Anderson Daniel M, Benson James D, Kearsley Anthony J
Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-8910, United States; Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, United States.
Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, MD 20899-8910, United States; Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115-2888, United States.
Cryobiology. 2014 Dec;69(3):349-60. doi: 10.1016/j.cryobiol.2014.09.004. Epub 2014 Sep 21.
Mathematical modeling plays an enormously important role in understanding the behavior of cells, tissues, and organs undergoing cryopreservation. Uses of these models range from explanation of phenomena, exploration of potential theories of damage or success, development of equipment, and refinement of optimal cryopreservation/cryoablation strategies. Over the last half century there has been a considerable amount of work in bio-heat and mass-transport, and these models and theories have been readily and repeatedly applied to cryobiology with much success. However, there are significant gaps between experimental and theoretical results that suggest missing links in models. One source for these potential gaps is that cryobiology is at the intersection of several very challenging aspects of transport theory: it couples multi-component, moving boundary, multiphase solutions that interact through a semipermeable elastic membrane with multicomponent solutions in a second time-varying domain, during a two-hundred Kelvin temperature change with multi-molar concentration gradients and multi-atmosphere pressure changes. In order to better identify potential sources of error, and to point to future directions in modeling and experimental research, we present a three part series to build from first principles a theory of coupled heat and mass transport in cryobiological systems accounting for all of these effects. The hope of this series is that by presenting and justifying all steps, conclusions may be made about the importance of key assumptions, perhaps pointing to areas of future research or model development, but importantly, lending weight to standard simplification arguments that are often made in heat and mass transport. In this first part, we review concentration variable relationships, their impact on choices for Gibbs energy models, and their impact on chemical potentials.
数学建模在理解经历冷冻保存的细胞、组织和器官的行为方面发挥着极其重要的作用。这些模型的用途广泛，包括解释现象、探索损伤或成功的潜在理论、开发设备以及完善最佳冷冻保存/冷冻消融策略。在过去的半个世纪里，生物热和质量传输方面已经开展了大量工作，并且这些模型和理论已被成功地反复应用于低温生物学。然而，实验结果与理论结果之间存在显著差距，这表明模型中存在缺失环节。这些潜在差距的一个来源是，低温生物学处于传输理论中几个极具挑战性的方面的交叉点：它将通过半透性弹性膜相互作用的多组分、移动边界、多相溶液与第二个随时间变化的域中的多组分溶液耦合在一起，这一过程发生在200开尔文的温度变化、多摩尔浓度梯度和多大气压变化期间。为了更好地识别潜在的误差来源，并指出建模和实验研究的未来方向，我们推出一个由三部分组成的系列文章，从第一原理出发构建一个考虑所有这些效应的低温生物学系统中热质耦合传输理论。本系列文章的期望是，通过展示并论证所有步骤，可以就关键假设的重要性得出结论，或许能指出未来研究或模型开发的领域，但重要的是，为热质传输中经常采用的标准简化论点提供依据。在第一部分中，我们回顾浓度变量关系、它们对吉布斯能量模型选择的影响以及它们对化学势的影响。
