Fractal dimension of trabecular bone projection texture is related to three-dimensional microarchitecture

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.