Quantitative 3D structural analysis of the cellular microstructure of sea urchin spines (I): Methodology.

The mineralized skeletons of echinoderms are characterized by their complex, open-cell porous microstructure (also known as stereom), which exhibits vast variations in pore sizes, branch morphology, and three-dimensional (3D) organization patterns among different species. Quantitative description and analysis of these cellular structures in 3D are needed in order to understand their mechanical properties and underlying design strategies. In this paper series, we present a framework for analyzing such structures based on high-resolution 3D tomography data and utilize this framework to investigate the structural designs of stereom by using the spines from the sea urchin Heterocentrotus mamillatus as a model system. The first paper here reports the proposed cellular network analysis framework, which consists of five major steps: synchrotron-based tomography and hierarchical convolutional neural network-based reconstruction, machine learning-based segmentation, cellular network registration, feature extraction, and data representation and analysis. This framework enables the characterization of the porous stereom structures at the individual node and branch level (10 µm), the local cellular level (100 µm), and the global network level (~1 mm). We define and quantify multiple structural descriptors at each level, such as node connectivity, branch length and orientation, branch profile, ring structure, etc., which allows us to investigate the cellular network construction of H. mamillatus spines quantitatively. The methodology reported here could be tailored to analyze other natural or engineering open-cell porous materials for a comprehensive multiscale network representation and mechanical analysis. STATEMENT OF SIGNIFICANCE: The mechanical robustness of the biomineralized porous structures in sea urchin spines has long been recognized. However, quantitative cellular network representation and analysis of this class of natural cellular solids are still limited in the literature. This constrains our capability to fully understand the mechanical properties and design strategies in sea urchin spines and other similar echinoderms' porous skeletal structures. Combining high-resolution tomography and computer vision-based analysis, this work presents a multiscale 3D network analysis framework, which allows for extraction, registration, and quantification of sea urchin spines' complex porous structure from the individual branch and node level to the global network level. This 3D structural analysis is relevant to a diversity of research fields, such as biomineralization, skeletal biology, biomimetics, material science, etc.