Direct mechanics assessment of elastic symmetries and properties of trabecular bone architecture

Effect of collagen fibril orientation on the anisotropic properties of peri-implant bone

In orthopedic and dental surgery, the implantation of biomaterials within the bone to restore the integrity of the treated organ has become a standard procedure. Their long-term stability relies on the osseointegration phenomena, where bone grows onto and around metallic implants, creating a bone-implant interface. Bone is a highly hierarchical material that evolves spatially and temporally during this healing phase. A deeper understanding of its biomechanical characteristics is needed, as they are determinants for surgical success. In this context, we propose a multiscale homogenization model to evaluate the effective elastic properties of bone as a function of the distance from the implant, based on the tissue's structure and composition at lower scales. The model considers three scales: hydroxyapatite foam (nanoscale), ultrastructure (microscale), and tissue (mesoscale). The elastic properties and the volume fraction of the elementary constituents of bone matrix (mineral, collagen, and water), the orientation of the collagen fibril relative to the implant surface, and the mesoscale porosity constitute the input data of the model. The effect of a spatiotemporal variation in the collagen fibrils' orientation on the bone anisotropic properties in the proximity of the implant was investigated. The findings revealed a strong variation of the components of the effective elasticity tensor of the bone as a function of the distance from the implant. The effective elasticity appears to be primarily sensitive to the porosity (mesoscale) rather than to the collagen fibrils' orientation (sub-micro scale). However, the orientation of the fibrils has a significant influence on the isotropy of the bone. When analyzing the symmetry properties of the effective elasticity tensor, the ratio between the isotropic and hexagonal components is determined by a combination of the porosity and the fibrils' orientation. A decrease in porosity leads to a decrease in bone isotropy and, in turn, an increase in the impact of the fibrils' orientation. These results demonstrate that the collagen fibril orientation should be taken into account to properly describe the effective elastic anisotropy of bone at the organ scale.

Does the bone mineral density measured on a preoperative CT scan before total hip arthroplasty reflect the bone's mechanical properties?

INTRODUCTION

No method exists to quantify the bone quality and factors that will ensure osteointegration of total hip arthroplasty (THA) implants. A preoperative CT scan can be used to evaluate the bone mineral density (BMD) when planning a THA procedure. The aim of this study was to validate BMD measurement as a marker of bone quality based on a preoperative CT scan.

HYPOTHESIS

BMD reflects the bone's mechanical properties for the purposes of preoperative THA planning.

METHODS

Patients who underwent primary THA for hip osteoarthritis or dysplasia with cementless implants and 3D preoperative plan were enrolled prospectively. The cortical BMD was calculated on CT scans used in the preoperative planning process. During the surgical procedure, the femoral head and neck were collected. These bone samples were subsequently scanned with a calibrated micro-CT scanner. The BMD was derived from the micro-CT scan and used as input for a finite element model to determine the bone's mechanical properties. Correlations between BMD, apparent moduli of elasticity and porosity were calculated.

RESULTS

The values of cortical BMD measured on the micro-CT and CT scan were significantly correlated (cc=0.52). The mean angular cortical BMD measured with the micro-CT scan was 1472.33mg/cm³ (SD: 357.53mg/cm³, 980.64-2830.6mg/cm³). There was no significant correlation between cortical BMD and the various apparent moduli of elasticity, except for E_yy and G_zy. Cortical BMD and porosity were inversely correlated with a Spearman coefficient of -0.41 (CI₉₅: [-0.71; -0.02], p=0.03). There was also an inverse correlation between the apparent moduli of elasticity (independent of their orientation) and porosity (p<0.01).

DISCUSSION

BMD provides information about porosity, which is a major factor when evaluating the bone's mechanical properties before THA.

LEVEL OF EVIDENCE

IV.

Biomimetic chitosan with biocomposite nanomaterials for bone tissue repair and regeneration

Biomimetic materials for better bone graft substitutes are a thrust area of research among researchers and clinicians. Autografts, allografts, and synthetic grafts are often utilized to repair and regenerate bone defects. Autografts are still considered the gold-standard method/material to treat bone-related issues with satisfactory outcomes. It is important that the material used for bone tissue repair is simultaneously osteoconductive, osteoinductive, and osteogenic. To overcome this problem, researchers have tried several ways to develop different materials using chitosan-based nanocomposites of silver, copper, gold, zinc oxide, titanium oxide, carbon nanotubes, graphene oxide, and biosilica. The combination of materials helps in the expression of ideal bone formation genes of alkaline phosphatase, bone morphogenic protein, runt-related transcription factor-2, bone sialoprotein, and osteocalcin. In vitro and in vivo studies highlight the scientific findings of antibacterial activity, tissue integration, stiffness, mechanical strength, and degradation behaviour of composite materials for tissue engineering applications.

MRI-based mechanical competence assessment of bone using micro finite element analysis (micro-FEA): Review

Areal bone mineral density (aBMD) from dual-energy x-ray absorptiometry (DEXA) and volumetric bone mineral density (vBMD) have demonstrated limited capabilities in the evaluation of bone mechanical competence and prediction of bone fracture. Predicting the macroscopic mechanical behavior of the bone structure has been challenging because of the heterogeneous and anisotropic nature of bone, such as the dependencies on loading direction, anatomical location, and sample dimensions. Magnetic resonance imaging (MRI) has been introduced as a promising modality that can be coupled with finite element analysis (FEA) for the assessment of bone mechanical competence. This review article describes studies investigating MRI-based micro-FEA as a potential non-invasive method to predict bone mechanical competence and facilitate bone fracture risk estimation without exposure to ionizing radiation. Specifically, the steps, applications, and future potential of FEA using indirect and direct bone imaging are discussed.

Determination of anisotropic elastic parameters from morphological parameters of cancellous bone for osteoporotic lumbar spine

In biomechanics, large finite element models with macroscopic representation of several bones or joints are necessary to analyze implant failure mechanisms. In order to handle large simulation models of human bone, it is crucial to homogenize the trabecular structure regarding the mechanical behavior without losing information about the realistic material properties. Accordingly, morphology and fabric measurements of 60 vertebral cancellous bone samples from three osteoporotic lumbar spines were performed on the basis of X-ray microtomography (μCT) images to determine anisotropic elastic parameters as a function of bone density in the area of pedicle screw anchorage. The fabric tensor was mapped in cubic bone volumes by a 3D mean-intercept-length method. Fabric measurements resulted in a high degree of anisotropy (DA = 0.554). For the Young’s and shear moduli as a function of bone volume fraction (BV/TV, bone volume/total volume), an individually fit function was determined and high correlations were found (97.3 ≤ R² ≤ 99.1,p < 0.005). The results suggest that the mathematical formulation for the relationship between anisotropic elastic constants and BV/TV is applicable to current μCT data of cancellous bone in the osteoporotic lumbar spine. In combination with the obtained results and findings, the developed routine allows determination of elastic constants of osteoporotic lumbar spine. Based on this, the elastic constants determined using homogenization theory can enable efficient investigation of human bone using finite element analysis (FEA).

Graphical Abstract

Damage Function of a Quasi-Brittle Material, Damage Rate, Acceleration and Jerk during Uniaxial Compression: Model and Application to Analysis of Trabecular Bone Tissue Destruction

A diversity of quasi-brittle materials can be observed in various engineering structures and natural objects (rocks, frozen soil, concrete, ceramics, bones, etc.). In order to predict the condition and safety of these objects, a large number of studies aimed at analyzing the strength of quasi-brittle materials has been conducted and presented in publications. However, at the modeling level, the problem of estimating the rate and acceleration of destruction of a quasi-brittle material under loading remains relevant. The purpose of the study was to substantiate the function of damage to a quasi-brittle material under uniaxial compression, determine the rate, acceleration and jerk of the damage process, and also to apply the results obtained to predicting the destruction of trabecular bone tissue. In accordance with the purpose of the study, the basic concepts of fracture mechanics and standard methods of mathematical modeling were used. The proposed model is based on the application of the previously obtained differentiable damage function without parameters. The results of the study are presented in the form of plots and analytical relations for computing the rate, acceleration and jerk of the damage process. Examples are given. The predicted peak of the combined effect of rate, acceleration and jerk of the damage process are found to be of practical interest as an additional criterion for destruction. The simulation results agree with the experimental data known from the available literature.

Validation of HR-pQCT against micro-CT for morphometric and biomechanical analyses: A review

High-resolution peripheral quantitative computed-tomography (HR-pQCT) has the potential to become a powerful clinical assessment and diagnostic tool. Given the recent improvements in image resolution, from 82 to 61 μm, this technology may be used to accurately quantify in vivo bone microarchitecture, a key biomarker of degenerative bone diseases. However, computational methods to assess bone microarchitecture were developed for micro computed tomography (micro-CT), a higher-resolution technology only available for ex vivo studies, and validation of these computational analysis techniques against the gold-standard micro-CT has been inconsistent and incomplete. Herein, we review methods for segmentation of bone compartments and microstructure, quantification of bone morphology, and estimation of mechanical strength using finite-element analysis, highlighting the need throughout for improved standardization across the field. Studies have relied on homogenous datasets for validation, which does not allow for robust comparisons between methods. Consequently, the adaptation and validation of novel segmentation approaches has been slow to non-existent, with most studies still using the manufacturer's segmentation for morphometric analysis despite the existence of better performing alternative approaches. The promising accuracy of HR-pQCT for capturing morphometric indices is overshadowed by considerable variability in outcomes between studies. For finite element analysis (FEA) methods, the use of disparate material models and FEA tools has led to a fragmented ability to assess mechanical bone strength with HR-pQCT. Further, the scarcity of studies comparing 62 μm HR-pQCT to the gold standard micro-CT leaves the validation of this imaging modality incomplete. This review revealed that without standardization, the capabilities of HR-pQCT cannot be adequately assessed. The need for a public, extendable, heterogeneous dataset of HR-pQCT and corresponding gold-standard micro-CT images, which would allow HR-pQCT users to benchmark existing and novel methods and select optimal methods depending on the scientific question and data at hand, is now evident. With more recent advancements in HR-pQCT, the community must learn from its past and provide properly validated technologies to ensure that HR-pQCT can truly provide value in patient diagnosis and care.

Differences in subchondral trabecular bone microstructure and finite element analysis-based biomechanical properties between osteoporosis and osteoarthritis

Background/Objective

The microstructure of the subchondral trabecular bone, including the composition and distribution of plates and rods, has an important influence on the disease progression and mechanical properties of osteoarthritis (OA) and osteoporosis (OP). We aimed to determine whether differences in plates and rods influence the variations in the quantities and qualities of the subchondral trabecular bone between OA and OP.

Materials and methods

Thirty-eight femoral head samples [OA, n = 13; OP, n = 17; normal control (NC), n = 8] were collected from male patients undergoing total hip arthroplasty. They were scanned using microcomputed tomography, and subchondral trabecular structures were analysed using individual trabecular segmentation. Micro-finite element analysis (μFEA) was applied to assess the mechanical property of the trabecular bone. Cartilage changes were evaluated by using histological assessment. Analysis of variance was used to compare intergroup differences in structural and mechanical properties and cartilage degradation. Pearson analysis was used to evaluate the relationship between the trabecula microstructure and biomechanical properties.

Results

Compared with the OP and NC group, there was serious cartilage damage in the OA group. With respect to the microstructure results, the OA group had the highest plate and rod trabecular microstructures including number and junction density among the three groups. For the mechanical properties detected via μFEA, the OA group had higher stiffness and failure load than did the OP group. Pearson analysis revealed that compared with OP, OA had a higher number of microstructure parameters (e.g., rod bone volume fraction and rod trabecular number) that were positively correlated with its mechanical property.

Conclusions

Compared with OP, the OA subchondral bone has both increased plate and rod microarchitecture and has more microstructures positively related with its mechanical property. These differences may help explain the variation in mechanical properties between these bone diseases.

The translational potential of this article

Our findings suggested that changes in the plates and rods of the subchondral trabecular bone play a critical role in OA and OP progression and that the improvement of the subchondral trabecular bone may be a promising treatment approach.

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

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

Synthetic bone: Design by additive manufacturing

A broad range of synthetic trabecular-like metallic lattices are 3D printed, to study the extra design freedom conferred by this new manufacturing process. The aim is to propose new conceptual types of implant structures for superior bio-mechanical matching and osseo-integration: synthetic bone. The target designs are 3D printed in Ti-6Al-4V alloy using a laser-bed process. Systematic evaluation is then carried out: (i) their accuracy is characterised at high spatial resolution using computed X-ray tomography, to assess manufacturing robustness with respect to the original geometrical design intent and (ii) the mechanical properties - stiffness and strength - are experimentally measured, evaluated, and compared. Finally, this new knowledge is synthesised in a conceptual framework to allow the construction of so-called implant design maps, to define the processing conditions of bone tailored substitutes, with focus on spine fusion devices. The design criteria emphasise the bone stiffness-matching, preferred range of pore structure for bone in-growth, manufacturability of the device and choice of inherent materials properties which are needed for durable implants. Examples of the use of such maps are given with focus on spine fusion devices, emphasising the stiffness-matching, osseo-integration properties and choice of inherent materials properties which are needed for durable implants. STATEMENT OF SIGNIFICANCE: We present a conceptual bio-engineering design methodology for new biomedical lattices produced by additive manufacturing, which addresses some of the critical points in currently existing porous implant materials. Amongst others: (i) feasibility and accuracy of manufacturing, (ii) design to the elastic properties of bone, and (iii) sensible pores sizes for osseointegration. This has inspired new and novel geometrical latticed designs which aim at improving the properties of intervertebral fusion devices. In their fundamental form, these structures are here fabricated and tested. When integrated into medical devices, these concepts could offer superior medical outcomes.

Are we crying Wolff? 3D printed replicas of trabecular bone structure demonstrate higher stiffness and strength during off-axis loading

Roux's principle of bone functional adaptation postulates that bone tissue, and particularly trabecular bone tissue, responds to mechanical stimuli by adjusting (modeling) its architecture accordingly. Hence, it predicts that the new modeled trabecular structure is mechanically improved (stiffer and stronger) in line with the habitual in vivo loading direction. While previous studies found indirect evidence to support this theory, direct support was so far unattainable. This is attributed to the fact that each trabecular bone is unique, and that trabecular bone tissue tends to be damaged during mechanical testing. Consequently, a unique modeled trabecular structure can be mechanically tested only along one direction and a comparison to other directions for that specific structure is impossible. To address this issue, we have 3D printed 10 replicas of a trabecular structure from a sheep talus cropped along the 3 principal axes of the bone and in line with the principal direction of loading (denoted on-axis model). Next, we have rotated the same cropped trabecular structure in increments of 10° up to 90° to the bone principal direction of loading (denoted off-axis models) and printed 10 replicas of each off-axis model. Finally, all on-axis and off-axis 3D printed replicas were loaded in compression until failure and trabecular structure stiffness and strength were calculated. Contrary to our prediction, and conflicting with Roux's principle of bone functional adaptation, we found that a trabecular structure loaded off-axis tended to have higher stiffness and strength values when compared to the same trabecular structure loaded on-axis. These unexpected results may not disprove Roux's principle of bone functional adaptation, but they do imply that trabecular bone adaptation may serve additional purposes than simply optimizing bone structure to one principal loading scenario and this suggests that we still don't fully understand bone modeling in its entirety.

Different subchondral trabecular bone microstructure and biomechanical properties between developmental dysplasia of the hip and primary osteoarthritis

Objective

Developmental dysplasia of the hip (DDH) is recognized as a frequent cause of secondary osteoarthritis (OA). The purpose in this study was to compare structural and biomechanical properties of subchondral trabecular bone ​and its relationship with cartilage damage between patients with DDH and patients with primary hip OA.

Methods

Forty-three femoral head specimens obtained from patients who underwent total hip arthroplasty [DDH, n ​= ​17; primary OA, n ​= ​16; and normal control (NC), n ​= ​10] were scanned by microcomputed tomography and analyzed by individual trabecula segmentation to obtain the microstructural types of subchondral trabecular bone. The biomechanical properties were analyzed by micro-finite element analysis, and cartilage damage was evaluated by histology. The linear regression analysis was used to indicate the association between microstructures, biomechanical property, and articular cartilage.

Results

The DDH group showed the lowest total bone volume fractions (BV/TV) and plate BV/TV in the three groups (p ​< ​0.05). There were also different discrepancies between the three groups in plate/rod trabecular number, plate/rod trabecular thickness, trabecular plate surface area/trabecular rod length, and junction density with different modes (plate-plate, rod-rod, and plate-rod junction density). The micro-finite element analysis, histology, and linear regression revealed that the subchondral trabecular bone in the DDH group had inferior biomechanical properties ​and cartilage damage of patients with DDH was more serious with different subchondral trabecular bone microstructures.

Conclusion

Our findings detected deteriorating subchondral trabecular bone microstructures in patients with DDH. The mass and type of subchondral trabecular bone play a key role in mechanical properties in DDH, which might be related to cartilage damage.

The translational potential of this article

Our findings suggested that changes of subchondral trabecular bone play a critical role ​in DDH progression and that the improvement on subchondral trabecular bone may be a sensitive and promising way in treatment of DDH.

Homogenization of cortical bone reveals that the organization and shape of pores marginally affect elasticity

With ageing and various diseases, the vascular pore volume fraction (porosity) in cortical bone increases, and the morphology of the pore network is altered. Cortical bone elasticity is known to decrease with increasing porosity, but the effect of the microstructure is largely unknown, while it has been thoroughly studied for trabecular bone. Also, popular micromechanical models have disregarded several micro-architectural features, idealizing pores as cylinders aligned with the axis of the diaphysis. The aim of this paper is to quantify the relative effects on cortical bone anisotropic elasticity of porosity and other descriptors of the pore network micro-architecture associated with pore number, size and shape. The five stiffness constants of bone assumed to be a transversely isotropic material were measured with resonant ultrasound spectroscopy in 55 specimens from the femoral diaphysis of 29 donors. The pore network, imaged with synchrotron radiation X-ray micro-computed tomography, was used to derive the pore descriptors and to build a homogenization model using the fast Fourier transform (FFT) method. The model was calibrated using experimental elasticity. A detailed analysis of the computed effective elasticity revealed in particular that porosity explains most of the variations of the five stiffness constants and that the effects of other micro-architectural features are small compared to usual experimental errors. We also have evidence that modelling the pore network as an ensemble of cylinders yields biased elasticity values compared to predictions based on the real micro-architecture. The FFT homogenization method is shown to be particularly efficient to model cortical bone.

Association of High-resolution Peripheral Quantitative Computed Tomography (HR-pQCT) bone microarchitectural parameters with previous clinical fracture in older men: The Osteoporotic Fractures in Men (MrOS) study

High-resolution peripheral quantitative computed tomography (HR-pQCT) assesses both volumetric bone mineral density (vBMD) and trabecular and cortical microarchitecture. However, studies of the association of HR-pQCT parameters with fracture history have been small, predominantly limited to postmenopausal women, often performed limited adjustment for potential confounders including for BMD, and infrequently assessed strength or failure measures. We used data from the Osteoporotic Fractures in Men (MrOS) study, a prospective cohort study of community-dwelling men aged ≥65 years, to evaluate the association of distal radius, proximal (diaphyseal) tibia and distal tibia HR-pQCT parameters measured at the Year 14 (Y14) study visit with prior clinical fracture. The primary HR-pQCT exposure variables were finite element analysis estimated failure loads (EFL) for each skeletal site; secondary exposure variables were total vBMD, total bone area, trabecular vBMD, trabecular bone area, trabecular thickness, trabecular number, cortical vBMD, cortical bone area, cortical thickness, and cortical porosity. Clinical fractures were ascertained from questionnaires administered every 4 months between MrOS study baseline and the Y14 visit and centrally adjudicated by masked review of radiographic reports. We used multivariate-adjusted logistic regression to estimate the odds of prior clinical fracture per 1 SD decrement for each Y14 HR-pQCT parameter. Three hundred forty-four (19.2%) of the 1794 men with available HR-pQCT measures had a confirmed clinical fracture between baseline and Y14. After multivariable adjustment, including for total hip areal BMD, decreased HR-pQCT finite element analysis EFL for each site was associated with significantly greater odds of prior confirmed clinical fracture and major osteoporotic fracture. Among other HR-pQCT parameters, decreased cortical area appeared to have the strongest independent association with prior clinical fracture. Future studies should explore associations of HR-pQCT parameters with specific fracture types and risk of incident fractures and the impact of age and sex on these relationships.

Mapping anisotropy improves QCT-based finite element estimation of hip strength in pooled stance and side-fall load configurations

Hip fractures are one of the most severe consequences of osteoporosis. Compared to the clinical standard of DXA-based aBMD at the femoral neck, QCT-based FEA delivers a better surrogate of femoral strength and gains acceptance for the calculation of hip fracture risk when a CT reconstruction is available. Isotropic, homogenised voxel-based, finite element (hvFE) models are widely used to estimate femoral strength in cross-sectional and longitudinal clinical studies. However, fabric anisotropy is a classical feature of the architecture of the proximal femur and the second determinant of the homogenised mechanical properties of trabecular bone. Due to the limited resolution, fabric anisotropy cannot be derived from clinical CT reconstructions. Alternatively, fabric anisotropy can be extracted from HR-pQCT images of cadaveric femora. In this study, fabric anisotropy from HR-pQCT images was mapped onto QCT-based hvFE models of 71 human proximal femora for which both HR-pQCT and QCT images were available. Stiffness and ultimate load computed from anisotropic hvFE models were compared with previous biomechanical tests in both stance and side-fall configurations. The influence of using the femur-specific versus a mean fabric distribution on the hvFE predictions was assessed. Femur-specific and mean fabric enhance the prediction of experimental ultimate force for the pooled, i.e. stance and side-fall, (isotropic: r²=0.81, femur-specific fabric: r²=0.88, mean fabric: r²=0.86,p<0.001) but not for the individual configurations. Fabric anisotropy significantly improves bone strength prediction for the pooled configurations, and mapped fabric provides a comparable prediction to true fabric. The mapping of fabric anisotropy is therefore expected to help generate more accurate QCT-based hvFE models of the proximal femur for personalised or multiple load configurations.

Using Non-linear Homogenization to Improve the Performance of Macroscopic Damage Models of Trabecular Bone

Realistic macro-level finite element simulations of the mechanical behavior of trabecular bone, a cellular anisotropic material, require a suitable constitutive model; a model that incorporates the mechanical response of bone for complex loading scenarios and includes post-elastic phenomena, such as plasticity (permanent deformations) and damage (permanent stiffness reduction), which bone is likely to experience. Some such models have been developed by conducting homogenization-based multiscale finite element simulations on bone micro-structure. While homogenization has been fairly successful in the elastic regime and, to some extent, in modeling the macroscopic plastic response, it has remained a challenge with respect to modeling damage. This study uses a homogenization scheme to upscale the damage behavior from the tissue level (microscale) to the organ level (macroscale) and assesses the suitability of different damage constitutive laws. Ten cubic specimens were each subjected to 21 strain-controlled load cases for a small range of macroscopic post-elastic strains. Isotropic and anisotropic criteria were considered, density and fabric relationships were used in the formulation of the damage law, and a combined isotropic/anisotropic law with tension/compression asymmetry was formulated, based on the homogenized results, as a possible alternative to the currently used single scalar damage criterion. This computational study enhances the current knowledge on the macroscopic damage behavior of trabecular bone. By developing relationships of damage progression with bone's micro-architectural indices (density and fabric) the study also provides an aid for the creation of more precise macroscale continuum models, which are likely to improve clinical predictions.

Accuracy of MRI-based finite element assessment of distal tibia compared to mechanical testing

High-resolution MRI-derived finite element analysis (FEA) has been used in translational research to estimate the mechanical competence of human bone. However, this method has yet to be validated adequately under in vivo imaging spatial resolution or signal-to-noise conditions. We therefore compared MRI-based metrics of bone strength to those obtained from direct, mechanical testing. The study was conducted on tibiae from 17 human donors (12 males and five females, aged 33 to 88years) with no medical history of conditions affecting bone mineral homeostasis. A 25mm segment from each distal tibia underwent MR imaging in a clinical 3-Tesla scanner using a fast large-angle spin-echo (FLASE) sequence at 0.137mm×0.137mm×0.410mm voxel size, in accordance with in vivo scanning protocol. The resulting high-resolution MR images were processed and used to generate bone volume fraction maps, which served as input for the micro-level FEA model. Simulated compression was applied to compute stiffness, yield strength, ultimate strength, modulus of resilience, and toughness, which were then compared to metrics obtained from mechanical testing. Moderate to strong positive correlations were found between computationally and experimentally derived values of stiffness (R²=0.77, p<0.0001), yield strength (R²=0.38, p=0.0082), ultimate strength (R²=0.40, p=0.0067), and resilience (R²=0.46, p=0.0026), but only a weak, albeit significant, correlation was found for toughness (R²=0.26, p=0.036). Furthermore, experimentally derived yield strength and ultimate strength were moderately correlated with MRI-derived stiffness (R²=0.48, p=0.0022 and R²=0.58, p=0.0004, respectively). These results suggest that high-resolution MRI-based finite element (FE) models are effective in assessing mechanical parameters of distal skeletal extremities.

Calculation of cancellous bone elastic properties with the polarization-based FFT iterative scheme

The Fast Fourier Transform-based method, originally introduced by Moulinec and Suquet in 1994 has gained popularity for computing homogenized properties of composites. In this work, the method is used for the computational homogenization of the elastic properties of cancellous bone. To the authors' knowledge, this is the first study where the Fast Fourier Transform scheme is applied to bone mechanics. The performance of the method is analyzed for artificial and natural bone samples of 2 species: bovine femoral heads and implanted femurs of Hokkaido rats. Model geometries are constructed using data from X-ray tomographies, and the bone tissue elastic properties are measured using microindentation and nanoindentation tests. Computed results are in excellent agreement with those available in the literature. The study shows the suitability of the method to accurately estimate the fully anisotropic elastic response of cancellous bone. Guidelines are provided for the construction of the models and the setting of the algorithm.

Effect of including damage at the tissue level in the nonlinear homogenisation of trabecular bone

Being able to predict bone fracture or implant stability needs a proper constitutive model of trabecular bone at the macroscale in multiaxial, non-monotonic loading modes. Its macroscopic damage behaviour has been investigated experimentally in the past, mostly with the restriction of uniaxial cyclic loading experiments for different samples, which does not allow for the investigation of several load cases in the same sample as damage in one direction may affect the behaviour in other directions. Homogenised finite element models of whole bones have the potential to assess complicated scenarios and thus improve clinical predictions. The aim of this study is to use a homogenisation-based multiscale procedure to upscale the damage behaviour of bone from an assumed solid phase constitutive law and investigate its multiaxial behaviour for the first time. Twelve cubic specimens were each submitted to nine proportional strain histories by using a parallel code developed in-house. Evolution of post-elastic properties for trabecular bone was assessed for a small range of macroscopic plastic strains in these nine load cases. Damage evolution was found to be non-isotropic, and both damage and hardening were found to depend on the loading mode (tensile, compression or shear); both were characterised by linear laws with relatively high coefficients of determination. It is expected that the knowledge of the macroscopic behaviour of trabecular bone gained in this study will help in creating more precise continuum FE models of whole bones that improve clinical predictions.

Operator variability in scan positioning is a major component of HR-pQCT precision error and is reduced by standardized training

In this study, we determined that operator positioning precision contributes significant measurement error in high-resolution peripheral quantitative computed tomography (HR-pQCT). Moreover, we developed software to quantify intra- and inter-operator variability and demonstrated that standard positioning training (now available as a web-based application) can significantly reduce inter-operator variability.

INTRODUCTION

HR-pQCT is increasingly used to assess bone quality, fracture risk, and anti-fracture interventions. The contribution of the operator has not been adequately accounted in measurement precision. Operators acquire a 2D projection ("scout view image") and define the region to be scanned by positioning a "reference line" on a standard anatomical landmark. In this study, we (i) evaluated the contribution of positioning variability to in vivo measurement precision, (ii) measured intra- and inter-operator positioning variability, and (iii) tested if custom training software led to superior reproducibility in new operators compared to experienced operators.

METHODS

To evaluate the operator in vivo measurement precision, we compared precision errors calculated in 64 co-registered and non-co-registered scan-rescan images. To quantify operator variability, we developed software that simulates the positioning process of the scanner's software. Eight experienced operators positioned reference lines on scout view images designed to test intra- and inter-operator reproducibility. Finally, we developed modules for training and evaluation of reference line positioning. We enrolled six new operators to participate in a common training, followed by the same reproducibility experiments performed by the experienced group.

RESULTS

In vivo precision errors were up to threefold greater (Tt.BMD and Ct.Th) when variability in scan positioning was included. The inter-operator precision errors were significantly greater than the short-term intra-operator precision (p < 0.001). New trained operators achieved comparable intra-operator reproducibility to experienced operators and lower inter-operator reproducibility (p < 0.001). Precision errors were significantly greater for the radius than for the tibia.

CONCLUSION

Operator reference line positioning contributes significantly to in vivo measurement precision and is significantly greater for multi-operator datasets. Inter-operator variability can be significantly reduced using a systematic training platform, now available online ( http://webapps.radiology.ucsf.edu/refline/ ).

Structural and Mechanical Properties of Mandibular Condylar Bone

The trabecular bone of the mandibular condyle is structurally anisotropic and heterogeneous. We hypothesized that its apparent elastic moduli are also anisotropic and heterogeneous, and depend on trabecular density and orientation. Eleven condyles were scanned with a micro-CT system. Volumes of interest were selected for the construction of finite element models. We simulated compressive and shear tests to determine the principal mechanical directions and the apparent elastic moduli. Compressive moduli were relatively large in directions acting in the sagittal plane, and small in the mediolateral direction. The degree of mechanical anisotropy ranged from 4.7 to 10.8. Shear moduli were largest in the sagittal plane and smallest in the transverse plane. The magnitudes of the moduli varied with the condylar region and were proportional to the bone volume fraction. Furthermore, principal mechanical direction correlated significantly with principal structural direction. It was concluded that variation in trabecular structure coincides with variation in apparent mechanical properties.

Nonlinear homogenisation of trabecular bone: Effect of solid phase constitutive model

Micro-finite element models have been extensively employed to evaluate the elastic properties of trabecular bone and, to a limited extent, its yield behaviour. The macroscopic stiffness tensor and yield surface are of special interest since they are essential in the prediction of bone strength and stability of implants at the whole bone level. While macroscopic elastic properties are now well understood, yield and post-yield properties are not. The aim of this study is to shed some light on what the effect of the solid phase yield criterion is on the macroscopic yield of trabecular bone for samples with different microstructure. Three samples with very different density were subjected to a large set of apparent load cases (which is important since physiological loading is complex and can have multiple components in stress or strain space) with two different solid phase yield criteria: Drucker-Prager and eccentric-ellipsoid. The study found that these two criteria led to small differences in the macroscopic yield strains for most load cases except for those that were compression-dominated; in these load cases, the yield strains for the Drucker-Prager criterion were significantly higher. Higher density samples resulted in higher differences between the two criteria. This work provides a comprehensive assessment of the effect of two different solid phase yield criteria on the macroscopic yield strains of trabecular bone, for a wide range of load cases, and for samples with different morphology.

Bone microstructure in men assessed by HR-pQCT: Associations with risk factors and differences between men with normal, low, and osteoporosis-range areal BMD

Purpose

The primary objective of this study was to analyze the relationships between bone microstructure and strength, and male osteoporosis risk factors including age, body mass index, serum 25-hydroxyvitamin D level, and testosterone level. A secondary objective was to compare microstructural and strength parameters between men with normal, low, and osteoporosis-range areal bone mineral density (aBMD).

Methods

Seventy-eight healthy male volunteers (mean age 62.4 ± 7.8 years, range 50–84 years) were recruited. The participants underwent dual-energy X-ray absorptiometry (DXA) and high-resolution peripheral quantitative computed tomography (HR-pQCT) of the ultra-distal radius and tibia. From the HR-pQCT images, volumetric bone mineral density (BMD) and cortical and trabecular bone microstructure were evaluated, and bone strength and cortical load fraction (Ct.LF) were estimated using micro-finite element analysis (μFEA).

Results

Age was more strongly correlated with bone microstructure than other risk factors. Age had significant positive correlations with cortical porosity at both ultra-distal radius and tibia (r = 0.36, p = 0.001, and r = 0.47, p < 0.001, respectively). At the tibia, age was negatively correlated with cortical BMD, whereas it was positively correlated with trabecular BMD. In μFEA, age was negatively correlated with Ct.LF, although not with bone strength. Compared with men with normal aBMD, men with low or osteoporosis-range aBMD had significantly poor trabecular bone microstructure and lower bone strength at the both sites, while there was no significant difference in cortical bone.

Conclusions

Cortical bone microstructure was negatively affected by aging, and there was a suggestion that the influence of aging may be particularly important at the weight-bearing sites.

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Bone microstructure of the ultra-distal radius and tibia was analyzed by HR-pQCT.

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The subjects consisted of 78 healthy male volunteers ranging from 50 to 84 years.

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Cortical bone was more impaired with age compared with trabecular bone.

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Cortical porosity was increased with age, particularly at the ultra-distal tibia.

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.

The quartic piecewise-linear criterion for the multiaxial yield behavior of human trabecular bone

Prior multiaxial strength studies on trabecular bone have either not addressed large variations in bone volume fraction and microarchitecture, or have not addressed the full range of multiaxial stress states. Addressing these limitations, we utilized micro-computed tomography (lCT) based nonlinear finite element analysis to investigate the complete 3D multiaxial failure behavior of ten specimens (5mm cube) of human trabecular bone, taken from three anatomic sites and spanning a wide range of bone volume fraction (0.09–0.36),mechanical anisotropy (range of E3/E1¼3.0–12.0), and microarchitecture. We found that most of the observed variation in multiaxial strength behavior could be accounted for by normalizing the multiaxial strength by specimen-specific values of uniaxial strength (tension,compression in the longitudinal and transverse directions). Scatter between specimens was reduced further when the normalized multiaxial strength was described in strain space.The resulting multiaxial failure envelope in this normalized-strain space had a rectangular boxlike shape for normal–normal loading and either a rhomboidal box like shape or a triangular shape for normal-shear loading, depending on the loading direction. The finite element data were well described by a single quartic yield criterion in the 6D normalized strain space combined with a piecewise linear yield criterion in two planes for normalshear loading (mean error SD: 4.660.8% for the finite element data versus the criterion).This multiaxial yield criterion in normalized-strain space can be used to describe the complete 3D multiaxial failure behavior of human trabecular bone across a wide range of bone volume fraction, mechanical anisotropy, and microarchitecture.

Elastic Anisotropy of Trabecular Bone in the Elderly Human Vertebra

Knowledge of the nature of the elastic symmetry of trabecular bone is fundamental to the study of bone adaptation and failure. Previous studies have classified human vertebral trabecular bone as orthotropic or transversely isotropic but have typically obtained samples from only selected regions of the centrum. In this study, the elastic symmetry of human vertebral trabecular bone was characterized using microfinite element (μFE) analyses performed on 1019 cubic regions of side length equal to 5 mm, obtained via thorough sampling of the centrums of 18 human L1 vertebrae (age = 81.17 ± 7.7 yr; eight males and ten females). An optimization procedure was used to find the closest orthotropic representation of the resulting stiffness tensor for each cube. The orthotropic elastic constants and orientation of the principal elastic axes were then recorded for each cube and were compared to the constants predicted from Cowin's fabric-based constitutive model (Cowin, 1985, "The Relationship Between the Elasticity Tensor and the Fabric Tensor," Mech. Mater., 4(2), pp. 137-147.) and the orientation of the principal axes of the fabric tensor, respectively. Deviations from orthotropy were quantified by the "orthotropic error" (van Rietbergen et al., 1996, "Direct Mechanics Assessment of Elastic Symmetries and Properties of Trabecular Bone Architecture," J. Biomech., 29(12), pp. 1653-1657), and deviations from transverse isotropy were determined by statistical comparison of the secondary and tertiary elastic moduli. The orthotropic error was greater than 50% for nearly half of the cubes, and the secondary and tertiary moduli differed from one another (p < 0.0001). Both the orthotropic error and the difference between secondary and tertiary moduli decreased with increasing bone volume fraction (BV/TV; p ≤ 0.007). Considering only the cubes with an orthotropic error less than 50%, only moderate correlations were observed between the fabric-based and the μFE-computed elastic moduli (R2 ≥ 0.337; p < 0.0001). These results indicate that when using a criterion of 5 mm for a representative volume element (RVE), transverse isotropy or orthotropy cannot be assumed for elderly human vertebral trabecular bone. Particularly at low values of BV/TV, this criterion does not ensure applicability of theories of continuous media. In light of the very sparse and inhomogeneous microstructure found in the specimens analyzed in this study, further work is needed to establish guidelines for selecting a RVE within the aged vertebral centrum.

Biomechanics and mechanobiology of trabecular bone: a review

Trabecular bone is a highly porous, heterogeneous, and anisotropic material which can be found at the epiphyses of long bones and in the vertebral bodies. Studying the mechanical properties of trabecular bone is important, since trabecular bone is the main load bearing bone in vertebral bodies and also transfers the load from joints to the compact bone of the cortex of long bones. This review article highlights the high dependency of the mechanical properties of trabecular bone on species, age, anatomic site, loading direction, and size of the sample under consideration. In recent years, high resolution micro finite element methods have been extensively used to specifically address the mechanical properties of the trabecular bone and provide unique tools to interpret and model the mechanical testing experiments. The aims of the current work are to first review the mechanobiology of trabecular bone and then present classical and new approaches for modeling and analyzing the trabecular bone microstructure and macrostructure and corresponding mechanical properties such as elastic properties and strength.

Bone cell mechanosensitivity, estrogen deficiency, and osteoporosis

Adaptation of bone to mechanical stresses normally produces a bone architecture that combines a proper resistance against failure with a minimal use of material. This adaptive process is governed by mechanosensitive osteocytes that transduce the mechanical signals into chemical responses, i.e. the osteocytes release signaling molecules, which orchestrate the recruitment and activity of bone forming osteoblasts and/or bone resorbing osteoclasts. Computer models have shown that the maintenance of a mechanically-efficient bone architecture depends on the intensity and spatial distribution of the mechanical stimulus as well as on the osteocyte response. Osteoporosis is a condition characterized by a reduced bone mass and a compromized resistance of bone against mechanical loads, which has led us to hypothesize that mechanotransduction by osteocytes is altered in osteoporosis. One of the major causal factors for osteoporosis is the loss of estrogen, the major hormonal regulator of bone metabolism. Loss of estrogen may increase osteocyte-mediated activation of bone remodeling, resulting in impaired bone mass and architecture. In this review we highlight current insights on how osteocytes perceive mechanical stimuli placed on whole bones. Particular emphasis is placed on the role of estrogen in signaling pathway activation by mechanical stimuli, and on computer simulation in combination with cell biology to unravel biological processes contributing to bone strength.

Changes of elastic constants and anisotropy patterns in trabecular bone during disuse-induced bone loss assessed by poroelastic ultrasound

Currently, the approach most widely used to examine bone loss is the measurement of bone mineral density (BMD) using dual X-ray absorptiometry (DXA). However, bone loss due to immobilization creates changes in bone microarchitecture, which in turn are related to changes in bone mechanical function and competence to resist fracture.Unfortunately, the relationship between microarchitecture and mechanical function within the framework of immobilization and antiresorptive therapy has not being fully investigated. The goal of the present study was to investigate the structure–function relationship in trabecular bone in the real-world situations of a rapidly evolving osteoporosis(disuse), both with and without antiresorptive treatment. We evaluated the structure–function relationship in trabecular bone after bone loss (disuse-induced osteoporosis)and bisphosphonate treatment (antiresorptive therapy using risedronate) in canine trabecular bone using lCT and ultrasound wave propagation. Microstructure values determined from lCT images were used into the anisotropic poroelastic model of wave propagation in order to compute the apparent elastic constants (EC) and elastic anisotropy pattern of bone. Immobilization resulted in a significant reduction in trabecular thickness (Tb.Th) and bone volume fraction (BV/TV), while risedronate treatment combined with immobilization exhibited a lesser reduction in Tb.Th and BV/TV, suggesting that risedronate treatment decelerates bone loss, but it was unable to fully stop it. Risedronate treatment also increased the tissue mineral density (TMD), which when combined with the decrease in Tb.Th and BV/TV may explain the lack of significant differences invBMD in both immobilization and risedronate treated groups. Interestingly, changes inapparent EC were much stronger in the superior–inferior (SI) direction than in the medial–lateral (ML) and anterior–posterior (AP) anatomical directions, producing changes in elastic anisotropy patterns. When data were pooled together, vBMD was able to explain 58% of ultrasound measurements variability, a poroelastic wave propagation analytical model (i.e., BMD modulated by fabric directionality) was able to predict 81%of experimental wave velocity variability, and also explained 91% of apparent EC and changes in elastic anisotropy patterns. Overall, measurements of vBMD were unable to distinguish changes in apparent EC due to immobilization or risedronate treatment.However, anisotropic poroelastic ultrasound (PEUS) wave propagation was able to distinguish functional changes in apparent EC and elastic anisotropy patterns due to immobilization and antiresorptive therapy, providing an enhanced discrimination of anisotropic bone loss and the structure–function relationship in immobilized and risedronate-treated bone, beyond vBMD.

Improved trabecular bone structure of 20-month-old male spontaneously hypertensive rats

A few clinical studies have reported that elderly male participants with hypertensive disease frequently have higher bone mineral density (BMD) than the normotensive participants at several skeletal sites. The detailed mechanism is still unknown; therefore, a study of bone structure and density using the hypertensive animal models could be informative. We used micro-computed tomography to quantitatively evaluate the tibial and 3rd lumbar vertebral bones in the 20-month-old male spontaneous hypertensive rat (SHR). The BMD, volume fraction, and the microarchitecture changes of the SHR were compared to those of same-age normotensive controls (Wistar-Kyoto rat, WKY). We found that in the very old (20 month) male rats, the trabecular bone fraction and microstructure were higher than those in the same-age normotensive controls. The observation of the association of hypertension with BMD and bone strength in hypertensive rats warrants further investigations of bone mass and strength in elderly males with hypertension.

Biaxial normal strength behavior in the axial-transverse plane for human trabecular bone--effects of bone volume fraction, microarchitecture, and anisotropy

The biaxial failure behavior of the human trabecular bone, which has potential relevance both for fall and gait loading conditions, is not well understood, particularly for low-density bone, which can display considerable mechanical anisotropy. Addressing this issue, we investigated the biaxial normal strength behavior and the underlying failure mechanisms for human trabecular bone displaying a wide range of bone volume fraction (0.06-0.34) and elastic anisotropy. Micro-computed tomography (CT)-based nonlinear finite element analysis was used to simulate biaxial failure in 15 specimens (5 mm cubes), spanning the complete biaxial normal stress failure space in the axial-transverse plane. The specimens, treated as approximately transversely isotropic, were loaded in the principal material orientation. We found that the biaxial stress yield surface was well characterized by the superposition of two ellipses--one each for yield failure in the longitudinal and transverse loading directions--and the size, shape, and orientation of which depended on bone volume fraction and elastic anisotropy. However, when normalized by the uniaxial tensile and compressive strengths in the longitudinal and transverse directions, all of which depended on bone volume fraction, microarchitecture, and mechanical anisotropy, the resulting normalized biaxial strength behavior was well described by a single pair of (longitudinal and transverse) ellipses, with little interspecimen variation. Taken together, these results indicate that the role of bone volume fraction, microarchitecture, and mechanical anisotropy is mostly accounted for in determining the uniaxial strength behavior and the effect of these parameters on the axial-transverse biaxial normal strength behavior per se is minor.

Quantification of trabecular spatial orientation from low-resolution images

No accepted methodology exists to assess trabecular bone orientation from clinical CT scans. The aim of this study was to test the hypothesis that the distribution of grey values in clinical CT images is related to the underlying trabecular architecture and that this distribution can be used to identify the principal directions and local anisotropy of trabecular bone. Fourteen trabecular bone samples were extracted from high-resolution (30 μm) micro-CT scans of seven human femoral heads. Trabecular orientations and local anisotropy were calculated using grey-level deviation (GLD), a novel method providing a measure of the three-dimensional distribution of image grey values. This was repeated for different image resolutions down to 300 μm and for volumes of interest (VOIs) ranging from 1 to 7 mm. Outcomes were compared with the principal mechanical directions and with mean intercept length (MIL) as calculated for the segmented 30-μm images. For the 30-μm images, GLD predicted the mechanical principal directions equally well as MIL. For the 300-μm images, which are resolutions that can be obtained in vivo using clinical CT, only a small increase (3°-6°) in the deviation from the mechanical orientations was found. VOIs of 5 mm resulted in a robust quantification of the orientation. We conclude that GLD can quantify structural bone parameters from low-resolution CT images.

Alterations in trabecular bone microarchitecture in the ovine spine and distal femur following ovariectomy

Osteoporosis is a bone disease resulting in increased fracture risk as a result of alterations in both quantity and quality of bone. Bone quality is a combination of metabolic and microarchitectural properties of bone that can help to explain the increased susceptibility to fracture. Translational animal models are essential to understanding the pathology and for evaluating potential treatments of this disease. Large animals, such as the ovariectomized sheep, have been used as models for post-menopausal osteoporosis. However, long-term studies have not been carried out to observe the effects of ovariectomy after more than one year. This study employed micro-computed tomography to quantify changes in microarchitectural and mechanical parameters in femoral condyles and vertebral bodies of sheep that were sacrificed one or two years following ovariectomy. In the vertebral body, microarchitectural characteristics were significantly degraded following one year of ovariectomy in comparison to controls. The mechanical anisotropy, determined from micro-scale finite element models, was also greater in the ovariectomized groups, although the fabric tensor anisotropy was similar. There was no greater architectural degradation following two years of ovariectomy compared to one. Ovariectomy had minimal effects on the trabecular architecture of the distal femur even after two years. These results indicate that the vertebral body is the preferred anatomic site for studying bone from the ovariectomized sheep model, and that architectural changes stabilize after the first year.

Bone strength and structural deficits in children and adolescents with a distal forearm fracture resulting from mild trauma

Although distal forearm fractures (DFFs) are common during childhood and adolescence, it is unclear whether they reflect underlying skeletal deficits or are simply a consequence of the usual physical activities, and associated trauma, during growth. Therefore, we examined whether a recent DFF, resulting from mild or moderate trauma, is related to deficits in bone strength and cortical and trabecular bone macro- and microstructure compared with nonfracture controls. High-resolution peripheral quantitative computed tomography was used to assess micro-finite element-derived bone strength (ie, failure load) and to measure cortical and trabecular bone parameters at the distal radius and tibia in 115 boys and girls with a recent (<1 year) DFF and 108 nonfracture controls aged 8 to 15 years. Trauma levels (mild versus moderate) were assigned based on a validated classification scheme. Compared with sex-matched controls, boys and girls with a mild-trauma DFF (eg, fall from standing height) showed significant deficits at the distal radius in failure load (-13% and -11%, respectively; p < 0.05) and had higher ("worse") fall load-to-strength ratios (both +10%; p < 0.05 for boys and p = 0.06 for girls). In addition, boys and girls with a mild-trauma DFF had significant reductions in cortical area (-26% and -23%, respectively; p < 0.01) and cortical thickness (-14% and -13%, respectively; p < 0.01) compared with controls. The skeletal deficits in the mild-trauma DFF patients were generalized, as similar changes were present at the distal tibia. By contrast, both boys and girls with a moderate-trauma DFF (eg, fall from a bicycle) had virtually identical values for all of the measured bone parameters compared with controls. In conclusion, DFFs during growth have two distinct etiologies: those owing to underlying skeletal deficits leading to fractures with mild trauma versus those owing to more significant trauma in the setting of normal bone strength.

Assessment of trabecular bone yield and post-yield behavior from high-resolution MRI-based nonlinear finite element analysis at the distal radius of premenopausal and postmenopausal women susceptible to osteoporosis

RATIONALE AND OBJECTIVES

To assess the performance of a nonlinear microfinite element model on predicting trabecular bone yield and post-yield behavior based on high-resolution in vivo magnetic resonance images via the serial reproducibility.

MATERIALS AND METHODS

The nonlinear model captures material nonlinearity by iteratively adjusting tissue-level modulus based on tissue-level effective strain. It enables simulations of trabecular bone yield and post-yield behavior from micro magnetic resonance images at in vivo resolution by solving a series of nonlinear systems via an iterative algorithm on a desktop computer. Measures of mechanical competence (yield strain/strength, ultimate strain/strength, modulus of resilience, and toughness) were estimated at the distal radius of premenopausal and postmenopausal women (N = 20, age range 50-75) in whom osteoporotic fractures typically occur. Each subject underwent three scans (20.2 ± 14.5 days). Serial reproducibility was evaluated via coefficient of variation (CV) and intraclass correlation coefficient (ICC).

RESULTS

Nonlinear simulations were completed in an average of 14 minutes per three-dimensional image data set involving analysis of 61 strain levels. The predicted yield strain/strength, ultimate strain/strength, modulus of resilience, and toughness had a mean value of 0.78%, 3.09 MPa, 1.35%, 3.48 MPa, 14.30 kPa, and 32.66 kPa, respectively, covering a substantial range by a factor of up to 4. Intraclass correlation coefficient ranged from 0.986 to 0.994 (average 0.991); CV ranged from 1.01% to 5.62% (average 3.6%), with yield strain and toughness having the lowest and highest CV values, respectively.

CONCLUSIONS

The data suggest that the yield and post-yield parameters have adequate reproducibility to evaluate treatment effects in interventional studies within short follow-up periods.

Postmenopausal women treated with combination parathyroid hormone (1-84) and ibandronate demonstrate different microstructural changes at the radius vs. tibia: the PTH and Ibandronate Combination Study (PICS)

SUMMARY

In postmenopausal women receiving combination parathyroid hormone (PTH) (1-84) therapy and ibandronate, we evaluated bone microarchitecture and biomechanics using high-resolution peripheral quantitative computed tomography (HR-pQCT). Cortical and trabecular changes were different at the nonweight-bearing radius vs. the weight-bearing tibia, with more favorable overall changes at the tibia.

INTRODUCTION

PTH therapy and bisphosphonates decrease fracture risk in postmenopausal osteoporosis, but their effects on bone microstructure and strength have not been fully characterized, particularly during combination therapy. PTH increases trabecular bone mineral density (BMD) substantially but may decrease cortical BMD, possibly by stimulating intracortical remodeling. We evaluated bone microarchitecture and biomechanics with HR-pQCT at the radius (a nonweight-bearing site) and tibia (weight bearing) in women receiving combination PTH(1-84) and ibandronate.

METHODS

Postmenopausal women with low bone mass (n = 43) were treated with 6 months of PTH(1-84) (100 μg/day), either as one 6- or two 3-month courses, in combination with ibandronate (150 mg/month) over 2 years. HR-pQCT was performed before and after therapy.

RESULTS

Because changes in HR-pQCT parameters did not differ between treatment arms, groups were pooled into one cohort for analysis. Trabecular BMD increased at both radius and tibia (p < 0.01 for each). Cortical thickness and BMD decreased at the radius (p < 0.01), consistent with changes in dual-energy X-ray absorptiometry, while these parameters did not change at the tibia (p ≤ 0.02 for difference between radius and tibia). In contrast, cortical porosity increased at the tibia (p < 0.01) but not radius. Stiffness and failure load decreased at the radius (p < 0.0001) but did not change at the tibia.

CONCLUSIONS

Cortical and trabecular changes in response to the PTH/ibandronate treatment combinations utilized in this study were different at the nonweight-bearing radius vs. the weight-bearing tibia, with more favorable overall changes at the tibia. Our findings support the possibility that weight bearing may optimize the effects of osteoporosis therapy.

In vivo microdamage is an indicator of susceptibility to initiation and propagation of microdamage in human femoral trabecular bone

Microdamage has been cited as an important element of trabecular bone quality and fracture risk, as materials with flaws have lower modulus and strength than equivalent undamaged materials. However, the magnitude of the effect of damage on failure properties depends on its tendency to propagate. Human femoral trabecular bone from the neck and greater trochanter was subjected to one of compressive, torsional, or combined compression and torsion. The in vivo, new, and propagating damage were then quantified in thick sections under epifluorescent microscopy. Multiaxial loading, which was intended to represent an off-axis load such as a fall or accident, caused much more damage than either simple compression or shear, and similarly caused the greatest stiffness loss. In all cases, initiation of new damage far exceeded the propagation of existing damage. This may reflect stress redistribution away from damaged trabeculae, resulting in new damage sites. However, the accumulation of new damage was positively correlated with quantity of pre-existing damage in all loading modes, indicating that damaged bone is inherently more prone to further damage formation. Moreover, about 50% of in vivo microcracks propagated under each type of loading. Finally, damage formation was positively correlated to decreased compressive stiffness following both axial and shear loading. Taken together, these results demonstrate that damage in trabecular bone adversely affects its mechanical properties, and is indicative of bone that is more susceptible to further damage.

Predicting trabecular bone elastic properties from measures of bone volume fraction and fabric on the basis of micromagnetic resonance images

The relationship between fabric (a measure of structural anisotropy) and elastic properties of trabecular bone was examined by invoking morphology and homogenization theory on the basis of micromagnetic resonance images from the distal tibia in specimens (N = 30) and human subjects (N = 16) acquired at a 160 × 160 × 160 μm(3) voxel size. The fabric tensor was mapped in 7.5 × 7.5 × 7.5 mm(3) cubic subvolumes by a three-dimensional mean-intercept-length method. Elastic constants (three Young's and three shear moduli) were derived from linear microfinite element simulations of three-dimensional grayscale bone volume fraction-mapped images. In the specimen data, moduli fit power laws of bone volume fraction (bone volume/total volume) for all three test directions and subvolumes (R(2) = 0.92-0.98) with exponents ranging from 1.3 to 1.8. Weaker linear relationships were found for the in vivo data because of a narrower range in bone volume/total volume. When pooling the data for all test directions and subvolumes, bone volume/total volume predicted elastic moduli less well in the specimens (mean R(2) = 0.74) and not at all in vivo. A model of bone volume/total volume and fabric was highly predictive of microfinite element-derived Young's moduli: mean R(2) s of 0.98 and 0.82 (in vivo). The results show that fabric, an important predictor of bone mechanical properties, can be assessed in the limited resolution and signal-to-noise ratio regime of micromagnetic resonance images.

Unique suites of trabecular bone features characterize locomotor behavior in human and non-human anthropoid primates

Understanding the mechanically-mediated response of trabecular bone to locomotion-specific loading patterns would be of great benefit to comparative mammalian evolutionary morphology. Unfortunately, assessments of the correspondence between individual trabecular bone features and inferred behavior patterns have failed to reveal a strong locomotion-specific signal. This study assesses the relationship between inferred locomotor activity and a suite of trabecular bone structural features that characterize bone architecture. High-resolution computed tomography images were collected from the humeral and femoral heads of 115 individuals from eight anthropoid primate genera (Alouatta, Homo, Macaca, Pan, Papio, Pongo, Trachypithecus, Symphalangus). Discriminant function analyses reveal that subarticular trabecular bone in the femoral and humeral heads is significantly different among most locomotor groups. The results indicate that when a suite of femoral head trabecular features is considered, trabecular number and connectivity density, together with fabric anisotropy and the relative proportion of rods and plates, differentiate locomotor groups reasonably well. A similar, yet weaker, relationship is also evident in the trabecular architecture of the humeral head. The application of this multivariate approach to analyses of trabecular bone morphology in recent and fossil primates may enhance our ability to reconstruct locomotor behavior in the fossil record.

Relating age and micro-architecture with apparent-level elastic constants: a micro-finite element study of female cortical bone from the anterior femoral midshaft

Homogenized elastic properties are often assumed for macro-finite element (FE) models used in orthopaedic biomechanics. The accuracy of material property assignments may have a strong effect on the ability of these models to make accurate predictions. For cortical bone, most macro-scale FE models assume isotropic elastic material behaviour and do not include variation of material properties due to bone micro-architecture. The first aim of the present study was to evaluate the variation of apparent-level (homogenized) orthotropic elastic constants of cortical bone with age and indices of bone micro-architecture. Considerable age-dependent differences in porosity were noted across the cortical thickness in previous research. The second aim of the study was to quantify the resulting differences in elastic constants between the periosteum and endosteum. Specimens were taken from the anterior femoral midshaft of 27 female donors (age 53.4 ± 23.6 years) and micro-FE (µFE) analysis was used to derive orthotropic elastic constants. The variation of orthotropic elastic constants (Young’s moduli, shear moduli, and Poisson’s ratios) with various cortical bone micro-architectural indices was investigated. The ratio of canal volume to tissue volume, Ca.V/TV, analogous to porosity, was found to be the strongest predictor ( r ave2 = 0.958) of the elastic constants. Age was less predictive ( r ave2 = 0.385) than Ca.V/TV. Elastic anisotropy increased with increasing Ca.V/TV, leading to lower elastic moduli in the transverse, typically less frequently loaded, directions. Increased Ca.V/TV led to a more substantial reduction in elastic constants at the endosteal aspect than at the periosteal aspect. The results are expected to be most applicable in similar midshaft locations of long bones; specific analysis of other sites would be necessary to evaluate elastic properties elsewhere. It was concluded that Ca.V/TV was the most predictive of cortical bone elastic constants and that considerable periosteal–endosteal variations in these constants can develop with bone loss.

Performance of μMRI-Based virtual bone biopsy for structural and mechanical analysis at the distal tibia at 7T field strength

PURPOSE

To assess the performance of a 3D fast spin echo (FSE) pulse sequence utilizing out-of-slab cancellation through phase alternation and micro-magnetic resonance imaging (μMRI)-based virtual bone biopsy processing methods to probe the serial reproducibility and sensitivity of structural and mechanical parameters of the distal tibia at 7.0T.

MATERIALS AND METHODS

The distal tibia of five healthy subjects was imaged at three timepoints with a 3D FSE sequence at 137 × 137 × 410 μm(3) voxel size. Follow-up images were retrospectively 3D registered to baseline images. Coefficients of variation (CV) and intraclass correlation coefficients (ICCs) for measures of scale and topology of the whole tibial trabecular bone (TB) cross-section as well as finite-element-derived Young's and shear moduli of central cuboidal TB subvolumes (8 × 8 × 5 mm(3) ) were evaluated as measures of reproducibility and reliability. Four additional cubic TB subregions (anterior, medial, lateral, and posterior) of similar dimensions were extracted and analyzed to determine associations between whole cross-section and subregional structural parameters.

RESULTS

The mean signal-to-noise ratio (SNR) over the 15 image acquisitions was 27.5 ± 2.1. Retrospective registration yielded an average common analysis volume of 67% across the three exams per subject. Reproducibility (mean CV = 3.6%; range, 1.5%-5%) and reliability (ICCs, 0.95-0.99) of all parameters permitted parameter-based discrimination of the five subjects in spite of the narrow age range (26-36 years) covered. Parameters characterizing topology were better able to distinguish two individuals who demonstrated similar values for scalar measurements (≈ 34% difference, P < 0.001). Whole-section axial stiffness encompassing the cortex was superior at distinguishing two individuals relative to its central subregional TB counterpart (≈ 8% difference; P < 0.05). Interregion comparisons showed that although all parameters were correlated (mean R(2) = 0.78; range 0.57-0.99), the strongest associations observed were those for the erosion index (mean R(2) = 0.95, P ≤ 0.01).

CONCLUSION

The reproducibility and structural and mechanical parameter-based discriminative ability achieved in five healthy subjects suggests that 7T-derived μMRI of TB can be applied towards serial patient studies of osteoporosis and may enable earlier detection of disease or treatment-based effects.

Fabric dependence of quasi-waves in anisotropic porous media

Assessment of bone loss and osteoporosis by ultrasound systems is based on the speed of sound and broadband ultrasound attenuation of a single wave. However, the existence of a second wave in cancellous bone has been reported and its existence is an unequivocal signature of poroelastic media. To account for the fact that ultrasound is sensitive to microarchitecture as well as bone mineral density (BMD), a fabric-dependent anisotropic poroelastic wave propagation theory was recently developed for pure wave modes propagating along a plane of symmetry in an anisotropic medium. Key to this development was the inclusion of the fabric tensor--a quantitative stereological measure of the degree of structural anisotropy of bone--into the linear poroelasticity theory. In the present study, this framework is extended to the propagation of mixed wave modes along an arbitrary direction in anisotropic porous media called quasi-waves. It was found that differences between phase and group velocities are due to the anisotropy of the bone microarchitecture, and that the experimental wave velocities are more accurately predicted by the poroelastic model when the fabric tensor variable is taken into account. This poroelastic wave propagation theory represents an alternative for bone quality assessment beyond BMD.

Trabecular bone remodelling simulated by a stochastic exchange of discrete bone packets from the surface

Human bone is constantly renewed through life via the process of bone remodelling, in which individual packets of bone are removed by osteoclasts and replaced by osteoblasts. Remodelling is mechanically controlled, where osteocytes embedded within the bone matrix are thought to act as mechanical sensors. In this computational work, a stochastic model for bone remodelling is used in which the renewal of bone material occurs by exchange of discrete bone packets. We tested different hypotheses of how the mechanical stimulus for bone remodelling is integrated by osteocytes and sent to actor cells on the bone's surface. A collective (summed) signal from multiple osteocytes as opposed to an individual (maximal) signal from a single osteocyte was found to lead to lower inner porosity and surface roughness of the simulated bone structure. This observation can be interpreted in that collective osteocyte signalling provides an effective surface tension to the remodelling process. Furthermore, the material heterogeneity due to remodelling was studied on a network of trabeculae. As the model is discrete, the age of individual bone packets can be monitored with time. The simulation results were compared with experimental data coming from quantitative back scattered electron imaging by transforming the information about the age of the bone packet into a mineral content. Discrepancies with experiments indicate that osteoclasts preferentially resorb low mineralized, i.e. young, bone at the bone's surface.

Fabric dependence of wave propagation in anisotropic porous media

Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as speed of sound (SOS) and broadband ultrasound attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot's poroelastic wave propagation theory. In this paper, the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric-a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone.