Federico Salvatore, Grillo Alfio, La Rosa Guido, Giaquinta Gaetano, Herzog Walter
Human Performance Laboratory, Faculty of Kinesiology, The University of Calgary, Alb., Canada.
J Biomech. 2005 Oct;38(10):2008-18. doi: 10.1016/j.jbiomech.2004.09.020. Epub 2004 Dec 9.
Articular cartilage is a multi-phasic, composite, fibre-reinforced material. Therefore, its mechanical properties are determined by the tissue microstructure. The presence of cells (chondrocytes) and collagen fibres within the proteoglycan matrix influences, at a local and a global level, the material symmetries. The volumetric concentration and shape of chondrocytes, and the volumetric concentration and spatial arrangement of collagen fibres have been observed to change as a function of depth in articular cartilage. In particular, collagen fibres are perpendicular to the bone-cartilage interface in the deep zone, their orientation is almost random in the middle zone, and they are parallel to the surface in the superficial zone. The aim of this work is to develop a model of elastic properties of articular cartilage based on its microstructure. In previous work, we addressed this problem based on Piola's notation for fourth-order tensors. Here, mathematical tools initially developed for transversely isotropic composite materials comprised of a statistical orientation of spheroidal inclusions are extended to articular cartilage, while taking into account the dependence of the elastic properties on cartilage depth. The resulting model is transversely isotropic and transversely homogeneous (TITH), the transverse plane being parallel to the bone-cartilage interface and the articular surface. Our results demonstrate that the axial elastic modulus decreases from the deep zone to the articular surface, a result that is in good agreement with experimental findings. Finite element simulations were carried out, in order to explore the TITH model's behaviour in articular cartilage compression tests. The force response, fluid flow and displacement fields obtained with the TITH model were compared with the classical linear elastic, isotropic, homogeneous (IH) model, showing that the IH model is unable to predict the non-uniform behaviour of the tissue. Based on considerations that the mechanical stability of the tissue depends on its topological and microstructural properties, our long-term goal is to clearly understand the stability conditions in topological terms, and the relationship with the growth and remodelling mechanisms in the healthy and diseased tissue.
关节软骨是一种多相、复合、纤维增强材料。因此，其力学性能由组织微观结构决定。蛋白聚糖基质中细胞（软骨细胞）和胶原纤维的存在在局部和整体水平上影响材料对称性。已观察到软骨细胞的体积浓度和形状以及胶原纤维的体积浓度和空间排列随关节软骨深度而变化。特别是，胶原纤维在深层垂直于骨 - 软骨界面，在中层其取向几乎是随机的，而在表层它们平行于表面。这项工作的目的是基于其微观结构开发一种关节软骨弹性特性模型。在先前的工作中，我们基于皮奥拉关于四阶张量的记号解决了这个问题。在此，最初为包含球状夹杂物统计取向的横观各向同性复合材料开发的数学工具扩展到关节软骨，同时考虑弹性特性对软骨深度的依赖性。所得模型是横观各向同性且横向均匀的（TITH），横向平面平行于骨 - 软骨界面和关节表面。我们的结果表明，轴向弹性模量从深层到关节表面降低，这一结果与实验结果高度一致。进行了有限元模拟，以探究TITH模型在关节软骨压缩试验中的行为。将TITH模型获得的力响应、流体流动和位移场与经典的线性弹性、各向同性、均匀（IH）模型进行比较，结果表明IH模型无法预测组织的非均匀行为。基于组织的机械稳定性取决于其拓扑和微观结构特性的考虑，我们的长期目标是从拓扑角度清楚地理解稳定性条件，以及与健康和患病组织中的生长和重塑机制的关系。
