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

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

Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection

International audienceIt has been shown that the analysis of two dimensional (2D) bone X-ray images based on the fractional Brownian motion (fBm) model is a good indicator for quantifying alterations in the three dimensional (3D) bone micro-architecture. However, this 2D measurement is not a direct assessment of the 3D bone properties. In this paper, we first show that S3D, the self-similarity parameter of 3D fBm, is linked to S2D, that of its 2D projection, by S3D = S2D 0.5. In the light of this theoretical result, we have experimentally examined whether this relation holds for trabecular bone. Twenty one specimens of trabecular bone were derived from frozen human femoral heads. They were digitized using a high resolution l-CT. Their projections were simulated numerically by summing the data in the three orthogonal directions and both 3D and 2D self-similarity parameters were measured. Results show that the self-similarity of the 3D bone volumes and that of their projections are linked by the previous equation. This demonstrates that a simple projection provides 3D information about the bone structure. This information can be a valuable adjunct to the bone mineral density for the early diagnosis of osteoporosis

Efficient estimation of osteoporosis using artificial neural networks

In this communication, Artificial Neural Network (ANN) is applied to discriminate osteoporotic fracture and control cases in a group of 304 patients. ANN is one of the popular methods in optimization of complex engineering problems compared to the classical statistical methods. In our study group, we consider some parameters as inputs: three bone densitometry parameters (BMD) (Femoral neck BNID, Total Body BMD and L2L4 spine BNID), three fractal parameters [1,5] (Hmin, Hmean, Hmax), and age of the patient. We studied three ANN structures with various inputs and hidden neurons. We have reached up to 81.66% correct classification. In comparison we have tested a classical discriminant analysis (Mahalanobis-Fisher) and we only obtained 72% of correct classification. We can conclude that ANN is one of the promising methods in the diagnosis of osteoporosis