Evaluation of the plate-rod model assumption of trabecular bone

Trabecular bone has traditionally been assumed to be composed of plate- and rod-like trabeculae. This paper proposes a method to numerically evaluate the appropriateness of this assumption. In a first step, local constancy of thickness is estimated by comparing the maximum and mean diameter of the maximum inscribed balls centered at the medial axis/surface that includes every local point. In a second step, deviations from null curvature at the medial axis/surface are locally measured by comparing the geodesic and Euclidean distances from a point to its neighbors in the medial axis/surface. Finally, these two measurements are combined in order to locally estimate the compliance of the dataset with the plate-rod model assumption. Experiments on synthetic datasets show that the proposed measurements can be used to decide the compliance of a 3D shape with the plate-rod model. Results on micro computed tomography images show that the plate-rod model is more valid for a vertebra than for a radius. Thus, especially for the radius, measurements based on this model should be complemented with the proposed measurements.