Fractal analysis of trabecular architecture. With special reference to slice thickness and pixel size of the image

Many analyses of bone microarchitecture using three-dimensional images of micro CT(μCT) have been reported recently. However, as extirpated bone is the subject of measurement on μCT, various kinds of information are not available clinically. Our aim is to evaluate usefulness of fractal dimension as an index of bone strength different from bone mineral density in in-vivo, to which μCT could not be applied. In this fundamental study, the relation between pixel size and the slice thickness of images was examined when fractal analysis was applied to clinical images. We examined 40 lumbar spine specimens extirpated from 16 male cadavers (30-88 years; mean age, 60.8 years). Three-dimensional images of the trabeculae of 150 slices were obtained by a μCT system under the following conditions: matrix size, 512 x 512; slice thickness, 23.2 μm; and pixel size, 18.6 μm. Based on images of 150 slices, images of four different matrix sizes and nine different slice thicknesses were made using public domain software (National Institutes of Health (NIH) Image). The threshold value for image binarization, and the relation between pixel size and the slice thickness of an image used for two-dimensional and three-dimensional fractal analyses were studied. In addition, the box counting method was used for fractal analysis. One hundred forty-five in box counting was most suitable as the threshold value for image binarization on the 256 gray levels. The correlation coefficients between two-dimensional fractal dimensions of processed images and three-dimensional fractal dimensions of original images were more than 0.9 for pixel sizes ≤148.8 μm at a slice thickness of 1 mm, and ≤74.4 μm at one of 2 mm. In terms of the relation between the three-dimensional fractal dimension of processed images and three-dimensional fractal dimension of original images, when pixel size was less than 74.4 μm, a correlation coefficient of more than 0.9 was obtained even for the maximal slice thickness (1.74 mm) examined in this study. (author)