The Structure Model Index has some well-known flaws, including not accounting for concave surfaces. Plateness is an experimental replacement for the structure model index. It uses the axis lengths from prolate and oblate spheroids to determine how prolate or oblate the trabecular space is around a particular point. Highly prolate (javelin-shaped, rod-like) spheroids have a single long axis (a) and two short axes (b, c) such that a >> b > c , whereas highly oblate (discus-shaped, plate-like) spheroids have two longer axes (a, b) and one much shorter axis (c) so that a > b >> c. So, b/a is close to 0 for prolate spheroids and close to 1 for oblate spheroids, while c/a is normally close to 0, except in more spherical spheroids (a ~ b ~ c), when both b/a and c/a are closer to 1. Plateness runs Skeletonise 3D, to get the medial axis of the trabeculae, which is used as the seed for sampling. Random vectors are seeded from each voxel on the medial axis until every vector has hit a foreground-background boundary. For each seed voxel, a covariance matrix is constructed from the vectors times their lengths. Eigenvalue decomposition results in an ordered list of three axis lengths. The three lengths are summed over all seed points to give ∑a, ∑b and ∑c, from which the relative proportions of rod- and plate-like structures may be inferred.
Plateness was replaced by the more robustly tested Ellipsoid Factor in BoneJ version 1.4.0. The star volumes used by Plateness are irregular in shape and not well approximated by ellipsoids. Furthermore, the best-fitting ellipsoid to a star volume usually is not contained within the foreground (bone) volume. Ellipsoid Factor is like Thickness in that the fitting objects (ellipsoid/spheres) are forced to remain inside the bone volume.
