Modeling Shear Wave Propagation in an Incompressible, Transversely Isotropic Material Using Physics-Informed Neural Networks

There is increasing interest in using ultrasound shear wave elasticity imaging to study tissues described as incompressible, transversely isotropic (ITI) materials, such as skeletal muscle. In silico modeling helps us predict and understand shear wave behavior in complex materials like the ITI model, which supports two shear polarizations with different, direction-dependent propagation speeds. Existing techniques, the finite element method (FEM) and Greens functions, are computationally expensive and generate large file sizes. Physics-informed neural networks (PINNs) is a relatively novel technique to solve partial differential equations and produces solutions that are compressed, analytic, and free of space-time discretization. Here, we solve the 3D wave equation for an ITI material using PINNs and show that solutions match FEM simulations to first order for material parameters based on skeletal muscle. Estimated shear wave speeds for the PINN and FEM solutions differed by an average of 4.7%. Unlike the FEM simulation, the PINN solution had no reflection artifacts at the boundaries. Second-order differences in frequency content and amplitude distribution suggest the need for further validation. PINNs can enable rapid exploration of the complex shear wave behavior in ITI materials and can be extended to different material models by adjusting the wave equation and initial conditions.