E. Lespessailles et al., ANISOTROPY MEASUREMENTS OBTAINED BY FRACTAL ANALYSIS OF TRABECULAR BONE AT THE CALCANEUS AND RADIUS, Revue du rhumatisme, 63(5), 1996, pp. 337-343
The resistance of bone tissue is influenced not only by bone density p
arameters but also by bone architecture parameters, such as the microa
rchitecture and anisotropy of trabecular bone. We have developed and v
alidated 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 giv
es the value of D according to the angle of analysis. By decomposing t
his diagram using polar Fourier Transform analysis, the parameters rel
ated 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 o
f results and therefore on the anisotropy of the images under study. T
he purpose of this study was to compare roentgenograms of the calcaneu
s and radius in the same subjects to determine whether texture and ani
sotropy parameters discriminated between these two bones, Roentgenogra
ms of the calcaneus and radius were obtained in ten nonosteoporotic su
bjects. The radius had a smaller fractal dimension than the calcaneus
(mean+/-standard deviation: 1.215+/-0.025 and 1.285+/-0.066, respectiv
ely; p=0.014). Differences in the shape of the polar diagram were foun
d 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 characterizati
on of texture and anisotropy differences between the calcaneus and rad
ius. The smaller fractal dimension of the radius probably reflects the
simpler architecture of (his non weight-bearing bone. The differences
in polar diagram shape allow to evaluate anisotropy differences betwe
en the calcaneus and radius.