PINN Simulation of the Temperature Rise Due to Ultrasound Wave Propagation

In the past few years, deep learning and its practical form of deep neural networks have been effectively used in a wide range of research areas. Researchers applied the deep learning techniques into solving Partial Differential Equations (PDEs) achieved significant results. A current approach known as Physics-Informed Neural Network (PINN), has evolved as a remarkable method to implement deep learning with the corresponding physics laws in forms of given linear or nonlinear PDEs. Using PINNs to solve PDEs can eliminate the requirements of elements grid needed in classical computational methods, such as finite difference or finite element methods. When approximating the solution of a PDE using a machine learning algorithm, it is vital to constrain the neural network to minimize the PDE residual. In this paper, a PINN architecture is presented, which employs the transient bioheat transfer equation (tBHTE) into a neural network to predict the temperature rise. The thermal model simulates the heat conduction generated from the wave propagating from ultrasound transducers. The solution of the tBHTE using PINNs utilizes a mesh-free domain while still maintaining a certain accuracy compared to conventional numerical methods. Further study of solving tBHTE with multi-elements ultrasound transducers can be generally applied to focused ultrasound treatments in order to predict the heat generation in more complex heterogeneous domains.