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

• Autorzy: Skorupa Anna , Piasecka-Belkhayat Alicja

Identyfikatory

DOI

10.37190/ABB-02520-2024-03

• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

cryopreservation; heat transfer; mass transfer; fuzzy numbers; Gaussian membership function; α-cuts concept

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Acta of Bioengineering and Biomechanics
• Rocznik: 2025
• Tom: Vol. 27, no. 1
• Strony: 47--56
• Opis fizyczny: Bibliogr. 35 poz., rys., tab., wykr.

Twórcy

autor

Skorupa Anna

• Department of Computational Mechanics and Engineering, Silesian University of Technology, Gliwice, Poland.

autor

Piasecka-Belkhayat Alicja

• Department of Computational Mechanics and Engineering, Silesian University of Technology, Gliwice, Poland.

Bibliografia

• [1] BEHROU R., FOROUGHI H., HAGHPANAH F., Numerical study of temperature effects on the poro-viscoelastic behavior of artic-ular cartilage, Journal of the Mechanical Behavior of Biomed-ical Materials, 2018, 78, 214–223, DOI: 10.1016/j.jmbbm. 2017.11.023.
• [2] CANIANI D., LIOI D.S., MANCINI I.M., MASI S., Application of fuzzy logic and sensitivity analysis for soil contamination haz-ard classification, Waste Management, 2011, 31 (3), 583–594, DOI: 10.1016/j.wasman.2010.09.012.
• [3] ÇENGEL Y.A., GHAJAR A.J., Heat and mass transfer: fundamen-tals and applications, McGraw-Hill Higher Education, 2015.
• [4] CICHOCKI B., Albert Einstein – praca o ruchach Browna z 1905 roku, DeltaMi, 2005. http://www.deltami.edu.pl/temat/fizyka/ struktura_materii/2011/01/01/Albert_Einstein-praca_o_ruchach/ [Accessed: 2.08.2022].
• [5] DUBOIS D.J., Fuzzy Sets and Systems: Theory and Applications, Academic Press, 1980.
• [6] FICK A., Ueber Diffusion, Annalen der Physik, 1855, 94 (1), 59–86, DOI: 10.1002/andp.18551700105.
• [7] FICK A., V. On liquid diffusion, Philosophical Magazine, 1855, 10 (63), 30–39, DOI: 10.1080/14786445508641925.
• [8] FOURIER J.B.J., Théorie analytique de la chaleur, Firmin Didot, 1882.
• [9] HANSS M., Applied Fuzzy Arithmetic, Springer, Berlin–Heidel- berg–New York 2005.
• [10] HATŁAS M., Modelling and optimisation of inhomogeneous ma- terials using granular computations, Doctoral thesis, Politechni-ka Śląska, Gliwice, 2021.
• [11] JANG T.H. et al., Cryopreservation and its clinical applications, Integrative Medicine Research, 2017, 6 (1), 12–18, DOI: 10.1016/j.imr.2016.12.001.
• [12] JUNGARE K.A., RADHA R., SREEKANTH D., Cryopreservation of biological samples – A short review, Materials Today: Proceed-ings, 2022, 51, 1637–1641, DOI: 10.1016/j.matpr.2021.11.203.
• [13] KAY A.G., HOYLAND J.A., ROONEY P., KEARNEY J.N., PEGG D.E., A liquidus tracking approach to the cryopreservation of hu-man cartilage allografts, Cryobiology, 2015, 71 (1), 77–84, DOI: 10.1016/j.cryobiol.2015.05.005.
• [14] LEANDRY L., SOSOMA I., KOLOSENI D., Basic Fuzzy Arithmetic Operations Using –Cut for the Gaussian Membership Func-tion, Journal of Fuzzy Extension and Applications, 2022, 3 (4), 337–348, DOI: 10.22105/jfea.2022.339888.1218.
• [15] LIU W., ZHAO G., SHU Z., WANG T., ZHU K., GAO D., High- -precision approach based on microfluidic perfusion chamber for quantitative analysis of biophysical properties of cell mem-brane, International Journal of Heat and Mass Transfer, 2015, 86, 869–879, DOI: 10.1016/j.ijheatmasstransfer.2015.03.038.
• [16] LÜ H., SHANGGUAN W.-B., YU D., Uncertainty quantification of squeal instability under two fuzzy-interval cases, Fuzzy Sets and Systems, 2017, 328, 70–82, DOI: 10.1016/j.fss.2017.07.006.
• [17] MAZUR P., Kinetics of Water Loss from Cells at Subzero Temperatures and the Likelihood of Intracellular Freezing, Journal of General Physiology, 1963, 47 (2), 347–369, DOI: 10.1085/jgp.47.2.347.
• [18] MOCHNACKI B., SUCHY J., Modelowanie i symulacja krzepnięcia odlewów, Wydawnictwo Naukowe PWN, Warszawa 1993.
• [19] MOORE R.E., Interval Analysis, Prentice-Hall, New Jersey, USA, 1966.
• [20] PEGG D.E., WANG L., VAUGHAN D., Cryopreservation of articu-lar cartilage. Part 3: The liquidus-tracking method, Cryobiology, 2006, 52 (3), 360–368, DOI: 10.1016/j.cryobiol.2006.01.004.
• [21] PIASECKA-BELKHAYAT A., Przedziałowa metoda elementów brzegowych w nieprecezyjnych zadaniach nieustalonej dyfuzji ciepła, Wydawnictwo Politechniki Śląskiej, Gliwice, 2011.
• [22] PIASECKA-BELKHAYAT A., SKORUPA A., Application of interval arithmetic in numerical modeling of cryopreservation process during cryoprotectant loading to microchamber, Numerical Heat Transfer, Part A: Applications, 2022, 84 (2), 83–101, DOI: 10.1080/10407782.2022.2105078.
• [23] PIASECKA-BELKHAYAT A., SKORUPA A., Cryopreservation analysis considering degree of crystallisation using fuzzy arith- metic, Journal of Theoretical and Applied Mechanics, 2024, 207–218, DOI: 10.15632/jtam-pl/183697.
• [24] PIASECKA-BELKHAYAT A., SKORUPA A., Numerical Study of Heat and Mass Transfer during Cryopreservation Process with Application of Directed Interval Arithmetic, Materials, 2021, 14 (11), 2966, DOI: 10.3390/ma14112966.
• [25] SCHULZE B.M., WATKINS D.L., ZHANG J., GHIVIRIGA I., CASTELLANO R.K., Estimating the shape and size of supra- molecular assemblies by variable temperature diffusion ordered spectroscopy, Org. Biomol. Chem., 2014, 12 (40), 7932–7936, DOI: 10.1039/C4OB01373E.
• [26] SKORUPA A., Multi-scale modelling of heat and mass transfer in tissues and cells during cryopreservation including inter-val methods, Doctoral thesis, Politechnika Śląska, Gliwice, 2023. [Online]. Available: https://repolis.bg.polsl.pl/dlibra/publication/ 85590/edition/76693 [Accessed: 10.10.2023].
• [27] SKORUPA A., PIASECKA-BELKHAYAT A., Numerical Modeling of Heat and Mass Transfer during Cryopreservation Using Interval Analysis, Applied Sciences, 2020, 11 (1), 302, DOI: 10.3390/ app11010302.
• [28] TAYLOR M.J., HUNT C.J., A new preservation solution for stor-age of corneas at low temperatures, Current Eye Research, 1985, 4 (9), 963–973, DOI: 10.3109/02713689509000003.
• [29] WANG C., MATTHIES H.G., Coupled fuzzy-interval model and method for structural response analysis with non-probabilistic hybrid uncertainties, Fuzzy Sets and Systems, 2021, 417, 171–189, DOI: 10.1016/j.fss.2020.06.002.
• [30] WANG L., PEGG D.E., LORRISON J., VAUGHAN D., ROONEY P., Further work on the cryopreservation of articular cartilage with particular reference to the liquidus tracking (LT) method, Cryobiology, 2007, 55 (2), 138–147, DOI: 10.1016/ j.cryobiol.2007.06.005.
• [31] XU F., MOON S., ZHANG X., SHAO L., SONG Y.S., DEMIRCI U., Multi-scale heat and mass transfer modelling of cell and tissue cryopreservation, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2010, 368 (1912), 561–583, DOI: 10.1098/rsta.2009. 0248.
• [32] YOUN J.-I. et al., Optical and thermal properties of nasal septal cartilage, Lasers in Surgery and Medicine, 2000, 27 (2), 119–128, DOI: 10.1002/1096-9101(2000)27:2<119::AID-LSM3> 3.0.CO;2-V.
• [33] YU X., ZHANG S., CHEN G., Modeling the addition/removal of dimethyl sulfoxide into/from articular cartilage treated with the liquidus-tracking method, International Journal of Heat and Mass Transfer, 2019, 141, 719–730, DOI: 10.1016/ j.ijheatmasstransfer.2019.07.032.
• [34] ZADEH L.A., Fuzzy sets, Information and Control, 1965, 8 (3), 338–353.
• [35] ZHAO G., FU J., Microfluidics for cryopreservation, Bio-technology Advances, 2017, 35 (2), 323–336, DOI: 10.1016/ j.biotechadv.2017.01.006.