Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles

Both elastic modulus and fracture stress are known to increase with the amount of mineral deposited within collagen fibrils. Current mechanical models of mineralized fibrils, where mineral platelets are arranged in parallel arrays, reproduce the first effect but fail to predict an increase in fracture stress. Here, we propose a model with a staggered array of platelets that is in better agreement with results on molecular packing in collagen fibrils and that accounts for an increase of both elastic modulus and fracture stress with the amount of mineral in the fibril. Finally, we explore the dependence of the mechanical properties within the model, when the degree of mineralization and the thickness of the platelets as well as their distance varies.     

Hierarchical modeling of the elastic properties of bone at submicron scales: the role of extrafibrillar mineralization

We model the elastic properties of bone at the level of mineralized collagen fibrils via step-by-step homogenization from the staggered arrangement of collagen molecules up to an array of parallel mineralized fibrils. A new model for extrafibrillar mineralization is proposed, assuming that the extrafibrillar minerals are mechanically equivalent to reinforcing rings coating each individual fibril. Our modeling suggests that no more than 30% of the total mineral content is extrafibrillar and the fraction of extrafibrillar minerals grows linearly with the overall degree of mineralization. It is shown that the extrafibrillar mineralization considerably reinforces the fibrils’ mechanical properties in the transverse directions and the fibrils’ shear moduli. The model predictions for the elastic moduli and constants are found to be in a good agreement with the experimental data reported in the literature.     

Amelogenin-Collagen Interactions Regulate Calcium Phosphate Mineralization in Vitro

Collagen and amelogenin are two major extracellular organic matrix proteins of dentin and enamel, the mineralized tissues comprising a tooth crown. They both are present at the dentin-enamel boundary (DEB), a remarkably robust interface holding dentin and enamel together. It is believed that interactions of dentin and enamel protein assemblies regulate growth and structural organization of mineral crystals at the DEB, leading to a continuum at the molecular level between dentin and enamel organic and mineral phases. To gain insight into the mechanisms of the DEB formation and structural basis of its mechanical resiliency we have studied the interactions between collagen fibrils, amelogenin assemblies, and forming mineral in vitro, using electron microscopy. Our data indicate that collagen fibrils guide assembly of amelogenin into elongated chain or filament-like structures oriented along the long axes of the fibrils. We also show that the interactions between collagen fibrils and amelogenin-calcium phosphate mineral complexes lead to oriented deposition of elongated amorphous mineral particles along the fibril axes, triggering mineralization of the bulk of collagen fibril. The resulting structure was similar to the mineralized collagen fibrils found at the DEB, with arrays of smaller well organized crystals inside the collagen fibrils and bundles of larger crystals on the outside of the fibrils. These data suggest that interactions between collagen and amelogenin might play an important role in the formation of the DEB providing structural continuity between dentin and enamel.     

Vitamin K2, a gamma-carboxylating factor of gla-proteins, normalizes the bone crystal nucleation impaired by Mg-insufficiency

It has been reported that the Mg-insufficient bone is fragile upon mechanical loading, despite its high bone mineral density, while vitamin K2 (MK-4: menatetrenone) improved the mechanical strength of Mg-insufficient bone. Therefore, we aimed to elucidate the ultrastructural properties of bone in rats with dietary Mg insufficiency with and without MK-4 supplementation. Morphological examinations including histochemistry, transmission electron microscopy, electron probe microanalysis (EPMA) and X-ray diffraction were conducted on the femora and tibiae of 4-week-old Wistar male rats fed with 1) a normal diet (control group, 0.09% Mg), 2) a Mg-insufficient diet (low Mg group, 0.006% Mg), or 3) a Mg-insufficient diet supplemented with MK-4 (MK-4 group, 0.006% Mg, 0.03% MK-4). MK-4 appeared to inhibit the osteoclastic bone resorption that is stimulated by Mg insufficiency. EPMA analysis, however, revealed an increased concentration of Ca paralleling Mg reduction in the low Mg group. Assessment by X-ray diffraction revealed an abundance of a particular synthetic form of hydroxyapatite in the low Mg group, while control bones featured a variety of mineralized crystals. In addition, Mg-deficient bones featured larger mineral crystals, i.e., crystal overgrowth. This crystalline aberration in Mg-insufficient bones induced collagen fibrils to mineralize easily, even in the absence of mineralized nodules, which therefore led to an early collapse of the fibrils. MK-4 prevented premature collagen mineralization by normalizing the association of collagen fibrils with mineralized nodules. Thus, MK-4 appears to rescue the impaired collagen mineralization caused by Mg insufficiency by promoting a re-association of the process of collagen mineralization with mineralized nodules.     

Microstructural Features of Non-Union of Human Humeral Shaft Fracture

Microstructures of non-unions of human humeral shaft fractures were investigated by using scanning electron microscopy, transmission electron microscopy, and X-ray microdiffraction. The non-union has a trabeculae structural framework similar to woven bone. Among the trabeculae are cavities that are subdivided into small chambers by thin plates of collagen fibrils. Some chambers are filled with variously shaped mineralized particles several micrometers in size. The collagen fibrils in both the trabeculae and the thin plates were only slightly mineralized by hydroxyapatite. Vesicles loaded with noncrystalline calcium phosphate (NCP) were observed in most mineralized particles, and brushite crystals with special morphology were seen to be embedded in some particles in irregular shapes. X-ray microdiffraction results indicated that the mineral phases in the non-unions were mainly NCP in addition to small amounts of hydroxyapatite and brushite. NCP deposition and insufficient mineralization of the collagen fibrils may be two important microstructural features of the non-unions of human humeral shaft fractures different from normally repaired bone callus.     

Possible role of DMP1 in dentin mineralization

Dentin Matrix Protein 1 (DMP1), the essential noncollagenous proteins in dentin and bone, is believed to play an important role in the mineralization of these tissues, although the mechanisms of its action are not fully understood. To gain insight into DMP1 functions in dentin mineralization we have performed immunomapping of DMP1 in fully mineralized rat incisors and in vitro calcium phosphate mineralization experiments in the presence of DMP1. DMP1 immunofluorescene was localized in peritubular dentin (PTD) and along the dentin-enamel boundary. In vitro phosphorylated DMP1 induced the formation of parallel arrays of crystallites with their c-axes co-aligned. Such crystalline arrangement is a hallmark of mineralized collagen fibrils of bone and dentin. Interestingly, in DMP1-rich PTD, which lacks collagen fibrils, the crystals are organized in a similar manner. Based on our findings we hypothesize, that in vivo DMP1 controls the mineral organization outside of the collagen fibrils and plays a major role in the mineralization of PTD.     

Aspects of Mineral Structure in Normally Calcifying Avian Tendon

Structural characteristics of normally calcifying leg tendons of the domestic turkey Meleagris gallopavo have been observed for the first time by tapping mode atomic force microscopy (TMAFM), and phase as well as corresponding topographic images were acquired to gain insight into the features of mineralizing collagen fibrils and fibers. Analysis of different regions of the tendon has yielded new information concerning the structural interrelationships in vivo between collagen fibrils and fibers and mineral crystals appearing in the form of plates and plate aggregates. TMAFM images show numerous mineralized collagen structures exhibiting characteristic periodicity (54-70 nm), organized with their respective long axes parallel to each other. In some instances, mineral plates (30-40 nm thick) are found interspersed between and in intimate contact with the mineralized collagen. The edges of such plates lie parallel to the neighboring collagen. Many of these plates appear to be aligned to form larger aggregates (475-600 nm long x 75-90 nm thick) that also retain collagen periodicity along their exposed edges. Intrinsic structural properties of the mineralizing avian tendon have not previously been described on the scale reported in this study. These data provide the first visual evidence supporting the concept that larger plates form from parallel association of smaller ones, and the data fill a gap in knowledge between macromolecular- and anatomic-scale studies of the mineralization of avian tendon and connective tissues in general. The observed organization of mineralized collagen, plates, and plate aggregates maintaining a consistently parallel nature demonstrates the means by which increasing structural complexity may be achieved in a calcified tissue over greater levels of hierarchical order.     

Local variations in the micromechanical properties of mouse femur: the involvement of collagen fiber orientation and mineralization

In this study we sought to understand the material level basis for local variations in the uniaxial micromechanical properties of mouse cortical bone. It was hypothesized that the opposing anterior and posterior quadrants will significantly differ in terms of their mechanical function, such that, the anterior portion will be stronger in tension whereas the posterior quadrant will be stronger in compression. Mechanical properties were assessed via microtensile and microcompressive tests of standardized coupon-shaped specimens from femurs of Swiss Webster mice (9 weeks). The mineralization and mineral quality was assessed via Raman spectroscopy and the overall collagen orientation was investigated with quantitative polarized imaging. Micromechanical tests demonstrated that the modulus, yield stress, maximum stress and fracture energy of the posterior quadrant was 66%, 53%, 42% and 31% of anterior quadrant; however, the compressive properties did not differ between the two quadrants. Raman microspectroscopic analysis indicated that the mineral matrix ratio, mineral crystallinity and carbonation did not vary between the quadrants. However, the collagen fibers in the anterior quadrant were significantly (p<0.05) more oriented along the longer axis of the diaphyseal shaft than the collagen fibers of the posterior quadrant. Therefore, we concluded that the orientation of collagen fibers with respect to the anatomical loading axis has a profound effect on the uniaxial mechanical function of murine bone. It will be a matter of further research to reveal the role of local variations in the mode of stress on this material level dichotomy in tissue organization and mechanical function.     

Mechanical properties of mineralized collagen fibrils as influenced by demineralization

Dentin and bone derive their mechanical properties from a complex arrangement of collagen type-I fibrils reinforced with nanocrystalline apatite mineral in extra- and intrafibrillar compartments. While mechanical properties have been determined for the bulk of the mineralized tissue, information on the mechanics of the individual fibril is limited. Here, atomic force microscopy was used on individual collagen fibrils to study structural and mechanical changes during acid etching. The characteristic 67 nm periodicity of gap zones was not observed on the mineralized fibril, but became apparent and increasingly pronounced with continuous demineralization. AFM-nanoindentation showed a decrease in modulus from 1.5 GPa to 50 MPa during acid etching of individual collagen fibrils and revealed that the modulus profile followed the axial periodicity. The nanomechanical data, Raman spectroscopy and SAXS support the hypothesis that intrafibrillar mineral etches at a substantially slower rate than the extrafibrillar mineral. These findings are relevant for understanding the biomechanics and design principles of calcified tissues derived from collagen matrices.     

Sensitivity analysis and parametric study of elastic properties of an unidirectional mineralized bone fibril-array using mean field methods

The key parameters determining the elastic properties of an unidirectional mineralized bone fibril-array decomposed in two further hierarchical levels are investigated using mean field methods. Modeling of the elastic properties of mineralized micro- and nanostructures requires accurate information about the underlying topology and the constituents’ material properties. These input data are still afflicted by great uncertainties and their influence on computed elastic constants of a bone fibril-array remains unclear. In this work, mean field methods are applied to model mineralized fibrils, the extra-fibrillar matrix and the resulting fibril-array. The isotropic or transverse isotropic elastic constants of these constituents are computed as a function of degree of mineralization, mineral distribution between fibrils and extra-fibrillar matrix, collagen stiffness and fibril volume fraction. The linear sensitivity of the elastic constants was assessed at a default set of the above parameters. The strain ratios between the constituents as well as the axial and transverse indentation moduli of the fibril-array were calculated for comparison with experiments. Results indicate that the degree of mineralization and the collagen stiffness dominate fibril-array elasticity. Interestingly, the stiffness of the extra-fibrillar matrix has a strong influence on transverse and shear moduli of the fibril-array. The axial strain of the intra-fibrillar mineral platelets is 30–90% of the applied fibril strain, depending on mineralization and collagen stiffness. The fibril-to-fibril-array strain ratio is essentially ~1. This study provides an improved insight in the parameters, which govern the fibril-array stiffness of mineralized tissues such as bone.     

Mechanical properties of collagen fibrils

The formation of collagen fibers from staggered subfibrils still lacks a universally accepted model. Determining the mechanical properties of single collagen fibrils (diameter 50-200 nm) provides new insights into collagen structure. In this work, the reduced modulus of collagen was measured by nanoindentation using atomic force microscopy. For individual type 1 collagen fibrils from rat tail, the modulus was found to be in the range from 5 GPa to 11.5 GPa (in air and at room temperature). The hypothesis that collagen anisotropy is due to the subfibrils being aligned along the fibril axis is supported by nonuniform surface imprints performed by high load nanoindentation.     

Specimen-specific multi-scale model for the anisotropic elastic constants of human cortical bone

The anisotropic elastic constants of human cortical bone were predicted using a specimen-specific micromechanical model that accounted for structural parameters across multiple length scales. At the nano-scale, the elastic constants of the mineralized collagen fibril were estimated from measured volume fractions of the constituent phases, namely apatite crystals and Type I collagen. The elastic constants of the extracellular matrix (ECM) were predicted using the measured orientation distribution function (ODF) for the apatite crystals to average the contribution of misoriented mineralized collagen fibrils. Finally, the elastic constants of cortical bone tissue were determined by accounting for the measured volume fraction of Haversian porosity within the ECM. Model predictions using the measured apatite crystal ODF were not statistically different from experimental measurements for both the magnitude and anisotropy of elastic constants. In contrast, model predictions using common idealized assumptions of perfectly aligned or randomly oriented apatite crystals were significantly different from the experimental measurements. A sensitivity analysis indicated that the apatite crystal volume fraction and ODF were the most influential structural parameters affecting model predictions of the magnitude and anisotropy, respectively, of elastic constants.     

Three-dimensional spatial relationship between the collagen fibrils and the inorganic calcium phosphate crystals of pickerel (Americanus americanus) and herring (Clupea harengus) bone

High-voltage (1.0 MV) electron microscopy and stereomicroscopy, electron probe microanalysis, electron diffraction and three-dimensional computer reconstruction, have been used to examine the spatial relationship between the inorganic crystals of calcium phosphate and the collagen fibrils of pickerel and herring bone. High-voltage stereo electron-micrographs were obtained of cross-sections of the cylinder-shaped intramuscular bones in uncalcified regions, in regions where only one or only several crystals had been deposited in some of the fibrils, and in successive sections containing progressively more mineral crystals until the stage of full mineralization was reached. High-resolution electron probe microanalysis confirmed that the electron-dense particles contained calcium and phosphorus. In the earliest stages of mineralization and progressing throughout the mineralization process, the crystals are located only within the collagen fibrils; crystals are not observed free in the extracellular spaces between collagen fibrils. The progressive increase in the mass of mineral deposited in the bone tissue with time occurs, essentially, completely within the collagen fibrils including the stage of full mineralization. At this stage, cross-sectional profiles of collagen fibrils are completely obliterated by mineral. A small number of crystals that are located on or close to the surface of the fibrils appear to extend a very short distance into the spaces between the fibrils. These ultrastructural observations of the very onset of calcification in which nucleation of the calcium phosphate crystals is clearly shown to begin within specific volumes of collagen fibrils, and of the subsequent temporal and spatial sequences of this phenomenon, which shows that calcification continues wholly within the collagen fibrils until maximum calcification is achieved, add important information on the basic physical chemical mechanism of the calcification and the structural elements that are involved. The spatial and temporal independence of the sites where mineralization is initiated establishes that such ultrastructural locations within individual collagen fibrils represent independent, physical chemical nucleation loci. The findings are totally inconsistent with the proposal that crystals must first be deposited in matrix vesicles, or other components such as mitochondria, and subsequently released and propagated in the interfibrillar space, until they eventually reach and impregnate the hole zone regions of the collagen fibrils. Three-dimensional computer reconstruction of serial transverse and longitudinal sections demonstrates periodic swellings along the collagen fibrils, corresponding to the hole zone region of their axial period as mineralization proceeds.(ABSTRACT TRUNCATED AT 400 WORDS)     

Post-yield nanomechanics of human cortical bone in compression using synchrotron X-ray scattering techniques

The ultrastructural response to applied loads governs the post-yield deformation and failure behavior of bone, and is correlated with bone fragility fractures. Combining a novel progressive loading protocol and synchrotron X-ray scattering techniques, this study investigated the correlation of the local deformation (i.e., internal strains of the mineral and collagen phases) with the bulk mechanical behavior of bone. The results indicated that the internal strains of the longitudinally oriented collagen fibrils and mineral crystals increased almost linearly with respect to the macroscopic strain prior to yielding, but markedly decreased first and then gradually leveled off after yielding. Similar changes were also observed in the applied stress before and after yielding of bone. However, the collagen to mineral strain ratio remained nearly constant throughout the loading process. In addition, the internal strains of longitudinal mineral and collagen phases did not exhibit a linear relationship with either the modulus loss or the plastic deformation of bulk bone tissue. Finally, the time-dependent response of local deformation in the mineral phase was observed after yielding. Based on the results, we speculate that the mineral crystals and collagen fibrils aligned with the loading axis only partially explain the post-yield deformation, suggesting that shear deformation involving obliquely oriented crystals and fibrils (off axis) is dominant mechanism of yielding for human cortical bone in compression.     

Evidence of entropic elasticity of human bone trabeculae at low strains

We performed 60 microtensile tests on 6 single trabeculae excised from a human femur head at various maximum tensile loads. The obtained results show a clear dependence of the calculated stress-strain behaviour from the applied load and thus from the mean stress over the cross section of the trabecula. The pooled data were found in good agreement with a combination of both the model of the nonlinear stress-strain behaviour of collagen fibrils and that for the modulus of elasticity of staggered mineralized collagen. This circumstance could also suggest a realistic explanation of the extreme variability found in literature for the elastic modulus of the trabecular material. In particular, when the trabeculae are solicited with relatively low stresses, their mechanical properties are mainly affected by the entropic elasticity of collagen molecules. This work offers both experimental data and a reasonable interpretation of the behaviour of fully mineralized tissue at low strains, that is up to about 0.1%.     

Biomimetic mineralization of woven bone-like nanocomposites: role of collagen cross-links

Ideal biomaterials for bone grafts must be biocompatible, osteoconductive, osteoinductive and have appropriate mechanical properties. For this, the development of synthetic bone substitutes mimicking natural bone is desirable, but this requires controllable mineralization of the collagen matrix. In this study, densified collagen films (up to 100 μm thick) were fabricated by a plastic compression technique and cross-linked using carbodiimide. Then, collagen-hydroxyapatite composites were prepared by using a polymer-induced liquid-precursor (PILP) mineralization process. Compared to traditional methods that produce only extrafibrillar hydroxyapatite (HA) clusters on the surface of collagen scaffolds, by using the PILP mineralization process, homogeneous intra- and extrafibrillar minerals were achieved on densified collagen films, leading to a similar nanostructure as bone, and a woven microstructure analogous to woven bone. The role of collagen cross-links on mineralization was examined and it was found that the cross-linked collagen films stimulated the mineralization reaction, which in turn enhanced the mechanical properties (hardness and modulus). The highest value of hardness and elastic modulus was 0.7 ± 0.1 and 9.1 ± 1.4 GPa in the dry state, respectively, which is comparable to that of woven bone. In the wet state, the values were much lower (177 ± 31 and 8 ± 3 MPa) due to inherent microporosity in the films, but still comparable to those of woven bone in the same conditions. Mineralization of collagen films with controllable mineral content and good mechanical properties provide a biomimetic route toward the development of bone substitutes for the next generation of biomaterials. This work also provides insight into understanding the role of collagen fibrils on mineralization.     

Changes in glycosaminoglycan binding to collagen during desmoid mineralization as revealed by different electron-microscopic staining techniques.

Mineralization at collagen fibrils is regulated by glycosaminoglycans (GAG). Alterations in proteoglycan composition during mineralization as well as inhibition of mineralization by GAGs are well documented. Collagen-GAG interactions during desmoid osteogenesis in fetal rat calvariae were investigated ultrastructurally by means of different fixation techniques. Mineralization was restricted to the collagen of the osteoid at the ectocranial side. Beyond the osteoid, one layer containing degenerated cells was found, followed by sheets of healthy osteoblasts with nonmineralized collagen fibrils. These fibrils were ordered in bundles, but were irregularly arranged in the mineralized osteoid. After fixation in glutaraldehyde-ruthenium red (GA-RR), small RR-positive granules were periodically attached to the fibrils of the nonmineralized collagen. These granules were absent at collagen in the mineralized osteoid. Periodically bound granules (periodicity of 62 nm) could clearly be demonstrated along collagen fibrils by pretreatment with the positively charged protamine sulfate and subsequent fixation in GA-RR in the nonmineralized collagen. In the mineralized osteoid, however, these granules were present, but periodic binding was missing. Heparin pretreatment followed by fixation in GA-RR revealed periodically bound fine strands between collagen fibrils running parallel in the nonmineralized collagen; these threads were absent in the mineralizing osteoid. Restriction of mineralization to osteoid at the mineralization border may be reflected by the observed changes in GAG binding to collagen fibrils within the osteoid of developing fetal calvariae in contrast to binding to collagen in nonmineralized areas.     

Elastic modulus of hard tissues

This work aims at evaluating the elastic modulus of hard biological tissues by considering their staggered platelet micro-structure. An analytical expression for the effective modulus along the stagger direction is formulated using three non-dimensional structural variables. Structures with a single staggered hierarchy (e.g. collagen fibril) are first studied and predictions are compared with the experimental results and finite element simulations from the literature. A more complicated configuration, such as an array of fibrils, is analyzed next. Finally, a mechanical model is proposed for tooth dentin, in which variations in the multi-scale structural hierarchy are shown to significantly affect the macroscopic mechanical properties.     

Lateral packing of mineral crystals in bone collagen fibrils

Combined small-angle x-ray scattering and transmission electron microscopy studies of intramuscular fish bone (shad and herring) indicate that the lateral packing of nanoscale calcium-phosphate crystals in collagen fibrils can be represented by irregular stacks of platelet-shaped crystals, intercalated with organic layers of collagen molecules. The scattering intensity distribution in this system can be described by a modified Zernike-Prins model, taking preferred orientation effects into account. Using the model, the diffuse fan-shaped small-angle x-ray scattering intensity profile, dominating the equatorial region of the scattering pattern, could be quantitatively analyzed as a function of the degree of mineralization. The mineral platelets were found to be very thin (1.5 nm ∼ 2.0 nm), having a narrow thickness distribution. The thickness of the organic layers between adjacent mineral platelets within a stack is more broadly distributed with the average value varying from 6 nm to 10 nm, depending on the extent of mineralization. The two-dimensional analytical scheme also leads to quantitative information about the preferred orientation of mineral stacks and the average height of crystals along the crystallographic c axis.     

Ductile sliding between mineral crystals followed by rupture of collagen crosslinks: Experimentally supported micromechanical explanation of bone strength

There is an ongoing discussion on how bone strength could be explained from its internal structure and composition. Reviewing recent experimental and molecular dynamics studies, we here propose a new vision on bone material failure: mutual ductile sliding of hydroxyapatite mineral crystals along layered water films is followed by rupture of collagen crosslinks. In order to cast this vision into a mathematical form, a multiscale continuum micromechanics theory for upscaling of elastoplastic properties is developed, based on the concept of concentration and influence tensors for eigenstressed microheterogeneous materials. The model reflects bone's hierarchical organization, in terms of representative volume elements for cortical bone, for extravascular and extracellular bone material, for mineralized fibrils and the extrafibrillar space, and for wet collagen. In order to get access to the stress states at the interfaces between crystals, the extrafibrillar mineral is resolved into an infinite amount of cylindrical material phases oriented in all directions in space. The multiscale micromechanics model is shown to be able to satisfactorily predict the strength characteristics of different bones from different species, on the basis of their mineral/collagen content, their intercrystalline, intermolecular, lacunar, and vascular porosities, and the elastic and strength properties of hydroxyapatite and (molecular) collagen.