A Conjugate Model for Hepatic Cancer Cryosurgery Using a Liquid-Nitrogen Cryorobe

Cryosurgery is a surgical technique using low temperature cryogen to achieve selective tissue destruction by freezing. During cryosurgery, the cryoprobe, which is usually cooled by inner circulation of liquid nitrogen (LN₂), is inserted into the targeted tumor tissue. The tissue surrounding the cryoprobe is then cooled down to sub-zero temperature and subsequently frozen. Extensive studies have been conducted to understand the mechanism of tissue injury, and various numerical models have been developed to predict the thermal history of the targeted tissues during cryosurgery. Most of the existing models, however, focused on the tissue freezing and applied simplified thermal boundary conditions at the interface between cryoprobe and surrounding tissue, e.g. a constant temperature or a constant heat flux. This paper presents a conjugate model for cryosurgery. The new model treats with both tissue freezing outside of the cryoprobe and turbulent convective heat transfer of LN2 inside the cryoprobe. The thermal condition along the cryoprobe surface is then part of the solution, instead of a presumption. The turbulent convection of single phase LN₂ inside the cryoprobe is described by a Realizable κ-ε model, while the Pennes equation is used to address the heat transfer within the hepatic tissue. An apparent heat capacity method is used to deal with tissue freezing. As an example, the model is used to simulate the hepatic cryosurgery with a single cryoprobe. The model predicts a dynamic, non-unform surface temperature along the cryoprobe surface, which shows a large effect on the ice ball formation outside the cryoprobe. Results are also presented to illustrate the effect of the flow condition and the cryoprobe design on the interface thermal condition in cryosurgery.