Grun TB and Nebelsick JH (2018), Structural design of the echinoid's trabecular ...

ECB-ART-46618

PLoS One 2018 Sep 27;139:e0204432. doi: 10.1371/journal.pone.0204432.

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Structural design of the echinoid''s trabecular system.

Grun TB , Nebelsick JH .

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The multi-plated skeleton of echinoids is made of the stereom, a light-weight construction which resembles a micro-beam framework. Although the two-dimensional design of the stereom has been studied, its spatial architecture is only little known. It is, however, imperative to understand the spatial architecture of the trabecular system in order to interpret its structural principles of this load-bearing construction. The echinoid''s trabecular system is thus analyzed in-depth with respect to eight topological descriptors. The echinoid''s plates are divided into two regions, the center of which consists of an unordered stereom, and the margin which consists of an ordered stereom. The eight trabecular descriptors indicate that the basal topology of the two plate regions are similar. The trabecular system predominantly consists of short and stocky trabeculae that show little tortuosity. The majority of trabeculae intersect in a 3N configuration, where three trabeculae intersect in one common node. Trabeculae in the 3N configuration intersect in an angle of around 120° resulting in a planar and triangular motif. These planar elements, when arranged in an angular off-set, can resist multi-dimensional loads. Results also show that the trabecular orientation perpendicular to the plate''s surface is at an angle of 60°. The trabecular orientation in the plate''s horizontal plane is directional. Both trabecular orientations reflect a construction which is capable of resisting applied loads and can distribute these loads over the entire skeleton. The spatial architecture of the echinoid''s trabecular system is thus considered to be a performative light-weight and load-bearing system.

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Genes referenced: LOC100893907 LOC583082 mxd1

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References [+] :

Grun, Structural design of the minute clypeasteroid echinoid Echinocyamus pusillus. 2018, Pubmed, Echinobase

	Fig 1. The echinoid skeleton is hierarchically organized.(A) Echinocyamus pusillus with spines (arrows). (B) Denuded skeleton. (C) Micro-CT section showing individual plates (arrows). (D) Micrograph of the stereom network and trabeculae (arrows).
	Fig 2. Data generation.(A) Micro-CT section of Echinocyamus pusillus. Blue squares indicate the areas of data origin. (B) 3d reconstruction of a subvolume of the stereom. (C) Network scheme of the stereom. Blue spheres indicate nodes; yellow lines represent trabeculae. (D) Close-up of the trabecular network. The node configuration indicates how many trabeculae intersect in a common node. The course of trabeculae is described by light-blue spheres.
	Fig 3. Trabecular descriptors.The trabecular length can be measured by its chord length (Lc) which is defined by the maximum extension of a trabecula, and its curved length (Lt) which describes the length of a trabecula following its center line. The trabecular radius is given by r.
	Fig 4. Definition of the theta and phi.Horizontal plane (blue) and the z-axis (yellow) of a plate model.
	Fig 5. Stereographic rendering of the stereom.(A) Trabeculae at the plate’s center are unordered. (B) The visualization of thinned and color-coded trabeculae shows the sturdy trabeculae. (C) trabeculae at the plate’s margin are more ordered, and (D) the trabeculae are slenderer than those of the plate’s center.
	Fig 6. Histograms of the inter-trabecular angles.(A) All inter trabecular angles of the plate centers. (B) Inter trabecular angles of the plate centers, where 3 segments intersect in a single common node. (C) All inter trabecular angles of the plate margins. (D) Inter trabecular angles of the plate margins, where 3 segments intersect in a common node. N = sample size, med. = median, mad. = median absolute deviation, mode is indicated by arrows.
	Fig 7. Histograms of the trabecular orientation with respect to the plate’s horizontal plane.(A) Trabecular distribution at the plate’s center. (B) Trabecular distribution at the plate’s margin. N = sample size, med. = median, mad. = median absolute deviation, mode is indicated by arrows.
	Fig 8. Rose diagrams of the trabecular orientation within the plate’s horizontal plane.(A) Phi distribution at the plate’s center. (B) Phi distribution at the plate’s margin. Both diagrams indicate that the trabeculae are directional aligned within the plate’s horizontal plane.
	Fig 9. Lattice-system.Built-up from multiple 3N members. All inter-trabecular angles possess an offset of 120 degrees to one another.