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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.
Loads and resulting strains in bone are transferred through the trabecular tissue, which has been optimized to the local mechanical loading demands through remodeling13. Locally, the primary orientation of the trabeculae is aligned with the global main force direction7, while secondary oriented trabeculae complete the optimized network of the tissue14. The forces deform the trabecular structure in such a way that individual trabeculae endure strains that can be compressive, tensile, or in shear, depending on the direction of the load and the trabecular network. At the organ scale, bone mineral density (BMD) is an important contributor to overall strength and fracture toughness, while the contribution of the local micro-scale tissue mineral density (TMD) and structural variations on crack resistance remains unknown. Hypothetically, there are two factors that can directly affect the location of the failure at the trabecular level: (1) the trabecular microstructure and organization, i.e. the amount, connectivity, and orientation of the trabecular bone network, and (2) the local material properties, e.g. TMD. Earlier studies have investigated their effects on the resulting strains in trabecular bone by considering the structure of the trabecular network10,11,12, 15 or on isolated single trabeculae16,17,18,19,20,21, respectively.
The aims of this study were to investigate the distribution and magnitudes of internal strains at sub-trabecular resolution in human trabecular bone and their evolution during loading. Moreover, the study aims to investigate the relationship between material and tissue level biomechanical properties and to bridge the discrepancies in strain levels when investigated in single trabeculae or in whole trabecular structure. A subsequent aim was to investigate the influence of image voxel size on the strain magnitudes. Finally, this study describes the links between local crack sites, tissue mineral density, trabecular microstructure, and local tissue strains with sub-trabecular resolution.
The crack regions in the DVC sub-regions were determined for each sample from the final scan (after global yield) of each sample (Fig. 2f) using two consecutive steps: (1) a custom-made automated crack identification and segmentation algorithm followed by (2) a manual inspection (both in MatLab). A crack was defined as a visible discontinuity in the structure in the last scan, which was not present in earlier scans. The final segmentation was based solely on visual inspection. Although the automated crack identification and segmentation algorithm was used only as a tool to aid the final visual segmentation, it is introduced here briefly.
As the automated procedure also captured canals within the trabeculae and did not reveal cracks that had low contrast compared to the surrounding bone or cracks that were too small, the automated segmentation was corrected manually. The manual correction included removal of falsely detected cracks (e.g. canals) and addition of undetected cracks by comparing visually the corrected image stack with cracks with an image stack at an earlier time-point to ensure that the cracks were not present before. Finally, the corrected BSc was overlaid on the original stack to mark the crack regions (Fig. 2f).
The DVC strain analysis was performed only on images from load-steps before reaching global yield, thus when no cracks were visually observed. Only strains from nodes with a correlation coefficient greater than 0.95 were included in the analysis. The DVC strain maps were linearly interpolated to fit the voxel size of the TMD and trabecular thickness maps to enable comparison of the same regions. Cumulative volumetric strains were calculated for each voxel by summing strains from every loading step voxel-by-voxel (Fig. 4). Each voxel at each step had a negative (compressive strain) or positive (tensile strain) volumetric strain value (Supplementary Fig. 2). Strain values after global yield or in regions where a crack was visible were not included in the analysis. After cumulative summing of each load step, absolute cumulative strain maps for each load step were generated. The absolute cumulative strain curves were normalized to extend from the first DVC step until global yield point by interpolation. Since the DVC was performed between two image stacks, the local strains obtained at each loading step represent the total accumulated local strains at the latter acquisition. Average absolute volumetric strain magnitudes, TMDs, and trabecular thicknesses from regions surrounding cracks and from non-crack regions were calculated, analyzed and plotted using custom made MatLab scripts.
For comparison of the strains between the high-resolution and downscaled data, the binary images of the dilated crack regions were also downscaled using the same factors as the downscaled SR-µCT data. Thus, the strains in the same regions for each voxel size (resolution) image were used for the calculation of the average strains in the crack and non-crack regions during loading. To compare the strain magnitudes in crack regions between the high-resolution and downscaled data, histograms of the strain magnitudes were created for each voxel size image, normalized to the total number of points in the crack regions.
The distribution and evolution of strain magnitudes within the trabecular bone was assessed by DVC between two consecutive image stacks. The summed point-by-point local strains within the trabeculae obtained at each loading step represent the total accumulated local strains at the latter acquisition time (Fig. 4). These strain maps clearly display elevated strains in the crack regions. 2b1af7f3a8