A robust method for measuring trabecular bone orientation anisotropy at in vivo resolution using tensor scale

Abstract

Trabecular bone (TB) is a network of interconnected struts and plates that constantly remodels to adapt dynamically to the stresses to which it is subjected in such a manner that the trabeculae are oriented along the major stress lines (Wolff's Law). Next to bone density, TB anisotropy has been found to be one of the most significant determinants of the bone's biomechanical behavior. Typically, orientational anisotropy of TB networks is expressed in terms of the fabric tensor, obtained by measuring the mean intercept length between structure elements along test lines. This method, however, can provide only a global statistical average of TB orientation anisotropy and, in general, requires a large sampling volume. Here, we present a new method, based on the recently conceived notion of “tensor scale”, which provides regional information of TB orientation anisotropy. Regional structure is represented by local best fit ellipsoid (ellipse in 2D) and the structural orientation is determined from the eigenvectors along the semi-axes. The method is found to be remarkably robust over a wide range of resolution regimes and image rotation as shown with micro-CT images from specimens of the human distal radius, the latter showing the characteristic differences in structural anisotropy for transverse and longitudinal sections. Finally, the method's applicability to in vivo MR imaging is demonstrated with data from the distal tibia.