A Time-Fractional Bioheat Model with Perfusion and Spatial Source for Laser Thermal Coagulation in Hepatic Tissue

Abstract

This work presents an analytical investigation of a time-fractional bioheat transfer model for laser thermal coagulation (LTC) in hepatic tissue. The model incorporates a Caputo fractional time derivative of order $\beta \in (0,1]$ to account for thermal memory effects and nonlocal temporal behavior in biological tissues. A spatially decaying laser heat source and blood perfusion are included to simulate realistic in vivo and ex vivo thermal scenarios. We formulate the problem in a one-dimensional semi-infinite domain and derive closed-form solutions using Laplace transforms, involving the Mittag-Leffler and scaled Wright functions. These solutions capture the anomalous diffusion phenomena typically neglected by the classical Pennes Bioheat Equation (PBE). Comparisons with experimental data reveal that the fractional-order model significantly improves accuracy in predicting early-time temperature dynamics. In particular, for $\beta = 0.9$, the model closely replicates the experimental temperature profile, while the classical PBE overestimates it. This study demonstrates the potential of fractional heat transport models for more precise thermal predictions in minimally invasive therapies such as LTC.