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J R Soc Interface
2024 Mar 13;21212:20230597. doi: 10.1098/rsif.2023.0597.
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Composite material in the sea urchin Cidaris rugosa: ordered and disordered micrometre-scale bicontinuous geometries.
Jessop AL
,
Millsteed AJ
,
Kirkensgaard JJK
,
Shaw J
,
Clode PL
,
Schröder-Turk GE
.
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The sponge-like biomineralized calcite materials found in echinoderm skeletons are of interest in terms of both structure formation and biological function. Despite their crystalline atomic structure, they exhibit curved interfaces that have been related to known triply periodic minimal surfaces. Here, we investigate the endoskeleton of the sea urchin Cidaris rugosa that has long been known to form a microstructure related to the Primitive surface. Using X-ray tomography, we find that the endoskeleton is organized as a composite material consisting of domains of bicontinuous microstructures with different structural properties. We describe, for the first time, the co-occurrence of ordered single Primitive and single Diamond structures and of a disordered structure within a single skeletal plate. We show that these structures can be distinguished by structural properties including solid volume fraction, trabeculae width and, to a lesser extent, interface area and mean curvature. In doing so, we present a robust method that extracts interface areas and curvature integrals from voxelized datasets using the Steiner polynomial for parallel body volumes. We discuss these very large-scale bicontinuous structures in the context of their function, formation and evolution.
Figure 1. . Reconstructed micro-CT data of the sea urchin C. rugosa. (a) Three-dimensional visualization of the whole urchin skeleton depicting the approximate location of the sectioned interambulacral plate shown in (b). The oral surface of the skeleton is pointing upwards, and the aboral surface is pointing downwards. Scale bar = 1 cm. (b) Three-dimensional visualization of the sectioned interambulacral plate depicting the location of the slice shown in (c). Scale bar = 1 mm. (c) A single slice through the interambulacral plate indicated by C in (b) approximately oriented with the tubercle in the positive Z-direction. The outlined section depicts a close-up of this slice shown in (d). Scale bar = 1 mm. (d) Close up of outlined section in (c), where the red highlight shows the region of the interambulacral plate that was scanned with a resolution of 1.69 μm and the blue highlight shows the region of the plate scanned with a resolution of 732 nm. Scale bar = 100 μm.
Figure 2. . A representative subvolume of the stereom that closely resembles a single Primitive surface. (a) Cross-section through the interambulacral plate showing the location of the representative subvolume. Scale bar = 1 mm. (b) The subvolume of the sea urchin stereom (in grey; isotropic voxel size of 732 nm) and a simulated nodal approximation of the single Primitive surface with a solid volume fraction ϕ = 0.38 (in yellow) and lattice parameter a = 30 μm. Scale bar = 100 μm. (c) Perpendicular slices through the sea urchin subvolume depicted in (b). Scale bar = 50 μm.
Figure 3. . A representative subvolume of the stereom that closely resembles a single Diamond structure. (a) Cross-section through the interambulacral plate showing the location of the representative subvolume. Scale bar = 1 mm. (b) The subvolume of the sea urchin stereom (in grey; isotropic voxel size of 732 nm) and a simulated nodal approximation of the a single Diamond surface with a solid volume fraction ϕ = 0.3 (in yellow) and lattice parameter a = 39 μm. Scale bar = 50 μm. The rectangular domain is oriented such that its orthogonal axes are the [112¯], [11¯0] and [111] crystallographic directions of the Diamond geometry (in Miller index notation). (c) Slices through this subvolume showing the urchin and simulated data in the [111], [112¯] and [11¯0] planes. Scale bar=50 μm.
Figure 4. . Orientation of the [111] direction of the sea urchin D-like stereom relative to the direction of the spine (the positive Z-direction of the tomography dataset). (a,b) Volume render of the intermabulacral plate viewed along the Z-axis (a) and Y-axis (b) showing locations of eight sampled D-like stereom. (c) Orientation of the [111] direction of each sample (black points) relative to the spine (grey point) represented by vectors projected onto a sphere. The sphere is presented in (c) as a perspective along the Z-axis. The mean orientation of the [111] direction relative to the spine (the positive Z-direction) is 16 ± 2°.
Figure 5. . A representative subvolume of the Disordered stereom. (a) Cross-section through the interambulacral plate showing the location of the representative subvolume. Scale bar = 1 mm. (b) The subvolume of the sea urchin stereom (isotropic voxel size of 1.69 μm). Scale bar = 100 μm. (c) Perpendicular slices through the subvolume depicted in (b). Scale bar = 50 μm.
Figure 6. . The distribution of solid volume fraction, pore sizes and trabeculae widths across the interambulacral plate. (a) The distribution of solid volume fraction showing distinct differences across the plate. Scale bar = 1 mm. Squares P, D and Di show locations of subsampled stereom where P is the P-like, D is the D-like and Di is the Disordered stereom. (b) and (c) show the maximum pore sizes and trabeculae widths, respectively. (d), (e) and (f) show the distribution of solid volume fraction, pore sizes and trabeculae widths across a subsample of each stereom type.
Figure 7. . Azimuthally averaged intensities of SAXS (a) and WAXS (b) data from internal and external regions of the stereom that are characterized by micrometre-scale ‘Internal (Disordered)’ and ‘External (P-like)’ surface structures, respectively. The data labelled ‘Calcite’ are reference data for calcite [33]. (c,d) Two-dimensional detector images of and WAXS for the ‘External (P-like)’ and ‘Internal (Disordered)’ samples.
