Topological analysis of trabecular bone MR images.

Recently, imaging techniques have become available which permit nondestructive analysis of the three-dimensional (3-D) architecture of trabecular bone (TB), which forms a network of interconnected plates and rods. Most osteoporotic fractures occur at locations rich in TB, which has spurred the search for architectural parameters as determinants of bone strength. In this paper, we present a new approach to quantitative characterization of the 3-D microarchitecture of TB, based on digital topology. The method classifies each voxel of the 3-D structure based on the connectivity information of neighboring voxels. Following conversion of the 3-D digital image to a skeletonized surface representation containing only one-dimensional (1-D) and two-dimensional (2-D) structures, each voxel is classified as a curve, surface, or junction. The method has been validated by means of synthesized images and has subsequently been applied to TB images from the human wrist. The topological parameters were found to predict Young's modulus (YM) for uniaxial loading, specifically, the surface-to-curve ratio was found to be the single strongest predictor of YM (r2 = 0.69). Finally, the method has been applied to TB images from a group of patients showing very large variations in topological parameters that parallel much smaller changes in bone volume fraction (BVF).