Minimum-energy coils for transcranial magnetic stimulation: Application to focal stimulation

Lari M. Koponen*, Jaakko O. Nieminen, Risto J. Ilmoniemi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)
52 Downloads (Pure)


Background In transcranial magnetic stimulation (TMS), the stimulation-coil current is typically increased from 0 to over 5000 A in less than 100 μs. At the peak current, the energy stored in the magnetic field is over 300 J. Thus, the average power during a pulse exceeds 3 MW; the stimulator needs to be built from high-power electronics. The power requirements often limit the duration and frequency of repetitive TMS, for example, via coil heating.

Objective We introduce a method for finding the minimum-energy solution for a TMS coil with given focality constraints.

Methods This optimization is performed by using a spherically symmetric head model and by expressing the coil as a continuous surface current density, which is eventually discretized to form the coil windings. For the optimization, we defined TMS focality separately for the directions parallel and perpendicular to the field direction at the maximum of induced electric field.

Results The computational model used for optimization was verified by manufacturing a prototype coil and measuring the electric field it induces in a spherically symmetric conductor. The optimized coil design requires significantly less power than existing TMS coil designs (a 73% reduction compared to an existing TMS coil with similar focality).

Conclusion The described method allows for more efficient, more focal TMS coils, which may reduce coil heating and the coil click.

Original languageEnglish
Pages (from-to)124-134
Number of pages11
JournalBrain stimulation
Issue number1
Publication statusPublished - 1 Jan 2015

Bibliographical note

Funding Information:
This research received funding from the Academy of Finland (Decisions No. 255347 and 265680 ). Conflict of interest statement: Risto Ilmoniemi is an advisor and a minority shareholder of Nexstim Ltd. The other authors declare no conflict of interest.

Publisher Copyright:
© 2015 Elsevier Inc. All rights reserved.


  • Coil design
  • Focality
  • Minimum-energy
  • Optimization
  • Spherical harmonics
  • TMS
  • Transcranial magnetic stimulation

ASJC Scopus subject areas

  • Biophysics
  • Neuroscience(all)
  • Clinical Neurology


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