Modeling transcranial magnetic stimulation coil with magnetic cores

Area of Science:

• Biomedical Engineering
• Computational Electromagnetics

Background:

• Accurate modeling of transcranial magnetic stimulation (TMS) coils, particularly those with magnetic cores, remains a challenge for existing simulation software.
• Commercial solvers often lack specific field outputs (e.g., induced electric field) and struggle with realistic head models.
• Many open-source TMS software packages do not account for magnetic core properties.

Purpose of the Study:

• To develop and validate an algorithm for accurately modeling TMS coils incorporating nonlinear magnetic cores.
• To enable the calculation of coil inductances with and without magnetic cores.
• To facilitate model-informed design and material selection for more efficient TMS systems.

Main Methods:

• Utilizes the boundary element fast multipole method for a single-state solution of the core mesh.
• Employs the successive substitution method for nonlinear convergence of core states.
• Solves the coil-core interaction once before integrating the head model, using precomputed core magnetization for electric field calculation.

Main Results:

• The solver shows excellent convergence for typical TMS field strengths and analytical B-H approximations.
• Achieves typical execution times of 1-3 minutes on a standard multicore workstation.
• Computed inductance values closely match results from ANSYS Maxwell and experimental measurements (within 5% for a rodent TMS coil).

Conclusions:

• The developed algorithm accurately models TMS coils with magnetic cores, addressing a significant gap in current simulation capabilities.
• The software package aids in designing more efficient TMS systems and selecting appropriate core materials.
• These models can also improve the understanding and application of existing clinical TMS devices with magnetic cores.