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Water-Mediated Collagen and Mineral Nanoparticle Interactions Guide Functional Deformation of Human Tooth Dentin Jean-Baptiste Forien, Ivo Zizak, Claudia Fleck, Ansgar Petersen, Peter Fratzl, Emil Zolotoyabko, and Paul Zaslansky Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b00811 • Publication Date (Web): 26 Apr 2016 Downloaded from http://pubs.acs.org on April 27, 2016

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Chemistry of Materials

Water-Mediated Collagen and Mineral Nanoparticle Functional Deformation of Human Tooth Dentin

Interactions

Guide

Jean-Baptiste Forien†,*, Ivo Zizak‡, Claudia Fleck§, Ansgar Petersen†,ǁ, Peter Fratzl⊥, Emil Zolotoyabko#, Paul Zaslansky†,* †

Julius Wolff Institute, Charité – Universitätsmedizin, 13353 Berlin, Germany Helmholtz-Zentrum Berlin für Materialien und Energie – Speicherring BESSY II, 12489 Berlin, Germany § Berlin Institute of Technology, Materials Engineering, 10623 Berlin, Germany ǁ Berlin-Brandenburg Center for Regenerative Therapies, Charité– Universitätsmedizin, 13353 Berlin, Germany ⊥ Max Planck Institute of Colloids and Interfaces, Department of Biomaterials, 14424 Potsdam, Germany # Technion – Israel Institute of Technology, Department of Materials Science and Engineering, 32000 Haifa, Israel ‡

ABSTRACT Dentin in teeth is a bone-like nanocomposite built of carbonated hydroxyapatite (cHAP) mineral particles, protein and water that does not remodel nor heal. It is assumed to be excellently adapted for decades of mechanical function, due to the interplay between its constituents. Using samples of human origin, we combine heat treatments with synchrotron X-ray diffraction, second-harmonic generation microscopy, Raman spectroscopy, and phase contrast-enhanced nano-tomography to study the waterassisted functional coupling of the biocomposite components. Across roots we find a gradual reduction in the c-lattice parameter of the cHAP nano-crystals, from 6.894 Å externally down to 6.885 Å on the inside. Thus, the tissue formed at later stages of tooth development around the pulp contains crystals with smaller unit cells. In all regions, a compressive strain of ~0.3 % is observed upon drying by mild heating (125 ºC). Dehydration results in a substantial increase in the averaged microstrain fluctuations in the mineral nanoparticles. The mineral crystallite platelet lengths fall off from ~36 nm externally to ~26 nm closer to the pulp. Our results suggest that both morphology and tight mineral-collagen coupling allow mineral nano-particles in dentin to sustain rather large stresses of 300 MPa, far exceeding mastication stresses.

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INTRODUCTION Teeth are complex structures, consisting macroscopically of an external, stiff and brittle enamel cap that encases a mass of dentin. Unlike enamel that is composed primarily of a carbonated hydroxyapatite (cHAP) mineral (dahllite), dentin is a bone-like nanocomposite of cHAP mineral particles, collagen and water. Teeth remarkably sustain decades of daily, cyclic mechanical stress, much due to the tough mechanical backing provided by dentin.1 Many bone-based tissues develop micro-cracks under repeated load,2 damage that is typically repaired by remodeling activity of living cells. But tooth dentin is different because it does not heal or remodel implying that damage does not form at all, or that if it does, it is contained, thus avoiding tooth fracture. Curiously in intact teeth, fracture is rare,3 essentially occurring only due to trauma or following dental treatment. The notable scarceness of failure of dentin suggests that this tissue is particularly well adapted to endure the repeated loads encountered during mastication. In other words, because teeth are usually loaded cyclically under varying conditions of humidity and temperature, tooth dentin is most probably designed to deform and recover elastically. This makes it an excellent material to sustain compressive loads that are repeatedly introduced through the outer hard enamel shell. Doubtlessly, teeth circumvent permanent damage and failure due to an excellent evolutionary adaptation of the structure. Dentin is known to contain regional structural variations that contribute to shielding against damage propagation and overload, for example the dentin ‘soft zone’, up to 300 µm thick, lining the enamel cap;4,5 however, important elastic responses to load also take place at the micron and submicron length scales,6 in a manner that we hypothesize is essential for proper dentin function, which is not completely understood. All members of the bone family of materials, including dentin, share a common structural motif: mineral nanoparticles reinforce a network of collagen fibers made of woven nano-fibrils.7 Mineral takes up about 48 % of the volume of dentin8 whereas protein occupies about 35 %, but these ratios vary in different regions of teeth.9 Peculiar to dentin is the predominant organization of the collagen 2


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fibers in ‘onion-like’ layers that more or less encase the pulp.10 Further, dentin morphology differs from typical bone tissues as it lacks osteocyte cells. The dentin matrix is acellular, but it contains a dense array of micron-sized ‘dentinal tubules’ that are either empty or may contain cell extensions. The tubules traverse the entire dentin bulk (Figure 1) at increasing diameters and increasing densities (20,000 to 45,000 tubules per mm2),11 reaching highest packing densities near the pulp where they are plugged by the odontoblast cells that produce them. Tubules are lined by a high-stiffness rim of a collagen-free apatite sheath,12–16 known as peritubular dentin (PTD). PTD is usually thick (> 1 µm) in the crown but is thinner and more scant in the root,13 and it contains about 13 vol. % proteolipids and non-collagenous proteins17 interspersed between the mineral particles.18 The dental matrix embedding and surrounding tubules, known as intertubular dentin (ITD, Figure 1), is made of felt-like layers of mineralized collagen fibers. The fibers are therefore arranged more or less orthogonally to the tubules (see schematics in Figure 1b). Human tooth dentin is thus a structured composite of PTD and ITD, with a significant proportion (> 70 %) of ITD, where collagen and mineral are tightly bound.

Figure 1. (a) Scanning electron micrograph of human root dentin. The tubules (black arrows) with thin surrounding peritubular dentin (PTD) are embedded in a mineralized collagen matrix of the intertubular dentin (ITD). (b) Schematic representation of dentin in the region marked by the dashed line in (a) showing a PTD-surrounded tubule (black arrow) embedded in a mesh of 3



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more-or-less tangentially arranged mineralized collagen fibers (mineral particles covering the fibers/fibrils are depicted in brown/yellow). The cHAP crystals of dentin are amongst the smallest found in nature,7 and both transmission electron microscopy (TEM) and X-ray diffraction (XRD) have been used to study their dimensions and attributes (see Table S1). Direct observations by TEM revealed crystallite lengths of the tablet-shaped particles in both ITD and PTD tissues. While early works18,19 identified particle sizes of 100 nm, later studies reported smaller crystal lengths of 40-60 nm.20,21 Comparisons of the crystallite sizes measured by XRD and TEM occasionally match using both methods,22 where reported lengths span 17-50 nm. Xray studies of powdered samples23,24 found crystallite lengths of ~20 nm and 17.6 ± 0.7 nm. When nonpowdered samples were studied in whole dentin slabs, crystallite lengths along the c-axis of cHAP were 24 nm,25 27.2 ± 10.3 nm,26 30 nm27 and even 50 ± 8 nm.28 In addition to length, other attributes of the mineral crystallites have also been documented, e.g. widths: 36.5 ± 1.5 nm and 36 ± 1.9 nm were reported for ITD29 and PTD15, respectively. Some of these authors also reported platelet thickness to be less than 10 nm, which is significantly larger than values reported by small angle X-ray scattering (SAXS) that revealed mean particle thicknesses of 2.5~3.5 nm.8,30 The mineral particles therefore probably have a high (> 10) aspect ratio, as suggested also for bone by bright-field TEM studies.31 Xray diffraction measurements can further provide information about averaged microstrain fluctuations in the nanocrystals.32 Microstrain fluctuations usually originate from inhomogeneous strain fields existing in the crystals, typically produced by lattice defects (such as vacancies, impurity atoms, dislocations, twin boundaries, etc.). In the case of aggregates of nanoscale sized crystallites, strain fluctuations can be induced also by local variations of forces imposed by the extra crystalline environment. Indeed a handful of studies27,28 have reported averaged microstrain fluctuations in dentin nanocrystals, ranging from 10-4 to 5·10-3 ~ 6·5.10-3.

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In the natural state, dentin cHAP crystals function within a biocomposite and some studies examined the load transfer between collagen and cHAP crystals, in large mechanically-loaded mmsized bovine dentin samples.33 These authors used XRD to track effects of macroscopically applied stress on both the mineral and the collagen, and they reported observations of strain evolution in the nanocomposite components. In follow-up work,34 the authors correlated similar measurements with 3D structural density maps (essentially mineral, mapped by tomography) as well as elastic moduli measured by acoustic wave propagation. In transverse sections of roots spaced 0.5 mm apart, they found little inter-specimen but strong intra-specimen variability, suggesting that tooth microstructure varies considerably in different parts of teeth. Another study27 used a combination of mechanical loading and XRD developed for bone studies35 to examine deformation of the mineral near the dentinenamel junction. Those authors reported a gradient of strains in the mineral in dentin, as a function of externally applied stress at increasing distances from the dentin-enamel junction. With increasing load and coupled with the appearance of macroscopic signs of damage, they found maximal apatite strain values of about 1 % in compression, presumably reflecting an upper limit on the highest strains that may be transferred into the mineralized nanoparticles. Much is therefore already known about the interrelations and properties of the dentin nanocomposite constituents and interactions, but an understanding of just how the mineral particles contribute to distributing strain energy that is encountered during tooth loading is still lacking. Recently, Forien et al.36 showed that the mineral particle operating in the different environments of ITD and PTD deform differently within the macroscopic dentin tissue. Using the (002) Debye ring of cHAP to precisely measure the c-lattice parameter and derive strains observed in the mineral particles, they found that collagen-associated mineral in partially dried tissue has a slightly smaller lattice parameter along the c-axis of the crystals of ITD, compared to particles associated with PTD. Accurate measurements of the strain in these mineral nanoparticles demonstrated a preferred compressed state of 5



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particles corresponding to the layers of the mineralized collagen fibers, essentially orthogonal to the tubule orientation. That work suggested that within normal, elastic, reversible loading conditions, the mineral nanoparticles become compressed by the tightly coupled collagen. This mechanism is seemingly well suited to repeatedly support and counteract mechanical deformation of the tissue occurring under daily loading conditions, while preventing cracks from developing or advancing towards the pulp. Here, we examine the range of mechanical deformation responses observed in dentin while taking a closer look at the structure-function relations linking water, collagen and the apatite mineral particles. Using a combination of methods, including high resolution XRD and phase-contrast enhanced X-ray nano-tomography, Raman spectroscopy and second harmonic generation (SHG) microscopy, we examine the cHAP nanoparticle size and strain bearing capacities that are central for fulfilling elastic, cyclic deformation functions. By changing the tissue water content to maximize and minimize hydration, we induce osmotic pressure that either swells or shrinks the collagen fibers.37 This pressure directly affects the cHAP stress state in mineralized tissues.38 We compare results from watersaturated dentin samples with those obtained in the same samples after water removal (drying at 125 °C). Our results quantify basic structural and functional relationships between the cHAP crystals and the proteins in dentin and highlight the capacity of water in mediating strains in this biologically-static biocomposite. EXPERIMENTAL SECTION Materials and methods Sample preparation Root dentin was harvested from 7 caries-free adult human incisors and canines, extracted for reasons unrelated to this study, and collected from anonymous patients according to the guidelines of 6


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the ethics committee of the Charité-Universitätsmedizin, Berlin, Germany. Upon removal from the patients, teeth were stored wet and refrigerated at 4 °C in a chloramine 0.5 % solution. Slices were created on a bucco-lingual (i.e. cheek-tongue) orientation using a water-cooled slow-speed saw (Isomet Buehler Ltd., Lake Bluff, IL, USA). Each slice was ground down to a thickness of about 250 µm and subsequently polished down to 170~180 µm using a series of wet emery sheets. Samples were maintained moist until further use within 36 hours. Three complete crown-root slices from upper and lower incisors were used for high-resolution diffraction characterization of both buccal and lingual root dentin (Figure 2). Four other teeth were used to cut out elongated root dentin slabs for in situ XRD/Raman spectroscopy measurements combined with heat treatment experiments. Adjacent slices from the same teeth were used for second-harmonic confocal imaging, scanning electron microscopy (SEM), and X-ray nano-tomography. For the latter, three tooth slices were further cut into thin bars along the root-crown axis. The SEM and tomography samples were air dried.

Figure 2. Illustration of our high-resolution XRD line scans. Diffraction patterns were collected by scanning points across the samples that were placed on a membrane onto which corundum powder was affixed, on both the lingual (left) and the buccal (right) sides of the sample. The (002) Debye ring was used to track the local strain in the dentin bio-composite via the extracted clattice parameters of the cHAp particles.

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X-ray diffraction measurements X-ray diffraction experiments were performed at the mySpot beamline of the BESSY II synchrotron light source (HZB - Helmholtz-Zentrum Berlin, Berlin, Germany). A (111)Si doublecrystal monochromator conditioned the incident X-ray beam and diffraction patterns were collected with a MarMosaic 225 (Mar USA, Evanston, IL, USA) with a 3072 x 3072 pixel flat-panel detector. Detector orientation and rotation, as well as sample-to-detector distances were determined using powdered corundum (grains < 50 µm) as a calibration standard. For ex situ line-scan experiments, an energy of 15 keV, sample-to-detector distance of 310 mm, and an X-ray beam size of 72 µm were used. The three complete tooth slices were immersed in pure water (DDW) for 36-48 h prior to performing high-resolution measurements. Each sample was mounted on an adhesive tape membrane (“Tesafilm”, Tesa, Norderstedt, Germany), covered with a thin cellophane sheet (50 µm) adhering with several drops of water, maintaining hydration during wet-state diffraction measurements. Following X-ray line-scanning, each sample was removed and placed in an oven at 125 °C for 1 h for complete drying and was then measured again. In each of the ex situ linescan experiments, a series of diffraction images were obtained at 200 µm increments at several heights on lines across the entire root cross sections, beneath the crown (see Figure 2). Patches of corundum standard were affixed on both sides (buccal and lingual) of each tooth and measured with the line scans. For in situ drying experiments, an energy of 18 keV, sample-to-detector distance of 347 mm, and a beam size of 25 µm were used. The four mid-root dentin slabs were measured following watersoaking in tap water for 24-48 h prior to synchrotron experiments. These samples were tightly fixed to a silver heating plate of a dedicated Linkam in situ testing chamber (THMS600; Linkam Scientific Instruments, Todham, UK) with a central X-ray beam entry point, and they were clamped in place by 8


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using a large stiff copper ring with a central window allowing X-ray radiation escape as well as laser radiation entry for Raman measurements (supplementary Figure S1). During the these measurements, the mid-section of each sample, corresponding approximately to mid-root dentin situated half way between cementum and the pulp was investigated by both X-ray and laser irradiation, applied in series (by moving the in situ sample chamber in and out of the X-ray beam). Each sample was first measured wet at room temperature, then following heat-drying (at 125 °C) and finally after annealing (at 250 °C). All heating and cooling were performed with a rate of 6 °C/min. All in situ measurements were confined to the X-ray hole in the silver Linkam heating plate and measurements were limited to the central region of the samples, corresponding to mid-root dentin situated between the cementum and the pulp. In each experimental stage, diffraction patterns were collected over a small rectangular grid, after which the setup was moved out of the X-ray beam for Raman spectroscopy (see below). To avoid beam radiation damage, each sample was measured in different non-overlapping points by moving the sample both laterally and along the tooth-root axis. Exposure times spanned 12 to 30 s, and multiple diffraction patterns (16 to 20) were collected at each state. The radiation dose for each diffraction pattern was estimated as previously described.34,36 The X-ray dose spanned 49 ± 11 kGy, remaining beneath the lower limit of damaging irradiation.39 In situ Raman spectroscopy Raman spectra were collected in each sample mounted for in situ testing, and were acquired after each set of XRD measurements in the wet, dry and annealed samples states. A Ventana-785-Raman high-sensitivity spectrometer (Ocean Optics, Dunedin, FL, USA) was used, and the sample was illuminated through the window in the copper holder (supplementary Figure S1) with a fiber-optic cable coupled to a stabilized diode laser (λ = 785 nm, Ocean Optics, Dunedin, FL, USA). The measurement spectral range spanned 300 to 2000 cm−1. 9



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Second harmonic generation imaging Second harmonic generation (SHG) imaging was used to visualize fibrillar collagen in the pristine and heat-treated dentin tissues. Collagen fibrils exhibit endogenous second harmonic generated signals arising from their well-known non-center-symmetric molecular structure.40,41 SHG is able to monitor changes in collagen fibril structure following protein denaturation upon heat treatment.42,43 Measurements were performed using a Leica SP5 II microscope (Leica Mikrosysteme Vertrieb GmbH, Wetzlar, Germany). The SHG signal was generated using a Spectra Physics Ti:sapphire laser (Mai Tai HP, Spectra Physics, Santa Clara, California, USA) with 100 fs pulse width at 80 MHz and wavelength of 910 nm. The SHG collagen signal was detected in the range of 450-460 nm. The excitation wavelength was optimized using rat tendon fascicles. Images were recorded using 40x and 63x water immersion objectives with numerical apertures of 1.1 and 1.2, respectively. SHG image stacks were recorded with 1 µm depth (z)-steps followed by measurements of the auto-fluorescence signal (800 nm excitation, 450-570 nm detection). Both SHG and auto-fluorescence signals were monitored in pristine samples that were then heat-treated at 125 °C and 250 °C. X-ray nano-tomography Three air-dried bar-shaped root dentin samples were scanned at the partial-coherence BAM-line imaging station44 of the BESSY II synchrotron light source (HZB, Berlin, Germany) using an X-ray energy of 15 keV. Datasets of 1200 phase contrast-enhanced radiographs were collected (2 s exposure times) with a sample-to-detector distance of 15 mm and using effective pixel sizes of 876 and 438 nm. Each sample was measured both air-dried and also after annealing at 220 °C for 1 h. The resulting projection images were normalized conventionally using empty-beam images and 3D volumes were reconstructed with PyHST (ESRF, Grenoble France). Corresponding reconstructions of the same samples imaged before and after heat-treatment were co-aligned and analyzed using Fiji (1.48b).45 10


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Scanning electron microscopy Fracture surfaces of dentin were imaged using the variable pressure mode of an FEG-SEM Zeiss Supra VP 55 (Carl Zeiss GmbH, Oberkochen, Germany) at an acceleration voltage of 2 kV (without coating) and in-chamber vacuum of 1.3·10-6 Torr. Data analysis X-ray diffraction The software package XRDUA (V.6432)46 was used to analyze the diffraction patterns including refinement of the sample-to-detector distance, beam center, rotation and tilt angle calibrations. Diffraction patterns of dentin showed well-defined (002) Debye rings, which allowed us to extract the cHAP c-axis lattice parameter, crystallite size, and averaged microstrain fluctuations. For this purpose, azimuthal integration along the (002) cHAP Debye rings was followed by analysis of the corresponding one-dimensional diffraction intensity profiles I(2θ) as a function of the scattering angle 2θ. For further structural analysis, the I(2θ) profiles were fitted using a Voigt function (see Figure 3) with custom Octave (V. 3.2.4) fitting code. The c-lattice parameters of cHAP were determined from the fitted peak positions and then converted to strain values, ε, using Equation (1): ε = (ct- cwet)/cwet

(1)

where ct and cwet are the c-lattice parameters measured in the heat-treated and pristine (wet) samples, respectively. The mineral stress, σ, was calculated as: σ = Eε

(2)

where E = 96 GPa is the Young’s modulus of biogenic cHAP in dentin along the c-axis.47 11



The Voigt function is a convolution of Gaussian and Lorentzian functions. Both Gaussian, WG, and Lorentzian widths, WL were therefore separately determined, and the averaged microstrain fluctuations, δav and crystallite sizes, L,32 were extracted as: δav= WG / [4(2ln2)1/2 .tanθ]

(3)

L = 2d tanθ / WL

(4)

where d is the (002) cHAP d-spacing and θ is half of the scattering angle, 2θ. Due to the usage of a double-crystal monochromator, the instrumental contribution to the diffraction profile broadening was negligible.

Experiment Gaussian Voigt

Intensity (a.u.)

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10.8

11.3

2-theta (deg)

11.8

Figure 3. An example of fitting the azimuthally integrated (002) cHAP diffraction profile (data represented by black dots) to a Voigt function. Note excellent fit of green dashed line. For comparison, a Gaussian fit (red line) is shown, highlighting the considerable mismatch between this function and the data as seen mainly at the profile tails. The Voigt fit is thus better suited to correctly extract crystallite sizes and averaged microstrain fluctuations from, respectively, the Lorentzian and Gaussian contributions to the diffraction profile.32

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Tomography and SHG image analysis Both SHG and tomography images were evaluated by FFT (fast Fourier transform). For SHG analysis, the signal of collagen and its almost-orthogonal spatial relationship to the dentin tubules was revealed in the 2D power spectra of each sample. For the tomographic data, analysis was performed on 16 sub-volumes each containing approximately 10x10 tubules. Matching 3D data pairs were extracted from the high-resolution tomograms of the same sample, imaged both prior to and following annealing. Each volume pair was aligned along the mean axis of the tubules, and the data was binarized using the Otsu method of Fiji. In a following analysis step, the inter-tubule spacing (frequency spectrum) was calculated for each cross-sectional slice in every sub-volume, as determined by 2D FFT, revealing the average distance between tubules both across and along the sample long axis (root-crown direction). The spatially-varying inter-tubule spacing was calculated from a polar transform of each FFT power spectrum, from which plots of intensities of the reciprocal lateral versus axial (root-crown) tubule spacings were generated, both before and after heating. For each such plot, maxima were determined separately for tubules across and along the reciprocal sample width/height. In this manner, inter-tubular spacing was obtained for each of the 16 sub-volumes containing 150~180 slices from multiple zones of the sample, both closer to and farther away from the pulp. The extracted tubule densities were compared to previous reports.11 By plotting a pairwise correlation of tubule spacings from each slice, we determined the overall sample shrinkage. For additional confirmation, the external dimensions of dentin samples in three other tomographic data sets were measured visually at several sample locations to within several microns. Corresponding breadth and depth measurements of each root sample before and after heat treatment were also pairwise correlated, and used to determine volume changes of three different samples.

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RESULTS AND DISCUSSION cHAP nanoparticlec-axis lattice parameters and strains The ex situ XRD line-scan measurements of the fully hydrated and dry states after annealing at 125 °C of three teeth, yielded the c-lattice parameters at different locations in dentin, from the outer cementum layer, inwards towards the pulp. The c-lattice parameters of the cHAP nano-particles in the three samples, each measured on two different sides of each tooth are shown in Figure 4a. In the pristine wet state, the c-lattice parameter decreases more or less monotonically, from about 6.895 Å near cementum to ~ 6.885 Å near the pulp. The crystal c-lattice parameter in the dry state is nearly 0.02 Å smaller than the observations in the same tooth regions in the wet state, yielding c-lattice parameters of 6.875 Å ~ 6.865 Å. A clear difference is thus observed between each of the samples in the wet and dry states. In both these states, the outermost points, corresponding to cementum on the outside and deep, possibly disorganized dentin inside, reveal a slightly smaller difference in c-lattice parameter as compared with the bulk of dentin (Figure 4a).

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Figure 4. (a) Plots of the c-lattice parameter of the three different root samples (averaged buccal and lingual sides) with respect to the spatial position of cementum and pulp. Blue and red lines represent the average of all three samples for wet and dry measurement states, respectively. Arrows indicate the c-lattice parameters for 0 wt% and 4 wt% carbonated apatites reported in the literature.48 The decrease in c-lattice parameter suggests that in human teeth there is a reduction in the apatite carbonate content as a function of root maturation. A schematic representative cross-section of root dentin (with cement on one edge and the pulp on the other) is depicted on the left-hand side. (b) Lattice strain/stress in mineral particles across root dentin, calculated by means of Equations (1) and (2), averaging the results for three different teeth (error bars show standard deviations). The strain values are derived from measurements at room temperature after heat treatment of the samples at 125 °C and by taking each initial room temperature measurement as the reference. (c, d) Crystallite sizes L (c) and averaged microstrain fluctuations δav (d) across dentin samples, as derived from the fits of experimental diffraction profiles to Voigt functions. Error bars represent the standard error of the mean, based on n= 3 samples. Average lattice strains calculated for the different samples using Equation (1) revealed significant deformation in particles in the dry samples as compared with the initial, wet sample state. The strain and stress values obtained across the roots of the three different samples on both buccal and lingual sides, are plotted in Figure 4b (error bars depict standard deviations). In most tooth-root regions the 15



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hydration-mediated strain magnitude slightly exceeds 0.3 % in compression, with a standard deviation of about 0.03 %. The strains in the outer near-cementum points or inner secondary dentin are somewhat lower. With these values and based on Equation (2), we find the corresponding drying-mediated compressive stress of most regions of bulk dentin to be about σ ≈ 300 MPa. Microstrain fluctuations and crystallite size Crystallite sizes, L, along the c-axis of the cHAP particles, as well as averaged microstrain fluctuations, δav, change with increasing distance from cementum. The magnitudes of δav are seen to be strongly affected by dehydration. The changes in the magnitudes of L and, δav along the cement-pulp trajectory are plotted in Figure 4c and 4d for both the water-saturated and dry sample states, averaged for the three samples. A gradual decrease in L, from nearly 35 to 25 nm, is observed from the outer cementum regions towards the pulp, with no observable difference between the wet and dry states of the teeth. Microstrain fluctuations on the other hand, appear to be very uniform across all samples until approximately 1.5 mm deep of the cementum, with δav= 0.25±0.02 % in the wet state and δav= 0.37±0.03 % in the dry state, after water removal at 125 °C. Closer to the pulp where the dentin structures become less well organized, e.g. in secondary dentin, a substantial increase in δav is observed. Overall, the averaged microstrain fluctuations that we found in human dentin are within the range of 0.2-0.5 %, slightly smaller than values reported for bovine dentin.28 Mean wet-dry nanoparticle characteristics Averaged X-ray based microstructural characteristics for all teeth are shown in Table 1, summarizing drying-induced mean lattice strains, crystallite sizes and microstrain fluctuations. This includes the three samples that were removed from the beam for drying in an oven, as well as the four samples that were dehydrated in situ. While some variability is seen between different teeth, the overall average findings mirror the main observations seen by the line scans. We find a 0.3~0.4 % compressive 16


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strain due to dehydration; Voigt fitting shows that crystallite sizes in the dentin central region span L = 30~32 nm (remaining unchanged following mild heating at 125 °C and following in situ annealing at 250 °C, as expected). A significant nearly twofold average microstrain-fluctuation increase always accompanies drying (δav≈ 0.25 % in the water-saturated samples to δav≈ 0.4~0.45 % after dehydration). Table 1. Mean dehydration strain, crystallite sizes (length), and averaged microstrain fluctuations determined by XRD in 7 different teeth (± standard deviation). “Dry” refers to the 125 °C mildly heated state. Sample

Strain (%)

Line scans: LH1 -0.34 ± 0.02 LH2 -0.31 ± 0.02 LH3 -0.28 ± 0.03 In situ heating: T4S2 -0.45 ± 0.08 T6S1 -0.29 ± 0.04 T1S2 -0.30 ± 0.09 T5S2 -0.36 ± 0.12

Sample average

-0.33 ± 0.06

Crystallite size (nm) WET DRY 250 °C

Microstrain fluctuation (%) WET DRY 250 °C

33 ± 2 34 ± 1 33 ± 2

33 ± 2 34 ± 1 35 ± 2

-

0.23 ± 0.02 0.24 ± 0.02 0.27 ± 0.05

0.39 ± 0.06 0.36 ± 0.02 0.36 ± 0.02

-

33 ± 2 30 ± 3 32 ± 1 33 ± 1

32 ± 3 29 ± 2 30 ± 2 30 ± 3

30 ± 2 27 ± 3 29 ± 1 31 ± 1

0.27 ± 0.01 0.26 ± 0.01 0.26 ± 0.01 0.25 ± 0.01

0.43 ± 0.05 0.50 ± 0.09 0.43 ± 0.08 0.41 ± 0.07

0.47 ± 0.04 0.60 ± 0.07 0.47 ± 0.06 0.44 ± 0.05

33 ± 1

32 ± 2

29 ± 2

0.25 ± 0.02

0.41 ± 0.05

0.50 ± 0.07

Monitoring collagen presence by Raman spectroscopy and SHG imaging Raman measurements carried out at room temperature before and after heat treatment at 125 °C, show similar spectral features (see Figure 5), attesting to the presence of intact collagen in the wet and dry sample states. Collagen produces characteristic amide I and III bands (marked by the symbol (*) in Figure 5) located, respectively, at 1616–1720 cm-1 and 1243–1320 cm-1.49 The peak, associated with the PO4 band (marked with (+)) is located at 960 cm-1, whereas peaks, assigned to PO (marked by (#)), appear at 590 cm-1 and 430 cm-1. Note that all typical dentin spectral features remain unchanged between the wet and dry states of the samples, despite heating, which confirms collagen endurance at 17



125 °C. In contrast, Raman measurements, acquired following in situ annealing at 250 °C, reveal extensive collagen destruction. This can be seen by the featureless Raman spectra (see inset in Figure 5), which was accompanied by significant fluorescence and frequent detector saturation completely masking the apatite PO4 band that is not visible anymore (inset in Figure 4). These observations are in line with previous calorimetry reports of dentin collagen destruction occurring at temperatures exceeding 150 °C.50

25°C 125°C Intensity (a.u.)

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200

# #

+

250°C

200

*

700

1200

Raman Shift

2200

* 1700

2200

(cm-1)

Figure 5. Raman spectra of dentin collected at room temperature in wet and dry (after heat treatment at 125 °C) state. Peaks, marked by the symbols (#) and (+) are PO and PO4 signals respectively. Amide I and III bands, marked by symbol (*), confirm the presence of intact collagen. The inset shows a spectrum of the same sample after heating to 250 °C in situ. No signs of collagen are to be seen in the strongly fluorescence saturated signal, that masks the strong PO4 peak. SHG provided additional information on the collagen state following heat treatment, as the collagen signal vanishes upon annealing at 250 °C. Four different samples all demonstrate the same patterns, and typical examples are shown for one of the samples imaged in the native pristine state, after drying at 125 °C and after annealing at 250 °C (see Figure 6). Prior to collagen destruction, silhouettes of tubules are seen running horizontally, whereas collagen fibril traces appear to course almost orthogonal 18


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to the tubules, well-fitting previous descriptions of native dentin structure.4 The insets in each SHG image (Figure 6a and 6b) show the corresponding 2D FFT power spectra, where vertical lines correspond to the repeated occurrence of tubules, and the horizontal lines correspond to the overall almost orthogonal collagen fiber orientations. In contrast, SHG images of four different samples after annealing at 250 °C revealed no traces of collagen patterns, as seen in both SHG and FFT images (e.g. Figure 6c). Collagen is thus destroyed in dentin following heat treatment at temperatures above 200 °C, and we are thus confident that collagen remained intact during drying at 125 °C in all our experiments.

19



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Figure 6. Second harmonic generation (SHG) confocal microscopy imaging of human dentin. (a) Wet pristine samples reveal the orthogonal spatial relationship between the tubules (with a slanting approximately horizontal orientation, as highlighted by the dashed lines) and vertical traces of the 2nd harmonic signal of the collagen fibers. The inset shows FFT power spectra that clearly reveal the (inversely related) almost horizontal and vertical orientations of the repeating structural features of dental tubules and collagen fibrils. (b) Following drying by mild heat treatment at 125 °C, both tubules and collagen fibrils are still visible. The SHG signal is proof for 20


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the presence of significant amounts of intact collagen in the structure, where it maintains the orthogonal relationship to the tubule orientations, as seen again by the Fourier transform inset. (c) Following annealing at 250 °C, no SHG signal is obtained in neither real space nor in the Fourier domain.

Macroscopic observations in 3D A rendering of the three-dimensional tomographic data of an air-dried sample scanned both before and after annealing at 220 °C for 75 min reveals the tubule arrangements of dentin (see Figure 7). None of the samples showed any visible cracks or other signs of macroscopic damage due to drying. Corresponding regions in the sample before and after annealing could therefore be well co-aligned (Figure 7c, see supporting information movie 1 and 2). Examples of typical, closely matching crosssections in one of the air-dry and heat-treated samples are given in Figure 7b and 7c. The insets in Figure 7b and 7c show typical 2D power spectra. Note that frequency profiles were azimuthally integrated independently for each slice, aligned orthogonal to the tubule axes, to obtain the independent frequency spectrums corresponding to the repeating tubule occurrence in 2 orthogonal orientations: along and also across the crown-root macroscopic sample axis. In many regions, a strong anisotropy was observed (appearing in the power spectra as oval rings), attesting to a marked difference in the average distance between tubules in the root-crown (axial) direction as compared with the radial sample orientation. Nevertheless, shrinkage appears to be uniform in the different sub-volumes, as seen in the pairwise correlations of inter tubule distances of identical regions in each slice in the 3D data before and after annealing, shown in Figure 7d. Shrinkage of the sample is observed by noting the difference from unity of the linear fit to the data (black line with slope of 0.977 and R² equals 0.8722). The dashed line plotted as a guide for the eye corresponds to a perfect correlation of 1. From this analysis we conclude that the annealed samples exhibit a slight shrinkage of ~2.3 % with respect to the 21



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measurement (air-dry) state. Additional manual estimates of the outer dimensions of three samples tomographically imaged before and after heat-treatment, revealed a similar shrinkage based on changes in width and thickness. Figure 7e shows a correlation plot through all breadth/width measurements performed in three different samples (black line with slope of 0.978 and R² equals 0.9997), revealing a typical annealing shrinkage of 2.2 % in all air-dried root-dentin samples

22


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Figure 7. (a) Three-dimensional sub-micron phase-contrast enhanced microtomography: reconstruction of a human root dentin sample following annealing at 220 °C for 75 min. The tubule silhouettes are seen to follow a course from the outer root surface deep into the root/pulp interior. Such 3D data forms the basis of the tubule density analysis. (b, c) Typical cross-sectional slices of an air-dry and a 220 °C annealed sample of root dentin (imaged with a 438 nm effective pixel size, 15 keV, 10 mm camera-sample propagation distance). Insets in (b) and (c) represent power spectra of FFT planes in the 3D FFT data of the dry and annealed states. Radial integration of axial and lateral anisotropic (oval) intensities in the FFT spatial frequencies produce profiles in which the maximum intensity can be converted into the reciprocal radial or axial tubule spacing, respectively. Analysis revealed the mean inter-tubule distance in the microstructure which in the root spans 4~9 µm, varying in different heights along the root-crown axis. (d) Pairwise plot of corresponding axial/lateral tubule spacings obtained in each slice both before and after annealing. The regression (black) line reveals a slope of 0.977, corresponding to a more or less uniform shrinkage of ~2.3 %. The dashed (red) line is a guide for the eye and corresponds to a correlation of 1. (e) Shrinkage of different annealed air-dried dentin samples by direct 3D measurements of breadth and width in microtomography reconstructions: the figure shows the correlation of multiple measurements of breadth and width of 3 different samples, measured both prior to and following heat-treatment. The slope of the regression line is equal to 0.978. A line depicting a correlation ratio of 1 is plotted as a guide for the eye. The air-dry (ambient ~35 % RH equilibrated) samples thus undergo a shrinkage of ~2.2 %. Our results provide insight into some key attributes of the cHAP nanocrystals in dentin, determined under a wide range of possible hydration-induced osmotic pressures to which this tissue might be exposed. By measuring samples under conditions spanning full hydration to complete dehydration we reveal the full possible range of interactions of the mineral particles with water and collagen, which we believe represent the maximal spectrum of realistic functional loading of this biocomposite. Water plays an especially important role in this context. Water drives osmotic-pressure elongation of collagen molecules,37 and presumably defines the swollen, gel-like state of the organic matrix,51 which is attained following saturation with salt-free water, as we conducted in our experiments. At the same time, collagen contraction under drying is well-documented and was shown to be important for the normal shape and function of collagen.52–55 Collagen, the main protein found in the dentin matrix, may undergo shrinkage that is large enough to be effectively used in 23



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mechanochemical engine models56 and appears to generate significant strain/stress in the mineral particles upon drying (Figure 4b). Recent results employing osmotic-pressure-induced tensile forces in rat tendon collagen55 clearly show the substantial extent to which collagen fibrils contract when dehydrated. The present study quantifies the magnitude of such compressive strains and stresses engendered by collagen in the tightly attached cHAP crystallites of pristine human dentin. Simply changing the water content of dentin activates a 'collagen engine' such that due to protein contraction, the mineral particles experience nearly 300 MPa in compression, see Figure 4b, as long as the collagen remains intact. This process is schematically depicted in Figure 8. The osmotic-pressure-driven contraction of the collagen fibrils under drying55 generates forces that are effectively transmitted to, and sustained by the mineral particles in dentin.

24


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Figure 8. Schematic representation of the working mechanism of the dentin composite (not drawn to scale, the d-spacings along the c-axis of the apatite crystals are depicted by the vertical planes), where cHAP and collagen interact in the presence of water: (a) in the fully hydrated state, water saturates the composite adhering to both the mineral and protein phases, and the collagen attains its maximum swollen state such that the attached cHAP crystal c-lattice parameter is at a maximum; (b) after heat treatment at 125 °C, much of the surface-bound water is lost and as the collagen molecules contract, the mineral particles undergo compression-like deformation due to the strong interaction with the shrinking collagen. The full range of stresses that we find is on the same order as results obtained for mineral crystallites in turkey tendon and bone.38 This stress is far greater than the stresses expected in the mineral within dentin under mastication loads (15~20 MPa was measured in teeth during normal mastication)57 where the external forces in teeth are on the order of 150 N.58 Thus, even the highest reported bite-forces of up to 1000 N59 cannot reach the full range of stresses that the cHAP particles are able to sustain, originating in osmotic pressure. The highest reported tensile strength for hydroxyapatite is about 200 MPa60 whereas the highest reported compressive strength is about 900 MPa,60 although most accepted values are below 300-400 MPa.61–63 We contend that the stress of 300 MPa demonstrated in the dentin nanoparticle crystals due to dehydration in our XRD measurements is rather high and is mediated by the strong mineral-collagen link. This directly defines the range of loads that can, in principle, be repeatedly sustained by dentin in vivo. Reports of mineral strains on the order of 1 % in compression during dentin failure under extreme mechanical overload27 suggest that the dentin nanocomposite has a design safety factor of about 3, which presumably offers some additional protection against rare events of extreme overload (e.g. when unexpectedly one chews forcefully on to a piece of bone or rock). In all teeth measured, we found a twofold increase in the averaged microstrain fluctuations (δav) following dehydration. In the nanometer-sized cHAP crystallites of dentin, microstrain fluctuations are certainly mediated by the water molecules surrounding the mineral nano-particles. It is likely that the 25



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protein contribution to this effect is negligible, as there is essentially no difference between δav in the heat-dried (125 °C) and annealed (250 °C) states. Our results show that the protein still remains essentially undamaged at 125 °C, despite the relatively high temperature and the water loss. This is clearly seen from both direct in situ Raman and SHG microscopy measurements (see Figures 5 and 6) and is also known from previously published indirect reports.50,64,65 It appears therefore that, in addition to introducing large macroscopic strain in the crystals (Figure 4b), removal of water results in strong inhomogeneous local deformations within the environment near the mineral nanocrystals. Although not fully understood, the significant increase in microstrain fluctuations might arise during dehydration due to Laplace pressure interactions between water and the surrounding stiff matrix,66 which might be caused by extraction of water that is present on the outer surfaces of the mineral particles in the natural state.67,68 Surface water is known to play a key role in ordering and binding of the cHAP/collagen structures69 and drying therefore causes a major increase in the magnitudes of the averaged microstrain fluctuations, possibly by increasing the near-surface lattice disorder in the cHAP crystallites. Measurements and careful analysis of the diffraction profile broadening allowed us to extract local crystallite lengths and, on this basis, draw additional conclusions regarding the design principles of human dentin. We speculate that the small crystal lengths of 30-35 nm along the mineral platelet long axis (see Figure 4c) play a key role in allowing the mineral particles of dentin to elastically sustain an impressive range of stresses. The fact that we observe no changes in crystallite sizes due to any of the heat treatments in our experiments suggests that they do not break-up due to the extensive collagen contraction that we induce. Indeed, according to theoretical predictions,70 for particles with Young’s modulus, Em ≈ 100 GPa, a critical length-scale of 30 nm renders the particles insensitive to flaws, at least in tension, and probably more so in compression. Below this critical length, strength approaches its theoretical limit, σth, which for ideal crystals is σth = Em/30 ≈ 3 GPa. Dentin cHAP crystals have a 26


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Young’s modulus of 96 GPa,47 and a length of about 30 nm, and are therefore exceedingly strong, well suitable to sustain large stresses. In order to correctly extract the crystallite sizes, we meticulously separated Gaussian and Lorentzian contributions to the XRD profile shapes, by fitting them to Voigt functions.32 Unlike TEM observations that may be affected by lack of particle disaggregation,31 crystallite sizes determined by X-ray are due to an average signal produced by internal scattering within the coherent crystalline domains of the cHAP crystals. These are possibly only domains that exist within larger ~100 nm long particles found within the mineralized collagen fibers, reported for many bone-mineral based tissues. We therefore guess that 3 such domains, detected by X-ray, combine to form larger particles detected by TEM. We observe a gradual, reproducible, 33 % decrease in crystallite sizes for dentin closer to the pulp (see Figure 4c). From the average of all measurements shown in Table 1, we found a small change in the mean crystallite sizes when our samples were heated to 125 °C and 250 °C, corresponding to the strain observed in the c-lattice parameter. It is known from other authors that for dental cHAP, an increase in crystallite sizes through thermodynamically driven crystal re-growth at elevated temperatures is expected to take place only above 600 °C.71–73 Noteworthy, the 25~35 nm crystallite sizes that we found (L values) agree well with TEM data15 and various other X-ray diffraction results reported for dentin,27 and are well in line with the magnitudes published for the mineral particles of bone.31,74–76 The gradient that we observe may explain the range of crystal sizes reported for dentin in the literature, where unfortunately most authors did not report the precise location from which their samples were harvested. Note that in nano-crystalline materials in general, an inverse relationship exists between microstrain fluctuations δav and crystallite size L, i.e. lower averaged microstrain fluctuations are observed in larger crystals and vice versa77 which we also found in dentin (Figure 4d). An important observation of our ex situ experiments is a gradual, reproducible change in the clattice parameter of the cHAP particles across root dentin. The crystals situated closer to the pulp have 27



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a lattice constant of 6.885Å which is 0.15 % smaller than those found in the early-formed tissue, on the outer margins of the root, abutting cementum. This reduction in lattice parameter size might be related to a decreased carbonate content during tissue genesis48 suggesting that outer mineralized particles contain about 4 % carbonate, whereas less carbonate may be present in regions near the pulp. The clattice parameters of cHAP with 4 % and 0 % carbonate content are marked in Figure 4a. We speculate that the carbonate content of the crystallites is related to the physical dimensions of the tablet shaped mineral particles: we find a ~30 % reduction in the crystallite length for particles closer to the pulp, echoing observations by Märten et al.8 who found a similar 30 % reduction in particle thickness (measured as the T parameter by SAXS) as compared to the outer regions of dentin. Conceivably the increased volume to surface ratio of the particles on the outer regions of dentin makes it easier for the larger particles to accommodate higher percentages of carbonate substitutions in the cHAP lattice. We are confident that dehydration by heating to 125 °C did not cause any significant damage to collagen nor to the bond between the collagen molecules and the mineral. This however can only be shown indirectly, by inducing irreversible damage by heat treatment above 190 °C.50 We observed that such heat treatment leads to collagen destruction as evidenced by a complete signal loss in SHG images (Figure 6c) coupled with a major increase in the SHG fluorescence signal (data not shown). Corroborative evidence is also provided by the Raman results that become featureless following heat treatment at 250 °C (inset, Figure 5). From our tomography measurements revealing the tubules in root dentin, we observe the effects of heating of the air-dried samples resulting in removal of remaining (ambient) water in the dentin samples (see Figure 7). Based on 3D image analysis (Figure 7d and 7e), dentin shrinkage estimated by both the decrease in mean distance between tubules and from multiple correlated measurements of sample width and breadth is about 2.3 %. This shrinkage observed by the aid of synchrotron phase contrast-enhanced microtomography is consistent with previous direct size measurements of heat-treated bone and tooth samples.73 We conclude that at temperatures up to 250 28


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°C, sample shrinkage is almost entirely related to the removal of water, with relatively small amounts of carbonization products (e.g. CO2) lost from the organic constituents. Our findings allow us to draw additional conclusions about the functional attributes of the mineral in dentin. The more or less constant crystallite sizes extracted from our in situ XRD measurements in wet samples, following drying (at 125 °C) and following annealing (at 250 °C) summarized in Table 1 give clear indication that the biogenic apatite particles in dentin do not contain significant amounts of intercalated organic molecules, known to exist in other biomineralized structures, such as e.g. mollusk shells.78 Any protein disintegrating during heating presumably resides outside of the coherent crystalline domains of dental cHAP crystals. Water on the surfaces of cHAP nanoparticles in mineralized collagen-based tissues is thought to play an important role in maintaining the mineral stability, preventing the nanoparticles from fusing while allowing the formation of links to neighboring protein molecules.68,69,79 Our results suggest that the averaged microstrain fluctuations in the cHAP particles induced by dehydration are due mainly to a loss of water on free surfaces, and not due to loss of attachments sites with the contracting protein matrix.38 Despite the water loss, most of the mineral is still attached to the surrounding organic matrix, and is consequently strongly compressed when samples are dehydrated at 125 °C (Figure 4b and see schematics in Figure 8). Densification of the nanocomposite due to dehydration without damage to the protein component may explain the increased stiffness and strength observed in other studies where dentin mechanical properties were reported following ethanol dehydration80 as well as heat-drying.64 Thus, the mineral nanoparticle compressive stress observed in dentin contributes to the improved macroscopic mechanical resistance to damage-propagation, as previously suggested.36 The small shrinkage that macroscopic, dry samples undergo during heating above 200 °C, as demonstrated by our tomographic data, may be due in part to initial organic decomposition or due to further loss of water that remains entrapped in the air-dried nanostructure. Interestingly, it has been shown by nuclear magnetic resonance (NMR) measurements 29



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that only about ⅔ of the water normally present in bone tissues is removed following heat treatment to 225 °C.68 The brownish color of our annealed samples attests to partial disintegration of the protein and carbonization. However the uniform shrinkage of the mineralized matrix observed both along and across the tubules is probably due to removal of the highly-bound water, rather than due to loss of organic component during our heat treatments. CONCLUSIONS

The water/collagen/mineral interactions coupled with the tiny sizes of the cHAP crystallites directly contribute to the evolutionary optimization of tooth dentin to reliably resist the loads to which it is exposed. Presumably this design helps dentin sustain a large range of repeated mastication stresses, rendering teeth well suited for enduring cyclic mechanical loads throughout decades of elastic functioning in the mouth. Our work revealed water-induced and heat-treatment-mediated effects on particle strain/stress, averaged microstrain fluctuations, and sizes of the cHAP nanoparticles in human tooth dentin. Though our experimental results were not obtained under normal, physiological functional conditions of teeth, they allow us to draw the following major conclusions:

1. There is a notable gradient in the c-lattice parameter of the mineral particles of dentin, determined in different parts of the root structure, from the outer regions abutting cementum, to the inner regions approaching the pulp. We hypothesize that this trend is due to reduced carbonate content in later-formed dentin tissue closer to the pulp. 2. cHAP mineral particles of dentin deform significantly due to osmotic pressure following dehydration and can sustain stresses spanning ~300 MPa when dentin is dehydrated at 125 °C. Under these conditions, dentin nanoparticles experience a uniform 0.3 % compressive strain. It remains unclear to what extent osmotic pressure mediates dentin deformation in vivo. 30


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3. cHAP particles in root dentin have lengths of about 35 nm in the outer root regions and they are 30 % shorter, about 25 nm, in the deeper regions of the root approaching the pulp. The sizes of all crystallites remain practically unchanged in both hydrated and dehydrated states. 4. Dehydration induces a nearly twofold increase in the averaged microstrain fluctuations of the cHAP mineral particles.

SUPPORTING INFORMATION AVAILABLE: Literature survey of tooth mineral particle lengths, widths and thickness. Optical pictures of the experimental in situ setup. 3D reconstruction movies of dentin obtained by tomography before and after heat treatment. This materials is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Authors: *e-mails : [email protected]; [email protected]; [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS The Helmholtz-Zentrum Berlin (Bessy II) is gratefully acknowledged for beamtime allocation; special thanks to Wolfgang Wagermaier and his colleagues in MPIKG for making the high-resolution ex situ experiments possible. We thank Vittorio Becker with Voigt data-processing assistance. J-B.F., C.F. and P.Z. thank the DFG for financial support through SPP1420. E.Z. acknowledges partial financial support by the Shore Research Fund in Advanced Composites (Technion). REFERENCES (1) (2) (3)

Fratzl, P. Collagen: Structure and Mechanics, 1st ed.; Springer Science+Business Media: New York,NY, USA, 2008. Currey, J. D. Bones: Structure and Mechanics; Princeton University Press: Princeton, NJ, USA, 2002. Lubisich, E. B.; Hilton, T. J.; Ferracane, J. Cracked Teeth: A Review of the Literature. J. Esthet. Restor. Dent. 2010, 22, 158–167. 31



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(6)

(7) (8) (9)

(10) (11) (12) (13) (14) (15) (16)

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Water-Mediated


Collagen

and

Mineral

Nanoparticle

Interactions

Guide

Functional Deformation of Human Tooth Dentin Jean-Baptiste Forien, Ivo Zizak, Claudia Fleck, Ansgar Petersen, Peter Fratzl, Emil Zolotoyabko, Paul Zaslansky

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Water-Mediated Collagen and Mineral ... - ACS Publications

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