Computation of transcranial magnetic stimulation electric fields using self-supervised deep learning.

Journal Article (Journal Article)

Electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) can be modeled using partial differential equations (PDEs). Using state-of-the-art finite-element methods (FEM), it often takes tens of seconds to solve the PDEs for computing a high-resolution E-field, hampering the wide application of the E-field modeling in practice and research. To improve the E-field modeling's computational efficiency, we developed a self-supervised deep learning (DL) method to compute precise TMS E-fields. Given a head model and the primary E-field generated by TMS coils, a DL model was built to generate a E-field by minimizing a loss function that measures how well the generated E-field fits the governing PDE. The DL model was trained in a self-supervised manner, which does not require any external supervision. We evaluated the DL model using both a simulated sphere head model and realistic head models of 125 individuals and compared the accuracy and computational speed of the DL model with a state-of-the-art FEM. In realistic head models, the DL model obtained accurate E-fields that were significantly correlated with the FEM solutions. The DL model could obtain precise E-fields within seconds for whole head models at a high spatial resolution, faster than the FEM. The DL model built for the simulated sphere head model also obtained an accurate E-field whose average difference from the analytical E-fields was 0.0054, comparable to the FEM solution. These results demonstrated that the self-supervised DL method could obtain precise E-fields comparable to the FEM solutions with improved computational speed.

Full Text

Duke Authors

Cited Authors

  • Li, H; Deng, Z-D; Oathes, D; Fan, Y

Published Date

  • December 2022

Published In

Volume / Issue

  • 264 /

Start / End Page

  • 119705 -

PubMed ID

  • 36280099

Pubmed Central ID

  • PMC9854270

Electronic International Standard Serial Number (EISSN)

  • 1095-9572

International Standard Serial Number (ISSN)

  • 1053-8119

Digital Object Identifier (DOI)

  • 10.1016/j.neuroimage.2022.119705


  • eng