Mathematical modeling is often used in tissue engineering in order to overcome one of its major challenges: transformation of complex biological and rheological behaviors of cells and tissue in a mathematically predictive and physically manipulative engineering process. The successive accomplishment of this task will greatly help in quantifying and optimizing clinical application of the tissue engineering products. One of the problems emerging in this area is the relation between resting and migrating cell groups, as well as between different configurations of migrating cells and viscoelasticity. A deeper comprehension of the relation between various configurations of migrating cells and viscoelasticity at the supracellular level represents the prerequisite for optimization of the performance of the artificial epithelium. Since resting and migrating cell groups have a considerable difference in stiffness, a change in their mutual volume ratio and distribution may affect the viscoelasticity of multicellular surfaces. If those cell groups are treated as different phases, then an analogous model may be applied to represent such systems. In this work, a two-step Eyring model is developed in order to demonstrate the main mechanical and biochemical factors that influence configurations of migrating cells. This model could be also used for considering the long-time cell rearrangement under various types of applied stress. The results of this theoretical analysis point out the cause-consequence relationship between the configuration of migrating cells and rheological behavior of multicellular surfaces. Configuration of migrating cells is influenced by mechanical and biochemical perturbations, difficult to measure experimentally, which lead to uncorrelated motility. Uncorrelated motility results in (1) decrease of the volume fraction of migrating cells, (2) change of their configuration, and (3) softening of multicellular surfaces.

中文翻译：

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在体外条件下对施加的压力作出反应的功能性上皮重塑。

组织工程中经常使用数学建模来克服其主要挑战之一：在数学预测和物理操纵的工程过程中转变细胞和组织的复杂生物学和流变行为。这项任务的连续完成将极大地帮助量化和优化组织工程产品的临床应用。该领域出现的问题之一是静止和迁移细胞群之间的关系，以及迁移细胞的不同构型与粘弹性之间的关系。更深入地了解迁移细胞的各种构型与细胞上水平的粘弹性之间的关系，是优化人造上皮性能的前提。由于静止和迁移的细胞组在刚度上有很大差异，因此它们相互体积比和分布的变化可能会影响多细胞表面的粘弹性。如果将那些细胞组视为不同的阶段，则可以应用类似的模型来表示此类系统。在这项工作中，建立了两步式Eyring模型，以证明影响迁移细胞构型的主要机械和生化因素。该模型还可以用于考虑各种类型的应力下的长期细胞重排。该理论分析的结果指出了迁移细胞的构型与多细胞表面流变行为之间的因果关系。迁移细胞的构型受机械和生化扰动的影响，很难通过实验进行测量，这会导致不相关的运动性。不相关的运动性导致（1）迁移细胞的体积分数减少，（2）它们的构型改变，以及（3）多细胞表面的软化。