Mathematical Modeling of Cell Biopreservation by Desiccation

描述(申请人提供)：拟议的合作研究的目标是对通过玻璃化和干燥法进行细胞生物保存的关键过程进行全面的数学调查。这项研究将集中在生物溶液中玻璃态的形成以及传播的玻璃转变前沿与细胞膜和细胞内细胞器的相互作用。这将通过建立相应的数学模型，并利用渐近和数值方法进行研究和求解来实现。拟议中的研究计划是西北大学的一个理论小组与哈佛医学院和马萨诸塞州总医院的一个实验小组之间的密切合作。理论分析的结果将被对比、分析并得到实验的支持。 玻璃系统的特点是扩散输运是反常的，因为它用分数导数的次扩散方程来描述。从根本上讲，这项研究将使人们能够理解基于细胞内玻璃形成的生物保存机制。从生物医学的角度来看，这一认识将导致生物保存技术和方案的改进和优化，以实现更高的细胞存活率。从应用数学的角度出发，本研究将发展新的模型和方法来解决特殊类型的非平凡分数阶微分方程组及其相关的自由边界问题。计划中的实验工作将作为制定数学模型的指导。在可应用渐近和摄动法的几种极限情况下，将寻求解析解，而在更一般的情况下，将进行计算研究。

DESCRIPTION (provided by applicant): The objective of the proposed collaborative research is to carry out a comprehensive mathematical investigation of the key processes governing biopreservation of cells by vitrification and desiccation. The research will be focused on the formation of a glassy state in biological solutions and the interaction of the propagating glass transition fronts with cell membranes and intracellular organelles. This will be done by formulating the corresponding mathematical models and their investigation and solution by means of asymptotic and numerical methods. The proposed research program is planned as a close collaboration between a theoretical group at Northwestern University and an experimental group at the Harvard Medical School and the Massachusetts General Hospital. The results of theoretical analysis will be compared, analyzed and supported by experiments. The peculiarity of glassy systems is that the diffusion transport there is anomalous in that it is described by subdiffusion equations with fractional derivatives. From fundamental point of view, this research will allow one to understand the mechanisms of biopreservation based on the formation of glass inside the cell. From the biomedical point of view, this understanding will lead to improvement and optimization of biopreservation techniques and protocols to achieve higher cell survival rates. From the applied mathematics point of view, this research will develop new models and methods of solving special classes of non-trivial fractional PDEs (integro-differential equations) and associated free-boundary problems. The planned experimental work will be used as a guide in formulating the mathematical models. Analytical solutions will be sought in several limiting cases where asymptotic and perturbation methods can be applied, while a computational investigation will be done in the more general cases.