Generalized solution and estimation method for cooling performance of downscaled cryoprobe

In cryosurgery, downscaling of cryoprobes is important to minimize surgical invasion. In this study, a set of analytical solutions to the freezing phenomenon around a cryoprobe in a dimensionless form is derived and the general trend is discussed to clarify the relationship between the freezing ability of a biological tissue and the cooling power of a cryoprobe. A one-dimensional axisymmetric model in the steady-state condition is considered. The relationship between the size of the frozen region, fluid temperature in the cryoprobe, and heat transfer coefficient on the wall of the cryoprobe in the dimensional form is derived under the condition mentioned above. The fluid temperature and heat transfer coefficient are eliminated from the solutions by introducing the steady-state cryoprobe surface temperature. This transformation indicates that the steady-state surface temperature directly affects the size of the frozen region and combination of fluid temperature and heat transfer coefficient occurs, which has the same cooling effect. The derived solutions are transformed into a dimensionless form using the characteristic length of bioheat transfer and normalizing the temperature distribution in an unfrozen tissue. The applicability of these analytical solutions is evaluated by comparing them with numerical simulation results from existing studies. The dimensionless solutions describe the general trend of the relationship between the frozen region and the cooling power of a cryoprobe, which is independent of the type of organ, fluid temperature, and heat transfer coefficient. Finally, the concept of freezing limit is established using the derived solutions. The freezing limit describes the minimum requirements to freeze a tissue, and it can be used as guideline to design future downscaled cryoprobes with a suitable cooling mechanism.