Numerical simulation of cryosurgery in biological tissue with developed circulatory system

This paper is devoted to the modeling of the cryogenic impact on biological tissue with a developed circulatory system: large blood vessels, dense distributed small vessels and capillaries penetrating the tissue. The case of cryogenic destruction of a cancer tumor localized near a large artery is considered. The paper presents a direct numerical simulation of the temperature distribution evolution in biological tissue including the calculation of blood flow parameters in a vessel. The mathematical model is based on the Pennes bioheat transfer model with enthalpy modification and the quasi-one-dimensional hemodynamic model of blood flow in arteries, taking into account local changes in the elastic properties of the vessel walls due to strong cooling of adjacent tissue. A numerical algorithm based on explicit finite-volume approximation of the heat transfer model and the hybrid characteristic scheme (after splitting the equation with respect to physical processes) for numerical solution of hyperbolic systems is developed in order to simulate cryosurgery for the tumor near the artery. The main focus of the paper is a numerical study of the circulatory system parameters' influence on the shape of the final distribution of the cellular necrosis zone. We study the dependence of the necrosis front penetration depth on the perfusion power which characterizes the density of capillary distribution, the peak and background rates of blood flow in the artery, the diameter of the blood vessel and the thickness of its walls.