Haïat G, Padilla F, Peyrin F, Laugier P
CNRS, Université Paris 7, Laboratoire de Recherches Orthopédiques, UMR CNRS 7052 B2OA, 10, avenue de Verdun, 75010 Paris, France.
J Acoust Soc Am. 2008 Mar;123(3):1694-705. doi: 10.1121/1.2832611.
Our goal is to assess the potential of computational methods as an alternative to analytical models to predict the two longitudinal wave modes observed in cancellous bone and predicted by the Biot theory. A three-dimensional (3D) finite-difference time-domain method is coupled with 34 human femoral trabecular microstructures measured using microcomputed tomography. The main trabecular alignment (MTA) and the degree of anisotropy (DA) were assessed for all samples. DA values were comprised between 1.02 and 1.9. The influence of bone volume fraction (BV/TV) between 5% and 25% on the properties of the fast and slow waves was studied using a dedicated image processing algorithm to modify the initial 3D microstructures. A heuristic method was devised to determine when both wave modes are time separated. The simulations (performed in three perpendicular directions) predicted that both waves generally overlap in time for a direction of propagation perpendicular to the MTA. When these directions are parallel, both waves are separated in time for samples with high DA and BV/TV values. A relationship was found between the least bone volume fraction required for the observation of nonoverlapping waves and the degree of anisotropy: The higher the DA, the lower the least BV/TV.
我们的目标是评估计算方法作为分析模型的替代方法来预测在松质骨中观察到并由比奥理论预测的两种纵向波模式的潜力。一种三维（3D）时域有限差分方法与使用微型计算机断层扫描测量的34个人类股骨小梁微观结构相结合。对所有样本评估了主要小梁排列（MTA）和各向异性程度（DA）。DA值在1.02至1.9之间。使用专用图像处理算法修改初始3D微观结构，研究了5%至25%的骨体积分数（BV/TV）对快波和慢波特性的影响。设计了一种启发式方法来确定两种波模式何时在时间上分离。模拟（在三个垂直方向上进行）预测，对于垂直于MTA的传播方向，两种波通常在时间上重叠。当这些方向平行时，对于具有高DA和BV/TV值的样本，两种波在时间上分离。发现观察到非重叠波所需的最小骨体积分数与各向异性程度之间存在关系：DA越高，最小BV/TV越低。
