Conditions for numerically accurate TMS electric field simulation.

Area of Science:

• Computational neuroscience
• Biophysics
• Medical physics

Background:

• Computational simulations of electric fields (E-fields) in transcranial magnetic stimulation (TMS) are vital for understanding mechanisms and optimizing administration.
• A lack of characterization exists regarding the accuracy of these simulation methods and the factors influencing it.

Purpose of the Study:

• To systematically quantify numerical error in TMS E-field simulations.
• To provide guidelines for setting up accurate TMS simulations.

Main Methods:

• Benchmarking accuracy of common TMS E-field simulation methods: finite element method (FEM) with and without superconvergent patch recovery (SPR), boundary element method (BEM), and finite difference method (FDM).
• Evaluating coil modeling methods including magnetic and current dipoles.

Main Results:

• Achieving <2% cortical E-field error requires specific mesh densities: FDM/1st order FEM (<0.4 mm), 1st order SPR-FEM (<0.8 mm), BEM/2nd+ order FEM (<2.9 mm).
• Coil models need 200+ dipoles (magnetic) or 3000+ (current). Winding eddy currents may require modeling for thick coils >3 kHz.
• BEM, FDM, and FEM converge to the same solution; BEM and higher-order FEM achieve accuracy with lower mesh densities than FDM/1st order FEM.

Conclusions:

• BEM and higher-order FEM offer more efficient high-accuracy TMS E-field simulations compared to FDM and 1st order FEM.
• Appropriate coil modeling and mesh density are crucial for accurate TMS E-field simulations.
• Consideration of coil winding eddy currents is necessary in specific scenarios for precise modeling.