinated axons, threshold values are similar for both cable equations and within the range of magnetic stimulators. Whereas the transverse field contributes negligibly to the activation thresholds of myelinated fibers, axonal undulation can significantly increase or decrease thresholds depending on coil position. The analysis provides a rigorous theoretical foundation and implementation methods for the use of the cable equation to model neuronal response to magnetically induced electric fields. Experimentally observed stimulation with the electric fields perpendicular to the nerve trunk cannot be explained by transverse polarization and is likely due to nerve fiber undulation and other geometrical inhomogeneities.
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