No abstract

Accurate measurement of local strain in heterogeneous and anisotropic bone tissue is fundamental to understand the pathophysiology of musculoskeletal diseases, to evaluate the effect of interventions from preclinical studies, and to optimize the design and delivery of biomaterials. Digital volume correlation (DVC) can be used to measure the three-dimensional displacement and strain fields from micro-computed tomography (μCT) images of loaded specimens. However, this approach is affected by the quality of the input images, by the morphology and density of the tissue under investigation, by the correlation scheme, and by the operational parameters used in the computation. Therefore, for each application, the precision of the method should be evaluated. In this paper, we present the results collected from datasets analyzed in previous studies as well as new data from a recent experimental campaign for characterizing the relationship between the precision of two different DVC approaches and the spatial resolution of the outputs. Different bone structures scanned with laboratory source μCT or synchrotron light μCT (SRμCT) were processed in zero-strain tests to evaluate the precision of the DVC methods as a function of the subvolume size that ranged from 8 to 2,500 µm. The results confirmed that for every microstructure the precision of DVC improves for larger subvolume size, following power laws. However, for the first time, large differences in the precision of both local and global DVC approaches have been highlighted when SRμCT or in vivo μCT images were used instead of conventional ex vivo μCT. These findings suggest that in situ mechanical testing protocols applied in SRμCT facilities should be optimized to allow DVC analyses of localized strain measurements. Moreover, for in vivo μCT applications, DVC analyses should be performed only with relatively course spatial resolution for achieving a reasonable precision of the method. In conclusion, we have extensively shown that the precision of both tested DVC approaches is affected by different bone structures, different input image resolution, and different subvolume sizes. Before each specific application, DVC users should always apply a similar approach to find the best compromise between precision and spatial resolution of the measurements.

The QCT-based hFE method provides a quantitative and significantly improved prediction of vertebral strength in vitro when compared to simulated DXA. This superior predictive power needs to be verified for loading conditions that simulate even more the in vivo case for human vertebrae.

Non-destructive 3D micro-computed tomography (microCT) based finite element (microFE) models are used to estimate bone mechanical properties at tissue level. However, their validation remains challenging. Recent improvements in the quantification of displacements in bone tissue biopsies subjected to staged compression, using refined Digital Volume Correlation (DVC) techniques, now provide a full field displacement information accurate enough to be used for microFE validation. In this study, three specimens (two humans and one bovine) were tested with two different experimental set-ups, and the resulting data processed with the same DVC algorithm. The resulting displacement vector field was compared to that predicted by microFE models solved with three different boundary conditions (BC): nominal force resultant, nominal displacement resultant, distributed displacement. The first two conditions were obtained directly from the measurements provided by the experimental jigs, whereas in the third case the displacement field measured by the DVC in the top and bottom layer of the specimen was applied. Results show excellent relationship between the numerical predictions (x) and the experiments (y) when using BC derived from the DVC measurements (U: y=1.07x-0.002, RMSE: 0.001mm; U: y=1.03x-0.001, RMSE: 0.001mm; U: y=x+0.0002, RMSE: 0.001 mm for bovine specimen), whereas only poor correlation was found using BCs according to experiment set-ups. In conclusion, microFE models were found to predict accurately the vectorial displacement field using interpolated displacement boundary condition from DVC measurement.

The accurate measurement of local strain is necessary to study bone mechanics and to validate micro computed tomography (µCT) based finite element (FE) models at the tissue scale. Digital volume correlation (DVC) has been used to provide a volumetric estimation of local strain in trabecular bone sample with a reasonable accuracy. However, nothing has been reported so far for µCT based analysis of cortical bone. The goal of this study was to evaluate accuracy and precision of a deformable registration method for prediction of local zero-strains in bovine cortical and trabecular bone samples.The accuracy and precision were analyzed by comparing scans virtually displaced, repeated scans without any repositioning of the sample in the scanner and repeated scans with repositioning of the samples.The analysis showed that both precision and accuracy errors decrease with increasing the size of the region analyzed, by following power laws. The main source of error was found to be the intrinsic noise of the images compared to the others investigated. The results, once extrapolated for larger regions of interest that are typically used in the literature, were in most cases better than the ones previously reported. For a nodal spacing equal to 50 voxels (498 µm), the accuracy and precision ranges were 425-692 µ and 202-394µ , respectively. In conclusion, it was shown that the proposed method can be used to study the local deformation of cortical and trabecular bone loaded beyond yield, if a sufficiently high nodal spacing is used.3

The estimation of local and structural mechanical properties of bones with micro Finite Element (microFE) models based on Micro Computed Tomography images depends on the quality bone geometry is captured, reconstructed and modelled. The aim of this study was to validate microFE models predictions of local displacements for vertebral bodies and to evaluate the effect of the elastic tissue modulus on model’s predictions of axial forces. Four porcine thoracic vertebrae were axially compressed in situ, in a step-wise fashion and scanned at approximately 39μm resolution in preloaded and loaded conditions. A global digital volume correlation (DVC) approach was used to compute the full-field displacements. Homogeneous, isotropic and linear elastic microFE models were generated with boundary conditions assigned from the interpolated displacement field measured from the DVC. Measured and predicted local displacements were compared for the cortical and trabecular compartments in the middle of the specimens. Models were run with two different tissue moduli defined from microindentation data (12.0GPa) and a back-calculation procedure (4.6GPa). The predicted sum of axial reaction forces was compared to the experimental values for each specimen. MicroFE models predicted more than 87% of the variation in the displacement measurements (R2 = 0.87–0.99). However, model predictions of axial forces were largely overestimated (80–369%) for a tissue modulus of 12.0GPa, whereas differences in the range 10–80% were found for a back-calculated tissue modulus. The specimen with the lowest density showed a large number of elements strained beyond yield and the highest predictive errors. This study shows that the simplest microFE models can accurately predict quantitatively the local displacements and qualitatively the strain distribution within the vertebral body, independently from the considered bone types.

No abstract

Background. The use of formalin fixed bone tissue is often avoided because of its assumed influence on the mechanical properties of bone. Fixed bone tissue would minimise biological risks and eliminate preservation issues for long duration experimental tests. This study aimed to determine the short-and long-term effects of embalming, using a solution with 4% formalin concentration, on the mechanical properties of human cortical bone.Methods. Three-millimetre cylindrical specimens of human cortical bone were extracted from two femoral diaphyses and divided in four groups. The first group was used as control, the remaining three groups were left in the embalming solution for 48 h, 4 week, and 8 week, respectively. Compressive mechanical properties, hardness and ash density were assessed. The last was used to check the homogeneity among the four groups.Findings. No significant differences were found among the four groups in yield stress, ultimate stress and hardness. The specimens stored for 8 week in the embalming solution had significant lower Young's modulus (À24%), higher yield strain (+20%) and ultimate strain (+53%) compared to the other groups.Interpretation. On a short-term perspective, embalming did not affect the compressive mechanical properties, nor hardness of human cortical bone, whereas a long-term preservation (8 week) did significantly affect Young's modulus, yield strain and ultimate strain in compression. Preserving bone segments for up to 4 week in an embalming solution with low formalin concentration seems to be an interesting alternative when collecting and/or managing fresh or fresh-frozen bone segments for biomechanical experiments is not possible.