A Finite Element Model for Ice Ball Evolution in a Multi-probe Cryosurgery

The ice formation in a water body is examined for the computation of temperature field, phase change and a moving ice-water interface whose location is not known á priori. This is classically referred to as the Stefan problem [Rubinstein, L.I. (1971) The Stefan Problem (American Mathematical Society, Providence, Rhode Island 02904]. Based on the Duvaut [Duvaut, G. (1973) "Résolution d'un probléme Stefan" C.R. Acad Sci. Paris 276, 1461-1463] transformation, the governing equations for heat conduction are formulated within a variational principle that is readily amenable to a standard finite element solution without remeshing. Numerical simulation results pertaining to the freezing of tumour tissue in a multi-cryoprobe cryosurgery are presented. These results lend both quantitative and graphical support to the current empirical standards of "effective therapy" in view of refining clinical applications.