A physics-informed neural network method for thermal analysis in laser-irradiated 3D skin tissues with embedded vasculature, tumor and gold nanorods

Abstract

Obtaining an accurate temperature field of the entire treatment region and controlling the laser intensity is vital for successful clinical outcomes in hyperthermia skin cancer treatment. This article presents a Physics-Informed Neural Network (PINN) method to accurately predict transient temperature distributions and thermal damage in 3D triple-layered skin tissues with an embedded tumor, gold nanorods, and a vascular network that is designed based on the constructal theory of multi-scale tree-shaped heat exchangers. Fourier and non-Fourier Pennes bioheat transfer equations in triple-layered tissues and the convective energy balance equations in blood vessels are employed in the loss function, where the Gaussian-shaped laser beam with the laser power as a parametric variable is modeled. The convergence of the neural network solution is analyzed theoretically. The new algorithm with time sequence is tested for a duration of at least 400 seconds over three different case studies. Results show that the PINN-predicted temperatures agree well with those predicted temperatures based on the finite element/finite difference methods. In particular, for the case study with a tumor, the thermal damage analysis reveals that with an optimal power of 0.9 W/cm, the skin tissues remain undamaged over 600 seconds, while the tumor cells’ death begins after 330 seconds, with the tumor's average temperature reaching about 43.7 °C. The advantage of the PINN method is that it can be easily applied to determine the optimal laser power when dealing with the irregulate tumor shape without mesh constructions that are used in the common numerical methods.