Institute for Biomechanics, Department of Health Sciences and Technology, ETH Zürich, Zürich, Switzerland.
PLoS One. 2019 Jul 17;14(7):e0219360. doi: 10.1371/journal.pone.0219360. eCollection 2019.
Cortical thickness (cTh) is one of the main factors determining a bone's mechanical properties, and its quantification is therefore critical for understanding and monitoring bone pathologies such as osteoporosis. Axial quantitative acoustics (ax-QA) offers a non-radiative, non-invasive method to measure cTh. Even though previous works have ascertained ax-QA's ability to measure azimuthally varying cTh, the effect of axially varying cTh remains unclear. Furthermore, previous experiments and theoretical predictions indicate that measurement of the fundamental flexural mode at low frequencies in the kHz range could increase sensitivity to cTh. However, due to the associated long wavelengths, the approximation of bone geometry as a tube could break down at such frequencies. The presented study therefore investigates a) the sensitivity of ax-QA measurements to cTh in the kHz-regime, b) the applicability of tube theory in this regime, and c) the effect of varying cTh along the long axis on the bone.
Axial-transmission acoustic measurements were performed at 3kHz on 14 bone phantoms with a femur-like cross-section and a) axially varying cortical thickness or b) axially and azimuthally varying cortical thickness (cTh-range: 1.5mm-7.5mm). Experimental results were compared to theoretical predictions based on an exact elastic tube theory.
Phase velocity measurements using low-frequency ax-QA exhibited a high sensitivity to local cTh less than 4mm, albeit with a complex, not yet understood pattern. Tube theory failed to predict the wave's behavior in the kHz range, indicating that due to the corresponding long wavelengths the bone can no longer be approximated by a tube, thus requiring more faithful modelling of the bone geometry. The fact that results from both types of phantoms were similar (Pearson correlation coefficient: 0.94) further indicates that the slowly varying cTh along the bone's long axis did not strongly affect wave propagation as measured by ax-QA measurements.
皮质厚度（cTh）是决定骨骼机械性能的主要因素之一，因此定量评估皮质厚度对于理解和监测骨质疏松症等骨骼疾病至关重要。轴向定量声学（ax-QA）提供了一种非辐射、非侵入性的方法来测量 cTh。尽管先前的研究已经证实了 ax-QA 测量方位变化的 cTh 的能力，但轴向变化的 cTh 的影响尚不清楚。此外，先前的实验和理论预测表明，在 kHz 范围内低频下测量基本弯曲模态可以提高对 cTh 的灵敏度。然而，由于相关的长波长，在如此高的频率下，将骨骼几何形状近似为管的方法可能会失效。因此，本研究调查了：a）ax-QA 在 kHz 范围内测量 cTh 的灵敏度，b）管理论在该范围内的适用性，以及 c）cTh 沿长轴变化对骨骼的影响。
在 3kHz 下对 14 个具有类似股骨横截面的骨标本进行轴向透射声测量，这些骨标本的 a）皮质厚度沿轴向变化，或 b）皮质厚度沿轴向和方位变化（cTh 范围：1.5mm-7.5mm）。实验结果与基于精确弹性管理论的理论预测进行了比较。
使用低频 ax-QA 进行的相速度测量对小于 4mm 的局部 cTh 表现出高灵敏度，尽管存在复杂且尚未理解的模式。管理论未能预测波在 kHz 范围内的行为，这表明由于相应的长波长，骨骼不能再用管来近似，因此需要更真实地模拟骨骼的几何形状。两种类型的标本的结果都相似（皮尔逊相关系数：0.94），这进一步表明，cTh 沿骨骼长轴的缓慢变化并未强烈影响 ax-QA 测量所测量的波传播。
