How the brain tissue shapes the electric field induced by transcranial magnetic stimulation

Alexander Opitz, Mirko Windhoff, Robin M. Heidemann, Robert Turner, Axel Thielscher

Research output: Contribution to journalArticlepeer-review

195 Scopus citations


In transcranial magnetic stimulation (TMS), knowledge of the distribution of the induced electric field is fundamental for a better understanding of the position and extent of the stimulated brain region. However, the different tissue types and the varying fibre orientation in the brain tissue result in an inhomogeneous and anisotropic conductivity distribution and distort the electric field in a non-trivial way. Here, the field induced by a figure-8 coil is characterized in detail using finite element calculations and a geometrically accurate model of an individual head combined with high-resolution diffusion-weighted imaging for conductivity mapping. It is demonstrated that the field strength is significantly enhanced when the currents run approximately perpendicular to the local gyral orientation. Importantly, the spatial distribution of this effect differs distinctly between gray matter (GM) and white matter (WM): While the field in GM is selectively enhanced at the gyral crowns and lips, high field strengths can still occur rather deep in WM. Taking the anisotropy of brain tissue into account tends to further boost this effect in WM, but not in GM. Spatial variations in the WM anisotropy affect the local field strength in a systematic way and result in localized increases of up to 40% (on average ~. 7% for coil orientations perpendicular to the underlying gyri). We suggest that these effects might create hot spots in WM that might contribute to the excitation of WM structures by TMS. However, our results also demonstrate the necessity of using realistic nerve models in the future to allow for more definitive conclusions.

Original languageEnglish (US)
Pages (from-to)849-859
Number of pages11
Issue number3
StatePublished - Oct 1 2011

Bibliographical note

Funding Information:
The authors would like to thank the Max Planck Society for financial support, in particular Heinrich H. Bülthoff for encouragement of this study. We thankfully acknowledge the initial help of Alexandra Reichenbach in setting up the DTI analysis. We deeply appreciate the help of Alfred Anwander (MPI for Human Cognitive and Brain Sciences) when pre-processing the high-resolution DW data. The support of Yves Renard when implementing the field equations in GetFEM++ is gratefully acknowledged.


  • Conductivity anisotropy
  • Diffusion-weighted imaging
  • Electric field calculation
  • Finite element method
  • High field magnetic resonance imaging
  • Transcranial magnetic stimulation


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