Modeling of multidimensional freezing problem during cryosurgery by the dual reciprocity boundary element method

Abstract

The main difficulties encountered in cryosurgery are the unknowns on the extent of the irregular shape of the frozen region, the direction of ice growth, and the temperature distribution within the ice balls during the freezing process. In this study, a numerical algorithm based on the dual reciprocity boundary element method (DRBEM) is developed to solve multidimensional phase change problem of biological tissues subject to cryosurgery. The tissues are treated as nonideal materials, freezing over a temperature range, and the effects of blood perfusion and metabolic heat generation in the unfrozen tissues are also taken into account in the heat transfer model. The accuracy of this DRBEM algorithm is validated through comparisons of the calculation results with the one-dimensional numerical solutions by the finite difference method. Comprehensive analyses are performed respectively, on the freezing behaviors of normal biological tissue and diseased tissue with tumors. For treatment of large tumors where large cooling power is required, a single probe will not be able to address a sufficiently large volume. On this account, the freezing problems by two- and three-cryoprobe system are solved for illustration purpose. The present algorithm can serve as a useful tool for post-treatment planning in cryosurgery.