Physics-Informed Neural Networks with Resampling Technique to Model Ultrasound Wave Propagation of a Multi-Element Transducer

Multi-element Focused Ultrasound Transducers (FUSTs) are gaining increasing acceptance as a form of treatment for various tissue abnormalities. This in turn requires treatment planning and development, which is performed through common numerical methods. Numerical modeling enables studying the outcomes of clinical procedures and adjust critical parameters on system-level interventions. However, given the oscillatory and multi-scale nature of the forward problem when modeling the ultrasound waves propagation, it can be challenging to simulate multidimensional domains. The performance of conventional modeling methods like the Finite Difference Method (FDM) endures difficulties caused by the curse of dimensionality (CoD). In our work, we utilize the concept of Physics-Informed Neural Networks (PINNs) with resampling and applying initial and boundary conditions in the form of hard constraints to model the linear wave equation with multiple forcing continuous time-dependent source terms in 2 spatial dimensions with no prior training data. We also show that with the use of anchor training points that are located near the source points enhances the the prediction accuracy. This implementation models a wavefield of a 5-element focused ultrasound transducer. The proposed approach presents a lower mean residual error and L2 relative error values indicating better model nrediction than a baseline PINN.