Physics-informed neural networks for modeling acoustic radiation force-induced shear wave propagation and the reconstruction of material parameters from observations

Physics-informed neural networks (PINNs) solve differential equations and give compressed, analytic solutions free of discretization. Previous work used PINNs to model shear wave propagation from a spherical Gaussian impulse in an incompressible, transversely isotropic (ITI) material. Here, we extend this method to model the more complex geometry of an acoustic radiation force impulse (ARFI) and subsequent 3D shear wave propagation in both isotropic and ITI materials. We find that PINNs produce high-fidelity 3D solutions across different material models. PINN solutions qualitatively matched paired finite element method (FEM) simulations and without artifacts seen in FEM related to spatial discretization. The frequency content of PINN solutions differed slightly from the FEM, depending on the initial excitation geometry. PINNs have the potential to help rapidly explore material model parameter spaces. We also investigate the feasibility of solving the inverse problem to reconstruct material parameters from observed data by setting these parameters as variable outputs of the PINN model. PINNs were able to reconstruct the shear modulus using data measured in an isotropic elastic phantom to within 3 percent. Lastly, we show that PINNs can reconstruct all three independent parameters of an ITI material model from data.