Abstract In this study, a new mathematical model describing the cryosurgical treatment of skin cancer in multilayer tissue has been developed. The cryoprobe whose temperature decreases linearly by time is placed at the skin tumor tissue. The outer surface of the skin i.e. dermis layer has been imposed by different boundary conditions. The mathematical model of this bio-heat transfer problem is a moving boundary value problem. Using finite differences, the boundary value problem is converted into initial value problem of vector matrix form. Further applying Legendre wavelet Galerkin method, the problem has been converted into generalized system of sylvester equation which are solved by Bartels-Stewart Algorithm, where the idea of generalized inverse has been used. Here, we have found the temperature distribution of all the four layers. These results are used in interface condition to obtain the moving layer thickness. We have validated the present numerical study with the recent experimental result which are in good agreement. We have seen the difference in the temperature profile when perfluoro hexane (PfH) which has a low thermal conductivity is injected to cover the portion of the tumor. And due to this approach, freezing becomes very fast and significant. It also helps in achieving a lethal temperature in lesser time. We have also seen the effect of gel concentration of 0.2%, 0.6%, 1.0% on the temperature distribution with probe insertion depth 10 mm. We have seen that significant results are obtained when we have used these parameters (PfH, gel concentration, probe insertion depth). We have also developed the two dimensional model of dermis layer and have seen the temperature distribution under different boundary conditions. The variability of temperature distribution and moving layer thickness on different layer of skin have been discussed in detail. In this paper.

中文翻译：

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皮肤癌冷冻治疗的数值研究

摘要 在这项研究中，开发了一种新的数学模型，描述了多层组织中皮肤癌的冷冻手术治疗。将温度随时间线性降低的冷冻探针放置在皮肤肿瘤组织处。皮肤的外表面即真皮层受到不同边界条件的影响。这个生物传热问题的数学模型是一个移动边值问题。利用有限差分，将边值问题转化为向量矩阵形式的初值问题。进一步应用Legendre小波Galerkin方法，将问题转化为用Bartels-Stewart算法求解的sylvester方程的广义系统，其中使用了广义逆的思想。在这里，我们已经找到了所有四层的温度分布。这些结果用于界面条件以获得移动层厚度。我们已经验证了当前的数值研究与最近的实验结果非常吻合。我们已经看到了当注射具有低热导率的全氟己烷 (PfH) 以覆盖肿瘤部分时的温度分布差异。由于这种方法，冻结变得非常快速和重要。它还有助于在更短的时间内达到致死温度。我们还看到了 0.2%、0.6%、1.0% 的凝胶浓度对探针插入深度 10 mm 的温度分布的影响。我们已经看到，当我们使用这些参数（PfH、凝胶浓度、探针插入深度）时，获得了显着的结果。我们还开发了真皮层的二维模型，并看到了不同边界条件下的温度分布。详细讨论了不同皮肤层上温度分布和移动层厚度的变化。在本文中。