Background

Microindentation is a technique with high sensitivity and spatial resolution, allowing for measurements at small-scale indentation depths. Various methods of indentation analysis to determine output properties exist.

Objective

Here, the Oliver-Pharr Method and Hertzian Method were compared for stiffness analyses of articular cartilage at varying length-scales before and after bioreactor loading.

Methods

Using three different conospherical tips with varying radii (20, 100, 793.75 µm), a bioreactor-indenter workflow was performed on cartilage explants to assess changes in stiffness due to articular loading. For all data, both the Oliver-Pharr Method and Hertzian Method were applied for indentation analysis.

Results

The reduced moduli calculated by the Hertzian Method were found to be similar to those of the Oliver-Pharr Method when the 20 µm tip size was used. The reduced moduli calculated using the Hertzian Method were found to be consistent across the varying length-scales, whereas for the Oliver-Pharr Method, adhesion/suction led to the largest tip exhibiting an increased average reduced modulus compared to the two smaller tips. Loading induced stiffening of articular cartilage was observed consistently, regardless of tip size or indentation analysis applied.

Conclusions

Overall, geometric linearity is preserved across all tip sizes for the Hertzian Method and may be assumed for the two smaller tip sizes using the Oliver-Pharr Method. These findings further validate the previously described stiffening response of the superficial zone of cartilage after articular loading and demonstrate that the finding is length-scale independent.

中文翻译：

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生物反应器中关节加载前后软骨的显微压痕：使用两种分析方法评估长度尺度依赖性

背景

微压痕是一种具有高灵敏度和空间分辨率的技术，允许在小尺度压痕深度进行测量。存在多种确定输出属性的压痕分析方法。

客观的

在这里，比较了 Oliver-Pharr 方法和 Hertzian 方法在生物反应器加载前后不同长度尺度的关节软骨刚度分析。

方法

使用具有不同半径（20、100、793.75 µm）的三个不同的锥体尖端，在软骨外植体上执行生物反应器-压头工作流程，以评估由于关节负荷引起的刚度变化。对于所有数据，均采用 Oliver-Pharr 方法和 Hertzian 方法进行压痕分析。

结果

当使用 20 µm 尖端尺寸时，发现通过 Hertzian 方法计算的缩减模量与 Oliver-Pharr 方法的相似。发现使用赫兹方法计算的减少模量在不同的长度尺度上是一致的，而对于 Oliver-Pharr 方法，与两个较小的尖端相比，粘附/吸力导致最大的尖端表现出增加的平均减少模量。无论尖端大小或应用的压痕分析如何，始终观察到负载引起的关节软骨硬化。

结论

总体而言，对于 Hertzian 方法的所有尖端尺寸都保留了几何线性，并且可以使用 Oliver-Pharr 方法假设两个较小的尖端尺寸。这些发现进一步验证了先前描述的关节负荷后软骨表面区域的硬化反应，并证明该发现与长度尺度无关。