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 finally obtains a partial differential 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 estimate the influence of cryoprobe geometry on the course of the process, the shape sensitivity analysis is applied. In particular, a direct approach is used (explicit differentiation 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.