How the tooth got its stripes: patterning via strain-cued motility

Interaction of rod decussation and crack growth in enamel

Enamel possesses ingenious hierarchical structure that gives rise to superior fracture resistance. Despite considerable efforts devoted to characterization of fracture behavior of enamel, the role of rod decussation in fracture of enamel is largely unknown. In this study, the features of rod decussation in the inner enamel are experimentally identified, and analyses of crack growth in enamel are carried out using a micromechanical model of enamel, in which the structural features of the outer enamel and rod decussation of the inner enamel are incorporated. We carry out calculations within a framework based on the extended finite element method, and the crack growth and crack path selection are natural outcomes of imposed loading. We show that crack deflection in enamel is controlled by rod decussation. For crack growth in the parazone, the crack path is oriented along the axis of enamel rods, leading to gross crack deflection. The microstructure of inner enamel with intermediate inclination angle enables multiple crack deflections, giving rise to enhanced toughness. For crack growth in the diazone, the transition in orientation of crack deflection occurs as inclination angle increases. The relatively straight crack path emerges in the case of the microstructure of enamel with intermediate inclination angle, leading to weak fracture resistance. It is further found that compared with the diazone, the gross crack deflection in the parazone provides greater contribution to fracture resistance of enamel. The findings of this study provide a good mechanistic understanding of the role of rod decussation in enamel.

Characteristics of the transverse 2D uniserial arrangement of rows of decussating enamel rods in the inner enamel layer of mouse mandibular incisors

The 2D arrangement of rows of enamel rods with alternating (decussating) tilt angles across the thickness of the inner layer in rat and mouse incisor enamel is well known and assumed to occur in a uniform and repetitive pattern. Some irregularities in the arrangement of rows have been reported, but no detailed investigation of row structure across the entire inner enamel layer currently exists. This investigation was undertaken to determine if the global row pattern in mouse mandibular incisor enamel is predominately regular in nature with only occasional anomalies or if rows of enamel rods have more spatial complexity than previously suspected. The data from this investigation indicate that rows of enamel rods are highly variable in length and have complex transverse arrangements across the width and thickness of the inner enamel layer. The majority of rows are short or medium in length, with 87% having < 100 rods per row. The remaining 13% are long rows (with 100-233 rods per row) that contain 46% of all enamel rods seen in transverse sections. Variable numbers of rows were associated with the lateral, central and mesial regions of the enamel layer. Each region contained different ratios of short, medium and long rows. A variety of relationships was found along the transverse length of rows in each region, including uniform associations of alternating rod tilts between neighboring rows, and instances where two rows having the same rod tilt were paired for variable distances then moved apart to accommodate rows of opposite tilt. Sometimes a row appeared to branch into two rows with the same tilt, or conversely where two rows merged into one row depending upon the mesial-to-lateral direction in which the row was viewed. Some rows showed both pairing and branching/merging along their length. These tended to be among the longest rows identified, and they often crossed the central region with extensions into the lateral and mesial regions. The most frequent row arrangement was a row of petite length nestled at the side of another row having the same rod tilt (30% of all rows). These were termed 'focal stacks' and may relate to the evolution of uniserial rat and mouse incisor enamel from a multilayered ancestor. The mesial and lateral endpoints of rows also showed complex arrangements with the dentinoenamel junction (DEJ), the inner enamel layer itself, and the boundary area to the outer enamel layer. It was concluded that the diversity in row lengths and various spatial arrangements both within and between rows across the transverse plane provides a method to interlock the enamel layer across each region and keep the enamel layer compact relative to the curving DEJ surface. The uniserial pattern for rows in mouse mandibular incisors is not uniform, but diverse and very complex.

Discrete element models of tooth enamel, a complex three-dimensional biological composite

Enamel, the hard surface layer of teeth, is a three-dimensional biological composite made of crisscrossing mineral rods bonded by softer proteins. Structure-property relationships in this complex material have been difficult to capture and usually require computationally expensive models. Here we present more efficient discrete element models (DEM) of tooth enamel that can capture the effects of rod decussation and rod-to-interface stiffness contrast on modulus, hardness, and fracture resistance. Enamel-like microstructures were generated using an idealized biological growth model that captures rod decussation. The orthotropic elastic moduli were modeled with a unit cell, and surface hardness was captured with virtual indentation test. Macroscopic crack growth was also modeled directly through rupture of interfaces and rods in a virtual fracture specimen with an initial notch. We show that the resistance curves increase indefinitely when rod fracture is avoided, with the inelastic region, crack branching, and 3D tortuosity being the main sources of toughness. Increasing the decussation angle simultaneously increases the size of the inelastic region and the crack resistance while decreasing the enamel axial modulus, hardness, and rod stress. In addition, larger contrasts of stiffness between the rods and their interfaces promote high overall stiffness, hardness, and crack resistance. These insights provide better guidelines for reconstructive dental materials, and for development of bioinspired hard materials with unique combinations of mechanical properties. STATEMENT OF SIGNIFICANCE: Enamel is the hardest, most mineralized material in the human body with a complex 3D micro-architecture consisting of crisscrossing mineral rods bonded by softer proteins. Like many hard biological composites, enamel displays an attractive combination of toughness, hardness, and stiffness, owing to its unique microstructure. However few numerical models explore the enamel structure-property relations, as modeling large volumes of this complex microstructure presents computational bottlenecks. In this study, we present a computationally efficient Discrete-element method (DEM) based approach that captures the effect of rod crisscrossing and stiffness mismatch on the enamel hardness, stiffness, and toughness. The models offer new insight into the micromechanics of enamel that could improve design guidelines for reconstructive dental materials and bioinspired composites.

Quantitative analysis of the core 2D arrangement and distribution of enamel rods in cross-sections of mandibular mouse incisors

Considerable descriptive information about the overall organization of mouse mandibular incisor enamel is available but almost nothing is known about the quantitative characteristics of enamel rod arrangement and distribution in these teeth. This has important implications concerning cell movement during the secretory stage because each ameloblast makes one enamel rod. Knowing how many enamel rods are cut open in a cross-section of the enamel layer could provide insights into understanding the dynamics of how groups of ameloblasts form the enamel layer. In this study, cross-sections of fully mineralized enamel were cut on 24 mandibular mouse incisors, polished and etched, and imaged by scanning electron microscopy in backscatter mode. Montaged maps of the entire enamel layer were made at high magnification and the enamel rod profiles in each map were color-coded based upon rod category. Quantitative analyses of each color layer in the maps were then performed using standard routines available in imagej. The data indicated that that there were on average 7233 ± 575 enamel rod profiles per cross-section in mandibular incisors of 7-week-old mice, with 70% located in the inner enamel layer, 27% located in the outer enamel layer, and 3% positioned near the mesial and lateral cementoenamel junctions. All enamel rod profiles showed progressive increases in tilt angles, some very large in magnitude, from the lateral to mesial sides of the enamel layer, whereas only minor variations in tilt angle were found relative to enamel thickness at given locations across the enamel layer. The decussation angle between alternating rows of rod profiles within the inner enamel layer was fairly constant from the lateral to central labial sides of the enamel layer, but it increased dramatically in the mesial region of the enamel layer. The packing density of all rod profiles decreased from lateral to central labial regions of the enamel layer and then in progressing mesially, decreased slightly (inner enamel, mesial tilt), increased slightly (outer enamel layer) or almost doubled in magnitude (inner enamel, lateral tilt). It was concluded that these variations in rod tilt angle and packing densities are adaptations that allow the tooth to maintain a sharp incisal edge and shovel-shape as renewing segments formed by around 7200 ameloblasts are brought onto the occluding surface of the tooth by continuous renewal.

Crystallographic texture and mineral concentration quantification of developing and mature human incisal enamel

For human dental enamel, what is the precise mineralization progression spatially and the precise timing of mineralization? This is an important question in the fundamental understanding of matrix-mediated biomineralization events, but in particular because we can use our understanding of this natural tissue growth in humans to develop biomimetic approaches to repair and replace lost enamel tissue. It is important to understand human tissues in particular since different species have quite distinct spatial and temporal progression of mineralization. In this study, five human central incisors at different stages of enamel maturation/mineralization were spatially mapped using synchrotron X-ray diffraction and X-ray microtomography techniques. From the earliest developmental stage, two crystallite-orientation populations coexist with angular separations between the crystallite populations of approximately 40° varying as a function of position within the tooth crown. In general, one population had significantly lower texture magnitude and contributed a higher percentage to the overall crystalline structure, compared to the other population which contributed only 20-30% but had significantly higher texture magnitude. This quantitative analysis allows us to understand the complex and co-operative structure-function relationship between two populations of crystallites within human enamel. There was an increase in the mineral concentration from the enamel-dentin junction peripherally and from the incisal tip cervically as a function of maturation time. Quantitative backscattered-electron analyses showed that mineralization of prism cores precedes that of prism boundaries. These results provide new insights into the precise understanding of the natural growth of human enamel.

Heterogeneity and Developmental Connections between Cell Types Inhabiting Teeth

Every tissue is composed of multiple cell types that are developmentally, evolutionary and functionally integrated into the unit we call an organ. Teeth, our organs for biting and mastication, are complex and made of many different cell types connected or disconnected in terms of their ontogeny. In general, epithelial and mesenchymal compartments represent the major framework of tooth formation. Thus, they give rise to the two most important matrix–producing populations: ameloblasts generating enamel and odontoblasts producing dentin. However, the real picture is far from this quite simplified view. Diverse pulp cells, the immune system, the vascular system, the innervation and cells organizing the dental follicle all interact, and jointly participate in transforming lifeless matrix into a functional organ that can sense and protect itself. Here we outline the heterogeneity of cell types that inhabit the tooth, and also provide a life history of the major populations. The mouse model system has been indispensable not only for the studies of cell lineages and heterogeneity, but also for the investigation of dental stem cells and tooth patterning during development. Finally, we briefly discuss the evolutionary aspects of cell type diversity and dental tissue integration.

Cells as strain-cued automata

We argue in favor of representing living cells as automata and review demonstrations that autonomous cells can form patterns by responding to local variations in the strain fields that arise from their individual or collective motions. An autonomous cell's response to strain stimuli is assumed to be effected by internally-generated, internally-powered forces, which generally move the cell in directions other than those implied by external energy gradients. Evidence of cells acting as strain-cued automata have been inferred from patterns observed in nature and from experiments conducted in vitro. Simulations that mimic particular cases of pattern forming share the idealization that cells are assumed to pass information among themselves solely via mechanical boundary conditions, i.e., the tractions and displacements present at their membranes. This assumption opens three mechanisms for pattern formation in large cell populations: wavelike behavior, kinematic feedback in cell motility that can lead to sliding and rotational patterns, and directed migration during invasions. Wavelike behavior among ameloblast cells during amelogenesis (the formation of dental enamel) has been inferred from enamel microstructure, while strain waves in populations of epithelial cells have been observed in vitro. One hypothesized kinematic feedback mechanism, "enhanced shear motility", accounts successfully for the spontaneous formation of layered patterns during amelogenesis in the mouse incisor. Directed migration is exemplified by a theory of invader cells that sense and respond to the strains they themselves create in the host population as they invade it: analysis shows that the strain fields contain positional information that could aid the formation of cell network structures, stabilizing the slender geometry of branches and helping govern the frequency of branch bifurcation and branch coalescence (the formation of closed networks). In simulations of pattern formation in homogeneous populations and network formation by invaders, morphological outcomes are governed by the ratio of the rates of two competing time dependent processes, one a migration velocity and the other a relaxation velocity related to the propagation of strain information. Relaxation velocities are approximately constant for different species and organs, whereas cell migration rates vary by three orders of magnitude. We conjecture that developmental processes use rapid cell migration to achieve certain outcomes, and slow migration to achieve others. We infer from analysis of host relaxation during network formation that a transition exists in the mechanical response of a host cell from animate to inanimate behavior when its strain changes at a rate that exceeds 10-4-10-3s-1. The transition has previously been observed in experiments conducted in vitro.