Variability in the elastic properties of bovine dentin at multiple length scales

Crossing length scales: X-ray approaches to studying the structure of biological materials

Biological materials have outstanding properties. With ease, challenging mechanical, optical or electrical properties are realised from comparatively `humble' building blocks. The key strategy to realise these properties is through extensive hierarchical structuring of the material from the millimetre to the nanometre scale in 3D. Though hierarchical structuring in biological materials has long been recognized, the 3D characterization of such structures remains a challenge. To understand the behaviour of materials, multimodal and multi-scale characterization approaches are needed. In this review, we outline current X-ray analysis approaches using the structures of bone and shells as examples. We show how recent advances have aided our understanding of hierarchical structures and their functions, and how these could be exploited for future research directions. We also discuss current roadblocks including radiation damage, data quantity and sample preparation, as well as strategies to address them.

The elasto-plastic nano- and microscale compressive behaviour of rehydrated mineralised collagen fibres

The hierarchical design of bio-based nanostructured materials such as bone enables them to combine unique structure-mechanical properties. As one of its main components, water plays an important role in bone's material multiscale mechanical interplay. However, its influence has not been quantified at the length-scale of a mineralised collagen fibre. Here, we couple in situ micropillar compression, and simultaneous synchrotron small angle X-ray scattering (SAXS) and X-ray diffraction (XRD) with a statistical constitutive model. Since the synchrotron data contain statistical information on the nanostructure, we establish a direct connection between experiment and model to identify the rehydrated elasto-plastic micro- and nanomechanical fibre behaviour. Rehydration led to a decrease of 65%-75% in fibre yield stress and compressive strength, and 70% in stiffness with a 3x higher effect on stresses than strains. While in agreement with bone extracellular matrix, the decrease is 1.5-3x higher compared to micro-indentation and macro-compression. Hydration influences mineral more than fibril strain with the highest difference to the macroscale when comparing mineral and tissue levels. The effect of hydration seems to be strongly mediated by ultrastructural interfaces while results provide insights towards mechanical consequences of reported water-mediated structuring of bone apatite. The missing reinforcing capacity of surrounding tissue for an excised fibril array is more pronounced in wet than dry conditions, mainly related to fibril swelling. Differences leading to higher compressive strength between mineralised tissues seem not to depend on rehydration while the lack of kink bands supports the role of water as an elastic embedding influencing energy-absorption mechanisms. STATEMENT OF SIGNIFICANCE: Characterising structure-property-function relationships in hierarchical biological materials helps us to elucidate mechanisms that enable their unique properties. Experimental and computational methods can advance our understanding of their complex behaviour with the potential to inform bio-inspired material development. In this study, we close a gap for bone's fundamental mechanical building block at micro- and nanometre length scales. We establish a direct connection between experiments and simulations by coupling in situ synchrotron tests with a statistical model and quantify the behaviour of rehydrated single mineralised collagen fibres. Results suggest a high influence of hydration on structural interfaces, and the role of water as an elastic embedding by outlining important differences between wet and dry elasto-plastic properties of mineral nanocrystals, fibrils and fibres.

Synchrotron X-ray Studies of the Structural and Functional Hierarchies in Mineralised Human Dental Enamel: A State-of-the-Art Review

Hard dental tissues possess a complex hierarchical structure that is particularly evident in enamel, the most mineralised substance in the human body. Its complex and interlinked organisation at the Ångstrom (crystal lattice), nano-, micro-, and macro-scales is the result of evolutionary optimisation for mechanical and functional performance: hardness and stiffness, fracture toughness, thermal, and chemical resistance. Understanding the physical-chemical-structural relationships at each scale requires the application of appropriately sensitive and resolving probes. Synchrotron X-ray techniques offer the possibility to progress significantly beyond the capabilities of conventional laboratory instruments, i.e., X-ray diffractometers, and electron and atomic force microscopes. The last few decades have witnessed the accumulation of results obtained from X-ray scattering (diffraction), spectroscopy (including polarisation analysis), and imaging (including ptychography and tomography). The current article presents a multi-disciplinary review of nearly 40 years of discoveries and advancements, primarily pertaining to the study of enamel and its demineralisation (caries), but also linked to the investigations of other mineralised tissues such as dentine, bone, etc. The modelling approaches informed by these observations are also overviewed. The strategic aim of the present review was to identify and evaluate prospective avenues for analysing dental tissues and developing treatments and prophylaxis for improved dental health.

Nanomechanical variability in the early evolution of vertebrate dentition

Conodonts are an extinct group of primitive jawless vertebrates whose elements represent the earliest examples of a mineralized feeding apparatus in vertebrates. Their relative relationship within vertebrates remains unresolved. As teeth, conodont elements are not homologous with the dentition of vertebrates, but they exhibit similarities in mineralization, growth patterns, and function. They clearly represent an early evolutionary experiment in mineralized dentition and offer insight into analogous dentition in other groups. Unfortunately, analysis of functional performance has been limited to a handful of derived morphologies and material properties that may inform ecology and functional analysis are virtually unknown. Here we applied a nanoscale approach to evaluate material properties of conodont bioapatite by utilizing Atomic Force Microscopy (AFM) nanoindentation to determine Young's modulus (E) along multiple elements representing different ontogenetic stages of development in the coniform-bearing apparatus of Dapsilodus obliquicostatus. We observed extreme and systematic variation in E along the length (oral to aboral) of each element that largely mirrors the spatial and ontogenetic variability in the crystalline structure of these specimens. Extreme spatial variability of E likely contributed to breakage of elements that were regularly repaired/regrown in conodonts but later vertebrate dentition strategies that lacked the ability to repair/regrow likely required the development of different material properties to avoid structural failure.

Collagen Fibril Orientation in Tissue Specimens From Atherosclerotic Plaque Explored Using Small Angle X-Ray Scattering

Atherosclerotic plaques can gradually develop in certain arteries. Disruption of fibrous tissue in plaques can result in plaque rupture and thromboembolism, leading to heart attacks and strokes. Collagen fibrils are important tissue building blocks and tissue strength depends on how fibrils are oriented. Fibril orientation in plaque tissue may potentially influence vulnerability to disruption. While X-ray scattering has previously been used to characterize fibril orientations in soft tissues and bones, it has never been used for characterization of human atherosclerotic plaque tissue. This study served to explore fibril orientation in specimens from human plaques using small angle X-ray scattering (SAXS). Plaque tissue was extracted from human femoral and carotid arteries, and each tissue specimen contained a region of calcified material. Three-dimensional (3D) collagen fibril orientation was determined along scan lines that started away from and then extended toward a given calcification. Fibrils were found to be oriented mainly in the circumferential direction of the plaque tissue at the majority of locations away from calcifications. However, in a number of cases, the dominant fibril direction differed near a calcification, changing from circumferential to longitudinal or thickness (radial) directions. Further study is needed to elucidate how these fibril orientations may influence plaque tissue stress-strain behavior and vulnerability to rupture.

An experimentally informed statistical elasto-plastic mineralised collagen fibre model at the micrometre and nanometre lengthscale

Bone is an intriguingly complex material. It combines high strength, toughness and lightweight via an elaborate hierarchical structure. This structure results from a biologically driven self-assembly and self-organisation, and leads to different deformation mechanisms along the length scales. Characterising multiscale bone mechanics is fundamental to better understand these mechanisms including changes due to bone-related diseases. It also guides us in the design of new bio-inspired materials. A key-gap in understanding bone's behaviour exists for its fundamental mechanical unit, the mineralised collagen fibre, a composite of organic collagen molecules and inorganic mineral nanocrystals. Here, we report an experimentally informed statistical elasto-plastic model to explain the fibre behaviour including the nanoscale interplay and load transfer with its main mechanical components. We utilise data from synchrotron nanoscale imaging, and combined micropillar compression and synchrotron X-ray scattering to develop the model. We see that a 10-15% micro- and nanomechanical heterogeneity in mechanical properties is essential to promote the ductile microscale behaviour preventing an abrupt overall failure even when individual fibrils have failed. We see that mineral particles take up 45% of strain compared to collagen molecules while interfibrillar shearing seems to enable the ductile post-yield behaviour. Our results suggest that a change in mineralisation and fibril-to-matrix interaction leads to different mechanical properties among mineralised tissues. Our model operates at crystalline-, molecular- and continuum-levels and sheds light on the micro- and nanoscale deformation of fibril-matrix reinforced composites.

Breaking crown dentine in whole teeth: 3D observations of prevalent fracture patterns following overload

Teeth with intact crowns rarely split or fracture, despite decades of cyclic loading and occasional unexpected overload. This is largely attributed to the presence of dentine, since cracking and fracture of enamel have been frequently reported. Dentine is similar to bone, comprising mineralised collagen fibres as a main constituent. Unlike cortical bone, however, where microcracking and damage arrest are essential for re/modelling and healing, dentine can neither remodel nor regenerate. This raises questions regarding the evolutionary benefits of toughening, leading to uncertainty whether cracks actually appear in dentine in situ. Here we study the notion that circumpulpal dentine is usually protected against, rather than damaged by severe overloads, even though it is not much more massive or stronger than it needs to be. To address this, we examined hydrated teeth still within whole jawbones of freshly-slaughtered skeletally mature pigs, mechanically loaded until fracture. Force displacement curves, optical and electron microscopy combined with 3D microstructural analysis by conventional micro-computed tomography (μCT) revealed mostly brittle fracture paths in circumpulpal crown dentine. Once overload cracks reach this mass of dentine they propagate rapidly along straight paths often parallel to the enamel flanks of the oblong shovel shaped premolars. We find infrequent signs of active toughening mechanisms with minimal crack diversion, ligament bridging and microcracking. When such toughening is seen, it mainly appears in softer dentine in the root, or near the dentine-enamel-junction (DEJ) in mantle dentine. We observed shear bands in overloaded circumpulpal dentine, due to mutual gliding of upper and lower segments. These shear bands are formed as periodic arrays of rotated dentine fragments. The 3D data consistently demonstrate the importance of the layered tooth structure, containing a stiff outer enamel shell, a soft sub-DEJ interlayer and a stiff circumpulpal dentine bulk, for deflecting cracks from splitting the tooth.

Compressive behaviour of uniaxially aligned individual mineralised collagen fibres at the micro- and nanoscale

The increasing incidence of osteoporotic bone fractures makes fracture risk prediction an important clinical challenge. Computational models can be utilised to facilitate such analyses. However, they critically depend on bone's underlying hierarchical material description. To understand bone's irreversible behaviour at the micro- and nanoscale, we developed an in situ testing protocol that allows us to directly relate the experimental data to the mechanical behaviour of individual mineralised collagen fibres and its main constitutive phases, the mineralised collagen fibrils and the mineral nanocrystals, by combining micropillar compression of single fibres with small angle X-ray scattering (SAXS) and X-ray diffraction (XRD). Failure modes were assessed by SEM. Strain ratios in the elastic region at fibre, fibril and mineral levels were found to be approximately 22:5:2 with strain ratios at the point of compressive strength of 0.23 ± 0.11 for fibril-to-fibre and 0.07 ± 0.01 for mineral-to-fibre levels. Mineral-to-fibre levels showed highest strain ratios around the apparent yield point, fibril-to-fibre around apparent strength. The mineralised collagen fibrils showed a delayed mechanical response, contrary to the mineral phase, which points towards preceding deformations of mineral nanocrystals in the extrafibrillar matrix. No damage was measured at the level of the mineralised collagen fibre which indicates an incomplete separation of the mineral and collagen, and an extrafibrillar interface failure. The formation of kink bands and the gradual recruitment of fibrils upon compressive loading presumably led to localised strains. Our results from a well-controlled fibrillar architecture provide valuable input for micromechanical models and computational non-linear bone strength analyses that may provide further insights for personalised diagnosis and treatment as well as bio-inspired implants for patients with bone diseases. STATEMENT OF SIGNIFICANCE: Musculoskeletal diseases such as osteoporosis, osteoarthritis or bone cancer significantly challenge health care systems and make fracture risk prediction and treatment optimisation important clinical goals. Computational methods such as finite element models have the potential to optimise analyses but highly depend on underlying material descriptions. We developed an in situ testing set-up to directly relate experimental data to the mechanical behaviour of bone's fundamental building block, the individual mineralised collagen fibre and its main constituents. Low multilevel strain ratios suggest high deformations in the extrafibrillar matrix and energy dissipation at the interfaces, the absence of damage indicates both an incomplete separation between mineral and collagen and an extrafibrillar interface failure. The formation of kink bands in the fibril-reinforced composite presumably led to localised strains. The deformation behaviour of a well-controlled fibrillar architecture provides valuable input for non-linear bone strength analyses.

The Mineral-Collagen Interface in Bone

The interface between collagen and the mineral reinforcement phase, carbonated hydroxyapatite (cAp), is essential for bone's remarkable functionality as a biological composite material. The very small dimensions of the cAp phase and the disparate natures of the reinforcement and matrix are essential to the material's performance but also complicate study of this interface. This article summarizes what is known about the cAp-collagen interface in bone and begins with descriptions of the matrix and reinforcement roles in composites, of the phases bounding the interface, of growth of cAp growing within the collagen matrix, and of the effect of intra- and extrafibrilar mineral on determinations of interfacial properties. Different observed interfacial interactions with cAp (collagen, water, non-collagenous proteins) are reviewed; experimental results on interface interactions during loading are reported as are their influence on macroscopic mechanical properties; conclusions of numerical modeling of interfacial interactions are also presented. The data suggest interfacial interlocking (bending of collagen molecules around cAp nanoplatelets) and water-mediated bonding between collagen and cAp are essential to load transfer. The review concludes with descriptions of areas where new research is needed to improve understanding of how the interface functions.

Compressive Residual Strains in Mineral Nanoparticles as a Possible Origin of Enhanced Crack Resistance in Human Tooth Dentin

The tough bulk of dentin in teeth supports enamel, creating cutting and grinding biostructures with superior failure resistance that is not fully understood. Synchrotron-based diffraction methods, utilizing micro- and nanofocused X-ray beams, reveal that the nm-sized mineral particles aligned with collagen are precompressed and that the residual strains vanish upon mild annealing. We show the link between the mineral nanoparticles and known damage propagation trajectories in dentin, suggesting a previously overlooked compression-mediated toughening mechanism.

Effect of cyclic loading on the nanoscale deformation of hydroxyapatite and collagen fibrils in bovine bone

Cyclic compressive loading tests were carried out on bovine femoral bones at body temperature (37 °C), with varying mean stresses (-55 to -80 MPa) and loading frequencies (0.5-5 Hz). At various times, the cyclic loading was interrupted to carry out high-energy X-ray scattering measurements of the internal strains developing in the hydroxyapatite (HAP) platelets and the collagen fibrils. The residual strains upon unloading were always tensile in the HAP and compressive in the fibrils, and each increases in magnitude with loading cycles, which can be explained from damage at the HAP–collagen interface and accumulation of plastic deformation within the collagen phase. The samples tested at a higher mean stress and stress amplitude, and at lower loading frequencies exhibit greater plastic deformation and damage accumulation, which is attributed to greater contribution of creep. Synchrotron microcomputed tomography of some of the specimens showed that cracks are produced during cyclic loading and that they mostly occur concentric with Haversian canals.

Bovine and equine peritubular and intertubular dentin

Dentin contains 1-2μm diameter tubules extending from the pulp cavity to near the junction with enamel. Peritubular dentin (PTD) borders the tubule lumens and is surrounded by intertubular dentin (ITD). Differences in PTD and ITD composition and microstructure remain poorly understood. Here, a (∼200nm)(2), 10.1keV synchrotron X-ray beam maps X-ray fluorescence and X-ray diffraction simultaneously around tubules in 15-30μm thick bovine and equine specimens. Increased Ca fluorescence surrounding tubule lumens confirms that PTD is present, and the relative intensities in PTD and ITD correspond to carbonated apatite (cAp) volume fraction of ∼0.8 in PTD vs. 0.65 assumed for ITD. In the PTD near the lumen edges, Zn intensity is strongly peaked, corresponding to a Zn content of ∼0.9mgg(-1) for an assumed concentration of ∼0.4mgg(-1) for ITD. In the equine specimen, the Zn K-edge position indicates that Zn(2+) is present, similar to bovine dentin (Deymier-Black et al., 2013), and the above edge structure is consistent with spectra from macromolecules related to biomineralization. Transmission X-ray diffraction shows only cAp, and the 00.2 diffraction peak (Miller-Bravais indices) width is constant from ITD to the lumen edge. The cAp 00.2 average preferred orientation is axisymmetric (about the tubule axis) in both bovine and equine dentin, and the axisymmetric preferred orientation continues from ITD through the PTD to the tubule lumen. These data indicate that cAp structure does not vary from PTD to ITD.

The mechanics of PLGA nanofiber scaffolds with biomimetic gradients in mineral for tendon-to-bone repair

Attachment of dissimilar materials is prone to failure due to stress concentrations that can arise their interface. A compositionally or structurally graded transition can dissipate these stress concentrations and thereby toughen an attachment. The interface between compliant tendon and stiff bone utilizes a monotonic change in hydroxylapatite mineral ("mineral") content to produce a gradient in mechanical properties and mitigate stress concentrations. Previous efforts to mimic the natural tendon-to-bone attachment have included electrospun nanofibrous polymer scaffolds with gradients in mineral. Mineralization of the nanofiber scaffolds has typically been achieved using simulated body fluid (SBF). Depending on the specific formulation of SBF, mineral morphologies ranged from densely packed small crystals to platelike crystal florets. Although this mineralization of scaffolds produced increases in modulus, the peak modulus achieved remained significantly below that of bone. Missing from these prior empirical approaches was insight into the effect of mineral morphology on scaffold mechanics and on the potential for the approach to ultimately achieve moduli approaching that of bone. Here, we applied two mineralization methods to generate scaffolds with spatial gradations in mineral content, and developed methods to quantify the stiffening effects and evaluate them in the context of theoretical bounds. We asked whether either of the mineralization methods we developed holds potential to achieve adequate stiffening of the scaffold, and tested the hypothesis that the smoother, denser mineral coating could attain more potent stiffening effects. Testing this hypothesis required development of and comparison to homogenization bounds, and development of techniques to estimate mineral volume fractions and spatial gradations in modulus. For both mineralization strategies, energy dispersive X-ray analysis demonstrated the formation of linear gradients in mineral concentration along the length of the scaffolds, and Raman spectroscopic analysis revealed that the mineral produced was hydroxylapatite. Mechanical testing showed that the stiffness gradient using the new method was significantly steeper. By analyzing the scaffolds using micromechanical modeling techniques and extrapolating from our experimental results, we present evidence that the new mineralization protocol has the potential to achieve levels of stiffness adequate to contribute to enhanced repair of tendon-to-bone attachments.

Multiscale modelling and diffraction-based characterization of elastic behaviour of human dentine

Human dentine is a hierarchical mineralized tissue with a two-level composite structure, with tubules being the prominent structural feature at a microlevel, and collagen fibres decorated with hydroxyapatite (HAp) crystallite platelets dominating the nanoscale. Few studies have focused on this two-level structure of human dentine, where the response to mechanical loading is thought to be affected not only by the tubule volume fraction at the microscale, but also by the shape and orientation distribution of mineral crystallites, and their nanoscale spatial arrangement and alignment. In this paper, in situ elastic strain evolution within HAp in dentine subjected to uniaxial compressive loading along both longitudinal and transverse directions was characterized simultaneously by two synchrotron X-ray scattering techniques: small- and wide-angle X-ray scattering (SAXS and WAXS, respectively). WAXS allows the evaluation of the apparent modulus linking the external load to the internal HAp crystallite strain, while the nanoscale HAp distribution and arrangement can be quantified by SAXS. We proposed an improved multiscale Eshelby inclusion model that takes into account the two-level hierarchical structure, and validated it with a multidirectional experimental strain evaluation. The agreement between the simulation and measurement indicates that the multiscale hierarchical model developed here accurately reflects the structural arrangement and mechanical response of human dentine. This study benefits the comprehensive understanding of the mechanical behaviour of hierarchical biomaterials. The knowledge of the mechanical properties related to the hierarchical structure is essential for the understanding and predicting the effects of structural alterations that may occur due to disease or treatment on the performance of dental tissues and their artificial replacements.

Effect of X-ray irradiation on the elastic strain evolution in the mineral phase of bovine bone under creep and load-free conditions

Both the load partitioning between hydroxyapatite (HAP) and collagen during compressive creep deformation of bone and the HAP residual strain in unloaded bone have been shown in previous synchrotron X-ray diffraction studies to be affected by the X-ray irradiation dose. Here, through detailed analysis of the X-ray diffraction patterns of bovine bone, the effect of X-ray dose on (i) the rate of HAP elastic strain accumulation/shedding under creep conditions and (ii) the HAP lattice spacing and average root mean square (RMS) strain under load-free conditions are examined. These strain measurements exhibit three stages in response to increasing X-ray dose. Up to ∼75 kGy (stage I) no effect of dose is observed, indicating a threshold behavior. Between ∼75 and ∼300 kGy (stage II) in unloaded bone the HAP d-spacing increases and the RMS strain decreases with dose, indicating strain relaxation of HAP. Furthermore, under constant compressive load creep conditions, the rate of compressive elastic strain accumulation in HAP decreases with increasing dose until, at ∼115 kGy, it changes sign, indicating that the HAP phase is shedding load during creep deformation. These stage II behaviors are consistent with HAP-collagen interfacial damage, which allows the HAP elastic strain to relax within both the loaded and unloaded samples. Finally, for doses in excess of ∼300 kGy (stage III, measured up to 7771 kGy) the HAP lattice spacing and RMS strain for load-free samples and the rate of HAP elastic strain shedding for crept samples remain independent of dose, suggesting a saturation of damage and/or stiffening of the collagen matrix due to intermolecular cross-linking.

Variability in the nanoscale deformation of hydroxyapatite during compressive loading in bovine bone

High-energy synchrotron X-ray diffraction is used to study in situ elastic strains in hydroxyapatite (HAP) for bovine femur cortical bone subjected to uniaxial compressive loading. Load-unload tests at room temperature (27°C) and body temperature (37°C) show that the load transfer to the stiff nanosized HAP platelets from the surrounding compliant protein matrix does not vary significantly (p<0.05) with temperature. This emphasizes that the stiffness of bone is controlled by the stiffness of the HAP phase, which remains unaffected by this change in temperature. Both the extent of hysteresis and the residual value of internal strains developed in HAP during load-unload cycling from 0 to -100 MPa increase significantly (p<0.05) with the number of loading cycles, indicative of strain energy dissipation and accumulation of permanent deformation. Monotonic loading tests, conducted at body temperature to determine the spatial variation of properties within the femur, illustrate that the HAP phase carries lower strain (and thus stresses) at the anterio-medial aspect of the femur than at the anterio-lateral aspect. This is correlated to higher HAP volume fractions in the former location (p<0.05). The Young's modulus of the bone is also found to correlate with the HAP volume fraction and porosity (p<0.05). Finally, samples with a primarily plexiform microstructure are found to be stiffer than those with a primarily Haversian microstructure (p<0.05).