Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone

The anisotropic elastic constants of human cortical bone were predicted using a specimen-specific micromechanical model that accounted for structural parameters across multiple length scales. At the nano-scale, the elastic constants of the mineralized collagen fibril were estimated from measured volume fractions of the constituent phases, namely apatite crystals and Type I collagen. The elastic constants of the extracellular matrix (ECM) were predicted using the measured orientation distribution function (ODF) for the apatite crystals to average the contribution of misoriented mineralized collagen fibrils. Finally, the elastic constants of cortical bone tissue were determined by accounting for the measured volume fraction of Haversian porosity within the ECM. Model predictions using the measured apatite crystal ODF were not statistically different from experimental measurements for both the magnitude and anisotropy of elastic constants. In contrast, model predictions using common idealized assumptions of perfectly aligned or randomly oriented apatite crystals were significantly different from the experimental measurements. A sensitivity analysis indicated that the apatite crystal volume fraction and ODF were the most influential structural parameters affecting model predictions of the magnitude and anisotropy, respectively, of elastic constants.     

Theoretical detection of a dark contrast line in twinned apatite bicrystals and its possible correlation with the chemical properties of human dentin and enamel crystals.

Electron microscope images of twinned apatite bicrystals oriented along the [1120] crystallographic direction have been simulated for various experimental conditions, and the validity of the calculation has been checked. These images show a dark contrast line similar to the one observed experimentally in enamel and dentin crystals and therefore strongly suggest the presence of a twin plane parallel to the (1100) crystallographic planes, in these crystals. The presence of a twin boundary in teeth and bone crystals is of prime importance for the adsorption and the dissolution properties of the calcified tissues as a whole.     

High-resolution electron microscope and computed images of human tooth enamel crystals

The structure of human enamel crystallites has been studied at a near atomic level by high-resolution electron microscopy. Electron micrographs have been obtained from crystallites present in human enamel with a structure resolution of 0.2 nm in the [0001], [1210], [1213], [1100] and [4510] zone axes directions. In most cases it was possible to match the experimental images with images calculated using the atomic positions of mineral hydroxyapatite. However, in some cases a discrepancy between calculated and experimental image detail was observed in the c direction of the [1210] and the [1100] images. This shows: (i) a structural heterogeneity of the crystals, and (ii) a loss of hexagonal symmetry of the structure. The resolution required to distinguish individual atomic sites in the different zones has been determined, and this will provide a useful basis for future work. As the determination of the "real structure" of biological crystals is of prime importance for the study of calcification mechanisms (crystal growth), biological properties and destructive phenomena of calcified tissues (i.e., dental caries and bone resorption).     

Stress distribution in the scapula studied by neutron diffraction.

High intensity neutron beams provide a method of measuring the preferred orientation of apatite crystals in bulk samples of bone. Measurements at seven different sites on the scapula show that the c axes of the crystals lie preferentially along the directions of pull of the attached muscles. The highest orientation is found at positions under the influence of only a single group of muscles, such as M. teres major or M. infraspinatus. In intermediate regions a multiple distribution of crystals is found, able to withstand stresses in more than one direction. The technique provides a method of assessing the distribution of stress in bones.     

Linear measurements of cortical bone and dental enamel by computed tomography: Applications and problems

This paper explores the potential of high-resolution computed tomography (CT) as a morphometric tool in paleoanthropology. The accuracy of linear measurements of enamel thickness and cortical bone thickness taken from CT scans is evaluated by making comparison with measurements taken directly from physical sections. The measurements of cortical bone are taken on extant and fossil specimens with and without attached matrix, and the dental specimens studied include a sample of 12 extant human molars. Local CT numbers (representing X-ray, attenuation) are used to determine the exact position of the boundaries of a structure. Using this technique most studied dimensions, including four of human molar enamel thickness, could be obtained from CT scans with a maximum error range of ±0.1 mm. The limitations of the method are discussed with special reference to problems associated with highly mineralized fossils. © 1993 Wiley-Liss, Inc.     

Amelogenesis: Transformation of a protein-mineral matrix into tooth enamel

During enamel formation, the organic enamel protein matrix interacts with calcium phosphate minerals to form elongated, parallel, and bundled enamel apatite crystals of extraordinary hardness and biomechanical resilience. The enamel protein matrix consists of unique enamel proteins such as amelogenin, ameloblastin, and enamelin, which are secreted by highly specialized cells called ameloblasts. The ameloblasts also facilitate calcium and phosphate ion transport toward the enamel layer. Within ameloblasts, enamel proteins are transported as a polygonal matrix with 5 nm subunits in secretory vesicles. Upon expulsion from the ameloblasts, the enamel protein matrix is re-organized into 20 nm subunit compartments. Enamel matrix subunit compartment assembly and expansion coincide with C-terminal cleavage by the MMP20 enamel protease and N-terminal amelogenin self-assembly. Upon enamel crystal precipitation, the enamel protein phase is reconfigured to surround the elongating enamel crystals and facilitate their elongation in C-axis direction. At this stage of development, and upon further amelogenin cleavage, central and polyproline-rich fragments of the amelogenin molecule associate with the growing mineral crystals through a process termed “shedding”, while hexagonal apatite crystals fuse in longitudinal direction. Enamel protein sheath-coated enamel “dahlite” crystals continue to elongate until a dense bundle of parallel apatite crystals is formed, while the enamel matrix is continuously degraded by proteolytic enzymes. Together, these insights portrait enamel mineral nucleation and growth as a complex and dynamic set of interactions between enamel proteins and mineral ions that facilitate regularly seeded apatite growth and parallel enamel crystal elongation.     

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.     

CRYSTAL GROWTH IN RAT ENAMEL

Observations have been made, using electron microscopy and x-ray diffraction, on the changes in crystal size and shape which occur in developing rodent enamel during mineralization. Small enamel pieces isolated from ground sections of rat molars and incisors were either embedded in methacrylate and sectioned with a diamond knife for electron microscopy, or they were mounted intact on glass fibers in a Debye-Sherrer type powder camera for x-ray diffraction. By either approach it was found that the apatite crystals were very long in the c axis direction from the beginning of enamel mineralization. Morphologically, the early crystals took the shape of extremely thin, long plates arranged in such a manner that there seemed to be little room for any further length-wise growth. It was demonstrated clearly, on the other hand, that the crystals increased in both thickness and width with advancing mineralization. As a result, the thin crystal plates gradually developed into hexagonal rods, which in the most mature enamel examined measured 500 to 600 A in width and 250 to 300 A in thickness.     

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.     

Modeling of bone at a single lamella level

This paper focuses on the ultrastructure of bone at a single lamella level. At this scale, collagen fibrils reinforced with apatite crystals are aligned preferentially to form a lamella. At the next structural level, such lamella are stacked in different orientations to form either osteons in cortical bone or trabecular pockets in trabecular bone. We use a finite element model, which treats small strain elasticity of a spatially random network of collagen fibrils, and compute anisotropic effective stiffness tensors and deformations of such a single lamella as a function of fibril volume fractions (or porosities), prescribed microgeometries, and fibril geometric and elastic properties.     

High-resolution electron-microscopic study of the relationship between human enamel and dentin crystals at the dentinoenamel junction

The development of dentin and of enamel share a common starting locus: the dentinoenamel junction (DEJ). In this study the relationship between enamel and dentin crystals has been investigated in order to highlight the guiding or modulating role of the previously mineralized dentin layer during enamel formation. Observations were made with a high-resolution electron microscope and, after digitalization, image-analysis software was used to obtain digital diffractograms of individual crystals. In general no direct epitaxial growth of enamel crystals onto dentin crystals could be demonstrated. The absence of direct contact between the two kinds of crystals and the presence of amorphous areas within enamel particles at the junction with dentin crystals were always noted. Only in a few cases was the relationship between enamel and dentin crystals observed, which suggested a preorganization of the enamel matrix influenced by the dentin surface structure. This could be explained either by the existence of a proteinaceous continuum between enamel and dentin or by the orientation of enamel proteins by dentin crystals.     

THE STRUCTURE AND ORGANIZATION OF, AND THE RELATIONSHIP BETWEEN THE ORGANIC MATRIX AND THE INORGANIC CRYSTALS OF EMBRYONIC BOVINE ENAMEL

Electron microscope and electron diffraction studies of developing embryonic bovine enamel have revealed the organization of the organic matrix and the inorganic crystals. The most recently deposited inorganic crystals located at the ameloblast-enamel junction are thin plates, approximately 1300 A long, 400 A wide, and 19 A thick. During maturation of the enamel, crystal growth occurs primarily by an increase in crystal thickness. Statistical analyses failed to show a significant change in either the width or the length of the crystals during the period of maturation studied. Even in the earliest stages of calcification, the crystals are organized within the prisms so that their long axes (c-axes) are oriented parallel to the long axes of the prisms but randomly distributed about their long axes. With maturation of the enamel, the crystals become more densely packed and more highly oriented within the prisms. The organic matrix in decalcified sections of enamel is strikingly similar in its over-all organization to that of the fully mineralized tissue. When viewed in longitudinal prism profiles, the intraprismatic organic matrix is composed of relatively thin dense lines, approximately 48 A wide, which are relatively parallel to each other and have their fiber axes parallel to the long axes of the prisms within which they are located. Many of these dense lines, which have the appearance of thin filaments, are organized into doublets, the individual 48 A wide filaments of the doublets being separated by approximately 120 A. When observed in oblique prism profiles, the intraprismatic organic matrix is likewise remarkably similar in general orientation and organization to that of the fully mineralized tissue. Moreover, the spaces between adjacent doublets or between single filaments have the appearance of compartments. These compartments, more clearly visualized in cross- or near cross-sectional prism profiles, are oval or near oval in shape. Therefore, the appearance of the intraprismatic organic matrix (in longitudinal, oblique, and cross-sectional prism profiles) indicates that it is organized into tubular sheaths which are oriented with their long axes parallel to the long axes of the prisms in which they are located, but randomly oriented about their own long axes, an orientation again remarkably "blue printing" that of the inorganic crystals. The predominant feature of the walls of the tubular sheaths, when viewed in cross- or near cross-section, is that of continuous sheets, although in many cases closely packed dot-like structures of approximately 48 A were also observed, suggesting that the wall of the sheaths consists of a series of closely packed filaments. The 48 A wide dense lines (filaments) representing the width of the sheath wall were resolved into two dense strands when viewed in longitudinal prism profiles. Each strand was 12 A wide and was separated by a less electron-dense space 17 A wide. The intraprismatic organic matrix is surrounded by a prism sheath which corresponds in mineralized sections to the electron-lucent uncalcified regions separating adjacent prisms. Structurally, the prism sheaths appear to consist of filaments arranged in basket-weave fashion.     

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     

On the nature of the opaque and translucent enamel regions of some macropodinae (Macropus giganteus,Wallabia bicolor and Peradorcas concinna)

Summary Teeth of three macropod species, M. giganteus, W. bicolor and P. concinna, have been studied using the techniques of light microscopy, scanning- and transmission-electron microscopy and hardness measurement. Light microscope observations showed that the teeth of these species had a translucent enamel region close to the dentine and an outer opaque enamel region at the tooth's surface. These regions were not related to the presence or absence of tubules which are a characteristic feature of marsupial enamel. Hardness tests showed that the opaque enamel was softer than the translucent enamel. Scanning electron microscope observations revealed that there was no correlation between any particular prism packing or orientation and the opaque and translucent enamel regions. Transmission electron microscope observations showed that the translucent enamel region consisted of well defined prisms and well packed, lath-like crystals, whereas the opaque enamel was disrupted by voids (which ranged in size from enlarged micropores to about 2 m in diameter in extreme cases) between crystals and some randomly oriented, loosely packed crystals. This disruption within the opaque enamel region was more common at prism boundaries but pockets of disrupted enamel were also found within prisms and interprismatic regions. The opacity of the enamel was caused by scattering of light from the voids. The ultrastructure of the opaque enamel region indicated that this region was hypomineralized; hardness tests and polarized light microscope observations were consistent with these results.     

Comparative Properties of Deciduous and Permanent (Young and Old) Human Enamel1

Some physico-chemical properties of the enamel of deciduous and permanent (young and old) teeth were investigated and compared using x-ray diffraction, infrared absorption spectroscopy, scanning electron microscopy and chemical analyses. Results demonstrated the following: all enamel samples gave x-ray diffraction patterns of only apatite; all enamel samples gave IR absorption spectra of carbonate-containing apatite; the α-axis of deciduous enamel apatite was larger than that of permanent (both young and old) enamel apatite (mean values, deciduous = 9.458 ± 0.003A; permanent =9 443 ± 0.003A); apatite crystallite dimensions increased with age especially along the c-axis; when compared to permanent, deciduous enamel contained slightly more carbonate, magnesium and HPO₄^2-; the prism (enamel rods) dimensions were slightly smaller, and the extent of acid-etching was more extensive in deciduous enamel than in permanent enamel. These observations combined with other factors such as the difference in the orientation of and crystal density in prism rods and the difference in conditions of the oral environment between deciduous and permanent enamel may account for the reported observations of a decrease in caries prevalance with age.     

Dependence of ultrasonic attenuation on bone mass and microstructure in bovine cortical bone

The development of the axial transmission technique now enables in vivo evaluation of cortical bone quality, which plays an important role in bone fragility. Cortical bone is a complex multiscale material, which may be made of different types of microstructure. The interaction between ultrasound and cortical bone remains unclear and most studies have been confined to wave speed analysis. The first aim of this study is to investigate the dependence of the frequency-dependent attenuation on the type of bone microstructure. The second goal is to determine whether broadband ultrasonic attenuation (BUA) is related to volumetric bone mineral density (vBMD) and mass density. Parallelepipedic samples of bovine cortical bone were cut from three specimens and tested in the axial, radial and tangential directions using an ultrasonic transmission device. BUA was evaluated over a 1-MHz wide bandwidth around 4MHz. In addition, the microstructure of each sample was determined using an optical microscope. BUA values measured in porotic microstructure are significantly higher than in Haversian microstructure. The lowest BUA values are obtained for plexiform microstructure. For all structures, BUA in the axial direction is significantly smaller than in the radial and tangential directions. Moreover, BUA is correlated with both vBMD and density (determination coefficient (R2) equal to 0.44 and 0.65, respectively, in the axial direction). BUA variations can be explained by scattering and viscoelastic mechanisms. This study suggests that BUA measurements have the potential to discriminate among different cortical bone microstructures in addition to providing material properties.     

Assessment of composition and anisotropic elastic properties of secondary osteon lamellae

Measurement of the elastic properties of single osteon lamellae is still one of the most demanding tasks in bone mechanics to be solved. By means of site-matched Raman microspectroscopy, acoustic microscopy and nanoindentation the structure, chemical composition and anisotropic elasticity of individual lamellae in secondary osteons were investigated. Acoustic impedance images (911-MHz) and two-dimensional Raman spectra were acquired in sections of human femoral bone. The samples were prepared with orientations at various observation angles theta relative to the femoral long axis. Nanoindentations provided local estimations of the elastic modulus and landmarks necessary for spatial fusion of the acoustic and spectral Raman images. Phosphate nu(1) (961 cm(-1)) and amide I (1665 cm(-1)) band images representing spatial distributions of mineral and collagen were fused with the acoustic images. Acoustic impedance was correlated with the indentation elastic modulus E(IT) (R(2)=0.61). Both parameters are sensitive to elastic tissue anisotropy. The lowest values were obtained in the direction perpendicular to the femoral long axis. Acoustic images exhibit a characteristic bimodal lamellar pattern of alternating high and low impedance values. Since this undulation was not associated with a variation of the phosphate nu(1)-band intensity in the Raman images, it was attributed to variations of the lamellar orientation. After threshold segmentation and conversion to elastic modulus the orientation and transverse isotropic elastic constants were derived for individual ensembles of apparent thin and thick lamellae. Our results suggest that this model represents the effective anisotropic properties of an asymmetric twisted plywood structure made of transverse isotropic fibrils. This is the first report that proves experimentally the ability of acoustic microscopy to map tissue elasticity in two dimensions with micrometer resolution. The combination with Raman microspectroscopy provides a unique way to study bone and mineral metabolism and the relation with mechanical function at the ultrastructural tissue level.     

Crystal-associated matrix components in rat incisor enamel

Summary Sections of glutaraldehyde-OsO₄-fixed, plastic-embedded rat incisor enamel were left untreated, stained, decalcifed (1% formic acid in 10% sodium citrate), or decalcified-stained. The presence of apatite crystals was monitored with electron diffraction. After brief decalcification and staining, apatite crystals and matrix components were visualized in the same field. The ghost was continuous with crystal fragments, and the coat appeared as a dense line next to crystals and ghosts. Position of ghosts and crystals at the ameloblast-enamel junction (AEJ) of the secretion zone suggested that there may be a lag of no more than 1/5 min between the elaboration of ghost and crystal. A major change in enamel morphology occurs between the AEJ and the deep enamel of the secretion zone. The ghost becomes thinner, the coat more pronounced, and the crystal enlarges. There is only little change from the deep secretion to the maturation zone enamel.     

Technical note: interpreting stable carbon isotopes in human tooth enamel: an examination of tissue spacings from South Africa

Stable isotope analysis of skeletal tissues is widely used in archeology and paleoanthropology to reconstruct diet. In material that is poorly preserved or very old, the tissue of choice is frequently tooth enamel, since this is less susceptible to diagenesis. The relationships between carbon isotope ratios in tooth enamel (δ(13) C(enamel) ), bone collagen (δ(13) C(collagen) ), and bone apatite (δ(13) C(bone apatite) ) are, however, not well understood. To elucidate these, we have measured all three indicators in archeological humans from the western and southern Cape coastal regions of South Africa. The correlation between δ(13) C(enamel) and δ(13) C(collagen) is good (R(2) = 0.71 if two outliers are excluded, n = 79). The correlation between δ(13) C(enamel) and δ(13) C(bone apatite) is weaker (R(2) = 0.37, n = 33) possibly due to bone diagenesis. No systematic offset between δ(13) C(bone apatite) and δ(13) C(enamel) was observed in this sample of archeological humans. Intertooth comparisons of δ(13) C(enamel) in three individuals showed little variation, despite the different ages of crown formation. Carbon isotope ratios in both enamel and bone collagen are good proxies for δ(13) C(diet) .     

Electronic structure of Q-A in reaction centers from Rhodobacter sphaeroides. I. Electron paramagnetic resonance in single crystals.

The magnitude and orientation of the electronic g-tensor of the primary electron acceptor quinone radical anion, Q-A, has been determined in single crystals of zinc-substituted reaction centers of Rhodobacter sphaeroides R-26 at 275 K and at 80 K. To obtain high spectral resolution, EPR experiments were performed at 35 GHz and the native ubiquinone-10 (UQ10) in the reaction center was replaced by fully deuterated UQ10. The principal values and the direction cosines of the g-tensor axes with respect to the crystal axes a, b, c were determined. Freezing of the single crystals resulted in only minor changes in magnitude and orientation of the g-tensor. The orientation of Q-A as determined by the g-tensor axes deviates only by a few degrees (< or = 8 degrees) from the orientation of the neutral QA obtained from an average of four different x-ray structures of Rb. sphaeroides reaction centers. This deviation lies within the accuracy of the x-ray structure determinations. The g-tensor values measured in single crystals agree well with those in frozen solutions. Variations in g-values between Q-A, Q-B, and UQ10 radical ion in frozen solutions were observed and attributed to different environments.