Trabecular bone microarchitecture and bone mineral density (BMD) are two main factors related to osteoporotic fractures. Currently, however, microarchitecture is not evaluated. We have developed and validated a trabecular bone texture analysis from radiographic images. The objective was to determine if the fractal analysis of texture was able to distinguish osteoporotic fracture groups from control groups, either in vertebrae, hip, or wrist fractures, and to determine if this indicator and BMD were independent and complementary. In this cross-sectional unicenter case-control population study in postmenopausal women, 107 fracture cases were enrolled and age-matched with 197 control cases. This population comprised 40 vertebral fractures (with 70 controls), 30 hip fractures (55 controls), and 37 wrist fractures (62 controls). Hip and lumbar spine BMD were measured by double-energy X-ray absorptiometry. Fractal analysis of texture was performed on calcaneus radiographs and the result was expressed as the H parameter (H = 2-fractal dimension). The H parameter showed a lower value (0.679 ± 0.053 SD) in fracture cases versus control cases (0.696 ± 0.030; p = 0.007), the statistical significance persisting after adjustment for age and for lumbar spine (LS) or hip BMD. This result was confirmed in vertebral fractures (p = 0.0001) and hip fractures (p = 0.003) but not wrist fractures (p = 0.07). We determined the threshold between high and low H values and then the odds ratios (OR) of fracture for low H for BMD ≤ −2.5 SD in T score and for the combinations of both parameters. The OR of fracture for low H was 1.6 (95% CI, 1.1–2.6). For LS BMD ≤ −2.5 SD the OR of 6.1 (3.4–10.8) shifted to 9.0 (4.0–20.4) when we added low H and for hip BMD it shifted from 5.6 (3.3–9.4) to 8.1 (4.0–16.8). In vertebral, hip, and wrist fracture cases the results were also significant. These data have shown that the fractal analysis of texture on calcaneus radiographs can distinguish osteoporotic fracture groups from control groups. This analysis and BMD provide independent and complementary information. These data suggest that we can improve the fracture risk evaluation by adding information related to microarchitecture, derived from analysis of conventional radiographic images.

Bone density is not the unique factor conditioning bone strength. Trabecular bone microarchitecture also plays an important role. We have developed a fractal evaluation of trabecular bone microarchitecture on calcaneus radiographs. Fractal models may provide a single numeric evaluation (the fractal dimension) of such complex structures. Our evaluation results from an analysis of images with a varying range of gray levels, without binarization of the image. It is based on the fractional brownian motion model, or more precisely on the analysis of its increment, the fractional gaussian noise (FGN). The use of this model may be considered validated if two conditions are fulfilled: the gaussian repartition and the self-similarity of our data. The gaussian repartition of intermediate lines of these images was tested on a sample of 32,800 lines from 82 images. Following a chi-square goodness-of-fit test, it was checked in 86% of these lines for α = 0.01. The self-similarity was tested on 20 images by two estimators, the variance method of Pentland and the spectrum method of Fourier. Self-similarity is defined by lined-up points in a log-log plot of the FGN spectrum or of the variance as a function of the lag. We found two self-similarity areas between scales of analysis ranging from 105 to 420 μm, then above 900 μm, where linear regression produced high mean correlation coefficients (r ≥ 0.97). Following this validation, we studied the reproducibility of this new technique. Intra- and interobserver reproducibility, influence of transferring the region of interest, and long-term reproducibility were assessed and given CV of 0.61 ± 0.15, 0.68 ± 0.47, 0.53 ± 0.16, and 2.07 ± 0.84%, respectively. These data have allowed us to validate the use of this fractal model by checking the fractal organization of our radiographic images analyzed by the model. The good reproducibility of successive x-rays in the same subject allows us to undertake population studies and to envisage longitudinal series.

OsteoArthritis (OA) is the most common disorder of the musculoskeletal system and the major cause of reduced mobility among seniors. The visual evaluation of OA still suffers from subjectivity. Recently, Computer- Aided Diagnosis (CAD) systems based on learning methods showed potential for improving knee OA diagnostic accuracy. However, learning discriminative properties can be a challenging task, particularly when dealing with complex data such as X-ray images, typically used for knee OA diagnosis. In this paper, we introduce a Discriminative Regularized Auto Encoder (DRAE) that allows to learn both relevant and discriminative properties that improve the classification performance. More specifically, a penalty term, called discriminative loss is combined with the standard Auto-Encoder training criterion. This additional term aims to force the learned representation to contain discriminative information. Our experimental results on data from the public multicenter OsteoArthritis Initiative (OAI) show that the developed method presents potential results for early knee OA detection.