Micro-CT data and associated MATLAB scripts from the skeleton of the sea urchin Cidaris rugosa at four different resolutions

The sponge-like biomineralised 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 organised 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 Primitive and 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.

Methods
Urchin samples were scanned with a Versa 520 XRM (Zeiss, Pleasanton, CA, USA) running Scout and Scan software (v15.0.17350.39816) at the Centre for Microscopy, Characterisation, and Analysis at the University of Western Australia. The whole urchin was scanned with a voltage of 65 kV at a magnification of 0.4X using the LE3 source filter delivering an isotropic voxel size of 22.8 μm. The sectioned interambulacral plate was scanned with a voltage of 80 kV at a magnification of 4X using the LE2 source filter delivering an isotropic voxel size of 3.72 μm. Two higher magnification scans were also conducted on an inner section of the interambulacral plate using a voltage of 80 kV, a magnfication of 4X, and the LE2 filter, delivering isotropic voxel sizes of 1.69 μm and 732 nm. Raw projection data were reconstructed using XRM Reconstructor software (v15.0.17350.39816) following a standard centre shift and beam hardening correction.