Freezing of blood perfused tissue: An improved quasi-steady solution

An approximate analytic solution is obtained for the temperature distribution and freezing front propagation in tissue. The solution accounts for blood perfusion and metabolic heat generation. The method of solution is based on the introduction of assumed temperature profiles in the frozen and unfrozen regions. The assumed profiles satisfy all boundary conditions as well as the governing heat equations at the moving interface. In addition, the steady state interface location is identically satisfied. Two cases are considered: freezing of a semi-infinite blood perfused tissue over a planar probe and around a spherical probe. The accuracy of the solution is verified in two test cases with known exact solutions: the limiting case of Neumann’s problem and a numerical solution to tissue freezing around a spherical probe. The present theory represents a significant improvement over the quasi-steady model.