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.