Human Trabecular Bone Samples Research Articles

The application of an isotropic crushable foam model to predict the femoral fracture risk.

For biomechanical simulations of orthopaedic interventions, it is imperative to implement a material model that can realistically reproduce the nonlinear behavior of the bone structure. However, a proper material model that adequately combines the trabecular and cortical bone response is not yet widely identified. The current paper aims to investigate the possibility of using an isotropic crushable foam (ICF) model dependent on local bone mineral density (BMD) for simulating the femoral fracture risk. The elastoplastic properties of fifty-nine human femoral trabecular cadaveric bone samples were determined and combined with existing cortical bone properties to characterize two forms of the ICF model, a continuous and discontinuous model. Subsequently, the appropriateness of this combined material model was evaluated by simulating femoral fracture experiments, and a comparison with earlier published results of a softening Von-Mises (sVM) material model was made. The obtained mechanical properties of the trabecular bone specimens were comparable to previous findings. Furthermore, the ultimate failure load predicted by the simulations of femoral fractures was on average 79% and 90% for the continuous and discontinuous forms of the ICF model and 82% of the experimental value for the sVM material model. Also, the fracture locations predicted by ICF models were comparable to the experiments. In conclusion, a nonlinear material model dependent on BMD was characterized for human femoral bone. Our findings indicate that the ICF model could predict the femoral bone strength and reproduce the variable fracture locations in the experiments.

Application of phase-field fracture theories and digital volume correlation to synchrotron X-ray monitored fractures in human trabecular bone: A case study

Fracture processes of trabecular bone have been studied using various approaches over the years. However, reliable methods to analyse fracture at the single trabecula level are limited. In this study, a digital volume correlation (DVC) and a phase-field fracture model are applied and contrasted for human trabecular bone to analyse its failure under global compression at high resolution.A human trabecular bone sample was fractured in situ under synchrotron-based X-ray micro computed tomography (CT). Reconstructed CT data was then used in DVC algorithms to obtain high-resolution displacement fields in the bone at different load steps. A high-resolution specimen-specific structural mesh was discretized from the CT data and used for the phase-field simulation of the fracturing bone.The DVC analysis showed opening mode cracks as well as shear mode cracks. Strains in cracked regions were analysed. The load distribution in the trabecular structure resulted in two completely separated fracture regions in the sample body. A phenomenon that was also captured in the phase-field model. The results encourage us to believe improvements in boundary conditions and material models are worthwhile pursuing. Findings in this study support further development of a phase-field method to analyse fracture in samples with complex morphology, such as trabecular bone, and the capacity of DVC to quantify strains and slowly growing stable fractures during step-wise loading of trabecular bone.

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).

Sub-trabecular strain evolution in human trabecular bone

To comprehend the most detrimental characteristics behind bone fractures, it is key to understand the material and tissue level strain limits and their relation to failure sites. The aim of this study was to investigate the three-dimensional strain distribution and its evolution during loading at the sub-trabecular level in trabecular bone tissue. Human cadaver trabecular bone samples were compressed in situ until failure, while imaging with high-resolution synchrotron radiation X-ray tomography. Digital volume correlation was used to determine the strains inside the trabeculae. Regions without emerging damage were compared to those about to crack. Local strains in close vicinity of developing cracks were higher than previously reported for a whole trabecular structure and similar to those reported for single isolated trabeculae. Early literature on bone fracture strain thresholds at the tissue level seem to underestimate the maximum strain magnitudes in trabecular bone. Furthermore, we found lower strain levels and a reduced ability to capture detailed crack-paths with increased image voxel size. This highlights the dependence between the observed strain levels and the voxel size and that high-resolution is needed to investigate behavior of individual trabeculae. Furthermore, low trabecular thickness appears to be one predictor of developing cracks. In summary, this study investigated the local strains in whole trabecular structure at sub-trabecular resolution in human bone and confirmed the high strain magnitudes reported for single trabeculae under loading and, importantly extends its translation to the whole trabecular structure.

Comparison of different microCT-based morphology assessment tools using human trabecular bone

MicroCT-based morphological parameters are often used to quantify the structural properties of trabecular bone. Various software tools are available for calculating these parameters. Studies that examine the comparability of their results are rare. Four different software tools were used to analyse a set of 701 microCT images from human trabecular bone samples. Bone volume to total volume (BV/TV), bone surface (BS), trabecular thickness (Tb. Th.) and degree of anisotropy (DA) were evaluated. BV/TV shows very low difference (−0.18 ± 0.15%). The difference in BS could be reduced below 5% if artificial cut surfaces are not included. Tb. Th. and Tb. Sp. show differences of maximal −12% although the same theoretical background is used. DA is most critical with differences from 4.75 ± 3.70% (medtool vs. Scanco), over −38.61 ± 13.15% (BoneJ vs. Scanco), up to 80.52 ± 50.04% (medtool vs. BoneJ). Quantitative results should be considered with caution, especially when comparing different studies. Introducing standardization procedures and the disclosure of underlying algorithms and their respective implementations could improve this issue.

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.

Tissue viscoelasticity is related to tissue composition but may not fully predict the apparent-level viscoelasticity in human trabecular bone – An experimental and finite element study

Trabecular bone is viscoelastic under dynamic loading. However, it is unclear how tissue viscoelasticity controls viscoelasticity at the apparent-level. In this study, viscoelasticity of cylindrical human trabecular bone samples (n=11, male, age 18–78 years) from 11 proximal femurs were characterized using dynamic and stress-relaxation testing at the apparent-level and with creep nanoindentation at the tissue-level. In addition, bone tissue elasticity was determined using scanning acoustic microscope (SAM). Tissue composition and collagen crosslinks were assessed using Raman micro-spectroscopy and high performance liquid chromatography (HPLC), respectively. Values of material parameters were obtained from finite element (FE) models by optimizing tissue-level creep and apparent-level stress-relaxation to experimental nanoindentation and unconfined compression testing values, respectively, utilizing the second order Prony series to depict viscoelasticity. FE simulations showed that tissue-level equilibrium elastic modulus (Eeq) increased with increasing crystallinity (r=0.730, p=.011) while at the apparent-level it increased with increasing hydroxylysyl pyridinoline content (r=0.718, p=.019). In addition, the normalized shear modulus g1 (r=−0.780, p=.005) decreased with increasing collagen ratio (amide III/CH2) at the tissue-level, but increased (r=0.696, p=.025) with increasing collagen ratio at the apparent-level. No significant relations were found between the measured or simulated viscoelastic parameters at the tissue- and apparent-levels nor were the parameters related to tissue elasticity determined with SAM. However, only Eeq, g2 and relaxation time τ1 from simulated viscoelastic values were statistically different between tissue- and apparent-levels (p<.01). These findings indicate that bone tissue viscoelasticity is affected by tissue composition but may not fully predict the macroscale viscoelasticity in human trabecular bone.

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10μm. We show that a trabecular bone RVE in the order of 2×2×2mm3 is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens.For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10−8m2, with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies.

Differences in acoustic impedance of fresh and embedded human trabecular bone samples-Scanning acoustic microscopy and numerical evaluation.

Trabecular bone samples are traditionally embedded and polished for scanning acoustic microscopy (SAM). The effect of sample processing, including dehydration, on the acoustic impedance of bone is unknown. In this study, acoustic impedance of human trabecular bone samples (n = 8) was experimentally assessed before (fresh) and after embedding using SAM and two-dimensional (2-D) finite-difference time domain simulations. Fresh samples were polished with sandpapers of different grit (P1000, P2500, and P4000). Experimental results indicated that acoustic impedance of samples increased significantly after embedding [mean values 3.7 MRayl (fresh), 6.1 MRayl (embedded), p < 0.001]. After polishing with different papers, no significant changes in acoustic impedance were found, even though higher mean values were detected after polishing with finer (P2500 and P4000) papers. A linear correlation (r = 0.854, p < 0.05) was found between the acoustic impedance values of embedded and fresh bone samples polished using P2500 SiC paper. In numerical simulations dehydration increased the acoustic impedance of trabecular bone (38%), whereas changes in surface roughness of bone had a minor effect on the acoustic impedance (-1.56%/0.1 μm). Thereby, the numerical simulations corroborated the experimental findings. In conclusion, acoustic impedance measurement of fresh trabecular bone is possible and may provide realistic material values similar to those of living bone.

Isolation of osteocytes from human trabecular bone

Osteocytes are essential regulators of bone homeostasis. However, they are difficult to study due to their location within the bone mineralised matrix. Although several techniques have been published for the isolation of osteocytes from mouse bone, no such technique has been described for human osteocytes. We have therefore developed a protocol for the isolation of osteocytes from human trabecular bone samples acquired during surgery. The cells were digested from the bone matrix by sequential collagenase and ethylenediaminetetraacetic acid (EDTA) digestions and the cells from later digests displayed characteristic dendritic osteocyte morphology when cultured ex vivo. Furthermore, the cells expressed characteristic osteocyte marker genes, such as E11, dentin matrix protein 1 (DMP1), SOST, matrix extracellular phosphoglycoprotein (MEPE) and phosphate regulating endopeptidase homologue, X-linked (PHEX). In addition, genes associated with osteocyte perilacunar remodelling, including matrix metallopeptidase-13 (MMP13), cathepsin K (CTSK) and carbonic anhydrase 2 (CAR2) were expressed. The cells also responded to parathyroid hormone (PTH) by downregulating SOST mRNA expression and to 1α,25-dihydroxyvitamin D3 (1,25D) by upregulating fibroblast growth factor 23 (FGF23) mRNA expression. Therefore, the cells behave in a similar manner to osteocytes in vivo. These cells represent an important tool in enhancing current knowledge in human osteocyte biology.

Laser-wakefield accelerators as hard x-ray sources for 3D medical imaging of human bone.

A bright μm-sized source of hard synchrotron x-rays (critical energy Ecrit > 30 keV) based on the betatron oscillations of laser wakefield accelerated electrons has been developed. The potential of this source for medical imaging was demonstrated by performing micro-computed tomography of a human femoral trabecular bone sample, allowing full 3D reconstruction to a resolution below 50 μm. The use of a 1 cm long wakefield accelerator means that the length of the beamline (excluding the laser) is dominated by the x-ray imaging distances rather than the electron acceleration distances. The source possesses high peak brightness, which allows each image to be recorded with a single exposure and reduces the time required for a full tomographic scan. These properties make this an interesting laboratory source for many tomographic imaging applications.

1α,25-dihydroxyvitamin D3 stimulates human SOST gene expression and sclerostin secretion

Sclerostin, the SOST gene product, is a negative regulator of bone formation and a positive regulator of bone resorption. In this study, treatment of human primary osteoblasts, including cells differentiated to an osteocyte-like stage, with 1α,25-dihydroxyvitaminD3 (1,25D) resulted in the dose-dependent increased expression of SOST mRNA. A similar effect was observed in human trabecular bone samples cultured ex vivo, and in osteocyte-like cultures of differentiated SAOS2 cells. Treatment of SAOS2 cells with 1,25D resulted in the production and secretion of sclerostin protein. In silico analysis of the human SOST gene revealed a single putative DR3-type vitamin D response element (VDRE) at position −6216 bp upstream of the transcription start site (TSS). This sequence was confirmed to have strong VDRE activity by luciferase reporter assays and electrophoretic mobility shift analysis (EMSA). Sequence substitution in the VDR/RXR half-sites abolished VDRE reporter activity and binding of nuclear proteins. A 6.3 kb fragment of the human proximal SOST promoter demonstrated responsiveness to 1,25D. The addition of the evolutionary conserved region 5 (ECR5), a known bone specific enhancer region, ahead of the 6.3 kb fragment increased basal promoter activity but did not increase 1,25D responsiveness. Site-specific mutagenesis abolished the responsiveness of the 6.3 kb promoter to 1,25D. We conclude that 1,25D is a direct regulator of human SOST gene and sclerostin protein expression, extending the pathways of control of sclerostin expression. At least some of this responsiveness is mediated by the identified classical VDRE however the nature of the transcriptional regulation by 1,25D warrants further investigation.

Creep of trabecular bone from the human proximal tibia

Creep is the deformation that occurs under a prolonged, sustained load and can lead to permanent damage in bone. Creep in bone is a complex phenomenon and varies with type of loading and local mechanical properties. Human trabecular bone samples from proximal tibia were harvested from a 71-year old female cadaver with osteoporosis. The samples were initially subjected to one cycle load up to 1% strain to determine the creep load. Samples were then loaded in compression under a constant stress for 2h and immediately unloaded. All tests were conducted with the specimens soaked in phosphate buffered saline with proteinase inhibitors at 37°C. Steady state creep rate and final creep strain were estimated from mechanical testing and compared with published data. The steady state creep rate correlated well with values obtained from bovine tibial and human vertebral trabecular bone, and was higher for lower density samples. Tissue architecture was analyzed by micro-computed tomography (μCT) both before and after creep testing to assess creep deformation and damage accumulated. Quantitative morphometric analysis indicated that creep induced changes in trabecular separation and the structural model index. A main mode of deformation was bending of trabeculae.

Sclerostin Regulates Release of Bone Mineral by Osteocytes by Induction of Carbonic Anhydrase 2

The osteocyte product sclerostin is emerging as an important paracrine regulator of bone mass. It has recently been shown that osteocyte production of receptor activator of NF-κB ligand (RANKL) is important in osteoclastic bone resorption, and we reported that exogenous treatment of osteocytes with sclerostin can increase RANKL-mediated osteoclast activity. There is good evidence that osteocytes can themselves liberate mineral from bone in a process known as osteocytic osteolysis. In the current study, we investigated sclerostin-stimulated mineral dissolution by human primary osteocyte-like cells (hOCy) and mouse MLO-Y4 cells. We found that sclerostin upregulated osteocyte expression of carbonic anhydrase 2 (CA2/Car2), cathepsin K (CTSK/Ctsk), and tartrate-resistant acid phosphatase (ACP5/Acp5). Because acidification of the extracellular matrix is a critical step in the release of mineral from bone, we further examined the regulation by sclerostin of CA2. Sclerostin stimulated CA2 mRNA and protein expression in hOCy and in MLO-Y4 cells. Sclerostin induced a decrease in intracellular pH (pHi) in both cell types as well as a decrease in extracellular pH (pHo) and the release of calcium ions from mineralized substrate. These effects were reversed in the co-presence of the carbonic anhydrase inhibitor, acetozolamide. Car2-siRNA knockdown in MLO-Y4 cells significantly inhibited the ability of sclerostin to both reduce the pHo and release calcium from a mineralized substrate. Knockdown in MLO-Y4 cells of each of the putative sclerostin receptors, Lrp4, Lrp5 and Lrp6, using siRNA, inhibited the sclerostin induction of Car2, Catk and Acp5 mRNA, as well as pHo and calcium release. Consistent with this activity of sclerostin resulting in osteocytic osteolysis, human trabecular bone samples treated ex vivo with recombinant human sclerostin for 7 days exhibited an increased osteocyte lacunar area, an effect that was reversed by the co-addition of acetozolamide. These findings suggest a new role for sclerostin in the regulation of perilacunar mineral by osteocytes.

Methodological approach for the detection of both microdamage and fluorochrome labels in ewe bone and human trabecular bone

The purpose of this study was to adapt various staining methods for the detection of microdamage in human bone, while preserving tetracycline labels. We describe two staining methods using calcein green and xylenol orange, first developed in ewe bone samples and validated in human trabecular bone samples. In ewe bones, we found that calcein green at 0.5 mM concentration diluted in 100% ethanol as well as xylenol orange at 5 mM were the most adequate fluorochromes both to detect microdamage and preserve the double tetracycline labeling. These results were verified in human trabecular bone (iliac crest for the tetracycline label, and vertebral bone for the double labeling). Results obtained in human bone samples were identical to those in ewes, so this combination of fluorochromes is now used in our laboratory.

Experimental poromechanics of trabecular bone strength: Role of Terzaghi's effective stress and of tissue level stress fluctuations

In the 1920s and 1930s, Terzaghi and coworkers realized that the failure of various porous geomaterials under internal pore pressure is given through evaluating the failure function for the same materials at zero pressure, with ‘total stress plus pore pressure’ instead of ‘total stress alone’ as argument. As to check, probably for the first time, the relevance of this (‘Terzaghi's’) failure criterion for trabecular bone, a series of poromechanical and ultrasonic tests was conducted on bovine and human trabecular bone samples. Evaluation of respective experimental results within the theoretical framework of microporomechanics showed that (i) Terzaghi's effective stress indeed governs trabecular bone failure, (ii) deviatoric stress states at the level of the solid bone matrix (also called tissue level) are primary candidates for initiating bone failure, and (iii) the high heterogeneity of these deviatoric tissue stresses, which increases with increasing intertrabecular porosity, governs the overall failure of trabecular bone. Result (i) lets us use the widely documented experimental results for strength values of bone samples without pore pressure, as to predict failure of the same bone samples under internal pore pressure. Result (ii) suggests a favorable mode for strength modeling of solid bone matrix. Finally, result (iii) underlines the suitability of microfinite element simulations for trabecular bone microstructures.

Structural parameters of normal and osteoporotic human trabecular bone are affected differently by microCT image resolution

This study employed microCT to investigate whether image resolution affects bone structural parameters differently in healthy normal and osteoporotic trabecular bone. With increasing image voxel size, the originally detected differences between sample groups diminished. The results suggest that structural differences may not be reliably detected with clinical scanners. Structural parameters of bone reflect its health status, but are highly dependent on the image resolution. We hypothesized that image resolution affects bone structural parameters differently in normal and osteoporotic trabecular bone. Human trabecular bone samples from the iliac crest and the knee were analyzed (normal n = 11, osteoporotic n = 15) using a high-resolution microCT (14 or 18µm voxel sizes). Images were re-sampled to voxel sizes 1-16 times larger than the original image and thresholded with global or local adaptive algorithms. Absolute and normalized values of each structural parameter were calculated, and the effect of decreasing image resolution was compared between the normal and osteoporotic samples. Normal and osteoporotic samples had different (p < 0.05) absolute bone volume fractions. However, the normalized values showed that the osteoporotic samples were more prone to errors (p < 0.05) with increased voxel size. The absolute values of trabecular number, trabecular separation, degree of anisotropy, and structure model index were different between the groups at the original voxel size (p < 0.05), but at voxel sizes between 60 and 110µm, those differences were no longer significant. The results suggest that structural differences between osteoporotic and normal trabecular bone may not be reliably detected with clinical CT scanners providing image voxel sizes above 100µm.

Comparison of optical coherence tomography, microcomputed tomography, and histology at a three-dimensionally imaged trabecular bone sample

We investigate optical coherence tomography (OCT) as a method for imaging bone. The OCT images are compared directly to those of the standard methods of bone histology and microcomputed tomography (microCT) on a single, fixed human femoral trabecular bone sample. An advantage of OCT over bone histology is its noninvasive nature. OCT also images the lamellar structure of trabeculae at slightly higher contrast than normal bone histology. While microCT visualizes the trabecular framework of the whole sample, OCT can image additionally cells with a penetration depth limited approximately to 1 mm. The most significant advantage of OCT, however, is the absence of toxic effects (no ionizing radiation), i.e., continuous images may be made and individual cell tracking may be performed. The penetration depth of OCT, however, limits its use to small animal models and small bone organ cultures.

Relationship between ultrasonic parameters and apparent trabecular bone elastic modulus: A numerical approach

The physical principles underlying quantitative ultrasound (QUS) measurements in trabecular bone are not fully understood. The translation of QUS results into bone strength remains elusive. However, ultrasound being mechanical waves, it is likely to assess apparent bone elasticity. The aim of this study is to derive the sensitivity of QUS parameters to variations of apparent bone elasticity, a surrogate for strength. The geometry of 34 human trabecular bone samples cut in the great trochanter was reconstructed using 3-D synchrotron micro-computed tomography. Finite-difference time-domain simulations coupled to 3-D micro-structural models were performed in the three perpendicular directions for each sample and each direction. A voxel-based micro-finite element linear analysis was employed to compute the apparent Young's modulus ( E) of each sample for each direction. For the antero-posterior direction, the predictive power of speed of sound and normalized broadband ultrasonic attenuation to assess E was equal to 0.9 and 0.87, respectively, which is better than what is obtained using bone density alone or coupled with micro-architectural parameters and of the same order of what can be achieved with the fabric tensor approach. When the direction of testing is parallel to the main trabecular orientation, the predictive power of QUS parameters decreases and the fabric tensor approach always gives the best results. This decrease can be explained by the presence of two longitudinal wave modes. Our results, which were obtained using two distinct simulation tools applied on the same set of samples, highlight the potential of QUS techniques to assess bone strength.

Sampling sphere orientation distribution: An efficient method to quantify trabecular bone fabric on grayscale images

A novel Sampling Sphere Orientation Distribution (SSOD) method based on mobile sampling spheres is developed for describing microstructural anisotropy of trabecular bone using grayscale images. Efficient implementation of SSOD on segmented and unsegmented 3D microCT images of human trabecular bone samples from different anatomical locations is demonstrated. The second order fabric tensor of SSOD corresponds well with the one derived from the mean intercept length (MIL) method applied on segmented images. The results of SSOD are extended to higher order fabric approximations and the effect of sampling sphere radius is examined. Finally, performance of the method on artificial microstructures is presented.