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.