L. Pothuaud et al., Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture, J BONE MIN, 15(4), 2000, pp. 691-699
The purpose of this work was to understand how fractal dimension of two-dim
ensional (2D) trabecular bone projection images could be related to three-d
imensional (3D) trabecular bone properties such as porosity or connectivity
. Two alteration processes were applied to trabecular bone images obtained
by magnetic resonance imaging: a trabeculae dilation process and a trabecul
ae removal process. The trabeculae dilation process was applied from the 3D
skeleton graph to the 3D initial structure with constant connectivity. The
trabeculae removal process was applied from the initial structure to an al
tered structure having 99% of porosity, in which both porosity and connecti
vity were modified during this second process. Gray-level projection images
of each of the altered structures were simply obtained by summation of vox
els, and fractal dimension (D-f) was calculated. Porosity (phi) and connect
ivity per unit volume (C-V) were calculated from the 3D structure. Signific
ant relationships were found between D-f, phi, and C-V, D-f values increase
d when porosity increased (dilation and removal processes) and when connect
ivity decreased (only removal process). These variations were in accordance
with all previous clinical studies, suggesting that fractal evaluation of
trabecular bone projection has real meaning in terms of porosity and connec
tivity of the 3D architecture. Furthermore, there was a statistically signi
ficant linear dependence between D-f and C-V when phi remained constant. Po
rosity is directly related to bone mineral density and fractal dimension ca
n be easily evaluated in clinical routine. These two parameters could be as
sociated to evaluate the connectivity of the structure.