Approximate analytical solution for one-dimensional tissue freezing around cylindrical cryoprobes

An approximate analytical solution for the temperature distribution and interface motion is determined for the freezing of blood-perfused tissue around a cylindrical cryoprobe. The solution is based on an improved quasi-steady model in which assumed temperature profiles in the frozen and unfrozen tissue are used to determine the interface motion. The approximate solution satisfies all temperature boundary conditions as well as the transient heat equations at the interface. Due to blood perfusion in the unfrozen tissue, a steady state is reached where the interface becomes stationary. The solution converges to the exact steady state interface location. Improvement over the quasi-steady solution and the accuracy of the present theory are verified by comparison with numerical solutions for the limiting case of zero blood perfusion and metabolic heat production. Results show that a typical quasi-steady error of 73% is reduced to 8% using the present theory. Parametric charts are presented to evaluate the effect of the governing parameters on interface location.