Considering uncertain quantities in the model of cryopreservation process of biological samples

Purpose: This paper presents numerical modelling of the heat and mass transfer process in a cryopreserved biological sample. The simulation of the cooling process was carried out according to the liquidus-tracking (LT) protocol developed by Pegg et al., including eight stages in which both the bath solution concentration and temperature are controlled to prevent the formation of ice crystals. Methods: To determine the temperature distribution during cryopreservation processes, one uses the Fourier equation, while mass transfer was taken into account using an equation based on the Fick's laws. This paper considers a model assuming fuzzy thermophysical parameters described by a triangular and a Gaussian membership function. The numerical problem was solved using the finite difference method including fuzzy set theory. Results: The diagrams of temperature and mass distributions as a function on time and the distribution of the fuzzy variable at a given moment in time were prepared. Moreover, the fuzzy temperatures and concentrations were compared with experimental results from the literature in table. Conclusions: In the conclusions, two different types of membership functions were compared with each other, with which the fuzzy variables were described. It can be said that the Gaussian membership function works well for experimental data where the mean and standard deviation are known. In addition, the obtained results were confronted with experimental data. The calculated fuzzy temperatures are consistent with the temperature values occurring in the LT protocol. Larger differences between the experimental data and the calculated values are observed for the fuzzy dimethyl sulfoxide (DMSO) concentration.