3D Architecture of Trabecular Bone in the Pig Mandible and Femur: Inter-Trabecular Angle Distributions

Abstract

Cancellous bone is an intricate network of interconnected trabeculae, to which analysis of network topology can be applied. The inter-trabecular angle (ITA) analysis - an analysis of network topological parameters and regularity of network-forming nodes, was previously carried out on human proximal femora and showed that trabecular bone follows two main principles: sparsity of the network connectedness (prevalence of nodes with low connectivity in the network) and maximal space spanning (angular offset of connected elements is maximal for their number and approximates the values of geometrically symmetric shapes). These observations suggest that 3D organization of trabecular bone, irrespective of size and shape of individual elements, reflects a tradeoff between minimal metabolic cost of maintenance and maximal network stability under conditions of multidirectional loading. In this study we validate the ITA application using additional 3D structures (cork and 3D-printed metal lattices), analyze the ITA parameters in porcine proximal femora and mandibles and carry out a spatial analysis of the most common node type in the porcine mandibular condyle. The validation shows that the ITA application reliably detects designed or evolved topological parameters. The ITA parameters of porcine trabecular bones are similar to those of human bones. We demonstrate functional adaptation in the pig mandibular condyle by showing that the planar nodes with 3 edges are preferentially aligned in relation to the muscle forces that are applied to the condyle. We conclude that the ITA topological parameters are remarkable conserved, but locally do adapt to applied stresses.