Background and objective

Investigating the biomechanics of cartilage could help to understand the unique load-bearing property of the cartilage and optimize the scaffold design in tissue-engineering. It is important to model the cartilage as a highly inhomogeneous fibril-reinforced biphasic material to represent its complex composition and structure. The depth-dependent and strain-dependent properties of the cartilage would also play an important role in its mechanical behaviour. However, the differences in representing the cartilage as a highly inhomogeneous model or as simplified models still remain unclear. Hence, in this study, a highly inhomogeneous fibril-reinforced biphasic cartilage model considering both the depth-dependent and strain-dependent properties was constructed; the effect of highly inhomogeneous properties on the mechanical behaviour of articular cartilage was investigated.

Methods

A finite element model of the cartilage was developed based on a flat-ended indentation test. Compressive forces were applied to four various inhomogeneous layered models through a porous indenter (Model 1: nine layers with strain-dependent permeability; Model 2: three layers with strain-dependent permeability; Model 3: single layer with strain-dependent permeability; Model 4: nine layers with constant permeability).

Results

Models 1 and 2 provided similar results with less than 3% difference in the peak effective stress, contact pressure, fluid pressure as well as fluid support ratio. However, Model 1 to Model 3 differed in stress and strain distribution patterns along depth over prolonged loads, which may provide an important insight into the highly inhomogeneous depth-dependent properties of cartilage. In addition, Model 1 with strain-dependent permeability demonstrated an enhanced capability on fluid pressurisation as compared with Model 4 which had constant permeability.

Conclusions

A highly inhomogeneous fibril-reinforced biphasic model considering both depth-dependent and strain-dependent properties was developed in this study, in order to illustrate the effect of highly inhomogeneous properties on the mechanical behaviour of the articular cartilage. The number of layers in the models with depth-dependent properties should be selected according to the research questions and clinical demands. The model with strain-dependent permeability offers an enhanced capability on fluid pressurisation. In future studies, the proposed model could be adopted in cell-models to provide more in-depth information or in tissue-engineering to optimize the depth-dependent scaffold structure.

中文翻译：

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高度不均匀的双相特性对关节软骨力学行为的影响

背景和目标

研究软骨的生物力学可以帮助了解软骨的独特承重特性，并优化组织工程中的支架设计。重要的是将软骨建模为高度不均匀的原纤维增强双相材料，以代表其复杂的成分和结构。软骨的深度依赖性和应变依赖性也将在其机械行为中起重要作用。然而，将软骨表示为高度不均匀模型或简化模型的差异仍然不清楚。因此，在这项研究中，建立了高度不均匀的原纤维增强的双相软骨模型，该模型同时考虑了深度依赖性和应变依赖性。

方法

基于平端压痕测试，开发了软骨的有限元模型。通过多孔压头将压缩力应用于四个不同的不均匀分层模型（模型1：具有应变相关渗透性的九层；模型2：具有应变相关渗透性的三层；模型3：具有应变相关渗透性的单层；模型4 ：具有恒定渗透率的九层）。

结果

模型1和2提供了相似的结果，峰值有效应力，接触压力，流体压力以及流体支持率的差异小于3％。但是，模型1至模型3在长期载荷下沿深度的应力和应变分布模式有所不同，这可能为深入了解高度依赖于软骨的软骨特性提供重要信息。此外，与具有恒定渗透率的模型4相比，具有与应变有关的渗透率的模型1显示出了更高的流体加压能力。

结论

为了说明高度非均质特性对关节软骨力学行为的影响，本研究开发了一种高度非均质原纤维增强双相模型，该模型同时考虑了深度依赖性和应变依赖性。应根据研究问题和临床需求选择模型中具有深度相关特性的层数。具有与应变有关的渗透率的模型提供了增强的流体增压能力。在未来的研究中，可以在细胞模型中采用所提出的模型以提供更多的深入信息，或者在组织工程中采用该模型以优化与深度相关的支架结构。