Modeling of the Wave Propagation of a Multi-Element Ultrasound Transducer Using Neural Networks

Ultrasonic transducers design involves studying their operation in many critical clinical procedures. This requires modeling the propagation of waves produced by the ultrasonic transducer elements. The linear wave equation is the fundamental modeled Partial Differential Equation (PDE) for understanding the behaviour of of an acoustic wave field. Modeling the wave equation is commonly done by utilizing mathematical approximations like Finite Difference Methods (FDMs) or Finite Element Methods (FEMs) to numerically solve the PDE. However, these conventional methods are mesh-based and cannot survive the curse of dimensionality (CoD) as the number of dimensions in the modeled system increases. This harshly affects the time of the simulation and the precision of results. The recent active research track of Physics-Informed Neural Networks (PINNs) has been presented as a mesh-free high accuracy simulation tool without the necessity of having a large set of training data at hand. We perform a simulation of a 3-element transducer via modeling the two-dimensional wave equation in geometrically square acoustic wave field. The constructed PINN is trained to predict the resultant values in the wave field while considering the time-dependent source elements. Modeling Multi-element transducers using PINNs opens a promising vast field for modeling and simulation of different domains and setups in ultrasound imaging and therapeutics.