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

Skorupa Anna, Piasecka-Belkhayat Alicja

Acta of Bioengineering and Biomechanics

2025

Vol. 27, no. 1

47--56

This paper presents numerical modelling of the heat and mass transfer process in a cryopreserved biological sample. The simula-tion 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 triangu-lar 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.

Cryopreservation analysis considering degree of crystallisation using fuzzy arithmetic

Piasecka-Belkhayat Alicja, Skorupa Anna

Journal of Theoretical and Applied Mechanics

2024

Vol. 62 nr 2

207--218

This article presents numerical modelling of the heat transfer process in a sample during cryopreservation by vitrification in a microfluidic system. Single-phase flow of the working fluid in the microchannels during warming was considered, while two-phase flow during cooling. The mathematical model is based on the Fourier equation with a source term that takes into account the degree of ice crystallisation. Fuzzy thermophysical parameters were assumed in the model. The problem was solved by the finite difference method and the fourth-order Runge-Kutta algorithm, using the concept of α-cuts. The results of numerical simulation were compared with the results from the literature.