Godunov method for computerized lung cancer cryosurgery planning with efficient freezing time

Cryosurgery is a technique of cancer treatment by providing extremely cold temperature to destroy abnormal cells. In this article, cryosurgery simulation of lung cancer is presented. Mathematical formulation of cryosurgery procedure is governed by heat conduction equations both in the solid and liquid phase which then reformulated into enthalpy form. Godunov method is used to obtain the numerical solutions of enthalpy equation. Numerical results for one-dimensional case are validated against the exact solution. In two-dimensional simulation, efficient freezing time, which is a time when all cancer areas are frozen, is obtained by calculating the area of ice ball formation which covers the cancer cells area in each time. It is found that for lung cancer configuration being studied, the efficient cryosurgery time is 522.24 seconds. Temperature distribution and interface position during cryosurgery and heating process are then simulated based on efficient freezing time. The simulation results provide an important information for computerized lung cancer cryosurgery planning.