An efficient algorithm for phase change problem in tumor treatment using αfEM

Cryosurgery is an effective treatment for killing tumor tissues. During the cryosurgery process, a phase transformation occurs in the undesired tissue. The most popular numerical method for simulation of phase change problem is fixed grid methods where the latent heat is function of temperature. In this paper, a fixed grid method using the alpha finite element (αFEM) formulation is presented to simulate the phase transformation and temperature field during the cryosurgery process for liver tumor treatment. The αFEM model is first established and tuned to have a close-to-exact stiffness compared with the standard finite element method (FEM). Three examples of liver tumor treatment including the single probe for regular shape of tumor, and multiple probes for regular and irregular shape of tumor are presented. The numerical results using alpha finite element method have demonstrated the effectiveness of the procedure.