Mesoscale structural gradients in human tooth enamel

Significance

Dental enamel is integral to the function of human teeth, and its lifelong robustness is critical to well-being. An accurate multiscale model of enamel is vital in many human health contexts, including tooth decay, enamel development and malformation, and restorative dentistry. Submicrometer resolution, synchrotron X-ray microdiffraction shows that crystallographic parameters differ across the intricate rod/interrod microstructure, connecting variations in nanoscale crystallite properties with the mesoscale organization of enamel. Variation of lattice parameters strongly suggests analogous compositional variation. While rod and interrod enamel consistently differ within samples, interindividual variation hints at additional modulating factors. These results demonstrate at least one additional level in the hierarchical architecture of human enamel, with implications for mechanisms governing its formation, functional performance, and degradation.

Abstract

The outstanding mechanical and chemical properties of dental enamel emerge from its complex hierarchical architecture. An accurate, detailed multiscale model of the structure and composition of enamel is important for understanding lesion formation in tooth decay (dental caries), enamel development (amelogenesis) and associated pathologies (e.g., amelogenesis imperfecta or molar hypomineralization), and minimally invasive dentistry. Although features at length scales smaller than 100 nm (individual crystallites) and greater than 50 µm (multiple rods) are well understood, competing field of view and sampling considerations have hindered exploration of mesoscale features, i.e., at the level of single enamel rods and the interrod enamel (1 to 10 µm). Here, we combine synchrotron X-ray diffraction at submicrometer resolution, analysis of crystallite orientation distribution, and unsupervised machine learning to show that crystallographic parameters differ between rod head and rod tail/interrod enamel. This variation strongly suggests that crystallites in different microarchitectural domains also differ in their composition. Thus, we use a dilute linear model to predict the concentrations of minority ions in hydroxylapatite (Mg²⁺ and CO₃²⁻/Na⁺) that plausibly explain the observed lattice parameter variations. While differences within samples are highly significant and of similar magnitude, absolute values and the sign of the effect for some crystallographic parameters show interindividual variation that warrants further investigation. By revealing additional complexity at the rod/interrod level of human enamel and leaving open the possibility of modulation across larger length scales, these results inform future investigations into mechanisms governing amelogenesis and introduce another feature to consider when modeling the mechanical and chemical performance of enamel.

Mature human enamel consists of 95% hydroxylapatite (OHAp, Ca₅(PO₄)₃OH), 1% water, and 4% residual biomacromolecules by weight (1). The mineral phase comprises crystallites with approximately rhombohedral cross-sections that are approximately 25 nm × 70 nm in size in the basal plane and extend over potentially much larger length in the third dimension (2). A thin layer of amorphous calcium phosphate surrounds the crystallites and is enriched in compositional impurities like magnesium, fluoride, sodium, carbonate, and water (3–5). At the micrometer scale, a tessellating pattern of parallel enamel rods with teardrop-shaped cross-sections, each ~5 µm across and ~9 µm tall and comprised of more than 10⁴ crystallites, runs from the dentinoenamel junction (DEJ) to the external enamel surface (EES) of the tooth (Fig. 1 A–C) (1). At the center of the rod, the crystallites’ c-axes are predominantly parallel to the long axis of the rod; toward the rod boundaries and in the bounding “interrod” enamel, the c-axes diverge significantly from the rod axis (Fig. 1 D–E) (6). While interrod enamel is also primarily composed of OHAp crystallites, their packing density was thought to be lower than that in the rod centers, and the orientation distribution is wider, but this notion has recently been challenged for human enamel (1, 7). Differential etching across the rod/interrod structure has been assumed to primarily arise from the orientation of the crystallites with respect to the surface (1), but other factors, including variation in crystallite composition, intergranular phase fraction, and packing density, have not been ruled out.

Fig. 1.

Schemata of human tooth enamel and experimental geometry. A: Section normal to the buccal–lingual axis of human premolar. B: Isometric view of enamel microstructure. (1) Teardrop-shaped enamel rods (dark gray, front face) run from the DEJ to EES, surrounded by a continuum of interrod enamel (light gray). White arrows indicate the putative c-axis orientation of OHAp crystallites. D and E identify structures reproduced in the respective panels. Cyan highlighted in panel A corresponds to the cyan face of panel B (orientation conserved). C: SEM image of lightly etched human premolar, illustrating the teardrop shape of enamel rods and variation in morphological crystallite orientation between rod and interrod enamel. D and E: Plan view of putative crystallite orientations across the rod head in the cervical plane (D) and on the plane normal to the mesiodistal direction that bisects the rod (E).

While evidence for this model of enamel rests on a broad range of techniques, including light and electron microscopies and X-ray methods, it has been challenging to determine both crystallite orientation and crystallographic parameters over length scales commensurate with the rod/interrod microstructure of human enamel (8–15). Even polarization induced contrast (PIC) mapping, while providing striking visualization of the orientation distribution of crystallites, does not report on crystallographic parameters (7). Because of these challenges, the variation of crystallite dimensions and crystallographic characteristics at the subrod level remains poorly understood.

Here, we use synchrotron X-ray diffraction with a 500-nm probe to analyze 1-µm-thick human outer enamel plates extracted using focused ion beam (FIB) techniques and oriented perpendicular to the rod axis (SI Appendix, Fig. S1). Translation of the specimen in the beam produces 2D diffraction patterns across multiple rods with minimal convolution between microstructural regions. We previously introduced the combined local azimuthal autocorrelation (CLAA, Mapping Order/Disorder in Enamel via Azimuthal Autocorrelation) of key OHAp reflections as an index that reduces the rich texture information contained in individual diffraction patterns to a metric for orientational clustering and have shown that it clearly distinguishes the rod/interrod microstructure (Fig. 2A) (16, 17). Herein, we analyze the correlation between the crystallographic parameters measured from each probed volume and their position within the enamel microstructure for enamel samples extracted from teeth of three individuals (samples s1, s2, and s3). This allows us to not only map variations in lattice parameters and crystallite size across the rod/interrod structure of human enamel but also predict the average composition.

Fig. 2.

Rod vs. interrod diffraction patterns. A: CLAA map of human enamel (sample s3) oriented such that the X-ray beam is roughly parallel to the rod axes. Higher CLAA values correspond to ordered enamel (rod), while lower CLAA values correspond to disordered regions (interrod). B and C: Map of diffracted intensity as a function of azimuthal angle (χ) and d-spacing generated by unwrapping wide-angle X-ray scattering patterns (SI Appendix, Fig. S1D) recorded at the positions indicated in (A). D and E: Plot of azimuthally averaged diffracted intensity vs. d-spacing for the patterns in (B and C). OHAp reflections are labeled. Note that in this orientation, the enamel c axes are close to parallel to the incident beam direction, and the 002 and 004 reflections cannot be observed. F and G: Close-up of the shaded area indicated in (D and E) corresponding to the OHAp quadruplet reflections (open circles). Data, summed overall fit (dark blue line), residuals (cyan stem plots), and four pseudo-Voigt components (red, yellow, purple, and green lines) are indicated.

The CLAA maps of each enamel sample reveal a regular pattern (Figs. 2A and 3A and SI Appendix, Fig. S3 A–C). Teardrop-shaped regions with higher CLAA values, corresponding to ordered regions, are bordered by thinner regions with lower order. The tessellating pattern has dimensions roughly 5 to 7 µm across (here in the mesiodistal direction) and 8 to 10 µm tall (in the cuspal–cervical direction), consistent with the rod/interrod structure of human enamel. In fact, rod head and interrod enamel can be segmented simply by applying a threshold to the CLAA: Larger values correspond to the rod head, and lower values correspond to interrod regions.

Fig. 3.

Variation of crystallographic parameters with enamel microstructure. A–D: Maps of CLAA (A); crystallite size normal to the {121} family of planes (B); a (C) and c (D) lattice parameters for sample 1 (s1). Color bars for B–D indicate the absolute value for each parameter. E: k-means cluster assignment (k = 2) overlaid on the CLAA map; cyan: rod head (RH, n = 388 patterns/pixel) and green: interrod and rod tail (IR/RT, n = 347). F–I: Box plots of the CLAA (F), crystallite size (s₁₂₁, G), a lattice parameter (H), and c lattice parameter (I) grouped by cluster (RH: cyan and IR/RT: green) for samples s1 to s3. Color bars for s1 reproduced for reference on the left axis. Notch indicates median and 95% CI of the median; whiskers indicate the range of values in each cluster, discounting outliers (red dots) determined as points more than 1.5 times the interquartile range away from the top or bottom of their respective box. Multiple comparison analysis indicates that for each variable (F–I), means between clusters are significantly different from each other (P < 10⁻⁹ for all except s2, s₁₂₁, with P < 8.7⋅10⁻⁴; SI Appendix, Table S3).

After careful calibration using a Keri reference material (SI Appendix, Polar-to-Cartesian Transform of 2D Diffraction Patterns and Calibration of Synchrotron Diffraction Experimental Parameters, Fig. S2, and Table S1) and applying a polar transform to unwrap diffraction patterns along the azimuthal direction, χ (Fig. 2 B and C), and then integrating along χ, the four peaks of the OHAp quadruplet (Fig. 2 D–G) were fit simultaneously to determine peak position and peak width (SI Appendix, Fitting of 1D Diffraction Patterns). From these fits, the average crystallite size (normal to the {121} planes, s₁₂₁) and the a and c lattice parameters for each pattern were computed (Computing Crystallographic Parameters, SI Appendix, Fitting of 1D Diffraction Patterns and Williamson-Hall Analysis and Fig. S5). By processing all patterns within each dataset in this way, 2D maps of each crystallographic parameter were generated for all three samples (Fig. 3 and SI Appendix, Fig. S3). Just as observed in CLAA maps, the characteristic tessellating pattern of enamel is a prominent feature in maps of crystallite size and both a and c lattice parameters of all three samples, demonstrating that variations in these parameters are correlated with the rod/interrod microstructure. For the case of sample 1 (s1), it appears that thinner crystallites exist in rod heads, and thicker crystallites are found in interrod/tail regions (Fig. 3B). Relatively lower values for the a parameter fall primarily within rod head regions, with higher values observed in the interrod/tail (Fig. 3C). Conversely, relatively higher values for the c parameter are seen in apparent rod head regions, with lower values in the interrod/tail (Fig. 3D).

To minimize investigator bias, we used k-means clustering (18), an unsupervised machine learning algorithm, to partition diffraction patterns into two clusters. Clusters based on the CLAA, s₁₂₁, a, and c parameters extracted from each pattern map well onto the microstructure of human enamel: The rod head (cyan) and interrod/rod tail (green) regions are clearly demarcated for all samples (Fig. 3E and SI Appendix, Fig. S3 Q–S). Computing parameter means grouped by cluster supports the previous qualitative observations (Fig. 3 F–I and SI Appendix, Fig. S3 and Tables S2 and S3) and confirms that statistically significant quantitative differences exist between rod head and interrod/tail microstructural regions for each parameter in each of the three samples (P < 10⁻⁹ for all except sample s2, s₁₂₁, with P < 8.7⋅10⁻⁴, SI Appendix, Table S3). Note that clustered parameters show predominantly weak pairwise correlations (SI Appendix, Fig. S6), justifying their use as independent variables for k-means clustering.

Comparing means between individuals (samples) reveals that absolute values and trends vary. In all samples, CLAA values in the rod head are greater than those in the interrod/tail (Fig. 3F). This reflects a decrease in crystallite orientation clustering in the interrod (16). It is not necessarily in contradiction to the recent finding of long-range alignment along the c-axis by PIC mapping (7); due to the orientation of the sample, we do not directly assess orientation along the c-axes, and our probe is sensitive specifically to the local orientation distribution within submicron voxels. Similar to the CLAA, the rod head has significantly thinner crystallites than the interrod/tail regions (Fig. 3G). However, there is greater variation in the absolute values. It is possible that the size increase from rod head to interrod is related to the decrease in orientation clustering, as less orderly crystallite packing, and thus lower packing density, might result in prolonged growth of crystallites in the basal plane during amelogenesis. The magnitude of the difference of the a and c parameters in rod head vs. interrod enamel is similar. However, the direction of the effect is reversed in one of the three samples (Fig. 3 H and I). Specifically, in samples s1 and s3, a is smaller and c is larger in the rod head compared with the interrod. Sample s2 shows the opposite trends for both a and c. We will return to this difference later in the discussion.

The sample-wide mean lattice parameters (e.g., for sample 1, a = 9.451 ± 0.002 Å and c = 6.883 ± 0.011 Å) agree well with those determined by others using bulk powder diffraction and fall within the range of values determined by microdiffraction (SI Appendix, Fig. S7). The sample averages for s₁₂₁ range from 28 to 43 nm, in agreement with ranges previously reported for human enamel (SI Appendix, Table S4). Note that discriminating crystallite size differences smaller than those reported here is now routine to ±1 nm for peak width analyses (19) and that the values in this study are based on sets of 500+ separate diffraction patterns collected under identical experimental conditions for each sample.

Absolute values for the Bragg angle (2θ) and corresponding lattice parameters determined by fitting 2D diffraction patterns are sensitive to systematic error, particularly in the sample-to-detector distance. In the physically small sample we probed, each position is similarly affected, and thus relative differences are quite reliable. Because the specimens were oriented with the beam parallel to the enamel rod axes, with nearly no 002 diffraction and incomplete 030 and 121 diffraction rings, one must rely on precise determination of the beam center. This can typically be done to ± 0.1 detector pixels (20, 21). Assuming a systematic displacement of the beam center of this magnitude, the absolute values of computed parameters shift slightly, but the pattern of spatial variation does not (SI Appendix, The Effect of Errors in Beam Center Assignment on Crystallographic Parameter Maps and Fig. S8), lending confidence to the sensitivity and robustness of the analyses. Inclusion of an internal standard placed immediately adjacent to the specimen in future experiments is recommended to further improve the precision of the sample-to-detector distance determination. Uncertainty in this measurement may explain some of the sample-to-sample variation in computed lattice parameters. It is also possible that this variation simply reflects differences between individuals. It is intriguing to note that such differences may be connected to interindividual variation in the susceptibility to caries. However, it is also possible that similar variations occur within one tooth and reflect, for instance, circadian cycles.

It is highly likely that the differences in lattice parameters between rod head and interrod/tail are due to differences in crystallite composition (22). Bulk enamel contains carbonate (2.7 to 5 wt%), magnesium (0.2 to 0.6 wt%), sodium (0.2 to 0.9 wt%), and fluoride (0.01 wt%) both as solutes in OHAp lattice positions and in the amorphous intergranular phase (3–5, 23, 24). In addition, water, citrate (0.1 dry wt%) (25), and residual protein are known to be present. There is some evidence supporting the notion that water and organics partition to the amorphous intergranular phase at multiple grain boundaries (5), where they would not appear in the current probe of the purely crystalline components of enamel.

Small changes in lattice parameters could also result from elastic strain due to organic inclusions within crystallites (26, 27) or the modulation of the surface energy by ligands. Entrapment of full-length amelogenin has been reported in secretory and maturation stage enamel mineral (28), but there is no direct evidence that organic molecules are occluded in the crystallites of fully mature mineral or even in the intergranular phase at flat grain boundaries (5). Modulation of surface energy is a factor that likely affects lattice parameters in the case of bone and dentin (29). It is unlikely to be relevant in enamel because of the substantially larger size of the crystallites. A back-of-the-envelope calculation indicates that the observed differences in lattice parameters would require modulation of the interfacial free energy on the order of multiples of the vacuum surface energy of hydroxylapatite, which is unrealistically high (SI Appendix, Consideration of Surface Energy Modifications on Lattice Strain for Enamel Crystallites), especially as there is no evidence that supports the presence of a modulating ligand. Thus, neither organic inclusion nor surface energy modulation seem likely candidates to explain the observed variation in lattice parameters.

We therefore consider only well-documented substitutional defects as potential contributors to the change in lattice parameters. While solute expansion coefficients for Mg²⁺ on Ca²⁺ positions, and for coupled substitution of CO₃²⁻ on PO₄³⁻ and of Na⁺ ions on Ca²⁺ positions have been determined (SI Appendix, Table S5), those for F⁻ substituting on OH sites have not in the relevant concentration range (3, 30, 31). Interpolating between OHAp and fluorapatite end-members at the low fluoride concentrations, we find that the impact of F⁻ substitution is negligible (SI Appendix, Table S5).

In the dilute limit, a linear, additive model for multiple substitution is a reasonable assumption. We thus predicted the deviation of the mole fraction of Mg²⁺ and CO₃²⁻/Na⁺ from the sample mean in crystallites based on the observed differences in lattice parameters (SI Appendix, Linear Model to Estimate Lattice Parameter Changes). For each sample, the trends observed in the a and c parameters are analogously reflected in the composition maps (Fig. 4 and SI Appendix, Fig. S4). For samples s1 and s3, maps clearly predict that the Mg²⁺ mole fraction is elevated in crystallites in interrod enamel and rod tail regions (Fig. 4 C and H) relative to the rod heads. Meanwhile, the trend for CO₃²⁻ (and by extension, that for Na⁺) is reversed, with elevated levels predicted in the rod head crystallites and reduced levels in the rod tail and interrod (Fig. 4 D and I). For sample s2, these trends are opposite, reflecting the reversed trends in the a and c parameters between rod head and interrod/tail. Note that these predictions do not account for the amorphous intergranular phase, and they average over any gradients within crystallites (3).

Fig. 4.

Predicted compositional variation at the subrod length scale. A: Map of the a lattice parameter in s1, expressed in units of mean-normalized difference from the mean: $a^{*}=\left(a-\overline{a}\right){\overline{a}}^{-1}$. B: Analogous map of the c lattice parameter: $c^{*}=\left(c-\overline{c}\right){\overline{c}}^{-1}$. C: Map of the deviation of the Mg²⁺ concentration from the sample mean (ΔX_Mg). D: Map of the deviation of the CO₃²⁻ concentration from the sample mean (ΔX_CO3). E: k-means cluster assignment (k = 2) overlaid on the CLAA map; cyan: rod head (RH, n = 388 patterns/pixel) and green: (IR/RT, n = 347). F–I: Box plots for clusters corresponding to rod head (RHcyan) and (IR/RT, green) enamel for $a^{\ast }$ (F), $c^{*}$ (G), ΔX_Mg (H), and ΔX_CO3 (I). Multiple comparison analysis indicates that for each variable (F–I), means between clusters are significantly different from each other (P < 10⁻⁹; SI Appendix, Table S3).

Grouping patterns by cluster assignment as previously, we predict significant differences between the mean composition of the rod and interrod/tail regions on the order of 0.25 at% (Fig. 4 H and I). Meanwhile, the maximum pixel-to-pixel difference is 1.43 at% Mg in sample s1. The predicted range in composition across several rods is thus comparable with the range observed across the entire thickness of enamel (23). Although differences on the order of 0.25 at% may seem modest, they are comparable with those observed within single enamel crystallites, where there is little doubt that they are responsible for the preferential dissolution of the crystallite core (3). In fact, because magnesium, carbonate, and sodium are concentrated in the core, which has a smaller volume than the shell of the crystallite, the differences could easily be more than three times larger than the averages over the entire crystal that we report here.

Summarizing, our data demonstrate that there are structural differences at the subrod level and strongly suggest linked compositional differences. Specifically, there are statistically significant differences in the mean of the CLAA order parameter, all three crystallographic parameters, and the two predicted compositional variables between rod head and interrod enamel within each of the three samples that we analyzed. More work is required to establish whether the interindividual variations in absolute values and the direction of the effect (increase vs. decrease of lattice parameter going from rod head to interrod) observed here also occur within one tooth at length scales larger than the ones we sampled, for instance, as a function of the distance between the EES and the dentinoenamel junction. It would also be valuable, even if quite challenging, to confirm the existence of the concentration gradients using an independent technique. Atom probe tomography (APT) and potentially nanoscale resolution -secondary ion mass spectrometry (nano-SIMS) and Raman spectromicroscopy are techniques that combine the necessary spatial resolution and sensitivity for low–atomic number elements, even though the latter two would likely not be able to differentiate between crystallites and the intergranular phase. Last, it remains possible that occluded organic material that has thus far eluded detection by APT contributes to the observed lattice parameter changes.

Because enamel is acellular and experiences very little natural turnover after tooth eruption, any spatial variation of the composition across the enamel microstructure can be read as a record of differences in the environment in which crystallites form during amelogenesis (1). During the secretory stage, ameloblast cells pattern the rod/interrod structure with precursor mineral ribbons within an organic extracellular matrix (ECM). After the enamel layer is patterned to full thickness in this way, the enamel matrix is degraded, and crystallites grow laterally during the maturation stage. The weight fraction of mineral increases from about 30 wt% to more than 95 wt% during this stage. Recent data suggest that the core–shell structure of enamel likely reflects these two stages of growth, with a core that is enriched in minor ions (Mg²⁺, Na⁺, and CO₃²⁻) deposited in the secretory and an impurity-depleted shell added during the maturation stage (3).

It thus seems likely that the difference in average composition reflects the composition of the crystallite cores and is established during the secretory stage. In this stage, the enamel growth front has a characteristic shape, a roughly hexagonal array of pits (SI Appendix, Fig. S9A) (1, 32). Each pit contains the distal part of Tomes process (dpTP), a projection of the ameloblast. In a three-dimensional (3D) model of the growth front based on data from the human deciduous molar (SI Appendix, Fig. S9 B–D) (33), the dpTP has an asymmetric shape (Fig. 5A), with a shallow ramp inclined 30 to 35° from the plane of the growth front and a steep face that abuts the enamel rod (Fig. 5B and SI Appendix, Fig. S9F). As the growth front moves in the direction of the rods, approximately parallel to the ramp, dpTPs lay down ECM and mineral precursor ribbons for the rod at the steep face. At the same time, interrod enamel forms at the proximal part of Tomes process (ppTP, Fig. 5C) in the canyons between neighboring processes (≤1 µm wide at the bottom and 4 to 6 µm deep).

Fig. 5.

Formation of compositional gradients in human enamel. A: Rendering of a 3D model of the secretory stage growth front in human deciduous enamel (SI Appendix, Fig. S9) showing the distal (dpTP) and proximal part of Tomes process (ppTP). Based on data in ref. 33. B. Line profiles of Tomes processes in the direction from rod head to tail (SI Appendix, Fig. S9F) reveal a ramp (red dashed line) with characteristic shallow angle $(\alpha =31.7\pm {1.8}^{°}$ for the sampled ameloblasts) and a steep face that is more variable (arrows). C: Idealized line profile (to scale). Each ameloblast (gray) produces one enamel rod (cyan and light green) at the steep face and interrod enamel (dark green) at the ppTP as it moves parallel to the direction of the ramp (black arrow). Black dashed line indicates profiles of out-of-plane ameloblasts. White dashed line indicates the section illustrated in (F). D. Rendering of a 3D model in (A) showing the pits in the enamel surface in which dpTPs reside. The color indicates the distance to a plane normal to the rod direction and corresponds to the time at which enamel was first deposited. Note that newly forming enamel in the rod head is almost completely encircled by older (more distant) interrod enamel (white arrows). E and F. Experimental (E) and idealized sections (F) through mature enamel viewed down the rod axis. Color scheme in (E) is identical to (D). Dashed line in (F) indicates the section in (C). Putative gradients exemplify a possible condition to result in the observed lattice parameter differences in samples 1 and 3.

Crystallites in the rod head therefore grow in a space that is almost, but not entirely, encircled by partially mineralized interrod enamel (Fig. 5D). Mineralization occurs simultaneously at the dpTP and ppTP (as indicated by the gradient from light to dark color in the direction of the rod axis in Fig. 5C). However, nascent ribbons right at the growth front, i.e., the cell membrane of the dpTP at the upper rim of the rod head (point N in Fig. 5 C and F), form near those of the interrod that are already at a distance of 9 to 10 µm from the growth front at the ppTP (point O’ relative to point O in Fig. 5 C and F) (33). At this distance, the cross-sectional area of the ribbon has approximately doubled already (SI Appendix, Fig. S10A) (34). In the direction from rod head to rod tail, the depth of the pit decreases such that the bottom of the tail and nearby interrod form very nearly at the same time (Fig. 5 D and E). Because diffusion of small inorganic ions is fast on the timescale of enamel growth, and the volume fraction of mineral is less than 10% (SI Appendix, Fig. S10B), one would expect that concentration gradients dissipate quickly unless they are actively maintained. In the case of sample s1 or s3, one could imagine that Mg is secreted at a higher rate across the ppTP membrane and/or removed at a higher rate across the dpTP opposite the rod head (Fig. 5F). Transport rates could be just the opposite for carbonate, or the concentration of carbonate could be modulated by the local pH. Alternatively, gradients could be established if ions were tightly bound by the enamel matrix and only released as the matrix is degraded. This may be especially important for magnesium as it is incorporated later in secretory stage than carbonate and sodium.

Because the core composition may influence enamel dissolution directly, through the impact of composition on solubility, and indirectly, by generating residual stresses, it is important to map out enamel composition—including organics—systematically, for instance, as a function of the distance from the EES to the dentinoenamel junction. This would reveal not only whether the crystallite composition in rod head and interrod/tail enamel varies between inner and outer enamel, but also whether it is modulated over shorter periods of time similar to those seen in dentin (35). Such cycles could result in the reversal of the trends for lattice parameters and composition from samples s1 and s3 to sample s2. In fact, periodic modulation of the concentration of Mg and carbonate and thus solubility of crystallites across the rod/interrod structure might contribute to the two predominant etch patterns that are observed (1). Taken together, such analyses will provide valuable information for modeling caries lesion progression and provide deep insights into the conditions under which enamel crystals grow during both normal and pathological amelogenesis.

Methods

Consumables.

Tooth storage and mounting utilized ethanol (VWR), formaldehyde (CH₂O) (Alfa Aesar), PELCO® liquid silver paint, graphite tape (Ted Pella), and EPO-TEK 301 (Epoxy Technology). Coarse sectioning/polishing utilized CarbiMet SiC grinding paper, Metadi supreme polycrystalline aqueous diamond polishing suspension, Microcloth polishing cloth (Buehler). Enamel sections extracted with focused ion beam techniques were mounted onto Omniprobe lift-out grids, Cu with four posts, prod 460-204 (Ted Pella). A ceria standard, from Standard Reference Material 674b (National Institute of Standards and Technology), or Sigma Aldrich (>99.995% trace metals basis, cat. no 202975), was used for calibration.

Sample Preparation.

Deidentified healthy human premolars extracted for orthodontic reasons were obtained from Drs. Akers, Stohle, and Borden of The Center for Oral, Maxillofacial, and Implant Surgery, disinfected in 10% buffered formalin at room temperature for 10 d, rinsed with water and dried under nitrogen, and stored at 4 °C. A section of 1 µm thickness was prepared in a controlled orientation as described previously (16). Briefly, whole teeth were embedded in Epofix 301 cold-cure epoxy (Epotek), coarsely sectioned with a diamond saw, and progressively ground and polished to 50 nm roughness using SiC grit paper and diamond slurries (Buehler). Next, an established FIB lift-out procedure (4, 5) was used to extract and clean a thin plate (approximately 20 µm × 8 µm × 1 µm) of outer enamel oriented such that the thinnest dimension runs nearly parallel to the enamel rod axes (SI Appendix, Fig. S1A and B).

Synchrotron X-ray Microdiffraction.

Synchrotron X-ray microdiffraction was performed at beamline 34 ID-E of the Advanced Photon Source at Argonne National Laboratory. Monochromatic X-rays (17,000 ± 1 eV) were focused to a probe size of approximately 250 nm × 250 nm (s1 and s2) or 500 nm × 500 nm (s3), and 2D diffraction patterns were collected in transmission on a MAR165 area detector (square pixels, pitch 79.278 μm) positioned with its face perpendicular to the incident X-ray beam (SI Appendix, Fig. S1). The sample was mounted on a translational stage with 100-nm precision in x (horizontal), y (vertical), and z (depth parallel to X-ray beam) motions and positioned at the focal point of the beam. Diffraction patterns were collected with two 30-s integrations and correlated to remove spurious counts from gamma rays or electronic noise, yielding an effective exposure time of 60 s per pattern. 2D maps with 500-nm steps in x and y were collected across the enamel sections in a raster sequence, including patterns through air, the FIB platinum used for sample mounting, and the copper grid. Diffraction patterns were additionally collected from a NIST powdered ceria standard (NIST Standard Reference Material 674b) and single-crystalline silicon (for instrumental broadening).

Calibration and Background Correction.

Raw 2D diffraction patterns (2048 × 2048 16-bit TIFFs) were processed using ImageJ (36), Fit2D (37), and MATLAB (MathWorks 2020b) in a workflow similar to that described elsewhere (16). In brief, ImageJ and MATLAB were first used to perform background subtraction with averaged air patterns, normalized to the intensity of each pattern. Next, the ceria calibrant was analyzed with Fit2D to fit the experimental parameters, and a MATLAB script (MathWorks 2018b) developed by the authors was used to further refine the beam center and detector tilt (SI Appendix, Calibration of Synchrotron Diffraction Experimental Parameters). Using the refined experimental parameters, each diffraction pattern was transformed from polar to Cartesian coordinates (azimuthal angle χ vs. d-spacing and 2θ, see example in Fig. 2 and SI Appendix, Polar-to-Cartesian Transform of 2D Diffraction Patterns). All further analyses (described below) and plotting were performed using MATLAB scripts developed by the authors.

Mapping Order/Disorder in Enamel via Azimuthal Autocorrelation.

The CLAA, an order parameter that describes the orientation distribution (texture) of microdiffraction patterns, was determined as described previously (16). Briefly, the distribution of crystallite orientations within the irradiated volume is reflected in the azimuthal distribution of scattered intensity in any individual hkl diffraction ring. If diffraction spots within a ring cluster together, i.e., are azimuthally correlated, there is greater crystallographic order (texture) within the sampled volume than if the spots are more widely spread around the diffraction ring. The azimuthal autocorrelation measures this clustering for a specific hkl ring.

The intensity (counts) within each diffraction ring is averaged within L = 180 bins of ~2° azimuthal width. Within a given diffraction ring hkl, the azimuthal autocorrelation r_j of proximity j relates the intensity $I_{hkl}\left(\chi \right)$ within each azimuthal bin to those that are j bins away over the entire profile via the following equation:

$$r_j=\frac{c_j}{c_0},$$ [1]

where

$$c_j=\frac{1}{L}{{\displaystyle \sum }}_{i=1}^{L-j}(I_i-\overline{I})(I_{i+j}-\overline{I}),$$ [2]

$L$ is the total number of azimuthal bins, $\overline{I}$ is the mean intensity, and ${\text{c}}_0$ reduces to the sample variance. The value of $r_j$ can vary between −1 and 1. The summed autocorrelation of the first eight proximities is defined as the local azimuthal autocorrelation, $\overline{r}$ (LAA). This captures the autocorrelation in highly localized neighborhoods and insulates against artifacts introduced by the selection of azimuthal bin size. Pure powder patterns with a uniform azimuthal intensity distribution have a low LAA, and patterns with high crystallographic texture have regions of localized high intensity and an increased LAA. Inspection of 2D diffraction patterns of enamel suggested that the 022, 030, 112, and 121 quadruplet reflections hold texture information, so a final quantity, termed the CLAA, was defined as the sum of LAA values for each reflection weighted by their total intensity. Values of LLA and CLAA were calculated for each position (x,y) using a custom MATLAB (MathWorks) code. More details appear elsewhere (16).

1D Diffraction Profile Peak Fitting.

2D diffraction patterns were integrated over χ to yield 1D profiles (Fig. 2 B–E). Diffraction peaks of the hydroxylapatite quadruplet (hkl = 121, 112, 030, and 022) within these 1D patterns were simultaneously fit by a linear combination of four symmetric pseudo-Voigt profiles (38), yielding precise values of peak position (mean), peak breadths (full width at half maximum intensity, FWHM, and integral breadth, β), and peak intensities (intensity of the mean) for each reflection in each pattern (SI Appendix, Fitting of 1D Diffraction Patterns).

Computing Crystallographic Parameters.

The a and c lattice parameters were computed from the peak positions of the 030 and 121 reflections. Because the 030 and 121 peaks fall very close to the 112 and 022 reflections in the OHAp quadruplet, all four of the peaks were simultaneously fit by a linear combination of four pseudo-Voigt functions. Lattice parameters can be computed from the mean peak positions (d_hkl) through manipulation of the general equation for lattice spacing in a hexagonal crystal system.

$$\frac{1}{d_{hkl}^2}=\frac{4}{3}\left(\frac{h^2+hk+k^2}{a^2}\right)+\frac{l^2}{c^2}$$ [3]

The a and c lattice parameters can be easily computed from the 030 and 002 mean peak positions (if present). For these cases, Eq. 3 simplifies to

$$a=2\sqrt{3}\cdot d_{030}.$$ [4]

$$c=2\cdot d_{002}.$$ [5]

However, when the enamel orientation does not yield 002 diffraction, as is the case for nearly all patterns taken down the rod axis, the c lattice parameter was instead computed using the computed value of a and the 121 peak position, again rearranging Eq. 3 as follows:

$$\begin{array}{c}c={\left[\frac{1}{d_{121}^2}-\frac{28}{3}\left(\frac{1}{a^2}\right)\right]}^{-\frac{1}{2}}={\left[\frac{1}{d_{121}^2}-\frac{7}{9}\left(\frac{1}{d_{030}^2}\right)\right]}^{-\frac{1}{2}}.\hfill \end{array}$$ [6]

Thus, values for a and c are determined for each voxel in the diffraction map. As a lower bound of the physical crystallite size, we extracted the coherently scattering domain size (“crystallite size,” s_hkl) in the direction normal to the (hkl) planes according to the Scherrer equation:

$$s_{hkl}=\frac{K\lambda }{{\beta }_{hkl}cos\theta },$$ [7]

where K is a constant (assumed to be 1 here), λ is the X-ray wavelength, and θ is the Bragg angle (39). Here, the integral breadth definition of peak broadening is used, i.e., the width of a rectangle that is as tall as the diffraction peak with the same integrated area. Conveniently, the total integrated area is just the leading coefficient in the pseudo-Voigt formulation by Thompson, Cox, and Hastings (SI Appendix, Fitting of 1D diffraction patterns), so the integral breadth is computed directly by dividing this fit value by the peak intensity evaluated at the mean. This computed integral breadth is then corrected for both instrumental broadening (β_Si ~ 0.0665° 2θ) and a linear subtraction of broadening due to the relatively consistent strain determined through the Williamson–Hall (WH) analysis (β_WH, ranging from 0.0164° to 0.0176° 2θ for the quadruplet reflections) (SI Appendix, Williamson-Hall analysis and Fig. S5) according to the following equation:

$${\beta }_{\mathrm{cor}}=\sqrt{{\beta }_{\exp }^2-{\beta }_{\mathrm{Si}}^2}-{\beta }_{\mathrm{WH}}.$$ [8]

This finally yields the corrected values for peak broadening (β_cor) from which estimates of crystallite size are computed according to the Scherrer equation above (Eq. 7).

Supplementary Material

Appendix 01 (PDF)

Dataset S01 (CSV)

Dataset S02 (CSV)

Dataset S03 (CSV)

Dataset S04 (CSV)

Dataset S05 (CSV)

Dataset S06 (CSV)

Data, Materials, and Software Availability

All data and code used in the analysis, with exception of the raw X-ray diffraction patterns, are available on GitHub at: https://github.com/bbimat-group/human_enamel_mesoscale_variation/ (40). An archive is additionally published on zenodo.org at: 10.5281/zenodo.7275445 (41). X-ray diffraction patterns are available to qualified researchers upon reasonable request.