A Study of Cryosurgery of Prostate Cancer Using Mathematical Model

In this study, a two-dimensional three-phase lag (TPL) bio-heat transfer model during cryosurgery of prostate cancer is developed. The cryoprobe, with a temperature that decreases linearly with time, is placed at the prostate tumor tissue. 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 the initial value problem of vector-matrix form. Further applying the Legendre wavelet Galerkin method, the problem has been converted into a generalized system of the Sylvester equation, which is solved by the Bartels-Stewart algorithm, where the idea of generalized inverse has been used. We found the temperature distribution using the TPL model and, using these in interface conditions, we obtained the moving layer thicknesses. We compared the present numerical study with the exact solution and see that the results are in good agreement. We have also seen the effects of τq (phase lag due to heat flux), τT (phase lag due to temperature gradient) and τν (phase lag due to temperature displacement gradient) on temperature distribution.