Lu M H, Zheng Y P
Rehabilitation Engineering Center, The Hong Kong Polytechnic University, Hong Kong, China.
Med Biol Eng Comput. 2004 Jul;42(4):535-40. doi: 10.1007/BF02350996.
Indentation is a commonly used approach to measure the mechanical properties of soft tissues, such as articular cartilage and limb tissues. The Young's modulus of tissue can be calculated from the indentation test using a mechanical model, where the soft tissue is normally assumed to have a flat substrate. In this study, a series of 2D finite element models were established to investigate the effects of bones with various curvatures embedded in the soft tissues during an indentation test. For each curvature of the hard substrate, the errors in the calculation of the Young's modulus were estimated for different indentation depths (0-10%) and aspect ratios a/h of the indentor diameter and the tissue thickness (0.2-2 in seven steps). The radius ratio a/R of the indentor and the curved substrate ranged from 0 to 0.38 in nine steps. Results showed that the error in calculation of the Young's modulus increased by 21.2% when the curvature a/R of the bone increased from 0 to 0.38 (under the condition of a/h=1.0, Poisson's ratio v=0.45). The error increased from 6.0 to 18.2% when the tissue thickness increased from 0.2 to 2 (a/R=0.18, v=0.45). It was found that the error in the Young's modulus calculation caused by the curved hard substrates could be corrected by a single factor for different indentation depths. This factor depends on the Poisson's ratio, the aspect ratio a/h and the radius ratio a/R.
压痕法是一种常用于测量软组织力学性能的方法，如关节软骨和肢体组织。组织的杨氏模量可以通过使用力学模型的压痕试验来计算，其中通常假定软组织具有平坦的基底。在本研究中，建立了一系列二维有限元模型，以研究在压痕试验过程中嵌入软组织中的各种曲率的骨骼的影响。对于硬基底的每种曲率，针对不同的压痕深度（0 - 10%）以及压头直径与组织厚度的纵横比a/h（分七步，范围为0.2 - 2），估计杨氏模量计算中的误差。压头与弯曲基底的半径比a/R分九步，范围从0到0.38。结果表明，当骨骼的曲率a/R从0增加到0.38时（在a/h = 1.0、泊松比v = 0.45的条件下），杨氏模量计算中的误差增加了21.2%。当组织厚度从0.2增加到2时（a/R = 0.18，v = 0.45），误差从6.0%增加到18.2%。研究发现，对于不同的压痕深度，由弯曲硬基底引起的杨氏模量计算误差可以通过一个单一因素来校正。该因素取决于泊松比、纵横比a/h和半径比a/R。
