Numerical study of cryosurgical treatment of skin cancer

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. © 2020 Elsevier Masson SAS