Ultrasound Velocity of Trabecular Cubes Reflects Mainly Bone Density and Elasticity

Abstract

Studies have indicated that quantitative ultrasound (QUS) variables may be influenced by the mechanical properties of bone which in turn are determined by bone's material and structural properties. However, from these studies it is unclear what role density, elasticity, and structure play in determining velocity. Eighteen defatted, 12-mm cubic trabecular bone specimens were cut from cadaveric specimens. Amplitude-dependent speed of sound (SOS) using a single point QUS system was assessed in three orthogonal axes. Magnetic resonance images were obtained, from which measures of apparent trabeuclar structure were derived. The specimens were nondestructively tested in compression along three orthogonal axes defined by the sides of the cubes. The elastic modulus (in the three directions) and the strength (in one direction) were determined. Trabecular BMD was measured by quantitative computed tomography. SOS varied significantly with direction of measurement, with the highest value in the axial direction (axial:1715 m/s, sagittal: 1662 m/second, and coronal: 1676 m/s). SOS of each of the three axes was generally associated with the various mechanical (r = 0.30-0.87), density (r = 0.81-0.93), and bone structural variables (0.3-0.8). However, after adjusting the SOS correlations by density, only the correlation with elasticity remained significant in the coronal direction. BMD alone explained 88-93% of variance in SOS whereas in the multivariate model, BMD plus elasticity and/or anisotropic variables explained 96-98% of the variance in SOS. Variability of SOS is explained mostly by density and to a small extent by elasticity or anisotropy. Since only 2-6% of the variance of the QUS measurement is not explained by density and elasticity, one could conclude that the remaining variance reflects other properties of bone or perhaps simply measurement error. Evidence that these other properties may be structure related is only found in the anisotropy of QUS parameter.

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

“…15,32,33,35 In the present study, SOS accounted for 84%-92% of the variance in FEA-estimated Young's modulus in each of the three perpendicular directions, and for 89% when the directions were pooled. In previous studies, the associations between stiffness and ultrasound velocity in human bone specimens were reported as r values between 0.44 and 0.77, 12,15,36 and r 2 values between 0.41 and 0.72. 5,17 In the bovine model, r 2 values of between 0.79 and 0.83 have been reported.…”

“…These studies differed also with respect to location and type of trabecular bone used (human calcaneal, lumbar spine or femoral neck bone samples, 5,12,15,36 bovine femoral bone samples, 35 or both human and bovine samples, 17 ), the preparation and size of the bone samples, and the ultrasound system used, so it is difficult to compare the results with our study. Nevertheless, it seems evident that the associations between SOS and stiffness, estimated by FEA in the present study, are stronger than the associations reported in the studies in which stiffness was assessed by mechanical testing.…”

“…These associations are similar to those reported by others. 3,5,12,15,17,19,23,35,36 Because density is a scalar quantity, which cannot account for anisotropy, different relationships between Young's modulus and SOS, on the one hand, and BMD, on the other, are bound to be found in the different directions. This also explains the weaker association between BMD and Young's modulus when the directions were pooled.…”

“…Trabecular arrangement is expressed in morphometric scalar parameters such as connectivity, trabecular number, trabecular spacing, and trabecular thickness. In recent studies, modest correlations between these scalar parameters, as evaluated by magnetic resonance imaging, 15 CT 10,32 and histomorphometry, 13 and ultrasound velocity were reported. Furthermore, significance was lost after adjustment for density.…”

“…4,14 Postmortem specimen studies have shown that ultrasound velocity is structure-related, as evidenced by its dependence on the measuring direction in bone cubes. 15,18,33,35,36 Furthermore, strong correlations between elastic moduli and ultimate strength, on the one hand, and ultrasound velocity, on the other, have been found in bovine 17,35,43 and human 5,12,15,17,36 trabecular bone samples. Recently, high-resolution microcomputed tomography (CT) reconstruction of trabecular bone was introduced.…”