Introduction: The structure of trabecular bone represents an aspect of bone properties that affects vertebral bone strength independently of bone mineral density [M. Kleerekoper, A. Villanueva, J. Stanciu, D. Rao, and A. Parfitt. The role of three-dimensional trabecular microstructure in the pathogenesis of vertebral compression fractures. Calcif. Tissue Int., 37:594-597, Dec 1985; E. Seeman and P. Delmas. Bone quality-the material and structural basis of bone strength and fragility. N. Engl. J. Med., 354:2250-2261, May 2006.]. Using the mathematical concept of fuzzy distance transformation (FDT), we evaluated the accuracy of measurements of trabecular distance (Tb.Di(f)) which can be determined for vertebrae in vivo using high resolution computed tomography (HRCT).
Methods: In a first step extrema voxels with a very high likelihood of representing bone or marrow are identified. A probability level of being a bone voxel is assigned to all other voxel. This probability is based on the FDT of the voxel's gray-level, preprint submitted to Elsevier June 10, 2008; revised July 15, 2008 i.e. the shortest gray-value weighted distance to the marrow background. Next, the resulting bone structure is skeletonized. The space between the ridges of the skeleton is filled with the largest possible spheres. The average over the radii of the spheres defines Tb.Di(f), a measure of trabecular distance. 14 whole vertebrae embedded in polymethyl methylacrylate were scanned by HRCT (voxel size 156 x 156 x 400 mum(3)) inside an anthropomorphic abdomen phantom. Scans obtained on Scanco Xtreme CT (XCT, voxel size 82(3) microm(3)) without the phantom were used as reference.
Results: Tb.Di(f) calculated on XCT data were almost identical to trabecular distance values (1/Tb.N*) determined with the manufacturer's standard software (r(2)=0.98). Tb.Di(f) values obtained with HRCT correlated strongly with Tb.Di(f) values obtained by XCT (r(2)=0.89). Over the range from 400 to 1400 microm trabecular distance could be estimated with a residual error of 78 microm.
Conclusions: The FDT based variable Tb.Di(f) provides 3D estimates of trabecular distances with residual errors of less than 100 microm using a HRCT protocol which also can be employed in vivo for assessing vertebral microarchitecture.