Analysis of Thermal Stresses around a Cryosurgical Probe

Large thermal stresses easily exceeding the tissue yield strength may develop in the frozen region around a cryosurgical probe. A new integrodifferential solution for the heat transfer problem of biological tissues freezing around a cryosurgical probe is presented in this article. This solution is suitable for cases of high Stephan numbers and for a temperature-dependent forcing function at the cryoprobe. A new solution for the thermal stresses around a cryosurgical probe is also presented, based on an elastic-perfectly plastic model. It is proposed that thermal stresses beyond the elastic limit of the frozen region may sharply increase the mechanical damage to the cell membranes due to plastic deformation. It was found that plastic deformation always starts at the cryoprobe surface; however, plastic deformation may also be formed near the freezing front at high cooling rates and large cryoprobes. It is demonstrated that under some conditions plastic deformation may occur in the entire frozen region. A parametric study to identify the best cooling protocol for maximal plastic deformation is presented.