基于非Fourier生物热传导解析解的激光辐照皮肤组织热损伤分析

Thermal Damage Analysis in Skin Tissue Under Laser Irradiation by Analytical Solution to Non-Fourier Bioheat Transfer

  • 摘要: 较为准确地预测激光辐照下皮肤组织内部的热分布和热损伤是生物医学领域的一个难题. 为探究这个问题,提出了一种使用 Laplace 和 Hankel 变换推导出解析解的策略. 建立三维非Fourier热传导模型,并引入升温函数简化问题. 通过积分变换及其逆变换推导出解析解,并基于该解析解进行数值模拟,得到了不同辐照时间和半径下皮肤热分布和热损伤的预测结果,进而研究了激光辐照持续时间和半径对皮肤组织的影响. 此外,对非 Fourier 热传导模型和经典 Fourier 热传导模型得到的皮肤组织热损伤预测结果进行了全面比较. 分析结果表明,非Fourier和经典Fourier两种热传导模型所预测的热损伤深度是不同的. 具体来讲,在短时间辐照时,非Fourier热传导理论的预测深度要小于Fourier热传导理论,而长时间辐照时,结果恰好相反.

     

    Abstract: Accurate prediction of thermal distribution and thermal damage inside skin tissue subjected to laser irradiation is a difficult problem in the biomedical field. To explore this problem, a strategy to derive an analytical solution using Laplace and Hankel transforms was proposed. A three-dimensional non-Fourier heat conduction model was established, and temperature-rise function was introduced to simplify the problem. The analytical solution was derived through integral transforms and their inversions. The prediction results of skin thermal distribution and thermal damage under different irradiation durations and radii were obtained. And the effects of laser irradiation duration and beam radius on skin tissue were researched. Furthermore, a comprehensive comparison was made between the skin tissue damage prediction outcomes achieved through non-Fourier heat conduction models and through classical Fourier heat conduction models. The analytical results indicate distinct differences in predicted thermal damage depth between the non-Fourier and classical Fourier heat conduction models. Specifically, under short-duration irradiation, the non-Fourier model predicts shallower damage depth than the Fourier model, while the opposite trend is observed under prolonged irradiation.

     

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