A new numerical concept for modeling hydroxyapatite in human cortical bone

This research presents a new modelling procedure which allows the computation of the physical properties of the human cortical bone, considered as a strongly heterogeneous medium consisting of bony architecture and the physical properties of the two basic components: the collagen and the hydroxyapatite (Hap). The numerical simulations are based on the homogenisation theory, however, since the size of the Hap crystals are small compared to the size of a collagen stick, a new entity (the elementary volume of mineral content (EVMC)) is defined at the nanoscopic scale. This model permits the testing of all the possible structural configurations that may be present and suggests that the anisotropy of the bone is not only induced by the haversian structure but by the properties of the Hap crystals and their special organisation.     

'Universal' microstructural patterns in cortical and trabecular, extracellular and extravascular bone materials: micromechanics-based prediction of anisotropic elasticity

Bone materials are characterized by an astonishing variability and diversity. Still, because of 'architectural constraints' due to once chosen material constituents and their physical interaction, the fundamental hierarchical organization or basic building plans of bone materials remain largely unchanged during biological evolution. Such universal patterns of microstructural organization govern the mechanical interaction of the elementary components of bone (hydroxyapatite, collagen, water; with directly measurable tissue-independent elastic properties), which are here quantified through a multiscale homogenization scheme delivering effective elastic properties of bone materials: at a scale of 10nm, long cylindrical collagen molecules, attached to each other at their ends by approximately 1.5nm long crosslinks and hosting intermolecular water inbetween, form a contiguous matrix called wet collagen. At a scale of several hundred nanometers, wet collagen and mineral crystal agglomerations interpenetrate each other, forming the mineralized fibril. At a scale of 5-10microm, the extracellular solid bone matrix is represented as collagen fibril inclusions embedded in a foam of largely disordered (extrafibrillar) mineral crystals. At a scale above the ultrastructure, where lacunae are embedded in extracellular bone matrix, the extravascular bone material is observed. Model estimates predicted from tissue-specific composition data gained from a multitude of chemical and physical tests agree remarkably well with corresponding acoustic stiffness experiments across a variety of cortical and trabecular, extracellular and extravascular materials. Besides from reconciling the well-documented, seemingly opposed concepts of 'mineral-reinforced collagen matrix' and 'collagen-reinforced mineral matrix' for bone ultrastructure, this approach opens new possibilities in the exploitation of computer tomographic data for nano-to-macro mechanics of bone organs.     

Do mineral crystals stiffen bone by straitjacketing its collagen?

Theories that assume that the collagen and the mineral of bone have the same properties in bone as they do when they are by themselves have difficulty in accounting for bone's tensile stiffness. The collagen fibers are long but stretchy: the apatite crystals are stiff enough, but too short to be effective tension carriers. In bone the mineral is so finely divided that each collagen molecule may have a mineral crystal next to it. It is proposed that collagen is the prime tension carrier in bone, and that via short molecular struts the mineral crystals prevent the naturally kinky collagen molecules from straightening under tensile stress, which greatly increases the collagen's tensile stiffness.     

The size exclusion characteristics of type I collagen: implications for the role of noncollagenous bone constituents in mineralization

The mineral in bone is located primarily within the collagen fibril, and during mineralization the fibril is formed first and then water within the fibril is replaced with mineral. The collagen fibril therefore provides the aqueous compartment in which mineral grows. Although knowledge of the size of molecules that can diffuse into the fibril to affect crystal growth is critical to understanding the mechanism of bone mineralization, there have been as yet no studies on the size exclusion properties of the collagen fibril. To determine the size exclusion characteristics of collagen, we developed a gel filtration-like procedure that uses columns containing collagen from tendon and bone. The elution volumes of test molecules show the volume within the packed column that is accessible to the test molecules, and therefore reveal the size exclusion characteristics of the collagen within the column. These experiments show that molecules smaller than a 6-kDa protein diffuse into all of the water within the collagen fibril, whereas molecules larger than a 40-kDa protein are excluded from this water. These studies provide an insight into the mechanism of bone mineralization. Molecules and apatite crystals smaller than a 6-kDa protein can diffuse into all water within the fibril and so can directly impact mineralization. Although molecules larger than a 40-kDa protein are excluded from the fibril, they can initiate mineralization by forming small apatite crystal nuclei that diffuse into the fibril, or can favor fibril mineralization by inhibiting apatite growth everywhere but within the fibril.     

Systematic fabrication of nano-carbonated hydroxyapatite/collagen composites for biomimetic bone grafts

A novel biomimetic self-assembly method was designed to create nano-carbonated hydroxyapatite/collagen (nCHAC) composites by means of incorporating various collagen and carbonate concentrations using solutions such as CaCl(2), H(3)PO(4), and Na(2)CO(3). At a given range of collagen and carbonate content, the nanosized inorganic phase of the newly synthesized material has a low degree of crystallinity which resembles that of natural bone. By manipulating the concentrations of collagen and carbonates, various morphologies of the nCHAC can be obtained. The crystal size of nCHAC is dependent on the concentration of carbonate and collagen present in the composites. For instance, higher collagen concentration results in smaller crystal nCHAC crystal size. Conversely, the higher the carbonate content, the smaller are the crystal size and the collagen fibril assembly. As the carbonate content increased, the plate-like crystals first became needle-like structures, subsequently short needle-like crystals and eventually became spherical particles. From this study, our method showcased the flexibility of fabricating various types of nCHAC composites which can be designed for different bone applications.     

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.     

Elastic deformation of mineralized collagen fibrils: an equivalent inclusion based composite model

Mineralized collagen fibrils are the basic building blocks of bone tissue at the supramolecular level. Several disease states, manipulation of the expression of specific proteins involved in biomineralization, and treatment with different agents alter the extent of mineralization as well as the morphology of mineral crystals which in turn affect the mechanical function of bone tissue. An experimental assessment of mineralized fibers' mechanical properties is challenged by their small size, leaving analytical and computational models as a viable alternative for investigation of the fibril-level mechanical properties. In the current study the variation of the elastic stiffness tensor of mineralized collagen fibrils with changing mineral volume fraction and mineral aspect ratios was predicted via a micromechanical model. The partitioning of applied stresses between mineral and collagen phases is also predicted for normal and shear loading of fibrils. Model predictions resulted in transversely isotropic collagen fibrils in which the modulus along the longer axis of the fibril was the greatest. All the elastic moduli increased with increasing mineral volume fraction whereas Poisson's ratios decreased with the exception of v12 (=v21). The partitioning of applied stresses were such that the stresses acting on mineral crystals were about 1.5, 15, and 3 times greater than collagen stresses when fibrils were loaded transversely, longitudinally, and in shear, respectively. In the overall the predictions were such that: (a) greatest modulus along longer axis; (b) the greatest mineral/collagen stress ratio along the longer axis of collagen fibers (i.e., greatest relief of stresses acting on collagen); and (c) minimal lateral contraction when fibers are loaded along the longer axis. Overall, the pattern of mineralization as put forth in this model predicts a superior mechanical function along the longer axis of collagen fibers, the direction which is more likely to experience greater stresses.     

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)     

Bone material properties and mineral matrix contributions to fracture risk or age in women and men

The strength of bone is related to its mass and geometry, but also to the physical properties of the tissue itself. Bone tissue is composed primarily of collagen and mineral, each of which changes with age, and each of which can be affected by pharmaceutical treatments designed to prevent or reverse the loss of bone. With age, there is a decrease in collagen content, which is associated with an increased mean tissue mineralization, but there is no difference in cross-link levels compared to younger adult bone. In osteoporosis, however, there is a decrease in the reducible collagen cross-links without an alteration in collagen concentration; this would tend to increase bone fragility. In older people, the mean tissue age (MTA) increases, causing the tissue to become more highly mineralized. The increased bone turnover following menopause may reduce global MTA, and would reduce overall tissue mineralization. Bone strength and toughness are positively correlated to bone mineral content, but when bone tissue becomes too highly mineralized, it tends to become brittle. This reduces its toughness, and makes it more prone to fracture from repeated loads and accumulated microcracking. Most approved pharmaceutical treatments for osteoporosis suppress bone turnover, increasing MTA and mineralization of the tissue. This might have either or both of two effects. It could increase bone volume from refilling of the remodeling space, reducing the risk for fracture. Alternatively, the increased MTA could increase the propensity to develop microcracks, and reduce the toughness of bone, making it more likely to fracture. There may also be changes in the morphology of the mineral crystals that could affect the homogeneity of the tissue and impact mechanical properties. These changes might have large positive or negative effects on fracture incidence, and could contribute to the paradox that both large and small increases in density have about the same effect on fracture risk. Bone mineral density measured by DXA does not discriminate between density differences caused by volume changes, and those caused by changes in mineralization. As such, it does not entirely reflect material property changes in aging or osteoporotic bone that contribute to bone's risk for fracture.     

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.     

Modeling of bone at a single lamella level

This paper focuses on the ultrastructure of bone at a single lamella level. At this scale, collagen fibrils reinforced with apatite crystals are aligned preferentially to form a lamella. At the next structural level, such lamella are stacked in different orientations to form either osteons in cortical bone or trabecular pockets in trabecular bone. We use a finite element model, which treats small strain elasticity of a spatially random network of collagen fibrils, and compute anisotropic effective stiffness tensors and deformations of such a single lamella as a function of fibril volume fractions (or porosities), prescribed microgeometries, and fibril geometric and elastic properties.     

Mineralization regulation and biological influence of bioactive glass-collagen-phosphatidylserine composite scaffolds

Biomimetic scaffolds are appealing products for the repair of bone defects using tissue engineering strategies. In the present study, novel biomimetic composite scaffolds, with similar properties to natural bone, were prepared, blended and cross-linked with bioactive glass, type I collagen and phosphatidylserine. When exposed to cell culture solution in the absence of a cellular source, the composite scaffolds form crystals with octahedral structure. These crystals are similar to the products derived from MC3T3-E1 cell mineralization within the composite scaffolds, with respect to both composition and morphology. Furthermore, crystals with octahedral structure were observed to develop into plate-like hydroxyapatite. The bio-mineralization behavior of the composite scaffolds is likely influenced by inorganic components. Finally, a rabbit tibia defect model shows that the highly bioactive properties of the investigated composites result in excellent bone repair.     

Bone stiffness explained by the liquid crystal model for the collagen fibril

A liquid crystal model for the structure of the collagen fibril explains how calcium phosphate crystals are capable of stiffening collagen fibrils in bone. Collagen fibrils consist of an oriented array of parallel rod-shaped collagen molecules. According to the liquid crystal model fibrils respond to tensile stress, applied in the axial direction, by some of the molecules tilting and changing their side-to-side arrangement. In bone the presence of crystals packed between the collagen molecules hinders the side-to-side rearrangement so that the response of the fibrils to stress is inhibited. Therefore the fibrils are stiffer in bone than in uncalcified tissue.     

Homogenized stiffness matrices for mineralized collagen fibrils and lamellar bone using unit cell finite element models

Mineralized collagen fibrils have been usually analyzed like a two-phase composite material where crystals are considered as platelets that constitute the reinforcement phase. Different models have been used to describe the elastic behavior of the material. In this work, it is shown that when Halpin–Tsai equations are applied to estimate elastic constants from typical constituent properties, not all crystal dimensions yield a model that satisfy thermodynamic restrictions. We provide the ranges of platelet dimensions that lead to positive definite stiffness matrices. On the other hand, a finite element model of a mineralized collagen fibril unit cell under periodic boundary conditions is analyzed. By applying six canonical load cases, homogenized stiffness matrices are numerically calculated. Results show a monoclinic behavior of the mineralized collagen fibril. In addition, a 5-layer lamellar structure is also considered where crystals rotate in adjacent layers of a lamella. The stiffness matrix of each layer is calculated applying Lekhnitskii transformations, and a new finite element model under periodic boundary conditions is analyzed to calculate the homogenized 3D anisotropic stiffness matrix of a unit cell of lamellar bone. Results are compared with the rule-of-mixtures showing in general good agreement.     

Prismatic dentine in the Australian lungfish, Neoceratodus forsteri (Osteichthyes: Dipnoi)

The Australian lungfish, Neoceratodus forsteri, has a dentition consisting of enamel, mantle dentine and bone, enclosing circumdenteonal, core and interdenteonal dentines. Branching processes from cells that produce interdenteonal dentine leave the cell surface at different angles, with collagen fibrils aligned parallel to the long axis of each process. In the interdenteonal dentine, crystals of calcium hydroxyapatite form within fibrils of collagen, and grow within a matrix of non-collagenous protein. Crystals are aligned parallel to the cell process, as are the original collagen fibrils. Because the processes are angled to the cell surface, the crystals within the core or interdenteonal dentine are arranged in bundles set at angles to each other. Apatite crystals in circumdenteonal dentine are finer and denser than those of the interdenteonal dentine, and form outside the fibrils of collagen. In mature circumdenteonal dentine the crystals of circumdenteonal dentine form a dense tangled mass, linked to interdenteonal dentine by isolated crystals. The functional lungfish tooth plate contains prisms of large apatite crystals in the interdenteonal dentine and masses of fine tangled crystals around each denteon. This confers mechanical strength on a structure with little enamel that is subjected to heavy wear.     

Beneath the minerals, a layer of round lipid particles was identified to mediate collagen calcification in compact bone formation

Astronauts lose 1-2% of their bone minerals per month during space flights. A systematic search for a countermeasure relies on a good understanding of the mechanism of bone formation at the molecular level. How collagen fibers, the dominant matrix protein in bones, are mineralized remains mysterious. Atomic force microscopy was carried out, in combination with immunostaining and Western blotting, on bovine tibia to identify unrecognized building blocks involved in bone formation and for an elucidation of the process of collagen calcification in bone formation. Before demineralization, tiles of hydroxyapatite crystals were found stacked along bundles of collagen fibers. These tiles were homogeneous in size and shape with dimensions 0.69 x 0.77 x 0.2 micro m(3). Demineralization dissolved these tiles and revealed small spheres with an apparent diameter around 145 nm. These spheres appeared to be lipid particles since organic solvents dissolved them. The parallel collagen bundles had widths mostly <2 micro m. Composition analysis of compact bones indicated a high content of apolar lipids, including triglycerides and cholesterol esters. Apolar lipids are known to form lipid droplets or lipoproteins, and these spheres are unlikely to be matrix vesicles as reported for collagen calcification in epiphyseal cartilages. Results from this study suggest that the layer of round lipid particles on collagen fibers mediates the mineral deposition onto the fibers. The homogeneous size of these lipid particles and the presence of apolipoprotein in demineralized bone tissue suggest the possibility that these particles might be of lipoprotein origin. More studies are needed to verify the last claim and to exclude the possibility that they are secreted lipid droplets.     

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.     

Microfibril Orientation Dominates the Microelastic Properties of Human Bone Tissue at the Lamellar Length Scale

The elastic properties of bone tissue determine the biomechanical behavior of bone at the organ level. It is now widely accepted that the nanoscale structure of bone plays an important role to determine the elastic properties at the tissue level. Hence, in addition to the mineral density, the structure and organization of the mineral nanoparticles and of the collagen microfibrils appear as potential key factors governing the elasticity. Many studies exist on the role of the organization of collagen microfibril and mineral nanocrystals in strongly remodeled bone. However, there is no direct experimental proof to support the theoretical calculations. Here, we provide such evidence through a novel approach combining several high resolution imaging techniques: scanning acoustic microscopy, quantitative scanning small-Angle X-ray scattering imaging and synchrotron radiation computed microtomography. We find that the periodic modulations of elasticity across osteonal bone are essentially determined by the orientation of the mineral nanoparticles and to a lesser extent only by the particle size and density. Based on the strong correlation between the orientation of the mineral nanoparticles and the collagen molecules, we conclude that the microfibril orientation is the main determinant of the observed undulations of microelastic properties in regions of constant mineralization in osteonal lamellar bone. This multimodal approach could be applied to a much broader range of fibrous biological materials for the purpose of biomimetic technologies.