Measurement of guided mode wave numbers in anisotropic absorbing material: Application to cortical bone evaluation

Abstract

Recent studies indicate that, despite absorption and heterogeneity, long cortical bones support guided waves propagation in the axial transmission configuration. Currently, there is a need to implement a robust method to extract guided mode wave numbers adapted to clinical requirements. Particularly the probe dimensions are limited by the accessibility to the skeletal site. Recently, an approach based on the singular value decomposition (SVD) applied to the configuration of multi-emitters and multi-receivers has been proposed [Minonzio et al. J. Acoust. Soc. Am. 127, 2913–2919 (2010)]. The method has been validated on an isotropic and weak absorbing metallic plate. The objective of the present study is to apply the method to anisotropic and absorbing materials using actual clinical probes. Experiments have been carried out on 2 mm thick plates in the 0.2–2 MHz bandwidth. This thickness corresponds to typical radius cortical bone thickness. Two materials are inspected: PMMA (isotropic with absorption) and artificial composite bones (Sawbones, Pacific Research Laboratory Inc, Vashon WA) which is a transverse isotropic absorbing medium. Bulk wave velocities have been evaluated from transmission measurements in different directions. These values were used to compute theoretical Lamb mode phase velocities which are consistent with the experimental ones obtained with the SVD-based approach.