Scholarlink

Background <p>Accurate prediction of temperature distribution within biological tissues is essential for ensuring the safety and effectiveness of thermal therapies, such as laser ablation, radiofrequency ablation, and hyperthermia. Classical bioheat formulas, such as Pennes’ equation, are based on the assumption of an instantaneous heat propagation and local thermal equilibrium, and are limited in their capacity to capture the memory-dependent and non-local heat transmission found in heterogeneous soft tissues.</p> Objective <p>The present work proposes and analyzes a fractional-order bioheat transfer model that extends classical and non-Fourier formulations to more accurately describe realistic thermal transport in biological tissues, combining analytical, numerical and experimental studies to improve thermal therapy modeling.</p> Materials and methods <p>A one-dimensional (1D) transient fractional-order bioheat equation was derived and solved using Laplace transforms with numerical inversion to analyze temporal temperature evolution. The model was then extended to a two-dimensional (2D) steady-state configuration, solved using an iterative Gauss–Seidel method under defined boundary conditions. Ex-vivo thermal properties—thermal diffusivity (<i>D</i>), thermal conductivity (<i>k</i>), and volumetric heat capacity (<i>C</i><sub><i>h</i></sub>)—were experimentally measured for bovine heart, liver, and kidney tissues at room temperature (21 ~ 25&#xa0;°C) and incorporated as model inputs. Model predictions were compared with those of the classical Pennes, Cattaneo–Vernotte (CV), and dual-phase lag (DPL) formulations bioheat models.</p> Results <p>The fractional-order model reproduced delayed thermal response and experimentally consistent cooling profiles in agreement with the experimental data, and showed lower quantitative errors (RMSE &lt; 0.42&#xa0;°C, MAE &lt; 0.35&#xa0;°C) with respect to other models. Measured thermal properties across tissues were comparable—<i>D</i> ≈ 0.15&#xa0;mm²/s, <i>k</i> ≈ 0.5&#xa0;W/(m·K), and <i>C</i><sub><i>h</i></sub> between 3.4 and 3.7&#xa0;MJ/m³·K— confirming comparable thermophysical properties across the investigated tissues within experimental uncertainty.</p> Conclusions <p>The proposed fractional-order bioheat framework provides a unified and flexible extension of existing bioheat models, effectively capturing anomalous and memory-dependent heat conduction in soft tissues. The approach establishes a foundation for clinically relevant thermal therapy modeling and can be readily extended to temperature-dependent properties, convective boundary conditions, and real-time imaging integration for treatment planning and optimization.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Fractional-order thermo-biophysical modeling of soft tissues: analytical, numerical, and experimental insights for thermal therapies

  • 期刊论文

  • 发表日期：

    2026年7月29日

查看全文
  • Mohamed Hisham Fouad Aref,
  • Abdallah Abdelkader Hussein,
  • Yasser M. Sabry,
  • Yasser H. El-Sharkawy

摘要

Background

Accurate prediction of temperature distribution within biological tissues is essential for ensuring the safety and effectiveness of thermal therapies, such as laser ablation, radiofrequency ablation, and hyperthermia. Classical bioheat formulas, such as Pennes’ equation, are based on the assumption of an instantaneous heat propagation and local thermal equilibrium, and are limited in their capacity to capture the memory-dependent and non-local heat transmission found in heterogeneous soft tissues.

Objective

The present work proposes and analyzes a fractional-order bioheat transfer model that extends classical and non-Fourier formulations to more accurately describe realistic thermal transport in biological tissues, combining analytical, numerical and experimental studies to improve thermal therapy modeling.

Materials and methods

A one-dimensional (1D) transient fractional-order bioheat equation was derived and solved using Laplace transforms with numerical inversion to analyze temporal temperature evolution. The model was then extended to a two-dimensional (2D) steady-state configuration, solved using an iterative Gauss–Seidel method under defined boundary conditions. Ex-vivo thermal properties—thermal diffusivity (D), thermal conductivity (k), and volumetric heat capacity (Ch)—were experimentally measured for bovine heart, liver, and kidney tissues at room temperature (21 ~ 25 °C) and incorporated as model inputs. Model predictions were compared with those of the classical Pennes, Cattaneo–Vernotte (CV), and dual-phase lag (DPL) formulations bioheat models.

Results

The fractional-order model reproduced delayed thermal response and experimentally consistent cooling profiles in agreement with the experimental data, and showed lower quantitative errors (RMSE < 0.42 °C, MAE < 0.35 °C) with respect to other models. Measured thermal properties across tissues were comparable—D ≈ 0.15 mm²/s, k ≈ 0.5 W/(m·K), and Ch between 3.4 and 3.7 MJ/m³·K— confirming comparable thermophysical properties across the investigated tissues within experimental uncertainty.

Conclusions

The proposed fractional-order bioheat framework provides a unified and flexible extension of existing bioheat models, effectively capturing anomalous and memory-dependent heat conduction in soft tissues. The approach establishes a foundation for clinically relevant thermal therapy modeling and can be readily extended to temperature-dependent properties, convective boundary conditions, and real-time imaging integration for treatment planning and optimization.