High-Throughput Segmentation of Tiled Biological Structures using Random-Walk Distance Transforms

Growth of a Tessellation: Geometric rules for the Development of Stingray Skeletal Patterns

The skeletons of sharks and rays, fashioned from cartilage, and armored by a veneer of mineralized tiles (tesserae) present a mathematical challenge: How can the continuous covering be maintained as the skeleton expands? This study, using microCT and custom visual data analyses of growing stingray skeletons, systematically examines tessellation patterns and morphologies of the many thousand interacting tesserae covering the hyomandibula (a skeletal element critical to feeding), over a two-fold developmental change in hyomandibula length. The number of tesserae remains surprisingly constant, even as the hyomandibula expands isometrically, with all hyomandibulae displaying self-similar distributions of tesserae shapes/sizes. Although the distribution of tesserae geometries largely agrees with the rules for polyhedra tiling of complex surfaces-dominated by hexagons and a minor fraction of pentagons and heptagons, but very few other polygons-the agreement with Euler's classic mathematical laws is not perfect. Contrary to the assumed uniform growth rate (which is shown would create geometric incompatibilities), larger tesserae grow faster to accommodate skeletal expansion. It is hypothesized that this local regulation of global system complexity is driven by tension (from cartilaginous core expansion) in the fibers connecting tesserae, with strain-responsive cells orchestrating local mineral apposition.

Comparative architecture of the tessellated boxfish (Ostracioidea) carapace

Tessellations (surface architectures of arrays of hard tiles) are common in natural and man-made designs. Boxfishes (Ostracioidea) are almost completely encased in a tessellated armor and have evolved a plethora of cross-sectional carapace shapes, yet whether the scutes constructing these exhibit comparable variation is unknown. Using high-resolution microCT and semi-automatic segmentation algorithms, we quantitatively examined thousands of scutes from 13 species of diverse body form. A cluster analysis revealed that certain scute types are associated with specific carapace regions independent of carapace shape. Scute types differentiate between carapace edges and flat regions, as well as between the head region with many carapace openings and the more consistently closed abdominal region, pointing at a constructional commonality or constraint shared by all boxfish species. However, the dimensions of edge scutes varied systematically with carapace shape (e.g., scute aspect ratio tended to increase with decreasing carapace height). This suggests that protection is maintained across body forms by managing scute- and carapace-level mechanisms for increasing bending resistance. Future studies on other taxa are necessary to understand whether these architectural principles are specific evolutionary solutions for building a boxfish carapace or whether they are shared by other biological systems that serve a similar protective function.

High-throughput segmentation, data visualization, and analysis of sea star skeletal networks

The remarkably complex skeletal systems of the sea stars (Echinodermata, Asteroidea), consisting of hundreds to thousands of individual elements (ossicles), have intrigued investigators for more than 150 years. While the general features and structural diversity of isolated asteroid ossicles have been well documented in the literature, the task of mapping the spatial organization of these constituent skeletal elements in a whole-animal context represents an incredibly laborious process, and as such, has remained largely unexplored. To address this unmet need, particularly in the context of understanding structure-function relationships in these complex skeletal systems, we present an integrated approach that combines micro-computed tomography, semi-automated ossicle segmentation, data visualization tools, and the production of additively manufactured tangible models to reveal biologically relevant structural data that can be rapidly analyzed in an intuitive manner. In the present study, we demonstrate this high-throughput workflow by segmenting and analyzing entire skeletal systems of the giant knobby star, Pisaster giganteus, at four different stages of growth. The in-depth analysis, presented herein, provides a fundamental understanding of the three-dimensional skeletal architecture of the sea star body wall, the process of skeletal maturation during growth, and the relationship between skeletal organization and morphological characteristics of individual ossicles. The widespread implementation of this approach for investigating other species, subspecies, and growth series has the potential to fundamentally improve our understanding of asteroid skeletal architecture and biodiversity in relation to mobility, feeding habits, and environmental specialization in this fascinating group of echinoderms.

Untangling the Mechanisms of Lattice Distortions in Biogenic Crystals across Scales

Biomineralized structures are complex functional hierarchical assemblies composed of biomineral building blocks joined together by an organic phase. The formation of individual mineral units is governed by the cellular tissue component that orchestrates the process of biomineral nucleation, growth, and morphogenesis. These processes are imprinted in the structural, compositional, and crystallographic properties of the emerging biominerals on all scales. Measurement of these properties can provide crucial information on the mechanisms that are employed by the organism to form these complex 3D architectures and to unravel principles of their functionality. Nevertheless, so far, this has only been possible at the macroscopic scale, by averaging the properties of the entire composite assembly, or at the mesoscale, by looking at extremely small parts of the entire picture. In this study, the newly developed synchrotron-based dark-field X-ray microscopy method is employed to study the link between 3D crystallographic properties of relatively large calcitic prisms in the shell of the mollusc Pinna nobilis and their local lattice properties with extremely high angular resolution down to 0.001°. Mechanistic links between variations in local lattice parameters and spacing, crystal orientation, chemical composition, and the deposition process of the entire mineral unit are unraveled.

Ontogeny of a tessellated surface: Carapace growth of the longhorn cowfish Lactoria cornuta

Biological armors derive their mechanical integrity in part from their geometric architectures, often involving tessellations: individual structural elements tiled together to form surface shells. The carapace of boxfish, for example, is composed of mineralized polygonal plates, called scutes, arranged in a complex geometric pattern and nearly completely encasing the body. In contrast to artificial armors, the boxfish exoskeleton grows with the fish; the relationship between the tessellation and the gross structure of the armor is therefore critical to sustained protection throughout growth. To clarify whether or how the boxfish tessellation is maintained or altered with age, we quantify architectural aspects of the tessellated carapace of the longhorn cowfish Lactoria cornuta through ontogeny (across nearly an order of magnitude in standard length) and in a high‐throughput fashion, using high‐resolution microCT data and segmentation algorithms to characterize the hundreds of scutes that cover each individual. We show that carapace growth is canalized with little variability across individuals: rather than continually adding scutes to enlarge the carapace surface, the number of scutes is surprisingly constant, with scutes increasing in volume, thickness, and especially width with age. As cowfish and their scutes grow, scutes become comparatively thinner, with the scutes at the edges (weak points in a boxy architecture) being some of the thickest and most reinforced in younger animals and thinning most slowly across ontogeny. In contrast, smaller scutes with more variable curvature were found in the limited areas of more complex topology (e.g., around fin insertions, mouth, and anus). Measurements of Gaussian and mean curvature illustrate that cowfish are essentially tessellated boxes throughout life: predominantly zero curvature surfaces comprised of mostly flat scutes, and with scutes with sharp bends used sparingly to form box edges. Since growth of a curved, tiled surface with a fixed number of tiles would require tile restructuring to accommodate the surface's changing radius of curvature, our results therefore illustrate a previously unappreciated advantage of the odd boxfish morphology: by having predominantly flat surfaces, it is the box‐like body form that in fact permits a relatively straightforward growth system of this tessellated architecture (i.e., where material is added to scute edges). Our characterization of the ontogeny and maintenance of the carapace tessellation provides insights into the potentially conflicting mechanical, geometric, and developmental constraints of this species but also perspectives into natural strategies for constructing mutable tiled architectures.

The carapace of boxfish is composed of mineralized polygonal plates, called scutes, arranged in a complex geometric pattern and nearly completely encasing the body. To clarify whether or how this armor is maintained or altered with age, we quantify architectural aspects of the carapace of the longhorn cowfish Lactoria cornuta through ontogeny, using high‐resolution microCT data and segmentation algorithms to characterize the hundreds of scutes that cover each individual.

The Structure and First-Passage Properties of Generalized Weighted Koch Networks

Characterizing the topology and random walk of a random network is difficult because the connections in the network are uncertain. We propose a class of the generalized weighted Koch network by replacing the triangles in the traditional Koch network with a graph Rs according to probability 0≤p≤1 and assign weight to the network. Then, we determine the range of several indicators that can characterize the topological properties of generalized weighted Koch networks by examining the two models under extreme conditions, p=0 and p=1, including average degree, degree distribution, clustering coefficient, diameter, and average weighted shortest path. In addition, we give a lower bound on the average trapping time (ATT) in the trapping problem of generalized weighted Koch networks and also reveal the linear, super-linear, and sub-linear relationships between ATT and the number of nodes in the network.

Architectural and ultrastructural features of tessellated calcified cartilage in modern and extinct chondrichthyan fishes

Tessellated calcified cartilage (TCC) is a distinctive kind of biomineralized perichondral tissue found in many modern and extinct chondrichthyans (sharks, rays, chimaeroids and their extinct allies). Customarily, this feature has been treated somewhat superficially in phylogenetic analyses, often as a single "defining" character of a chondrichthyan clade. TCC is actually a complex hard tissue with numerous distinctive attributes, but its use as a character complex for phylogenetic analysis has not yet been optimized. This study attempts to improve this situation by presenting new terminology for certain aspects of tesseral architecture, including single-monolayered, multiple-monolayered, polylayered and voussoir tesserae; new histological data, including thin sections of TCC in several Palaeozoic taxa, and new proposals for ways in which various characters and states (many of which are defined here for the first time) could be applied in future phylogenetic analyses of chondrichthyan fishes. It can be concluded that many, but not all, of the unique attributes of modern TCC evolved by the Early Devonian (ca. 400 before present (bp)). The globular calcified cartilage reported in Silurian sinacanthids and the so-called subtessellated perichondral biomineralization (with irregular and ill-defined geometries of a layer or layers of calcified cartilage blocks) of certain extinct "acanthodians" (e.g., Climatius, Ischnacanthus, Cheiracanthus) could represent evolutionary precursors of TCC, which seems to characterize only part of the chondrichthyan total group. It is hypothesized that heavily biomineralized "layer-cake" TCC in certain Palaeozoic chondrichthyans perhaps served a dual physiological role, as a phosphate sink and in providing increased skeletal density in very large (>7 m) Devonian-Permian marine sharks such as ctenacanths and as an adaptation to calcium-deficient environments among Permo-Carboniferous non-marine sharks such as xenacanths. By contrast, the equivalent tissue in modern elasmobranchs probably serves only to reinforce regions of cartilage (mostly in the jaws) subjected to high loading. It is also noted that much of the variation observed in tesseral architecture (including localized remodelling), ultrastructure and histology in modern and extinct chondrichthyans is confined to the perichondrally facing cap zone (where Type-1 collagen matrix predominates in modern TCC), whereas the main body of the tessera (where Type-2 collagen matrix predominates) exhibits comparatively little evidence of remodelling and histological or structural variation.

The multiscale architecture of tessellated cartilage and its relation to function

When describing the architecture and ultrastructure of animal skeletons, introductory biology, anatomy and histology textbooks typically focus on the few bone and cartilage types prevalent in humans. In reality, cartilage and bone are far more diverse in the animal kingdom, particularly within fishes (Chondrichthyes and Actinopterygii), where cartilage and bone types are characterized by features that are anomalous or even pathological in human skeletons. This review discusses the curious and complex architectures of shark and ray tessellated cartilage, highlighting similarities and differences with their mammalian skeletal tissue counterparts. By synthesizing older anatomical literature with recent high-resolution structural and materials characterization work, this review frames emerging pictures of form-function relationships in this tissue and of the evolution and true diversity of cartilage and bone.

Scattering and phase-contrast X-ray methods reveal damage to glass fibers in endodontic posts following dental bur trimming

OBJECTIVES

There is concern that the integrity of fiberglass dental posts may be affected by chairside trimming during treatment. We hypothesize that hard X-ray methods of phase contrast-enhanced micro-CT (PCE-CT) and synchrotron based X-ray refraction (SXRR) can reliably identify and help characterize the extent of damage.

METHODS

Fiberglass posts were imaged both as manufactured and following trimming with a diamond bur. Each of the posts was imaged by SXRR and by PCE-CT. Datasets from PCE-CT were used to visualize and quantify 2D and 3D morphological characteristics of intact and of damage-affected regions caused by trimming.

RESULTS

The SXRR images revealed fiber inhomogeneities from manufacturing with a significant increase in internal surfaces in sample regions corresponding to damage from trimming. PCE-CT volumes unveiled the micromorphology of single fibers in the posts and some damage in the trimmed area (e.g. fractures, splinters and cracks). Area, perimeter, circularity, roundness, volume and thickness of the glass fibers in the trimmed area were statistically different from the control (p < 0.01).

SIGNIFICANCE

The integrity of single fibers in the post is critical for bending resistance and for long-term adhesion to the cement in the root canals. Damage to the fibers causes substantial structural weakening across the post diameter. Glass fragments produced due to contact with the dental bur may separate from the post and may significantly reduce bond capacity. The above mentioned synchrotron-based imaging techniques can further facilitate assessment of the structural integrity and the appearance of defects in posts (e.g. after mechanical load).

Endoskeletal mineralization in chimaera and a comparative guide to tessellated cartilage in chondrichthyan fishes (sharks, rays and chimaera)

An accepted uniting character of modern cartilaginous fishes (sharks, rays, chimaera) is the presence of a mineralized, skeletal crust, tiled by numerous minute plates called tesserae. Tesserae have, however, never been demonstrated in modern chimaera and it is debated whether the skeleton mineralizes at all. We show for the first time that tessellated cartilage was not lost in chimaera, as has been previously postulated, and is in many ways similar to that of sharks and rays. Tesserae in Chimaera monstrosa are less regular in shape and size in comparison to the general scheme of polygonal tesserae in sharks and rays, yet share several features with them. For example, Chimaera tesserae, like those of elasmobranchs, possess both intertesseral joints (unmineralized regions, where fibrous tissue links adjacent tesserae) and recurring patterns of local mineral density variation (e.g. Liesegang lines, hypermineralized ‘spokes’), reflecting periodic accretion of mineral at tesseral edges as tesserae grow. Chimaera monstrosa's tesserae, however, appear to lack the internal cell networks that characterize tesserae in elasmobranchs, indicating fundamental differences among chondrichthyan groups in how calcification is controlled. By compiling and comparing recent ultrastructure data on tesserae, we also provide a synthesized, up-to-date and comparative glossary on tessellated cartilage, as well as a perspective on the current state of research into the topic, offering benchmark context for future research into modern and extinct vertebrate skeletal tissues.

Image analysis pipeline for segmentation of a biological porosity network, the lacuno-canalicular system in stingray tesserae

A prerequisite for many analysis tasks in modern comparative biology is the segmentation of 3-dimensional (3D) images of the specimens being investigated (e.g. from microCT data). Depending on the specific imaging technique that was used to acquire the images and on the image resolution, different segmentation tools are required. While some standard tools exist that can often be applied for specific subtasks, building whole processing pipelines solely from standard tools is often difficult. Some tasks may even necessitate the implementation of manual interaction tools to achieve a quality that is sufficient for subsequent analysis. In this work, we present a pipeline of segmentation tools that can be used for the semiautomatic segmentation and quantitative analysis of voids in tissue (i.e. internal structural porosity). We use this pipeline to analyze lacuno-canalicular networks in stingray tesserae from 3D images acquired with synchrotron microCT.•

The first step of this pipeline, the segmentation of the tesserae, was performed using standard marker-based watershed segmentation.

•

The efficient processing of the next two steps, that is, the segmentation of all lacunae spaces belonging to a specific tessera and the separation of these spaces into individual lacunae required recently developed, novel tools.

•

For error correction, we developed an interactive method that allowed us to quickly split lacunae that were accidentally merged, and to merge lacunae that were wrongly split.

•

Finally, the tesserae and their corresponding lacunae were subdivided into structural wedges (i.e. specific anatomical regions) using a semi-manual approach.

With this processing pipeline, analysis of a variety of interconnected structural networks (e.g. vascular or lacuno-canalicular networks) can be achieved in a comparatively high-throughput fashion. In our study system, we were able to efficiently segment more than 12,000 lacunae in high-resolution scans of nine tesserae, providing a robust data set for statistical analysis.

Mechanical properties of stingray tesserae: High-resolution correlative analysis of mineral density and indentation moduli in tessellated cartilage

Skeletal tissues are built and shaped through complex, interacting active and passive processes. These spatial and temporal variabilities make interpreting growth mechanisms from morphology difficult, particularly in bone, where the remodeling process erases and rewrites local structural records of growth throughout life. In contrast to the majority of bony vertebrates, the elasmobranch fishes (sharks, rays, and their relatives) have skeletons made of cartilage, reinforced by an outer layer of mineralized tiles (tesserae), which are believed to grow only by deposition, without remodeling. We exploit this structural permanence, performing the first fine-scale correlation of structure and material properties in an elasmobranch skeleton. Our characterization across an age series of stingray tesserae allows unique insight into the growth processes and mechanical influences shaping the skeleton. Correlated quantitative backscattered electron imaging (qBEI) and nanoindentation measurements show a positive relationship between mineral density and tissue stiffness/hardness. Although tessellated cartilage as a whole (tesserae plus unmineralized cartilage) is considerably less dense than bone, we demonstrate that tesserae have exceptional local material properties, exceeding those of (mammal) bone and calcified cartilage. We show that the finescale ultrastructures recently described in tesserae have characteristic material properties suggesting distinct mechanical roles and that regions of high mineral density/stiffness in tesserae are confined predominantly to regions expected to bear high loads. In particular, tesseral spokes (laminated structures flanking joints) exhibit particularly high mineral densities and tissue material properties, more akin to teeth than bone or calcified cartilage. We conclude that these spokes toughen tesserae and reinforce points of contact between them. These toughening and reinforcing functions are supported by finite element simulations incorporating our material data. The high stresses predicted for spokes, and evidence we provide that new spoke laminae are deposited according to their local mechanical environment, suggest tessellated cartilage is both mutable and responsive, despite lacking remodeling capability. STATEMENT OF SIGNIFICANCE: The study of vertebrate skeletal materials is heavily biased toward mammal bone, despite evidence that bone and cartilage are extremely diverse. We broaden the perspective on vertebrate skeleton materials and evolution in an investigation of stingray tessellated cartilage, a curious type of unmineralized cartilage with a shell of mineralized tiles (tesserae). Combining high-resolution imaging and material testing, we demonstrate that tesserae have impressive local material properties for a vertebrate skeletal tissue, arguing for unique tissue organization relative to mammalian calcified cartilage and bone. Incorporating our materials data into mechanical models, we show that finescale material arrangements allow this cartilage to act as a functional and responsive alternative to bone, despite lacking bone's ability to remodel. These results are relevant to a diversity of researchers, from skeletal, developmental, and evolutionary biologists, to materials scientists interested in high-performance, low-density composites.

Adaptation and Evolution of Biological Materials

Research into biological materials often centers on the impressive material properties produced in Nature. In the process, however, this research often neglects the ecologies of the materials, the organismal contexts relating to how a biological material is actually used. In biology, materials are vital to organismal interactions with their environment and their physiology, and also provide records of their phylogenetic relationships and the selective pressures that drive biological novelties. With the papers in this symposium, we provide a view on cutting-edge work in biological materials science. The collected research delivers new perspectives on fundamental materials concepts, offering surprising insights into biological innovations and challenging the boundaries of materials’ characterization techniques. The topics, systems, and disciplines covered offer a glimpse into the wide range of contemporary biological materials work. They also demonstrate the need for progressive “whole organism thinking” when characterizing biological materials, and the importance of framing biological materials research in relevant, biological contexts.