Visualization of crystal-matrix structure. In situ demineralization of mineralized turkey leg tendon and bone

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.

Modeling of bending and torsional stiffnesses of bone at sub-microscale: Effect of curved mineral lamellae

Recent transmission electron microscopy images of transverse sections of human cortical bone showed that mineral lamellae (polycrystalline sheets of apatite crystals) form arcuate multi-radius patterns around collagen fibrils. The 3-6 nm thick mineral lamellae are arranged in stacks of 3-20 layers and curve around individual fibrils, few fibrils, and higher numbers of collagen fibrils. We evaluate the effect of these stacked mineral lamellae with various radius of curvature patterns on the elastic bending and torsional responses of bone at the sub-microscale using a finite element method. We find that the curved multi-radius stack patterns increased the bending and torsional stiffnesses by 7% and 23%, respectively, compared to when the stacks of mineral lamellae only encircle individual fibrils for the idealized geometric models considered. This study provides new insights into the structure-property relations for the bone ultrastructure.

"Variances" and "in-variances" in hierarchical porosity and composition, across femoral tissues from cow, horse, ostrich, emu, pig, rabbit, and frog

It is very well known that bone is a hierarchically organized material produced by bone cells residing in the fluid environments filling (larger) vascular pores and (smaller) lacunar pores. The extracellular space consists of hydroxyapatite crystals, collagen type I molecules, and water with non-collageneous organics. It is less known to which extent the associated quantities (mineral, organic, and water concentrations; vascular, lacunar, and extracellular porosities) vary across species, organs, and ages. We here investigate the aforementioned quantities across femoral shaft tissues from cow, horse, emu, frog, ostrich, pig, and rabbit; by means of light microscopy and dehydration-demineralization tests; thereby revealing interesting invariances: The extracellular volume fractions of organic matter turn out to be similar across all tested non-amphibian tissues; as do the extracellular volume fractions of hydroxyapatite across all tested mammals. Hence, the chemical composition of the femoral extracellular bone matrix is remarkably "invariant" across differently aged mammals; while the water content shows significant variations, as does the partitions of water between the different pore spaces. The latter exhibit strikingly varying morphologies as well. This finding adds to the ample "universal patterns" in the sense of evolutionary developmental biology; and it provides interesting design requirements for the development of novel biomimetic tissue engineering solutions.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

High-resolution large-area imaging of nanoscale structure and mineralization of a sclerosing osteosarcoma in human bone

Osteosarcoma is the most common primary bone cancer type in humans. It is predominantly found in young individuals, with a second peak later in life. The tumour is formed by malignant osteoblasts and consists of collagenous, sometimes also mineralized, bone matrix. While the morphology of osteosarcoma has been well studied, there is virtually no information about the nanostructure of the tumour and changes in mineralization on the nanoscale level. In the present paper, human bone tissue inside, next to and remote from a sclerosing osteosarcoma was studied with small angle x-ray scattering, x-ray diffraction and electron microscopy. Quantitative evaluation of nanostructure parameters was combined with high resolution, large area mapping to obtain microscopic images with nanostructure parameter contrast. It was found that the tumour regions were characterized by a notable reduction in mineral particle size, while the mineral content was even higher than that in normal bone. Furthermore, the normal preferential orientation of mineral particles along the longitudinal direction of corticalis or trabeculae was largely suppressed. Also the bone mineral crystal structure was affected: severe crystal lattice distortions were detected in mineralized tumour tissue pointing to a different ion substitution of hydroxyl apatite in tumorous tissue than in healthy tissue.

Modeling of Stiffness and Strength of Bone at Nanoscale

Two distinct geometrical models of bone at the nanoscale (collagen fibril and mineral platelets) are analyzed computationally. In the first model (model I), minerals are periodically distributed in a staggered manner in a collagen matrix while in the second model (model II), minerals form continuous layers outside the collagen fibril. Elastic modulus and strength of bone at the nanoscale, represented by these two models under longitudinal tensile loading, are studied using a finite element (FE) software abaqus. The analysis employs a traction-separation law (cohesive surface modeling) at various interfaces in the models to account for interfacial delaminations. Plane stress, plane strain, and axisymmetric versions of the two models are considered. Model II is found to have a higher stiffness than model I for all cases. For strength, the two models alternate the superiority of performance depending on the inputs and assumptions used. For model II, the axisymmetric case gives higher results than the plane stress and plane strain cases while an opposite trend is observed for model I. For axisymmetric case, model II shows greater strength and stiffness compared to model I. The collagen–mineral arrangement of bone at nanoscale forms a basic building block of bone. Thus, knowledge of its mechanical properties is of high scientific and clinical interests.

Patient-specific fracture risk assessment of vertebrae: A multiscale approach coupling X-ray physics and continuum micromechanics

While in clinical settings, bone mineral density measured by computed tomography (CT) remains the key indicator for bone fracture risk, there is an ongoing quest for more engineering mechanics-based approaches for safety analyses of the skeleton. This calls for determination of suitable material properties from respective CT data, where the traditional approach consists of regression analyses between attenuation-related grey values and mechanical properties. We here present a physics-oriented approach, considering that elasticity and strength of bone tissue originate from the material microstructure and the mechanical properties of its elementary components. Firstly, we reconstruct the linear relation between the clinically accessible grey values making up a CT, and the X-ray attenuation coefficients quantifying the intensity losses from which the image is actually reconstructed. Therefore, we combine X-ray attenuation averaging at different length scales and over different tissues, with recently identified 'universal' composition characteristics of the latter. This gives access to both the normally non-disclosed X-ray energy employed in the CT-device and to in vivo patient-specific and location-specific bone composition variables, such as voxel-specific mass density, as well as collagen and mineral contents. The latter feed an experimentally validated multiscale elastoplastic model based on the hierarchical organization of bone. Corresponding elasticity maps across the organ enter a finite element simulation of a typical load case, and the resulting stress states are increased in a proportional fashion, so as to check the safety against ultimate material failure. In the young patient investigated, even normal physiological loading is probable to already imply plastic events associated with the hydrated mineral crystals in the bone ultrastructure, while the safety factor against failure is still as high as five. Copyright © 2016 John Wiley & Sons, Ltd.

Tunability of collagen matrix mechanical properties via multiple modes of mineralization

Functionally graded, mineralized collagen tissues exist at soft-to-hard material attachments throughout the body. However, the details of how collagen and hydroxyapatite mineral (HA) interact are not fully understood, hampering efforts to develop tissue-engineered constructs that can assist with repair of injuries at the attachments of soft tissues to bone. In this study, spatial control of mineralization was achieved in collagen matrices using simulated body fluids (SBFs). Based upon previous observations of poor bonding between reconstituted collagen and HA deposited using SBF, we hypothesized that mineralizing collagen in the presence of fetuin (which inhibits surface mineralization) would lead to more mineral deposition within the scaffold and therefore a greater increase in stiffness and toughness compared with collagen mineralized without fetuin. We tested this hypothesis through integrated synthesis, mechanical testing and modelling of graded, mineralized reconstituted collagen constructs. Results supported the hypothesis, and further suggested that mineralization on the interior of reconstituted collagen constructs, as promoted by fetuin, led to superior bonding between HA and collagen. The results provide us guidance for the development of mineralized collagen scaffolds, with implications for bone and tendon-to-bone tissue engineering.

Effect of water on nanomechanics of bone is different between tension and compression

Water, an important constituent in bone, resides in different compartments in bone matrix and may impose significant effects on its bulk mechanical properties. However, a clear understanding of the mechanistic role of water in toughening bone is yet to emerge. To address this issue, this study used a progressive loading protocol, coupled with measurements of in situ mineral and collagen fibril deformations using synchrotron X-ray diffraction techniques. Using this unique approach, the contribution of water to the ultrastructural behavior of bone was examined by testing bone specimens in different loading modes (tension and compression) and hydration states (wet and dehydrated). The results indicated that the effect of water on the mechanical behavior of mineral and collagen phases at the ultrastructural level was loading-mode dependent and correlated with the bulk behavior of bone. Tensile loading elicited a transitional drop followed by an increase in load bearing by the mineral phase at the ultrastructural level, which was correlated with a strain hardening behavior of bone at the bulk level. Compression loading caused a continuous loss of load bearing by the mineral phase, which was reflected at the bulk level as a strain softening behavior. In addition, viscous strain relaxation and pre-strain reduction were observed in the mineral phase in the presence of water. Taken together, the results of this study suggest that water dictates the bulk behavior of bone by altering the interaction between mineral crystals and their surrounding matrix.

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

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

Is trabecular bone permeability governed by molecular ordering-induced fluid viscosity gain? Arguments from re-evaluation of experimental data in the framework of homogenization theory

It is generally agreed on that trabecular bone permeability, a physiologically important quantity, is governed by the material׳s (vascular or intertrabecular) porosity as well as by the viscosity of the pore-filling fluids. Still, there is less agreement on how these two key factors govern bone permeability. In order to shed more light onto this somewhat open issue, we here develop a random homogenization scheme for upscaling Poiseuille flow in the vascular porosity, up to Darcy-type permeability of the overall porous medium "trabecular bone". The underlying representative volume element of the macroscopic bone material contains two types of phases: a spherical, impermeable extracellular bone matrix phase interacts with interpenetrating cylindrical pore channel phases that are oriented in all different space directions. This type of interaction is modeled by means of a self-consistent homogenization scheme. While the permeability of the bone matrix equals to zero, the permeability of the pore phase is found through expressing the classical Hagen-Poiseuille law for laminar flow in the format of a "micro-Darcy law". The upscaling scheme contains pore size and porosity as geometrical input variables; however, they can be related to each other, based on well-known relations between porosity and specific bone surface. As two key results, validated through comprehensive experimental data, it appears (i) that the famous Kozeny-Carman constant (which relates bone permeability to the cube of the porosity, the square of the specific surface, as well as to the bone fluid viscosity) needs to be replaced by an again porosity-dependent rational function, and (ii) that the overall bone permeability is strongly affected by the pore fluid viscosity, which, in case of polarized fluids, is strongly increased due to the presence of electrically charged pore walls.

Understanding nanocalcification: a role suggested for crystal ghosts

The present survey deals with the initial stage of the calcification process in bone and other hard tissues, with special reference to the organic-inorganic relationship and the transformation that the early inorganic particles undergo as the process moves towards completion. Electron microscope studies clearly exclude the possibility that these particles might be crystalline structures, as often believed, by showing that they are, instead, organic-inorganic hybrids, each comprising a filamentous organic component (the crystal ghost) made up of acidic proteins. The hypothesis is suggested that the crystal ghosts bind and stabilize amorphous calcium phosphate and that their subsequent degradation allows the calcium phosphate, once released, to acquire a hydroxyapatite, crystal-like organization. A conclusive view of the mechanism of biological calcification cannot yet be proposed; even so, however, the role of crystal ghosts as a template of the structures usually called “crystallites” is a concept that has gathered increasing support and can no longer be disregarded.

Mineralization-driven bone tissue evolution follows from fluid-to-solid phase transformations in closed thermodynamic systems

The fundamental mechanisms that govern bone mineralization have been fairly well evidenced by means of experimental research. However, rules for the evolution of the volume and composition of the bone tissue compartments (such as the mineralized collagen fibrils and the extrafibrillar space in between) have not been provided yet. As an original contribution to this open question, we here test whether mineralizing bone tissue can be represented as a thermodynamically closed system, where crystals precipitate from an ionic solution, while the masses of the fibrillar and extrafibrillar bone tissue compartments are preserved. When translating, based on various experimental and theoretical findings, this mass conservation proposition into diffraction-mass density relations, the latter are remarkably well confirmed by independent experimental data from various sources. Resulting shrinkage and composition rules are deemed beneficial for further progress in bone materials science and biomedical engineering.

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.

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

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

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.

Primary structure and phosphorylation of dentin matrix protein 1 (DMP1) and dentin phosphophoryn (DPP) uniquely determine their role in biomineralization

The SIBLING (small integrin-binding ligand N-linked glycoproteins) family is the major group of noncollagenous proteins in bone and dentin. These extremely acidic and highly phosphorylated extracellular proteins play critical roles in the formation of collagenous mineralized tissues. Whereas the lack of individual SIBLINGs causes significant mineralization defects in vivo, none of them led to a complete cessation of mineralization suggesting that these proteins have overlapping functions. To assess whether different SIBLINGs regulate biomineralization in a similar manner and how phosphorylation impacts their activity, we studied the effects of two SIBLINGs, dentin matrix protein 1 (DMP1) and dentin phosphophoryn (DPP), on mineral morphology and organization in vitro. Our results demonstrate distinct differences in the effects of these proteins on mineralization. We show that phosphorylation has a profound effect on the regulation of mineralization by both proteins. Specifically, both phosphorylated proteins facilitated organized mineralization of collagen fibrils and phosphorylated DMP1-induced formation of organized mineral bundles in the absence of collagen. In summary, these results indicate that the primary structure and phosphorylation uniquely determine functions of individual SIBLINGs in regulation of mineral morphology and organization.

Biominerals--hierarchical nanocomposites: the example of bone

Many organisms incorporate inorganic solids in their tissues to enhance their functional, primarily mechanical, properties. These mineralized tissues, also called biominerals, are unique organo-mineral nanocomposites, organized at several hierarchical levels, from nano- to macroscale. Unlike man-made composite materials, which often are simple physical blends of their components, the organic and inorganic phases in biominerals interface at the molecular level. Although these tissues are made of relatively weak components under ambient conditions, their hierarchical structural organization and intimate interactions between different elements lead to superior mechanical properties. Understanding basic principles of formation, structure, and functional properties of these tissues might lead to novel bioinspired strategies for material design and better treatments for diseases of the mineralized tissues. This review focuses on general principles of structural organization, formation, and functional properties of biominerals on the example the bone tissues.

A new technique for imaging Mineralized Fibrils on Bovine Trabecular Bone Fracture Surfaces by Atomic Force Microscopy

High resolution atomic force microscopy (AFM) images of bovine trabecular bone fracture surfaces reveal individual fibrils coated with extrafibrillar mineral particles. The mineral particles are distinctly different in different regions. In some regions the particles have average dimensions of (70 ± 35) nm along the fibrils and about half that across the fibrils. In other regions they are smaller and rounder, of order (53 ± 14) nm both along and across the fibrils. In other regions they are smaller and rounder, of order (25 ± 15) nm both along and across the fibrils, with more rounded top surfaces.

Significantly, we rarely observed bare collagen fibrils. If the observed particles can be verified to be native extrafibrillar mineral, this could imply that the fractures which created the observed areas propagated within the mineralized extrafibrillar matrix.

A mechanistic study for strain rate sensitivity of rabbit patellar tendon

The ultrastructural mechanism for strain rate sensitivity of collagenous tissue has not been well studied at the collagen fibril level. Our objective is to reveal the mechanistic contribution of tendon's key structural component to strain rate sensitivity. We have investigated the structure of the collagen fibril undergoing tension at different strain rates. Tendon fascicles were pulled and fixed within the linear region (12% local tissue strain) at multiple strain rates. Although samples were pulled to the same percent elongation, the fibrils were noticed to elongate differently, increasing with strain rate. For the 0.1, 10, and 70%/s strain rates, there were 1.84±3.6%, 5.5±1.9%, and 7.03±2.2% elongations (mean±S.D.), respectively. We concluded that the collagen fibrils underwent significantly greater recruitment (fibril strain relative to global tissue strain) at higher strain rates. A better understanding of tendon mechanisms at lower hierarchical levels would help establish a basis for future development of constitutive models and assist in tissue replacement design.

Effects of crystalline phase on the biological properties of collagen-hydroxyapatite composites

The objective of this study was to investigate the effects of spatial structure and crystalline phase on the biological performance of collagen-hydroxyapatite (Col-HA) composite prepared by biomineralization crystallization. Two types of Col-HA composites were prepared using mineralization crystallization (MC composites) and pre-crystallization (PC composites), respectively. Structural characteristics were analyzed by scanning electron microscopy and transmission electron microscopy. Surface elemental compositions were measured by electron spectroscopy for chemical analysis (ESCA). These composites were used in in vivo repair of bone defects. The effects of the crystalline phase on the biological performance of Col-HA composites were investigated using radionuclide bone scan, histopathology and morphological observation. It was observed that in MC composites, HA was located on the surface of the collagen fibers and aggregated into crystal balls, whereas HA in PC composites was scattered among the collagen fibers. ESCA showed that phosphorus and calcium were 8.99% and 17.56% on MC composite surface, compared with 4.39% and 5.86% on the PC composite surface. In vivo bone defect repair experiments revealed that radionuclide uptake was significantly higher in the area implanted with the PC composite than in the contralateral area implanted with the MC composite. Throughout the whole repair process, the PC composite proved to be superior to the MC composite with regard to capillary-forming capacity and the amount of newly formed bone tissue. So it could be concluded that HA placement on collagen fibers affected the biological performance of Col-HA composites. Pre-crystallization made HA scattered among collagen fibers, creating a better structure for bone defect repair in comparison with MC Col-HA composites.

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.

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.

Electron holography of biological samples

In this paper, we summarise the development of off-axis electron holography on biological samples starting in 1986 with the first results on ferritin from the group of Tonomura. In the middle of the 1990s strong interest was evoked, but then stagnation took place because the results obtained at that stage did not reach the contrast and the resolution achieved by conventional electron microscopy. To date, there exist only a few ( approximately 12) publications on electron holography of biological objects, thus this topic is quite small and concise. The reason for this could be that holography is mostly established in materials science by physicists. Therefore, applications for off-axis holography were powerfully pushed forward in the area of imaging, e.g. electric or magnetic micro- and nanofields. Unstained biological systems investigated by means of off-axis electron holography up to now are ferritin, tobacco mosaic virus, a bacterial flagellum, T5 bacteriophage virus, hexagonal packed intermediate layer of bacteria and the Semliki Forest virus. New results of the authors on collagen fibres and surface layer of bacteria, the so-called S-layer 2D crystal lattice are presented in this review. For the sake of completeness, we will shortly discuss in-line holography of biological samples and off-axis holography of materials related to biological systems, such as biomaterial composites or magnetotactic bacteria.

Accretion of bone quantity and quality in the developing mouse skeleton

In this work, we found that bone mineral formation proceeded very rapidly in mice by 1 day of age, where the degree of mineralization, the tissue mineral density, and the mineral crystallinity reached 36%, 51%, and 87% of the adult values, respectively. However, even though significant mineralization had occurred, the elastic modulus of 1-day-old bone was only 14% of its adult value, indicating that the intrinsic stiffening of the bone lags considerably behind the initial mineral formation.

INTRODUCTION

To meet the mechanical challenges during early development, the skeleton requires the rapid accretion of bone quality and bone quantity. Here, we describe early bone development in the mouse skeleton and test the hypothesis that specific compositional properties determine the stiffness of the tissue.

MATERIALS AND METHODS

Tibias of female BALB mice were harvested at eight time-points (n = 4 each) distributed between 1 and 40 days of age and subjected to morphometric (muCT), chemical (Fourier transform infrared microspectroscopy), and mechanical (nanoindentation) analyses. Tibias of 450-day-old mice served as fully mineralized control specimens.

RESULTS

Bone growth proceeded very rapidly; at 1 day of age, the degree of mineralization (phosphate/protein ratio), the density of mineralized bone (TMD), and mineral crystallinity had reached 36%, 51%, and 87% of the adult (450 days) values, respectively. Spatially, the variability in mineralization across the mid-diaphysis was very high for the early time-points and declined over time. In contrast to the notable changes in mineralization, carbonate substitution into the mineral lattice (carbonate/phosphate ratio) and collagen cross-linking did not show any significant changes over this time period. Even though significant mineralization had occurred, the elastic modulus of 1-day-old bone was only 14% of the adult value and increased to 89% (of its adult value) after 40 days. Between samples of different time-points, significant positive correlations were observed between the elastic modulus and TMD (r(2) = 0.84), phosphate/protein ratio (r(2) = 0.59), and crystallinity (r(2) = 0.23), whereas collagen cross-linking showed a small but significant negative correlation (r(2) = 0.15).

CONCLUSIONS

These data indicate that specific chemical and morphometric properties modulate bone's stiffness during early growth. The intrinsic stiffening of the bone, however, lags considerably behind the initial mineral formation, emphasizing the importance of bone mineral quality for optimizing matrix integrity.

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.

'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.

The TEM characterization of the lamellar structure of osteoporotic human trabecular bone

The lamellar structure of osteoporotic human trabecular bone was characterized experimentally by means of transmission electron microscopy (TEM). More specifically, the TEM was used to determine if trabecular bone exhibits similar lamellar structural motifs as cortical bone by analyzing unmineralized, mineralized and demineralized bone, and to study the influence of the osteocyte network on the lamellar structure of osteoporotic trabecular bone. Comparison with normal trabecular bone is included. This paper summarizes partial results of a larger study, which addressed the characterization of the hierarchical structure of normal versus osteoporotic human trabecular bone [Rubin, M.A., 2001. Multiscale characterization of the ultrastructure of trabecular bone in osteoporotic and normal humans and in two inbred strains of mice. MS Thesis, Georgia Institute of Technology.] at several structural scales.

SEM and TEM study of the hierarchical structure of C57BL/6J and C3H/HeJ mice trabecular bone

Transmission electron microscopy (TEM) and scanning electron microscopy (SEM) were used to study the hierarchical structure of trabecular bone from C57BL/6J (low bone mass) and C3H/HeJ mice (high bone mass). Bone was harvested from two different anatomical locations: femoral metaphysis and L5 vertebra. This investigation focused on three structural scales: the mesostructural (porous network of trabecular struts), the microstructural (collagen fibril arrangements in trabecular packets), and the nanostructural (collagen fibril and apatite crystals) levels. At the mesostructural level, no distinct differences were found in the trabecular structure of femoral metaphysis but thinner trabecular struts were observed in L5 vertebra for C57BL/6J mice strain. At the microstructural level, the collagen fibrils forming the rotated, twisted, and orthogonal plywood arrangements were distinguished as well as atypical arrangements. At the nanostructural level, the shape and size of apatite crystals, and their arrangement with respect to collagen fibrils were studied. In spite of very different bone mass densities, both mice strains had similar structures at the nanostructural and microstructural levels.

TEM analysis of the nanostructure of normal and osteoporotic human trabecular bone

Transmission electron microscopy (TEM) was used to investigate the crystal-collagen interactions in normal and osteoporotic human trabecular bone at the nanostructural level. More specifically, two-dimensional TEM observations were used to infer the three-dimensional information on the shape, the size, the orientation, and the alignment of apatite crystals in collagen fibrils in normal and osteoporotic bone. We found that crystals were of platelet shape with irregular edges and that there was no substantial difference in crystal length or crystal thickness between normal and osteoporotic trabecular bone. The crystal arrangement in cross-sectioned fibrils did not neatly conform to the parallel arrangement of crystals seen in longitudinally-sectioned fibrils. Instead, the crystal arrangement in both normal and osteoporotic trabecular bone took on more of a random, undulated arrangement, with certain localized areas demonstrating circular oriented patterns. The TEM imaging was done using bright fields only. Thus, the results presented are within the limitations of this approach.

Mineralization of type I collagen

It was previously found that the lateral spacing of the collagen molecules in wet mineralized tissues is exactly proportional to the inverse wet density. Several properties were investigated and the same type of relationship was observed each time. A possible explanation is offered. It is hypothesized that mineral is deposited initially in the extrafibrillar space so as to isolate the fibrils. Further deposition reduces the net free fibril volume thereby decreasing the spacing between collagen molecules. The linear relationship is derived from density considerations together with limitations on the collagen packing structure described as the generalized packing model. Three experimental situations were studied: lateral spacing wet tissue versus density; lateral spacing dry tissue versus density; and lateral spacing versus water content. The observed variations of the spacing can be attributed to a structure where the mass of the tissue remains constant but the volume decreases linearly with increasing mineral content.

Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments

Which of the elementary components (hydroxyapatite (HA) crystals, collagen, non-collagenous organic matter, water) do significantly contribute to the ultrastructural elastic stiffness magnitude and anisotropy of mineralized tissues; and how, i.e. through which shapes and assemblages (which micromechanical morphology)? We suggest answers to these questions by analyzing stiffness-volume fraction relationships of wet and dry tissue specimens in the framework of strain energy considerations. Radial stiffness values of both isotropic and anisotropic tissues are found to depend linearly to quadratically on only the mineral volume fraction. This suggests the isotropic contribution of HA to the ultrastructural stiffness. An energy-based analysis of the difference between the axial and radial stiffness values of anisotropic, collagen-rich tissues allows us to assess the collagen elasticity contribution, which is found to depend linearly on the extra-collagenous mineral concentration. These results suggest that collagen and hydroxyapatite are the elementary components governing the ultrastructural elastic stiffness magnitude and anisotropy of bone and mineralized tendons. The elastic stiffness of water and non-collagenous organic matter does not play a significant role. As for the morphological issue, we suggest that mineralized tissues are isotropic open crystal foams; and that these foams are reinforced unidirectionally by collagen molecules which are mechanically activated through tight links between these molecules and HA-crystals. The HA crystals are mechanically activated through stretching and bending in long bone tissues, they are predominantly stretched in mineralized tendons, and bent in hyperpycnotic tissues.

The ultrastructure of anorganic bovine bone and selected synthetic hyroxyapatites used as bone graft substitute materials

The objective of this study was to investigate the morphology and organization of apatite crystallites in mature mammalian bone. Anorganic bovine bone was studied in this investigation to allow for the examination of the mineral crystallites after removal of the organic phase. Field-emission low-voltage scanning electron microscopy (FE-LVSEM) was employed to obtain images at nanometer resolution without the application of a conductive coating. Transmission electron microscopy (TEM) of the samples was also performed to confirm the identification of features observed in the SEM and to allow for comparison with earlier studies of bone mineral architecture. For comparison, in order to demonstrate how the interaction of collagen and apatite results in the architecture and crystal structure of bone mineral, two synthetic hydroxyapatite materials were also analyzed: OsteoGen and OsteoGraf/LD300. FE-LVSEM revealed distinctive features of bone mineral: a fibrillar organization of crystallites, a periodic spacing of crystallites along the fibrils consistent with the banding pattern of collagen, inter-fibrillar bridging crystallites, and a plate-like habit of the crystallites. These findings supported the hypothesis, derived from the earlier TEM data of others, that the mineralization of collagen comprising osteoid proceeds by the formation of apatite crystallites within the fibers at selected periodic sites along their length. Moreover, the very presence in this anorganic material of distinct fibers comprised of the crystallites is demonstration of inter-crystallite bonding. The crystallites of the synthetic hydroxyapatite materials did not display any of these ultrastructural features.

Twisted plywood pattern of collagen fibrils in teleost scales: an X-ray diffraction investigation

The distribution and orientation of collagen fibrils, and apatite crystals, in the scales of a bony fish (Leuciscus cephalus) were investigated by X-ray diffraction. The small-angle diffraction patterns obtained with a microfocus scanning setup from most of the examined areas exhibit a distribution of intensity of the collagen reflections according to five preferential orientations, at 36 degrees from one another. It is suggested that the peculiar small-angle X-ray diffraction pattern is due to a plywood arrangement of collagen fibrils in successive layers parallel to the surface of the scale. The fibrils are strictly aligned in each layer and the alignment rotates by 36 degrees in successive layers, according to a discontinuous twist that generates a symmetric plywood pattern. The large spread of the wide-angle reflections does not allow one to distinguish the five directions of orientation in the intensity distribution of the 002 reflection of apatite. However, the patterns recorded from the less ordered regions of the scales display two different orientations of the 002 reflection and allow one to infer a preferential distribution of the apatite crystals with their c-axes parallel to the collagen fibrils. Although much electron microscopic evidence of plywood arrangements in calcified, as well as uncalcified, tissues has been reported, these are the very first diffraction data which unambiguously confirm the presence of these peculiar structures and suggest that this kind of investigation represents a powerful tool with which to study plywood arrangements in biological tissues.

Interpreting the equatorial diffraction pattern of collagenous tissues in the light of molecular motion

The equatorial diffraction pattern associated with collagenous tissues, particularly type I collagen, is diffuse and clearly unlike that from crystals. Hukins and Woodhead-Galloway proposed a statistical model that they termed a "liquid crystal" for collagen fibers in tendons. Fratzl et al. applied this model to both unmineralized and mineralized turkey leg tendon, a model that ignores the organization imposed by the well-known cross-linking. The justification for adopting this model is that the curve fits the data. It is shown that the data can be equally well matched by fitting a least-squares curve consisting of a second-order polynomial plus a Gaussian. The peak of the Gaussian is taken as the equatorial spacing of the collagen. A physical explanation for this model is given, as is a reason for the changes in the spacing with changes in water content of the tissue. The diffusion is attributed to thermally driven agitation of the molecules, in accordance with the Debye-Waller theory including the Gaussian distribution. The remainder of the diffusion is attributed to other scattering sources like the mineral crystallites.