Analysis of thermal stress in cryosurgery of kidneys

In this study, the thermal stress distribution in cryosurgery of kidney was investigated using a multiphysics finite element model developed in ANSYS (V8.1). The thermal portion of the model was verified using experimental data and the mechanics portion of the model (elastic) was verified using classic analytical solutions. Temperature dependent thermal and mechanical properties were used in the model. Moreover, the model accounts for thermal expansion due to both thermal expansion in single phase and volumetric expansion associated with phase change of tissue water to ice. For a clinical cylindrical cryoprobe inserted into the renal cortex from the top-middle renal capsule, it was found that the thermal stress distributions along the radial position are very different at different depths from the top renal capsule. The thermal stress is much higher at both ends than in the middle of the cryoprobe surface. It was found that there might be more tissue next to the top renal capsule than other region undergoing microcrack formation or plastic deformation. Furthermore, it was found that macrocrack formation is more likely to occur in tissue adjacent to the cryoprobe surface (especially on the sharp point tip) and during the thawing phase of cryosurgery. It was further found that the volumetric expansion associated with phase change induced much higher thermal stress than thermal expansion in a single phase and might therefore be the main cause of the frequently observed crack formation shortly after initiation of thawing in cryosurgery. Because the thermal stress adjacent to the cryoprobe is much higher than the yield stress of frozen renal tissue, a plastic stress model is required for better modeling of the thermal stress distribution in cryosurgery of kidney in future. However the computational effort will then be drastically increased due to the strong nonlinear nature of the plastic model and more experimental studies are indispensable for better understanding of the mechanical behavior of frozen tissue in cryosurgery.