Power Spectral Analysis of Vertebral Trabecular Bone Structure from Radiographs: Orientation Dependence and Correlation with Bone Mineral Density and Mechanical Properties

Abstract. Trabecular bone structure and bone density contribute to the strength of bone and are potentially important in the study of osteoporosis. Fourier transforms of the textural patterns in radiographs of trabecular bone have previously been used for the measurement of trabecular bone structure in subjects, however, the relationship between these measures and biomechanical properties of bone have not previously been established. In this study radiographs were acquired of 28 cubic specimens of spinal trabecular bone along each of the three anatomic axes: cranio-caudal or superior-inferior (SI), medial-lateral (ML), and anterior-posterior (AP). The radiographs were digitized, background corrected, and uniformly aligned. The Fast Fourier transform (FFT) was performed on a region comprised solely of trabecular bone for each image. The zero (DC), first (FMO), and second moments (SMO) of the Fourier power spectrum and the fractal dimension (FD) as determined from the Fourier power spectrum were correlated with stereology measures, with bone mineral density (BMD) as well as with measured biomechanical properties [Young's elastic modulus (YM) and ultimate strength] of the cubes. The results show that the power spectra-based measures, when compared with structural parameters determined using 3D stereology, show good correlations with bone volume fraction, trabecular spacing, thickness, and number. These power spectral measures showed fair to good correlations with BMD and the biomechanical properties. Moreover, the correlations between the power spectral measures of trabecular structure and the BMD, YM, and stereology measures of structure depend on the orientation of the radiographic image. Specifically, these were significant differences in the measured biomechanical properties and the power spectral measures of the trabecular structure between the SI and ML and the SI and AP directions. In addition, depending on the spatial frequency range for analysis, the fractal dimension showed opposite trends with changes in BMD and biomechanical properties. Multivariate regression models showed the correlation coefficients increasing with the inclusion of some of the power spectral measures, suggesting that FFT-based texture analysis may play a potential role in studies of osteoporosis.