An XFEM-based numerical strategy to model mechanical interactions between biological cells and a deformable substrate
An XFEM-based numerical strategy to model mechanical interactions between biological cells and a deformable substrate
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DOI：
10.1002/nme.4335
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发表时间：
2012-10-19
影响因子：
2.9
通讯作者：
Vernerey, Franck J.
中科院分区：
文献类型：
--
作者：
Farsad, Mehdi;Vernerey, Franck J.
已知收缩细胞通过机械感测不断探测和响应其机械环境。尽管导致这种行为的机制仍然不清楚，但现在很清楚，细胞充分利用力学，化学和运输之间的交叉对话来组织它们的结构并产生力。为了研究这些过程，重要的是要推导出数学和数值模型，可以准确地捕捉细胞和下面的可变形基板之间的相互作用。因此，本文介绍了一个计算框架，基于扩展有限元法（XFEM）和水平集方法，模拟二维（平面应力）细胞的演变躺在弹性基板上，其属性可以改变。细胞建模与连续混合物的方法，以前开发的作者描述细胞传感的关键现象，如应力纤维的形成，mechanosensitive收缩，和分子运输，而cellsubstrate粘附制定了一个线性弹性凝聚力模型。从数值的角度来看，细胞和基板上的一个单一的，定期的有限元网格离散化，而潜在的复杂的细胞的几何形状定义的水平集函数，是独立的离散化。跨细胞膜的场不连续性然后自然地使用传统上用于XFEM制定的丰富的形状函数来执行。由此产生的方法提供了一个灵活的平台，可以处理复杂的细胞几何形状，可以避免昂贵的网格技术，并可以潜在地扩展到研究细胞的生长和迁移的弹性基板。此外，XFEM的形式主义有利于考虑细胞的皮质弹性，一个功能是已知的细胞变形过程中是重要的。所提出的方法说明了一些生物相关的例子cellsubstrate相互作用。一般来说，该方法能够捕获生物系统中观察到的一些关键现象，并以适度的计算成本显示数值通用性和准确性。版权所有（c）2012 John Wiley & Sons，Ltd.
Contractile cells are known to constantly probe and respond to their mechanical environment through mechanosensing. Although the very mechanisms responsible for this behavior are still obscure, it is now clear that cells make full use of cross-talks between mechanics, chemistry, and transport to organize their structure and generate forces. To investigate these processes, it is important to derive mathematical and numerical models that can accurately capture the interactions between cells and an underlying deformable substrate. The present paper therefore introduces a computational framework, based on the extended FEM (XFEM) and the level set method, to model the evolution of two-dimensional (plane stress) cells lying on an elastic substrate whose properties can be varied. Cells are modeled with a continuum mixture approach previously developed by the authors to describe key phenomena of cell sensing, such as stress fiber formation, mechanosensitive contraction, and molecular transport whereas cellsubstrate adhesion is formulated with a linear elastic cohesive model. From a numerical viewpoint, cell and substrate are discretized on a single, regular finite element mesh, whereas the potentially complex cell geometry is defined in terms of a level set function that is independent of discretization. Field discontinuities across the cell membrane are then naturally enforced using enriched shape functions traditionally used in the XFEM formulation. The resulting method provides a flexible platform that can handle complex cell geometries, can avoid expensive meshing techniques, and can potentially be extended to study cell growth and migration on an elastic substrate. In addition, the XFEM formalism facilitates the consideration of the cell's cortical elasticity, a feature that is known to be important during cell deformation. The proposed method is illustrated with a few biologically relevant examples of cellsubstrate interactions. Generally, the method is able to capture some key phenomena observed in biological systems and displays numerical versatility and accuracy at a moderate computational cost.Copyright (c) 2012 John Wiley & Sons, Ltd.