Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 84, 2023 - Issue 2
118
Views
1
CrossRef citations to date
0
Altmetric
Research Articles

Application of interval arithmetic in numerical modeling of cryopreservation process during cryoprotectant loading to microchamber

ORCID Icon & ORCID Icon
Pages 83-101 | Received 13 Apr 2022, Accepted 18 Jul 2022, Published online: 03 Aug 2022

References

  • F. Xu, S. Moon, X. Zhang, L. Shao, Y. S. Song and U. Demirci, “Multi-scale heat and mass transfer modelling of cell and tissue cryopreservation,” Philos. Trans. A. Math. Phys. Eng. Sci., vol. 368, no. 1912, pp. 561–583, 2010. DOI: 10.1098/rsta.2009.0248.
  • J.-B. J. Fourier, Théorie Analytique de la Chaleur. Firmin Didot, 1822.
  • O. Popczyk and G. Dziatkiewicz, “Kansa method for solving initial-value problem of hyperbolic heat conduction in nonhomogeneous medium,” Int. J. Heat Mass Transf., vol. 183, pp. 122088, Feb. 2022. DOI: 10.1016/j.ijheatmasstransfer.2021.122088.
  • B. Mochnacki and E. Majchrzak, “Numerical model of thermal interactions between cylindrical cryoprobe and biological tissue using the dual-phase lag equation,” Int. J. Heat Mass Transf., vol. 108, pp. 1–10, 2017. DOI: 10.1016/j.ijheatmasstransfer.2016.11.103.
  • H. H. Pennes, “Analysis of tissue and arterial blood temperatures in the restin human forearm,” J. Appl. Physiol., vol. 1, no. 2, pp. 93–122, 1948. DOI: 10.1152/jappl.1948.1.2.93.
  • C. Cattaneo, “Sulla conduzione de calor,” Atti Semin. Mat. e Fis. Della Univ. di Modena, vol. 3, no. 3, pp. 3–21, 1948.
  • C. Cattaneo, “A form of heat conduction equation which eliminates the paradox of instantaneous propagation,” Compte Rendus, vol. 247, no. 4, pp. 431–433, 1958.
  • M. P. Vernotte, “Les paradoxes de la theorie continue de l’equation de la chaleur,” Comptes Rendus, vol. 246, no. 3, pp. 3154–3155, 1958.
  • M. Y. Ge, C. Shu, W. M. Yang and K. J. Chua, “Incorporating an immersed boundary method to study thermal effects of vascular systems during tissue cryo-freezing,” J. Therm. Biol., vol. 64, pp. 92–99, Feb. 2017. DOI: 10.1016/J.JTHERBIO.2017.01.006.
  • Z. Wang, G. Zhao, T. Wang, Q. Yu, M. Su and X. He, “Three-dimensional numerical simulation of the effects of fractal vascular trees on tissue temperature and intracelluar ice formation during combined cancer therapy of cryosurgery and hyperthermia,” Appl. Therm. Eng., vol. 90, pp. 296–304, 2015. DOI: 10.1016/j.applthermaleng.2015.06.103.
  • Z.-S. Deng and J. Liu, “Numerical simulation of selective freezing of target biological tissues following injection of solutions with specific thermal properties,” Cryobiology, vol. 50, no. 2, pp. 183–192, Apr. 2005. DOI: 10.1016/J.CRYOBIOL.2004.12.007.
  • E. Majchrzak and M. Paruch, “Identification of electromagnetic field parameters assuring the cancer destruction during hyperthermia treatment,” Inverse Probl. Sci. Eng., vol. 19, no. 1, pp. 45–58, Jan. 2011. DOI: 10.1080/17415977.2010.531473.
  • E. Majchrzak, B. Mochnacki and M. Jasiński, “Numerical modelling of bioheat transfer in multi-layer skin tissue domain subjected to a flash fire,” Comput. Fluid Solid Mech., vol. 1and, no. 2, pp. 1766–1770, 2003.
  • S. Singh and S. Kumar, “Freezing of biological tissues during cryosurgery using hyperbolic heat conduction model,” Math. Model. Anal., vol. 20, no. 4, pp. 443–456, 2015. DOI: 10.3846/13926292.2015.1064486.
  • H. Ahmadikia and A. Moradi, “Non-Fourier phase change heat transfer in biological tissues during solidification,” Heat Mass Transf., vol. 48, no. 9, pp. 1559–1568, 2012. DOI: 10.1007/s00231-012-1002-1.
  • S. Kumar and S. Singh, “Numerical Study on Biological Tissue Freezing Using Dual Phase Lag Bio-Heat Equation,” Trend. Biomath. Modeling, Optimiz. Comput. Prob. pp. 283–300, 2018. in DOI: 10.1007/978-3-319-91092-5_19.
  • A. Moradi and H. Ahmadikia, “Numerical study of the solidification process in biological tissue with blood flow and metabolism effects by the dual phase lag model,” Proc. Inst. Mech. Eng. H., vol. 226, no. 5, pp. 406–416, 2012. DOI: 10.1177/0954411912441305.
  • E. Majchrzak, Ł. Turchan and J. Dziatkiewicz, “Modeling of skin tissue heating using the generalized dual phase-lag equation,” Arch. Mech., vol. 67, pp. 417–437, 2015.
  • M. Shi, S. Feng, X. Zhang, C. Ji, F. Xu and T. J. Lu, “Droplet based vitrification for cell aggregates: Numerical analysis,” J. Mech. Behav. Biomed. Mater., vol. 82, no. February, pp. 383–393, 2018. DOI: 10.1016/j.jmbbm.2018.03.026.
  • N. Shardt, K. K. Al-Abbasi, H. Yu, N. M. Jomha, L. E. McGann and J. A. W. Elliott, “Cryoprotectant kinetic analysis of a human articular cartilage vitrification protocol,” Cryobiology, vol. 73, no. 1, pp. 80–92, Aug. 2016. DOI: 10.1016/J.CRYOBIOL.2016.05.007.
  • X. Yu, S. Zhang and G. Chen, “Modeling the addition/removal of dimethyl sulfoxide into/from articular cartilage treated with the liquidus-tracking method,” Int. J. Heat Mass Transf., vol. 141, pp. 719–730, 2019. DOI: 10.1016/j.ijheatmasstransfer.2019.07.032.
  • S. Z. Zhang, X. Y. Yu and G. M. Chen, “Permeation of dimethyl sulfoxide into articular cartilage at subzero temperatures,” J. Zhejiang Univ. Sci. B., vol. 13, no. 3, pp. 213–220, 2012. DOI: 10.1631/jzus.B11a0041.
  • IN. Mukherjee, Y. Li, Y. C. Song, R. C. Long and A. Sambanis, “Cryoprotectant transport through articular cartilage for long-term storage: Experimental and modeling studies,” Osteoarthritis Cartil., vol. 16, no. 11, pp. 1379–1386, 2008. DOI: 10.1016/j.joca.2008.03.027.
  • J. D. Benson, A. Z. Higgins, K. Desai and A. Eroglu, “A toxicity cost function approach to optimal CPA equilibration in tissues,” Cryobiology, vol. 80, pp. 144–155, 2018. DOI: 10.1016/j.cryobiol.2017.09.005.
  • A. Lawson, IN. Mukherjee and A. Sambanis, “Mathematical modeling of cryoprotectant addition and removal for the cryopreservation of engineered or natural tissues,” Cryobiology, vol. 64, no. 1, pp. 1–11, 2012. DOI: 10.1016/j.cryobiol.2011.11.006.
  • X. Zhou, et al., “Microfiltration-based sequential perfusion: A new approach for improved loading/unloading of cryoprotectants,” Sensors Actuators B Chem., vol. 312, no. 26, pp. 127957, 2020. DOI: 10.1016/j.snb.2020.127957.
  • Y. S. Song, S. Moon, L. Hulli, S. K. Hasan, E. Kayaalp and U. Demirci, “Microfluidics for cryopreservation,” Lab. Chip., vol. 9, no. 13, pp. 1874–81, Jul. 2009. DOI: 10.1039/b823062e.
  • W. Liu, G. Zhao, Z. Shu, T. Wang, K. Zhu and D. Gao, “High-precision approach based on microfluidic perfusion chamber for quantitative analysis of biophysical properties of cell membrane,” Int. J. Heat Mass Transf., vol. 86, pp. 869–879, 2015. DOI: 10.1016/j.ijheatmasstransfer.2015.03.038.
  • M. H. Jacobs, “The simultaneous measurement of cell permeability to water and to dissolved substances,” J. Cell. Comp. Physiol., vol. 2, no. 4, pp. 427–444, 1933. DOI: 10.1002/jcp.1030020405.
  • M. H. Jacobs and D. R. Stewart, “A simple method for the quantitative measurement of cell permeability,” J. Cell. Comp. Physiol., vol. 1, no. 1, pp. 71–82, Feb. 1932. DOI: 10.1002/jcp.1030010107.
  • H. Y. Elmoazzen, J. A. W. Elliott and L. E. McGann, “Osmotic transport across cell membranes in nondilute solutions: A new nondilute solute transport equation,” Biophys. J., vol. 96, no. 7, pp. 2559–2571, Apr. 2009. DOI: 10.1016/J.BPJ.2008.12.3929.
  • Y. Zheng, G. Zhao, Y. Zhang and R. Gao, “On-chip loading and unloading of cryoprotectants facilitate cell cryopreservation by rapid freezing,” Sensors Actuators B Chem., vol. 255, pp. 647–656, 2018. DOI: 10.1016/j.snb.2017.08.084.
  • X. Xu, Z. Cui and J. P. Urban, “Measurement of the chondrocyte membrane permeability to Me2SO, glycerol and 1,2-propanediol,” Med. Eng. Phys., vol. 25, no. 7, pp. 573–579, Sep. 2003. DOI: 10.1016/S1350-4533(03)00073-0.
  • O. Kedem and A. Katchalsky, “Thermodynamic analysis of the permeability of biological membranes to non-electrolytes,” Biochim. Biophys. Acta., vol. 27, pp. 229–246, 1958. DOI: 10.1016/0006-3002(58)90330-5.
  • X. Zhou, X. M. Liang, J. Wang, P. Du and D. Gao, “Theoretical and experimental study of a membrane-based microfluidics for loading and unloading of cryoprotective agents,” Int. J. Heat Mass Transf., vol. 127, pp. 637–644, Dec. 2018. DOI: 10.1016/j.ijheatmasstransfer.2018.06.137.
  • Y. Xu, L. Zhang, J. Xu, Y. Wei and X. Xu, “Membrane permeability of the human pluripotent stem cells to Me 2SO, glycerol and 1,2-propanediol,” Arch. Biochem. Biophys., vol. 550–551, pp. 67–76, 2014. DOI: 10.1016/j.abb.2014.04.010.
  • X. Xu, Z. F. Cui, R. J. Wilkins and J. P. G. Urban, “Intracellular pH changes in isolated bovine articular chondrocytes during the loading and removal of cryoprotective agents,” Cryobiology, vol. 46, no. 2, pp. 161–173, Apr. 2003. DOI: 10.1016/S0011-2240(03)00022-1.
  • P. Mazur, “Kinetics of water loss from cells at subzero temperatures and the likelihood of intracellular freezing,” J. Gen. Physiol., vol. 47, pp. 347–369, 1963. DOI: 10.1085/jgp.47.2.347.
  • R. L. Levin, E. G. Cravalho and C. E. Huggins, “A membrane model describing the effect of temperature on the water conductivity of erythrocyte membranes at subzero temperatures,” Cryobiology, vol. 13, no. 4, pp. 415–429, 1976. DOI: 10.1016/0011-2240(76)90097-3.
  • W. T. Wu, S.-R. Lyu and W. H. Hsieh, “Cryopreservation and biophysical properties of articular cartilage chondrocytes,” Cryobiology, vol. 51, no. 3, pp. 330–338, Dec. 2005. DOI: 10.1016/J.CRYOBIOL.2005.08.006.
  • D. Devismita and A. Kumar, “Effect of cryoprotectant on optimal cooling rate during cryopreservation,” Cryobiology, vol. 70, no. 1, pp. 53–59, Feb. 2015. DOI: 10.1016/J.CRYOBIOL.2014.12.002.
  • S. Thirumala, J. M. Gimble and R. V. Devireddy, “Transport phenomena during freezing of adipose tissue derived adult stem cells,” Biotechnol Bioeng., vol. 92, no. 3, pp. 372–383, 2005. DOI: 10.1002/bit.20615.
  • T. H. Jang, et al., “Cryopreservation and its clinical applications,” Integr. Med. Res., vol. 6, no. 1, pp. 12–18, Mar. 2017. DOI: 10.1016/J.IMR.2016.12.001.
  • J. Farrant, “Mechanism of cell damage during freezing and thawing and its prevention,” Nature, vol. 205, no. 4978, pp. 1284–1287, 1965. DOI: 10.1038/2051284a0.
  • B. C. Elford and C. A. Walter, “Effects of electrolyte composition and pH on the structure and function of smooth muscle cooled to −79 °C in unfrozen media,” Cryobiology, vol. 9, no. 2, pp. 82–100, 1972. DOI: 10.1016/0011-2240(72)90015-6.
  • A. G. Kay, J. A. Hoyland, P. Rooney, J. N. Kearney and D. E. Pegg, “A liquidus tracking approach to the cryopreservation of human cartilage allografts,” Cryobiology, vol. 71, no. 1, pp. 77–84, Aug. 2015. DOI: 10.1016/J.CRYOBIOL.2015.05.005.
  • D. E. Pegg, L. Wang and D. Vaughan, “Cryopreservation of articular cartilage. Part 3: The liquidus-tracking method,” Cryobiology, vol. 52, no. 3, pp. 360–368, Jun. 2006. DOI: 10.1016/J.CRYOBIOL.2006.01.004.
  • L. Wang, D. E. Pegg, J. Lorrison, D. Vaughan and P. Rooney, “Further work on the cryopreservation of articular cartilage with particular reference to the liquidus tracking (LT) method,” Cryobiology, vol. 55, no. 2, pp. 138–147, Oct. 2007. DOI: 10.1016/J.CRYOBIOL.2007.06.005.
  • G. Zhao and J. Fu, “Microfluidics for cryopreservation,” Biotechnol. Adv., vol. 35, no. 2, pp. 323–336, 2017. DOI: 10.1016/j.biotechadv.2017.01.006.
  • T. Scherr, S. Pursley, W. T. Monroe and K. Nandakumar, “A numerical study on the loading of cryoprotectant cocktails-on-a-chip, Part I: Interacting miscible viscous fluids,” Int. J. Heat Mass Transf., vol. 78, pp. 1284–1291, 2014. DOI: 10.1016/j.ijheatmasstransfer.2014.07.026.
  • T. Scherr, S. Pursley, W. T. Monroe and K. Nandakumar, “A numerical study on the loading of cryoprotectant cocktails-on-a-chip. Part II: The cellular experience,” Int. J. Heat Mass Transf., vol. 78, pp. 1292–1299, 2014. DOI: 10.1016/j.ijheatmasstransfer.2014.07.025.
  • B. Mochnacki and A. Piasecka - Belkhayat, “Numerical modeling of skin tissue heating using the interval finite difference method,” Mol. Cell Biomech., vol. 10, no. 3, pp. 233–244, 2013. DOI: 10.3970/mcb.2013.010.233.
  • A. Piasecka-Belkhayat, “Interval boundary element method for 2D transient diffusion problem using the directed interval arithmetic,” Eng. Anal. Bound. Elem., vol. 35, pp. 259–263, Mar. 2011. DOI: 10.1016/j.enganabound.2010.11.005.
  • A. Skorupa and A. Piasecka-Belkhayat, “Numerical modeling of heat and mass transfer during cryopreservation using interval analysis,” Appl. Sci., vol. 11, no. 1, pp. 302, 2020. DOI: 10.3390/app11010302.
  • A. Piasecka-Belkhayat and A. Skorupa, “Numerical study of heat and mass transfer during cryopreservation process with application of directed interval arithmetic,” Materials (Basel), vol. 14, no. 11, pp. 2966, 2021. DOI: 10.3390/ma14112966.
  • J. Wang and T. Hou, “Application of molecular dynamics simulations in molecular property prediction II: Diffusion coefficient,” J. Comput. Chem., vol. 32, no. 16, pp. 3505–3519, 2011. DOI: 10.1002/jcc.21939.
  • B. Mochnacki and J. Suchy, Numerical Methods in Computations of Foundry Processes. Cracow: Polish Scientific Publishers PWN, 1993.
  • E. Scannapieco and F. H. Harlow, Introduction to Finite-Difference Methods for Numerical Fluid Dynamics. United States: N.P., 1995.
  • C. W. Hirt, B. D. Nichols and N. C. Romero, “SOLA: A numerical solution algorithm for transient fluid flows,” Los Alamos Scientific Lab., N. Mex. (USA), LA-5852, 1975.
  • D. E. Pegg, M. C. Wusteman and L. Wang, “Cryopreservation of articular cartilage. Part 1: Conventional cryopreservation methods,” Cryobiology, vol. 52, no. 3, pp. 335–346, 2006. DOI: 10.1016/j.cryobiol.2006.01.005.
  • L. E. McGann, M. Stevenson, K. Muldrew and N. Schachar, “Kinetics of osmotic water movement in chondrocytes isolated from articular cartilage and applications to cryopreservation,” J. Orthop. Res., vol. 6, no. 1, pp. 109–115, 1988. DOI: 10.1002/jor.1100060114.
  • E. Majchrzak and B. Mochnacki, Numerical Methods. Theoretical Base, Practical Aspects, Algorithms. Gliwice: Publ. of the Silesian Univ. of Technology, 2004,
  • S. Markov, “On directed interval arithmetic and its applications,” J. UCS J. Univ. Comput. Sci., vol. 1, no. 7, pp. 514–526, 1996. in Springer Berlin Heidelberg, DOI: 10.1007/978-3-642-80350-5_43.
  • A. Neumaier, Interval Methods for Systems of Equations. Cambridge, New York, Port Chester, Melbourne, Sydney: Cambridge University Press, 1990.
  • B. M. Schulze, D. L. Watkins, J. Zhang, I. Ghiviriga and R. K. Castellano, “Estimating the shape and size of supramolecular assemblies by variable temperature diffusion ordered spectroscopy,” Org. Biomol. Chem. Suppl. Mater., vol. 12, no. 40, pp. 7932–S27, 2014. DOI: 10.1039/C4OB01373E.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.