Irina Sidorenko

Strength through structure: visualization and local assessment of the trabecular bone structure

The visualization and subsequent assessment of the inner human bone structures play an important role for better understanding the disease- or drug-induced changes of bone in the context of osteoporosis giving prospect for better predictions of bone strength and thus of the fracture risk of osteoporotic patients. In this work, we show how the complex trabecular bone structure can be visualized using μCT imaging techniques at an isotropic resolution of 26 μm. We quantify these structures by calculating global and local topological and morphological measures, namely Minkowski functionals (MFs) and utilizing the (an-)isotropic scaling index method (SIM) and by deriving suitable texture measures based on MF and SIM. Using a sample of 151 specimens taken from human vertebrae in vitro, we correlate the texture measures with the mechanically measured maximum compressive strength (MCS), which quantifies the strength of the bone probe, by using Pearsons correlation coefficient. The structure parameters derived from the local measures yield good correlations with the bone strength as measured in mechanical tests. We investigate whether the performance of the texture measures depends on the MCS value by selecting different subsamples according to MCS. Considering the whole sample the results for the newly defined parameters are better than those obtained for the standard global histomorphometric parameters except for bone volume/total volume (BV/TV). If a subsample consisting only of weak bones is analysed, the local structural analysis leads to similar and even better correlations with MCS as compared to BV/TV. Thus, the MF and SIM yield additional information about the stability of the bone especially in the case of weak bones, which corroborates the hypothesis that the bone structure (and not only its mineral mass) constitutes an important component of bone stability.

Prediction of bone strength by μCT and MDCT-based finite-element-models: How much spatial resolution is needed?

OBJECTIVES Finite-element-models (FEM) are a promising technology to predict bone strength and fracture risk. Usually, the highest spatial resolution technically available is used, but this requires excessive computation time and memory in numerical simulations of large volumes. Thus, FEM were compared at decreasing resolutions with respect to local strain distribution and prediction of failure load to (1) validate MDCT-based FEM and to (2) optimize spatial resolution to save computation time. MATERIALS AND METHODS 20 cylindrical trabecular bone specimens (diameter 12 mm, length 15-20mm) were harvested from elderly formalin-fixed human thoracic spines. All specimens were examined by micro-CT (isotropic resolution 30 μm) and whole-body multi-row-detector computed tomography (MDCT, 250 μm × 250 μm × 500 μm). The resolution of all datasets was lowered in eight steps to ~ 2,000 μm × 2000 μm × 500 μm and FEM were calculated at all resolutions. Failure load was determined by biomechanical testing. Probability density functions of local micro-strains were compared in all datasets and correlations between FEM-based and biomechanically measured failure loads were determined. RESULTS The distribution of local micro-strains was similar for micro-CT and MDCT at comparable resolutions and showed a shift toward higher average values with decreasing resolution, corresponding to the increasing apparent trabecular thickness. Small micro-strains (εeff<0.005) could be calculated down to 250 μm × 250 μm × 500 μm. Biomechanically determined failure load showed significant correlations with all FEM, up to r=0.85 and did not significantly change with lower resolution but decreased with high thresholds, due to loss of trabecular connectivity. CONCLUSION When choosing connectivity-preserving thresholds, both micro-CT- and MDCT-based finite-element-models well predicted failure load and still accurately revealed the distribution of local micro-strains in spatial resolutions, available in vivo (250 μm × 250 μm × 500 μm), that thus seemed to be the optimal compromise between high accuracy and low computation time.

Reproducibility of trabecular bone structure measurements of the distal radius at 1.5 and 3.0 T magnetic resonance imaging.

Abstract The purpose of this study was to assess and compare the reproducibility of trabecular bone structure measurements of the distal radius at 1.5 and 3.0 T magnetic resonance imaging (MRI). Root mean square reproducibility errors ranged from 0.69% to 4.94% at 1.5 T MRI and from 0.38% to 5.80% at 3.0 T MRI. Thus, reproducibility errors of trabecular bone structure measurements are overall in an acceptable range and similar at 1.5 and 3.0 T MRI.

Assessing methods for characterising local and global structural and biomechanical properties of the trabecular bone network

We apply noval techniques, the Scaling Index Method (SIM), which reveals local topology of the structure, and the Minkowski Functionals (MF), which provide four global topological characteristics, to assess strength of the trabecular network of the human bone. We compare capabilities of these methods with the standard analysis, biomechanical Finite Element Method (FEM) and morphological parameters, in prediction of bone strength and fracture risk. Our study is based on a sample of 151 specimens taken from the trabecular part of human thoracic and lumbar vertebrae in vitro, visualised using µCT imaging (isotropic resolution 26µm) and tested by uniaxial compression. The sample of donors is heterogeneous, consisting of 58 male and 54 female cadavers with a mean age of 80 ±10 years. To estimate the predictive power of the methods, we correlate texture measures derived from µCT images with the maximum compressive strength (MCS) as obtained in biomechanical tests. A linear regression analysis reveals that the failure load estimated by FEM shows the highest correlation with MCS (Pearsons correlation coefficient r=0.76). None of the methods in current study is superior to the FEM: morphometric parameters give r<0.5, global topological characteristics show r=0.73 for the first Minkowski Functional MF₁, which coincides with bone volume fraction BV/TV and r=0.61 for the second Minkowski functional MF₂, which coincides with bone surface BS. Although scaling indices provided by SIM correlate only moderately with MCS (r=0.55), texture measures based on the nonlinear combination of local (SIM) and global (MF) topological characteristics demonstrate high correlation with experimental MCS (r=0.74) and with failure load estimated by FEM (r=0.95). Additional advantage of the proposed texture measures is possibility to reveal the role of the topologically different trabecular structure elements for the bone strength.

Assessment of the human trabecular bone structure using Minkowski functionals

Osteoporosis is bone disease which leads to low bone mass and the deterioration of the bone micro-architecture. Rarefied bone structures are more susceptible to fractures which are the worst complications of osteoporosis. Bone mineral density is considered to be the standard technique for predicting the bone strength and the effects of drug therapy. However, other properties of the bone like the trabecular structure and connectivity may also contribute. Here, we analyze μ-CT tomographic images for a sample of 151 specimens taken from human vertebrae in vitro. Using the local structural characterization of the bone trabecular network given by isotropic and anisotropic scaling indices, we generate structural decompositions of the μ-CT image and quantify the resulting patterns applying topological measures, namely the Minkowski Functionals (MF). The values of the MF are then used to assess the biomechanical properties of trabecular bone via a correlation analysis. Biomechanical properties were quantified by the maximum compressive strength calculated in an uniaxial compression test. We compare our results with those obtained using standard global histomorphometric parameters and the bone fraction BV/TV . Results obtained using structural decompositions obtained from anisotropic scaling indices were superior to those given by isotropic scaling indices. The highest correlation coefficient (r = 0.72) was better than those obtained for the standard global histomorphometric parameters and only comparable with the one given by BV/TV. Our results suggest that plate-like and dense column-like structures aligned along the direction of the external force play a relevant role for the prediction of bone strength.

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 (), 0.07 to 0.11 (), -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.

Role of trabecular microfractures in failure of human vertebrae estimated by the finite element method

Spine fractures are the most frequent complication of osteoporosis, a disease characterized by low bone mass and structural deterioration of bone tissue. In case of the spine, the trabecular network plays the main role in load carrying and distribution. A correct description of mechanical properties of this bone structure helps to differentiate between strong and weak bones and can be useful for fracture prediction and treatment monitoring. By means of the finite element method (FEM), applied to μCT images, we modelled biomechanical processes in probes during loading and correlated the estimated failure load with the maximum compressive strength (MCS), obtained in real biomechanical tests. We studied a sample of 151 specimens taken from the trabecular part of human vertebrae in vitro, visualised using μCT imaging at an isotropic resolution of 26μm and tested by uniaxial compression. Besides the standard way of estimating failure load, which takes into account only strong micro-fractures, we also included small micro-fractures, what improved the correlation with MCS (Pearsons correlation coefficient r=0.78 vs. r=0.58). This correlation coefficient was larger than that for both the standard morphometric parameters (r=0.73 for bone volume fraction) and for texture measures defined by the local (an-) isotropic scaling indices method (r=0.55) and Minkowski Functionals (r=0.61). However, the performance of the FEM was different for subsamples selected according to the MCS value. The correlation increased for strong specimens (r=0.88), slightly decreased for weak specimens (r=0.68) and markedly dropped for specimens with medium MCS, e.g. between 60

Comparison and combination of scaling index method and Minkowski Functionals in the analysis of high resolution magnetic resonance images of the distal radius in vitro

High resolution magnetic resonance (HRMR) imaging can reveal major characteristics of trabecular bone. The quantification of this trabecular micro architecture can be useful for better understanding the progression of osteoporosis and improve its diagnosis. In the present work we applied the scaling index method (SIM) and Minkowski Functionals (MF) for analysing tomographic images of distal radius specimens in vitro. For both methods, the correlation with the maximum compressive strength (MCS) as determined in a biomechanical test and the diagnostic performance with regard to the spine fracture status were calculated. Both local SIM and global MF methods showed significantly better results compared to bone mineral density measured by quantitative computed tomography. The receiver operating characteristic analysis for differentiating fractured and non-fractured subjects revealed area under the curve (AUC) values of 0.716 for BMD, 0.897 for SIM and 0.911 for MF. The correlation coefficients with MCS were 0.6771 for BMD, 0.843 for SIM and 0.772 for MF. We simulated the effect of perturbations, namely noise effects and intensity variations. Overall, MF method was more sensitive to noise than SIM. A combination of SIM and MF methods could, however, increase AUC values from 0.85 to 0.89 and correlation coefficients from 0.71 to 0.82. In conclusion, local SIM and global MF techniques can successfully be applied for analysing HRMR image data. Since these methods are complementary, their combination offers a new possibility of describing MR images of the trabecular bone, especially noisy ones.

Structure based classification of μ-CT images of human trabecular bone using local Minkowski Functionals

We analyse μ-CT tomographic images of human trabecular bone in vitro. We consider a sample consisting of 201 bone specimens harvested from six different skeletal sites within a narrow range of bone fraction values. Using the characterization of the trabecular bone network given by local Minkowski Functionals, we apply classification algorithms in order to reveal structural similarities in the sample. Clusters show some interesting specific structural features, like compact, porous, and fragmented structures. The contribution of the different skeletal sites to these clusters indicate some variability due to intrinsic structural differences of the specific skeletal site.

Studying the effect of noise on the performance of 2D and 3D texture measures for quantifying the trabecular bone structure as obtained with high resolution MR imaging at 3 Tesla

3.0 Tesla MRI devices are becoming popular in clinical applications since they render images with a higher signal-tonoise ratio than the former 1.5 Tesla MRI devices. Here, we investigate if higher signal-to-noise ratio can be beneficial for a quantitative image analysis in the context of bone research. We performed a detailed analysis of the effect of noise on the performance of 2D morphometric linear measures and a 3D nonlinear measure with respect to their correlation with biomechanical properties of the bone expressed by the maximum compressive strength. The performance of both 2D and 3D texture measures was relatively insensitive to superimposed artificial noise. This finding suggests that MR sequences for visualizing bone structures at 3T should rather be optimized to spatial resolution (or scanning time) than to signal-to-noise ratio.