About one two-dimensional mathematical model in cryomedicine

The work shows that in the case of a flat and sufficiently long cryosurgical instrument, the process of heat propagation in biological tissue is modeled by a two-dimensional Stefan-type initial-boundary value problem. The formulation of this problem for a rectangular area is considered. An algorithm for finding approximate values of temperature and position of isothermal surfaces is presented. A solution is given to a “smoothed” problem that approximates the original Stefan problem using a locally one-dimensional method. The resulting nonlinear algebraic systems were solved using Newton's iterative method.