Mineral heterogeneity has a minor influence on the apparent elastic properties of human cancellous bone: a SRμCT-based finite element study

Finite element analysis of bone mechanical properties using MRI-derived bound and pore water concentration maps

Ultrashort echo time (UTE) MRI techniques can be used to image the concentration of water in bones. Particularly, quantitative MRI imaging of collagen-bound water concentration (Cbw) and pore water concentration (Cpw) in cortical bone have been shown as potential biomarkers for bone fracture risk. To investigate the effect of Cbw and Cpw on the evaluation of bone mechanical properties, MRI-based finite element models of cadaver radii were generated with tissue material properties derived from 3 D maps of Cbw and Cpw measurements. Three-point bending tests were simulated by means of the finite element method to predict bending properties of the bone and the results were compared with those from direct mechanical testing. The study results demonstrate that these MRI-derived measures of Cbw and Cpw improve the prediction of bone mechanical properties in cadaver radii and have the potential to be useful in assessing patient-specific bone fragility risk.

Nonlinear micro finite element models based on digital volume correlation measurements predict early microdamage in newly formed bone

Bone regeneration in critical-sized defects is a clinical challenge, with biomaterials under constant development aiming at enhancing the natural bone healing process. The delivery of bone morphogenetic proteins (BMPs) in appropriate carriers represents a promising strategy for bone defect treatment but optimisation of the spatial-temporal release is still needed for the regeneration of bone with biological, structural, and mechanical properties comparable to the native tissue. Nonlinear micro finite element (μFE) models can address some of these challenges by providing a tool able to predict the biomechanical strength and microdamage onset in newly formed bone when subjected to physiological or supraphysiological loads. Yet, these models need to be validated against experimental data. In this study, experimental local displacements in newly formed bone induced by osteoinductive biomaterials subjected to in situ X-ray computed tomography compression in the apparent elastic regime and measured using digital volume correlation (DVC) were used to validate μFE models. Displacement predictions from homogeneous linear μFE models were highly correlated to DVC-measured local displacements, while tissue heterogeneity capturing mineralisation differences showed negligible effects. Nonlinear μFE models improved the correlation and showed that tissue microdamage occurs at low apparent strains. Microdamage seemed to occur next to large cavities or in biomaterial-induced thin trabeculae, independent of the mineralisation. While localisation of plastic strain accumulation was similar, the amount of damage accumulated in these locations was slightly higher when including material heterogeneity. These results demonstrate the ability of the nonlinear μFE model to capture local microdamage in newly formed bone tissue and can be exploited to improve the current understanding of healing bone and mechanical competence. This will ultimately aid the development of BMPs delivery systems for bone defect treatment able to regenerate bone with optimal biological, mechanical, and structural properties.

MicroFE models of porcine vertebrae with induced bone focal lesions: Validation of predicted displacements with digital volume correlation

The evaluation of the local mechanical behavior as a result of metastatic lesions is fundamental for the characterization of the mechanical competence of metastatic vertebrae. Micro finite element (microFE) models have the potential of addressing this challenge through laboratory studies but their predictions of local deformation due to the complexity of the bone structure compromized by the lesion must be validated against experiments. In this study, the displacements predicted by homogeneous, linear and isotropic microFE models of vertebrae were validated against experimental Digital Volume Correlation (DVC) measurements. Porcine spine segments, with and without mechanically induced focal lesions, were tested in compression within a micro computed tomography (microCT) scanner. The displacement within the bone were measured with an optimized global DVC approach (BoneDVC). MicroFE models of the intact and lesioned vertebrae, including or excluding the growth plates, were developed from the microCT images. The microFE and DVC boundary conditions were matched. The displacements measured by the DVC and predicted by the microFE along each Cartesian direction were compared. The results showed an excellent agreement between the measured and predicted displacements, both for intact and metastatic vertebrae, in the middle of the vertebra, in those cases where the structure was not loaded beyond yield (0.69 < R² < 1.00). Models with growth plates showed the worst correlations (0.02 < R² < 0.99), while a clear improvement was observed if the growth plates were excluded (0.56 < R² < 1.00). In conclusion, these simplified models can predict complex displacement fields in the elastic regime with high reliability, more complex non-linear models should be implemented to predict regions with high deformation, when the bone is loaded beyond yield.

Microstructure Determines Apparent-Level Mechanics Despite Tissue-Level Anisotropy and Heterogeneity of Individual Plates and Rods in Normal Human Trabecular Bone

Trabecular plates and rods determine apparent elastic modulus and yield strength of trabecular bone, serving as important indicators of bone's mechanical integrity in health and disease. Although trabecular bone's apparent-level mechanical properties have been widely reported, tissue mechanical properties of individual trabeculae have not been fully characterized. We systematically measured tissue mineral density (TMD)-dependent elastic modulus of individual trabeculae using microindentation and characterized its anisotropy as a function of trabecular type (plate or rod), trabecular orientation in the global coordinate (longitudinal, oblique, or transverse along the anatomic loading axis), and indentation direction along the local trabecular coordinate (axial or lateral). Human trabecular bone samples were scanned by micro-computed tomography for TMD and microstructural measurements. Individual trabecula segmentation was used to decompose trabecular network into individual trabeculae, where trabecular type and orientation were determined. We performed precise, selective indentation of trabeculae in each category using a custom-built, microscope-coupled microindentation device. Co-localization of TMD at each indentation site was performed to obtain TMD-to-modulus correlations. We found significantly higher TMD and tissue modulus in trabecular plates than rods. Regardless of trabecular type and orientation, axial tissue modulus was consistently higher than lateral tissue modulus, with ratios ranging from 1.13 to 1.41. Correlations between TMD and tissue modulus measured from axial and lateral indentations were strong but distinct: axial correlation predicted higher tissue modulus than lateral correlation at the same TMD level. To assess the contribution of experimentally measured anisotropic tissue properties of individual trabeculae to apparent-level mechanics, we constructed non-linear micro-finite element models using a new set of trabecular bone samples and compared model predictions to mechanical testing measurements. Heterogeneous anisotropic models accurately predicted apparent elastic modulus but were no better than a simple homogeneous isotropic model. Variances in tissue-level properties may therefore contribute nominally to apparent-level mechanics in normal human trabecular bone. © 2021 American Society for Bone and Mineral Research (ASBMR).

Finite Element Analysis of Fracture Fixation

PURPOSE OF REVIEW

Fracture fixation aims to provide stability and promote healing, but remains challenging in unstable and osteoporotic fractures with increased risk of construct failure and nonunion. The first part of this article reviews the clinical motivation behind finite element analysis of fracture fixation, its strengths and weaknesses, how models are developed and validated, and how outputs are typically interpreted. The second part reviews recent modeling studies of the femur and proximal humerus, areas with particular relevance to fragility fractures.

RECENT FINDINGS

There is some consensus in the literature around how certain modeling aspects are pragmatically formulated, including bone and implant geometries, meshing, material properties, interactions, and loads and boundary conditions. Studies most often focus on predicted implant stress, bone strain surrounding screws, or interfragmentary displacements. However, most models are not rigorously validated. With refined modeling methods, improved validation efforts, and large-scale systematic analyses, finite element analysis is poised to advance the understanding of fracture fixation failure, enable optimization of implant designs, and improve surgical guidance.

Evaluating a theoretical and an empirical model of "side effects" in cancellous bone

Accurate measurement of cancellous bone's apparent elastic modulus, E, is confounded by the experimental artefacts created when trabeculae are severed during specimen preparation. Although standardized axial testing protocols have been developed to deal with the so-called "end effects" caused by severed trabeculae at the loading surfaces, much less attention has been given to the "side effects" around the periphery and the specimen size dependence they create. Two models (one theoretical, one empirical) have been proposed in the literature to predict the reduction in E with decreasing specimen diameter. The current study used finite element method (FEM) modelling to analyze bovine cancellous bone from five different anatomic sites and quantify the changes in E that occurred with specimen diameter. The two models were adapted so that they could predict E based on diameter and architectural parameters (BV/TV, DA, Tb.Sp) alone, without requiring that a "true" modulus be known a priori. Both models fit the data equally well; however, the empirical model gives simpler estimations as a function of trabecular separation (Tb.Sp). A minimum diameter of 5-8 Tb.Sp is recommended.

Non-invasive prediction of the mouse tibia mechanical properties from microCT images: comparison between different finite element models

New treatments for bone diseases require testing in animal models before clinical translation, and the mouse tibia is among the most common models. In vivo micro-Computed Tomography (microCT)-based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experimental data. Different modelling techniques can be used to estimate the bone properties, and the accuracy associated with each is unclear. The aim of this study was to evaluate the ability of different microCT-based microFE models to predict the mechanical properties of the mouse tibia under compressive load. Twenty tibiae were microCT scanned at 10.4 µm voxel size and subsequently compressed at 0.03 mm/s until failure. Stiffness and failure load were measured from the load-displacement curves. Different microFE models were generated from each microCT image, with hexahedral or tetrahedral mesh, and homogeneous or heterogeneous material properties. Prediction accuracy was comparable among models. The best correlations between experimental and predicted mechanical properties, as well as lower errors, were obtained for hexahedral models with homogeneous material properties. Experimental stiffness and predicted stiffness were reasonably well correlated (R2 = 0.53-0.65, average error of 13-17%). A lower correlation was found for failure load (R2 = 0.21-0.48, average error of 9-15%). Experimental and predicted mechanical properties normalized by the total bone mass were strongly correlated (R2 = 0.75-0.80 for stiffness, R2 = 0.55-0.81 for failure load). In conclusion, hexahedral models with homogeneous material properties based on in vivo microCT images were shown to best predict the mechanical properties of the mouse tibia.

Empirical relationships between bone density and ultimate strength: A literature review

INTRODUCTION

Ultimate strength-density relationships for bone have been reported with widely varying results. Reliable bone strength predictions are crucial for many applications that aim to assess bone failure. Bone density and bone morphology have been proposed to explain most of the variance in measured bone strength. If this holds true, it could lead to the derivation of a single ultimate strength-density-morphology relationship for all anatomical sites.

METHODS

All relevant literature was reviewed. Ultimate strength-density relationships derived from mechanical testing of human bone tissue were included. The reported relationships were translated to ultimate strength-apparent density relationships and normalized with respect to strain rate. Results were grouped based on bone tissue type (cancellous or cortical), anatomical site, and loading mode (tension vs. compression). When possible, the relationships were compared to existing ultimate strength-density-morphology relationships.

RESULTS

Relationships that considered bone density and morphology covered the full spectrum of eight-fold inter-study difference in reported compressive ultimate strength-density relationships for trabecular bone. This was true for studies that tested specimens in different loading direction and tissue from different anatomical sites. Sparse data was found for ultimate strength-density relationships in tension and for cortical bone properties transverse to the main loading axis of the bone.

CONCLUSIONS

Ultimate strength-density-morphology relationships could explain measured strength across anatomical sites and loading directions. We recommend testing of bone specimens in other directions than along the main trabecular alignment and to include bone morphology in studies that investigate bone material properties. The lack of tensile strength data did not allow for drawing conclusions on ultimate strength-density-morphology relationships. Further studies are needed. Ideally, these studies would investigate both tensile and compressive strength-density relationships, including morphology, to close this gap and lead to more accurate evaluation of bone failure.

Finite element analysis of bone strength in osteogenesis imperfecta

As a dedicated experimentalist, John Currey praised the high potential of finite element (FE) analysis but also recognized its critical limitations. The application of the FE methodology to bone tissue is reviewed in the light of his enthusiastic and colorful statements. In the past decades, FE analysis contributed substantially to the understanding of structure-function properties in the hierarchical organization of bone and to the simulation of bone adaptation. The systematic experimental validation of FE analysis of bone strength in anatomical locations at risk of fracture led to its application in clinical studies to evaluate efficacy of antiresorptive or anabolic treatment of bone fragility. Beyond the successful analyses of healthy or osteoporotic bone, FE analysis becomes increasingly involved in the investigation of other fragility-related bone diseases. The case of osteogenesis imperfecta (OI) is exposed, the multiscale alterations of the bone tissue and the effect of treatment summarized. A few FE analyses attempting to answer open questions in OI are then reported. An original study is finally presented that explored the structural properties of the Brtl/+ murine model of OI type IV subjected to sclerostin neutralizing antibody treatment using microFE analysis. The use of identical material properties in the four-point bending FE simulations of the femora reproduced not only the experimental values but also the statistical comparisons examining the effect of disease and treatment. Further efforts are needed to build upon the extraordinary legacy of John Currey and clarify the impact of different bone diseases on the hierarchical mechanical properties of bone.

An explicit micro-FE approach to investigate the post-yield behaviour of trabecular bone under large deformations

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.

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.

Young's modulus of trabecular bone at the tissue level: A review

The tissue-level Young's modulus of trabecular bone is important for detailed mechanical analysis of bone and bone-implant mechanical interactions. However, the heterogeneity and small size of the trabecular struts complicate an accurate determination. Methods such as micro-mechanical testing of single trabeculae, ultrasonic testing, and nanoindentation have been used to estimate the trabecular Young's modulus. This review summarizes and classifies the trabecular Young's moduli reported in the literature. Information on species, anatomic site, and test condition of the samples has also been gathered. Advantages and disadvantages of the different methods together with recent developments are discussed, followed by some suggestions for potential improvement for future work. In summary, this review provides a thorough introduction to the approaches used for determining trabecular Young's modulus, highlights important considerations when applying these methods and summarizes the reported Young's modulus for follow-up studies on trabecular properties.

STATEMENT OF SIGNIFICANCE

The spongy trabecular bone provides mechanical support while maintaining a low weight. A correct measure of its mechanical properties at the tissue level, i.e. at a single-trabecula level, is crucial for analysis of interactions between bone and implants, necessary for understanding e.g. bone healing mechanisms. In this study, we comprehensively summarize the Young's moduli of trabecular bone estimated by currently available methods, and report their dependency on different factors. The critical review of different methods with recent updates is intended to inspire improvements in estimating trabecular Young's modulus. It is strongly suggested to report detailed information on the tested bone to enable statistical analysis in the future.

Trabecular bone patterning across the human hand

Hand bone morphology is regularly used to link particular hominin species with behaviors relevant to cognitive/technological progress. Debates about the functional significance of differing hominin hand bone morphologies tend to rely on establishing phylogenetic relationships and/or inferring behavior from epigenetic variation arising from mechanical loading and adaptive bone modeling. Most research focuses on variation in cortical bone structure, but additional information about hand function may be provided through the analysis of internal trabecular structure. While primate hand bone trabecular structure is known to vary in ways that are consistent with expected joint loading differences during manipulation and locomotion, no study exists that has documented this variation across the numerous bones of the hand. We quantify the trabecular structure in 22 bones of the human hand (early/extant modern Homo sapiens) and compare structural variation between two groups associated with post-agricultural/industrial (post-Neolithic) and foraging/hunter-gatherer (forager) subsistence strategies. We (1) establish trabecular bone volume fraction (BV/TV), modulus (E), degree of anisotropy (DA), mean trabecular thickness (Tb.Th) and spacing (Tb.Sp); (2) visualize the average distribution of site-specific BV/TV for each bone; and (3) examine if the variation in trabecular structure is consistent with expected joint loading differences among the regions of the hand and between the groups. Results indicate similar distributions of trabecular bone in both groups, with those of the forager sample presenting higher BV/TV, E, and lower DA, suggesting greater and more variable loading during manipulation. We find indications of higher loading along the ulnar side of the forager sample hand, with high site-specific BV/TV distributions among the carpals that are suggestive of high loading while the wrist moves through the 'dart-thrower's' motion. These results support the use of trabecular structure to infer behavior and have direct implications for refining our understanding of human hand evolution and fossil hominin hand use.

Nonlinear micro-CT based FE modeling of trabecular bone-Sensitivity of apparent response to tissue constitutive law and bone volume fraction

In this study, the sensitivity of the apparent response of trabecular bone to different constitutive models at the tissue level was investigated using finite element (FE) modeling based on micro-computed tomography (micro-CT). Trabecular bone specimens from porcine femurs were loaded under a uniaxial compression experimentally and computationally. The apparent behaviors computed using von Mises, Drucker-Prager, and Cast Iron plasticity models were compared. Secondly, the effect of bone volume fraction was studied by changing the bone volume fraction of a trabecular bone sample while keeping the same basic architecture. Also, constitutive models' parameters of the tissue were calibrated for porcine bone, and the effects of different parameters on resulting apparent response were investigated through a parametric study. The calibrated effective tissue elastic modulus of porcine trabecular bone was 10±1.2 GPa, which is in the lower range of modulus values reported in the literature for human and bovine trabecular bones (4-23.8 GPa). It was also observed that, unlike elastic modulus, yield properties of tissue could not be uniquely calibrated by fitting an apparent response from simulations to experiments under a uniaxial compression. Our results demonstrated that using these 3 tissue constitutive models had only a slight effect on the apparent response. As expected, there was a significant change in the apparent response with varying bone volume fraction. Also, both apparent modulus and maximum stress had a linear relation with bone volume fraction.

Micro-finite-element method to assess elastic properties of trabecular bone at micro- and macroscopic level

OBJECTIVE OF THE STUDY

The objective of the present study is to assess the mechanical behavior of trabecular bone based on microCT imaging and micro-finite-element analysis. In this way two methods are detailed: (i) direct determination of macroscopic elastic property of trabecular bone; (ii) inverse approach to assess mechanical properties of trabecular bone tissue.

PATIENTS

Thirty-five females and seven males (forty-two subjects) mean aged (±SD) 80±11.7 years from hospitals of Assistance publique-Hôpitaux de Paris (AP-HP) diagnosed with osteoporosis following a femoral neck fracture due to a fall from standing were included in this study.

MATERIALS AND METHODS

Fractured heads were collected during hip replacement surgery. Standardized bone cores were removed from the femoral head's equator by a trephine in a water bath. MicroCT images acquisition and analysis were performed with CTan^® software and bone volume fraction was then determined. Micro-finite-element simulations were per-formed using Abaqus 6.9-2^® software in order to determine the macroscopic mechanical behaviour of the trabecular bone. After microCT acquisition, a longitudinal compression test was performed and the experimental macroscopic Young's Modulus was extracted. An inverse approach based on the whole trabecular bone's mechanical response and micro-finite-element analysis was performed to determine microscopic mechanical properties of trabecular bone.

RESULTS

In the present study, elasticity of the tissue was shown to be similar to that of healthy tissue but with a lower yield stress.

CONCLUSION

Classical histomorphometric analysis form microCT imaging associated with an inverse micro-finite-element method allowed to assess microscopic mechanical trabecular bone parameters.

Incorporating tissue anisotropy and heterogeneity in finite element models of trabecular bone altered predicted local stress distributions

Trabecular bone is composed of organized mineralized collagen fibrils, which results in heterogeneous and anisotropic mechanical properties at the tissue level. Recently, biomechanical models computing stresses and strains in trabecular bone have indicated a significant effect of tissue heterogeneity on predicted stresses and strains. However, the effect of the tissue-level mechanical anisotropy on the trabecular bone biomechanical response is unknown. Here, a computational method was established to automatically impose physiologically relevant orientation inherent in trabecular bone tissue on a trabecular bone microscale finite element model. Spatially varying tissue-level anisotropic elastic properties were then applied according to the bone mineral density and the local tissue orientation. The model was used to test the hypothesis that anisotropy in both homogeneous and heterogeneous models alters the predicted distribution of stress invariants. Linear elastic finite element computations were performed on a 3 mm cube model isolated from a microcomputed tomography scan of human trabecular bone from the distal femur. Hydrostatic stress and von Mises equivalent stress were recorded at every element, and the distributions of these values were analyzed. Anisotropy reduced the range of hydrostatic stress in both tension and compression more strongly than the associated increase in von Mises equivalent stress. The effect of anisotropy was independent of the spatial redistribution high compressive stresses due to tissue elastic heterogeneity. Tissue anisotropy and heterogeneity are likely important mechanisms to protect bone from failure and should be included for stress analyses in trabecular bone.

Micro Finite Element models of the vertebral body: Validation of local displacement predictions

The estimation of local and structural mechanical properties of bones with micro Finite Element (microFE) models based on Micro Computed Tomography images depends on the quality bone geometry is captured, reconstructed and modelled. The aim of this study was to validate microFE models predictions of local displacements for vertebral bodies and to evaluate the effect of the elastic tissue modulus on model’s predictions of axial forces. Four porcine thoracic vertebrae were axially compressed in situ, in a step-wise fashion and scanned at approximately 39μm resolution in preloaded and loaded conditions. A global digital volume correlation (DVC) approach was used to compute the full-field displacements. Homogeneous, isotropic and linear elastic microFE models were generated with boundary conditions assigned from the interpolated displacement field measured from the DVC. Measured and predicted local displacements were compared for the cortical and trabecular compartments in the middle of the specimens. Models were run with two different tissue moduli defined from microindentation data (12.0GPa) and a back-calculation procedure (4.6GPa). The predicted sum of axial reaction forces was compared to the experimental values for each specimen. MicroFE models predicted more than 87% of the variation in the displacement measurements (R² = 0.87–0.99). However, model predictions of axial forces were largely overestimated (80–369%) for a tissue modulus of 12.0GPa, whereas differences in the range 10–80% were found for a back-calculated tissue modulus. The specimen with the lowest density showed a large number of elements strained beyond yield and the highest predictive errors. This study shows that the simplest microFE models can accurately predict quantitatively the local displacements and qualitatively the strain distribution within the vertebral body, independently from the considered bone types.

MicroCT-based finite element models as a tool for virtual testing of cortical bone

The aim of this study was to assess a virtual biomechanics testing approach purely based on microcomputed tomography (microCT or µCT) data, providing non-invasive methods for determining the stiffness and strength of cortical bone. Mouse femurs were µCT scanned prior to three-point-bend tests. Then microCT-based finite element models were generated with spatial variation in bone elastoplastic properties and subject-specific femur geometries. Empirical relationships of density versus Young's moduli and yield stress were used in assigning elastoplastic properties to each voxel. The microCT-based finite element modeling (µFEM) results were employed to investigate the model's accuracy through comparison with experimental tests. The correspondence of elastic stiffness and strength from the µFE analyses and tests was good. The interpretation of the derived data showed a 6.1%, 1.4%, 1.5%, and 1.6% difference between the experimental test result and µFEM output on global stiffness, nominal Young's modulus, nominal yield stress, and yield force, respectively. We conclude that virtual testing outputs could be used to predict global elastic-plastic properties and may reduce the cost, time, and number of test specimens in performing physical experiments.

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.

Chronic alcohol abuse in men alters bone mechanical properties by affecting both tissue mechanical properties and microarchitectural parameters

OBJECTIVE OF THE STUDY

Alcohol-induced secondary osteoporosis in men has been characterized by higher fracture prevalence and a modification of bone microarchitecture. Chronic alcohol consumption impairs bone cell activity and results in an increased fragility. A few studies highlighted effects of heavy alcohol consumption on some microarchitectural parameters of trabecular bone. But to date and to our knowledge, micro- and macro-mechanical properties of bone of alcoholic subjects have not been investigated.

PATIENTS

In the present study, mechanical properties and microarchitecture of trabecular bone samples from the iliac crest of alcoholic male patients (n=15) were analyzed and compared to a control group (n=8).

MATERIALS AND METHODS

Nanoindentation tests were performed to determine the tissue's micromechanical properties, micro-computed tomography was used to measure microarchitectural parameters, and numerical simulations provided the apparent mechanical properties of the samples.

RESULTS

Compared to controls, bone tissue from alcoholic patients exhibited an increase of micromechanical properties at tissue scale, a significant decrease of apparent mechanical properties at sample scale, and significant changes in several microarchitectural parameters. In particular, a crucial role of structure model index (SMI) on mechanical properties was identified.

CONCLUSIONS

3D microarchitectural parameters are at least as important as bone volume fraction to predict bone fracture risk in the case of alcoholic patients.

Micro-CT based finite element models of cancellous bone predict accurately displacement once the boundary condition is well replicated: A validation study

Non-destructive 3D micro-computed tomography (microCT) based finite element (microFE) models are used to estimate bone mechanical properties at tissue level. However, their validation remains challenging. Recent improvements in the quantification of displacements in bone tissue biopsies subjected to staged compression, using refined Digital Volume Correlation (DVC) techniques, now provide a full field displacement information accurate enough to be used for microFE validation. In this study, three specimens (two humans and one bovine) were tested with two different experimental set-ups, and the resulting data processed with the same DVC algorithm. The resulting displacement vector field was compared to that predicted by microFE models solved with three different boundary conditions (BC): nominal force resultant, nominal displacement resultant, distributed displacement. The first two conditions were obtained directly from the measurements provided by the experimental jigs, whereas in the third case the displacement field measured by the DVC in the top and bottom layer of the specimen was applied. Results show excellent relationship between the numerical predictions (x) and the experiments (y) when using BC derived from the DVC measurements (U_X: y=1.07x-0.002, RMSE: 0.001mm; U_Y: y=1.03x-0.001, RMSE: 0.001mm; U_Z: y=x+0.0002, RMSE: 0.001 mm for bovine specimen), whereas only poor correlation was found using BCs according to experiment set-ups. In conclusion, microFE models were found to predict accurately the vectorial displacement field using interpolated displacement boundary condition from DVC measurement.

New Ti-Alloys and Surface Modifications to Improve the Mechanical Properties and the Biological Response to Orthopedic and Dental Implants: A Review

Titanium implants are widely used in the orthopedic and dentistry fields for many decades, for joint arthroplasties, spinal and maxillofacial reconstructions, and dental prostheses. However, despite the quite satisfactory survival rates failures still exist. New Ti-alloys and surface treatments have been developed, in an attempt to overcome those failures. This review provides information about new Ti-alloys that provide better mechanical properties to the implants, such as superelasticity, mechanical strength, and corrosion resistance. Furthermore, in vitro and in vivo studies, which investigate the biocompatibility and cytotoxicity of these new biomaterials, are introduced. In addition, data regarding the bioactivity of new surface treatments and surface topographies on Ti-implants is provided. The aim of this paper is to discuss the current trends, advantages, and disadvantages of new titanium-based biomaterials, fabricated to enhance the quality of life of many patients around the world.

Inverse finite element modeling for characterization of local elastic properties in image-guided failure assessment of human trabecular bone

The local interpretation of microfinite element (μFE) simulations plays a pivotal role for studying bone structure–function relationships such as failure processes and bone remodeling.In the past μFE simulations have been successfully validated on the apparent level,however, at the tissue level validations are sparse and less promising. Furthermore,intra trabecular heterogeneity of the material properties has been shown by experimental studies. We proposed an inverse μFE algorithm that iteratively changes the tissue level Young's moduli such that the μFE simulation matches the experimental strain measurements.The algorithm is setup as a feedback loop where the modulus is iteratively adapted until the simulated strain matches the experimental strain. The experimental strain of human trabecular bone specimens was calculated from time-lapsed images that were gained by combining mechanical testing and synchrotron radiation microcomputed tomography(SRlCT). The inverse μFE algorithm was able to iterate the heterogeneous distribution of moduli such that the resulting μFE simulations matched artificially generated and experimentally measured strains.

Effect of intraspecimen spatial variation in tissue mineral density on the apparent stiffness of trabecular bone

This study investigated the effects of intraspecimen variations in tissue mineral density(TMD) on the apparent-level stiffness of human trabecular bone. High-resolution finite element (FE) models were created for each of 12 human trabecular bone specimens,using both microcomputed tomography (lCT) and “gold-standard” synchrotron radiation lCT (SRlCT) data. Our results confirm that incorporating TMD spatial variation reduces the calculated apparent stiffness compared to homogeneous TMD models. This effect exists for both lCT- and SRlCT-based FE models, but is exaggerated in lCT based models. This study provides a direct comparison of lCT to SRlCT data and is thereby able to conclude that the influence of including TMD heterogeneity is overestimated in lCT-based models.

Distinct Tissue Mineral Density in Plate- and Rod-like Trabeculae of Human Trabecular Bone

Trabecular bone quality includes both microstructural and intrinsic tissue mineralization properties. However, the tissue mineralization in individual trabeculae of different trabecular types and orientations has not yet been investigated. The aim of this study was to develop an individual trabecula mineralization (ITM) analysis technique to determine tissue mineral density (TMD) distributions in plate- and rod-like trabeculae, respectively, and to compare the TMD of trabeculae along various orientations in micro-computed tomography (μCT) images of trabecular bone samples from the femoral neck, greater trochanter, and proximal tibia. ITM analyses indicated that trabecular plates, on average, had significantly higher TMD than trabecular rods. In addition, the distribution of TMD in trabecular plates depended on trabecular orientation with the lowest TMD in longitudinal plates and the highest TMD in transverse plates. Conversely, there was a relatively uniform distribution of TMD among trabecular rods, with respect to trabecular orientation. Further analyses of TMD distribution revealed that trabecular plates had higher mean and peak TMD, whereas trabecular rods had a wider TMD distribution and a larger portion of low mineralized trabeculae. Comparison of apparent Young's moduli derived from micro-finite element models with and without heterogeneous TMD demonstrated that heterogeneous TMD in trabecular plates had a significant influence on the elastic mechanical property of trabecular bone. In conclusion, this study revealed differences in TMD between plate- and rod-like trabeculae and among various trabecular orientations. The observation of less mineralized longitudinal trabecular plates suggests interesting implications of these load-bearing plates in bone remodeling. The newly developed ITM analysis can be a valuable technique to assess the influence of metabolic bone diseases and their pharmaceutical treatments on not only microstructure of trabecular bone but also the microarchitectural heterogeneity of tissue mineralization.

Bone volume fraction and fabric anisotropy are better determinants of trabecular bone stiffness than other morphological variables

As our population ages, more individuals suffer from osteoporosis. This disease leads to impaired trabecular architecture and increased fracture risk. It is essential to understand how morphological and mechanical properties of the cancellous bone are related. Morphology-elasticity relationships based on bone volume fraction (BV/TV) and fabric anisotropy explain up to 98% of the variation in elastic properties. Yet, other morphological variables such as individual trabeculae segmentation (ITS) and trabecular bone score (TBS) could improve the stiffness predictions. A total of 743 micro-computed tomography (μCT) reconstructions of cubic trabecular bone samples extracted from femur, radius, vertebrae, and iliac crest were analyzed. Their morphology was assessed via 25 variables and their stiffness tensor (CFE) was computed from six independent load cases using micro finite element (μFE) analyses. Variance inflation factors were calculated to evaluate collinearity between morphological variables and decide upon their inclusion in morphology-elasticity relationships. The statistically admissible morphological variables were included in a multiple linear regression model of the dependent variable CFE. The contribution of each independent variable was evaluated (ANOVA). Our results show that BV/TV is the best determinant of CFE(r(2) adj  = 0.889), especially in combination with fabric anisotropy (r(2) adj  = 0.968). Including the other independent predictors hardly affected the amount of variance explained by the model (r(2) adj  = 0.975). Across all anatomical sites, BV/TV explained 87% of the variance of the bone elastic properties. Fabric anisotropy further described 10% of the bone stiffness, but the improvement in variance explanation by adding other independent factors was marginal (<1%). These findings confirm that BV/TV and fabric anisotropy are the best determinants of trabecular bone stiffness and show, against common belief, that other morphological variables do not bring any further contribution. These overall conclusions remain to be confirmed for specific bone diseases and postelastic properties.

Predicting mouse vertebra strength with micro-computed tomography-derived finite element analysis

As in clinical studies, finite element analysis (FEA) developed from computed tomography (CT) images of bones are useful in pre-clinical rodent studies assessing treatment effects on vertebral body (VB) strength. Since strength predictions from microCT-derived FEAs (μFEA) have not been validated against experimental measurements of mouse VB strength, a parametric analysis exploring material and failure definitions was performed to determine whether elastic μFEAs with linear failure criteria could reasonably assess VB strength in two studies, treatment and genetic, with differences in bone volume fraction between the control and the experimental groups. VBs were scanned with a 12-μm voxel size, and voxels were directly converted to 8-node, hexahedral elements. The coefficient of determination or R (2) between predicted VB strength and experimental VB strength, as determined from compression tests, was 62.3% for the treatment study and 85.3% for the genetic study when using a homogenous tissue modulus (E t) of 18 GPa for all elements, a failure volume of 2%, and an equivalent failure strain of 0.007. The difference between prediction and measurement (that is, error) increased when lowering the failure volume to 0.1% or increasing it to 4%. Using inhomogeneous tissue density-specific moduli improved the R (2) between predicted and experimental strength when compared with uniform E t=18 GPa. Also, the optimum failure volume is higher for the inhomogeneous than for the homogeneous material definition. Regardless of model assumptions, μFEA can assess differences in murine VB strength between experimental groups when the expected difference in strength is at least 20%.

Multiscale contribution of bone tissue material property heterogeneity to trabecular bone mechanical behavior

Heterogeneity of material properties is an important potential contributor to bone fracture resistance because of its putative contribution to toughness, but establishing the contribution of heterogeneity to fracture risk is still in an incipient stage. Experimental studies have demonstrated changes in distributions of compositional and nanomechanical properties with fragility fracture history, disease, and pharmacologic treatment. Computational studies have demonstrated that models with heterogeneous material properties predict apparent stiffness moderately better than homogeneous models and show greater energy dissipation. Collectively, these results suggest that microscale material heterogeneity affects not only microscale mechanics but also structural performance at larger length scales.

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.

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.

Stochastic multi-scale prediction on the apparent elastic moduli of trabecular bone considering uncertainties of biological apatite (BAp) crystallite orientation and image-based modelling

An assessment of the mechanical properties of trabecular bone is important in determining the fracture risk of human bones. Many uncertainty factors contribute to the dispersion of the estimated mechanical properties of trabecular bone. This study was undertaken in order to propose a computational scheme that will be able to predict the effective apparent elastic moduli of trabecular bone considering the uncertainties that are primarily caused by image-based modelling and trabecular stiffness orientation. The effect of image-based modelling which focused on the connectivity was also investigated. A stochastic multi-scale method using a first-order perturbation-based and asymptotic homogenisation theory was applied to formulate the stochastically apparent elastic properties of trabecular bone. The effective apparent elastic modulus was predicted with the introduction of a coefficient factor to represent the variation of bone characteristics due to inter-individual differences. The mean value of the predicted effective apparent Young's modulus in principal axis was found at approximately 460 MPa for respective 15.24% of bone volume fraction, and this is in good agreement with other experimental results. The proposed method may provide a reference for the reliable evaluation of the prediction of the apparent elastic properties of trabecular bone.

Shear strength behavior of human trabecular bone

The shear strength of human trabecular bone may influence overall bone strength under fall loading conditions and failure at bone-implant interfaces. Here, we sought to compare shear and compressive yield strengths of human trabecular bone and elucidate the underlying failure mechanisms. We analyzed 54 specimens (5-mm cubes), all aligned with the main trabecular orientation and spanning four anatomic sites, 44 different cadavers, and a wide range of bone volume fraction (0.06-0.38). Micro-CT-based non-linear finite element analysis was used to assess the compressive and shear strengths and the spatial distribution of yielded tissue; the tissue-level constitutive model allowed for kinematic non-linearity and yielding with strength asymmetry. We found that the computed values of both the shear and compressive strengths depended on bone volume fraction via power law relations having an exponent of 1.7 (R(2)=0.95 shear; R(2)=0.97 compression). The ratio of shear to compressive strengths (mean±SD, 0.44±0.16) did not depend on bone volume fraction (p=0.24) but did depend on microarchitecture, most notably the intra-trabecular standard deviation in trabecular spacing (R(2)=0.23, p<0.005). For shear, the main tissue-level failure mode was tensile yield of the obliquely oriented trabeculae. By contrast, for compression, specimens having low bone volume fraction failed primarily by large-deformation-related tensile yield of horizontal trabeculae and those having high bone volume failed primarily by compressive yield of vertical trabeculae. We conclude that human trabecular bone is generally much weaker in shear than compression at the apparent level, reflecting different failure mechanisms at the tissue level.

Trabecular architecture and vertebral fragility in osteoporosis

Osteoporosis heightens vertebral fragility owing to the biomechanical effects of diminished bone structure and composition. These biomechanical effects are only partially explained by loss in bone mass, so additional factors that are independent of bone mass are also thought to play an important role in vertebral fragility. Recent advances in imaging equipment, imaging-processing methods, and computational capacity allow researchers to quantify trabecular architecture in the vertebra at the level of the individual trabecular elements and to derive biomechanics-based measures of architecture that are independent of bone mass and density. These advances have shed light on the role of architecture in vertebral fragility. In addition to the adverse biomechanical consequences associated with trabecular thinning and loss of connectivity, a reduction in the number of vertical trabecular plates appears to be particularly harmful to vertebral strength. In the clinic, detailed architecture analysis is primarily applied to peripheral sites such as the distal radius and tibia. Analysis of trabecular architecture at these peripheral sites has shown mixed results for discriminating between patients with and without a vertebral fracture independent of bone mass, but has the potential to provide unique insight into the effects of therapeutic treatments. Overall, it does appear that trabecular architecture has an independent role on vertebral strength. Additional research is required to determine how and where architecture should be measured in vivo and whether assessment of trabecular architecture in a clinical setting improves prospective fracture risk assessment for the vertebra.