Speed of sound reflects Young's modulus as assessed by microstructural finite element analysis

Abstract

We analyzed the ability of the quantitative ultrasound (QUS) parameter, speed of sound (SOS), and bone mineral density (BMD), as measured by dual-energy X-ray absorptiometry (DXA), to predict Young's modulus, as assessed by microstructural finite element analysis (muFEA) from microcomputed tomography (muCT) reconstructions. With muFEA simulation, all bone elements in the model can be assigned the same isotropic Young's modulus; therefore, in contrast to mechanical tests, only the trabecular structure plays a role in the determination of the elastic properties of the specimen. SOS, BMD, and microCT measurements were performed in 15 cubes of pure trabecular bovine bone in three orthogonal directions: anteroposterior (AP); mediolateral (ML); and craniocaudal (CC). The anisotropy of the architecture was determined using mean intercept length (MIL) measurements. SOS, MIL, and Young's modulus (E) values were significantly different in all three directions (p < 0.001), with the highest values in the CC direction. There was a strong linear relationship between E and SOS in each of the three orthogonal directions, with r(2) being 0.88, 0.92, and 0.84 (all p < 0.0001) for the CC, ML, and AP directions, respectively. The relationship between E and BMD was less strong, with r(2) being between 0.66 and 0.85 (all p < 0.0001) in the different directions. There was also a significant, positive correlation between SOS and BMD in each of the three axes (r(2) being 0.81, 0.42, and 0.92 in the CC, ML, and AP directions, respectively; p < 0.0001). After correction for BMD, the correlations between SOS and E in each of the three directions remained highly significant (r(2) = 0.77, p < 0. 0001 for the AP direction; r(2) = 0.48, p < 0.001 for the CC direction; r(2) = 0.52, p < 0.005 for the ML direction). After correction for SOS, BMD remained significantly correlated with Young's modulus in the AP and CC directions (r(2) = 0.52, p < 0.005; r(2) = 0.30, p < 0.05, respectively), but the correlation in the ML direction was no longer statistically significant. In a stepwise regression model, E was best predicted by SOS in each of the orthogonal directions. These observations illustrate the ability of the SOS technique to assess the architectural mechanical quality of trabecular bone.