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

Area of Science:

• Computational neuroscience
• Medical physics
• Artificial intelligence

Background:

• Modeling electric fields (E-fields) induced by transcranial magnetic stimulation (TMS) is crucial for understanding its effects.
• Current finite-element methods (FEM) for solving the governing partial differential equations (PDEs) are computationally intensive, taking tens of seconds.
• This computational burden hinders the widespread adoption of E-field modeling in TMS research and practice.

Purpose of the Study:

• To develop a computationally efficient method for precise TMS E-field modeling.
• To introduce a self-supervised deep learning (DL) approach for accelerated E-field computation.
• To validate the accuracy and speed of the DL method against established FEM.

Main Methods:

• A self-supervised deep learning (DL) model was developed to predict TMS E-fields.
• The DL model was trained by minimizing a loss function ensuring adherence to the governing partial differential equations (PDEs).
• The DL model was evaluated on both a simulated spherical head model and realistic head models from 125 individuals, comparing results against FEM.

Main Results:

• The DL model achieved high accuracy, with E-field solutions significantly correlated with FEM results in realistic head models.
• The DL method computed precise E-fields for whole head models in seconds, outperforming FEM in speed.
• For a simulated sphere model, the DL method's E-field accuracy was comparable to FEM, with an average difference of 0.0054 from analytical solutions.

Conclusions:

• The self-supervised DL method offers a significant improvement in computational speed for TMS E-field modeling.
• The DL approach provides precise E-field calculations comparable in accuracy to FEM.
• This accelerated modeling has the potential to broaden the application of TMS E-field analysis in research and clinical settings.