On the relationship between the microstructure of bone and its mechanical stiffness.

A recent study of bone structure shows that the plate-shaped carbonate apatite crystals in individual lamellae are arranged in layers across the lamellae, and that the orientation of these layers are different in alternate lamellae. Based on these findings, a new micromechanical model for the Young's modulus of bone is proposed, which accounts for the anisotropy and geometrical characteristics of the material. The model incorporates the platelet-like geometry of the basic reinforcing unit, the presence of alternating thin and thick lamellae, and the orientations of the crystal platelets in the lamellae. The thin and thick lamellae are modeled as orthotropic composite layers made up of thin rectangular apatite platelets within a collagen matrix, and classical orthotropic elasticity theory is used to calculate the Young's modulus of the lamellae. Bone is viewed as an assembly of such orthotropic lamellae bent into cylindrical structures, and having a constant, alternating angle between successive lamellae. The micromechanical model employs a modified rule-of-mixtures to account for the two types of lamellae. The model provides a curve similar to the published experimental data on the angular dependence of Young's modulus, including a local maximum at an angle between 0 and 90 degrees. A rigorous testing of the model awaits additional experimental data.     

Crystal organization in rat bone lamellae

The plate-shaped crystals of rat bone are arranged in parallel layers that form coherent structures up to the level of individual lamellae. The crystal layers of the thin lamellae are parallel to the lamellar boundary, whereas those of the thicker lamellae are oblique to the boundary. The basic structure of rat bone can be described as 'rotated plywood'; a structure hitherto unrecognized in either biologic or synthetic materials.     

Corneal morphogenesis in the Indian garden lizard,Calotes versicolor (agamidae)

The present study traces corneal morphogenesis in a reptile, the lizard Calotes versicolor, from the lens placode stage (stage 24) until hatching (stage 42), and in the adult. The corneal epithelium separates from the lens placode as a double layer of peridermal and basal cells and remains bilayered throughout development and in the adult. Between stages 32– and 33+, the corneal epithelium is apposed to the lens, and limbic mesodermal cells migrate between the basement membrane of the epithelium and the lens capsule to form a monolayered corneal endothelium. Soon thereafter a matrix of amorphous ground substance and fine collagen fibrils, the presumptive stroma, is seen between the epithelium and the endothelium. Just before stage 34 a new set of limbic mesodermal cells, the keratocytes, migrate into the presumptive stroma. Migrating limbic mesodermal cells, both endothelial cells and keratocytes, use the basement membrane of the epithelium as substratum. Keratocytes may form up to six cell layers at stage 37, but in the adult stroma they form only one or two cell layers. The keratocytes sysnthesize collagen, which aggregates as fibrils and fibers organized in lamellae. The lamellae become condensed as dense collagen layers subepithelially or become compactly organized into a feltwork structure in the rest of the stroma. The basement membrane of the endothelium is always thin. Thickness of the entire cornea increases up to stage 38 and decreases thereafter until stage 41. In the adult the cornea is again nearly as thick as at stage 38.     

Ultrastructural data on the scales of the dipnoan Protoptems annectens (Sarcopterygii, Osteichthyes)

The structure and the mineralization of the scales of the living dipnoan (lungfish) Protoptems annectens have been investigated by transmission electron microscopy (TEM). The thin and imbricated scales are composed of two layers: the squamulae and the basal plate. At the outer surface, the squamulae form isolated plates superficially ornamented with spines and concretions and made up of acellular bone. After demineralization, the squamulae show a heterogeneous organic matrix composed of thin randomly oriented collagen fibrils forming a loose network within which the concretions appear as electronlucent circular areas. Abundant and aggregated concretions are located within the spines. The crystallites are oriented by the collagen fibrils except in the concretions. Anchoring bundles composed of parallel collagen fibrils arise from the squamulae and connect the scales to the overlying dermis.
The basal plate, the most developed part of the scale, is made up of isopedine. Its main component consists of thick, closely packed collagen fibrils organized in a 'double twisted plywood-like structure'. Fibroblasts are present in the basal plate. Mineralization occurs only in few plies located beneath the squamulae. Mandl's corpuscles are found in front of the mineralization front. The mineral deposit is oriented by the collagen fibrils.
The scales of Protoptems annectens differ from the typical elasmoid scales of the teleosts by the peculiar structure of the squamulae, nevertheless they show enough structural characteristics to support the hypothesis that they can be considered as scales of the elasmoid grade, which have retained some plesiomorphic characteristics.     

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.     

Lamellar bone: structure-function relations.

The term "bone" refers to a family of materials that have complex hierarchically organized structures. These structures are primarily adapted to the variety of mechanical functions that bone fulfills. Here we review the structure-mechanical relations of one bone structural type, lamellar bone. This is the most abundant type in many mammals, including humans. A lamellar unit is composed of five sublayers. Each sublayer is an array of aligned mineralized collagen fibrils. The orientations of these arrays differ in each sublayer with respect to both collagen fibril axes and crystal layers, such that a complex rotated plywood-like structure is formed. Specific functions for lamellar bone, as opposed to the other bone types, could not be identified. It is therefore proposed that the lamellar structure is multifunctional-the "concrete" of the bone family of materials. Experimentally measured mechanical properties of lamellar bone demonstrate a clear-cut anisotropy with respect to the axis direction of long bones. A comparison of the elastic and ultimate properties of parallel arrays of lamellar units formed in primary bone with cylindrically shaped osteonal structures in secondary formed bone shows that most of the intrinsic mechanical properties are built into the lamellar structure. The major advantages of osteonal bone are its fracture properties. Mathematical modeling of the elastic properties based on the lamellar structure and using a rule-of-mixtures approach can closely simulate the measured mechanical properties, providing greater insight into the structure-mechanical relations of lamellar bone.     

Collagen fibril biosynthesis in tendon: a review and recent insights

The development and evolution of multicellular animals relies on the ability of certain cell types to synthesise an extracellular matrix (ECM) comprising very long collagen fibrils that are arranged in very ordered 3-dimensional scaffolds. Tendon is a good example of a highly ordered ECM, in which tens of millions of collagen fibrils, each hundreds of microns long, are synthesised parallel to the tendon long axis. This review highlights recent discoveries showing that the assembly of collagen fibrils in tendon is hierarchical, and involves the formation of fairly short "collagen early fibrils" that are the fusion precursors of the very long fibrils that occur in mature tendon.     

Lamellar Bone: Structure–Function Relations

The term “bone” refers to a family of materials that have complex hierarchically organized structures. These structures are primarily adapted to the variety of mechanical functions that bone fulfills. Here we review the structure–mechanical relations of one bone structural type, lamellar bone. This is the most abundant type in many mammals, including humans. A lamellar unit is composed of five sublayers. Each sublayer is an array of aligned mineralized collagen fibrils. The orientations of these arrays differ in each sublayer with respect to both collagen fibril axes and crystal layers, such that a complex rotated plywood-like structure is formed. Specific functions for lamellar bone, as opposed to the other bone types, could not be identified. It is therefore proposed that the lamellar structure is multifunctional—the “concrete” of the bone family of materials. Experimentally measured mechanical properties of lamellar bone demonstrate a clear-cut anisotropy with respect to the axis direction of long bones. A comparison of the elastic and ultimate properties of parallel arrays of lamellar units formed in primary bone with cylindrically shaped osteonal structures in secondary formed bone shows that most of the intrinsic mechanical properties are built into the lamellar structure. The major advantages of osteonal bone are its fracture properties. Mathematical modeling of the elastic properties based on the lamellar structure and using a rule-of-mixtures approach can closely simulate the measured mechanical properties, providing greater insight into the structure–mechanical relations of lamellar bone.     

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.     

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.     

Fine structure of the fertilization membranes of sea urchin embryos

The fine structure of the fertilization membranes from S. purpuratus embryos has been studied with the electron microscope. Isolated membranes before and after their full development and membranes formed under the influence of 10⁻³% cystine have been observed. The membrane structure was found to be trilamella: a middle layer about 200 Å thick, which originally was the vitelline membrane, and about 175 Å thick peripheral layers organized by the “crystalline material” from the cortical granules. These surface layers were again found to be trilaminated structure composed of a monolayer of parallel, closely packed flat fibrils, about 160 Å wide and 75 Å thick, adhering on both sides to parallel, 40–50 Å thick filaments separated from each other by about 100 Å and intersecting with the fibrils by an angle of about 75 °.     

X-ray diffraction analysis of the 3D organization of collagen fibrils in the wall of the dogfish egg case

The wall of the egg case of the dogfish,Scyliorhinus canicula, contains a network-forming collagen assembled into a regular three-dimensional (3D) structure. It accomplishes supportive, protective and filtering functions for the embryo contained within it. The collagen molecules in the egg case are organized into a body-centred unit cell of dimensions (mean ± s.d.) (11.6 ± 1.0) nm X (11.6 ± 1.0) nm X (81.6 ± 3.2) nm, which belongs to the I422 space group. At a higher hierarchical level, the collagen molecules assemble into parallel arrays of fibrils, ca. 100 nm in diameter, which aggregate to form laminae ca. 0.5 μm thick. These laminae are organized into a plywood-like structure and account for 98% of the thickness of the wall of the egg case. X-ray diffraction patterns of the wall of the egg case were taken along mutually perpendicular directions, one being perpendicular to the surface of the egg case. Three different kinds of diffraction pattern were observed. One of the patterns was characteristic of an X-ray direction perpendicular to the laminae in the egg case (along the x-direction). The two other patterns were obtained with the X-rays directed parallel to the plane of the laminae, either along the capsule long axis (z) or perpendicular to this (y). These two patterns were observed interchangeably in either of the x- or y-directions depending on the specimen. The diffraction patterns were analysed and interpreted taking into consideration the 3D electron microscope data of the egg case. The results confirm and extend previous findings from transmission electron microscopy and low-angle X-ray diffraction and they suggest that there is only one major type of ordered collagen arrangement in the wall of the egg case.     

The estimated elastic constants for a single bone osteonal lamella

Micromechanical estimates of the elastic constants for a single bone osteonal lamella and its substructures are reported. These estimates of elastic constants are accomplished at three distinct and organized hierarchical levels, that of a mineralized collagen fibril, a collagen fiber, and a single lamella. The smallest collagen structure is the collagen fibril whose diameter is the order of 20 nm. The next structural level is the collagen fiber with a diameter of the order of 80 nm. A lamella is a laminate structure, composed of multiple collagen fibers with embedded minerals and consists of several laminates. The thickness of one laminate in the lamella is approximately 130 nm. All collagen fibers in a laminate in the lamella are oriented in one direction. However, the laminates rotate relative to the adjacent laminates. In this work, all collagen fibers in a lamella are assumed to be aligned in the longitudinal direction. This kind of bone with all collagen fibers aligned in one direction is called a parallel fibered bone. The effective elastic constants for a parallel fibered bone are estimated by assuming periodic substructures. These results provide a database for estimating the anisotropic poroelastic constants of an osteon and also provide a database for building mathematical or computational models in bone micromechanics, such as bone damage mechanics and bone poroelasticity.     

Probing the role of water in lamellar bone by dehydration in the environmental scanning electron microscope

Water, collagen and mineral are the three major components of bone. The structural organization of water and its functions within the bone were investigated using the environmental scanning electron microscope and by analyzing dimensional changes that occur when fresh equine osteonal bone is dehydrated and then rehydrated. These changes are attributed mainly to loss of bulk and weakly bound water. In longitudinal sections a contraction of 1.2% was observed perpendicular to the lamellae, whereas no contraction occurred parallel to the lamellae. In transverse sections a contraction of 1.4% was observed both parallel and perpendicular to the lamellae. SEM back scattered electron images showed that about half of an individual lamella is less mineralized, and thus has more water than the other half. We therefore propose that contractions perpendicular to lamellae are due to the presence of more water-filled rather than mineral-filled channels within the mineralized collagen fibril arrays. As these channels are also aligned with the crystal planes, the crystal arrays, oriented as depicted in the rotated plywood model for lamellar bone, facilitate or hinder contraction in different directions.     

Layered water in crystal interfaces as source for bone viscoelasticity: arguments from a multiscale approach

Extracellular bone material can be characterised as a nanocomposite where, in a liquid environment, nanometre-sized hydroxyapatite crystals precipitate within as well as between long fibre-like collagen fibrils (with diameters in the 100 nm range), as evidenced from neutron diffraction and transmission electron microscopy. Accordingly, these crystals are referred to as ‘interfibrillar mineral’ and ‘extrafibrillar mineral’, respectively. From a topological viewpoint, it is probable that the mineralisations start on the surfaces of the collagen fibrils (‘mineral-encrusted fibrils’), from where the crystals grow both into the fibril and into the extrafibrillar space. Since the mineral concentration depends on the pore spaces within the fibrils and between the fibrils (there is more space between them), the majority of the crystals (but clearly not all of them) typically lie in the extrafibrillar space. There, larger crystal agglomerations or clusters, spanning tens to hundreds of nanometers, develop in the course of mineralisation, and the micromechanics community has identified the pivotal role, which this extrafibrillar mineral plays for tissue elasticity. In such extrafibrillar crystal agglomerates, single crystals are stuck together, their surfaces being covered with very thin water layers. Recently, the latter have caught our interest regarding strength properties (Fritsch et al. 2009 J Theor Biol. 260(2): 230–252) – we have identified these water layers as weak interfaces in the extrafibrillar mineral of bone. Rate-independent gliding effects of crystals along the aforementioned interfaces, once an elastic threshold is surpassed, can be related to overall elastoplastic material behaviour of the hierarchical material ‘bone’. Extending this idea, the present paper is devoted to viscous gliding along these interfaces, expressing itself, at the macroscale, in the well-known experimentally evidenced phenomenon of bone viscoelasticity. In this context, a multiscale homogenisation scheme is extended to viscoelasticity, mineral-cluster-specific creep parameters are identified from three-point bending tests on hydrated bone samples, and the model is validated by statistically and physically independent experiments on partially dried samples. We expect this model to be relevant when it comes to prediction of time-dependent phenomena, e.g. in the context of bone remodelling.     

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.     

Cholesteric organization of DNA in the stallion sperm head

The fine structure of chromatin in sperm heads was investigated by different microscopic techniques: in vivo examinations in the polarizing microscope, thin sections and freeze-fracture replicas observed by transmission electron microscopy. The freeze-fractured chromatin appears to be formed of superimposed lamellae, each one 330 A thick. These lamellae are parallel to the flattening plane of the sperm head. This situation was already described in other mammal spermatozoa and in particular in the bull and the rabbit. This work presents a new interpretation of this lamellated aspect. The chromatin structure of these spermatozoa is that of a cholesteric liquid crystal. This structure resembles that of a plywood, made of superimposed layers of parallel filaments, but instead of having a right angle between two successive layers, there is a progressive rotation and similar orientation occurs at each 180 degrees rotation. The apparent lamellae result from cleavages due to freeze-fracture between levels of parallel filament orientation. The thickness of lamellae corresponds therefore to the half helicoidal pitch of the cholesteric liquid crystal. This model is consistent with our observations by polarizing microscopy. The lamellation is not visible in thin sections of stallion spermatozoa. There are however biochemical methods to decondense chromatin and we are able to observe this lamellation in sections normal to the flattening plane of sperm heads. The methods used classically to decondense the sperm chromatin lead to extremely varied aspects which are discussed, some of them being closely related to the structure of cholesteric liquid crystals.     

Fibrous long spacing type collagen fibrils have a hierarchical internal structure

Nanodissection of single fibrous long spacing (FLS) type collagen fibrils by atomic force microscopy (AFM) reveals hierarchical internal structure: Fibrillar subcomponents with diameters of approximately 10 to 20 nm were observed to be running parallel to the long axis of the fibril in which they are found. The fibrillar subcomponent displayed protrusions with characteristic approximately 270 nm periodicity, such that protrusions on neighboring subfibrils were aligned in register. Hence, the banding pattern of mature FLS-type collagen fibrils arises from the in-register alignment of these fibrillar subcomponents. This hierarchical organization observed in FLS-type collagen fibrils is different from that previously reported for native-type collagen fibrils, displaying no supercoiling at the level of organization observed.     

A model for the ultrastructure of bone based on electron microscopy of ion-milled sections

The relationship between the mineral component of bone and associated collagen has been a matter of continued dispute. We use transmission electron microscopy (TEM) of cryogenically ion milled sections of fully-mineralized cortical bone to study the spatial and topological relationship between mineral and collagen. We observe that hydroxyapatite (HA) occurs largely as elongated plate-like structures which are external to and oriented parallel to the collagen fibrils. Dark field images suggest that the structures ("mineral structures") are polycrystalline. They are approximately 5 nm thick, 70 nm wide and several hundred nm long. Using energy-dispersive X-ray analysis we show that approximately 70% of the HA occurs as mineral structures external to the fibrils. The remainder is found constrained to the gap zones. Comparative studies of other species suggest that this structural motif is ubiquitous in all vertebrates.     

Structural peculiarities of the tubercles in the skin of the turbot,Scophthalmus maximus (L., 1758) (Osteichthyes,Pleuronectiformes, Scophthalmidae)

The structure of the bony tubercles of the turbot, Scophthalmus maximus (L., 1758), was examined using ground sections, microradiography, SEM, and TEM. The tubercles are small, isolated, mineralized conical plates randomly distributed in the eyed side of the body. They are composed of three layers: the outer limiting layer, the external layer, and the basal plate, which make up the thin and flat elasmoid scales of Teleostei. The main difference between regular elasmoid scales and bony tubercles lies in the organization and the growth of the basal plate. Indeed, the conical shape of the tubercle is the result of a prominent thickening of the central part of the basal plate where the collagen matrix is organized in a complicated three-dimensional network. Densely packed thick collagen fibrils form superimposed plies organized in a plywood-like structure that resembles that of the elasmoid scales but it is criss-crossed by numerous vertical sheets of thin collagen fibrils. The tubercles originate from thin and flat plates located in the skin of larvae and juveniles, whose structure is that of regular-developing elasmoid scales. Thus, the tubercles of Scophthalmus maximus could be considered as modified elasmoid scales rather than bony structures. They might be the result of specific arrangements related to the general trend of reduction of the dermal skeleton in the teleostean lineage.