Strength, elasticity and the limits of energy dissipation in two related sea urchin spines with biomimetic potential

Hexagonal Voronoi pattern detected in the microstructural design of the echinoid skeleton

Repeated polygonal patterns are pervasive in natural forms and structures. These patterns provide inherent structural stability while optimizing strength-per-weight and minimizing construction costs. In echinoids (sea urchins), a visible regularity can be found in the endoskeleton, consisting of a lightweight and resistant micro-trabecular meshwork (stereom). This foam-like structure follows an intrinsic geometrical pattern that has never been investigated. This study aims to analyse and describe it by focusing on the boss of tubercles-spine attachment sites subject to strong mechanical stresses-in the common sea urchin Paracentrotus lividus. The boss microstructure was identified as a Voronoi construction characterized by 82% concordance to the computed Voronoi models, a prevalence of hexagonal polygons, and a regularly organized seed distribution. This pattern is interpreted as an evolutionary solution for the construction of the echinoid skeleton using a lightweight microstructural design that optimizes the trabecular arrangement, maximizes the structural strength and minimizes the metabolic costs of secreting calcitic stereom. Hence, this identification is particularly valuable to improve the understanding of the mechanical function of the stereom as well as to effectively model and reconstruct similar structures in view of future applications in biomimetic technologies and designs.

Mechanical defensive adaptations of three Mediterranean sea urchin species

In the Mediterranean, Paracentrotus lividus and Sphaerechinus granularis are important drivers of benthic ecosystems, often coexisting in sublittoral communities. However, the introduction of the invasive diadematoid Diadema setosum, which utilizes venomous spines, may affect these communities. To describe the mechanical properties of the test and spines of these three species, specimens were collected in winter of 2019 from the sublittoral zone of the Dodecanese island complex, southeastern Aegean Sea. This region serves as a gateway for invasive species to the Mediterranean Sea. Crushing test was conducted on live individuals, while 3-point bending test was used to estimate spine stiffness. Porosity and mineralogy of the test and spine, thickness of the test, and breaking length of the spine were measured and compared, while the microstructural architecture was also determined. The test of S. granularis was the most robust (194.35 ± 59.59 N), while the spines of D. setosum (4.76 ± 2.13 GPa) exhibited highest flexibility. Increased porosity and thickness of the test were related to increased robustness, whereas increased flexibility of the spine was attributed to high porosity, indicating that porosity in the skeleton plays a key role in preventing fracture. The spines of S. granularis exhibited highest length after fracture % (71.54 ± 5.5%). D. setosum exhibited higher values of Mg concentration in the test (10%) compared with the spines (4%). For the first time, the mineralogy of an invasive species is compared with its native counterpart, while a comparison of the mechanical properties of different species of the same ecosystem also takes place. This study highlights different ways, in which sea urchins utilize their skeleton and showcases the ecological significance of these adaptations, one of which is the different ways of utilization of the skeleton for defensive purposes, while the other is the ability of D. setosum to decrease the Mg % of its skeleton degrading its mechanical properties, without compromising its defense, by depending on venomous bearing spines. This enables this species to occupy not only tropical habitats, where it is indigenous, but also temperate like the eastern Mediterranean, which it has recently invaded.

Constructional design of echinoid endoskeleton: main structural components and their potential for biomimetic applications

The endoskeleton of echinoderms (Deuterostomia: Echinodermata) is of mesodermal origin and consists of cells, organic components, as well as an inorganic mineral matrix. The echinoderm skeleton forms a complex lattice-system, which represents a model structure for naturally inspired engineering in terms of construction, mechanical behaviour and functional design. The sea urchin (Echinodermata: Echinoidea) endoskeleton consists of three main structural components: test, dental apparatus and accessory appendages. Although, all parts of the echinoid skeleton consist of the same basic material, their microstructure displays a great potential in meeting several mechanical needs according to a direct and clear structure-function relationship. This versatility has allowed the echinoid skeleton to adapt to different activities such as structural support, defence, feeding, burrowing and cleaning. Although, constrained by energy and resource efficiency, many of the structures found in the echinoid skeleton are optimized in terms of functional performances. Therefore, these structures can be used as role models for bio-inspired solutions in various industrial sectors such as building constructions, robotics, biomedical and material engineering. The present review provides an overview of previous mechanical and biomimetic research on the echinoid endoskeleton, describing the current state of knowledge and providing a reference for future studies.

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. 0.32mm³). 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.