Quantitative 3D structural analysis of the cellular microstructure of sea urchin spines (II): Large-volume structural analysis.

Biological cellular materials have been a valuable source of inspiration for the design of lightweight engineering structures. In this process, a quantitative understanding of the biological cellular materials from the individual branch and node level to the global network level in 3D is required. Here we adopt a multiscale cellular network analysis workflow demonstrated in the first paper of this work series to analyze the biomineralized porous structure of sea urchin spines from the species Heterocentrotus mamillatus over a large volume (ca. 0.32mm). A comprehensive set of structural descriptors is utilized to quantitatively delineate the long-range microstructural variation from the spine center to the edge region. Our analysis shows that the branches gradually elongate (50% increase) and thicken (100% increase) from the spine center to edge, which dictates the spatial variation of relative density (from ~12% to ~40%). The branch morphology and network organization patterns also vary gradually with their positions and orientations. Additionally, the analysis of the cellular network of individual septa provides the interconnection characteristics between adjacent septa, which are the primary structural motifs used for the construction of the cellular structure in the edge region. Lastly, combining the extracted long-range cellular network and finite element simulations allows us to efficiently examine the spatial and orientational dependence of local effective Young's modulus across the spine's radius. The structural-mechanical analysis here sheds light on the structural designs of H. mamillatus' porous spines, which could provide important insights for the design and modeling of lightweight yet strong and damage-tolerant cellular materials. STATEMENT OF SIGNIFICANCE: Previous investigations on the cellular structures of sea urchin spines have been mainly based on 2D measurements or 3D quantification of small volumes with limited structural parameters. This limits our understanding of the interplay between the 3D microstructural variations and the mechanical properties in sea urchin spines, which hence constrains the derivation of the underlying principles for bio-inspired designs. This work utilizes our multiscale 3D network analysis, for the first time, to quantify the 3D cellular network and its variation across large volumes in sea urchin spines from individual branch and node level to the cellular network level. The network analysis demonstrated here is expected to be of great interest to the fields of biomineralization, functional biological materials, and bio-inspired material design.