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.

Different digital volume correlation (DVC) approaches are currently available or under development for bone tissue micromechanics. The aim of this study was to compare accuracy and precision errors of three DVC approaches for a particular three-dimensional (3D) zero-strain condition. Trabecular and cortical bone specimens were repeatedly scanned with a micro-computed tomography (CT). The errors affecting computed displacements and strains were extracted for a known virtual translation, as well as for repeated scans. Three DVC strategies were tested: two local approaches, based on fast-Fourier-transform (DaVis-FFT) or direct-correlation (DaVis-DC), and a global approach based on elastic registration and a finite element (FE) solver (ShIRT-FE). Different computation subvolume sizes were tested. Much larger errors were found for the repeated scans than for the virtual translation test. For each algorithm, errors decreased asymptotically for larger subvolume sizes in the range explored. Considering this particular set of images, ShIRT-FE showed an overall better accuracy and precision (a few hundreds microstrain for a subvolume of 50 voxels). When the largest subvolume (50-52 voxels) was applied to cortical bone, the accuracy error obtained for repeated scans with ShIRT-FE was approximately half of that for the best local approach (DaVis-DC). The difference was lower (250 microstrain) in the case of trabecular bone. In terms of precision, the errors shown by DaVis-DC were closer to the ones computed by ShIRT-FE (differences of 131 microstrain and 157 microstrain for cortical and trabecular bone, respectively). The multipass computation available for DaVis software improved the accuracy and precision only for the DaVis-FFT in the virtual translation, particularly for trabecular bone. The better accuracy and precision of ShIRT-FE, followed by DaVis-DC, were obtained with a higher computational cost when compared to DaVis-FFT. The results underline the importance of performing a quantitative comparison of DVC methods on the same set of samples by using also repeated scans, other than virtual translation tests only. ShIRT-FE provides the most accurate and precise results for this set of images. However, both DaVis approaches show reasonable results for large nodal spacing, particularly for trabecular bone. Finally, this study highlights the importance of using sufficiently large subvolumes, in order to achieve better accuracy and precision.

The strain distribution in vertebral body has been measured in vitro in the elastic regime but only on the bone surface by means of strain gauges and digital image correlation. Digital volume correlation (DVC) based on micro‐computed tomography (micro‐CT) images allowed measurements of the internal strain distribution in bone at both tissue (trabecular and cortical bone) and organ (vertebra) levels. However, DVC has been mainly used to investigate failure of the vertebral body but has not yet been deployed to investigate the internal strain distribution in the elastic regime. The aim of this study was to investigate strain in the elastic regime and up to failure inside the vertebral body, including analysis of strain in all directions. Three porcine thoracic vertebrae were loaded in a step‐wise fashion at increasing steps of compression (5, 10 and 15%). Micro‐CT images were acquired at each step of compression. DVC successfully provided the internal strain distribution both in the elastic regime and up to failure. Micro‐CT images successfully identified regions of failure initiation and progression, which were well quantified by DVC‐computed strains. Interestingly, the same regions where failure eventually occurred experienced the largest strain magnitude also for the lowest degrees of compression (yet in the elastic regime).

Digital Volume Correlation (DVC) has become popular for measuring the strain distribution inside bone structures. A number of methodological questions are still open: the reliability of DVC to investigate augmented bone tissue, the variability of the errors between different specimens of the same type, the distribution of measurement errors inside a bone, and the possible presence of preferential directions. To address these issues, five augmented and five natural porcine vertebrae were subjected to repeated zero-strain micro-CT scan (39μm voxel size). The acquired images were processed with two independent DVC approaches (a local and a global one), considering different computation sub-volume sizes, in order to assess the strain measurement uncertainties. The systematic errors generally ranged within ±100 microstrain and did not depend on the computational sub-volume. The random error was higher than 1000 microstrain for the smallest sub-volume and rapidly decreased: with a sub-volume of 48 voxels the random errors were typically within 200 microstrain for both DVC approaches. While these trends were rather consistent within the sample, two individual specimens had unpredictably larger errors. For this reason, a zero-strain check on each specimen should always be performed before any in-situ micro-CT testing campaign. This study clearly shows that, when sufficient care is dedicated to preliminary methodological work, different DVC computation approaches allow measuring the strain with a reduced overall error (approximately 200 microstrain). Therefore, DVC is a viable technique to investigate strain in the elastic regime in natural and augmented bones.

Understanding bone mechanics at different hierarchical levels is fundamental to improve preclinical and clinical assessments of bone strength. Digital Volume Correlation (DVC) is the only experimental measurement technique used for measuring local displacements and calculating local strains within bones. To date, its combination with laboratory source micro-computed tomography (LS-microCT) data typically leads to high uncertainties, which limit its application. Here, the benefits of synchrotron radiation micro-computed tomography (SR-microCT) for DVC are reported. Specimens of cortical and trabecular bovine bone and murine tibiae, were each scanned under zero-strain conditions with an effective voxel size of 1.6μm. In order to consider the effect of the voxel size, analyses were also performed on downsampled images with voxel size of 8μm. To evaluate displacement and strain uncertainties, each pair of tomograms was correlated using a global DVC algorithm (ShIRT-FE). Displacement random errors for original SR-microCT ranged from 0.024 to 0.226μm, depending on DVC nodal spacing. Standard deviation of strain errors was below 200 microstrain (ca. 1/10 of the strain associated with physiological loads) for correlations performed with a measurement spatial resolution better than 40μm for cortical bovine bone (240μm for downsampled images), 80μm for trabecular bovine bone (320μm for downsampled images) and murine tibiae (120μm for downsampled images). This study shows that the uncertainties of SR-microCT-based DVC, estimated from repeated scans, are lower than those obtained from LS-microCT-based DVC on similar specimens and low enough to measure accurately the local deformation at the tissue level.

Combination of micro-focus computed tomography (micro-CT) in conjunction with in situ mechanical testing and digital volume correlation (DVC) can be used to access the internal deformation of materials and structures. DVC has been exploited over the past decade to measure complex deformation fields within biological tissues and bone-biomaterial systems. However, before adopting it in a clinically-relevant context (i.e. bone augmentation in vertebroplasty), the research community should focus on understanding the reliability of such method in different orthopaedic applications involving the use of biomaterials. The aim of this study was to evaluate systematic and random errors affecting the strain computed with two different DVC approaches (a global one, "ShIRT-FE", and a local one, "DaVis-DC") in different microstructures within augmented vertebrae, such as trabecular bone, cortical bone and cement-bone interdigitation. The results showed that systematic error was insensitive to the size of the computation sub-volume used for the DVC correlation. Conversely, the random error (which was generally the largest component of error) was lower for a 48-voxel (1872micrometer) sub-volume (64-221 microstrain for ShIRT-FE, 88-274 microstrain for DaVis-DC), than for a 16-voxel (624micrometer) sub-volume (359-1203 microstrain for ShIRT-FE, 960-1771 microstrain for DaVis-DC) for the trabecular and cement regions. Overall, the local random error did not appear to be influenced by either bone microarchitecture or presence of biomaterial. For the 48-voxel sub-volume the global approach was less sensitive to the gradients in grey-values at the cortical surface (random error below 200 microstrain), while the local approach showed errors up to 770 microstrain. Mean absolute error (MAER) and standard deviation of error (SDER) were also calculated and substantially improved when compared to recent literature for the cement-bone interface. The multipass approach for DaVis-DC further reduced the random error for the largest volume of interest. The random error did not follow any recognizable pattern with the six strain components and only ShiRT-FE seemed to produce lower random errors in the normal strains. In conclusion this study has provided, for the first time, a preliminary indication of the reliability and limitations for the application of DVC in estimating the micromechanics of bone and cement-bone interface in augmented vertebrae.

Digital image correlation (DIC) is being introduced to the biomechanical field. However, as DIC relies on a number of major assumptions, it requires a careful optimization in order to obtain accurate and precise results. The first step was the preparation of the speckle pattern by an airbrush spray gun following a factorial design to explore the different settings: the different speckle patterns created were analyzed to achieve the optimal speckle size, with minimal dispersion of speckle sizes. A benchmark test, with an aluminum specimen prepared with the speckle pattern, was conducted in which the errors affecting the computed strain were measured in a zero-displacement, zero-strain condition. The software parameters (facet size, step, and local regression) were singularly analyzed in order to understand their behavior on the final output. Moreover, the hardware parameters (camera gain, exposure, lens distortion) were analyzed. The output showed that a careful optimization allowed the reducing the systematic and random errors, respectively, from 150 to 10 microstrain and from 600 to 110 microstrain. Finally, the acquired know-how was applied to a biological specimen (human vertebra).