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 three edges are preferentially aligned in relation to the muscle forces that are applied to the condyle. We conclude that the ITA topological parameters are remarkably conserved, but locally do adapt to applied stresses.

Structural design of the echinoid’s trabecular system

“…The inter-trabecular angle ITA [ 26 , 32 ] is the angle between any of two intersecting segments in a common node. Angle calculation is performed in two-step process, where in a first step, the position vectors of a segment are used to describe the direction vector of a segment, and in a second step, the angle between two direction vectors segments is calculated using Eq ( 6 ).…”

Trabecular architecture in the humeral metaphyses of non‐avian reptiles (Crocodylia, Squamata and Testudines): Lifestyle, allometry and phylogeny

“…Thanks to the development of X‐ray computed microtomography, 3D trabecular architecture could be extensively studied in birds (e.g., Bishop et al, ; Doube, Kłosowski, Wiktorowicz‐Conroy, Hutchinson, & Shefelbine, ; Fajardo, Hernandez, & O'Connor, ; Pontzer et al, ) and mammals (e.g., many orders [Doube et al, ], bovids [Mittra, Rubin, & Qin, , Sode, Burghardt, Nissenson, & Majumdar, ], lagomorphs [Marchand, Chen, Buschmann, & Hoemann, , van der Meulen et al, ], primates [Barak, Lieberman, Raichlen, et al, , Cunningham & Black, , Kivell, Skinner, Lazenby, & Hublin, , Lazenby, Skinner, Kivell, & Hublin, , Sode et al, ], rodents [Carlson, Lublinsky, & Judex, , Lambers et al, , Sode et al, ], sciuromorphs [Mielke et al, ], suids [Ben‐Zvi, Reznikov, Shahar, & Weiner, ], and xenarthrans [Amson et al, ]). In comparison, 3D trabecular architecture of nonavian reptiles has received little attention.…”

In-depth gaze at the astonishing mechanical behavior of bone: A review for designing bio-inspired hierarchical metamaterials

“…Certainly, the changes in the orientation of the external loads (the order of magnitude of time is seconds or minutes) and, consequently, of the principal stresses are faster than the capacity of the trabeculae of self-orientate accordingly (the order of magnitude of time is weeks or months, being related to the remodeling process). This means that the actual disposition of the trabeculae does not follow the principal directions of the stress exactly; indeed, locally the angles between different trabeculae are usually different from 90 • , ranging from 80 • to 160 • depending on whether we consider nodes that join 3, 4, 5, or 6 trabeculae, with mean values of about 116 • , 108 • , 103 • , and 100 • , respectively [40,41]. The trabecular architecture showing such a high level of complexity is, in the end, the result of a "self-organizational" optimization, owing to the bone remodeling, aimed at occupying the maximal volume with the smallest amount of material and conferring to the bone a multidirectional strength for bearing loads.…”