Numerical solution of inward solidification of a dilute ternary solution towards a semi-permeable spherical cell.

Autor: Anderson DM; Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8910, United States; Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, United States., Benson JD; Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8910, United States; Department of Biology, University of Saskatchewan, Saskatoon, Saskatchewan, S7N 5E2, Canada., Kearsley AJ; Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899-8910, United States. Electronic address: ajk@cam.nist.gov.
Jazyk: angličtina
Zdroj: Mathematical biosciences [Math Biosci] 2019 Oct; Vol. 316, pp. 108240. Date of Electronic Publication: 2019 Aug 27.
DOI: 10.1016/j.mbs.2019.108240
Abstrakt: Modeling a cell's response to encroaching ice has informed the development of cryopreservation protocols for four decades. It has been well documented that knowledge of the cellular state as a function of media and cooling rate faciliate informed cryopreservation protocol design and explain mechanisms of damage. However, previous efforts have neglected the interaction between solutes and the encroaching ice front and their effects on the cell state. To address this, here we examine the cryobiologically relevant setting of a spherically-symmetric model of a biological cell separated by a ternary fluid mixture from an encroaching solid-liquid interface. The cell and liquid regions contain cell membrane impermeable intracellular and extracellular salts, respectively, a cell membrane permeable solute commonly used in cryopreservation protocols known as a cryoprotective agent (CPA), and water as a membrane permeable solvent. As cooling and solidification proceed the extracellular chemical environment evolves and leads to mass transport across the cell membrane. Consequently, both the solidification front and the cell membrane are free boundaries whose dynamics are coupled through transport processes in the solid, liquid and cell regions. We describe a numerical procedure to solve this coupled free-boundary problem based on a domain transformation and method of lines approach. We also investigate how the thermal and chemical states inside the cell are influenced by different cooling protocols at the external boundary. Finally, we observe that the previously unaccounted-for partial solute rejection at the advancing solid-liquid interface increases the CPA and salt concentrations in the extracellular liquid as a function of the interface speed and segregation coefficients, suggesting that previous model predictions of the cell state during cryopreservation were inaccurate.
(Published by Elsevier Inc.)
Databáze: MEDLINE
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