全部

力学与实践 ›› 2019, Vol. 41 ›› Issue (1): 52-59.doi: 10.6052/1000-0879-18-215

• 应用研究 • 上一篇    下一篇

成纤维细胞在基质刚度梯度作用下趋硬性迁移数值模拟1)

宁乐, 张涵, 朱卫平2)   

  1. 上海大学,上海市应用数学和力学研究所,上海 200072
  • 收稿日期:2018-06-04 出版日期:2019-02-20
  • 通讯作者: 2)朱卫平,教授, 主要研究方向为固体力学, 细胞生物力学。 E-mail: wpzhu@shu.edu.cn
  • 基金资助:
    1)国家自然科学基金资助项目(31370940)

NUMERICAL SIMULATION OF FIBROBLAST DUROTAXIS MIGRATION INDUCED BY STIFFNESS GRADIENT OF SUBSTRATE1)

NING Le, ZHANG Han, ZHU Weiping2)   

  1. Shanghai University, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China
  • Received:2018-06-04 Online:2019-02-20

摘要: 建立了一种细胞趋硬性迁移的理论模型和有限元分析框架,为连续变刚度人工基质的试验设计提供理论依据。考虑了细胞体的黏弹性属性,以及细胞与基质间的配受体动态反应过程,并以配受体合成时间为时间步长,将细胞运动方程化为静力学形式进行求解。对有限元过程提出一种动约束,便于消除其结构矩阵的奇异性。结果表明,模型能够模拟黏着斑内部力的快速波动现象,细胞的运动速度与观测数据一致,可有效模拟20,h以上的长时程问题。

关键词: 组织工程, 基质刚度, 细胞趋硬性, 理论模型, 有限元

Abstract: A theoretical model and the finite element method (FEM) are used to simulate the durotaxis movement of the cell on an artificial substrate with a continuous varying stiffness for the test design. The viscoelastic properties of the cell and the dynamic reactions of the receptors and the ligands between the cell and the substrate, are all considered. The time step equal to that of producing a pair of receptor-ligand is used for discretizing the functions of the time, turning the dynamic FEM into a static one. And a condition of moving constraint for the cell structure is proposed for eliminating the singularity of the FEM matrix more easily. The simulation results show that there is a rapid fluctuation of the force in the focal adhesion during the cell durotaxis, the speed of the cell migration, as is consistent with the observation, and the migration process can efficiently last over 20 hours.

Key words: tissue engineering, substrate stiffness, cell durotaxis, theoretical model, FEM (finite element method)

中图分类号: 

  • R329.2