Cortical surface electric field estimation for real-time TMS with graph neural networks

<i>Objective.</i>Transcranial magnetic stimulation is a non-invasive neurostimulation and neuromodulation technique that induces electric fields (<i>E</i>-fields) in the brain via a coil placed over the scalp. Our objective is to develop a real-time estimation method for the<i>E</i>-field on the cortical surface from a subject's three-dimensional (3D) head magnetic Resonance (MR) image without constructing a 3D anatomical head model.<i>Approach.</i>A cortical mesh was generated using an existing deep learning-based cortical surface reconstruction method. The proposed method then estimates the<i>E</i>-field on that surface by utilizing a graph neural network (GNN) that has the same topological structure as a two-dimensional (2D) cortical surface mesh. The GNN operates in conjunction with a U-Net, which extracts multiscale features from a volumetric head MR image. By restricting the estimation of the<i>E</i>-field to a 2D surface, the proposed method achieved efficient and accelerated computation.<i>Main Results.</i>The proposed method achieves<i>E</i>-field estimation in 29 ms per coil configuration on the tested hardware, which is much faster than conventional existing simulation-based and deep learning-based methods. In addition, it achieves higher accuracy in estimating the<i>E</i>-field compared to conventional voxel-wise<i>E</i>-field estimation.<i>Significance.</i>The proposed method enables the real-time estimation of the<i>E</i>-field on the cortical surface without constructing a 3D anatomical head model or requiring extensive preprocessing such as tissue segmentation and volume mesh generation. Real-time<i>E</i>-field estimation is valuable for clinical applications, such as determining coil placement and helping to ensure that the intended target region is stimulated.