Unfrozen Regions Research Articles

Analysis of a Stefan-Like Problem in a Biological Tissue Around a Cryosurgical Probe

Analysis of a Stefan-like problem in the in vivo freezing of a biological tissue is presented in cartesian coordinates. The analysis allows the inclusion of blood perfusion, metabolic heat and tissue heat capacity. Solutions are obtained for the temperature distributions in the frozen and unfrozen regions at different times. A constant freezing rate, in accordance with the optimal tissue destruction rate, is assumed. Results indicate the importance of the blood perfusion factor in the problem and allow the prediction of probe temperature and heat flux variations for optimal results in tissue destruction.

Rate of lesion growth around spherical and cylindrical cryoprobes

Approximate analytical solutions have been developed for predicting the rate of formation of the frozen regions around spherical and cylindrical cryoprobes. These solutions include the contribution of blood flow and metabolic heat generation and do not require the tissue to be initially at its phase change temperature. Heat capacity effects in both the frozen and unfrozen regions have been neglected in the development of these solutions. Comparison of an approximate solution with an exact numerical solution indicates that ice front locations can be predicted to within 5% using these solutions. Illustrative numerical examples are presented.