A new anisotropy index on trabecular bone radiographic images using the fast Fourier transform

The degree of anisotropy (DA) on radiographs is related to bone structure, we present a new index to assess DA.

In a region of interest from calcaneus radiographs, we applied a Fast Fourier Transform (FFT). All the FFT spectra involve the horizontal and vertical components corresponding respectively to longitudinal and transversal trabeculae. By visual inspection, we measured the spreading angles: Dispersion Longitudinal Index (DLI) and Dispersion Transverse Index (DTI) and calculated DA = 180/(DLI+DTI). To test the reliability of DA assessment, we synthesized images simulating radiological projections of periodic structures with elements more or less disoriented.

Firstly, we tested synthetic images which comprised a large variety of structures from highly anisotropic structure to the almost isotropic, DA was ranging from 1.3 to 3.8 respectively. The analysis of the FFT spectra was performed by two observers, the Coefficients of Variation were 1.5% and 3.1 % for intra-and inter-observer reproducibility, respectively. In 22 post-menopausal women with osteoporotic fracture cases and 44 age-matched controls, DA values were respectively 1.87 +/- 0.15 versus 1.72 +/- 0.18 (p = 0.001). From the ROC analysis, the Area Under Curve (AUC) were respectively 0.65, 0.62, 0.64, 0.77 for lumbar spine, femoral neck, total femoral BMD and DA.

The highest DA values in fracture cases suggest that the structure is more anisotropic in osteoporosis due to preferential deletion of trabeculae in some directions.