Zhang Le, Szeri Andras Z
Department of Mechanical Engineering, Center for Biomedical Engineering Research, University of Delaware, Newark, DE 19716-3140, USA.
J Biomech. 2008;41(2):430-7. doi: 10.1016/j.jbiomech.2007.08.005. Epub 2007 Sep 24.
Due to the avascular nature of articular cartilage, solute transport through its extracellular matrix is critical for the maintenance and the functioning of the tissue. What is more, diffusion of macromolecules may be affected by the microstructure of the extracellular matrix in both undeformed and deformed cartilage and experiments demonstrate diffusion anisotropy in the case of large solute. However, these phenomena have not received sufficient theoretical attention to date. We hypothesize here that the diffusion anisotropy of macromolecules is brought about by the particular microstructure of the cartilage network. Based on this hypothesis, we then propose a mathematical model that correlates the diffusion coefficient tensor with the structural orientation tensor of the network. This model is shown to be successful in describing anisotropic diffusion of macromolecules in undeformed tissue and is capable of clarifying the effects of network reorientation as the tissue deforms under mechanical load. Additionally, our model explains the anomaly that at large strain, in a cylindrical plug under unconfined compression, solute diffusion in the radial direction increases with strain. Our results indicate that in cartilage the degree of diffusion anisotropy is site specific, but depends also on the size of the diffusing molecule. Mechanical loading initiates and/or further exacerbates this anisotropy. At small deformation, solute diffusion is near isotropic in a tissue that is isotropic in its unstressed state, becoming anisotropic as loading progresses. Mechanical loading leads to an attenuation of solute diffusion in all directions when deformation is small. However, loading, if it is high enough, enhances solute transport in the direction perpendicular to the load line, instead of inhibiting it.
由于关节软骨无血管的特性，溶质通过其细胞外基质的运输对于组织的维持和功能至关重要。此外，在未变形和变形的软骨中，大分子的扩散可能会受到细胞外基质微观结构的影响，实验表明在大溶质情况下存在扩散各向异性。然而，这些现象至今尚未得到足够的理论关注。我们在此假设大分子的扩散各向异性是由软骨网络的特殊微观结构引起的。基于这一假设，我们随后提出了一个数学模型，该模型将扩散系数张量与网络的结构取向张量相关联。结果表明，该模型能够成功描述未变形组织中大分子的各向异性扩散，并能够阐明在机械载荷作用下组织变形时网络重新取向的影响。此外，我们的模型解释了一个异常现象，即在大应变下，在无侧限压缩的圆柱形塞体中，溶质在径向的扩散随应变增加。我们的结果表明，在软骨中，扩散各向异性的程度具有部位特异性，但也取决于扩散分子的大小。机械加载会引发和/或进一步加剧这种各向异性。在小变形时，溶质在无应力状态下呈各向同性的组织中的扩散近乎各向同性，随着加载的进行而变得各向异性。当变形较小时，机械加载会导致溶质在各个方向上的扩散减弱。然而，如果加载足够高，溶质在垂直于加载线方向上的运输会增强，而不是受到抑制。
