Mineralized Collagen Fibrils Research Articles

Visualization of Collagen-Mineral Arrangement Using Atom Probe Tomography.

Bone is a functional material comprised of mainly two phases: an organic collagenous phase and an inorganic mineral phase. Collagen-mineral arrangement has implications for bone function, aging, and disease. However, theories on collagen-mineral arrangement have been confined to studies with low spatial and/or compositional resolution resulting in an extensive debate over the location of mineral with respect to collagen. Herein, a strategy is developed to extract a single mineralized collagen fibril from bone and analyze its composition and structure atom-by-atom with 3D sub-nanometer accuracy and compositional clarity using atom probe tomography (APT). It is shown for the first time a method to probe fibril-level mineralization and collagen-mineral arrangement from an in vivo system with both the spatial and compositional precision required to comment on nanoscale collagen-mineral arrangement. APT of leporine bone shows distinct and helical collagen fibrils with mineralized deposits both encapsulating and incorporated into the collagenous structures. This study demonstrates a novel fibril-level detection method that can be used to probe the composition of bone and contribute new insights to the structure and organization of mineralized materials such as bones and teeth.

3D random walk model of diffusion in human Hypo- and Hyper- mineralized collagen fibrils

Bone tissue is composed at the nanoscale of apatite minerals, collagen molecules and water that form the mineralized collagen fibril (MCF). Water has a crucial role in bone biomineralization. We developed a 3D random walk model to investigate the water diffusion process within the MCF for three different scenarios, namely low, intermediate and high mineral volume fraction. The MCF geometric model is obtained after applying 6·106 translational and rotational perturbations to an ordered arrangement of mineral. Subsequently, we compute 300 random trajectories of water molecules within the MCF for each mineral volume fraction. Every trajectory is constituted of up to 500 k positions of the water particle. We determined the diffusion coefficient from the linear fit of the mean squared displacement of water molecules as a function of time. We investigate changes in the diffusivity values in relation to variation of bone mineral content. The analysis performed on the random walk data, for all mineralization conditions, leads to diffusion coefficients in good agreement with the diffusivity outcomes achieved from previous experimental studies. Thus, the 3D geometrical configuration adopted in this numerical study appears suitable for modelling the MCF with different volume fractions, from hypo- to hyper-mineralized conditions. We observed that low mineral content is associated with an increase of the water diffusion, while lower values of diffusivity are determined in hypermineralized conditions. In agreement with experimental data, our results highlight the influence of the structural alterations on the mass transport properties.

Microtensile failure mechanisms in lamellar bone: Influence of fibrillar orientation, specimen size and hydration

A mechanistic understanding of bone fracture is indispensable for developing improved fracture risk assessment in clinics. Since bone is a hierarchically structured material, gaining such knowledge requires analysis at multiple length scales. Here, the tensile response of cortical bone is characterized at the lamellar length scale under dry and hydrated conditions with the aim of investigating the influence of bone's microstructure and hydration on its microscale strength and toughness. For individual lamellae, bone strength strongly correlates with the underlying mineralized collagen fibrils orientation and shows a 2.3-fold increase compared to the macroscale. When specimen size is increased to a few lamellae, the influence of fibril orientation and the size effect on strength are significantly reduced. These findings highlight the critical influence of defects, such as canaliculi and interlamellar interfaces, when assessing larger volumes. Hydration leads up to a 3-fold strength decrease but activates several toughening mechanisms enabling inelastic deformation. In axial specimens, toughening is seen through fibril bridging and crack kinking. In transverse specimens, water presence leads to a progressive but stable crack growth parallel to the fibril orientation, suggesting crack-tip plasticity at the fibrillar interfaces. This work offers a better understanding of the role of interfaces, porosity, and hydration in crack initiation under tensile loading, which is a crucial step towards improved clinical management of disease-related bone fractures through multiscale modeling approaches. Statement of significanceBone features a complex hierarchical structure which gives rise to several toughening mechanisms across several length scales. To better understand bone fracture, particularly the changes associated with age and disease, it is essential to investigate bone mechanical response at different levels of its hierarchical structure. For the first time, we were able to observe the nucleation of a single crack in hydrated bone lamellae under well-controlled uniaxial tensile loading conditions. These experiments highlight the role of water, interfaces, defects, and the ratio of defect to specimen size on bone's apparent strength and toughness. Such knowledge can be used in the future to develop multiscale models enabling improved clinical management of disease-related bone fractures.

Polyaminoacids in Biomimetic Collagen Mineralization: Roles of Isomerization and Disorder in Polyaspartic and Polyglutamic Acids.

The extracellular matrix of hard connective tissues is composed primarily of mineralized collagen fibrils. Acidic noncollagenous proteins play important roles in mediating mineralization of collagen. Polyaspartate, a homopolymer substitute for such proteins, has been used extensively in in vitro models to produce biomimetic mineralized collagen. Polyglutamate behaves differently in mineralization models, despite its chemical similarity. We show that polyaspartate is a 350 times more effective inhibitor of solution precipitation of hydroxyapatite than polyglutamate. Supersaturated CaP solutions stabilized with polyaspartic acid produce collagen with aligned intrafibrillar mineral, while solutions containing polyglutamate lead to the formation of unaligned mineral clusters on the fibril surface. Molecular analysis showed that the commercial polyaspartic acid contains substantial isomerization, unlike polyglutamic acid. Hence, the secondary structure of polyaspartic acid is more disordered than that of polyglutamic acid. The increased flexibility of the polyaspartic acid chain may explain its potency as an inhibitor of solution crystallization and a mediator of intrafibrillar collagen mineralization.

A stochastic micro to macro mechanical model for the evolution of bone-implant interface stiffness

Upon placement of an implant into living bone, an interface is formed through which various biochemical, biological, physical, and mechanical interactions take place. This interface evolves over time as the mechanical properties of peri-implant bone increase. Owing to the multifactorial nature of interfacial processes, it is challenging to devise a comprehensive model for predicting the mechanical behavior of the bone-implant interface. We propose a simple spatio-temporally evolving mechanical model – from an elementary unit cell comprising randomly oriented mineralized collagen fibrils having randomly assigned stiffness all the way up to a macroscopic bone-implant interface in a gap healing scenario. Each unit cell has an assigned Young's modulus value between 1.62 GPa and 25.73 GPa corresponding to minimum (i.e., 0) and maximum (i.e., 0.4) limits of mineral volume fraction, respectively, in the overlap region of the mineralized collagen fibril. Gap closure and subsequent stiffening are modeled to reflect the two main directions of peri-implant bone formation, i.e., contact osteogenesis and distance osteogenesis. The linear elastic stochastic finite element model reveals highly nonlinear temporal evolution of bone-implant interface stiffness, strongly dictated by the specific kinetics of contact osteogenesis and distance osteogenesis. The bone-implant interface possesses a small stiffness until gap closure, which subsequently evolves into a much higher stiffness, and this transition is reminiscent of a percolation transition whose threshold corresponds to gap closure. The model presented here, albeit preliminary, can be incorporated into future calculations of the bone-implant system where the interface is well-defined mechanically. Statement of significanceA simple, physically informed model for the mechanical characteristics of the bone-implant interface is still missing. Here, we start by extending the reported mechanical characteristics of a one cubic micrometre unit cell to a 250 µm long interface made of 1 µm thick layers. The stiffness of each cell (based on mineral content) is assigned randomly to mimic bone micro-heterogeneity. The numerical study of this interface representative structure allows for the simultaneous determination of the spatio-temporal evolution of the mechanical response at local (discrete element) and global (overall model) scales. The proposed model is the first of this kind that can easily be incorporated into realistic future models of bone-implant interaction with emphasis on implant stability and different loading conditions.

Percolation networks inside 3D model of the mineralized collagen fibril

Bone is a hierarchical biological material, characterized at the nanoscale by a recurring structure mainly composed of apatite mineral and collagen, i.e. the mineralized collagen fibril (MCF). Although the architecture of the MCF was extensively investigated by experimental and computational studies, it still represents a topic of debate. In this work, we developed a 3D continuum model of the mineral phase in the framework of percolation theory, that describes the transition from isolated to spanning cluster of connected platelets. Using Monte Carlo technique, we computed overall 120 × 106 iterations and investigated the formation of spanning networks of apatite minerals. We computed the percolation probability for different mineral volume fractions characteristic of human bone tissue. The findings highlight that the percolation threshold occurs at lower volume fractions for spanning clusters in the width direction with respect to the critical mineral volume fractions that characterize the percolation transition in the thickness and length directions. The formation of spanning clusters of minerals represents a condition of instability for the MCF, as it could be the onset of a high susceptibility to fracture. The 3D computational model developed in this study provides new, complementary insights to the experimental investigations concerning human MCF.

A Theoretical Study on the Mechanical Significance of Mineralized Collagen Fibril Orientation in Osteonal Lamellar Bone

In this study, the effect of orientation of mineralized collagen fibrils on bone mechanical properties relating to bone anisotropy was studied using data obtained from rehydrated lamellar bone samples. The dehydration-rehydration based and experimentally determined contraction, observed in orientations parallel and perpendicular to the osteonal axis was used to calculate bone anisotropy. The sublamellar bone model, with the layered mineralized collagen fibrils rotating at 5° was used. Following this model, the mineralized collagen layers were transformed at 5° relative to the orthogonal axes using a transform matrix. With dehydration, fibril diameter was reduced towards the mineral, forming contraction vectors. The x, y and z intercepts for these vectors were then calculated to give the u, v and w displacements, which gave anisotropy ratios ranging from 0.15266 to 6.55054. Compared with the experimental nanoindentation findings in the literature, there may be an indication of a correlation with the results of sublamellar arrangement at 20° angles. As the lateral indentation used in the anisotropy experiments may involve varying amounts of u and v displacements, the aspect angle of lateral indentation was evaluated in relation to the structural features of the model. This evaluation indicated the larger contribution of v displacement and thus relatively much smaller contribution of u displacement to lateral contraction. These findings indicate the significant effect of the mineralized collagen fibril arrangement on bone anisotropy.

Ordered Fibril Arrays in Osteons Promote the Multidirectional Nanodeflection of Cracks: In Situ AFM Imaging.

The high fracture resistance of cortical bone is not completely understood across its complex hierarchical structure, especially on micro- and nanolevels. Here, a novel in situ bending test combined with atomic force microscopy (AFM) is utilized to assess the micro-/nanoscale failure behavior of cortical bone under the external load. Unlike the smoother crack path in the transverse direction, the multilevel composite material model endows the longitudinal direction to show multilevel Y-shaped cracks with more failure interfaces for enhancing the fracture resistance. In the lamellae, the nanocracks originating from the interfibrillar nanointerface deflect multidirectionally at certain angles related to the periodic ordered arrangement of the mineralized collagen fibril (MCF) arrays. The ordered MCF arrays in the lamellae may use the nanodeflection of the dendritic nanocracks to adjust the direction of the crack tip, which subsequently reaches the interlamellae to sharply deflect and finally form a zigzag path. This work provides an insight into the relationship between the structure and the function of bone at a multilevel under load, specifically the role of the ordered MCF arrays in the lamellar structure.

Water promotes the formation of fibril bridging in antler bone illuminated by in situ AFM testing

Water, as one of the main components of bone, has a significant impact on the mechanical properties of bone. However, the micro-/nanoscale toughening mechanism induced by water in bone remains at only the theoretical level with static observations, and further research is still needed. In this study, a new in situ mechanical test combined with atomic force microscopy (AFM) was used to track the micro-/nanocrack propagation of hydrated and dehydrated antler bones in situ to explore the influence of water on the micro-/nanomechanical behavior of bone. In hydrated bone, observations of the crack tip region revealed major uncracked ligament bridging, and the conversion of mineralized collagen fibrils (MCFs) from bridging to breaking is clearly seen in real time. In dehydrated bone, multiple uncracked ligament bridges can be observed, but they are quickly broken by cracks, and the MCFs tend to break directly instead of forming fibril bridges. These experimental results indicate that the hydrated interface promotes slippage between collagen and the mineral phase and slippage between MCFs, while the dehydrated interface causes MCFs to fracture directly under lower strain. The platform we built provides new insights for studying the mechanism of toughening of the components in bones.

Podosome-Driven Defect Development in Lamellar Bone under the Conditions of Senile Osteoporosis Observed at the Nanometer Scale.

The degradation mechanism of human trabecular bone harvested from the central part of the femoral head of a patient with a fragility fracture of the femoral neck under conditions of senile osteoporosis was investigated by high-resolution electron microscopy. As evidenced by light microscopy, there is a disturbance of bone metabolism leading to severe and irreparable damages to the bone structure. These defects are evoked by osteoclasts and thus podosome activity. Podosomes create typical pit marks and holes of about 300–400 nm in diameter on the bone surface. Detailed analysis of the stress field caused by the podosomes in the extracellular bone matrix was performed. The calculations yielded maximum stress in the range of few megapascals resulting in formation of microcracks around the podosomes. Disintegration of hydroxyapatite and free lying collagen fibrils were observed at the edges of the plywood structure of the bone lamella. At the ultimate state, the disintegration of the mineralized collagen fibrils to a gelatinous matrix comes along with a delamination of the apatite nanoplatelets resulting in a brittle, porous bone structure. The nanoplatelets aggregate to big hydroxyapatite plates with a size of up to 10 x 20 μm2. The enhanced plate growth can be explained by the interaction of two mechanisms in the ruffled border zone: the accumulation of delaminated hydroxyapatite nanoplatelets near clusters of podosomes and the accelerated nucleation and random growth of HAP nanoplatelets due to a nonsufficient concentration of process-directing carboxylated osteocalcin cOC.

Altered collagen chemical compositional structure in osteopenic women with past fractures: A case-control Raman spectroscopic study.

Incidences of low-trauma fractures among osteopenic women may be related to changes in bone quality. In this blinded, prospective-controlled study, compositional and heterogeneity contributors of bone quality to fracture risk were examined. We hypothesize that Raman spectroscopy can differentiate between osteopenic women with one or more fractures (cases) from women without fractures (controls). This study involved the Raman spectroscopic analysis of cortical and cancellous bone composition using iliac crest biopsies obtained from 59-cases and 59-controls, matched for age (62.0±7.5 and 61.7±7.3years, respectively, p=0.38) and hip bone mineral density (BMD, 0.827±0.083 and 0.823±0.072g/cm3, respectively, p=0.57). Based on aggregate univariate case-control and odds ratio based logistic regression analyses, we discovered two Raman ratiometric parameters that were predictive of past fracture risk. Specifically, 1244/1268 and 1044/959cm-1 ratios, were identified as the most differential aspects of bone quality in cortical cases with odds ratios of 0.617 (0.406-0.938 95% CI, p=0.024) and 1.656 (1.083-2.534 95% CI, p=0.020), respectively. Both 1244/1268 and 1044/959cm-1 ratios exhibited moderate sensitivity (59.3-64.4%) but low specificity (49.2-52.5%). These results suggest that the organization of mineralized collagen fibrils were significantly altered in cortical cases compared to controls. In contrast, compositional and heterogeneity parameters related to mineral/matrix ratios, B-type carbonate substitutions, and mineral crystallinity, were not significantly different between cases and controls. In conclusion, a key outcome of this study is the significant odds ratios obtained for two Raman parameters (1244/1268 and 1044/959cm-1 ratios), which from a diagnostic perspective, may assist in the screening of osteopenic women with suspected low-trauma fractures. One important implication of these findings includes considering the possibility that changes in the organization of collagen compositional structure plays a far greater role in postmenopausal women with osteopenic fractures.

MC3T3 E1 cell response to mineralized nanofiber shish kebab structures.

Block copolymers (BCPs) are of growing interest because of their extensive utility in tissue engineering, particularly in biomimetic approaches where multifunctionality is critical. We synthesized polycaprolactone-polyacrylic acid (PCL-b-PAA) BCP and crystallized it onto PCL nanofibers, making BCP nanofiber shish kebab (BCP NFSK) structures. When mineralized in 2× simulated body fluid, BCP NFSK mimic the structure of mineralized collagen fibrils. We hypothesized that the addition of a calcium phosphate layer of graded roughness on the nano-structure of the nanofiber shish kebabs would enhance preosteoblast alkaline phosphatase (ALP) activity, which has been shown to be a critical component in bone matrix formation. The objectives in the study were to investigate the effect of mineralization on cell proliferation and ALP activity, and to also investigate the effect of BCP NFSK periodicity, a structural feature describing the distance between PCL-b-PAA crystals on the nanofiber core, on cell proliferation, and ALP activity. ALP activity of cells cultured on the mineralized BCP NFSK template was significantly higher than the nonmineralized BCP NFSK templates. Interestingly, no statistical difference was observed in ALP activity when the periodic varied, indicating that surface chemistry seemed to play a larger role than the surface roughness.

Role of strain rate sensitivity of extrafibrillar matrix on fracture in mineralized collagen fibril arrays

Bone is a biological composite possessing complex hierarchical structure, which endows it with extraordinary damage tolerance. Despite the progress on the relationship between fracture behavior and the hierarchical structure of bone, contributions of the submicroscale constituents to fracture resistance of bone remain elusive. In this study, the calculations are carried out for fracture in staggered mineralized collagen fibril (MCF) arrays using the cohesive zone framework. The strain rate hardening of extrafibrillar matrix (EFM), post-yield strain hardening of the EFM, plastic deformation of the MCF caused by mineral/collagen sliding, and debonding of the interface between MCF and EFM are accounted for in the analyses; the individual and combined effects of strain rate sensitivity of the EFM and fracture properties of the EFM-MCF interface are revealed. It is found that for the strong EFM-MCF interface, high degree of strain rate sensitivity of EFM gives rise to low toughness of MCF arrays. Compared with plastic deformations in MCFs and EFM, interfacial debonding provides smaller contribution to toughness of MCF arrays, and plastic dissipation of MCFs is the major source of toughening. For the tough EFM-MCF interface, the toughness of MCF arrays increases with increasing degree of strain rate sensitivity of EFM, and the EFM with high degree of strain rate sensitivity promotes spreading of plastic deformation, leading to amplified damage energy dissipation in interfaces. We have further identified that strain rate sensitivity of the EFM has negligible influence on toughness of MCF arrays in the case of weak EFM-MCF interface, where interfacial debonding serves as the major toughening mechanism. However, the strain rate sensitive EFM can still activate the mechanism of spreading plastic deformation in this case, giving rise to the increase in relative contribution of plastic dissipation in MCFs with increasing strain rate sensitivity of the EFM.

Molecular origin of viscoelasticity in mineralized collagen fibrils.

Bone is mineralized tissue constituting the skeletal system, supporting and protecting the body's organs and tissues. In addition to such fundamental mechanical functions, bone also plays a remarkable role in sound conduction. From a mechanical standpoint, bone is a composite material consisting of minerals and collagen arranged in multiple hierarchical structures, with a complex anisotropic viscoelastic response, capable of transmitting and dissipating energy. At the molecular level, mineralized collagen fibrils are the basic building blocks of bone tissue, and hence, understanding bone properties down to fundamental tissue structures enables better identification of the mechanisms of structural failures and damage. While efforts have focused on the study of micro- and macro-scale viscoelasticity related to bone damage and healing based on creep, mineralized collagen has not been explored at the molecular level. We report a study that aims at systematically exploring the viscoelasticity of collagenous fibrils with different mineralization levels. We investigate the dynamic mechanical response upon cyclic and impulsive loads to observe the viscoelastic phenomena from either shear or extensional strains via molecular dynamics. We perform a sensitivity analysis with several key benchmarks: intrafibrillar mineralization percentage, hydration state, and external load amplitude. Our results show an increase of the dynamic moduli with an increase of the mineral percentage, pronounced at low strains. When intrafibrillar water is present, the material softens the elastic component, but considerably increases its viscosity, especially at high frequencies. This behavior is confirmed from the material response upon impulsive loads, in which water drastically reduces the relaxation times throughout the input velocity range by one order of magnitude, with respect to the dehydrated counterparts. We find that, upon transient loads, water has a major impact on the mechanics of mineralized fibrillar collagen, being able to improve the capability of the tissue to passively and effectively dissipate energy, especially after fast and high-amplitude external loads. Our study provides knowledge of bone mechanics in relation to pathologies deriving from dehydration or traumas. Moreover, these findings show the potential for being used in designing new bioinspired materials not limited to tissue engineering applications, in which passive mechanisms for dissipating energy can prevent structural failures.

Growth of mineralized collagen films by oriented calcium fluoride nanocrystal assembly with enhanced cell proliferation.

Bone is a highly calcified tissue with 60 wt% inorganic components. It is made up of mineralized collagen fibrils, where the platelet-like hydroxyapatite nanocrystals deposit within the collagen fibrils in an oriented manner. Inspired by the special structure and biological activity of bone, we realize the intrafibrillar mineralization of collagen films with oriented calcium fluoride nanocrystals in vitro. Amorphous calcium fluoride (ACF) precursors are generated by polyacrylic acid through polymer-induced liquid precursor processes. The precursors are ready to infiltrate and fill the gap zones laterally and then diffuse to occupy the whole space inside the collagen longitudinally. Finally, the fully mineralized collagen fibrils exhibit a single-crystal-like structure after transforming precursors to co-oriented nanocrystals under the influence of arranged collagen molecules. Expanding the collagen mineralization from 1D fibrils to 2D films, the growth of mineralized areas on the films with a reaction-limited behavior is found. The kinetic rate of growth is around 0.2-0.3 μm min-1, which depends on the pH of the solution. Furthermore, the mineralized collagen films exhibit an enhanced ability of cell proliferation over the pure collagen matrices. Understanding the mineralization of artificial collagen-based scaffolds may have broad promising potentials for bone tissue regeneration and repair in the future.

Focused ion beam-SEM 3D analysis of mineralized osteonal bone: lamellae and cement sheath structures

The mineralized collagen fibril is the basic building block of bone, and hence is the key to understanding bone structure and function. Here we report imaging of mineralized pig bone samples in 3D using the focused ion beam-scanning electron microscope (FIB-SEM) under conditions that reveal the 67 nm D-banding of mineralized collagen fibrils. We show that in adult pig osteons, the lamellar bone comprises alternating layers with either collagen fibrils predominantly aligned in one direction, and layers in which fibrils are predominantly aligned in two directions. The cement sheath contains thin layers of both these motifs, but its dominant structural component comprises a very complex layer of fibrils predominantly aligned in three or more directions. The degree of mineralization of the cement sheath is comparable to that of the osteon interior. The extent of alignment (dispersion) of the collagen fibrils in the osteonal lamellar bone is significantly higher than in the cement sheath. Canaliculi within the cement sheath are mainly aligned parallel to the cement sheath boundary, whereas in the lamellar bone they are mainly aligned perpendicular to the lamellar boundaries. This study further characterizes the presence of two types of collagen fibril arrangements previously identified in demineralized lamellar bone from other species. The simple sample preparation procedure for mineralized bone and the lower risk of introducing artifacts opens the possibility of using FIB-SEM to study more samples, to obtain automatic quantitative information on collagen fibril organization and to evaluate the degrees of mineralization all in relatively large volumes of bone.

Piezoelectric Heterogeneity in Collagen Type I Fibrils Quantitatively Characterized by Piezoresponse Force Microscopy.

Piezoelectricity of Type I collagen can provide the stress-generated potential that is considered to be one of the candidate mechanisms to explain bone's adaptation to loading. However, it is still challenging to quantify piezoelectricity because of its heterogeneity and small magnitude. In this study, resonance-enhanced piezoresponse force microscopy (PFM) was utilized to amplify a weak piezoresponse of a single collagen fibril with a carefully calibrated cantilever. The quantitative PFM, combined with a dual-frequency resonance-tracking method, successfully identified the anisotropic and heterogenous nature of the piezoelectric properties in the collagen fibril. The profile of shear piezoelectric coefficient (d15) was obtained to be periodic along the collagen fibril, with a larger value in the gap zone (0.51 pm/V) compared to the value in the overlap zone (0.29 pm/V). Interestingly, this piezoelectric profile corresponds to the periodic profile of mechanical stiffness in a mineralized collagen fibril having a higher stiffness in the gap zone. Considering that apatite crystals are nucleated at the gap zone and subsequently grown along the collagen fibril, the heterogeneous and anisotropic nature of piezoelectric properties highlights the physiological importance of the collagen piezoelectricity in bone mineralization.

Combining polarized Raman spectroscopy and micropillar compression to study microscale structure-property relationships in mineralized tissues

Bone is a natural composite possessing outstanding mechanical properties combined with a lightweight design. The key feature contributing to this unusual combination of properties is the bone hierarchical organization ranging from the nano- to the macro-scale. Bone anisotropic mechanical properties from two orthogonal planes (along and perpendicular to the main bone axis) have already been widely studied. In this work, we demonstrate the dependence of the microscale compressive mechanical properties on the angle between loading direction and the mineralized collagen fibril orientation in the range between 0° and 82°. For this, we calibrated polarized Raman spectroscopy for quantitative collagen fibril orientation determination and validated the method using widely used techniques (small angle X-ray scattering, micro-computed tomography). We then performed compression tests on bovine cortical bone micropillars with known mineralized collagen fibril angles. A strong dependence of the compressive micromechanical properties of bone on the fibril orientation was found with a high degree of anisotropy for both the elastic modulus (Ea/Et=3.80) and the yield stress (σay/σty=2.54). Moreover, the post-yield behavior was found to depend on the MCF orientation with a transition between softening to hardening behavior at approximately 50°. The combination of methods described in this work allows to reliably determine structure-property relationships of bone at the microscale, which may be used as a measure of bone quality.

Effect of geometrical structure variations on the viscoelastic and anisotropic behaviour of cortical bone using multi-scale finite element modelling

Multi-scale finite element analysis is performed to ascertain the effect of geometrical changes at multiple structural scales on the mechanical properties of cortical bone. Finite element models are developed, with reference to experimental data from existing literature, to account for bone's viscoelastic behaviour and anisotropic structure from the most fundamental level of bone consisting of mineralised collagen fibrils, up to the macroscopic level consisting of osteons and the Haversian canals. A statistical approach is incorporated to perform sensitivity analyses on the effects of different geometrical parameters on the effective material properties of cortical bone at each length scale. Numerical results indicate that there is an exponential correlation between the mineral volume fraction and the effective stiffness constants at each length scale. This contributes to the exponential behaviour of the instantaneous moduli describing cortical bone's two-phase stress relaxation process: a fast and slow response relaxation behaviour. Results indicate that the fast response relaxation time is independent of bone's structural anisotropy, whilst being dependent on variations in the global mineral volume fraction between length scales. However, the slow response relaxation time is independent of the changes in mineral volume fraction. It is also observed that the slow response relaxation time varies with bone's anisotropic structure, and therefore, contributes to the anisotropic properties of bone.

Elastic modulus mapping for bovine cortical bone from submillimeter- to submicron-scales using PeakForce Tapping atomic force microscopy

Bone is a composite material consisting of organic and inorganic components that are organized into hierarchical structures to provide load-bearing functions. This paper presents the results of PeakForce Tapping atomic force microscopy (AFM) scans on cut and polished bovine cortical bone specimens that were submerged in water. The elastic modulus map and surface morphology were obtained for various bone hierarchical structures from submillimeter- to submicron-scales. The elastic modulus of osteons (20.51 ± 6.85 GPa) was slightly lower than the interstitial bone (21.87 ± 5.48 GPa); they were both much greater than that of the cement lines (7.49 ± 4.23 GPa). The elastic modulus in the lamella structures varied periodically from higher values in thick sub-lamellae (21.49 ± 6.58 GPa) to the lower values in thin sub-lamellae (9.67 ± 2.69 GPa). The results also show relatively softer mineralized collagen fibril bundle arrays (12.94 ± 2.71 GPa) embedded in harder matrix materials (28.39 ± 5.75 GPa). The variations in the elastic modulus suggest different degrees of mineralization or different fibril orientations. The histograms of elastic modulus indicate the dominating compositions or dominating fibril orientations.