Numerical simulation of the effect of localization of the front of cellular necrosis during cutaneous cryosurgery

In this paper, we consider the problem of planning and optimizing the destruction of the tumor tissue during cutaneous cryosurgery. A method of mounting additional heating elements is proposed as an approach to control propagation of the front of cellular necrosis. Mathematical simulation and Pareto optimality of calculable functions are used to improve the effectiveness of the proposed method. An explicit scheme that is based on the finite volume approximation of the Pennes bioheat transfer model is applied, together with an enthalpy method for computing blurred phase transitions. A flux relaxation method is used to improve the stability of the scheme.