The characterization of broadband ultrasound attenuation and fractal analysis by biomechanical properties

The purpose of this study was to show how the difference in structure affects the mechanical properties of bone and if BUA or fractal analysis is able to detect these changes in mechanical properties. A total of 38 cancellous bone cubes were obtained from seven bovine tibiae (32 specimens) and one human tibia (6 specimens). BUA was measured in the superior/inferior (SI), medial/lateral (ML), and anterior/posterior (AP) directions for each specimen. The fractal dimension was estimated by using the continuous alternating sequential filter (CASF) pyramid approach to handle fractal dimension estimation of small images. Nondestructive compressive tests were also performed in the three orthogonal directions for each sample. The correlations between BUA and density were statistically significant for all three directions. The correlation between BUA and elastic modulus varied depending on the direction in which the two parameters were measured. The best correlation was in the AP directions (r = 0.75, p < 0.0001), followed by the ML direction (r = 0.52, p = 0.0006), and finally the SI direction (r = 0.18, p = 0.28). The only significant correlation between fractal dimension and density was in the SI direction (r = 0.39, p = 0.015). There was significant correlation between fractal dimension and elastic modulus in all three directions, but the direction that exhibited the best correlation was the SI direction (r = 0.61, p < 0.0001). The correlation coefficients for the AP and ML directions were 0.45 (p = 0.0046) and 0.34 (p = 0.0377), respectively. A multivariate model, carried out to predict the elastic modulus from the BUA or fractal dimension including density, demonstrated that the correlation coefficient significantly increased in all three directions for BUA and fractal dimension. After adjustment for density, significant relationships between elastic modulus and BUA or fractal dimension were still found (p < 0.05).