Reinhardt James W, Gooch Keith J
Department of Biomedical Engineering, The Ohio State University, 270 Bevis Hall, 1080 Carmack Road, Columbus, OH 43210 e-mail: .
Department of Biomedical Engineering, The Ohio State University, 270 Bevis Hall, 1080 Carmack Road, Columbus, OH 43210.
J Biomech Eng. 2018 May 1;140(5). doi: 10.1115/1.4037947.
Microstructural properties of extracellular matrix (ECM) promote cell and tissue homeostasis as well as contribute to the formation and progression of disease. In order to understand how microstructural properties influence the mechanical properties and traction force-induced remodeling of ECM, we developed an agent-based model that incorporates repetitively applied traction force within a discrete fiber network. An important difference between our model and similar finite element models is that by implementing more biologically realistic dynamic traction, we can explore a greater range of matrix remodeling. Here, we validated our model by reproducing qualitative trends observed in three sets of experimental data reported by others: tensile and shear testing of cell-free collagen gels, collagen remodeling around a single isolated cell, and collagen remodeling between pairs of cells. In response to tensile and shear strain, simulated acellular networks with straight fibrils exhibited biphasic stress-strain curves indicative of strain-stiffening. When fibril curvature was introduced, stress-strain curves shifted to the right, delaying the onset of strain-stiffening. Our data support the notion that strain-stiffening might occur as individual fibrils successively align along the axis of strain and become engaged in tension. In simulations with a single, contractile cell, peak collagen displacement occurred closest to the cell and decreased with increasing distance. In simulations with two cells, compaction of collagen between cells appeared inversely related to the initial distance between cells. These results for cell-populated collagen networks match in vitro findings. A demonstrable benefit of modeling is that it allows for further analysis not feasible with experimentation. Within two-cell simulations, strain energy within the collagen network measured from the final state was relatively uniform around the outer surface of cells separated by 250 μm, but became increasingly nonuniform as the distance between cells decreased. For cells separated by 75 and 100 μm, strain energy peaked in the direction toward the other cell in the region in which fibrils become highly aligned and reached a minimum adjacent to this region, not on the opposite side of the cell as might be expected. This pattern of strain energy was partly attributable to the pattern of collagen compaction, but was still present when mapping strain energy divided by collagen density. Findings like these are of interest because fibril alignment, density, and strain energy may each contribute to contact guidance during tissue morphogenesis.
细胞外基质（ECM）的微观结构特性有助于维持细胞和组织的稳态，并参与疾病的形成和发展。为了理解微观结构特性如何影响ECM的力学性能以及牵引力诱导的重塑，我们开发了一种基于代理的模型，该模型在离散纤维网络中纳入了重复施加的牵引力。我们的模型与类似的有限元模型之间的一个重要区别在于，通过实现更符合生物学实际的动态牵引力，我们可以探索更大范围的基质重塑。在这里，我们通过重现他人报道的三组实验数据中观察到的定性趋势来验证我们的模型：无细胞胶原凝胶的拉伸和剪切测试、单个孤立细胞周围的胶原重塑以及成对细胞之间的胶原重塑。响应拉伸和剪切应变，具有直纤维的模拟无细胞网络表现出双相应力 - 应变曲线，表明应变硬化。当引入纤维曲率时，应力 - 应变曲线向右移动，延迟了应变硬化的开始。我们的数据支持这样一种观点，即应变硬化可能是由于单个纤维沿应变轴依次排列并进入张力状态而发生的。在单个收缩细胞的模拟中，胶原峰值位移发生在最靠近细胞的位置，并随着距离增加而减小。在两个细胞的模拟中，细胞间胶原的压实似乎与细胞间的初始距离成反比。这些关于细胞填充胶原网络的结果与体外研究结果相符。建模的一个明显好处是它允许进行实验无法实现的进一步分析。在两个细胞的模拟中，从最终状态测量的胶原网络内的应变能在被250μm隔开的细胞外表面周围相对均匀，但随着细胞间距离减小而变得越来越不均匀。对于被75μm和100μm隔开的细胞，应变能在纤维高度排列的区域中朝着另一个细胞的方向达到峰值，并在该区域相邻处达到最小值，而不是在细胞的另一侧，这与预期的情况不同。这种应变能模式部分归因于胶原压实模式，但在映射应变能除以胶原密度时仍然存在。这样的发现很有趣，因为纤维排列、密度和应变能可能各自在组织形态发生过程中对接触引导起作用。
