VoxHenry: FFT-Accelerated Inductance Extraction for Voxelized Geometries

Yücel, Abdulkadir C.; Georgakis, Ioannis P.; Polimeridis, Athanasios G.; Bağcı, Hakan; White, Jacob K.

doi:10.1109/tmtt.2017.2785842

Cited by 35 publications

(37 citation statements)

References 19 publications

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“…The currents flowing through the coil windings were determined by solving the current continuity equation via FEM. Additionally, eddy-current effects were modeled using a time-harmonic partial-element equivalent circuit method [21] developed in-house (details provided in the Supplement). We computed the primary Efield generated by the coil inside the spherical head region (i.e.…”

Section: Coil Modelingmentioning

confidence: 99%

“…Because of their small cross-section most TMS modeling frameworks assume that the currents flow uniformly through the wire [18e20]. However, the eddy currents cause the currents to redistribute and concentrate toward the wire surface [21]. Neglecting this eddy-current redistribution can potentially result in errors of the predicted primary E-field.…”

Section: Introductionmentioning

confidence: 99%

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Conditions for numerically accurate TMS electric field simulation

2020

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Background: Computational simulations of the E-field induced by transcranial magnetic stimulation (TMS) are increasingly used to understand its mechanisms and to inform its administration. However, characterization of the accuracy of the simulation methods and the factors that affect it is lacking. Objective: To ensure the accuracy of TMS E-field simulations, we systematically quantify their numerical error and provide guidelines for their setup. Method: We benchmark the accuracy of computational approaches that are commonly used for TMS Efield simulations, including the finite element method (FEM) with and without superconvergent patch recovery (SPR), boundary element method (BEM), finite difference method (FDM), and coil modeling methods. Results: To achieve cortical E-field error levels below 2%, the commonly used FDM and 1st order FEM require meshes with an average edge length below 0.4 mm, 1st order SPR-FEM requires edge lengths below 0.8 mm, and BEM and 2nd (or higher) order FEM require edge lengths below 2.9 mm. Coil models employing magnetic and current dipoles require at least 200 and 3000 dipoles, respectively. For thick solid-conductor coils and frequencies above 3 kHz, winding eddy currents may have to be modeled. Conclusion: BEM, FDM, and FEM all converge to the same solution. Compared to the common FDM and 1st order FEM approaches, BEM and 2nd (or higher) order FEM require significantly lower mesh densities to achieve the same error level. In some cases, coil winding eddy-currents must be modeled. Both electric current dipole and magnetic dipole models of the coil current can be accurate with sufficiently fine discretization.

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Section: Coil Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Conditions for numerically accurate TMS electric field simulation

2020

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“…The currents flowing through the coil windings were determined by solving the current continuity equation via FEM. Additionally, eddy-current effects were modeled using a timeharmonic partial-element equivalent circuit method [14] developed in-house (details provided as supplementary material). We computed the primary E-field generated by the coil inside the spherical head region using a first order accurate quadrature for each tetrahedron of the coil mesh.…”

Section: Coil Modelingmentioning

confidence: 99%

“…(S. 14) We solve Eqs. S.13-S.14 by first approximating the coil winding as a mesh consisting of tetrahedral elements.…”

Section: Coil Eddy Current Solvermentioning

confidence: 99%

“…Because of their small cross-section most TMS modeling frameworks assume that the currents flow uniformly through the wire [11][12][13]. However, the eddy currents cause the currents to redistribute and concentrate toward the wire surface [14]. Neglecting this eddy-current redistribution can potentially result in errors of the predicted primary E-field.…”

Section: Introductionmentioning

confidence: 99%

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Conditions for numerically accurate TMS electric field simulation

Gomez

Dannhauer

Koponen

et al. 2018

Preprint

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HIGHLIGHTS FDM and 1st order FEM with 1.5 mm average mesh edge length have numerical errors above 7%. BEM or 2nd order FEM are most efficient for achieving numerical errors < 2%.  Coil wire cross-section must be accounted to achieve E-field errors below < 2%. Coil eddy currents can account for > 2% of E-field when very brief pulses are used. ABSTRACTBackground: Computational simulations of the E-field induced by transcranial magnetic stimulation (TMS) are increasingly used to understand its mechanisms and to inform its administration. However, characterization of the accuracy of the simulation methods and the factors that affect it is lacking.Objective: To ensure the accuracy of TMS E-field simulations, we systematically quantify their numerical error and provide guidelines for their setup. Method:We benchmark the accuracy of computational approaches that are commonly used for TMS E-field simulations, including the finite element method (FEM), boundary element method (BEM), finite difference method (FDM), and coil modeling methods. Results:To achieve cortical E-field error levels below 2%, the commonly used FDM and 1 st order FEM require meshes with an average edge length below 0.4 mm, whereas BEM and 2 nd (or higher) order FEM require edge lengths below 1.5 mm, which is more practical. Coil models employing magnetic and current dipoles require at least 200 and 3,000 dipoles, respectively. For thick solid-conductor coils and frequencies above 3 kHz, winding eddy currents may have to be modeled.Conclusion: BEM, FDM, and FEM methods converge to the same solution. However, FDM and 1 st order FEM converge slowly with increasing mesh resolution; therefore, the use of BEM or 2 nd (or higher) order FEM is recommended. In some cases, coil 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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