Fractional-order bioheat modeling for enhanced prediction of tissue response in thermal therapies

Abstract

Introduction

Thermal ablation planning requires models that capture non-Fourier, memory-dependent heat transport in heterogeneous soft tissues. Classical Pennes’ formulations often misestimate temperature rise and damage extent under clinical heating protocols.

Objective

To experimentally validate a fractional-order extension of Pennes’ bioheat equation against ex-vivo thermographic data and quantify its predictive advantage over the classical model.

Materials and methods

We (i) measured thermal diffusivity (D), conductivity (k), and volumetric specific heat capacity (C_h) for 30 ex-vivo tissue samples (kidney, heart, liver) at room temperature (20–25 °C); (ii) performed controlled surface laser heating on liver samples with infrared thermography; and (iii) simulated temperature evolution with the classical (α = 1) and fractional (0 < α < 1) bioheat models. Agreement between measurements and simulations was assessed via mean absolute error (MAE), root-mean-square error (RMSE), residual analysis, and Bland–Altman plots.

Results

Across experiments, the fractional model reproduced the measured temperature trajectories with consistently lower MAE/RMSE than the classical model and reduced bias in Bland–Altman analysis. A 2D benchmark confirmed expected spatial gradients under fixed boundary conditions, while sensitivity analyses showed α controls the pace of thermal penetration and the extent of predicted thermal zones. Experimental results showed consistent thermal parameters across tissue types (ρ ≈ 1050 kg/m3, D ≈ 0.15 mm²/s and k ≈ 0.5 W/m °C), blood properties were characterized by ${\Omega }_p$ = 0.005 l/s, ${\rho }_b$ = 1060 kg/m³, $T_a$ = 37 °C, with metabolic heat generation estimated as $Q_m$ = 33800 W/m³. Minor, statistically insignificant variations were observed in specific heat capacity (C_h ≈ 3.71–3.43 MJ/m³. K), which aligned well with numerical predictions.

Conclusions

Integrating experimentally measured tissue properties with fractional bioheat modeling improves quantitative prediction of temperature evolution during ablative heating. This hybrid framework strengthens treatment planning by better delineating thermal spread and offers a practical path to patient- and tissue-specific calibration.