The effects of interphase and bonding on the elastic modulus of bone: changes with age-related osteoporosis

Micromechanical modelling of transverse fracture behaviour of lamellar bone using a phase-field damage model: The role of non-collagenous proteins and mineralised collagen fibrils

At the tissue-scale and above, there are now well-established structure-property relationships that provide good approximations of the biomechanical performance of bone through, for example, power-law relationships that relate tissue mineral density to elastic properties. However, below the tissue-level, the individual role of the constituents becomes prominent and these simple relationships tend to break down, with more detailed theoretical and computational models are required to describe the mechanical response. In this study, a two-dimensional micromechanics damage-based representative volume element (RVE) of lamellar bone was developed, which included a novel implementation of a phase-field damage model to describe the behaviour of non-collagenous proteins at mineral-mineral and mineral-fibril interface regions. It was found that, while the stiffness of the tissue was governed by the relative proportion of extra-fibrillar mineral and mineralised collagen fibrils, the strength and toughness of the tissue in transverse direction relied on the interactions occurring at mineral-mineral and mineral-fibril interfaces, highlighting the prominence of non-collagenous proteins in determine fracture-based processes at this scale. While fractures tended to initiate in mineral rich areas of the extra-fibrillar mineral matrix, it was found that the presence of mineralised collagen fibrils at low density did not provide a substantial contribution to crack propagation behaviour under transverse loading. However, at physiological volume fraction (VfMCF=50%), different scenarios could arise depending on the relative strength value of the interphase around the MCFs ( [Formula: see text] ) to the interphase between individual minerals ( [Formula: see text] ): (i) When [Formula: see text] , MCFs appear to facilitate crack propagation with MCF-mineral debonding being the dominant failure mode; (ii) once γ>1, the MCFs hinder the microcracks, leading to inhibition of crack propagation, which can be regarded as an energy dissipation mechanism. The effective fracture properties of the tissue also experience a sudden increase in fracture work density (J-integral) once the crack is arrested by MCFs or severely deflected. Collectively, the predicted behaviour of the model compared well to those reported through experimental and computational methods, highlighting its potential to provide further understanding into the mechanistic response of bone ultrastructure alterations related to the structural and compositional changes resulting from disease and aging.

A coarse-grained molecular dynamics investigation of the role of mineral arrangement on the mechanical properties of mineralized collagen fibrils

Mineralized collagen fibrils (MCFs) comprise collagen molecules and hydroxyapatite (HAp) crystals and are considered universal building blocks of bone tissue, across different bone types and species. In this study, we developed a coarse-grained molecular dynamics (CGMD) framework to investigate the role of mineral arrangement on the load-deformation behaviour of MCFs. Despite the common belief that the collagen molecules are responsible for flexibility and HAp minerals are responsible for stiffness, our results showed that the mineral phase was responsible for limiting collagen sliding in the large deformation regime, which helped the collagen molecules themselves undergo high tensile loading, providing a substantial contribution to the ultimate tensile strength of MCFs. This study also highlights different roles for the mineralized and non-mineralized protofibrils within the MCF, with the mineralized groups being primarily responsible for load carrying due to the presence of the mineral phase, while the non-mineralized groups are responsible for crack deflection. These results provide novel insight into the load-deformation behaviour of MCFs and highlight the intricate role that both collagen and mineral components have in dictating higher scale bone biomechanics.

Nanomaterials for bone tissue regeneration: updates and future perspectives

Joint replacement and bone reconstructive surgeries are on the rise globally. Current strategies for implants and bone regeneration are associated with poor integration and healing resulting in repeated surgeries. A multidisciplinary approach involving basic biological sciences, tissue engineering, regenerative medicine and clinical research is required to overcome this problem. Considering the nanostructured nature of bone, expertise and resources available through recent advancements in nanobiotechnology enable researchers to design and fabricate devices and drug delivery systems at the nanoscale to be more compatible with the bone tissue environment. The focus of this review is to present the recent progress made in the rationale and design of nanomaterials for tissue engineering and drug delivery relevant to bone regeneration.

Optimization of Taylor spatial frame half-pins diameter for bone deformity correction: Application to femur

Using external fixtures for bone deformity correction takes advantages of less soft tissue injury, better bone alignment and enhances strain development for bone formation on cutting section, which cause shorter healing time. Among these fixtures, Taylor spatial frame is widely used and includes two rings and six adjustable struts developing 6 degrees of freedom, making them very flexible for this type of application. The current study describes a method to optimize Taylor spatial frame pin-sizes currently chosen from the surgeon's experiences. A three-dimensional model of femur was created from computed tomography images; segmentation of the medical images was made based on the Hounsfield unit (gray scale) in order to allocate adequate mechanical properties into cortical and trabecular bone sections. Both the cortical and trabecular sections were assumed to be isotropic and homogeneous. The diameter optimization of Taylor spatial frame's half-pins was carried out by coupling genetic algorithm and finite element analysis. The finite element analysis was based on a static mechanical load corresponding to a standing person's body weight. Finite element analysis results were validated with experimentally measured strains obtained from bone compression tests. A cost function, based on the developed bone stresses, was defined close to the Taylor spatial frame's half-pins. The calculated cost function showed a decrease of over 33% from the initial half-pin selection by the surgeon and the genetic algorithm optimization. Consequently, the maximum stresses experienced by the bone in the connected location of the half-pins decreased from 121.4 MPa in the surgeon's selection to 73.07 MPa as a result of the optimization process.

A multiscale modelling of bone ultrastructure elastic proprieties using finite elements simulation and neural network method

Bone is a living material with a complex hierarchical structure which entails exceptional mechanical properties, including high fracture toughness, specific stiffness and strength. Bone tissue is essentially composed by two phases distributed in approximately 30-70%: an organic phase (mainly type I collagen and cells) and an inorganic phase (hydroxyapatite-HA-and water). The nanostructure of bone can be represented throughout three scale levels where different repetitive structural units or building blocks are found: at the first level, collagen molecules are arranged in a pentameric structure where mineral crystals grow in specific sites. This primary bone structure constitutes the mineralized collagen microfibril. A structural organization of inter-digitating microfibrils forms the mineralized collagen fibril which represents the second scale level. The third scale level corresponds to the mineralized collagen fibre which is composed by the binding of fibrils. The hierarchical nature of the bone tissue is largely responsible of their significant mechanical properties; consequently, this is a current outstanding research topic. Scarce works in literature correlates the elastic properties in the three scale levels at the bone nanoscale. The main goal of this work is to estimate the elastic properties of the bone tissue in a multiscale approach including a sensitivity analysis of the elastic behaviour at each length scale. This proposal is achieved by means of a novel hybrid multiscale modelling that involves neural network (NN) computations and finite elements method (FEM) analysis. The elastic properties are estimated using a neural network simulation that previously has been trained with the database results of the finite element models. In the results of this work, parametric analysis and averaged elastic constants for each length scale are provided. Likewise, the influence of the elastic constants of the tissue constituents is also depicted. Results highlight that intelligent numerical methods are powerful and accurate procedures to deal with the complex multiscale problem in the bone tissue with results in agreement with values found in literature for specific scale levels.

Experimentally-based multiscale model of the elastic moduli of bovine trabecular bone and its constituents

The elastic moduli of trabecular bone were modeled using an analytical multiscale approach. Trabecular bone was represented as a porous nanocomposite material with a hierarchical structure spanning from the collagen-mineral level to the trabecular architecture level. In parallel, compression testing was done on bovine femoral trabecular bone samples in two anatomical directions, parallel to the femoral neck axis and perpendicular to it, and the measured elastic moduli were compared with the corresponding theoretical results. To gain insights on the interaction of collagen and minerals at the nanoscale, bone samples were deproteinized or demineralized. After such processing, the treated samples remained as self-standing structures and were tested in compression. Micro-computed tomography was used to characterize the hierarchical structure of these three bone types and to quantify the amount of bone porosity. The obtained experimental data served as inputs to the multiscale model and guided us to represent bone as an interpenetrating composite material. Good agreement was found between the theory and experiments for the elastic moduli of the untreated, deproteinized, and demineralized trabecular bone.

Multiscale approach including microfibril scale to assess elastic constants of cortical bone based on neural network computation and homogenization method

The complexity and heterogeneity of bone tissue require a multiscale modeling to understand its mechanical behavior and its remodeling mechanisms. In this paper, a novel multiscale hierarchical approach including microfibril scale based on hybrid neural network (NN) computation and homogenization equations was developed to link nanoscopic and macroscopic scales to estimate the elastic properties of human cortical bone. The multiscale model is divided into three main phases: (i) in step 0, the elastic constants of collagen-water and mineral-water composites are calculated by averaging the upper and lower Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril are computed using a trained NN simulation. Finite element calculation is performed at nanoscopic levels to provide a database to train an in-house NN program; and (iii) in steps 2-10 from fibril to continuum cortical bone tissue, homogenization equations are used to perform the computation at the higher scales. The NN outputs (elastic properties of the microfibril) are used as inputs for the homogenization computation to determine the properties of mineralized collagen fibril. The mechanical and geometrical properties of bone constituents (mineral, collagen, and cross-links) as well as the porosity were taken in consideration. This paper aims to predict analytically the effective elastic constants of cortical bone by modeling its elastic response at these different scales, ranging from the nanostructural to mesostructural levels. Our findings of the lowest scale's output were well integrated with the other higher levels and serve as inputs for the next higher scale modeling. Good agreement was obtained between our predicted results and literature data.

Influence of Shear Stress on Behaviors of Piezoelectric Voltages in Bone

The piezoelectric properties of bone play an important role in the bone remodeling process and can be employed in clinical bone repair. In this study, the piezo-voltage of bone between two surfaces of a bone beam under bending deformation was measured using an ultra-high-input impedance bioamplifier. The influence of shear stress on the signs of piezo-voltages in bone was determined by comparing and contrasting the results from three-point and four-point bending experiments. From the three-point bending experiment, the study found that the signs of piezo-voltages depend only on shear stress and are not sensitive to the normal stress.

Elastic moduli of untreated, demineralized and deproteinized cortical bone: validation of a theoretical model of bone as an interpenetrating composite material

A theoretical experimentally based multi-scale model of the elastic response of cortical bone is presented. It portrays the hierarchical structure of bone as a composite with interpenetrating biopolymers (collagen and non-collagenous proteins) and minerals (hydroxyapatite), together with void spaces (porosity). The model involves a bottom-up approach and employs micromechanics and classical lamination theories of composite materials. Experiments on cortical bone samples from bovine femur include completely demineralized and deproteinized bones as well as untreated bone samples. Porosity and microstructure are characterized using optical and scanning electron microscopy, and micro-computed tomography. Compression testing is used to measure longitudinal and transverse elastic moduli of all three bone types. The characterization of structure and properties of these three bone states provides a deeper understanding of the contributions of the individual components of bone to its elastic response and allows fine tuning of modeling assumptions. Very good agreement is found between theoretical modeling and compression testing results, confirming the validity of the interpretation of bone as an interpenetrating composite material.

Nanostructural alteration in bone quantified in terms of orientation distribution of mineral crystals: a possible tool for fracture risk assessment

There may be different causes of failures in bone; however, their origin generally lies at the lowest level of structural hierarchy, i.e., at the mineral-collagen composite. Any change in the nanostructure affects the affinity or bonding effectiveness between and within the phases at this level, and hence determines the overall strength and quality of bone. In this study, we propose a novel concept to assess change in the nanostructure and thereby change in the bonding status at this level by revealing change in the orientation distribution characteristics of mineral crystals. Using X-ray diffraction method, a parameter called Degree of Orientation (DO) has been quantified. The DO accounts for the azimuthal distribution of mineral crystals and represents their effective amount along any direction. Changes in the DOs in cortical bone samples from bovine femur with different preferential orientations of mineral crystals were estimated under external loads. Depending on the applied loads, change in the azimuthal distribution of the DOs and the degree of reversibility of the crystals was observed to vary. The characteristics of nanostructural change and thereby possible affect on the strength of bone was then predicted from the reversible or irreversible characteristics of distributed mineral crystals. Significant changes in the organization of mineral crystals were observed; however, variations in the applied stresses and elastic moduli were not evinced at the macroscale level. A novel concept to assess the alteration in nanostructure on the basis of mineral crystals orientation distribution has been proposed. The importance of nanoscale level information obtained noninvasively has been emphasized, which acts as a precise tool to estimate the strength and predict the possible fracture risks in bone.

A new tool to assess the mechanical properties of bone due to collagen degradation

Current clinical tools for evaluating fracture risk focus only on the mineral phase of bone. However, changes in the collagen matrix may affect bone mechanical properties, increasing fracture risk while remaining undetected by conventional screening methods such as dual energy x-ray absorptiometry (DXA) and quantitative ultrasound (QUS). The mechanical response tissue analyzer (MRTA) is a non-invasive, radiation-free potential clinical tool for evaluating fracture risk. The objectives of this study were two-fold: to investigate the ability of the MRTA to detect changes in mechanical properties of bone as a result of treatment with 1 M potassium hydroxide (KOH) and to evaluate the differences between male and female bone in an emu model. DXA, QUS, MRTA and three-point bending measurements were performed on ex vivo emu tibiae before and after KOH treatment. Male and female emu tibiae were endocortically treated with 1 M KOH solution for 1-14 days, resulting in negligible collagen loss (0.05%; by hydroxyproline assay) and overall mass loss (0.5%). Three-point bending and MRTA detected significant changes in modulus between days 1 and 14 of KOH treatment (-18%) while all values measured by DXA and QUS varied by less than 2%. This close correlation between MRTA and three-point bending results support the utility of the MRTA as a clinical tool to predict fracture risk. In addition, the significant reduction in modulus contrasted with the negligible amount of collagen removal from the bone after KOH exposure. As such, the significant changes in bone mechanical properties may be due to partial debonding between the mineral and organic matrix or in situ collagen degradation rather than collagen removal. In terms of sex differences, male emu tibiae had significantly decreased failure stress and increased failure strain and toughness compared to female tibiae with increasing KOH treatment time.

The associations between mineral crystallinity and the mechanical properties of human cortical bone

It is well known that the amount of mineralization renders bone its stiffness. However, besides the mere amount of the mineral phase, size and shape of carbonated apatite crystals are postulated to affect the mechanical properties of bone tissue as predicted by composite mechanics models. Despite this predictive evidence, there is little experimental insight on the relation between the characteristics of mineral crystals and hard tissue mechanics. In this study, Raman spectroscopy was used to provide information on the crystallinity of bone's mineral phase, a parameter which is an overall indicator of mineral crystal size and stoichiometric perfection. Raman scans and mechanical tests (monotonic and fatigue; n=64 each) were performed on the anterior, medial, lateral and posterior quadrant sections of 16 human cadaveric femurs (52 y.o.-85 y.o.). The reported coefficient of determination values (R(2)) were adjusted for the effects of age to bring out the unbiased contribution of crystallinity. Crystallinity was able to explain 6.7% to 48.3% of the variation in monotonic mechanical properties. Results indicated that the tissue-level strength and stiffness increased with increasing crystallinity while the ductility reduced. Crystallinity explained 11.3% to 63.5% of the variation in fatigue properties. Moduli of specimens with greater crystallinity degraded at a slower rate and, also, they had longer fatigue lives. However, not every anatomical quadrant displayed these relationships. In conclusion, these results acknowledge crystal properties as an important bone quality factor and raise the possibility that aberrations in these properties may contribute to senile osteoporotic fractures.

Tensile behavior of cortical bone: Dependence of organic matrix material properties on bone mineral content

A porous composite model is developed to analyze the tensile mechanical properties of cortical bone. The effects of microporosity (volksman's canals, osteocyte lacunae) on the mechanical properties of bone tissue are taken into account. A simple shear lag theory, wherein tensile loads are transferred between overlapped mineral platelets by shearing of the organic matrix, is used to model the reinforcement provided by mineral platelets. It is assumed that the organic matrix is elastic in tension and elastic-perfectly plastic in shear until it fails. When organic matrix shear stresses at the ends of mineral platelets reach their yield values, the stress-strain curve of bone tissue starts to deviate from linear behavior. This is referred as the microscopic yield point. At the point where the stress-strain behavior of bone shows a sharp curvature, the organic phase reaches its shear yield stress value over the entire platelet. This is referred as the macroscopic yield point. It is assumed that after macroscopic yield, mineral platelets cannot contribute to the load bearing capacity of bone and that the mechanical behavior of cortical bone tissue is determined by the organic phase only. Bone fails when the principal stress of the organic matrix is reached. By assuming that mechanical properties of the organic matrix are dependent on bone mineral content below the macroscopic yield point, the model is used to predict the entire tensile mechanical behavior of cortical bone for different mineral contents. It is found that decreased shear yield stresses and organic matrix elastic moduli are required to explain the mechanical behavior of bones with lowered mineral contents. Under these conditions, the predicted values (elastic modulus, 0.002 yield stress and strain, and ultimate stress and strain) are within 15% of experimental data.

Prediction of microdamage formation using a mineral-collagen composite model of bone

Age-related changes in bone quality are mainly manifested in the reduced toughness. Since the post-yield deformation of bone is realized through microdamage formation (e.g., microcracking and diffuse damage), it is necessary to understand the mechanism of microdamage formation in bone in order to elucidate underlying mechanisms of age-related bone fractures. In this study, a two-dimensional shear lag model was developed to predict stress concentration fields around an initial crack in a mineral-collagen composite. In this model, non-linear elasticity was assumed for the collagen phase, and linear elasticity for the mineral. Based on the pattern of the stress concentration fields, the condition for microdamage formation was discussed. The results of our analyses indicate that: (1) an initial crack formed in mineral phase may cause stress concentration in the adjacent mineral layers; (2) the pattern of stress concentration fields depends not only on the spatial but also mechanical properties of the collagen and mineral phases; (3) the pattern of the stress concentration fields could determine either coalescence or scattering of nano cracks around the initial crack.

Effect of bone mineral content on the tensile properties of cortical bone: experiments and theory

The effect of mineral volume fraction on the tensile mechanical properties of cortical bone tissue is investigated by theoretical and experimental means. The mineral content of plexiform, bovine bone was lowered by 18% and 29% by immersion in fluoride solutions for 3 days and 12 days, respectively. The elastic modulus, yield strength and ultimate strength of bone tissue decreased, while the ultimate strain increased with a decrease in mineral content. The mechanical behavior of bone tissue was modeled by using a micromechanical shear lag theory consisting of overlapped mineral platelets reinforcing the organic matrix. The decrease in yield stress, by the 0.002 offset method, of the fluoride treated bones were matched in the theoretical curves by lowering the shear yield stress of the organic matrix. The failure criterion used was based on failure stresses determined from a failure envelope (Mohr's circle), which was constructed using experimental data. It was found that the model predictions of elastic modulus got worse with a decrease in mineral content (being 7.9%, 17.2% and 33.0% higher for the control, 3-day and 12-day fluoride-treated bones). As a result, the developed theory could not fully predict the yield strain of bones with lowered mineral content, being 12.9% and 21.7% lower than the experimental values. The predicted ultimate stresses of the bone tissues with lower mineral contents were within +/- 10% of the experimental values while the ultimate strains were 12.7% and 26.3% lower than the experimental values. Although the model developed in this study did not take into account the presence of hierarchical structures, voids, orientation of collagen molecules and micro cracks, it still indicated that the mechanical properties of the organic matrix depend on bone mineral content.

Modeling the tensile mechanical behavior of bone along the longitudinal direction

The tensile stress-strain behavior of bone along its longitudinal axis is modeled by using a simple shear-lag theory, wherein, stresses and strains in a unit cell consisting of an organic matrix reinforced by overlapped mineral platelets are computed. It is assumed that loads are transferred between overlapped mineral-platelets by shear in the organic matrix. The mechanical behavior of bone in which the matrix partially or completely debonds from the sides of the overlapped mineral platelets (after an ultimate interfacial shear stress value is exceeded) is modeled. It is shown that the tensile mechanical behavior of bone can be modeled only by assuming little or no debonding of the organic from the mineral. A physical phenomenon that explains the tensile behavior of bone is, after the interfacial shear stress has reached a constant value over the length of the mineral platelets, the collagen molecules/microfibrils (with the associated mineral platelets) move relative to one another. The tensile stress-strain curve of bovine bone is modeled using this model. The theory predicts the mechanical behavior of the tissue in the elastic, yield and post-yield region. The ultimate strain and strengths are not predicted in the present model.