Enamel and dentin as multi-scale bio-composites

High throughput automated characterization of enamel microstructure using synchrotron tomography and optical flow imaging

The remarkable damage-tolerance of enamel has been attributed to its hierarchical microstructure and the organized bands of decussated rods. A thorough characterization of the microscale rod evolution within the enamel is needed to elucidate this complex structure. While prior efforts in this area have made use of single particle tracking to track a single rod evolution to various degrees of success, such a process can be both computationally and labor intensive, limited to the evolution path of a single rod, and is therefore prone to error from potentially tracking outliers. Particle image velocimetry (PIV) is a well-established algorithm to derive field information from image sequences for processes that are time-dependent, such as fluid flows and structural deformation. In this work, we demonstrate the use of PIV in extracting the full-field microstructural distribution of rods within the enamel. Enamel samples from a wild African lion were analyzed using high-energy synchrotron X-ray micro-tomography. Results from the PIV analysis provide sufficient full-field information to reconstruct the growth of individual rods that can potentially enable rapid analysis of complex microstructures from high resolution synchrotron datasets. Such information can serve as a template for designing damage-tolerant bioinspired structures for advanced manufacturing. STATEMENT OF SIGNIFICANCE: Thorough characterization and analysis of biological microstructures (viz. dental enamel) allows us to understand the basis of their excellent mechanical properties. Prior efforts have successfully replicated these microstructures via single particle tracking, but the process is computationally and labor intensive. In this work, optical flow imaging algorithms were used to extract full-field microstructural distribution of enamel rods from synchrotron X-ray computed tomography datasets, and a field method was used to reconstruct the growth of individual rods. Such high throughput information allows for the rapid production/prototyping and advanced manufacturing of damage-tolerant bioinspired structures for specific engineering applications. Furthermore, the algorithms used herein are freely available and open source to broaden the availability of the proposed workflow to the general scientific community.

The multi-scale meso-mechanics model of viscoelastic dentin

Human dentin is a hierarchical material with multi-level micro-/nano-structures, consisting of tubule, perti-tubular dentin (PTD) and intertubular dentin (ITD) as the major constituents at microscale; and the PTD and ITD are further composed of collagen and hydroxyapatite (HAp) crystals with different volume fractions at nanoscale. In most cases, the HAp is considered as elastic while the collagen as viscoelastic material. It is of great significance to study the hierarchical structure and viscoelasticity of human dentin to understand the mechanical properties of dentin for further development of restorative materials. Based on this, this paper focuses on multiscale modeling of the elastic properties and dynamic viscoelastic response of dentin and establishes a bottom-up micromechanics model from nano-to macro-scale. In order to study the nanostructural effect on the viscoelastic behavior of hierarchical structures, the homogenization theories of random platelets composites (HTRPC) and the locally-exact homogenization theory (LEHT) are introduced for the homogenization of heterogeneous materials of microstructures at different levels. The HTRPC, based on Eshelby Inclusion theory, is used to predict the effective modulus of PTD and ITD. The LEHT is a method for homogenizing multiphase dentin characterized by repeated unit cells (RUCs). The resulting predictions are in very good agreement with several experimental data from the literature. In addition, the results of nanostructrual effect on dentin show that the viscoelasticity of dentin is majorly contributed by collagen and the HAp greatly provide the strength and hardness of dentin. Furthermore, the ageing effect on dentin's viscoelasticity is considered from the proposed multiscale micromechanics model. It is demonstrated that the ageing effect is much more influential in affecting the loss moduli of dentin than the storage.

Structure-function relationships in dog dentin

Investigations into teeth mechanical properties provide insight into physiological functions and pathological changes. This study sought to 1) quantify the spatial distribution of elastic modulus, hardness and the microstructural features of dog dentin and to 2) investigate quantitative relationships between the mechanical properties and the complex microstructure of dog dentin. Maxillary canine teeth of 10 mature dogs were sectioned in the transverse and vertical planes, then tested using nanoindentation and scanning electron microscopy (SEM). Microstructural features (dentin area fraction and dentinal tubule density) and mechanical properties (elastic modulus and hardness) were quantified. Results demonstrated significant anisotropy and spatial variation in elastic modulus, hardness, dentin area fraction and tubule density. These spatial variations adhered to a consistent distribution pattern; hardness, elastic modulus and dentin area fraction generally decreased from superficial to deep dentin and from crown tip to base; tubule density generally increased from superficial to deep dentin. Poor to moderate correlations between microstructural features and mechanical properties (R² = 0.032-0.466) were determined. The results of this study suggest that the other constituents may contribute to the mechanical behavior of mammalian dentin. Our results also present several remaining opportunities for further investigation into the roles of organic components (e.g., collagen) and mineral content on dentin mechanical behavior.

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.

The role of lateral branches on effective stiffness and local overstresses in dentin

The 3D microstructure of dentinal tissue, the main tissue of the tooth, is the subject of an increasingly comprehensive body of knowledge. The relationship between this microstructure and the mechanical behaviour of dentinal tissue remains, nonetheless, under question. This article proposes an original SEM analysis of dentin microstructure, accounting for lateral branches, and a mechanical model based on these findings. An interesting observation is that lateral branches have a dense collar, as do tubules. The diameter of these branches as well as a percentage area are quantified all along the depth of a dentin sample. We use these unprecedented data to build an orthotropic homogenized model of dentin. The heterogeneities of microstructure are taken into account using level-set functions. The results reveal that the lateral branches slightly influence the global homogenized elastic behavior of the dentin tissue, albeit creating stress concentration areas that are highly influenced by the inclination of the traction with respect to the tubule and branches.

Multiscale micromechanical modeling of the elastic properties of dentin

The paper focuses on multiscale modeling of the elastic properties of dentin. It is modeled as a hierarchical structure consisting of collagen fibers and hydroxyapatite particles at the lower level. Different concentrations of hydroxyapatite in this tissue correspond to peritubular and intertubular dentins. Then, the overall material is modeled as intertubular dentin matrix containing parallel cylindrical holes (the tubules) surrounded by layers of peritubular dentin. At each microstructural level, the model accounts for anisotropy of the constituents. The model predictions are compared with experimental data available in literature.

Structural differences in enamel and dentin in human, bovine, porcine, and ovine teeth

BACKGROUND

The aim was to study differences between crystalline nanostructures from the enamel and dentin of human, bovine, porcine, and ovine species.

METHODS

Dentine and enamel fragments extracted from sound human, bovine, porcine and ovine incisors and molars were mechanically ground up to a final particle size of <100μm. Samples were analyzed using X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), and differential scanning calorimetry (DSC).

RESULTS

Human enamel (HE) and dentin (HD) showed a-axis and c-axis lengths of the carbonate apatite (CAP) crystal lattice nearer to synthetic hydroxyapatite (SHA), which had the smallest size. Enamel crystal sizes were always higher than those of dentin for all species. HE and HD had the largest crystal, followed by bovine samples. Hydroxyapatites (HAs) in enamel had a higher crystallinity index (CI), CI_Rietveld and CI_FTIR, than the corresponding dentin of the same species. HE and HD had the highest CIs, followed by ovine enamel (OE). The changes in heat capacity that were nearest to values in human teeth during the glass transition (ΔCp) were in porcine specimens. There was a significant direct correlation between the size of the a-axis and the substitution by both type A and B carbonates. The size of the nanocrystals and the crystallinity (CI_Rietveld y CI_FTIR) were significantly and negatively correlated with the proteic phase of all the substrates. There was a strongly positive correlation between the caloric capacity, the CIs and the crystal size and a strongly negative correlation between carbonates type A and B and proteins.

CONCLUSIONS

There are differences in the organic and inorganic content of human, bovine, porcine and ovine enamels and dentins which should be taken into account when interpreting the results of studies using animal substrates as substitutes for human material.

The Difference of Structural State and Deformation Behavior between Teenage and Mature Human Dentin

Objective. The cause of considerable elasticity and plasticity of human dentin is discussed in the relationship with its microstructure. Methods. Structural state of teenage and mature human dentin is examined by using XRD and TEM techniques, and their deformation behavior under compression is studied as well. Result. XRD study has shown that crystallographic type of calcium hydroxyapatite in human dentin (calcium hydrogen phosphate hydroxide Ca9HPO4(PO4)5OH; Space Group P63/m (176); a = 9,441 A; c = 6,881 A; c/a = 0,729; Crystallite (Scherrer) 200 A) is the same for these age groups. In both cases, dentin matrix is X-ray amorphous. According to TEM examination, there are amorphous and ultrafine grain phases in teenage and mature dentin. Mature dentin is stronger on about 20% than teenage dentin, while teenage dentin is more elastic on about 20% but is less plastic on about 15% than mature dentin. Conclusion. The amorphous phase is dominant in teenage dentin, whereas the ultrafine grain phase becomes dominant in mature dentin. Mechanical properties of human dentin under compression depend on its structural state, too.

Damage modeling of small-scale experiments on dental enamel with hierarchical microstructure

Dental enamel is a highly anisotropic and heterogeneous material, which exhibits an optimal reliability with respect to the various loads occurring over years. In this work, enamel's microstructure of parallel aligned rods of mineral fibers is modeled and mechanical properties are evaluated in terms of strength and toughness with the help of a multiscale modeling method. The established model is validated by comparing it with the stress-strain curves identified by microcantilever beam experiments extracted from these rods. Moreover, in order to gain further insight in the damage-tolerant behavior of enamel, the size of crystallites below which the structure becomes insensitive to flaws is studied by a microstructural finite element model. The assumption regarding the fiber strength is verified by a numerical study leading to accordance of fiber size and flaw tolerance size, and the debonding strength is estimated by optimizing the failure behavior of the microstructure on the hierarchical level above the individual fibers. Based on these well-grounded properties, the material behavior is predicted well by homogenization of a representative unit cell including damage, taking imperfections (like microcracks in the present case) into account.

Extracellular matrix mineralization in periodontal tissues: Noncollagenous matrix proteins, enzymes, and relationship to hypophosphatasia and X-linked hypophosphatemia

As broadly demonstrated for the formation of a functional skeleton, proper mineralization of periodontal alveolar bone and teeth - where calcium phosphate crystals are deposited and grow within an extracellular matrix - is essential for dental function. Mineralization defects in tooth dentin and cementum of the periodontium invariably lead to a weak (soft or brittle) dentition in which teeth become loose and prone to infection and are lost prematurely. Mineralization of the extremities of periodontal ligament fibers (Sharpey's fibers) where they insert into tooth cementum and alveolar bone is also essential for the function of the tooth-suspensory apparatus in occlusion and mastication. Molecular determinants of mineralization in these tissues include mineral ion concentrations (phosphate and calcium), pyrophosphate, small integrin-binding ligand N-linked glycoproteins and matrix vesicles. Amongst the enzymes important in regulating these mineralization determinants, two are discussed at length here, with clinical examples given, namely tissue-nonspecific alkaline phosphatase and phosphate-regulating gene with homologies to endopeptidases on the X chromosome. Inactivating mutations in these enzymes in humans and in mouse models lead to the soft bones and teeth characteristic of hypophosphatasia and X-linked hypophosphatemia, respectively, where the levels of local and systemic circulating mineralization determinants are perturbed. In X-linked hypophosphatemia, in addition to renal phosphate wasting causing low circulating phosphate levels, phosphorylated mineralization-regulating small integrin-binding ligand N-linked glycoproteins, such as matrix extracellular phosphoglycoprotein and osteopontin, and the phosphorylated peptides proteolytically released from them, such as the acidic serine- and aspartate-rich-motif peptide, may accumulate locally to impair mineralization in this disease.

The emergence of an unusual stiffness profile in hierarchical biological tissues

Biological tissues usually exhibit complex multiscale structural architectures. In many of these, and particularly in mineralized tissues, the basic building block is a staggered array-a composite material made of soft matrix and stiff reinforcing elements. Here we study the stiffness of non-overlapping staggered arrays, a case that has not previously been considered in the literature, and introduce closed-form analytical expressions for its Young's modulus. These expressions are then used to estimate the stiffness of natural staggered biocomposites such as low-mineralized collagen fibril and mineralized tendon. We then consider a two-scale composite scheme for evaluating the modulus of a specific hierarchical structure, the compact bone tissue, which is made of mineralized collagen fibrils with weakly overlapping staggered architecture. It is found that small variations in the staggered structure induce significant differences in the macroscopic stiffness, and, in particular, provide a possible explanation for the as yet unexplained stiffening effects observed in medium-mineralized tissues.

Structural motifs and elastic properties of hierarchical biological tissues - a review

Recent progress made in the field of hierarchical biological materials is reviewed with an emphasis on the staggering characteristics at the smaller structural scale of a number of tissues. We show by means of selected examples that the small-scale architecture, and particularly the degree of staggering and overlap, plays a critical role in the macroscopic elastic behavior of those tissues.

Stiffness of the extrafibrillar phase in staggered biological arrays

A number of important biological tissues such as nacre, tendon, and bone consist of staggered structural arrays as universal motifs. Such arrays usually include stiff fibril-like (or plateletlike, or needlelike) elements embedded in an extrafibrillar (XF) phase. This work discusses the effect of the stiffness of such an XF matrix on the elastic properties of the resulting staggered composite. In the case of most biological composites, this XF stiffness is hardly accessible and very little data are available. We develop an analysis based on previous analytical formulation that results in a relation between the XF modulus and the deformations of the staggered particles. This analysis is then used to back-calculate the yet unmeasured modulus of the XF phase from experimental deformation data, thereby providing a simple alternative to potentially complex direct measurements. This is demonstrated and validated for parallel-fiber bone tissue.