EMulator: Rapid Estimation of Complex-valued Electric Fields using a U-Net Architecture

A common factor across electromagnetic methodologies of brain stimulation is the optimization of essential dosimetry parameters, like amplitude, phase, and location of one or more transducers, which controls the stimulation strength and targeting precision. Since obtaining in-vivo measurements for the electric field distribution inside the biological tissue is challenging, physics-based simulators are used. However, these simulators are computationally expensive and time-consuming, making repeated calculations of electric fields for optimization purposes computationally prohibitive. To overcome this issue, we developed EMulator, a U-Net architecture-based regression model, for fast and robust complex electric field estimation. We trained EMulator using electric fields generated by 43 antennas placed around 14 segmented human brain models. Once trained, EMulator uses a segmented human brain model with an antenna location as an input and outputs the corresponding electric field. A representative result of our study is that, at 1.5 GHz, on the validation dataset consisting of 6 subjects, we can estimate the electric field with the magnitude of complex correlation coefficient of 0.978. Additionally, we could calculate the electric field with a mean time of 4.4 ms. On average, this is at least x1200 faster than the time required by state-of-the-art physics-based simulator COMSOL. The significance of this work is that it shows the possibility of real-time calculation of the electric field from the segmented human head model and antenna location, making it possible to optimize the amplitude, phase, and location of several different transducers with stochastic gradient descent since our model is almost everywhere differentiable.