Quantification of stiffness measurement errors in resonant ultrasound spectroscopy of human cortical bone.
Quantification of stiffness measurement errors in resonant ultrasound spectroscopy of human cortical bone.
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DOI：
10.1121/1.5009453
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发表时间：
2017-11
期刊：
影响因子：
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通讯作者：
Xiran Cai;L. Peralta;P. Gouttenoire;C. Olivier;F. Peyrin;P. Laugier;Q. Grimal
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文献类型：
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作者：
Xiran Cai;L. Peralta;P. Gouttenoire;C. Olivier;F. Peyrin;P. Laugier;Q. Grimal
共振超声光谱（RUS）是研究各向异性固体弹性特性的最先进的方法。最近，RUS被用于测量人类皮质骨，这是一种低q因子（20）的各向异性材料，由于难以检索谐振频率，因此具有挑战性。确定估计刚度常数的精度并不简单，因为RUS是一种间接方法，涉及使用模型最小化测量和计算的谐振频率之间的距离。这项工作的动机是需要量化由于RUS中不同误差源引起的刚度常数误差，包括谐振频率和试件尺寸的不确定性以及不完美的矩形平行六面体（RP）试件几何形状。首先用蒙特卡罗模拟研究了这些误差，实验测量了谐振频率和尺寸的典型不确定值，假设了完美的RP几何形状。其次，通过同步辐射微计算机断层扫描记录了一组骨标本的精确几何形状。然后，提出了一个“虚拟”RUS实验来量化几何不完美引起的误差。结果表明，对于垂直度和平行度误差为1°的骨标本，所有刚度常数和工程模量的精度可达到几个百分点（<6.2%）。
Resonant ultrasound spectroscopy (RUS) is the state-of-the-art method used to investigate the elastic properties of anisotropic solids. Recently, RUS was applied to measure human cortical bone, an anisotropic material with low Q-factor (20), which is challenging due to the difficulty in retrieving resonant frequencies. Determining the precision of the estimated stiffness constants is not straightforward because RUS is an indirect method involving minimizing the distance between measured and calculated resonant frequencies using a model. This work was motivated by the need to quantify the errors on stiffness constants due to different error sources in RUS, including uncertainties on the resonant frequencies and specimen dimensions and imperfect rectangular parallelepiped (RP) specimen geometry. The errors were first investigated using Monte Carlo simulations with typical uncertainty values of experimentally measured resonant frequencies and dimensions assuming a perfect RP geometry. Second, the exact specimen geometry of a set of bone specimens were recorded by synchrotron radiation micro-computed tomography. Then, a "virtual" RUS experiment is proposed to quantify the errors induced by imperfect geometry. Results show that for a bone specimen of ∼1° perpendicularity and parallelism errors, an accuracy of a few percent ( <6.2%) for all the stiffness constants and engineering moduli is achievable.