Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford OX1 3QD, UK.
MMPE, MERF, Faculty of Engineering, Queensland University of Technology, Brisbane, QLD 4000, Australia.
Math Med Biol. 2022 Sep 8;39(3):251-298. doi: 10.1093/imammb/dqac005.
In skeletal joints two layers of adjacent cartilage are often in relative motion. The individual cartilage layers are often modelled as a poroviscoelastic material. To model the relative motion, noting the separation of scales between the pore level and the macroscale, a homogenization based on multiple scale asymptotic analysis has been used in this study to derive a macroscale model for the relative translation of two poroviscoelastic layers separated by a very thin layer of fluid. In particular the fluid layer thickness is essentially zero at the macroscale so that the two poroviscoelastic layers are effectively in contact and their interaction is captured in the derived model via a set of interfacial conditions, including a generalization of the Beavers-Joseph condition at the interface between a viscous fluid and a porous medium. In the simplifying context of a uniform geometry, constant fixed charge density, a Newtonian interstitial fluid and a viscoelastic scaffold, modelled via finite deformation theory, we present preliminary simulations that may be used to highlight predictions for how oscillatory relative movement of cartilage under load influences the peak force the cartilage experiences and the extent of the associated deformations. In addition to highlighting such cartilage mechanics, the systematic derivation of the macroscale models will enable the study of how nanoscale cartilage physics, such as the swelling pressure induced by fixed charges, manifests in cartilage mechanics at much higher lengthscales.
在骨骼关节中，两层相邻的软骨通常处于相对运动状态。各个软骨层通常被建模为多孔粘弹性材料。为了模拟相对运动，注意到孔尺度和宏观尺度之间的尺度分离，本研究使用基于多尺度渐近分析的均匀化方法，推导出了一种用于由非常薄的流体层分隔的两个多孔粘弹性层的相对平移的宏观模型。特别是，在宏观尺度上，流体层厚度实质上为零，因此两个多孔粘弹性层有效接触，并且它们的相互作用通过一组界面条件来捕获，包括粘性流体和多孔介质之间的界面处的 Beavers-Joseph 条件的推广。在均匀几何形状、恒定固定电荷密度、牛顿型间质流体和粘弹性支架的简化背景下，通过有限变形理论进行建模，我们提出了初步的模拟，这些模拟可用于突出预测，即在负载下软骨的振荡相对运动如何影响软骨所经历的峰值力以及相关变形的程度。除了突出这种软骨力学之外，宏观模型的系统推导还将能够研究纳米级软骨物理学（例如固定电荷引起的肿胀压力）如何在更高的尺度上表现为软骨力学。
