Haïat Guillaume, Naili Salah, Grimal Quentin, Talmant Maryline, Desceliers Christophe, Soize Christian
CNRS, Laboratoire de Recherches Orthopediques, UMR CNRS 7052 B2OA, Universite Paris 7, 75010 Paris, France.
J Acoust Soc Am. 2009 Jun;125(6):4043-52. doi: 10.1121/1.3117445.
The aim of this work is to evaluate the effect of a spatial gradient of material properties (mass density and stiffness coefficients) of cortical bone on its ultrasonic response obtained with an axial transmission device. Therefore, a two-dimensional finite element time-domain method is derived to model transient wave propagation in a three-layer medium composed of an inhomogeneous transverse isotropic solid layer sandwiched between two acoustic fluid layers and excited by an acoustic linear source located in one fluid layer, delivering broadband ultrasonic pulses. The model couples the acoustic propagation in both fluid media with the elastodynamic response of the solid layer. A constant spatial gradient of material properties is considered for two values of bone thicknesses corresponding to relatively thick and thin bone widths. For a thin bone (0.6 mm) compared to wavelength (around 4 mm at 1 MHz), the results are in good agreement with a S(0) Lamb wave assuming a homogeneous material with spatially averaged material properties. For a thick bone (4 mm), the results are in agreement with the propagation of a lateral wave and allow the derivation of an equivalent contributing depth in the case of a transverse isotropic inhomogeneous solid layer.
这项工作的目的是评估皮质骨材料特性（质量密度和刚度系数）的空间梯度对通过轴向传输装置获得的其超声响应的影响。因此，推导了一种二维有限元时域方法，以模拟瞬态波在由夹在两个声学流体层之间的非均匀横向各向同性固体层组成的三层介质中的传播，并由位于一个流体层中的声学线性源激发，传递宽带超声脉冲。该模型将两种流体介质中的声学传播与固体层的弹性动力学响应耦合起来。对于对应于相对厚和薄骨宽度的两种骨厚度值，考虑了材料特性的恒定空间梯度。对于与波长（在1MHz时约为4mm）相比的薄骨（0.6mm），结果与假设具有空间平均材料特性的均匀材料的S(0)兰姆波非常吻合。对于厚骨（4mm），结果与横向波的传播一致，并允许在横向各向同性非均匀固体层的情况下推导等效贡献深度。
