A Hybrid FDM–RNN–PINN Framework for Solving the Bioheat Transfer Equation in Thermal Cancer Therapy

Enhancements in safety and effectiveness of radiofrequency ablation (RFA) therapies require precise modeling of heat distribution in biological tissues. The traditional numerical solvers such as the Finite Difference Method (FDM) lack the capability to simulate nonlinear biological feedback, providing only limited physiologic simulation and feedback in real time. This research aims to develop a new hybrid computing methodology that combines FDM with Recurrent Neural Networks, RNNs, and Physics-Informed Neural Networks, PINNs, to solve the Bioheat Transfer Equation BHTE. In this model, the FDM generates ordered spatiotemporal temperature data, the RNN “learns” the spatiotemporal thermal diffusion, and the PINN imposes the required thermophysical constrains on the learning architecture. Classical FDM had an MAE of 5.389° and RMSE of 8.165°, while this method had 1.886° MAE and 2.261° RMSE. Benchmarking against analytic results demonstrated the hybrid model's significant improvement over traditional methods. The research findings show the model’s ability to multifactorial prediction within the constraints of physical realism, high efficiency computational resources, and speed, which makes the model suitable for real-time thermal therapy simulation tailored to the patient.