Coil optimisation for transcranial magnetic stimulation in realistic head geometry

Lari M. Koponen*, Jaakko O. Nieminen, Tuomas P. Mutanen, Matti Stenroos, Risto J. Ilmoniemi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)


Background Transcranial magnetic stimulation (TMS) allows focal, non-invasive stimulation of the cortex. A TMS pulse is inherently weakly coupled to the cortex; thus, magnetic stimulation requires both high current and high voltage to reach sufficient intensity. These requirements limit, for example, the maximum repetition rate and the maximum number of consecutive pulses with the same coil due to the rise of its temperature. Objective To develop methods to optimise, design, and manufacture energy-efficient TMS coils in realistic head geometry with an arbitrary overall coil shape. Methods We derive a semi-analytical integration scheme for computing the magnetic field energy of an arbitrary surface current distribution, compute the electric field induced by this distribution with a boundary element method, and optimise a TMS coil for focal stimulation. Additionally, we introduce a method for manufacturing such a coil by using Litz wire and a coil former machined from polyvinyl chloride. Results We designed, manufactured, and validated an optimised TMS coil and applied it to brain stimulation. Our simulations indicate that this coil requires less than half the power of a commercial figure-of-eight coil, with a 41% reduction due to the optimised winding geometry and a partial contribution due to our thinner coil former and reduced conductor height. With the optimised coil, the resting motor threshold of abductor pollicis brevis was reached with the capacitor voltage below 600 V and peak current below 3000 A. Conclusion The described method allows designing practical TMS coils that have considerably higher efficiency than conventional figure-of-eight coils.

Original languageEnglish
Pages (from-to)795-805
Number of pages11
JournalBrain stimulation
Issue number4
Publication statusPublished - 1 Jul 2017

Bibliographical note

Funding Information:
This work was supported by the Finnish Cultural Foundation and the Academy of Finland (Decisions No. 255347, 265680, and 294625).

Publisher Copyright:
© 2017 Elsevier Inc.


  • Boundary element method
  • Coil design
  • Induced electric field
  • Optimization
  • Transcranial magnetic stimulation

ASJC Scopus subject areas

  • Biophysics
  • General Neuroscience
  • Clinical Neurology


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