Numerical model of thermal interactions between cylindrical cryoprobe and biological tissue using the dual-phase lag equation

In the paper, the problem of biological tissue freezing is discussed. In contrast to the previously presented models based on the Pennes equation, the thermal interactions between the cryoprobe tip and soft tissue are described using the dual-phase lag model (DPLM). This model contains two delay times (the relaxation and thermalization times) and in this way, the finite velocity of the thermal wave is considered. The model of the freezing process is based on the introduction of a parameter called ‘substitute thermal capacity’ to the dual-phase lag equation. At the stage of numerical computations, the explicit scheme of the finite difference method is used. In the final part of the paper the examples of the computation are shown. A comparison with the solution resulting from the adoption of the Pennes equation and also the model verification with the experimental data are presented in the final part of the paper.