Enamel dictates whole tooth deformation: A finite element model study validated by a metrology method

In order to understand whole tooth behavior under load the biomechanical role of enamel and dentin has to be determined. We approach this question by comparing the deformation pattern and stiffness of intact teeth under load with the deformation pattern and stiffness of the same teeth after the enamel has been mechanically compromised by introducing a defect. FE models of intact human premolars, based on high resolution micro-CT scans, were generated and validated by in vitro electronic speckle pattern interferometry (ESPI) experiments. Once a valid FE model was established, we exploit the flexibility of the FE model to gain more insight into whole tooth function. Results show that the enamel cap is an intrinsically stiff biological structure and its morphology dictates the way a whole tooth will mechanically behave under load. The mechanical properties of the enamel cap were sufficient to mechanically maintain almost its entire stiffness function under load even when a small defect (cavity simulating caries) was introduced into its structure and breached the crown integrity. We conclude that for the most part, that enamel and not dentin dictates the mechanical behavior of the whole tooth.     

Acoustic microscope study of the elastic properties of fluorapatite and hydroxyapatite, tooth enamel and bone.

Measurements of Rayleigh velocity and attenuation were taken in single mineral crystals of hydroxyapatite and fluorapatite at angular intervals relative to their c axes, using an acoustic microscope. These results are compared with the values that were calculated using the elastic constants of apatite from Yoon and Newnham [(1969) Am. Miner. 54, 1193-1197.] and Katz and Ukraincik [(1971) J. Biomechanics 4, 221-227.]. The slowness curves of various wave modes are plotted and discussed in relation to cross-coupling effects that were found to cause instability in measurements of attenuation for the c axes direction. Velocity measurements were taken in specimens of tooth enamel and bone. Here comparisons are made with the values that were calculated by modelling the 'z' scan response of the microscope, using published data for the elastic and acoustic properties. Comparisons are also made with the measurements on single crystals, since apatite is a major component of enamel and bone.     

High resolution transmission electron microscopy of developing enamel in the Australian lungfish, Neoceratodus forsteri (Osteichthyes: Dipnoi)

The permanent tooth plates of the Australian lungfish, Neoceratodus forsteri, are covered by enamel that develops initially in a similar manner to that of other vertebrates. As the enamel layer matures, it acquires several unusual characteristics. It has radially oriented protoprismatic structures with the long axes of the protoprisms perpendicular to the enamel surface. Protoprisms can be defined as aggregations of hydroxyapatite crystals that lack the highly ordered arrangement of the rods of mammalian enamel but are not without a specific structure of their own. The protoprisms are arranged in layers of variable thickness that are deposited sequentially as the tooth plate grows. They may be confined to the separate layers, or may cross the boundary between each layer. Crystals within the protoprisms are long and thin with hydroxyapatite c-axis dimensions of between 30 and 350 nm, and with typical a-b axis dimensions of 5-10 nm. The hydroxyapatite crystals of lungfish enamel have no centre dark lines of octacalcium phosphate, an unusual character among vertebrates. As each crystal develops, arrays of atoms may change direction, and regions exist where dislocations and extra lattice planes are inserted into the long crystal. The resulting hydroxyapatite crystal is not straight, and has a rough surface. The crystals are arranged in tangled structures with their crystallographic c-axes closely aligned with the long axis of the protoprism. Lungfish enamel differs from the enamel of higher vertebrates in that the hydroxyapatite crystals are of different shape, and, in mature enamel, the protoprisms remain as protoprisms and do not develop into the conventional prismatic structures characteristic of mammalian enamel.     

Size dependent elastic modulus and mechanical resilience of dental enamel

Human tooth enamel exhibits a unique microstructure able to sustain repeated mechanical loading during dental function. Although notable advances have been made towards understanding the mechanical characteristics of enamel, challenges remain in the testing and interpretation of its mechanical properties. For example, enamel was often tested under dry conditions, significantly different from its native environment. In addition, constant load, rather than indentation depth, has been used when mapping the mechanical properties of enamel. In this work, tooth specimens are prepared under hydrated conditions and their stiffnesses are measured by depth control across the thickness of enamel. Crystal arrangement is postulated, among other factors, to be responsible for the size dependent indentation modulus of enamel. Supported by a simple structure model, effective crystal orientation angle is calculated and found to facilitate shear sliding in enamel under mechanical contact. In doing so, the stress build-up is eased and structural integrity is maintained.     

Initial enamel crystals are not spatially associated with mineralized dentine

During epithelial-mesenchymal interactions associated with mammalian tooth development, epithelially-derived and mesenchymally-derived extracellular matrix molecules form a discrete dentine-enamel junction. The developmental and molecular processes required to form this junction are not known. To address this problem we designed studies to test the hypothesis that ectodermally-derived epithelial cells synthesize and secrete enamel proteins which function to nucleate and regulate the growth of enamel calcium phosphate crystals. Initial enamel crystals were detected separate from the adiacent dentine. Electron-microprobe analyses revealed that early enamel crystals were octacalciumphosphate or tricalciumphosphate rather than hydroxyapatite. Thereafter, enamel crystals became confluent with the adjacent, albeit significantly smaller hydroxyapatite crystals associated with mineralized dentine. Therefore, we interpret our data to indicate that de novo enamel crystal nucleation and growth are independent from the mineralization processes characterized for dentine. We further argue that gene expression of enamel protein appears to have a constitutive function during early enamel formation and that supramolecular aggregates of amelogenin and enamelin provide the microenvironment for the nucleation and crystal growth of the initial enamel matrix.     

Prismatic dentine in the Australian lungfish, Neoceratodus forsteri (Osteichthyes: Dipnoi)

The Australian lungfish, Neoceratodus forsteri, has a dentition consisting of enamel, mantle dentine and bone, enclosing circumdenteonal, core and interdenteonal dentines. Branching processes from cells that produce interdenteonal dentine leave the cell surface at different angles, with collagen fibrils aligned parallel to the long axis of each process. In the interdenteonal dentine, crystals of calcium hydroxyapatite form within fibrils of collagen, and grow within a matrix of non-collagenous protein. Crystals are aligned parallel to the cell process, as are the original collagen fibrils. Because the processes are angled to the cell surface, the crystals within the core or interdenteonal dentine are arranged in bundles set at angles to each other. Apatite crystals in circumdenteonal dentine are finer and denser than those of the interdenteonal dentine, and form outside the fibrils of collagen. In mature circumdenteonal dentine the crystals of circumdenteonal dentine form a dense tangled mass, linked to interdenteonal dentine by isolated crystals. The functional lungfish tooth plate contains prisms of large apatite crystals in the interdenteonal dentine and masses of fine tangled crystals around each denteon. This confers mechanical strength on a structure with little enamel that is subjected to heavy wear.     

Interaction of amelogenin with hydroxyapatite crystals: An adherence effect through amelogenin molecular self-association

At the secretory stage of tooth enamel formation the majority of the organic matrix is composed of amelogenin proteins that are believed to provide the scaffolding for the initial carbonated hydroxyapatite crystals to grow. The primary objective of this study was to investigate the interaction between amelogenins and growing apatite crystals. Two in vitro strategies were used: first, we examined the influence of amelogenins as compared to two other macromolecules, on the kinetics of seeded growth of apatite crystals; second, using transmission electron micrographs of the crystal powders, based on a particle size distribution study, we evaluated the effect of the macromolecules on the aggregation of growing apatite crystals. Two recombinant amelogenins (rM179, rM166), the synthetic leucine-rich amelogenin polypeptide (LRAP), poly(L -proline), and phosvitin were used. It was shown that the rM179 amelogenin had some inhibitory effect on the kinetics of calcium hydroxyapatite seeded growth. The inhibitory effect, however, was not as destructive as that of other macromolecules tested. The degree of inhibition of the macromolecules was in the order of phosvitin < LRAP < poly(L -proline) < rM179 < rM166. Analysis of particle size distribution of apatite crystal aggregates indicated that the full-length amelogenin protein (rM179) caused aggregation of the growing apatite crystals more effectively than other macromolecules. We propose that during the formation of hydroxyapatite crystal clusters, the growing apatite crystals adhere to each other through the molecular self-association of interacting amelogenin molecules. The biological implications of this adherence effect with respect to enamel biomineralization are discussed. © 1998 John Wiley & Sons, Inc. Biopoly 46: 225–238, 1998     

True enamel covering in teeth of the Australian lungfish Neoceratodus forsteri

Lungfish are a unique order of sarcopterygian fish cleidographically positioned between tetrapods and fish. An uninterrupted 400-million-year-old fossil record has documented lungfish skeletal elements to remain virtually unchanged since the Early Devonian. In the current study we investigated the enamel layer of lungfish teeth in order to determine whether there was evidence for higher vertebrate "true" enamel in the Australian lungfish. Juvenile lungfish from the Brisbane River were processed for light and electron microscopy and analyzed for parameters indicative of true enamel formation. Using anti-amelogenin primary antibodies for immunodetection and Western blots, enamel protein epitopes were detected in developing lungfish teeth. Using transmission electron microscopy and electron diffraction analysis, long and parallel-oriented hydroxyapatite crystals were observed in lungfish outer tooth coverings. Our findings indicate that Australian lungfish teeth are covered by a layer of true enamel. Based on the lungfish fossil record we conclude that features of true enamel formation may be as old as 400 million years. Based on taxonomic classification we confirm that true enamel is found not only in tetrapods but also in the sarcopterygian clade of the Gnathostomata.     

Sequential expression and differential function of multiple enamel proteins during fetal, neonatal, and early postnatal stages of mouse molar organogenesis

We have established the time and position of expression for multiple enamel proteins during the development of the mouse molar tooth organ. Using high-resolution two-dimensional gel electrophoresis coupled with immunoblotting and immunocytochemistry, a 46-kDa enamel protein (pI, 5.5) was detected during late cap stage (18-days gestation, E18d) within differentiation-zone-II inner enamel epithelia associated with an intact basal lamina. At E19d a second enamel polypeptide of 72 kDa (pI, 5.8) was identified at the time and position of initial biomineralization in differentiation zone V. At 20 days, differentiation-zone-VI ameloblasts without basal lamina (late bell stage) expressed 46- and 72-kDa enamel proteins and, in addition, expressed a relatively more basic 26-kDa enamel protein (pI, 6.5-6.7); detected after initial formation of calcium hydroxyapatite crystals. Antibodies raised against chemically synthesized enamel peptides cross-reacted with both the 72-kDa and 26-kDa polypeptides, but did not cross-react with the 46-kDa enamel polypeptide. The sequential expression of multiple enamel proteins suggests several functions: (a) the anionic enamel proteins may provide an instructive template for calcium hydroxyapatite crystal formation; (b) the more neutral proteins possibly serve to regulate size, shape and rates of enamel crystal formation. We suggest that initial expression of enamel gene products during mouse tooth development possibly recapitulates ancestral features of amelogenesis documented in prereptilian vertebrates. These results imply that multiple instructive signals may be responsible for mammalian enamel protein induction and that the sequential expression of a family of enamel proteins reflects the evolutionary acquisition of a more complex genetic program for amelogenesis.     

Regulated fracture in tooth enamel: A nanotechnological strategy from nature

Tooth enamel is a very brittle material; however it has the ability to sustain cracks without suffering catastrophic failure throughout the lifetime of mechanical function. We propose that the nanostructure of enamel can play a significant role in defining its unique mechanical properties. Accordingly we analyzed the nanostructure and chemical composition of a group of teeth, and correlated it with the crack resistance of the same teeth. Here we show how the dimensions of apatite nanocrystals in enamel can affect its resistance to crack propagation. We conclude that the aspect ratio of apatite nanocrystals in enamel determines its resistance to crack propagation. According to this finding, we proposed a new model based on the Hall–Petch theory that accurately predicts crack propagation in enamel. Our new biomechanical model of enamel is the first model that can successfully explain the observed variations in the behavior of crack propagation of tooth enamel among different humans.     

Variation in the prismatic arrangement of dental enamel surfaces

Slightly etched prisms of human dental enamel surfaces were examined in the scanning electron microscope. The crystals in the central region of prisms showed a denser arrangement, similar to the crystals on the periphery, which determine their form here. A crevice-like space could be observed between the central and the peripheral region of a prism. The prisms on the enamel surface showed a wide variety in shape being either of fish-scale or key-hole form, in other places fully irregular. There was no uniform prism on a single tooth, and an interprismatic substance was never found. On the surface of a deciduous tooth a prismless enamel surface was observed consisting of edges of crystallites, which did not unite to prism formation.     

Effect of microstructure upon elastic behaviour of human tooth enamel

Tooth enamel is the stiffest tissue in the human body with a well-organized microstructure. Developmental diseases, such as enamel hypomineralisation, have been reported to cause marked reduction in the elastic modulus of enamel and consequently impair dental function. We produce evidence, using site-specific transmission electron microscopy (TEM), of difference in microstructure between sound and hypomineralised enamel. Built upon that, we develop a mechanical model to explore the relationship of the elastic modulus of the mineral–protein composite structure of enamel with the thickness of protein layers and the direction of mechanical loading. We conclude that when subject to complex mechanical loading conditions, sound enamel exhibits consistently high stiffness, which is essential for dental function. A marked decrease in stiffness of hypomineralised enamel is caused primarily by an increase in the thickness of protein layers between apatite crystals and to a lesser extent by an increase in the effective crystal orientation angle.     

Computational models for wall shear stress estimation in scaffolds: a comparative study of two complete geometries

Fluid mechanical stimuli are known to upregulate cell differentiation and matrix formation. Since wall shear stress plays an important role various studies tried to estimate the scaffold fluid dynamic environment. However, because of the geometrical complexity, nearly all studies created their CFD model based on a submodel of the entire scaffold assuming that the model covers heterogeneity sufficiently. However to the authors' knowledge no study exist providing guidelines in this matter. In a previous study we demonstrated that submodels are influenced by the boundary conditions, inevitable when flow channels are chopped off. For the current study we therefore developed μCT based models of two complete scaffold geometries (one titanium and one hydroxyapatite). Imposing a 0.04 ml/min flow rate resulted in a surface area averaged wall shear stress of 1.41 mPa for titanium and 1.09 mPa for hydroxyapatite. In order to get insight in required model size we subdivided the domain in regions of different size. From our results we propose a model size between 6 and 10 times the average pore size. The wall shears stress should be calculated on a region at least one pore size away from the boundaries. These guidelines could be of use for computationally more costly simulations where it is not possible to simulate the complete scaffold domain.     

Additional criteria for EPR dosimetry using tooth enamel

Currently, EPR measurements are based on the assumption that odontogenesis (the series of events between the bud formation stage until the complete maturation of the tooth) is finished as soon as the tooth erupts. Consequently, it is also assumed that the hydroxyapatite concentration of the enamel (source of free radicals) does not depend on tooth age. However, the present work provides evidence that odontogenesis does not end after tooth eruption but continues for several years after eruption. Fifty-nine molars and pre-molars were analyzed by EPR spectroscopy. Tooth enamel samples were irradiated with different doses of gamma radiation from a 60Co source. The resulting EPR signals were evaluated in terms of posteruption tooth age and tooth position. It was found that, except for wisdom teeth, the concentration of the dosimetric EPR free radicals increased with tooth age after eruption and became constant after a certain period. A mathematical equation was developed to describe this effect as a function of tooth age, tooth position and applied dose. The results suggest that EPR measurements obtained on young teeth should be interpreted carefully unless data are available that would allow one to describe the effect of posteruptive enamel maturation on the EPR estimated dose quantitatively. Little or no correction is needed for older teeth. Since only a limited number of young teeth were available for the present study, further studies are needed to clarify the situation and quantify this effect.     

Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models

Mineralized collagen fibrils have been usually analyzed like a two-phase composite material where crystals are considered as platelets that constitute the reinforcement phase. Different models have been used to describe the elastic behavior of the material. In this work, it is shown that when Halpin–Tsai equations are applied to estimate elastic constants from typical constituent properties, not all crystal dimensions yield a model that satisfy thermodynamic restrictions. We provide the ranges of platelet dimensions that lead to positive definite stiffness matrices. On the other hand, a finite element model of a mineralized collagen fibril unit cell under periodic boundary conditions is analyzed. By applying six canonical load cases, homogenized stiffness matrices are numerically calculated. Results show a monoclinic behavior of the mineralized collagen fibril. In addition, a 5-layer lamellar structure is also considered where crystals rotate in adjacent layers of a lamella. The stiffness matrix of each layer is calculated applying Lekhnitskii transformations, and a new finite element model under periodic boundary conditions is analyzed to calculate the homogenized 3D anisotropic stiffness matrix of a unit cell of lamellar bone. Results are compared with the rule-of-mixtures showing in general good agreement.     

Nanoindentation of lemur enamel: an ecological investigation of mechanical property variations within and between sympatric species

The common morphological metrics of size, shape, and enamel thickness of teeth are believed to reflect the functional requirements of a primate's diet. However, the mechanical and material properties of enamel also contribute to tooth function, yet are rarely studied. Substantial wear and tooth loss previously documented in Lemur catta at the Beza Mahafaly Special Reserve suggests that their dental morphology, structure, and possibly their enamel are not adapted for their current fallback food (the mechanically challenging tamarind fruit). In this study, we investigate the nanomechanical properties, mineralization, and microstructure of the enamel of three sympatric lemur species to provide insight into their dietary functional adaptations. Mechanical properties measured by nanoindentation were compared to measurements of mineral content, prism orientation, prism size, and enamel thickness using electron microscopy. Mechanical properties of all species were similar near the enamel dentin junction and variations correlated with changes in microstructure (e.g., prism size) and mineral content. Severe wear and microcracking within L. catta's enamel were associated with up to a 43% reduction in nanomechanical properties in regions of cracking versus intact enamel. The mechanical and material properties of L. catta's enamel are similar to those of sympatric folivores and suggest that they are not uniquely mechanically adapted to consume the physically challenging tamarind fruit. An understanding of the material and mechanical properties of enamel is required to fully elucidate the functional and ecological adaptations of primate teeth.     

Crystallographical analysis of tooth enamel using milligram samples

An X-ray diffraction microanalytical method, in which sample is loaded onto a silver membrane filter, was applied to assess the crystal content in tooth enamel. Each enamel powder was first examined at room temperature, and then examined again at intervals after heating to 200, 400, 600, 800, and 1000 degrees C. The hydroxyapatite composition weight and crystal weight of the samples were derived from the standard calibration curves. The "crystal content ratio" was defined as the ratio of crystal weight to sample weight. The following results were obtained: (1) beta-tricalcium phosphate (beta-TCP) replaced the hydroxyapatite after heating at the high temperatures; (2) the "crystal content ratio" in the tooth enamel increased with the rise in temperature; and (3) the lattice parameters of the enamel apatite and the beta-TCP were changed by the heating. The X-ray diffraction technique has the potential to analyze the crystal content using milligram samples.     

Analysis of self-assembly and apatite binding properties of amelogenin proteins lacking the hydrophilic C-terminal.

Amelogenins, the major protein component of the mineralizing enamel extracellular matrix, are critical for normal enamel formation as documented in the linkage studies of a group of inherited disorders, with defective enamel formation, called Amelogenesis imperfecta. Recent cases of Amelogenesis imperfecta include mutations that resulted in truncated amelogenin protein lacking the hydrophilic C-terminal amino acids. Current advances in knowledge on amelogenin structure, nanospheres assembly and their effects on crystal growth have supported the hypothesis that amelogenin nanospheres provide the organized microstructure for the initiation and modulated growth of enamel apatite crystals. In order to evaluate the function of the conserved hydrophilic C-terminal telopeptide during enamel biomineralization, the present study was designed to analyze the self-assembly and apatite binding behavior of amelogenin proteins and their isoforms lacking the hydrophilic C-terminal. We applied dynamic light scattering to investigate the size distribution of amelogenin nanospheres formed by a series of native and recombinant proteins. In addition, the apatite binding properties of these amelogenins were examined using commercially available hydroxyapatite crystals. Amelogenins lacking the carboxy-terminal (native P161 and recombinant rM166) formed larger nanospheres than those formed by their full-length precursors: native P173 and recombinant rM179. These data suggest that after removal of the hydrophilic carboxy-terminal segment further association of the nanospheres takes place through hydrophobic interactions. The affinity of amelogenins lacking the carboxy-terminal regions to apatite crystals was significantly lower than their parent amelogenins. These structure-functional analyses suggest that the hydrophilic carboxy-terminal plays critical functional roles in mineralization of enamel and that the lack of this segment causes abnormal mineralization.