Boundary Element Method Solution of a Fractional Bioheat Equation for Memory-Driven Heat Transfer in Biological Tissues
Mohamed Abdelsabour Fahmy, Ahmad Almutlg
Abstract
This work develops a Boundary Element Method (BEM) formulation for simulating bioheat transfer in perfused biological tissues using the Atangana–Baleanu fractional derivative in the Caputo sense (ABC). The ABC operator incorporates a nonsingular Mittag–Leffler kernel to model thermal memory effects while preserving compatibility with standard boundary conditions. The formulation combines boundary discretization with cell-based domain integration to account for volumetric heat sources, and a recursive time-stepping scheme to efficiently evaluate the fractional term. The model is applied to a one-dimensional cylindrical tissue domain subjected to metabolic heating and external energy deposition. Simulations are performed for multiple fractional orders, and the results are compared with classical BEM (a=1.0), Caputo-based fractional BEM, and in vitro experimental temperature data. The fractional order a≈0.894 yields the best agreement with experimental measurements, reducing the maximum temperature error to 1.2% while maintaining moderate computational cost. These results indicate that the proposed BEM–ABC framework effectively captures nonlocal and time-delayed heat conduction effects in biological tissues and provides an efficient alternative to conventional fractional models for thermal analysis in biomedical applications.