Analysis of trabecular bone mechanical properties from magnetic resonance images

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Bone mineral density (BMD) measured by dual energy x-ray absorptiometry (DXA) is often used in the clinical diagnosis of bone disorders such as osteoporosis. However, several studies have shown that measuring BMD alone does not provide sufficient discrimination between individuals with and without increased fracture risk. In fact, bone quality is affected also by the bone micro-architecture and material properties. The development of imaging techniques, particularly computed tomography (CT) and magnetic resonance (MR) imaging, allowed the generation of three-dimensional (3D) images for the morphological analysis of trabecular bone. Furthermore, the 3D image data can be the source of finite element (FE) models. FE analysis of such data represents a means to assess the mechanical response virtually. Whole-body CT and MRI scanners are able to provide three-dimensional images in vivo of human femoral and spinal sites but compared to μCT and μMR, have poorer resolution and lower signal-to-noise ratio. As a result of the low resolution, a significant partial volume effect is expected to affect the reconstructed images primarily by blurring the interface between bone and soft tissue. Thus, the implications of such limitations on the FE assessment of mechanical properties should be investigated. The main goal of this study was to assess the capability of whole-body low resolution MRI-based finite element model for the prediction of trabecular bone mechanical properties. The apparent elastic modulus and the displacement field were assessed and compared to a high resolution MR model. The effect of image voxel size on these properties was examined using μMR images acquired with different resolutions. The estimated mechanical properties of two trabecular bone samples (A and B), as assessed by whole-body MRI-based FE analysis, were compared with the corresponding measurements obtained from the validated μMRI-based FE analysis. It was found that increasing the voxel size from 30 μm to 200 μm raised the apparent elastic modulus by up to 13% and 21% for bone samples A and B, respectively. For whole-body MR, with voxel size of 260 μm, the overestimate rose to 24% for both bone samples. However, the apparent tissue elastic modulus stayed within the range (722- 1207) MPa, and (777 – 1228) MPa for bone samples A and B, respectively, imaged with high resolution μMR. The variations in the apparent elastic modulus appear to correlate with differences in the bone volume fraction, which varied between 0.44 and 0.68. FE analysis of load levels in the elastic range indicated that the more computationally costly geometric non-linear analysis did not improve the results significantly. Hence, a linear elastic FE analysis was deemed to be sufficiently accurate at low load levels. In addition to estimating the apparent elastic modulus, FE analysis can produce a displacement field that represents the response to applied compression at every point in the trabecular bone. The results show that increasing the voxel size leads to a systematic overestimation of the mean displacement compared to the reference values. However, the mean norm displacement estimated from whole-body MR (0.64 mm) in the direction of the applied compression force falls within the range obtained from high resolution μMR (0.64 ± 0.13 mm). The results also suggest that the information provided by displacement field values may be statistically uncorrelated with the apparent elastic modulus and hence serve as an additional source of parameterization of the mechanical response of trabecular bone. The application of whole-body MRI to trabecular bone analysis is expected to be affected not only by resolution but also by other effects arising from the low strength of the steady magnetic field, the large imaging volume, and motion artefacts. Nevertheless, both the estimated apparent elastic modulus and displacement field are compatible with those obtained from μMR of comparable resolution. Within the limit of this study the predictions of FE analysis derived from whole-body MR are within the range of predictions based on high resolution μMR, indicating a potential suitability of MR for assessment of bone strength.
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