A Deep Neural Network Model for Predicting Electric Fields Induced by Transcranial Magnetic Stimulation Coil

Abstract

This article proposes a deep neural network (DNN) model to predict the electric field induced by a transcranial magnetic stimulation (TMS) coil under high-amplitude and low-frequency current pulse conditions. The DNN model is comprised of an input layer with 6 neurons, three non-linear hidden layers with a total of 1088 neurons, and a linear single output layer. The model is developed in Google Colaboratory environment with TensorFlow framework using six features including coil turns of single wing, coil thickness, coil diameter, distance between two wings, distance between head and coil position, and angle between two wings of coil as the inputs and electric field as the output. The model performance is evaluated based on four verification statistic metrics such as coefficient of determination (R2), mean squared error (MSE), mean absolute error (MAE), and root mean squared error (RMSE) between the simulated and predicted values. The proposed model provides an adequate performance with $\text{R}^{2} =0.766$ , MSE = 0.184, MAE = 0.262, and RMSE = 0.429 in the testing stage. Therefore, the model can successfully predict the electric field in an assembly TMS coil without the aid of electromagnetic simulation software that suffers from an extensive computational cost.

Keywords

• Deep neural network
• deep learning
• electric field
• magnetic coil
• transcranial magnetic stimulation