Hierarchical modelling of in situ elastic deformation of human enamel based on photoelastic and diffraction analysis of stresses and strains

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.

Photoelasticity for Stress Concentration Analysis in Dentistry and Medicine

Complex stresses are created or applied as part of medical and dental treatments, which are linked to the achievement of treatment goals and favorable prognosis. Photoelasticity is an optical technique that can help observe and understand biomechanics, which is essential for planning, evaluation and treatment in health professions. The objective of this project was to review the existing information on the use of photoelasticity in medicine and dentistry and determine their purpose, the areas or treatments for which it was used, models used as well as to identify areas of opportunity for the application of the technique and the generation of new models. A literature review was carried out to identify publications in dentistry and medicine in which photoelasticity was used as an experimental method. The databases used were: Sciencedirect, PubMed, Scopus, Ovid, Springer, EBSCO, Wiley, Lilacs, Medigraphic Artemisa and SciELO. Duplicate and incomplete articles were eliminated, obtaining 84 articles published between 2000 and 2019 for analysis. In dentistry, ten subdisciplines were found in which photoelasticity was used; those related to implants for fixed prostheses were the most abundant. In medicine, orthopedic research predominates; and its application is not limited to hard tissues. No reports were found on the use of photoelastic models as a teaching aid in either medicine or dentistry. Photoelasticity has been widely used in the context of research where it has limitations due to the characteristics of the results provided by the technique, there is no evidence of use in the health area to exploit its application in learning biomechanics; on the other hand there is little development in models that faithfully represent the anatomy and characteristics of the different tissues of the human body, which opens the opportunity to take up the qualitative results offered by the technique to transpolate it to an application and clinical learning.

Finite Element Modelling and Experimental Validation of the Enamel Demineralisation Process at the Rod Level

In the past years, a significant amount of effort has been directed at the observation and characterisation of caries using experimental techniques. Nevertheless, relatively little progress has been made in numerical modelling of the underlying demineralisation process.

The present study is the first attempt to provide a simplified calculation framework for the numerical simulation of the demineralisation process at the length scale of enamel rods and its validation by comparing the data with statistical analysis of experimental results.

FEM model was employed to simulate a time-dependent reaction-diffusion equation process in which H ions diffuse and cause demineralisation of the enamel. The local orientation of the hydroxyapatite crystals was taken into account. Experimental analysis of the demineralising front was performed using advanced high-resolution synchrotron X-ray micro-Computed Tomography. Further experimental investigations were conducted by means of SEM and STEM imaging techniques.

Besides establishing and validating the new modelling framework, insights into the role of the etchant solution pH level were obtained. Additionally, some light was shed on the origin of different types of etching patterns by simulating the demineralisation process at different etching angles of attack.

The implications of this study pave the way for simulations of enamel demineralisation within different complex scenarios and across the range of length scales. Indeed, the framework proposed can incorporate the presence of chemical species other than H ions and their diffusion and reaction leading to dissolution and re-precipitation of hydroxyapatite. It is the authors’ hope and aspiration that ultimately this work will help identify new ways of controlling and preventing caries.

Insights into the reinforcement role of peritubular dentine subjected to acid dissolution

Human dentine is a mineralised dental tissue that consists of dentinal tubules surrounded by two distinct dentinal phases: peritubular dentine (PTD) and intertubular dentine (ITD). Dental caries, which manifests itself as a consequence of demineralisation, is one of the most common chronic diseases that affect the function of human teeth. Due to the difference in the packing density of crystallites, PTD and ITD exhibit different reaction rates to acid dissolution. The present study evaluates how the effective Young's modulus degrades and how the effective stress redistributes in demineralised human dentine as a result of incremental acid dissolution process. An analytical two-layer composite model is proposed and used for the effective Young's modulus calculation. 3D numerical representative volume elements (RVEs) with different variations in PTD fraction and dentinal tubule density are established to evaluate effective stress redistribution and examine the critical factors that can affect the mechanical performance. The models are then applied on an actual dentine bulk sample. The results reveal how PTD serves as a protection to ITD thus highlight the important role that PTD plays for the structural integrity of dentine. The obtained insights are crucial for advancing the understanding of a variety of natural and therapeutic effects from the mechanical perspective, e.g. the mechanical performance assessment of human dentine subject to complex dynamic processes of de- and re-mineralisation that can occur in human dental caries and dental treatments. It will ultimately inspire the biomimetic design towards strengthening the dentine and dentine-like materials.

A COMPUTATIONAL STRATEGY TO EXAMINE THE PROFILE EFFECTS OF MICROPRISM REGIONS ON THE OVERALL ANISOTROPY OF HUMAN ENAMELS

In this study, our attention is mainly on elaborating a computational strategy to effectively predict the influence of prism profiles on the overall anisotropic property of human enamels (HEs). At first, two distinct schemes are developed separately with the aid of the polynomial fitting technique and the general power functions to mathematically describe the practical irregular and simplified regular profiles of enamel prisms. Hereafter, two parametric piecewise formulas, which facilitate the definition of anisotropic material properties of finite elements at different locations and make the numerical simulation of HE microstructures consisting of irregularly shaped prisms feasible, are presented to describe the orientation of hydroxyapatite (HAP) crystallites embedded in microprisms. The effective anisotropic moduli over a representative unit cell (RUC) under the periodic displacement constraint is concisely introduced according to the micromechanics, and a computational strategy is established to calculate these moduli numerically. Finally, the evaluations in the open literature are employed to demonstrate the validity of the elaborated computational strategy, and more investigations are conducted and yield the conclusions such that the material property of the inter-prism regions as well as the prism shapes plays a crucial role in determining the overall anisotropy of HEs.

Biomimetic Enamel Regeneration Mediated by Leucine-Rich Amelogenin Peptide

We report here a novel biomimetic approach to the regeneration of human enamel. The approach combines the use of inorganic pyrophosphate (PPi) to control the onset and rate of enamel regeneration and the use of leucine-rich amelogenin peptide (LRAP), a nonphosphorylated 56-amino acid alternative splice product of amelogenin, to regulate the shape and orientation of growing enamel crystals. This study builds on our previous findings that show LRAP can effectively guide the formation of ordered arrays of needle-like hydroxyapatite (HA) crystals in vitro and on the known role mineralization inhibitors, like PPi, play in the regulation of mineralized tissue formation. Acid-etched enamel surfaces of extracted human molars, cut perpendicular or parallel to the direction of the enamel rods, were exposed to a PPi-stabilized supersaturated calcium phosphate (CaP) solution containing 0 to 0.06 mg/mL LRAP for 20 h. In the absence of LRAP, PPi inhibition was reversed by the presence of etched enamel surfaces and led to the formation of large, randomly distributed plate-like HA crystals that were weakly attached, regardless of rod orientation. In the presence of 0.04 mg/mL LRAP, however, densely packed mineral layers, comprising bundles of small needle-like HA crystals, formed on etched surfaces that were cut perpendicular to the enamel rods. These crystals were strongly attached, and their arrangement reflected to a significant degree the underlying enamel prism pattern. In contrast, under the same conditions with LRAP, little to no crystal formation was found on enamel surfaces that were cut parallel to the direction of the enamel rods. These results suggest that LRAP preferentially interacts with ab surfaces of mature enamel crystals, inhibiting their directional growth, thus selectively promoting linear growth along the c-axis of enamel crystals. The present findings demonstrate a potential for the development of a new approach to regenerate enamel structure and properties.

Strain softening of nano-scale fuzzy interfaces causes Mullins effect in thermoplastic polyurethane

The strain-induced softening of thermoplastic polyurethane elastomers (TPUs), known as the Mullins effect, arises from their multi-phase structure. We used the combination of small- and wide- angle X-ray scattering (SAXS/WAXS) during in situ repeated tensile loading to elucidate the relationship between molecular architecture, nano-strain, and macro-scale mechanical properties. Insights obtained from our analysis highlight the importance of the ‘fuzzy interface’ between the hard and soft regions that governs the structure evolution at nanometre length scales and leads to macroscopic stiffness reduction. We propose a hierarchical Eshelby inclusion model of phase interaction mediated by the ‘fuzzy interface’ that accommodates the nano-strain gradient between hard and soft regions and undergoes tension-induced softening, causing the Mullins effect that becomes apparent in TPUs even at moderate tensile strains.

Understanding nature's residual strain engineering at the human dentine-enamel junction interface

Human dental tissue is a hydrated biological mineral composite. In terms of volume and mass, a human tooth mainly consists of dentine and enamel. Human dental tissues have a hierarchical structure and versatile mechanical properties. The dentine enamel junction (DEJ) is an important biological interface that provides a durable bond between enamel and dentine that is a life-long success story: while intact and free from disease, this interface does not fail despite the harsh thermo-mechanical loading in the oral cavity. The underlying reasons for such remarkable strength and durability are still not fully clear from the structural and mechanical perspectives. One possibility is that, in an example of residual stress engineering, evolution has led to the formation of a layer of inelastic strain adjacent to the DEJ during odontogenesis (tooth formation). However, due to significant experimental and interpretational challenges, no meaningful quantification of residual stress in the vicinity of the DEJ at the appropriate spatial resolution has been reported to date. In this study, we applied a recently developed flexible and versatile method for measuring the residual elastic strain at (sub)micron-scale utilising focused ion beam (FIB) milling with digital image correlation (DIC). We report the results that span the transition from human dentine to enamel, and incorporate the material lying at and in the vicinity of the DEJ. The capability of observing the association between internal architecture and the residual elastic strain state at the micrometre scale is useful for understanding the remarkable performance of the DEJ and may help the creation of improved biomimetic materials for clinical and engineering applications.

STATEMENT OF SIGNIFICANCE

We studied the micron-scale residual stresses that exist within human teeth, between enamel (outer tooth shell, hardest substance in the human body) and dentine (soft bone-like vascularised tooth core). The dentine-enamel junction (DEJ) is an extremely interesting example of nature's design in terms of hierarchical structuring and residual stress management. Key developments reported are systematic focused ion beam (FIB) milling and digital image correlation (DIC) micrometre scale residual strain evaluation, and the determination of principal strain direction near DEJ, correlated with internal architecture responsible for remarkable strength. This work helps understanding DEJ performance and improving biomimetic materials design for clinical and engineering applications.

X-ray Study of Human Dental Tissues Affected by Erythroblastosis Fetalis

Numerous diseases are known to cause microstructural alteration of dental tissues structure. One type in particular is associated with neonatal jaundice and circulation of bilirubin in blood at high concentration due to increased hemolysis in conditions such as erythroblastosis fetalis, septicemia, biliary atresia, and other causes of hyperbilirubinemia. In those conditions, the products of the catabolism of hemoglobin end up deposited in various tissues, including teeth, where they can present clinically as visibly stained brown/green teeth. There is almost no information on the nature or extent of the structural changes taking place in these conditions. Here, advanced nondestructive wide-angle synchrotron X-ray scattering techniques combined with scanning microscopy methods were used to investigate for the first time the ultrastructure of the dental hard tissues in an archival case of intrinsically pigmented green teeth. Despite no obvious elemental variation across the pigmented tissue region, the high-resolution crystallographic properties probed by wide-angle synchrotron X-ray scattering revealed an ultrastructural variation (orientation, particle size, and lattice parameter of hydroxyapatite crystallites) associated with a pigmentation line in dentine and with a distinct neonatal line in enamel.

Structure-mechanical function relations at nano-scale in heat-affected human dental tissue

The knowledge of the mechanical properties of dental materials related to their hierarchical structure is essential for understanding and predicting the effect of microstructural alterations on the performance of dental tissues in the context of forensic and archaeological investigation as well as laser irradiation treatment of caries. So far, few studies have focused on the nano-scale structure-mechanical function relations of human teeth altered by chemical or thermal treatment. The response of dental tissues to thermal treatment is thought to be strongly affected by the mineral crystallite size, their spatial arrangement and preferred orientation. In this study, synchrotron-based small and wide angle X-ray scattering (SAXS/WAXS) techniques were used to investigate the micro-structural alterations (mean crystalline thickness, crystal perfection and degree of alignment) of heat-affected dentine and enamel in human dental teeth. Additionally, nanoindentation mapping was applied to detect the spatial and temperature-dependent nano-mechanical properties variation. The SAXS/WAXS results revealed that the mean crystalline thickness distribution in dentine was more uniform compared with that in enamel. Although in general the mean crystalline thickness increased both in dentine and enamel as the temperature increased, the local structural variations gradually reduced. Meanwhile, the hardness and reduced modulus in enamel decreased as the temperature increased, while for dentine, the tendency reversed at high temperature. The analysis of the correlation between the ultrastructure and mechanical properties coupled with the effect of temperature demonstrates the effect of mean thickness and orientation on the local variation of mechanical property. This structural-mechanical property alteration is likely to be due to changes of HAp crystallites, thus dentine and enamel exhibit different responses at different temperatures. Our results enable an improved understanding of the mechanical properties correlation in hierarchical biological materials, and human dental tissue in particular.