Comparative Analysis of PINN Architectures for Solving the Non-Dimensionalized Pennes' Bioheat Equation in Non-Homogeneous Domain

Accurate modeling of heat transfer in biological tissues is essential for biomedical applications such as thermal therapies. The Pennes' bioheat equation provides a fundamental framework for understanding thermal dynamics in tissues; however, solving it in non-homogeneous domains remains computationally challenging. In this paper, we employ Physics-Informed Neural Networks (PINNs) to solve the non-dimensionalized Pennes' bioheat equation in a non-homogeneous tissue environment, incorporating variations between muscle and fat through a smooth transition function. To increase stability and efficiency, we introduce a non-dimensionalization process that scales spatial, temporal, and thermal parameters based on characteristic values. A custom PINN framework is implemented to simulate the Pennes' bioheat equation using NVIDIA Modulus, and different neural architectures are evaluated across various collocation densities. Model performance is benchmarked against a Finite Difference Method (FDM) solution by assessing different metrics. Our findings reveal that PINNs demonstrate superior training stability especially with Fourier-based architectures, and reduced loss compared with other architectures. These results show the effectiveness of non-dimensionalization and PINNs in advancing computational models for biomedical simulations and therapeutic applications.Clinical Impact - Optimizing thermal treatments, such as laser-induced thermotherapy (LITT), cryosurgery, and hyperthermia treatment, requires an understanding of heat transmission in biological tissues. This study offers an efficient method for modeling tissue architectures using PINNs to solve the Pennes' bioheat equation in non-homogeneous environments.