Thermal stress modeling in cryosurgery

A new model of the mechanical stress development associated with an expanded freezing zone and its subsequent thawing is presented. The model is di€erent in that it computes stresses properly by considering only strains that occur after solidi®cation. A closed-form solution of the model is derived and results of a parametric study for typical parameters and conditions of cryosurgery around a spherical cryoprobe are presented. Results show that the stress distributions during the thawing stage are very di€erent than those during freezing. Furthermore, it is shown that signi®cant stresses remain in the frozen region during thawing, and even when the temperature distribution decays to the phase transition temperatures. The distributions are qualitatively consistent with limited cracking at the cryoprobe surface during freezing and large scale cracking during thawing, which were observed during validation testing of cryoprobes in water and gelatin solutions