非傅里叶热流边界条件对激光辐照生物组织热传导影响的研究

Effect of Non-Fourier Heat-Flux Boundary Conditions on Heat Conduction Behavior of Laser-Irradiated Biological Tissues

双相滞(DPL)非傅里叶导热模型能够反映脉冲激光与生物组织瞬态作用过程,但在很多运用DPL模型对生物组织传热机制进行研究的文献中,既有应用傅里叶边界条件也有应用非傅里叶边界条件,得出的很多传热机制结论是相互矛盾的。运用DPL非傅里叶模型控制方程,导出了非傅里叶和傅里叶边界条件,并利用积分变换及拉普拉斯变换法,分别给出了非傅里叶和傅里叶边界条件问题的解析解。以皮肤生物组织作为算例,计算结果表明,在非傅里叶控制方程条件下,基于非傅里叶边界条件预测的组织内的温度分布符合能量守恒定律,而基于傅里叶边界条件预测的组织内的温度分布则不符合能量守恒定律。非傅里叶边界条件下所得的温升幅值和温度的变化速率与傅里叶边界条件下所得的结论相反。采用傅里叶边界条件,对应的热损伤明显低于非傅里叶边界条件热损伤且过于保守。最后从能量守恒角度指出, DPL非傅里叶边界条件就是边界的DPL型能量守恒方程,傅里叶边界条件是傅里叶模型的能量守恒方程。傅里叶生物传热控制方程应与傅里叶型边界条件相配合,而DPL非傅里叶生物传热方程应与非傅里叶边界条件相配合。

The dual phase lagging(DPL) non-Fourier heat transfer model can reflect the transient interaction process between pulsed laser and biological tissues. However, in many literatures where the DPL model is used to study the heat conduction mechanism of biological tissues, there exist both Fourier and non-Fourier boundary conditions and thus many induced conclusions are contradictory. In this paper, the control equation based on the DPL non-Fourier model is adopted and the Fourier and non-Fourier boundary conditions are derived. Meanwhile, the analytical solutions under the above conditions are obtained by integral transformation and Laplace transformation. The biological tissues are taken as an example and the calculation results show that as for the non-Fourier control equation, the predicted temperature distribution in tissues based on the non-Fourier boundary condition is in accordance with the energy conservation law, while the result based on the Fourier boundary condition is not. The conclusions on the temperature rising amplitude and temperature rising rate are opposite for the two kinds of boundary conditions. Moreover, the thermal damage predicted under the Fourier boundary conditions is overly conservative and obviously lower than that under the non-Fourier boundary conditions. Finally, from the point view of energy conservation, the DPL non-Fourier boundary condition is just the DPL energy conservation equation of boundary, while the Fourier boundary condition is the energy conservation equation of the Fourier model. The Fourier control equation of bio-heat conduction should be matched with the Fourier boundary conditions, while the non-Fourier control equation of bio-heat conduction should be matched with the non-Fourier boundary conditions.