Measurement of structural anisotropy in femoral trabecular bone using clinical-resolution CT images

Discrepancies in finite-element model predictions of bone strength may be attributed to the simplified modeling of bone as an isotropic structure due to the resolution limitations of clinical-level Computed Tomography (CT) data. The aim of this study is to calculate the preferential orientations of bone (the principal directions) and the extent to which bone is deposited more in one direction compared to another (degree of anisotropy). Using 100 femoral trabecular samples, the principal directions and degree of anisotropy were calculated with a Gradient Structure Tensor (GST) and a Sobel Structure Tensor (SST) using clinical-level CT. The results were compared against those calculated with the gold standard Mean-Intercept-Length (MIL) fabric tensor using micro-CT. There was no significant difference between the GST and SST in the calculation of the main principal direction (median error=28°), and the error was inversely correlated to the degree of transverse isotropy (r=−0.34, p<0.01). The degree of anisotropy measured using the structure tensors was weakly correlated with the MIL-based measurements (r=0.2, p<0.001). Combining the principal directions with the degree of anisotropy resulted in a significant increase in the correlation of the tensor distributions (r=0.79, p<0.001). Both structure tensors were robust against simulated noise, kernel sizes, and bone volume fraction. We recommend the use of the GST because of its computational efficiency and ease of implementation. This methodology has the promise to predict the structural anisotropy of bone in areas with a high degree of anisotropy, and may improve the in vivo characterization of bone.

Effects of zoledronate versus placebo on spine bone mineral density and microarchitecture assessed by the trabecular bone score in postmenopausal women with osteoporosis: a three-year study

The trabecular bone score (TBS) is an index of bone microarchitectural texture calculated from anteroposterior dual-energy X-ray absorptiometry (DXA) scans of the lumbar spine (LS) that predicts fracture risk, independent of bone mineral density (BMD). The aim of this study was to compare the effects of yearly intravenous zoledronate (ZOL) versus placebo (PLB) on LS BMD and TBS in postmenopausal women with osteoporosis. Changes in TBS were assessed in the subset of 107 patients recruited at the Department of Osteoporosis of the University Hospital of Berne, Switzerland, who were included in the HORIZON trial. All subjects received adequate calcium and vitamin D3. In these patients randomly assigned to either ZOL (n = 54) or PLB (n = 53) for 3 years, BMD was measured by DXA and TBS assessed by TBS iNsight (v1.9) at baseline and 6, 12, 24, and 36 months after treatment initiation. Baseline characteristics (mean ± SD) were similar between groups in terms of age, 76.8 ± 5.0 years; body mass index (BMI), 24.5 ± 3.6 kg/m(2) ; TBS, 1.178 ± 0.1 but for LS T-score (ZOL-2.9 ± 1.5 versus PLB-2.1 ± 1.5). Changes in LS BMD were significantly greater with ZOL than with PLB at all time points (p < 0.0001 for all), reaching +9.58% versus +1.38% at month 36. Change in TBS was significantly greater with ZOL than with PLB as of month 24, reaching +1.41 versus-0.49% at month 36; p = 0.031, respectively. LS BMD and TBS were weakly correlated (r = 0.20) and there were no correlations between changes in BMD and TBS from baseline at any visit. In postmenopausal women with osteoporosis, once-yearly intravenous ZOL therapy significantly increased LS BMD relative to PLB over 3 years and TBS as of 2 years.

Microstructural Parameters of Bone Evaluated Using HR-pQCT Correlate with the DXA-Derived Cortical Index and the Trabecular Bone Score in a Cohort of Randomly Selected Premenopausal Women.

BACKGROUND Areal bone mineral density is predictive for fracture risk. Microstructural bone parameters evaluated at the appendicular skeleton by high-resolution peripheral quantitative computed tomography (HR-pQCT) display differences between healthy patients and fracture patients. With the simple geometry of the cortex at the distal tibial diaphysis, a cortical index of the tibia combining material and mechanical properties correlated highly with bone strength ex vivo. The trabecular bone score derived from the scan of the lumbar spine by dual-energy X-ray absorptiometry (DXA) correlated ex vivo with the micro architectural parameters. It is unknown if these microstructural correlations could be made in healthy premenopausal women. METHODS Randomly selected women between 20-40 years of age were examined by DXA and HR-pQCT at the standard regions of interest and at customized sub regions to focus on cortical and trabecular parameters of strength separately. For cortical strength, at the distal tibia the volumetric cortical index was calculated directly from HR-pQCT and the areal cortical index was derived from the DXA scan using a Canny threshold-based tool. For trabecular strength, the trabecular bone score was calculated based on the DXA scan of the lumbar spine and was compared with the corresponding parameters derived from the HR-pQCT measurements at radius and tibia. RESULTS Seventy-two healthy women were included (average age 33.8 years, average BMI 23.2 kg/m(2)). The areal cortical index correlated highly with the volumetric cortical index at the distal tibia (R  =  0.798). The trabecular bone score correlated moderately with the microstructural parameters of the trabecular bone. CONCLUSION This study in randomly selected premenopausal women demonstrated that microstructural parameters of the bone evaluated by HR-pQCT correlated with the DXA derived parameters of skeletal regions containing predominantly cortical or cancellous bone. Whether these indexes are suitable for better predictions of the fracture risk deserves further investigation.

Scaling relations between trabecular bone volume fraction and microstructure at different skeletal sites

In this study, we investigated the scaling relations between trabecular bone volume fraction (BV/TV) and parameters of the trabecular microstructure at different skeletal sites. Cylindrical bone samples with a diameter of 8mm were harvested from different skeletal sites of 154 human donors in vitro: 87 from the distal radius, 59/69 from the thoracic/lumbar spine, 51 from the femoral neck, and 83 from the greater trochanter. μCT images were obtained with an isotropic spatial resolution of 26μm. BV/TV and trabecular microstructure parameters (TbN, TbTh, TbSp, scaling indices (< > and σ of α and αz), and Minkowski Functionals (Surface, Curvature, Euler)) were computed for each sample. The regression coefficient β was determined for each skeletal site as the slope of a linear fit in the double-logarithmic representations of the correlations of BV/TV versus the respective microstructure parameter. Statistically significant correlation coefficients ranging from r=0.36 to r=0.97 were observed for BV/TV versus microstructure parameters, except for Curvature and Euler. The regression coefficients β were 0.19 to 0.23 (TbN), 0.21 to 0.30 (TbTh), −0.28 to −0.24 (TbSp), 0.58 to 0.71 (Surface) and 0.12 to 0.16 (<α>), 0.07 to 0.11 (<αz>), −0.44 to −0.30 (σ(α)), and −0.39 to −0.14 (σ(αz)) at the different skeletal sites. The 95% confidence intervals of β overlapped for almost all microstructure parameters at the different skeletal sites. The scaling relations were independent of vertebral fracture status and similar for subjects aged 60–69, 70–79, and >79years. In conclusion, the bone volume fraction–microstructure scaling relations showed a rather universal character.

Assessment of Transverse Isotropy in Clinical-Level CT Images of Trabecular Bone Using the Gradient Structure Tensor

The aim of this study was to develop a GST-based methodology for accurately measuring the degree of transverse isotropy in trabecular bone. Using femoral sub-regions scanned in high-resolution peripheral QCT (HR-pQCT) and clinical-level-resolution QCT, trabecular orientation was evaluated using the mean intercept length (MIL) and the gradient structure tensor (GST) on the HR-pQCT and QCT data, respectively. The influence of local degree of transverse isotropy (DTI) and bone mineral density (BMD) was incorporated into the investigation. In addition, a power based model was derived, rendering a 1:1 relationship between GST and MIL eigenvalues. A specific DTI threshold (DTI thres) was found for each investigated size of region of interest (ROI), above which the estimate of major trabecular direction of the GST deviated no more than 30° from the gold standard MIL in 95% of the remaining ROIs (mean error: 16°). An inverse relationship between ROI size and DTI thres was found for discrete ranges of BMD. A novel methodology has been developed, where transversal isotropic measures of trabecular bone can be obtained from clinical QCT images for a given ROI size, DTI thres and power coefficient. Including DTI may improve future clinical QCT finite-element predictions of bone strength and diagnoses of bone disease.

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. Morphologyelasticity 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 reconstructions of cubic trabecular bone samples extracted from femur, radius, vertebrae and iliac crest were analysed. Their morphology was assessed via 25 variables and their stiffness tensor (inline image) was computed from six independent load cases using micro finite element 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 multi-linear regression modelling the dependent variable inline image. The contribution of each independent variable was evaluated (ANOVA). Our results show that BV/TV is the best determinant of inline image (inline image=0.889), especially in combination with fabric (inline image=0.968). Including the other independent predictors hardly affected the amount of variance explained by the model (inline image=0.975). Across all anatomical sites, BV/TV explained 87% of the variance of the bone elastic properties. Fabric 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 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 post-elastic properties.

The Initial Slope of the Variogram, Foundation of the Trabecular Bone Score, Is Not or Poorly Associated With Vertebral Strength

Trabecular bone score (TBS) rests on the textural analysis of DXA to reflect the decay in trabecular structure characterising osteoporosis. Yet, its discriminative power in fracture studies remains incomprehensible as prior biomechanical tests found no correlation with vertebral strength. To verify this result possibly due to an unrealistic set-up and to cover a wide range of loading scenarios, the data from three previous biomechanical studies using different experimental settings was used. They involved the compressive failure of 62 human lumbar vertebrae loaded 1) via intervertebral discs to mimic the in vivo situation (“full vertebra”), 2) via the classical endplate embedding (“vertebral body”) or 3) via a ball joint to induce anterior wedge failure (“vertebral section”). HR-pQCT scans acquired prior testing were used to simulate anterior-posterior DXA from which areal bone mineral density (aBMD) and the initial slope of the variogram (ISV), the early definition of TBS, were evaluated. Finally, the relation of aBMD and ISV with failure load (Fexp) and apparent failure stress (σexp) was assessed and their relative contribution to a multi-linear model was quantified via ANOVA. We found that, unlike aBMD, ISV did not significantly correlate with Fexp and σexp, except for the “vertebral body” case (r2 = 0.396, p = 0.028). Aside from the “vertebra section” set-up where it explained only 6.4% of σexp (p = 0.037), it brought no significant improvement to aBMD. These results indicate that ISV, a replica of TBS, is a poor surrogate for vertebral strength no matter the testing set-up, which supports the prior observations and raises a fortiori the question of the deterministic factors underlying the statistical relationship between TBS and vertebral fracture risk.

Experimental validation of a nonlinear μ FE model based on cohesive-frictional plasticity for trabecular bone

Trabecular bone is a porous mineralized tissue playing a major load bearing role in the human body. Prediction of age-related and disease-related fractures and the behavior of bone implant systems needs a thorough understanding of its structure-mechanical property relationships, which can be obtained using microcomputed tomography-based finite element modeling. In this study, a nonlinear model for trabecular bone as a cohesive-frictional material was implemented in a large-scale computational framework and validated by comparison of μFE simulations with experimental tests in uniaxial tension and compression. A good correspondence of stiffness and yield points between simulations and experiments was found for a wide range of bone volume fraction and degree of anisotropy in both tension and compression using a non-calibrated, average set of material parameters. These results demonstrate the ability of the model to capture the effects leading to failure of bone for three anatomical sites and several donors, which may be used to determine the apparent behavior of trabecular bone and its evolution with age, disease, and treatment in the future.

Comparison of Mixed and Kinematic Uniform Boundary Conditions in Homogenized Elasticity of Femoral Trabecular Bone Using Microfinite Element Analyses

Mechanical properties of human trabecular bone play an important role in age-related bone fragility and implant stability. Micro-finite element (microFE) analysis allows computing the apparent elastic properties of trabecular bone biopsies, but the results depend on the type of applied boundary conditions (BCs). In this study, 167 femoral trabecular cubic biopsies with a side length of 5.3 mm were analyzed using microFE analysis to compare their stiffness systematically with kinematic uniform boundary conditions (KUBCs) and periodicity-compatible mixed uniform boundary conditions (PMUBCs). The obtained elastic constants were then used in the volume fraction and fabric-based orthotropic Zysset-Curnier model to identify their respective model parameters. As expected, PMUBCs lead to more compliant apparent elastic properties than KUBCs, especially in shear. The differences in stiffness decreased with bone volume fraction and mean intercept length. Unlike KUBCs, PMUBCs were sensitive to heterogeneity of the biopsies. The Zysset-Curnier model predicted apparent elastic constants successfully in both cases with adjusted coefficients of determination of 0.986 for KUBCs and 0.975 for PMUBCs. The role of these boundary conditions in finite element analyses of whole bones and bone-implant systems will need to be investigated in future work.

Effect of boundary conditions on yield properties of human femoral trabecular bone

Trabecular bone plays an important mechanical role in bone fractures and implant stability. Homogenized nonlinear finite element (FE) analysis of whole bones can deliver improved fracture risk and implant loosening assessment. Such simulations require the knowledge of mechanical properties such as an appropriate yield behavior and criterion for trabecular bone. Identification of a complete yield surface is extremely difficult experimentally but can be achieved in silico by using micro-FE analysis on cubical trabecular volume elements. Nevertheless, the influence of the boundary conditions (BCs), which are applied to such volume elements, on the obtained yield properties remains unknown. Therefore, this study compared homogenized yield properties along 17 load cases of 126 human femoral trabecular cubic specimens computed with classical kinematic uniform BCs (KUBCs) and a new set of mixed uniform BCs, namely periodicity-compatible mixed uniform BCs (PMUBCs). In stress space, PMUBCs lead to 7–72 % lower yield stresses compared to KUBCs. The yield surfaces obtained with both KUBCs and PMUBCs demonstrate a pressure-sensitive ellipsoidal shape. A volume fraction and fabric-based quadric yield function successfully fitted the yield surfaces of both BCs with a correlation coefficient R2≥0.93. As expected, yield strains show only a weak dependency on bone volume fraction and fabric. The role of the two BCs in homogenized FE analysis of whole bones will need to be investigated and validated with experimental results at the whole bone level in future studies.

Prediction of Trabecular Bone Anisotropy from Quantitative Computed Tomography using Supervised Learning and a Novel Morphometric Feature Descriptor

Patient-specific biomechanical models including local bone mineral density and anisotropy have gained importance for assessing musculoskeletal disorders. However the trabecular bone anisotropy captured by high-resolution imaging is only available at the peripheral skeleton in clinical practice. In this work, we propose a supervised learning approach to predict trabecular bone anisotropy that builds on a novel set of pose invariant feature descriptors. The statistical relationship between trabecular bone anisotropy and feature descriptors were learned from a database of pairs of high resolution QCT and clinical QCT reconstructions. On a set of leave-one-out experiments, we compared the accuracy of the proposed approach to previous ones, and report a mean prediction error of 6% for the tensor norm, 6% for the degree of anisotropy and 19◦ for the principal tensor direction. These findings show the potential of the proposed approach to predict trabecular bone anisotropy from clinically available QCT images.