Cell Invasion in Collagen Scaffold Architectures Characterized by Percolation Theory.
Cell Invasion in Collagen Scaffold Architectures Characterized by Percolation Theory.
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DOI：
10.1002/adhm.201500197
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发表时间：
2015-06-24
影响因子：
10
通讯作者：
Cameron RE
中科院分区：
文献类型：
--
作者：
Ashworth JC;Mehr M;Buxton PG;Best SM;Cameron RE
DOI：10.1002/adhm。使用201500197，如X射线显微计算机断层扫描（Micro-CT）。一种方法是测量可从支架外部进入的孔隙空间的分数。[9，10]然而，在将这些测量值从Micro-CT放大到在批量样品规模下有意义的结果方面存在问题。[11]逾渗理论，它涉及在多孔固体中的传输特性的数学处理，是一个公认的解决方案的问题的Micro-CT的可扩展性。[12]然而，它还没有被用于组织工程支架中细胞可及性的研究。尽管现有的Micro-CT表征方法专注于对单个孔和开窗进行彻底的参数化，[13，14]但这种方法很少强调开窗的空间分布，以及它们是否提供适合细胞侵入的连续途径。互连性评估的理想方法应该包括通过结构的传输途径的尺度独立的表征，这种方法所需的工具可以在渗流理论中找到。在这篇文章中，我们展示了使用渗流理论来研究细胞运输的特征尺寸方面的支架互连性。我们引入了一个尺度不变的参数，称为“渗透直径”，来描述入侵对象遇到的传输路径的特性。结合孔径的测量，我们证明了渗透直径的相关性，用于预测细胞侵袭的程度。根据萨克斯顿的工作命名，[15]渗透直径是能够穿过无限大支架的最大球形物体的尺寸。这可以被认为是互连路径方面的临界值：具有一定渗透直径的支架将阻碍大于该直径的任何物体的运输。其计算方法如图1所示，基于L和d的连续测量，其中d是能够通过孔隙空间行进线性距离L的最大球体的直径。使用来自逾渗理论的标度关系，这些测量值然后可以外推以找到当L接近无穷大时的d值：该值dc被称为逾渗直径。为了证明这种方法的功效，需要一系列具有可测量的结构差异的冻干胶原支架，以与观察到的生物反应相关。研究了冷冻干燥过程中的几个变量，以评估它们在支架互连性方面产生差异的潜力。其中最有前途的是悬浮介质的选择;一个变量，以前已被证明在支架结构产生显着的差异。[16]我们选择比较从悬浮介质的两种常见变体获得的结构：0.05 M乙酸和0.001 M盐酸（HCl）。醋酸是胶原蛋白的良好溶剂。胶原蛋白支架是受损或病变组织再生的生物模板。由于细胞侵入这些多孔支架对于健康的组织再生至关重要，因此在支架设计中必须考虑影响细胞反应的特征。例如，平均孔径的表征揭示了细胞迁移高度受支架结构的影响。[1，2]然而，为了入侵，细胞需要一个连接孔的通道：一个不能用平均孔径描述的特征。这种途径存在的程度被称为互连性。
DOI: 10.1002/adhm. 201500197 used, such as those from X-ray microcomputed tomography (Micro-CT). One approach is to measure the fraction of pore space accessible from the scaffold exterior.[9, 10] However, problems exist in scale-up of these measured values from Micro-CT to results that are meaningful at the scale of a bulk sample.[11] Percolation theory, which deals with the mathematical treatment of transport properties in porous solids, is a recognized solution to the problem of Micro-CT scalability.[12] It has not yet, however, been implemented for the study of cell accessibility in tissue engineering scaffolds. Whereas existing Micro-CT characterization methods focus on thorough parameterization of individual pores and fenestrations,[13, 14] with this approach there is little emphasis placed on the spatial distribution of the fenestrations, and whether or not they provide continuous pathways suitable for cell invasion. The ideal method for interconnectivity assessment should include scale-independent characterization of the transport pathways through the structure, and the tools necessary for this approach may be found in percolation theory. In this communication, we demonstrate the use of percolation theory to investigate scaffold interconnectivity in terms of a characteristic feature size for cell transport. We introduce a scale-invariant parameter, termed the “percolation diameter,” to describe the characteristics of the transport pathways encountered by an invading object. In combination with measurement of pore size, we demonstrate the relevance of the percolation diameter for predicting the extent of cell invasion. So named after the work of Saxton,[15] the percolation diameter is the size of the largest spherical object able to travel through an infinitely large scaffold. This may be considered a critical value in terms of interconnecting pathways: scaffolds with a certain percolation diameter will impede the transport of any object larger than this diameter. The methodology for its calculation, illustrated in Figure 1, is based on successive measurements of L and d, where d is the diameter of the largest sphere able to travel a linear distance L through the pore space. Using a scaling relationship from percolation theory, these measurements may then be extrapolated to find the value of d as L approaches infinity: this value dc is termed the percolation diameter. To demonstrate the power of this approach, a series of freezedried collagen scaffolds with measurable differences in structure was required, for correlation to observed biological response. Several of the variables in the freeze-drying process were investigated, to assess their potential for producing differences in scaffold interconnectivity. One of the most promising was the choice of suspension medium; a variable that has previously been shown to produce dramatic differences in scaffold architecture.[16] We chose to compare the structures obtained from two common variants of suspension medium: 0.05 M acetic acid and 0.001 M hydrochloric acid (HCl). Acetic acid is a good solvent for collagenCollagen scaffolds are biological templates for the regeneration of damaged or diseased tissues. Since cell invasion into these porous scaffolds is vital for healthy tissue regeneration, the characteristics that influence cellular response must be accounted for in scaffold design. For instance, characterization of mean pore size has revealed that cell migration is highly influenced by scaffold structure.[1, 2] However, in order to invade at all, cells require a pathway of connected pores: a characteristic that is not described by mean pore size. The extent to which such pathways are present is termed the interconnectivity …