Christoph W. Raeth

Local 3D scaling properties for the analysis of trabecular bone extracted from high-resolution magnetic resonance imaging of human trabecular bone : Comparison with bone mineral density in the prediction of biomechanical strength in vitro

Rationale and Objectives. A novel, nonlinear morphologic measure [&Dgr;P(&agr;)] based on local 3D scaling properties was applied to high-resolution magnetic resonance images (HR-MRI) of human trabecular bone to predict biomechanical strength in vitro. Methods. We extracted &Dgr;P(&agr;) and traditional morphologic parameters (apparent trabecular volume fraction, apparent trabecular separation) from HR-MR images of 32 femoral and 13 spinal bone specimens. Furthermore, bone mineral density (BMD) and maximum compressive strength (MCS) were determined. The morphologic measures were compared with BMD in predicting the biomechanical strength. Results. In the vertebral (femoral) specimens, R2 for MCS versus &Dgr;P(&agr;) was 0.87 (0.61) (P < 0.001). Correlation between BMD and MCS was 0.53 (P = 0.05) (0.79 [P < 0.001]) for the vertebral (femoral) specimens. For the femoral specimens, prediction of MCS could be improved further by combining BMD and morphologic parameters by multiple regression (R2 = 0.88). Conclusions. Morphologic measures extracted from HR-MRI considering local 3D-scaling properties can be used to predict biomechanical properties of bone in vitro. They are superior to 2-dimensional standard linear morphometric measures and, depending on the anatomic location, more reliably predict bone strength as measured by MCS than does BMD.

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.

Advances of 3T MR imaging in visualizing trabecular bone structure of the calcaneus are partially SNR-independent: analysis using simulated noise in relation to micro-CT, 1.5T MRI, and biomechanical strength.

To investigate differences in magnetic resonance imaging (MRI) of trabecular bone at 1.5T and 3.0T and to specifically study noise effects on the visualization and quantification of trabecular architecture using conventional histomorphometric and nonlinear measures of bone structure.

Analysis of the topological properties of the proximal femur on a regional scale: evaluation of multi-detector CT-scans for the assessment of biomechanical strength using local Minkowski functionals in 3D

In our recent studies on the analysis of bone texture in the context of Osteoporosis, we could already demonstrate the great potential of the topological evaluation of bone architecture based on the Minkowski Functionals (MF) in 2D and 3D for the prediction of the mechanical strength of cubic bone specimens depicted by high resolution MRI. Other than before, we now assess the mechanical characteristics of whole hip bone specimens imaged by multi-detector computed tomography. Due to the specific properties of the imaging modality and the bone tissue in the proximal femur, this requires to introduce a new analysis method. The internal architecture of the hip is functionally highly specialized to withstand the complex pattern of external and internal forces associated with human gait. Since the direction, connectivity and distribution of the trabeculae changes considerably within narrow spatial limits it seems most reasonable to evaluate the femoral bone structure on a local scale. The Minkowski functionals are a set of morphological descriptors for the topological characterization of binarized, multi-dimensional, convex objects with respect to shape, structure, and the connectivity of their components. The MF are usually used as global descriptors and may react very sensitively to minor structural variations which presents a major limitation in a number of applications. The objective of this work is to assess the mechanical competence of whole hip bone specimens using parameters based on the MF. We introduce an algorithm that considers the local topological aspects of the bone architecture of the proximal femur allowing to identify regions within the bone that contribute more to the overall mechanical strength than others.

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.

Quantifying changes in the bone microarchitecture using Minkowski-functionals and scaling vectors: a comparative study

Osteoporosis is a metabolic bone disease leading to de-mineralization and increased risk of fracture. The two major factors that determine the biomechanical competence of bone are the degree of mineralization and the micro-architectural integrity. Today, modern imaging modalities exist that allow to depict structural details of trabecular bone tissue. Recently, non-linear techniques in 2D and 3D based on the scaling vector method (SVM) and the Minkowski functionals (MF) have been introduced, which show excellent performance in predicting bone strength and fracture risk. However, little is known about the performance of the various parameters with respect to monitoring structural changes due to progression of osteoporosis or as a result of medical treatment. We test and compare the two methodologies using realistic two-dimensional simulations of bone structures, which model the effect of osteoblasts and osteoclasts on the local change of relative bone density. Different realizations with slightly varying control parameters are considered. Our results show that even small changes in the trabecular structures, which are induced by variation of a control parameter of the system, become discernible by applying both the MF and the locally adapted scaling vector method. The results obtained with SVM are superior to those obtained with the Minkowski functionals. An additive combination of both measures drastically increases the sensitivity to slight changes in bone structures. These findings may be especially important for monitoring the treatment of patients, where the early recognition of (drug-induced) changes in the trabecular structure is crucial.

Improving the textural characterization of trabecular bone structure to quantify its changes: the locally adapted scaling vector method

We extend the recently introduced scaling vector method (SVM) to improve the textural characterization of oriented trabecular bone structures in the context of osteoporosis. Using the concept of scaling vectors one obtains non-linear structural information from data sets, which can account for global anisotropies. In this work we present a method which allows us to determine the local directionalities in images by using scaling vectors. Thus it becomes possible to better account for local anisotropies and to implement this knowledge in the calculation of the scaling properties of the image. By applying this adaptive technique, a refined quantification of the image structure is possible: we test and evaluate our new method using realistic two-dimensional simulations of bone structures, which model the effect of osteoblasts and osteoclasts on the local change of relative bone density. The partial differential equations involved in the model are solved numerically using cellular automata (CA). Different realizations with slightly varying control parameters are considered. Our results show that even small changes in the trabecular structures, which are induced by variation of a control parameters of the system, become discernible by applying the locally adapted scaling vector method. The results are superior to those obtained by isotropic and/or bulk measures. These findings may be especially important for monitoring the treatment of patients, where the early recognition of (drug-induced) changes in the trabecular structure is crucial.

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.

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.