Moilanen Petro, Talmant Maryline, Nicholson Patrick H F, Cheng Sulin, Timonen Jussi, Laugier Pascal
Université Pierre et Marie Curie - Paris 6, Laboratoire d'Imagerie Paramétrique, UMR7623, Paris, F-75005, France.
J Acoust Soc Am. 2007 Oct;122(4):2439-45. doi: 10.1121/1.2769619.
It was reported in a previous study that simulated guided wave axial transmission velocities on two-dimensional (2D) numerically reproduced geometry of long bones predicted moderately real in vitro ultrasound data on the same bone samples. It was also shown that fitting of ultrasound velocity with simple analytical model yielded a precise estimate (UTh) for true cortical bone thickness. This current study expands the 2D bone model into three dimensions (3D). To this end, wave velocities and UTh were determined from experiments and from time-domain finite-difference simulations of wave propagation, both performed on a collection of 10 human radii (29 measurement sites). A 3D numerical bone model was developed with tuneable fixed material properties and individualized geometry based on X-ray computed tomography reconstructions of real bones. Simulated UTh data were in good accordance (root-mean-square error was 0.40 mm; r(2)=0.79, p<0.001) with true cortical thickness, and hence the measured phase velocity can be well estimated by using a simple analytical inversion model also in 3D. Prediction of in vitro data was improved significantly (by 10% units) and the upgraded bone model thus explained most of the variability (up to 95% when sites were carefully matched) observed in in vitro ultrasound data.
先前的一项研究报告称，在长骨的二维（2D）数值再现几何结构上模拟的导波轴向传播速度预测了相同骨样本的适度真实体外超声数据。研究还表明，用简单的分析模型拟合超声速度可得到真实皮质骨厚度的精确估计值（UTh）。当前的这项研究将二维骨模型扩展到了三维（3D）。为此，通过实验以及对波传播的时域有限差分模拟确定了波速和UTh，这两者都是在10根人桡骨（29个测量部位）的集合上进行的。基于真实骨骼的X射线计算机断层扫描重建，开发了一种具有可调固定材料属性和个性化几何结构的三维数值骨模型。模拟的UTh数据与真实皮质厚度高度吻合（均方根误差为0.40毫米；r(2)=0.79，p<0.001），因此，使用简单的分析反演模型也可以很好地估计三维中的测量相速度。体外数据的预测得到了显著改善（提高了10个百分点），因此升级后的骨模型解释了体外超声数据中观察到的大部分变异性（当部位仔细匹配时高达95%）。
