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

Bio-Informed Porous Mineral-Based Composites

Certain biominerals, such as sea sponges and echinoderm skeletons, display a fascinating combination of mechanical properties and adaptability due to the well-defined structures spanning various length scales. These materials often possess high density normalized mechanical properties because they contain well-defined pores. The density-normalized mechanical properties of synthetic minerals are often inferior because the pores are stochastically distributed, resulting in an inhomogeneous stress distribution. The mechanical properties of synthetic materials are limited by the degree of structural and compositional control currently available fabrication methods offer. In the first part of this review, examples of structural elements nature uses to impart exceptional density normalized Young's moduli to its porous biominerals are showcased. The second part highlights recent advancements in the fabrication of bio-informed mineral-based composites possessing pores with diameters that span a wide range of length scales. The influence of the processing of mineral-based composites on their structures and mechanical properties is summarized. Thereby, it is aimed at encouraging further research directed to the sustainable, energy-efficient fabrication of synthetic lightweight yet stiff mineral-based composites.

The ultrastructure of the starfish skeleton is correlated with mechanical stress

Echinoderms and vertebrates both possess mesodermal endoskeletons. In vertebrates, the response to mechanical loads and the capacity to remodel the ultrastructure of the skeletal system are fundamental attributes of their endoskeleton. To determine whether these characteristics are also inherent in Echinoderms, we conducted a comprehensive biomechanical and morphological study on the endoskeleton of Asterias rubens, a representative model organism for Echinoderm skeletons. Our analysis involved high-resolution X-ray CT scans of entire individual ossicles, covering the full stereom distribution along with the attached muscles. Leveraging this data, we conducted finite element analysis to explore the correlation between mechanical loads acting on an ossicle and its corresponding stereom structure. To understand the effects of localized stress concentration, we examined stereom regions subjected to high mechanical stress and compared them to areas with lower mechanical stress. Our results show that the stereom microstructure, both in terms of thickness and orientation, corresponds closely to the mechanical loading experienced by the ossicles. Additionally, by comparing the stereom structures of ossicles in various developmental stages, we assessed the general remodeling capacity of these ossicles. Our findings suggest that the ability to adapt to mechanical loads is a common feature of mesoderm endoskeletons within the Deuterostomia taxonomic group. However, the material remodelling may be a specific trait unique to vertebrate endoskeletons. STATEMENT OF SIGNIFICANCE: This study shows a correlation between the ultrastructure and the mechanical stress in the starfish endoskeleton, suggesting that this fundamental structure-function relationship may be an ancestral feature of not only vertebrate endoskeletons. However, unlike vertebrate skeletons, not all starfish ossicles remodel in response to changing stress, indicating a potential divergence in skeletal adaptation mechanisms. Our methodological approach combines morphometrics and finite element modeling and thus provides a powerful tool to investigate biomechanics in complex skeletal structures.

Numerical Homogenization of Orthotropic Functionally Graded Periodic Cellular Materials: Method Development and Implementation

This study advances the state of the art by computing the macroscopic elastic properties of 2D periodic functionally graded microcellular materials, incorporating both isotropic and orthotropic solid phases, as seen in additively manufactured components. This is achieved through numerical homogenization and several novel MATLAB implementations (known in this study as Cellular_Solid, Homogenize_test, homogenize_ortho, and Homogenize_test_ortho_principal). The developed codes in the current work treat each cell as a material point, compute the corresponding cell elasticity tensor using numerical homogenization, and assign it to that specific point. This is conducted based on the principle of scale separation, which is a fundamental concept in homogenization theory. Then, by deriving a fit function that maps the entire material domain, the homogenized material properties are predicted at any desired point. It is shown that this method is very capable of capturing the effects of orthotropy during the solid phase of the material and that it effectively accounts for the influence of void geometry on the macroscopic anisotropies, since the obtained elasticity tensor has different E1 and E2 values. Also, it is revealed that the complexity of the void patterns and the intensity of the void size changes from one cell to another can significantly affect the overall error in terms of the predicted material properties. As the stochasticity in the void sizes increases, the error also tends to increase, since it becomes more challenging to interpolate the data accurately. Therefore, utilizing advanced computational techniques, such as more sophisticated fitting methods like the Fourier series, and implementing machine learning algorithms can significantly improve the overall accuracy of the results. Furthermore, the developed codes can easily be extended to accommodate the homogenization of composite materials incorporating multiple orthotropic phases. This implementation is limited to periodic void distributions and currently supports circular, rectangular, square, and hexagonal void shapes.

A natural multifunction and multiscale hierarchical matrix as a drug-eluting scaffold for biomedical applications

Sea urchin spines are biogenic single crystals of magnesium calcite that are stiff, strong, damage tolerant and light and have a bicontinuous porous structure. Here, we showed that the removal of their intraskeletal organic matrix materials did not affect the compressive mechanical properties and generated an open porosity. This matrix was able to adsorb and release oxytetracycline, a broad-spectrum antibiotic. The drug-loaded sea urchin matrix induced bacterial cell death after 4 and 8 hours of incubation of both Gram-negative E. coli and Gram-positive S. aureus strains and this process induces an inhibition of bacterial cell adhesion. In conclusion, this study shows that thermally treated sea urchin spines are a compressive resistant and lightweight matrix able to load drugs and with potential use in spine fusion, a challenging application that requires withstanding high compressive loading.

Analysis of the topological motifs of the cellular structure of the tri-spine horseshoe crab (Tachypleus tridentatus) and its associated mechanical properties

Topological motifs in pore architecture can profoundly influence the structural properties of that architecture, such as its mass, porosity, modulus, strength, and surface permeability. Taking the irregular cellular structure of the tri-spine horseshoe crab as a research model, we present a new approach to the quantitative description and analysis of structure-property-function relationships. We employ a robust skeletonization method to construct a curve-skeleton that relies on high-resolution 3D tomographic data. The topological motifs and mechanical properties of the long-range cellular structure were investigated using the Grasshopper plugin and uniaxial compression test to identify the variation gradient. Finite element analysis was conducted for the sub-volumes to obtain the variation in effective modulus along the three principal directions. The results show that the branch length and node distribution density varied from the tip to the base of the sharp corner. These node types formed a low-connectivity network, in which the node types 3-N and 4-N tended to follow the motifs of ideal planar triangle and tetrahedral configurations, respectively, with the highest proportion of inter-branch angles in the angle ranges of 115-120° and 105-110°. In addition, mapping the mechanical gradients to topological properties indicated that narrower profiles with a given branch length gradient, preferred branch orientation, and network connectedness degree are the main factors that affect the mechanical properties. These factors suggest significant potential for designing a controllable, irregularly cellular structure in terms of both morphology and function.

High strength and damage-tolerance in echinoderm stereom as a natural bicontinuous ceramic cellular solid

Due to their low damage tolerance, engineering ceramic foams are often limited to non-structural usages. In this work, we report that stereom, a bioceramic cellular solid (relative density, 0.2-0.4) commonly found in the mineralized skeletal elements of echinoderms (e.g., sea urchin spines), achieves simultaneous high relative strength which approaches the Suquet bound and remarkable energy absorption capability (ca. 17.7 kJ kg-1) through its unique bicontinuous open-cell foam-like microstructure. The high strength is due to the ultra-low stress concentrations within the stereom during loading, resulted from their defect-free cellular morphologies with near-constant surface mean curvatures and negative Gaussian curvatures. Furthermore, the combination of bending-induced microfracture of branches and subsequent local jamming of fractured fragments facilitated by small throat openings in stereom leads to the progressive formation and growth of damage bands with significant microscopic densification of fragments, and consequently, contributes to stereom's exceptionally high damage tolerance.

Lightweight lattice-based skeleton of the sponge Euplectella aspergillum: On the multifunctional design

The glass sponge, Euplectella aspergillum, possesses a lightweight, silica spicule-based, cylindrical lattice-like skeleton, representing an excellent model system for bioinspired lattices. Previous analysis suggested that the E. aspergillum's skeletal lattice exhibits improved buckling resistance and suppressed vortex shedding. How the sponge's skeletal lattice with diagonally-oriented reinforcing bundle of fused spicules and the ridge system behaves under different loading conditions and achieves dual mechanical and fluidic transport performance requires further investigation. Here, we first quantified the structural descriptors such as length and thickness of the bundles of fused spicules and hole opening diameter of the sponge skeletons with and without the soft tissue covered. Secondly, parametric modeling and simulations of the sponge lattice in comparison with other bioinspired designs under different loading conditions were implemented to obtain the structure-mechanical property relationship. Our results reveal that the double-diagonal reinforcements of the E. aspergillum's lattices show i) tendency to maximize the torsional rigidity in comparison to longitudinal and radial modulus and flexural rigidity, and ii) independency of mechanical properties on the diagonal spacing, leaving freedom to control the hole-opening position for the sponge's fluid transport. Furthermore, our coupled fluid-mechanical simulations suggest that the ridge system spiraling the cylindrical lattice simultaneously improves the radial stiffness and fluid permeability. Finally, we discuss the general mechanical strategies and design flexibility in the sponge's skeletal lattice. Our work provides understanding of the mechanical and functional trade-offs in E. aspergillum's skeletal lattice which may shed light on the design of lightweight tubular lattices.

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.

Ordered stereom structure in sea urchin tubercles: High capability for energy dissipation

Tubercles in sea urchin shells serve as a base on the test plates connecting the spine; these undergo compressive or impact stress from the spines. As the volume fraction of the ordered stereom structure in a tubercle increases, the compressive load-displacement curves are gradually characterized by the typical behavior of ceramic foams. Although this ordered stereom structure only exhibits an average porosity of 50.6%, it also exhibits high fracture resistance and energy dissipation capacity. Such remarkable behavior of the ordered stereom structure is attributed to its unique hierarchical microstructure. Specifically, at the macroscale, the stereom structure is periodic. It has uniformly distributed pores that are typically round, which can effectively reduce the stress concentration around the pores, and the ordered arrangement of the trabeculae along the axial direction of the tubercle bears the most compressive stress. The trabeculae present a bottleneck shape with a specific dimension, ensuring the best fracture resistance with a relatively higher porosity. Furthermore, crack deflection in the trabeculae changes the local fracture mode of the mineral, thereby increasing the crack surface area. STATEMENT OF SIGNIFICANCE: The connecting bases of the spines in sea urchin shell, known as tubercle, effectively undergo the compressive stress or impact stress from the spines. An ordered stereom structure is found in the tubercle, and it shows an excellent fracture resistance and energy dissipation capacity. Such a fantastic behavior of the ordered stereom structure mainly takes advantage of its unique hierarchical microstructure. The stereom structure presents a periodic structure on macroscale, the trabeculae show a bottleneck shape with a specific dimension to guarantee the best fracture resistance with a relatively higher porosity, and the soft fillers among CaCO₃ nanoparticles in a trabecula cause consecutive crack deflections.

A damage-tolerant, dual-scale, single-crystalline microlattice in the knobby starfish, Protoreaster nodosus

Cellular solids (e.g., foams and honeycombs) are widely found in natural and engineering systems because of their high mechanical efficiency and tailorable properties. While these materials are often based on polycrystalline or amorphous constituents, here we report an unusual dual-scale, single-crystalline microlattice found in the biomineralized skeleton of the knobby starfish, Protoreaster nodosus. This structure has a diamond-triply periodic minimal surface geometry (lattice constant, approximately 30 micrometers), the [111] direction of which is aligned with the c-axis of the constituent calcite at the atomic scale. This dual-scale crystallographically coaligned microlattice, which exhibits lattice-level structural gradients and dislocations, combined with the atomic-level conchoidal fracture behavior of biogenic calcite, substantially enhances the damage tolerance of this hierarchical biological microlattice, thus providing important insights for designing synthetic architected cellular solids.