SENSITIVITY ANALYSIS OF BIOLOGICAL TISSUE FREEZING PROCESS WITH RESPECT TO THE RADIUS OF SPHERICAL CRYOPROBE

Application of the shape sensitivity analysis to the case of problems of the biological tissue freezing process is discussed. The freezing process described by a strongly non-linear bioheat transfer equation in which an additional term controlling the evolution of latent heat appears. Using the approach called 'the one domain method', one nally obtains a partial dierential equation containing the substitute thermal capacity of tissue. The boundary and initial conditions determine the thermal interaction between the tissue and cryoprobe tip. In the paper, we consider a spherical internal cryoprobe. In order to es-timate the in uence of cryoprobe geometry on the course of the process, the shape sensitivity analysis is applied. In particular, a direct approach is used (explicit dierentiation method). The results of numerical modeling (the boundary element method is applied) allow one to formulate essential practical conclusions concerning the course of cryosurgery treatments. Key words: freezing process, sensitivity analysis, boundary element method 1. Governing equations From the mathematical point of view, the freezing process belongs to a group of moving boundary problems because the shape and dimensions of the frozen region are time-dependent. In the case of internal spherical cryoprobe application (Fig. 1), the following equation written in the spherical co-ordinate system should be taken into account R1 < r < R2: C(T