Anisotropy changes in post-menopausal osteoporosis: characterization by a new index applied to trabecular bone radiographic images

Bone intrinsic strength is conditioned by several factors, including material property and trabecular micro-architecture. Bone mineral density (BMD) is a good surrogate for material property. Architectural anisotropy is of special interest in mechanics-architecture relations and characterizes the degree of directional organization of a material. We have developed anisotropy indices from the Fast Fourier Transform (FFT) on bone radiographs. We have validated these indices in a cross-sectional uni-center case-control study including 39 postmenopausal women with vertebral fracture and 70 age-matched control cases. BMD was measured at the lumbar spine and femoral neck. A fractal analysis of texture was performed on calcaneus radiographs at three regions of interest (ROIs), and the result was expressed as the H parameter (fractal dimension =H-2). The anisotropy evaluation was based on the FFT spectrum of these three ROIs extracted on calcaneus radiographs. On the FFT spectrum, we have measured the spreading angle of the longitudinal trabeculae called the dispersion longitudinal index (DLI) and the spreading angle of the transversal trabeculae called the dispersion transversal index (DTI). From the measured parameters, an anisotropy index was derived, and the degree of anisotropy (DA) calculated with DLI and DTI. We have compared the results from the vertebral fracture cases and control cases. The best distinction was obtained for the largest ROI located in the great tuberosity of the calcaneus for all parameters ( P < 10(-4)). The DA parameter showed a higher value in vertebral fracture cases (1.746 +/- 0.169) than in control cases (1.548 +/- 0.136); P < 10(-4), and the difference persisted after removal of the subjects with hormonal replacement therapy. The analysis of the receiver operating characteristics (ROC) has shown the best results with DA and Hmean: areas under curves (AUCs) respectively of 0.765 and 0.683, while AUCs associated to LS-BMD and FN-BMD were 0.614 and 0.591 lower, respectively. We determined the odds ratios (OR) by uni- and multivariate analysis. Crude ORs were respectively 3.91 (95% CI: 2.22-6.87) and 3.08 (95% CI: 1.72-5.52) for DA and Hmean. Crude ORs were respectively 1.71 (95% CI: 1.15-2.56) and 1.56 (95% CI: 1.05-2.31) for LS-BMD and FN-BMD. All ORs were statistically significant, and those associated to Hmean and anisotropy indices were higher than those of BMD measurements. From a multivariate analysis including anisotropy indices, Hmean, age and FN-BMD, the remaining significant ORs were respectively 6.33 (95% CI: 2.80-14.30) and 3.08 (95% CI: 1.48-6.37) for DA and Hmean. These data have shown that anisotropy indices on calcaneus radiographs can distinguish vertebral fracture cases from control cases. This analysis provides complementary information concerning the BMD and fractal parameter. These data suggest that we can improve the fracture risk evaluation by adding information related to the directional organization of trabecular bone derived from the FFT spectrum on conventional radiographic images.