FRACTAL ORGANIZATION OF TRABECULAR BONE IMAGES ON CALCANEUS RADIOGRAPHS

Bone density is not the unique factor conditioning bone strength. Trab ecular bone microarchitecture also plays an important role. We have de veloped a fractal evaluation of trabecular bone microarchitecture on c alcaneus radiographs. Fractal models may provide a single numeric eval uation (the fractal dimension) of such complex structures. Our evaluat ion results from an analysis of images with a varying range of gray le vels, without binarization of the image. It is based on the fractional brownian motion model, or more precisely on the analysis of its incre ment, the fractional gaussian noise (FGN). The use of this model may b e considered validated if two conditions are fulfilled: the gaussian r epartition and the self-similarity of our data. The gaussian repartiti on 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-simil arity was tested on 20 images by two estimators, the variance method o f Pentland and the spectrum method of Fourier. Self-similarity is defi ned 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 mu m, then above 9 00 mu m, where linear regression produced high mean correlation coeffi cients (r greater than or equal to 0.97). Following this validation, w e studied the reproducibility of this new technique. Intra- and intero bserver reproducibility, influence of transferring the region of inter est, 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%, respective ly. These data have allowed us to validate the use of this fractal mod el by checking the fractal organization of our radiographic images ana lyzed by the model. The good reproducibility of successive x-rays in t he same subject allows us to undertake population studies and to envis age longitudinal series.