Fractional Diffusion in Computational Modeling of Radiofrequency Tumor Ablation

Radiofrequency ablation (RFA) is commonly modeled using classical heat diffusion equations; however, growing evidence suggests that heat transport in biological tissues exhibits nonlocal and scale-dependent behavior driven by capillary perfusion. In this work, we develop a fractional diffusion framework for the computational modeling of hepatic tumor ablation based on the fractional Laplacian operator. A characteristic length scale is introduced to bridge microscale capillary effects and macroscale heat propagation, enabling the model to capture the superdiffusive thermal transport associated with hepatic vascular networks. Owing to its nonlocal nature, the fractional formulation entails significantly higher computational costs than classical diffusion models. To address this challenge, we investigate the complexity of two temporal discretization strategies: the backward Euler method with uniform time stepping and an adaptive backward–forward Euler scheme. Numerical experiments involving single- and double-probe ablation configurations demonstrate the robustness of the proposed framework and illustrate its applicability to realistic ablation scenarios. Overall, the results indicate that fractional diffusion provides a flexible and physiologically meaningful framework for modeling heat transfer during RFA.