Computational and experimental methodology for site-matched investigations of the influence of mineral mass fraction and collagen orientation on the axial indentation modulus of lamellar bone

Comparing age- and bone-related differences in collagen fiber orientation: A case study of bats and laboratory mice using quantitative polarized light microscopy

As bones age in most mammals, they typically become more fragile. This state of bone fragility is often associated with more homogenous collagen fiber orientations (CFO). Unlike most mammals, bats maintain mechanically competent bone throughout their lifespans, but little is known of positional and age-related changes in CFO within wing bones. This study tests the hypothesis that age-related changes in CFO in big brown bats (Eptesicus fuscus) differ from those of the standard mammalian model for skeletal aging, the C57BL/6 laboratory mouse. We used data from quantitative polarized light microscopy (qPLM) to compare CFO across the lifespan of long-lived big brown bats and age matched C57BL/6 mice. Eptesicus and C57BL/6 mice displayed idiosyncratic patterns of CFO. Consistent age-related changes were only apparent in the outer cortical bone of Eptesicus, where bone tissue is more longitudinally arranged and more anisotropic in older individuals. Both taxa displayed a ring of more transversely oriented bone tissue surrounding the medullary cavity. In Eptesicus, this tissue represents a greater proportion of the overall cross-section, and is more clearly helically aligned (arranged at 45° to the bone long axis) than similar bone tissue in mice. Bat wing bones displayed a proximodistal gradient in CFO anisotropy and longitudinal orientation in both outer and inner cortical bone compartments. This study lays a methodological foundation for the quantitative evaluation of bone tissue architecture in volant and non-volant mammals that may be expanded in the future.

Exploring the hierarchical structure of lamellar bone and its impact on fracture behaviour: A computational study using a phase field damage model

Bone is a naturally occurring composite material composed of a stiff mineral phase and a compliant organic matrix of collagen and non-collagenous proteins (NCP). While diverse mineral morphologies such as platelets and grains have been documented, the precise role of individual constituents, and their morphology, remains poorly understood. To understand the role of constituent morphology on the fracture behaviour of lamellar bone, a damage based representative volume element (RVE) was developed, which considered various mineral morphologies and mineralised collagen fibril (MCF) configurations. This model framework incorporated a novel phase-field damage model to predict the onset and evolution of damage at mineral-mineral and mineral-MCF interfaces. It was found that platelet-based mineral morphologies had superior mechanical performance over their granular counterparts, owing to their higher load-bearing capacity, resulting from a higher aspect ratio. It was also found that MCFs had a remarkable capacity for energy dissipation under axial loading, with these fibrillar structures acting as barriers to crack propagation, thereby enhancing overall elongation and toughness. Interestingly, the presence of extrafibrillar platelet-based minerals also provided an additional toughening through a similar mechanism, whereby these structures also inhibited crack propagation. These findings demonstrate that the two primary constituent materials of lamellar bone play a key role in its toughening behaviour, with combined effect by both mineral and MCFs to inhibit crack propagation at this scale. These results have provided novel insight into the fracture behaviour of lamellar bone, enhancing our understanding of microstructure-property relationships at the sub-tissue level.

Material and nanomechanical properties of bone structural units of cortical and trabecular iliac bone tissues from untreated postmenopausal osteoporotic women

The differences in bone nanomechanical properties between cortical (Ct) and trabecular (Tb) bone remain uncertain, whereas knowing the respective contribution of each compartment is critical to understand the origin of bone strength. Our purpose was to compare bone mechanical and intrinsic properties of Ct and Tb compartments, at the bone structural unit (BSU) level, in iliac bone taken from a homogeneous untreated human population.

Among 60 PMMA-embedded transiliac bone biopsies from untreated postmenopausal osteoporotic women (64 ± 7 year-old), >2000 BSUs were analysed by nanoindentation in physiological wet conditions [indentation modulus (elasticity), hardness, dissipated energy], by Fourier transform infrared (FTIRM) and Raman microspectroscopy (mineral and organic characteristics), and by X-ray microradiography (degree of mineralization of bone, DMB). BSUs were categorized based on tissue age, osteonal (Ost) and interstitial (Int) tissues location and bone compartments (Ct and Tb).

Indentation modulus was higher in Ct than in Tb BSUs, both in Ost and Int. dissipated energy was higher in Ct than Tb, in Int BSUs. Hardness was not different between Ct and Tb BSUs. In Ost or Int BSUs, mineral maturity (conversion of non-apatitic into apatitic phosphates) was higher in Ct than in Tb, as well as for collagen maturity (Ost). Mineral content assessed as mineral/matrix (FTIRM and Raman) or as DMB, was lower in Ct than in Tb. Crystallinity (FTIRM) was similar in BSUs from Ct and Tb, and slightly lower in Ct than in Tb when measured by Raman, indicating that the crystal size/perfection was quite similar between Ct and Tb BSUs. The differences found between Ost and Int tissues were much higher than the difference found between Ct and Tb for all those bone material properties. Multiple regression analysis showed that Indentation modulus and dissipated energy were mainly explained by mineral maturity in Ct and by collagen maturity in Tb, and hardness by mineral content in both Ct and Tb.

In conclusion, in untreated human iliac bone, Ct and Tb BSUs exhibit different characteristics. Ct BSUs have higher indentation modulus, dissipated energy (Int), mineral and organic maturities than Tb BSUs, without difference in hardness. Although those differences are relatively small compared to those found between Ost and Int BSUs, they may influence bone strength at macroscale.

A multiscale study of structural and compositional changes in a natural nanocomposite: Osteoporotic bone with chronic endogenous steroid excess

Glucocorticoid (or steroid) induced osteoporosis (GIOP) is the leading form of secondary osteoporosis, affecting up to 50% of patients receiving chronic glucocorticoid therapy. Bone quantity (bone mass) changes in GIOP patients alone are inadequate to explain the increased fracture risk, and bone material changes (bone quality) at multiple levels have been implicated in the reduced mechanics. Quantitative analysis of specific material-level changes is limited. Here, we combined multiscale experimental techniques (scanning small/wide-angle X-ray scattering/diffraction, backscattered electron imaging, and X-ray radiography) to investigate these changes in a mouse model (Crh^-120/+) with chronic endogenous steroid production. Nanoscale degree of orientation, the size distribution of mineral nanocrystals in the bone matrix, the spatial map of mineralization on the femoral cortex, and the microporosity showed significant changes between GIOP and the control, especially in the endosteal cortex. Our work can provide insight into the altered structure-property relationship leading to lowered mechanical properties in GIOP. SIGNIFICANCE STATEMENT: As a natural nanocomposite with a hierarchical structure, bone undergoes a staggered load transfer mechanism at the nanoscale. Disease and age-related deterioration of bone mechanics are caused by changes in bone structure at multiple length scales. Although clinical tools such as dual-energy X-ray absorptiometry (DXA) can be used to assess the reduction of bone quantity in these cases, little is known about how altered bone quality in diseased bone can increase fracture risk. It is clear that high-resolution diagnostic techniques need to be developed to narrow the gap between the onset and diagnosis of fracture-related changes. Here, by combining several scanning probe methods on a mouse model (Crh^-120/+) of glucocorticoid-induced osteoporosis (GIOP), we developed quantitative and spatially resolved maps of ultrastructural changes in collagen fibrils and mineral nanocrystals, mineralization distribution (microscale), and morphology (macroscale) across femoral osteoporotic bone. Our results indicate that the altered bone remodelling in GIOP leads to 1) heterogeneous bone structure and mineralization, 2) reduced degree of orientation of collagen fibrils and mineral nanocrystals, and 3) reduced length and increased thickness of mineral nanocrystals, which contribute to mechanical abnormalities. The combined multiscale experimental approach presented here will be used to understand musculoskeletal degeneration in aging and osteoporosis.

Regional Nanoindentation Properties in Different Locations on the Mouse Tibia From C57BL/6 and Balb/C Female Mice

The local spatial heterogeneity of the material properties of the cortical and trabecular bone extracted from the mouse tibia is not well-known. Nevertheless, its characterization is fundamental to be able to study comprehensively the effect of interventions and to generate computational models to predict the bone strength preclinically. The goal of this study was to evaluate the nanoindentation properties of bone tissue extracted from two different mouse strains across the tibia length and in different sectors. Left tibiae were collected from four female mice, two C57BL/6, and two Balb/C mice. Nanoindentations with maximum 6 mN load were performed on different microstructures, regions along the axis of the tibiae, and sectors (379 in total). Reduced modulus (Er) and hardness (H) were computed for each indentation. Trabecular bone of Balb/C mice was 21% stiffer than that of C57BL/6 mice (20.8 ± 4.1 GPa vs. 16.5 ± 7.1 GPa). Moreover, the proximal regions of the bones were 13-36% less stiff than the mid-shaft and distal regions of the same bones. No significant differences were found for the different sectors for E _r and H for Balb/C mice. The bone in the medial sector was found to be 8-14% harder and stiffer than the bone in the anterior or posterior sectors for C57BL/6 mice. In conclusion, this study showed that the nanoindentation properties of the mouse tibia are heterogeneous across the tibia length and the trabecular bone properties are different between Balb/C and C57BL/6 mice. These results will help the research community to identify regions where to characterize the mechanical properties of the bone during preclinical optimisation of treatments for skeletal diseases.

Extrafibrillar matrix yield stress and failure envelopes for mineralised collagen fibril arrays

Bone metabolic diseases such as osteoporosis constitute a major socio-economic challenge. A detailed understanding of the structure-property relationships of bone's underlying hierarchical levels has the potential to improve diagnosis and the ability to treat those diseases, especially with regards to the onset of failure. Therefore, elastic and yield properties of mineralised turkey leg tendon (MTLT), a mineralised tissue that is similar to bone but has a simpler multiscale structure, were investigated. Elastic properties were identified using a multiscale micromechanical model. The input parameters include constituent mechanical properties, volume fractions and inclusion aspect ratios and these were obtained from a wide variety of literature sources. The determined elastic properties were used to formulate micromechanically informed yield surfaces and to identify yield properties of MTLT at the nanometre length scale where failure is first reported to occur. This was done in conjunction with experimental results from the compression of micropillars extracted from individual mineralised collagen fibres. This data was then used to identify micromechanically informed failure envelopes. The shear yield stress of the extrafibrillar matrix, associated with interfibrillar sliding, was identified as 137.65 MPa. The ratio between tensile and compressive yield stress in the Drucker-Prager yield criterion was 0.65. For both criteria apparent yield stress of the mineralised collagen fibril decreased to 25.3-31.4% when varying fibril orientation from 0° to 90°. This study identified yield properties of extrafibrillar matrix using an aligned mineralised tissue. The ability to obtain yield stress data and unloading stiffness from micropillar compression tests of MTLT at the level of the mineralised collagen fibril array and downscaling these into the EM mitigates against possible errors associated with macroscopic stiffness predictions and proved to be an invaluable advantage compared to similar modelling approaches. Results may help to improve computational models that may then be used in pre-clinical testing or development of personalised treatment strategies.

Application of the Johnson-Cook plasticity model in the finite element simulations of the nanoindentation of the cortical bone

The mechanical behavior of the cortical bone in nanoindentation is a complicated mechanical problem. The finite element analysis has commonly been assumed to be the most appropriate approach to this issue. One significant problem in nanoindentation modeling of the elastic-plastic materials is pile-up deformation, which is not observed in cortical bone nanoindentation testing. This phenomenon depends on the work-hardening of materials; it doesn't occur for work-hardening materials, which suggests that the cortical bone could be considered as a work-hardening material. Furthermore, in a recent study [59], a plastic hardening until failure was observed on the micro-scale of a dry ovine osteonal bone samples subjected to micropillar compression. The purpose of the current study was to apply an isotropic hardening model in the finite element simulations of the nanoindentation of the cortical bone to predict its mechanical behavior. The Johnson-Cook (JC) model was chosen as the constitutive model. The finite element modeling in combination with numerical optimization was used to identify the unknown material constants and then the finite element solutions were compared to the experimental results. A good agreement of the numerical curves with the target loading curves was found and no pile-up was predicted. A Design Of Experiments (DOE) approach was performed to evaluate the linear effects of the material constants on the mechanical response of the material. The strain hardening modulus and the strain hardening exponent were the most influential parameters. While a positive effect was noticed with the Young's modulus, the initial yield stress and the strain hardening modulus, an opposite effect was found with the Poisson's ratio and the strain hardening exponent. Finally, the JC model showed a good capability to describe the elastoplastic behavior of the cortical bone.

Structure and collagen crimp patterns of functionally distinct equine tendons, revealed by quantitative polarised light microscopy (qPLM)

Structure-function relationships in tendons are directly influenced by the arrangement of collagen fibres. However, the details of such arrangements in functionally distinct tendons remain obscure. This study demonstrates the use of quantitative polarised light microscopy (qPLM) to identify structural differences in two major tendon compartments at the mesoscale: fascicles and interfascicular matrix (IFM). It contrasts functionally distinct positional and energy storing tendons, and considers changes with age. Of particular note, the technique facilitates the analysis of crimp parameters, in which cutting direction artefact can be accounted for and eliminated, enabling the first detailed analysis of crimp parameters across functionally distinct tendons.

IFM shows lower birefringence (0.0013 ± 0.0001 [−]), as compared to fascicles (0.0044 ± 0.0005 [−]), indicating that the volume fraction of fibres must be substantially lower in the IFM. Interestingly, no evidence of distinct fibre directional dispersions between equine energy storing superficial digital flexor tendons (SDFTs) and positional common digital extensor tendons (CDETs) were noted, suggesting either more subtle structural differences between tendon types or changes focused in the non-collagenous components.

By contrast, collagen crimp characteristics are strongly tendon type specific, indicating crimp specialisation is crucial in the respective mechanical function. SDFTs showed much finer crimp (21.1 ± 5.5 µm) than positional CDETs (135.4 ± 20.1 µm). Further, tendon crimp was finer in injured tendon, as compared to its healthy equivalents. Crimp angle differed strongly between tendon types as well, with average of 6.5 ± 1.4° in SDFTs and 13.1 ± 2.0° in CDETs, highlighting a substantially tighter crimp in the SDFT, likely contributing to its effective recoil capacity.

Statement of Significance

This is the first study to quantify birefringence in fascicles and interfascicular matrix of functionally distinct energy storing and positional tendons. It adopts a novel method – quantitative polarised light microscopy (qPLM) to measure collagen crimp angle, avoiding artefacts related to the direction of histological sectioning, and provides the first direct comparison of crimp characteristics of functionally distinct tendons of various ages.

A comparison of matched picrosirius red stained and unstained tendons sections identified non-homogenous staining effects, and leads us to recommend that only unstained sections are analysed in the quantitative manner.

qPLM is successfully used to assess birefringence in soft tissue sections, offering a promising tool for investigating the structural arrangements of fibres in (soft) tissues and other composite materials.

Finite Element-Based Mechanical Assessment of Bone Quality on the Basis of In Vivo Images

Beyond bone mineral density (BMD), bone quality designates the mechanical integrity of bone tissue. In vivo images based on X-ray attenuation, such as CT reconstructions, provide size, shape, and local BMD distribution and may be exploited as input for finite element analysis (FEA) to assess bone fragility. Further key input parameters of FEA are the material properties of bone tissue. This review discusses the main determinants of bone mechanical properties and emphasizes the added value, as well as the important assumptions underlying finite element analysis. Bone tissue is a sophisticated, multiscale composite material that undergoes remodeling but exhibits a rather narrow band of tissue mineralization. Mechanically, bone tissue behaves elastically under physiologic loads and yields by cracking beyond critical strain levels. Through adequate cell-orchestrated modeling, trabecular bone tunes its mechanical properties by volume fraction and fabric. With proper calibration, these mechanical properties may be incorporated in quantitative CT-based finite element analysis that has been validated extensively with ex vivo experiments and has been applied increasingly in clinical trials to assess treatment efficacy against osteoporosis.

Mechanical properties of cortical bone and their relationships with age, gender, composition and microindentation properties in the elderly

The growing incidence of skeletal fractures poses a significant challenge to ageing societies. Since a major part of physiological loading in the lower limbs is carried by cortical bone, it would be desirable to better understand the structure-mechanical property relationships and scale effects in this tissue. This study aimed at assessing whether microindentation properties combined with chemical and morphological information are usable to predict macroscopic elastic and strength properties in a donor- and site-matched manner. Specimens for quasi-static macroscopic tests in tension, compression, and torsion and microindentation were prepared from a cohort of 19 male and 20 female donors (46 to 99 years). All tests were performed under fully hydrated conditions. The chemical composition of the extra-cellular matrix was investigated with Raman spectroscopy. The results of the micro-mechanical tests were combined with morphological and compositional properties using a power law relationship to predict the macro-mechanical results. Microindentation properties were not gender dependent, remarkably constant over age, and showed an overall small variation with standard deviations of approximately 10 %. Similar results were obtained for chemical tissue composition. Macro-mechanical stiffness and strength were significantly related to porosity for all load cases (p<0.05). In case of macroscopic yield strain and work-to-failure this was only true in torsion and compression, respectively. The correlations of macro-mechanical with micro-mechanical, morphological, and chemical properties showed no significance for cement line density, mineralisation, or variations in the microindentation results and were dominated by porosity with a moderate explanatory power of predominately less than 50 %. The results confirm that age, with minor exceptions gender, and small variations in average mineralisation have negligible effect on the tissue microindentation properties of human lamellar bone in the elderly. Furthermore, our findings suggest that microindentation experiments are suitable to predict macroscopic mechanical properties in the elderly only on average and not on a one to one basis. The presented data may help to form a better understanding of the mechanisms of ageing in bone tissue and of the length scale at which they are active. This may be used for future prediction of fracture risk in the elderly.

TECHNOLOGIES FOR STRAIN ASSESSMENT FROM WHOLE BONE TO MINERALIZED OSTEOID LEVEL: A CRITICAL REVIEW

Bone has distinctive structures and mechanical properties at the whole bone, perilacunar and mineralized osteoid levels. A systematic understanding of bone strain magnitudes at different anatomical levels and their internal interactions is the prerequisite to advances in bone mechanobiology. However, due to the intrinsic shortcomings of the strain-measuring technologies, the systematic assessment of bone strain at different anatomical levels under physiological conditions and a deep understanding of their internal interactions are still restricted. To promote technological advances and provide systematic and valuable information for mechanical engineers and bone biomechanical researchers, the most useful methods for measuring bone strain at different anatomical levels are demonstrated in this review, and suggestions for the future development of the technologies and their potential integrated applications are proposed.

Multimodal correlative investigation of the interplaying micro-architecture, chemical composition and mechanical properties of human cortical bone tissue reveals predominant role of fibrillar organization in determining microelastic tissue properties

The mechanical competence of bone is crucially determined by its material composition and structural design. To investigate the interaction of the complex hierarchical architecture, the chemical composition and the resulting elastic properties of healthy femoral bone at the level of single bone lamellae and entire structural units, we combined polarized Raman spectroscopy (PRS), scanning acoustic microscopy (SAM) and synchrotron X-ray phase contrast nano tomography (SR-nanoCT). In line with earlier studies, mutual correlation analysis strongly suggested that the characteristic elastic modulations of bone lamellae within single units are the result of the twisting fibrillar orientation, rather than compositional variations, modulations of the mineral particle maturity, or mass density deviations. Furthermore, we show that predominant fibril orientations in entire tissue units can be rapidly assessed from Raman parameter maps. Coexisting twisted and oscillating fibril patterns were observed in all investigated tissue domains. Ultimately, our findings demonstrate in particular the potential of combined PRS and SAM measurements in providing multi-scalar analysis of correlated fundamental tissue properties. In future studies, the presented approach can be applied for non-destructive investigation of small pathologic samples from bone biopsies and a broad range of biological materials and tissues.

STATEMENT OF SIGNIFICANCE

Bone is a complex structured composite material consisting of collagen fibrils and mineral particles. Various studies have shown that not only composition, maturation, and packing of its components, but also their structural arrangement determine the mechanical performance of the tissue. However, prominent methodologies are usually not able to concurrently describe these factors on the micron scale and complementary tissue characterization remains challenging. In this study we combine X-ray nanoCT, polarized Raman imaging and scanning acoustic microscopy and propose a protocol for fast and easy assessment of predominant fibril orientations in bone. Based on our site-matched analysis of cortical bone, we conclude that the elastic modulations of bone lamellae are mainly determined by the fibril arrangement.

Post-yield and failure properties of cortical bone

Ageing and associated skeletal diseases pose a significant challenge for health care systems worldwide. Age-related fractures have a serious impact on personal, social and economic wellbeing. A significant proportion of physiological loading is carried by the cortical shell. Its role in the fracture resistance and strength of whole bones in the ageing skeleton is of utmost importance. Even though a large body of knowledge has been accumulated on this topic on the macroscale, the underlying micromechanical material behaviour and the scale transition of bone's mechanical properties are yet to be uncovered. Therefore, this review aims at providing an overview of the state-of-the-art of the post-yield and failure properties of cortical bone at the extracellular matrix and the tissue level.

Elastic Properties of Human Osteon and Osteonal Lamella Computed by a Bidirectional Micromechanical Model and Validated by Nanoindentation

Knowledge of the anisotropic elastic properties of osteon and osteonal lamellae provides a better understanding of various pathophysiological conditions, such as aging, osteoporosis, osteoarthritis, and other degenerative diseases. For this reason, it is important to investigate and understand the elasticity of cortical bone. We created a bidirectional micromechanical model based on inverse homogenization for predicting the elastic properties of osteon and osteonal lamellae of cortical bone. The shape, the dimensions, and the curvature of osteon and osteonal lamellae are described by appropriately chosen curvilinear coordinate systems, so that the model operates close to the real morphology of these bone components. The model was used to calculate nine orthotropic elastic constants of osteonal lamellae. The input values have the elastic properties of a single osteon. We also expressed the dependence of the elastic properties of the lamellae on the angle of orientation. To validate the model, we performed nanoindentation tests on several osteonal lamellae. We compared the experimental results with the calculated results, and there was good agreement between them. The inverted model was used to calculate the elastic properties of a single osteon, where the input values are the elastic constants of osteonal lamellae. These calculations reveal that the model can be used in both directions of homogenization, i.e., direct homogenization and also inverse homogenization. The model described here can provide either the unknown elastic properties of a single lamella from the known elastic properties at the level of a single osteon, or the unknown elastic properties of a single osteon from the known elastic properties at the level of a single lamella.

Tendon extracellular matrix damage, degradation and inflammation in response to in vitro overload exercise

The role of inflammation in tendon injury is uncertain and a topic of current interest. In vitro studies of tendon accelerated overload damage can serve as a valuable source of information on the early stages of tendinopathy. Viable fascicle bundles from bovine flexor tendons were subjected to cyclic uniaxial loading from 1-10% strain. Immuno-staining for inflammatory markers and matrix degradation markers was performed on the samples after mechanical testing. Loaded samples exhibited visible extracellular matrix damage, with disrupted collagen fibers and fiber kinks, and notable damage to the interfascicular matrix. Inflammatory markers COX-2 and IL-6 were only expressed in the cyclically loaded samples. Collagen degradation markers MMP-1 and C1,2C were colocalized in many areas, with staining occurring in the interfascicular matrix or the fascicular tenocytes. These markers were present in control samples, but staining became increasingly intense with loading. Little MMP-3 or MMP-13 was evident in control sections. In loaded samples, some sections showed intense staining of these markers, again localized to interfascicular regions. This study suggests that inflammatory markers may be expressed rapidly after tendon overload exercise. Interestingly, both inflammation and damage-induced matrix remodeling seem to be concentrated in, or in the vicinity of, the highly cellular interfascicular matrix.

EXPERIMENTAL VALIDATION OF A MEAN FILED MODEL OF MINERALIZED COLLAGEN FIBER ARRAYS AT TWO LEVELS OF HIERARCHY

In the course of this study, stiffness of a fibril array of mineralized collagen fibrils modeled with a mean field method was validated experimentally at site-matched two levels of tissue hierarchy using mineralized turkey leg tendons (MTLT). The applied modeling approaches allowed to model the properties of this unidirectional tissue from nanoscale (mineralized collagen fibrils) to macroscale (mineralized tendon).

At the microlevel, the indentation moduli obtained with a mean field homogenization scheme were compared to the experimental ones obtained with microindentation. At the macrolevel, the macroscopic stiffness predicted with micro finite element (μFE) models was compared to the experimental stiffness measured with uniaxial tensile tests. Elastic properties of the elements in μFE models were injected from the mean field model or two-directional microindentations.

Quantitatively, the indentation moduli can be properly predicted with the mean-field models. Local stiffness trends within specific tissue morphologies are very weak, suggesting additional factors responsible for the stiffness variations. At macrolevel, the μFE models underestimate the macroscopic stiffness, as compared to tensile tests, but the correlations are strong.