Rapid whole-brain electric field mapping in transcranial magnetic stimulation using deep learning

Abstract

Transcranial magnetic stimulation (TMS) is a non-invasive neurostimulation technique that is increasingly used in the treatment of neuropsychiatric disorders and neuroscience research. Due to the complex structure of the brain and the electrical conductivity variation across subjects, identification of subject-specific brain regions for TMS is important to improve the treatment efficacy and understand the mechanism of treatment response. Numerical computations have been used to estimate the stimulated electric field (E-field) by TMS in brain tissue. But the relative long computation time limits the application of this approach. In this paper, we propose a deep-neural-network based approach to expedite the estimation of whole-brain E-field by using a neural network architecture, named 3D-MSResUnet and multimodal imaging data. The 3D-MSResUnet network integrates the 3D U-net architecture, residual modules and a mechanism to combine multi-scale feature maps. It is trained using a large dataset with finite element method (FEM) based E-field and diffusion magnetic resonance imaging (MRI) based anisotropic volume conductivity or anatomical images. The performance of 3D-MSResUnet is evaluated using several evaluation metrics and different combinations of imaging modalities and coils. The experimental results show that the output E-field of 3D-MSResUnet provides reliable estimation of the E-field estimated by the state-of-the-art FEM method with significant reduction in prediction time to about 0.24 second. Thus, this study demonstrates that neural networks are potentially useful tools to accelerate the prediction of E-field for TMS targeting.

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

“…Instead of solving the governing PDEs from scratch, recently studies have demonstrated promising performance of deep neural networks for rapid estimation of E-fields (Xu et al, 2021;Yokota et al, 2019), in which deep neural networks are trained to directly predict the E-fields with high fidelity to those estimated using conventional E-field modeling methods, such as FEMs. Therefore, the deep neural networks are actually trained to predict the solutions obtained by the conventional E-field modeling methods and their performance is bounded by the conventional E-field modeling methods used for generating training data.…”

“…Inspired by self-supervised deep learning methods (Geneva and Zabaras, 2020;Guo et al, 2020;Li et al, 2021;Fan, 2018, 2020;Qin et al, 2019;Raissi et al, 2019;Rao et al, 2021;Tian et al, 2020;Winovich et al, 2019;Yang and Perdikaris, 2019;Zhu et al, 2019) and the pioneer deep learning based E-field computation methods (Xu et al, 2021;Yokota et al, 2019), we develop a novel selfsupervised deep learning based TMS E-field modeling method to obtain precise high-resolution E-fields.…”

“…Faster E-field modeling is achievable by using a dipole-based magnetic stimulation profile approach that has to compute a magnetic stimulation profile for each individual subject with several hours of CPU time (Daneshzand et al, 2021) or to compute the E-field only on sparse points or the mean of the E-field in a region of interest (ROI) by leveraging the reciprocity principle (Gomez et al, 2021; Koponen et al, 2019). Recent studies have demonstrated that superfast high-resolution E-field modeling can be achieved using deep neural networks (DNNs) (Xu et al, 2021; Yokota et al, 2019). Particularly, the magnitude of E-fields was estimated based on individualized MRI head scans and TMS coil positions by DNNs (Yokota et al, 2019), and 3D vector E-fields were predicted using deep DNNs by integrating both individualized neuroanatomy (scalar-valued tissue conductivity or anisotropic conductivity tensors) and primary E-fields generated by TMS coils as the input (Xu et al, 2021).…”

“…Recent studies have demonstrated that superfast high-resolution E-field modeling can be achieved using deep neural networks (DNNs) (Xu et al, 2021; Yokota et al, 2019). Particularly, the magnitude of E-fields was estimated based on individualized MRI head scans and TMS coil positions by DNNs (Yokota et al, 2019), and 3D vector E-fields were predicted using deep DNNs by integrating both individualized neuroanatomy (scalar-valued tissue conductivity or anisotropic conductivity tensors) and primary E-fields generated by TMS coils as the input (Xu et al, 2021). Though promising results have been obtained, the existing deep learning (DL) based models were driven and optimized in a supervised learning setting.…”

“…Therefore, their accuracy would be bounded by the conventional numerical methods used to generate the training data. Inspired by self-supervised deep learning methods (Geneva and Zabaras, 2020; Guo et al, 2020; Li et al, 2021; Li and Fan, 2018, 2020; Qin et al, 2019; Raissi et al, 2019; Rao et al, 2021; Tian et al, 2020; Winovich et al, 2019; Yang and Perdikaris, 2019; Zhu et al, 2019) and the pioneer deep learning based E-field computation methods (Xu et al, 2021; Yokota et al, 2019), we develop a novel self-supervised deep learning based TMS E-field modeling method to obtain precise high-resolution E-fields. Specially, given a head model and the primary E-field generated by TMS coil, a DL model is built to generate the electric scalar potential by minimizing a loss function that measures how well the generated electric scalar potential fits the governing PDE, from which the E-field can be derived directly.…”