Anisotropy, Anatomical Region, and Additional Variables Influence Young's Modulus of Bone: A Systematic Review and Meta-Analysis

The importance of finite element analysis (FEA) is growing in orthopedic research, especially in implant design. However, Young's modulus (E) values, one of the most fundamental parameters, can range across a wide scale. Therefore, our study aimed to identify factors influencing E values in human bone specimens. We report our systematic review and meta-analysis based on the recommendation of the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) 2020 guideline. We conducted the analysis on November 21, 2021. We included studies investigating healthy human bone specimens and reported on E values regarding demographic data, specimen characteristics, and measurement specifics. In addition, we included study types reporting individual specimen measurements. From the acquired data, we created a cohort in which we performed an exploratory data analysis that included the explanatory variables selected by random forest and regression trees methods, and the comparison of groups using independent samples Welch's t test. A total of 756 entries were included from 48 articles. Eleven different bones of the human body were included in these articles. The range of E values is between 0.008 and 33.7 GPa. The E values were most heavily influenced by the cortical or cancellous type of bone tested. Measuring method (compression, tension, bending, and nanoindentation), the anatomical region within a bone, the position of the bone within the skeleton, and the bone specimen size had a decreasing impact on the E values. Bone anisotropy, specimen condition, patient age, and sex were selected as important variables considering the value of E. On the basis of our results, E values of a bone change with bone characteristics, measurement techniques, and demographic variables. Therefore, the evaluation of FEA should be performed after the standardization of in vitro measurement protocol. © 2023 The Authors. JBMR Plus published by Wiley Periodicals LLC on behalf of American Society for Bone and Mineral Research.

Elasticity and material anisotropy of lamellar cortical bone in adult bovine tibia characterized via AFM nanoindentation

The research focuses on the evaluation of the mechanical properties of osteonal cortical bone at the lamellar level. Elastic properties of the mid-diaphysis region of the bovine tibia are investigated via cantilever-based nanoindentation at the submicron length scale utilizing Atomic Force Microscopy, where the force-displacement curves are used for the elastic assessment using the Derjaguin-Muller-Toropov model to calculate indentation modulus. Variations of the modulus and the directional mechanical response of the osteonal bone at different distances from the Haversian canal are investigated. Additionally, the effects of demineralization on the indentation modulus are discussed. It was found that in the axial direction, the first and last untreated thick lamella layers show a significant indentation modulus difference compared to all other layers (4.26 ± 0.4 and 4.6 ± 0.3 GPa vs ∼3.5 GPa). On the other hand, the indentation modulus of transverse thick lamella layers shows a periodic variation between ∼3 ± 0.7 GPa and ∼4 ± 0.3 GPa from near the Haversian canal to near the interstitial bone. A periodic variation in the anisotropy ratio was found. Mineral content was quantified via energy-dispersive X-ray microanalysis at different levels of mineralization and shows a positive correlation with the indentation modulus.

Microtensile properties and failure mechanisms of cortical bone at the lamellar level

Bone features a remarkable combination of toughness and strength which originates from its complex hierarchical structure and motivates its investigation on multiple length scales. Here, in situ microtensile experiments were performed on dry ovine osteonal bone for the first time at the length scale of a single lamella. The micromechanical response was brittle and revealed larger ultimate tensile strength compared to the macroscale (factor of 2.3). Ultimate tensile strength for axial and transverse specimens was 0.35 ± 0.05 GPa and 0.13 ± 0.02 GPa, respectively. A significantly greater strength anisotropy relative to compression was observed (axial to transverse strength ratio of 2.7:1 for tension, 1.3:1 for compression). Fracture surface and transmission electron microscopic analysis suggested that this may be rationalized by a change in failure mode from fibril-matrix interfacial shearing for axial specimens to fibril-matrix debonding in the transverse direction. An improved version of the classic Hashin's composite failure model was applied to describe lamellar bone strength as a function of fibril orientation. Together with our experimental observations, the model suggests that cortical bone strength at the lamellar level is remarkably tolerant to variations of fibrils orientation of about ±30°. This study highlights the importance of investigating bone's hierarchical organization at several length scales for gaining a deeper understanding of its macroscopic fracture behavior. STATEMENT OF SIGNIFICANCE: Understanding bone deformation and failure behavior at different length scales of its hierarchical structure is fundamental for the improvement of bone fracture prevention, as well as for the development of multifunctional bio-inspired materials combining toughness and strength. The experiments reported in this study shed light on the microtensile properties of dry primary osteonal bone and establish a baseline from which to start further investigations in more physiological conditions. Microtensile specimens were stronger than their macroscopic counterparts by a factor of 2.3. Lamellar bone strength seems remarkably tolerant to variations of the sub-lamellar fibril orientation with respect to the loading direction (±30°). This study underlines the importance of studying bone on all length scales for improving our understanding of bone's macroscopic mechanical response.

Combining polarized Raman spectroscopy and micropillar compression to study microscale structure-property relationships in mineralized tissues

Bone is a natural composite possessing outstanding mechanical properties combined with a lightweight design. The key feature contributing to this unusual combination of properties is the bone hierarchical organization ranging from the nano- to the macro-scale. Bone anisotropic mechanical properties from two orthogonal planes (along and perpendicular to the main bone axis) have already been widely studied. In this work, we demonstrate the dependence of the microscale compressive mechanical properties on the angle between loading direction and the mineralized collagen fibril orientation in the range between 0° and 82°. For this, we calibrated polarized Raman spectroscopy for quantitative collagen fibril orientation determination and validated the method using widely used techniques (small angle X-ray scattering, micro-computed tomography). We then performed compression tests on bovine cortical bone micropillars with known mineralized collagen fibril angles. A strong dependence of the compressive micromechanical properties of bone on the fibril orientation was found with a high degree of anisotropy for both the elastic modulus (E_a/E_t=3.80) and the yield stress (σ_a^y/σ_t^y=2.54). Moreover, the post-yield behavior was found to depend on the MCF orientation with a transition between softening to hardening behavior at approximately 50°. The combination of methods described in this work allows to reliably determine structure-property relationships of bone at the microscale, which may be used as a measure of bone quality.

Hardness, an Important Indicator of Bone Quality, and the Role of Collagen in Bone Hardness

Bone is a nanocomposite material where the hard inorganic (hydroxyapatite crystallites) and organic (collagen fibrils) components are hierarchically arranged in the nanometer scale. Bone quality is dependent on the spatial distributions in the shape, size and composition of bone constituents (mineral, collagen and water). Bone hardness is an important property of bone, which includes both elastic and plastic deformation. In this study, a microhardness test was performed on a deer bone samples. The deer tibia shaft (diaphysis) was divided into several cross-sections of equal thickness; samples were prepared in untreated, boiled water treatment (100 °C for 30 min) and sodium hypochlorite (NaOCl) treatment conditions. Microhardness tests were performed on various regions of the tibial diaphysis to study the heterogeneous characteristics of bone microhardness and highlight the role of the organic matrix in bone hardness. The results indicated that boiled water treatment has a strong negative correlation with bone hardness. The untreated bone was significantly (+20%) harder than the boiled-water-treated bone. In general, the hardness values near the periosteal surface was significantly (23 to 45%) higher than the ones near the endosteal surface. Samples treated with NaOCl showed a significant reduction in hardness.

Investigation of bone matrix composition, architecture and mechanical properties reflect structure-function relationship of cortical bone in glucocorticoid induced osteoporosis

Glucocorticoid induced osteoporosis (GIOP) is the most common negative consequence of long-term glucocorticoid treatment, leading to increased fracture risk followed by loss of mobility and high mortality risk. These biologically induced changes in bone quality at molecular level lead to changes both in bone matrix architecture and bone matrix composition. However, the quantitative details of changes in bone quality - and especially their link to reduced macroscale mechanical properties are still largely missing. In this study, a mouse model for glucocorticoid-induced osteoporosis (GIOP) was used to investigate mechanical and material alterations in bone cortex (natural nanocomposite) at different scale. By combining quantitative backscattered electron (qBSE) imaging, nanoindentation and high brilliance synchrotron X-ray nanomechanical imaging on a genetically modified mouse model of GIOP, we were able to quantify the local indentation modulus, mineralization distribution and the alterations of nanoscale structures and deformation mechanisms in the mid-diaphysis of femur, and relate them to the macroscopic mechanical changes. Our results showed clear and significant changes in terms of material quality of bone at nanoscale and microscale, which manifests itself in development of spatial heterogeneities in mineralization and indentation moduli across the bone organ, with potential implications for increased fracture risk.

Compositional and mechanical properties of growing cortical bone tissue: a study of the human fibula

Human cortical bone contains two types of tissue: osteonal and interstitial tissue. Growing bone is not well-known in terms of its intrinsic material properties. To date, distinctions between the mechanical properties of osteonal and interstitial regions have not been investigated in juvenile bone and compared to adult bone in a combined dataset. In this work, cortical bone samples obtained from fibulae of 13 juveniles patients (4 to 18 years old) during corrective surgery and from 17 adult donors (50 to 95 years old) were analyzed. Microindentation was used to assess the mechanical properties of the extracellular matrix, quantitative microradiography was used to measure the degree of bone mineralization (DMB), and Fourier transform infrared microspectroscopy was used to evaluate the physicochemical modifications of bone composition (organic versus mineral matrix). Juvenile and adult osteonal and interstitial regions were analyzed for DMB, crystallinity, mineral to organic matrix ratio, mineral maturity, collagen maturity, carbonation, indentation modulus, indicators of yield strain and tissue ductility using a mixed model. We found that the intrinsic properties of the juvenile bone were not all inferior to those of the adult bone. Mechanical properties were also differently explained in juvenile and adult groups. The study shows that different intrinsic properties should be used in case of juvenile bone investigation.

Functional disuse initiates medullary endosteal micro-architectural impairment in cortical bone characterized by nanoindentation

In this study, we evaluated the effect of functional disuse-induced bone remodeling on its mechanical properties, individually at periosteum and medullary endosteum regions of the cortical bone. Left middle tibiae were obtained from 5-month-old female Sprague-Dawley rats for the baseline control as well as hindlimb suspended (disuse) groups. Micro-nano-mechanical elastic moduli (at lateral region) was evaluated along axial (Z), circumferential (C) and radial (R) orientations using nanoindentation. Results indicated an anisotropic microstructure with axial orientation having the highest and radial orientation with the lowest moduli at periosteum and medullary endosteum for both baseline control as well as disuse groups. Between the groups: at periosteum, an insignificant difference was evaluated for each of the orientations (p > 0.05) and at endosteum, a significant decrease of elastic moduli in the radial (p < 0.0001), circumferential (p < 0.001) and statistically insignificant difference in axial (p > 0.05) orientation. For the moduli ratios between groups: at periosteum, only significant difference in the Z/R (p < 0.05) anisotropy ratio, whereas at endosteum, a statistically significant difference in Z/C (p < 0.001), and Z/R (p < 0.001), as well as C/R (p < 0.05) anisotropy ratios, was evaluated. The results suggested initial bone remodeling impaired bone micro-architecture predominantly at the medullary endosteum with possible alterations in the geometric orientations of collagen and mineral phases inside the bone. The findings could be significant for studying the mechanotransduction pathways involved in maintaining the bone micro-architecture and possibly have high clinical significance for drug use against impairment from functional disuse.

Quantitative ultrasound (QUS) axial transmission method reflects anisotropy in micro-arrangement of apatite crystallites in human long bones: A study with 3-MHz-frequency ultrasound

Anisotropic arrangement of apatite crystallites, i.e., preferential orientation of the apatite c-axis, is known to be an important bone quality parameter that governs the mechanical properties. However, noninvasive evaluation of apatite orientation has not been achieved to date. The present paper reports the potential of quantitative ultrasound (QUS) for noninvasive evaluation of the degree of apatite orientation in human bone for the first time. A novel QUS instrument for implementation of the axial transmission (AT) method is developed, so as to achieve precise measurement of the speed of sound (SOS) in the cortex (cSOS) of human long bone. The advantages of our QUS instrument are the following: (i) it is equipped with a cortical bone surface-morphology detection system to correct the ultrasound transmission distance, which should be necessary for AT measurement of long bone covered by soft tissue of non-uniform thickness; and (ii) ultrasound with a relatively high frequency of 3 MHz is employed, enabling thickness-independent cSOS measurement even for the thin cortex by preventing guide wave generation. The reliability of the proposed AT measurement system is confirmed through comparison with the well-established direct transmission (DT) method. The cSOS in human long bone is found to exhibit considerable direction-dependent anisotropy; the axial cSOS (3870 ± 66 m/s) is the highest, followed by the tangential (3411 ± 94 m/s) and radial (3320 ± 85 m/s) cSOSs. The degree of apatite orientation exhibits the same order, despite the unchanged bone mineral density. Multiple regression analysis reveals that the cSOS of human long bone strongly reflects the apatite orientation. The cSOS determined by the AT method is positively correlated with that determined by the DT method and sensitively reflects the apatite orientation variation, indicating the validity of the AT instrument developed in this study. Our instrument will be beneficial for noninvasive evaluation of the material integrity of the human long-bone cortex, as determined by apatite c-axis orientation along the axial direction.

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.

Estimation of the elastic modulus of child cortical bone specimens via microindentation

Purpose: Non-pathological child cortical bone (NPCCB) studies can provide clinicians with vital information and insights. However, assessing the anisotropic elastic properties of NPCCB remains a challenge for the biomechanical engineering community. For the first time, this paper provides elastic moduli values for NPCCB specimens in two perpendicular directions (longitudinal and transverse) and for two different structural components of bone tissue (osteon and interstitial lamellae). Materials and Methods: Microindentation is one of the reference methods used to measure bone stiffness. Here, 8 adult femurs (mean age 82 ± 8.9 years), 3 child femurs (mean age 13.3 ± 2.1 years), and 16 child fibulae (mean age 10.2 ± 3.9 years) were used to assess the elastic moduli of adult and child bones by microindentation. Results: For adult specimens, the mean moduli measured in this study are 18.1 (2.6) GPa for osteons, 21.3 (2.3) GPa for interstitial lamellae, and 13.8 (1.7) GPa in the transverse direction. For child femur specimens, the mean modulus is 14.1 (0.8) GPa for osteons, lower than that for interstitial lamellae: 15.5 (1.5) GPa. The mean modulus is 11.8 (0.7) GPa in the transverse direction. Child fibula specimens show a higher elastic modulus for interstitial lamellae 15.8 (1.5) than for osteons 13.5 (1.6), with 10.2 (1) GPa in the transverse direction. Conclusion: For the first time, NPCCB elastic modulus values are provided in longitudinal and transverse directions at the microscale level.

Analysis of Mechanical Properties and Mechanical Anisotropy in Canine Bone Tissues of Various Ages

The effect of age on mechanical behavior and microstructure anisotropy of bone is often ignored by researchers engaged in the study of biomechanics. The objective of our study was to determine the variations in mechanical properties of canine femoral cortical bone with age and the mechanical anisotropy between the longitudinal and transverse directions. Twelve beagles divided into three age groups (6, 12, and 36 months) were sacrificed and all femurs were extracted. The longitudinal and transverse samples of cortical bone were harvested from three regions of diaphysis (proximal, central, and distal). A nanoindentation technique was used for simultaneously measuring force and displacement of a diamond tip pressed 2000nm into the hydrated bone tissue. An elastic modulus was calculated from the unloading curve with an assumed Poisson ratio of 0.3, while hardness was defined as the maximal force divided by the corresponding contact area. The mechanical properties of cortical bone were determined from 852 indents on two orthogonal cross-sectional surfaces. Mean elastic modulus ranged from 7.56±0.32 GPa up to 21.56±2.35 GPa, while mean hardness ranged from 0.28±0.057 GPa up to 0.84±0.072 GPa. Mechanical properties of canine femoral cortical bone tended to increase with age, but the magnitudes of these increase for each region might be different. The longitudinal mechanical properties were significantly higher than that of transverse direction (P<0.01). A significant anisotropy was found in the mechanical properties while there was no significant correlation between the two orthogonal directions in each age group (r²<0.3). Beyond that, the longitudinal mechanical properties of the distal region in each age group were lower than the proximal and central regions. Hence, mechanical properties in nanostructure of bone tissue must differ mainly among age, sample direction, anatomical sites, and individuals. These results may help a number of researchers develop more accurate constitutive micromechanics models of bone tissue in future studies.

Bone Mechanical Properties in Healthy and Diseased States

The mechanical properties of bone are fundamental to the ability of our skeletons to support movement and to provide protection to our vital organs. As such, deterioration in mechanical behavior with aging and/or diseases such as osteoporosis and diabetes can have profound consequences for individuals' quality of life. This article reviews current knowledge of the basic mechanical behavior of bone at length scales ranging from hundreds of nanometers to tens of centimeters. We present the basic tenets of bone mechanics and connect them to some of the arcs of research that have brought the field to recent advances. We also discuss cortical bone, trabecular bone, and whole bones, as well as multiple aspects of material behavior, including elasticity, yield, fracture, fatigue, and damage. We describe the roles of bone quantity (e.g., density, porosity) and bone quality (e.g., cross-linking, protein composition), along with several avenues of future research.

Modal analysis of nanoindentation data, confirming that reduced bone turnover may cause increased tissue mineralization/elasticity

It is widely believed that the activities of bone cells at the tissue scale not only govern the size of the vascular pore spaces (and hence, the amount of bone tissue available for actually carrying the loads), but also the characteristics of the extracellular bone matrix itself. In this context, increased mechanical stimulation (in mediolateral regions of human femora, as compared to anteroposterior regions) may lead to increased bone turnover, lower bone matrix mineralization, and therefore lower tissue modulus. On the other hand, resorption-only processes (in endosteal versus periosteal regions) may have the opposite effect. A modal analysis of nanoindentation data obtained on femurs from the Melbourne Femur Research Collection (MFRC) indeed confirms that bone is stiffer in endosteal regions compared to periosteal regions (E̅_endost = 29.34 ± 0.75 GPa >E̅_periost = 24.67 ± 1.63 GPa), most likely due to the aging-related increase in resorption modeling on endosteal surfaces resulting in trabecularization of cortical bone. The results also show that bone is stiffer along the anteroposterior direction compared the mediolateral direction (E̅_anteropost = 28.89 ± 1.08 GPa >E̅_mediolat = 26.03 ± 2.31 GPa), the former being aligned with the neutral bending axis of the femur and, thus, undergoing more resorption modeling and consequently being more mineralized.

Nanoindentation analysis of the micromechanical anisotropy in mouse cortical bone

Studies investigating micromechanical properties in mouse cortical bone often solely focus on the mechanical behaviour along the long axis of the bone. Therefore, data on the anisotropy of mouse cortical bone is scarce. The aim of this study is the first-time evaluation of the anisotropy ratio between the longitudinal and transverse directions of reduced modulus and hardness in mouse femurs by using the nanoindentation technique. For this purpose, nine 22-week-old mice (C57BL/6) were sacrificed and all femurs extracted. A total of 648 indentations were performed with a Berkovich tip in the proximal (P), central (C) and distal (D) regions of the femoral shaft in the longitudinal and transverse directions. Higher values for reduced modulus are obtained for indentations in the longitudinal direction, with anisotropy ratios of 1.72 ± 0.40 (P), 1.75 ± 0.69 (C) and 1.34 ± 0.30 (D). Hardness is also higher in the longitudinal direction, with anisotropic ratios of 1.35 ± 0.27 (P), 1.35 ± 0.47 (C) and 1.17 ± 0.19 (D). We observed a significant anisotropy in the micromechanical properties of the mouse femur, but the correlation for reduced modulus and hardness between the two directions is low (r² < 0.3) and not significant. Therefore, we highly recommend performing independent indentation testing in both the longitudinal and transverse directions when knowledge of the tissue mechanical behaviour along multiple directions is required.

Nanoindentation analysis of the micromechanical anisotropy in mouse cortical bone

Studies investigating micromechanical properties in mouse cortical bone often solely focus on the mechanical behaviour along the long axis of the bone. Therefore, data on the anisotropy of mouse cortical bone is scarce. The aim of this study is the first-time evaluation of the anisotropy ratio between the longitudinal and transverse directions of reduced modulus and hardness in mouse femurs by using the nanoindentation technique. For this purpose, nine 22-week-old mice (C57BL/6) were sacrificed and all femurs extracted. A total of 648 indentations were performed with a Berkovich tip in the proximal (P), central (C) and distal (D) regions of the femoral shaft in the longitudinal and transverse directions. Higher values for reduced modulus are obtained for indentations in the longitudinal direction, with anisotropy ratios of 1.72 ± 0.40 (P), 1.75 ± 0.69 (C) and 1.34 ± 0.30 (D). Hardness is also higher in the longitudinal direction, with anisotropic ratios of 1.35 ± 0.27 (P), 1.35 ± 0.47 (C) and 1.17 ± 0.19 (D). We observed a significant anisotropy in the micromechanical properties of the mouse femur, but the correlation for reduced modulus and hardness between the two directions is low (r² < 0.3) and not significant. Therefore, we highly recommend performing independent indentation testing in both the longitudinal and transverse directions when knowledge of the tissue mechanical behaviour along multiple directions is required.

Microscopic assessment of bone toughness using scratch tests

Bone is a composite material with five distinct structural levels: collagen molecules, mineralized collagen fibrils, lamellae, osteon and whole bone. However, most fracture testing methods have been limited to the macroscopic scale and there is a need for advanced characterization methods to assess toughness at the osteon level and below. The goal of this investigation is to present a novel framework to measure the fracture properties of bone at the microscopic scale using scratch testing. A rigorous experimental protocol is articulated and applied to examine cortical bone specimens from porcine femurs. The observed fracture behavior is very complex: we observe a strong anisotropy of the response with toughening mechanisms and a competition between plastic flow and brittle fracture. The challenge consists then in applying nonlinear fracture mechanics methods such as the J-integral or the energetic Size Effect Law to quantify the fracture toughness in a rigorous fashion. Our result suggests that mixed-mode fracture is instrumental in determining the fracture resistance. There is also a pronounced coupling between fracture and elasticity. Our methodology opens the door to fracture assessment at multiple structural levels, microscopic and potentially nanometer length scale, due to the scalability of scratch tests.

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We measure bone toughness at the osteon level using microscopic scratch tests.

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Scratch tests induce a ductile-to-brittle transition in cortical bone.

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Toughening mechanisms are observed at the microscopic scale.

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The J-integral and the size effect law are employed to predict the fracture energy.

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.

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.

On the Use of Bone Remodelling Models to Estimate the Density Distribution of Bones. Uniqueness of the Solution

Bone remodelling models are widely used in a phenomenological manner to estimate numerically the distribution of apparent density in bones from the loads they are daily subjected to. These simulations start from an arbitrary initial distribution, usually homogeneous, and the density changes locally until a bone remodelling equilibrium is achieved. The bone response to mechanical stimulus is traditionally formulated with a mathematical relation that considers the existence of a range of stimulus, called dead or lazy zone, for which no net bone mass change occurs. Implementing a relation like that leads to different solutions depending on the starting density. The non-uniqueness of the solution has been shown in this paper using two different bone remodelling models: one isotropic and another anisotropic. It has also been shown that the problem of non-uniqueness is only mitigated by removing the dead zone, but it is not completely solved unless the bone formation and bone resorption rates are limited to certain maximum values.

Structural orientation dependent sub-lamellar bone mechanics

The lamellar unit is a critical component in defining the overall mechanical properties of bone. In this paper, micro-beams of bone with dimensions comparable to the lamellar unit were fabricated using focused ion beam (FIB) microscopy and mechanically tested in bending to failure using atomic force microscopy (AFM). A variation in the mechanical properties, including elastic modulus, strength and work to fracture of the micro-beams was observed and related to the collagen fibril orientation inferred from back-scattered scanning electron microscopy (SEM) imaging. Established mechanical models were further applied to describe the relationship between collagen fibril orientation and mechanical behaviour of the lamellar unit. Our results highlight the ability to measure mechanical properties of discrete bone volumes directly and correlate with structural orientation of collagen fibrils.

Insights into reference point indentation involving human cortical bone: sensitivity to tissue anisotropy and mechanical behavior

Reference point indentation (RPI) is a microindentation technique involving 20 cycles of loading in "force-control" that can directly assess a patient׳s bone tissue properties. Even though preliminary clinical studies indicate a capability for fracture discrimination, little is known about what mechanical behavior the various RPI properties characterize and how these properties relate to traditional mechanical properties of bone. To address this, the present study investigated the sensitivity of RPI properties to anatomical location and tissue organization as well as examined to what extent RPI measurements explain the intrinsic mechanical properties of human cortical bone. Multiple indents with a target force of 10N were done in 2 orthogonal directions (longitudinal and transverse) per quadrant (anterior, medial, posterior, and lateral) of the femoral mid-shaft acquired from 26 donors (25-101 years old). Additional RPI measurements were acquired for 3 orthogonal directions (medial only). Independent of age, most RPI properties did not vary among these locations, but they did exhibit transverse isotropy such that resistance to indentation is greater in the longitudinal (axial) direction than in the transverse direction (radial or circumferential). Next, beam specimens (~2mm×5mm×40mm) were extracted from the medial cortex of femoral mid-shafts, acquired from 34 donors (21-99 years old). After monotonically loading the specimens in three-point bending to failure, RPI properties were acquired from an adjacent region outside the span. Indent direction was orthogonal to the bending axis. A significant inverse relationship was found between resistance to indentation and the apparent-level mechanical properties. Indentation distance increase (IDI) and a linear combination of IDI and the loading slope, averaged over cycles 3 through 20, provided the best explanation of the variance in ultimate stress (r(2)=0.25, p=0.003) and toughness (r(2)=0.35, p=0.004), respectively. With a transverse isotropic behavior akin to tissue hardness and modulus as determined by micro- and nano-indentation and a significant association with toughness, RPI properties are likely influenced by both elastic and plastic behavior of bone tissue.

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

Relationships between mineralization, collagen orientation and indentation modulus were investigated in bone structural units from the mid-shaft of human femora using a site-matched design. Mineral mass fraction, collagen fibril angle and indentation moduli were measured in registered anatomical sites using backscattered electron imaging, polarized light microscopy and nano-indentation, respectively. Theoretical indentation moduli were calculated with a homogenization model from the quantified mineral densities and mean collagen fibril orientations. The average indentation moduli predicted based on local mineralization and collagen fibers arrangement were not significantly different from the average measured experimentally with nanoindentation (p=0.9). Surprisingly, no substantial correlation of the measured indentation moduli with tissue mineralization and/or collagen fiber arrangement was found. Nano-porosity, micro-damage, collagen cross-links, non-collagenous proteins or other parameters affect the indentation measurements. Additional testing/simulation methods need to be considered to properly understand the variability of indentation moduli, beyond the mineralization and collagen arrangement in bone structural units.

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Site-matched assessment of nanoindentation modulus, mineral mass fraction and collagen fibers orientation in human cortical bone sections.

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Comparison of experimental nanoindentation modulus with its computed equivalent based on the site-matched morphological data.

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While mean experimental and computed nanoindentation moduli match well, their variations exhibit very weak correlations.

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Considering factors like nano-porosity and damage may be necessary to understand variability of lamellar stiffness of bone structural units.

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This is not in conflict with the well known anisotropy associated with the rotated plywood model at the sublamellar scale.

Osteonal lamellae elementary units: lamellar microstructure, curvature and mechanical properties

The mechanical and structural properties of the sublayers of osteonal lamellae were studied. Young's modulus (E) of adjacent individual lamellae was measured by nanoindentation of parallel slices every 1-3 μm, in planes parallel and perpendicular to the osteon axis (OA). In planes parallel to the OA, the modulus of a lamella could vary significantly between sequential slices. Significant modulus variations were also sometimes found on opposing sides of the osteonal canal for the same lamella. These results are rationalized by considerations involving the microstructural organization of the collagen fibrils in the lamellae. Scanning electron microscope imaging of freeze fractured surfaces revealed that the substructure of a single lamella can vary significantly on the opposing sides of the osteonal axis. Using a serial surface view method, parallel planes were exposed every 8-10 nm using a dual-beam microscope. Analysis of the orientations of fibrils revealed that the structure is rotated plywood like, consisting of unidirectional sublayers of fibrils of several orientations, with occasional randomly oriented sublayers. The dependence of the measured mechanical properties of the lamellae on the indentation location may be explained by the observed structure, as well as by the curvature of the osteonal lamellae through simple geometrical-structural considerations. Mechanical advantages arising from the curved laminate structure are discussed.

Orientation and size-dependent mechanical modulation within individual secondary osteons in cortical bone tissue

Anisotropy is one of the most peculiar aspects of cortical bone mechanics; however, its anisotropic mechanical behaviour should be treated only with strict relationship to the length scale of investigation. In this study, we focus on quantifying the orientation and size dependence of the spatial mechanical modulation in individual secondary osteons of bovine cortical bone using nanoindentation. Tests were performed on the same osteonal structure in the axial (along the long bone axis) and transverse (normal to the long bone axis) directions along arrays going radially out from the Haversian canal at four different maximum depths on three secondary osteons. Results clearly show a periodic pattern of stiffness with spatial distance across the osteon. The effect of length scale on lamellar bone anisotropy and the critical length at which homogenization of the mechanical properties occurs were determined. Further, a laminate-composite-based analytical model was applied to the stiffness trends obtained at the highest spatial resolution to evaluate the elastic constants for a sub-layer of mineralized collagen fibrils within an osteonal lamella on the basis of the spatial arrangement of the fibrils. The hierarchical arrangement of lamellar bone is found to be a major determinant for modulation of mechanical properties and anisotropic mechanical behaviour of the tissue.

Influence of mineralization and microporosity on tissue elasticity: experimental and numerical investigation on mineralized turkey leg tendons

A combined experimental and numerical study correlating indentation stiffness with mineralization and microporosity was performed on mineralized turkey leg tendon. Two distinct tissue morphologies were distinguished by quantitative backscattered electron imaging and called "circumferential" and "interstitial" zones. These two zones showed different tissue organization, microporosity, and mineralization. Stiffness, measured by microindentation, was also different in the two zones. The mean field method of modeling of mineralized collagen fibers was employed to explain the differences.

Elastic anisotropy of uniaxial mineralized collagen fibers measured using two-directional indentation. Effects of hydration state and indentation depth

Mineralized turkey leg tendon (MTLT) is an attractive model of mineralized collagen fibers, which are also present in bone. Its longitudinal structure is advantageous for the relative simplicity in modeling, yet its anisotropic elastic properties remain unknown. The aim of this study was to quantify the extent of elastic anisotropy of mineralized collagen fibers by using nano- and microindentation to probe a number on MTLT samples in two orthogonal directions. The large dataset allowed the quantification of the extent of anisotropy, depending on the final indentation depth and on the hydration state of the sample. Anisotropy was observed to increase with the sample re-hydration process. Artifacts of indentation in a transverse direction to the main axis of the mineralized tendons in re-hydrated condition were observed. The indentation size effect, that is, the increase of the measured elastic properties with decreasing sampling volume, reported previously on variety of materials, was also observed in MTLT. Indentation work was quantified for both directions of indentation in dried and re-hydrated conditions. As hypothesized, MTLT showed a higher extent of anisotropy compared to cortical and trabecular bone, presumably due to the alignment of mineralized collagen fibers in this tissue.

Change in porosity is the major determinant of the variation of cortical bone elasticity at the millimeter scale in aged women

At the mesoscale (i.e. over a few millimeters), cortical bone can be described as two-phase composite material consisting of pores and a dense mineralized matrix. The cortical porosity is known to influence the mesoscopic elasticity. Our objective was to determine whether the variations of porosity are sufficient to predict the variations of bone mesoscopic anisotropic elasticity or if change in bone matrix elasticity is an important factor to consider. We measured 21 cortical bone specimens prepared from the mid-diaphysis of 10 women donors (aged from 66 to 98 years). A 50-MHz scanning acoustic microscope (SAM) was used to evaluate the bone matrix elasticity (reflected in impedance values) and porosity. Porosity evaluation with SAM was validated against Synchrotron Radiation μCT measurements. A standard contact ultrasonic method was applied to determine the mesoscopic elastic coefficients. Only matrix impedance in the direction of the bone axis correlated to mesoscale elasticity (adjusted R(2)=[0.16-0.25], p<0.05). The mesoscopic elasticity was found to be highly correlated to the cortical porosity (adj-R(2)=[0.72-0.84], p<10(-5)). Multivariate analysis including both matrix impedance and porosity did not provide a better statistical model of mesoscopic elasticity variations. Our results indicate that, for the elderly population, the elastic properties of the mineralized matrix do not undergo large variations among different samples, as reflected in the low coefficients of variation of matrix impedance (less than 6%). This work suggests that change in the intracortical porosity accounts for most of the variations of mesoscopic elasticity, at least when the analyzed porosity range is large (3-27% in this study). The trend in the variation of mesoscale elasticity with porosity is consistent with the predictions of a micromechanical model consisting of an anisotropic matrix pervaded by cylindrical pores.

A quantitative collagen fibers orientation assessment using birefringence measurements: calibration and application to human osteons

Even though mechanical properties depend strongly on the arrangement of collagen fibers in mineralized tissues, it is not yet well resolved. Only a few semi-quantitative evaluations of the fiber arrangement in bone, like spectroscopic techniques or circularly polarized light microscopy methods are available. In this study the out-of-plane collagen arrangement angle was calibrated to the linear birefringence of a longitudinally fibered mineralized turkey leg tendon cut at variety of angles to the main axis. The calibration curve was applied to human cortical bone osteons to quantify the out-of-plane collagen fibers arrangement. The proposed calibration curve is normalized to sample thickness and wavelength of the probing light to enable a universally applicable quantitative assessment. This approach may improve our understanding of the fibrillar structure of bone and its implications on mechanical properties.

Principal stiffness orientation and degree of anisotropy of human osteons based on nanoindentation in three distinct planes

Haversian systems or ‘osteons’ are cylindrical structures, formed by bone lamellae, that make up the major part of human cortical bone. Despite their discovery centuries ago in 1691 by Clopton Havers, their mechanical properties are still poorly understood.

The objective of this study is a detailed identification of the anisotropic elastic properties of the secondary osteon in the lamella plane. Additionally, the principal material orientation with respect to the osteon is assessed. Therefore a new nanoindentation method was developed which allows the measurement of indentation data in three distinct planes on a single osteon.

All investigated osteons appeared to be anisotropic with a preferred stiffness alignment along the axial direction with a small average helical winding around the osteon axis. The mean degree of anisotropy was 1.75 ± 0.36 and the mean helix angle was 10.3^°±0.8°.

These findings oppose two well established views of compact bone microstructure: first, the generally clear axial stiffness orientation contradicts a regular ‘twisted plywood’ collagen fibril orientation pattern in lamellar bone that would lead to a more isotropic behavior. Second, the class of transverse osteons were not observed from the mechanical point of view.

HR-pQCT based FE analysis of the most distal radius section provides an improved prediction of Colles' fracture load in vitro

The remarkable performances of high-resolution peripheral quantitative computed tomography (HR-pQCT) make the distal radius a favorable site for early diagnosis of osteoporosis and improved Colles' fracture risk assessment. The goal of this study was to investigate if the HR-pQCT-based micro finite element (μFE) method applied on specific sections of the distal radius provides improved predictions of Colles' fracture load in vitro compared to bone mineral content (BMC), bone mineral density (BMD), or histomorphometric indices. HR-pQCT based BMC, BMD, histomorphometric parameters, and μFE models of 9-mm-thick bone sections were used to predict fracture load of 21 distal radii assessed in an experimental model of Colles' fracture reported in a previous study. The analysis was performed on two bone sections: a standard one recommended by the HR-pQCT manufacturer and a second one defined just proximal to the distal subchondral plate. For most of the investigated parameters, significant differences were found between the values of the two sections. Correlations with experimental fracture load and strength were higher in the most distal section, and the difference was statistically significant for μFE strength. Furthermore, the most distal section was computed to have significantly lower ultimate force and strength by 13% and 35%, respectively, than the standard section. BMC provided a better estimation of Colles' fracture load (R(2)=0.942) than aBMD or any other histomorphometric indices. The best prediction was achieved with μFE analyses of the most distal slice (R(2)=0.962), which provided quantitatively correct ultimate forces.

Elastic anisotropy of bone lamellae as a function of fibril orientation pattern

In this study, the homogenized anisotropic elastic properties of single bone lamellae are computed using a finite element unit cell method. The resulting stiffness tensor is utilized to calculate indentation moduli for multiple indentation directions in the lamella plane which are then related to nanoindentation experiments. The model accounts for different fibril orientation patterns in the lamellae--the twisted and orthogonal plywood pattern, a 5-sublayer pattern and an X-ray diffraction-based pattern. Three-dimensional sectional views of each pattern facilitate the comparison to transmission electron (TEM) images of real lamella cuts. The model results indicate, that the 5-sublayer- and the X-ray diffraction-based patterns cause the lamellae to have a stiffness maximum between 0° and 45° to the osteon axis. Their in-plane stiffness characteristics are qualitatively matching the experimental findings that report a higher stiffness in the osteon axis than in the circumferential direction. In contrast, lamellae owning the orthogonal or twisted plywood fibril orientation patterns have no preferred stiffness alignment. This work shows that the variety of fibril orientation patterns leads to qualitative and quantitative differences in the lamella elastic mechanical behavior. The study is a step toward a deeper understanding of the structure-mechanical function relationship of bone lamellae.

Rehydration of vertebral trabecular bone: influences on its anisotropy, its stiffness and the indentation work with a view to age, gender and vertebral level

For understanding the fracture risk of vertebral bodies the macroscopic mechanical properties of the cancellous core are of major interest. Due to the hierarchical nature of bone, these depend in turn on the micromechanical properties of bone extracellular matrix which is at least linear elastic transverse isotropic. The experimental determination of local elastic properties of bone ex vivo necessitates a high spatial resolution which can be provided by depth-sensing indentation techniques. Using microindentation, this study investigated the effects of rehydration on the transverse isotropic elastic properties of vertebral trabecular bone matrix obtained from two orthogonal directions with a view to microanatomical location, age, gender, vertebral level and anatomic direction in a conjoint statistics. Biopsies were gained from 104 human vertebrae (T1-L3) with a median age of 65 years (21-94). Wet elastic moduli were 29% lower (p<0.05) than dry elastic moduli. For wet indentation the ratio of mean elastic moduli tested in axial to those tested in transverse indentation direction were 1.13 to 1.23 times higher than for dry indentation. The ratio of elastic moduli tested in the core to those tested in the periphery of trabeculae was 1.05 to 1.16 times higher when testing wet. Age and gender did not show any influence on the elastic moduli for wet and dry measurements. The correlation between vertebral level and elastic moduli became weaker after rehydration (p(wet)<0.09, r(wet)(2)=0.14) and (p(dry)<0.01, r(wet)(2)=0.38). Elastic and dissipated energies were similarly affected by rehydration compared to the elastic modulus. No significant difference in the energies could be found for gender (p>0.05). Significant differences in the energies were found for age (p<0.05) after rehydration. Qualitative and quantitative insights into the transverse isotropic elastic properties of trabecular bone matrix under two testing conditions over a broad spectrum of vertebrae could be given. This study could help to further improve understanding of the mechanical properties of vertebral trabecular bone.

Spatial and temporal variations of mechanical properties and mineral content of the external callus during bone healing

After bone fracture, various cellular activities lead to the formation of different tissue types, which form the basis for the process of secondary bone healing. Although these tissues have been quantified by histology, their material properties are not well understood. Thus, the aim of this study is to correlate the spatial and temporal variations in the mineral content and the nanoindentation modulus of the callus formed via intramembranous ossification over the course of bone healing. Midshaft tibial samples from a sheep osteotomy model at time points of 2, 3, 6 and 9 weeks were employed. PMMA embedded blocks were used for quantitative back scattered electron imaging and nanoindentation of the newly formed periosteal callus near the cortex. The resulting indentation modulus maps show the heterogeneity in the modulus in the selected regions of the callus. The indentation modulus of the embedded callus is about 6 GPa at the early stage. At later stages of mineralization, the average indentation modulus reaches 14 GPa. There is a slight decrease in average indentation modulus in regions distant to the cortex, probably due to remodelling of the peripheral callus. The spatial and temporal distribution of mineral content in the callus tissue also illustrates the ongoing remodelling process observed from histological analysis. Most interestingly the average indentation modulus, even at 9 weeks, remains as low as 13 GPa, which is roughly 60% of that for cortical sheep bone. The decreased indentation modulus in the callus compared to cortex is due to the lower average mineral content and may be perhaps also due to the properties of the organic matrix which might be different from normal bone.