Three phase bio-heat transfer model in three-dimensional space for multiprobe cryosurgery

This study addresses a three phase bio-heat transfer model in three-dimensional space consisting of tumor and normal tissues frozen with multiple cryoprobe. Mathematically, it is a three-dimensional, three region moving boundary problem with different types of boundary conditions. To solve this problem, we have developed a modified Legendre wavelet Galerkin method. We have calculated the operational matrix of integration of three dimensional Legendre wavelets and used in our problem. We have obtained the solution by using the idea of generalized inverse. In a particular case, when surface subjected to boundary condition of I kind, the results obtained are compared with exact solution and are in good agreement. This model is used to find the temperature in biological tissue when three, two or one cryoprobe are operated. Our results show that it is better to use three cryoprobes in place of two or one. In our problem, we have been obtained temperature distribution and moving layer thickness when three cryoprobes are placed. A variation is observed from the graphs of temperature distribution and moving layer thickness with respect to different boundary conditions. We see from the graphs of our results that temperature profile decreases and moving layer thickness increases when the time increases.