Fractal organization of trabecular bone images on calcaneus radiographs.

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 alpha = 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 microns, then above 900 microns, where linear regression produced high mean correlation coefficients (r > or = 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.

Long-term reproducibility optimization of an x-ray process for bone architectural evaluation during osteoporosis.

Non-invasive and in vivo assessment of bone architectural changes at high resolution is of considerable interest in osteoporosis. In this note, the use of an x-ray acquisition system in the evaluation of the architectural quality of trabecular bone by radiographic texture analysis is optimized to achieve good long-term reproducibility. First, radiographic and digitization processes are modelled and defined. Procedures to make radiographs and their digital images are fixed. Then, measurements of the modulation transfer function (MTF) of the entire acquisition chain were completed. These measurements provide an MTF in excess of 30% at a spatial frequency of 2.5 lp/mm. Also, results of a fractal texture analysis made on digital images of calcaneus radiographs show a mean coefficient of variation of 2.07%. These data show that good long-term reproducibility can make the x-ray acquisition system efficient for patient follow-up, or evaluation of treatment regimes for osteoporosis. Finally, it is shown that fractal texture parameters are statistically different in an osteoporotic population and in a control group. Therefore, this system should also be of medical interest.

Anisotropy measurements obtained by fractal analysis of trabecular bone at the calcaneus and radius.

The resistance of bone tissue is influenced not only by bone density parameters but also by bone architecture parameters, such as the microarchitecture and anisotropy of trabecular bone. We have developed and validated a fractal analysis method for studying bone microarchitecture on roentgenograms. This technique provides reproducible measurements of the fractal dimension (D) of bone, which reflects bone texture. The fractal dimension is determined in 36 different directions; the mean of these 36 values is representative of the image. A polar diagram gives the value of D according to the angle of analysis. By decomposing this diagram using polar Fourier Transform analysis, the parameters related to the shape of the polar diagram can be determined. This diagram image analysis technique has been used for other similar diagrams and applied to the results of our fractal analysis method. Diagram shape characterization may provide information on the angular distribution of results and therefore on the anisotropy of the images under study. The purpose of this study was to compare roentgenograms of the calcaneus and radius in the same subjects to determine whether texture and anisotropy parameters discriminated between these two bones. Roentgenograms of the calcaneus and radius were obtained in ten nonosteoporotic subjects. The radius had a smaller fractal dimension than the calcaneus (mean +/- standard deviation: 1.215 +/- 0.025 and 1.285 +/- 0.066, respectively; p = 0.014). Differences in the shape of the polar diagram were found between the two bones. The mean Fourier coefficient ratio C2/C4 was considerably smaller at the calcaneus (0.63 +/- 0.50) than at the radius (4.88 +/- 3.45; p = 0.005). Our method allows quantitative characterization of texture and anisotropy differences between the calcaneus and radius. The smaller fractal dimension of the radius probably reflects the simpler architecture of this non weight-bearing bone. The differences in polar diagram shape allow to evaluate anisotropy differences between the calcaneus and radius.