Advanced Pipeline for Designing Multi-Locus TMS Coils with Current Density Constraints

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Objective: This work aims for a method to design manufacturable windings for transcranial magnetic stimulation (TMS) coils with fine control over the induced electric field (E-field) distributions. Such TMS coils are required for multi-locus TMS (mTMS). Methods: We introduce a new mTMS coil design workflow with increased flexibility in target E-field definition and faster computations compared to our previous method. We also incorporate custom current density and E-field fidelity constraints to ensure that the target E-fields are accurately reproduced with feasible winding densities in the resulting coil designs. We validated the method by designing, manufacturing, and characterizing a 2-coil mTMS transducer for focal rat brain stimulation. Results: Applying the constraints reduced the computed maximum surface current densities from 15.4 and 6.6 kA/mm to the target value 4.7 kA/mm, yielding winding paths suitable for a 1.5-mm-diameter wire with 7-kA maximum currents while still replicating the target E-fields with the predefined 2.8% maximum error in the FOV. The optimization time was reduced by two thirds compared to our previous method. Conclusion: The developed method allowed us to design a manufacturable, focal 2-coil mTMS transducer for rat TMS impossible to attain with our previous design workflow. Significance: The presented workflow enables considerably faster design and manufacturing of previously unattainable mTMS transducers with increased control over the induced E-field distribution and winding density, opening new possibilities for brain research and clinical TMS.

Original languageEnglish
Pages (from-to)2025-2034
Number of pages10
JournalIEEE Transactions on Biomedical Engineering
Issue number7
Early online date2023
Publication statusPublished - 1 Jul 2023
MoE publication typeA1 Journal article-refereed


  • Coil design
  • coil optimization
  • Coils
  • Current density
  • current density
  • mTMS
  • multi-locus TMS
  • Optimization
  • TMS
  • transcranial magnetic stimulation
  • Transcranial magnetic stimulation
  • Transducers
  • Windings
  • Wires


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