A Physics-Based Neural Network (PNN) Approach to Solving the Heterogeneous Nonlinear Fullwave Equation

The fullwave equation describes nonlinear acoustic wave propagation in a heterogenerous medium, which accounts for the linear propagation of the wave, thermoviscous diffusivity, nonlinearily, attenuation, and variation in density. Numerical solutions of the fullwave equation, including the Fullwave and k-wave toolboxes, are used in medical ultrasound imaging research. However, despite of the wide applications of these numerical tools, they are computationally intensive. We propose a physics-based neural network (PNN) approach to numerically solving the fullwave equation that describes the nonlinear propagation in a heterogeneous nonattenuating medium. The proposed network has been implemented in PyTorch and its structure is based on the fullwave equation. The structure and weights of the proposed neural network have clear physical interpretations. As a proof-of-concept demonstration, we show in this work the simulations of the propagation of acoustic pulses through a representation of the human abdomen, as well as through water. The flexibility of the physics-based neural network implementation enables the migration of computation from CPU to GPU with minimal additional efforts, which accelerates the computation by a factor of 12 compared to the Fullwave toolbox on CPU.