Quantification and visualization of anisotropy in trabecular bone

A number of methods for measuring anisotropy in trabecular bone using high-resolution X-ray computed tomography exist, which give different answers but have not been compared in detail. In this study, we examine the mean-intercept length (MIL), star volume distribution (SVD) and star length distribution (SLD) methods, their algorithmic implementation for three-dimensional (3D) data, and how their results relate to each other. A uniform ordered sampling scheme for determining which orientations to sample during analysis enhances the reproducibility of anisotropy and principal component direction determinations, with no evident introduction of biasing. This scheme also facilitates the creation of a 3D rose diagram that can be used to gain additional insights from the data. The directed secant algorithm that is frequently used for traversing pixel and voxel grids for these calculations is prone to bias unless a previously unreported normalization is used. This normalization ameliorates the bias present when using cubic voxels, and also permits calculations on data sets in which the slice spacing is not equal to the pixel spacing. Overall, the three methods for quantification of anisotropy give broadly similar results, but there are systematic divergences that can be traced to their differences in data and processing, and which may impact on their relative utility in estimating mechanical properties. Although discussed in the context of computed tomography of trabecular bone, the methods described here may be applied to any 3D data set from which fabric information is desired.