Empirical angle-dependent Biot and MBA models for acoustic anisotropy in cancellous bone
Empirical angle-dependent Biot and MBA models for acoustic anisotropy in cancellous bone
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DOI：
10.1088/0031-9155/52/1/005
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发表时间：
2007-01
影响因子：
3.5
通讯作者：
K. Lee;E. R. Hughes;V. Humphrey;T. Leighton;M. Choi
中科院分区：
文献类型：
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作者：
K. Lee;E. R. Hughes;V. Humphrey;T. Leighton;M. Choi
人们发现 Biot 和修改后的 Biot-Attenborough (MBA) 模型对于了解超声波在松质骨中的传播很有用。然而，这两个模型（如之前应用于松质骨的模型）都没有考虑到声学特性与方向的角度依赖性。本研究旨在通过将高度定向结构定义的经验角度相关输入参数引入 Biot 和 MBA 模型来解释松质骨中的声学各向异性。角度相关 Biot 模型的各向异性归因于骨骼框架弹性模量相对于小梁排列的变化。角度相关 MBA 模型采用简单的经验方法，对快波和慢波速度进行参数拟合。角度相关模型用于预测快波速度和慢波速度，作为相对于松质骨小梁排列的传播角度的函数。将这些预测与松质骨各向异性的勋伯格模型的预测以及文献中的体外实验测量结果进行比较。角度相关模型成功地预测了快波相速度与方向的角度相关性。测量与预测的快波速度的均方根误差分别为 79.2 m s−1（角度相关的 Biot 模型）和 36.1 m s−1（角度相关的 MBA 模型）。他们还预测，对于大约 50° 的角度，慢波几乎与传播角无关，但始终低估了慢波速度，其均方根误差为 187.2 m s−1（角度相关的 Biot 模型）和 240.8 m s−1（角度相关的 MBA 模型）。研究表明，角度相关模型合理地复制了松质骨中的声学各向异性。
The Biot and the modified Biot–Attenborough (MBA) models have been found useful to understand ultrasonic wave propagation in cancellous bone. However, neither of the models, as previously applied to cancellous bone, allows for the angular dependence of acoustic properties with direction. The present study aims to account for the acoustic anisotropy in cancellous bone, by introducing empirical angle-dependent input parameters, as defined for a highly oriented structure, into the Biot and the MBA models. The anisotropy of the angle-dependent Biot model is attributed to the variation in the elastic moduli of the skeletal frame with respect to the trabecular alignment. The angle-dependent MBA model employs a simple empirical way of using the parametric fit for the fast and the slow wave speeds. The angle-dependent models were used to predict both the fast and slow wave velocities as a function of propagation angle with respect to the trabecular alignment of cancellous bone. The predictions were compared with those of the Schoenberg model for anisotropy in cancellous bone and in vitro experimental measurements from the literature. The angle-dependent models successfully predicted the angular dependence of phase velocity of the fast wave with direction. The root-mean-square errors of the measured versus predicted fast wave velocities were 79.2 m s−1 (angle-dependent Biot model) and 36.1 m s−1 (angle-dependent MBA model). They also predicted the fact that the slow wave is nearly independent of propagation angle for angles about 50°, but consistently underestimated the slow wave velocity with the root-mean-square errors of 187.2 m s−1 (angle-dependent Biot model) and 240.8 m s−1 (angle-dependent MBA model). The study indicates that the angle-dependent models reasonably replicate the acoustic anisotropy in cancellous bone.