Topology-based orientation analysis of trabecular bone networks.

After bone mineral density, orientation is the major determinant of trabecular bone strength and is thus of significant interest in understanding the clinical implications of osteoporotic bone loss. The methods used to measure orientation and anisotropy of the trabecular bone have largely relied on deriving global measures along test lines, computing the best-fit ellipsoid, and decomposing to eigenvalue-eigenvector pairs that yield the mean orientation and anisotropy of the region. These techniques ignore the differences between measuring the orientation of trabecular plates versus rods, and do not provide insight into the relationship between local orientation and biomechanical stresses. Digital topological analysis allows a unique determination of each voxel's topological class as belonging to a plate, rod, or junction. The digital topology-based orientation analysis (DTA-O) method extracts the voxels belonging to plates and determines the local surface normal by fitting a plane through the local neighborhood BVF map. Modeling regional distributions of these vectors allows assessment of anisotropy measures, such as mean and variance of the orientation distribution. High-resolution microcomputed tomography, synthetic, and in vivo images were used for a validation of the new method and compare the results with the mean intercept length (MIL) technique. The results indicate that DTA-O is a better measure of trabecular orientation and anisotropy than MIL. Applying DTA-O to a recently completed study on the distal radius of 82 subjects [F.W. Wehrli et al., J. Bone Min. Res. 16, 1520 (2001)] shows that the mean orientation and anisotropy at the medial and lateral sides in the distal radius mataphyseal trabecular network are consistent with the mechanical stresses acting on the radius during common tasks.