A mathematical model of temperature distribution in frozen tissue.

A computer simulation for a frozen region expansion around a cryoprobe in liver tissue is presented and compared with experimental measurements in liver tissue. Both the analytical solution under simplifying assumptions and the numerical solution of the heat equation were tested. No analytical solution is possible when studying the freezing process in the time scope of minutes. The problem is that the solution needs spherical coordinate transformation, which is singular in the origin. For the frozen region, the analytical solution is not constrained, and conclusions are unrealistic. Neither does it account for the cryoprobe diameter. The numeric solution to the same problem is much more informative. It adopts the natural boundary conditions that are the constant temperatures of both the cooling medium and the bath. Comparisons between the numerical solution and experimental measurements show good approximation of the problem by the model of temperature distribution in a homogeneous medium which freezes around a cryoprobe. Differences were smaller than the apparent measurement errors. Our approach allows relevant results to be obtained within the time period available during the surgery.