Digital Volume Correlation Measurements Research Articles

Accuracy and precision of internal displacement and strain measurements in long human bones using HR-pQCT and digital volume correlation

ABSTRACT Digital volume correlation (DVC) is a technique for measuring 3D, internal displacements and strains in loaded structures. One application of DVC is the study of internal bone mechanics and the validation of subject-specific finite element (FE) models. While micro-computed tomography (µCT) is a common choice for DVC studies of small samples of bone, long human bones such as the tibia may exceed the spatial limitations of conventional µCT. High resolution peripheral quantitative CT (HR-pQCT) scanners, with their large bore and open-ended design, may be a viable option for long-bone DVC. However, HR-pQCT is afflicted by stitching artefacts, caused by the stacking of scan blocks to form the large scan volume, resulting in erroneous steps in DVC displacements and bands of increased strain error. This study proposed a modified HR-pQCT scanning protocol and stitching methodology to mitigate the effects of stitching artefacts on DVC measurements of displacement and strain. With the application of the proposed scanning/stitching methodology, displacements greater than 11.7µm (0.29 voxels) and strains greater than 1633µε could be repeatedly measured by DVC. These results show that HR-pQCT combined with DVC is suitable for measuring internal bone displacements in long human bones with sub-voxel precision and strains greater than 1633µε.

Comparison of two contrast-enhancing staining agents for use in X-ray imaging and digital volume correlation measurements across the cartilage-bone interface

ObjectiveThe pathogenesis of osteoarthritis (OA) is associated with subchondral bone changes, which is linked to abnormal strain distribution in the overlying articular cartilage. This highlights the importance of understanding mechanical interaction at the cartilage-bone interface. The aim of this study is to compare solutions of two contrast-enhancing staining agents (CESA) for combining high-resolution Contrast-Enhanced X-ray microfocus Computed Tomography (CECT) with Digital Volume Correlation (DVC) for full-field strain measurements at the cartilage-bone interface. DesignBovine osteochondral plugs were stained with phosphotungstic acid (PTA) in 70% ethanol or 1:2 hafnium-substituted Wells-Dawson polyoxometalate (Hf-WD POM) in PBS. Mechanical properties were assessed using micromechanical probing and nanoindentation. Strain uncertainties (from CECT data) were evaluated following two consecutive unloaded scans. Residual strains were computed following unconfined compression (ex situ) testing. ResultsPTA and Hf-WD POM enabled the visualisation of structural features in cartilage, allowing DVC computation on the CECT data. Residual strains up to ∼10,000 μɛ were detected up to the tidemark. Nanoindentation showed that PTA-staining caused an average ∼6-fold increase in articular cartilage stiffness, a ∼19-fold increase in reduced modulus and ∼7-fold increase in hardness, whereas Hf-WD POM-stained specimens had mechanical properties similar to pre-stain tissue. Micromechanical probing showed a 77% increase in cartilage surface stiffness after PTA-staining, in comparison to a 16% increase in stiffness after staining with Hf-WD POM. ConclusionHf-WD POM is a more suitable CESA solution compared to PTA for CECT imaging combined with DVC as it allowed visualisation of structural features in the cartilage tissue whilst more closely maintaining tissue mechanical properties.

Investigation of carbon-aramid hybrid braided composites using digital volume correlation

Hybrid braided composites combine two or more reinforcing fibres in a matrix. Limited research on hybrid braided composites has been conducted. The Digital Image Correlation (DIC) method has been used to understand hybrid braided composites' external deformation and strain. However, DIC measurements do not provide sufficient information on the internal behaviour of hybrid braids. Therefore, this study focuses on understanding the behaviour of hybrid braids Digital Volume Correlation (DVC). DVC is a micro-computed tomography (Micro-CT) based volumetric strain measurement technique that allows for the internal strain fields of an object. Tensile loading of the Carbon-Aramid hybrid braided samples is achieved using an integrated material testing stage. DVC is used to generate three-dimensional displacement and strain fields and understand the internal strain behaviour of hybrid braided composites. The peak and strain observed for the sample was around −0.065 (µm/µm) and 0.017 (µm/µm), respectively. The effect of contrast-enhancing tracking particles on the DVC resulting DVC strain fields were also examined. Samples with and without contrast particles were subjected to in-situ loading and then analyzed using the DVC process. From this comparison, it was found that the addition of contrast-enhancing particles improves the volumetric strain results from the DVC measurements.

Evaluation of compressive behaviour of porous structures under large deformation using micro‐CT, DVC and micro‐FE

AbstractCompressive behaviour of open and closed cell polyurethane foam samples under large deformation is studied using micro‐Computed Tomography (micro‐CT), Digital Volume Correlation (DVC) technique and micro‐Finite Element (micro‐FE) modelling. The micro‐CT images of the foam samples at different compression strains are used to determine anisotropy in the foams, to obtain qualitative information on deformation mechanisms, to quantify the deformation and strains using a local DVC approach and to generate images for micro‐FE modelling of the foam samples. Micro‐FE modelling predicts the deformation using an elastoplastic material model coupled with continuum damage mechanics. Two different types of boundary conditions, experimentally derived (ExBC) and interpolated from DVC (IPBC), were implemented to evaluate the displacements in the micro‐FE models. A reduced integration scheme in micro‐FE analysis resulted in high artificial energy and was discarded in favour of full integration. The displacement predicted by IPBC matched with DVC displacement contours for closed cell foam. The ExBC‐predicted axial displacement (W) showed a better agreement with DVC than transverse displacements (U, V) contours. However, a significant statistical comparison (R2 > 0.70) of all displacements was obtained for both IPBC and ExBC. For open cell foam, both boundary conditions predicted a significant difference in the displacement contours with respect to DVC measurements. Still, the axial displacements of ExBC and IPBC showed a better statistical significance (R2 > 0.70).

Effect of the number of projections in X-ray CT imaging on image quality and digital volume correlation measurement

Digital volume correlation (DVC) quantifies internal 3D displacement and strain fields by correlating the volume images of a tested object acquired at different states. When using X-ray CT-based DVC, the number of projections is a key parameter that affects the acquisition time and quality of reconstructed volumetric images, and therefore the precision and temporal resolutions of DVC measurement. More projections result in high-quality volume images for DVC calculation but longer acquisition time and pronounced thermal drifts of the X-ray source. Few projections lead to quicker acquisition and fewer thermal drifts, but may degrade image quality and thus induce larger DVC measurement errors. Selecting an appropriate number of projections during CT imaging is therefore of practical significance for DVC measurement. To solve this dilemma, the effect of the number of projections on DVC measurements with X-ray CT is experimentally investigated in this work. First, numerically simulated speckle volume images with different numbers of projections were reconstructed by using FDK (Feldkamp) algorithm, and the influence of the number of projections on DVC measurement was analyzed. Then, real rescan and compression experiments performed on a copper foam sample were carried out to further study the effect of projection number on DVC measurements. Both simulation and real experiments show that more projections result in longer imaging time but higher quality volume image and DVC measurement. DVC measurement errors decrease with the increase of projections at different decline rates. Therefore, an appropriate number of projections can be specified based on the results according to the requirements of DVC measurement precision and temporal resolution. For the specific X-ray CT device used in this real compression experiment, 36 ∼ 60 projections are suggested to balance measurement precision and temporal resolution, and more than 720 projections are necessary for pursuing higher accuracy.

Full-field comparisons between strains predicted by QCT-derived finite element models of the scapula and experimental strains measured by digital volume correlation

Subject-specific finite element models (FEMs) of the shoulder can be used to evaluate joint replacement designs preclinically. However, to ensure accurate conclusions are drawn, experimental validation is critical. The objective of the current study was to evaluate the accuracy of strain predictions generated by subject-specific scapula FEMs through comparisons against full-field experimental strains measured using digital volume correlation (DVC). Three cadaveric scapulae were mechanically loaded using a custom-hexapod robot within a micro-CT scanner. BoneDVC was used to quantify resultant experimental full-field strains. Scapula FEMs were generated using three different density-modulus relationships to assign material properties. Two types of boundary conditions (BCs) were simulated: DVC-displacement-driven or applied-force-driven. Third principal strains were compared between the DVC measurements and FEM predictions. With applied-force BCs, poor agreement was observed between the predicted and measured strains (slope range: 0.16–0.19, r2 range: 0.04–0.30). Agreement was improved with the use of DVC-displacement BCs (slope range: 0.54–0.59, r2 range: 0.73–0.75). Strain predictions were independent of the density-modulus relationship used for DVC-displacement BCs, but differences were observed in the correlation coefficient and intercept for applied-force BCs. Overall, this study utilized full-field DVC-derived experimental strains for comparison with FEM predicted strains in models with varying material properties and BCs. It was found that fair agreement can be achieved in localized strain measurements between DVC measurements and FEM predictions when DVC-displacement BCs are used. However, performance suffered with use of applied-force BCs.

Performance of QCT-Derived scapula finite element models in predicting local displacements using digital volume correlation

Subject-specific finite element models (FEMs) of the shoulder complex are commonly used to predict differences in internal load distribution due to injury, treatment or disease. However, these models rely on various underlying assumptions, and although experimental validation is warranted, it is difficult to obtain and often not performed. The goal of the current study was to quantify the accuracy of local displacements predicted by subject-specific QCT-based FEMs of the scapula, compared to experimental measurements obtained by combining digital volume correlation (DVC) and mechanical loading of cadaveric specimens within a microCT scanner.Four cadaveric specimens were loaded within a microCT scanner using a custom-designed six degree-of-freedom hexapod robot augmented with carbon fiber struts for radiolucency. BoneDVC software was used to quantify full-field experimental displacements between pre- and post-loaded scans. Corresponding scapula QCT-FEMs were generated and three types of boundary conditions (BC) (idealized-displacement, idealized-force, and DVC-derived) were simulated for each specimen.DVC-derived BCs resulted in the closest match to the experimental results for all specimens (best agreement: slope ranging from 0.87 to 1.09; highest correlation: r2 ranging from 0.79 to 1.00). In addition, a two orders of magnitude decrease was observed in root-mean-square error when using QCT-FEMs with simulated DVC-derived BCs compared to idealized-displacement and idealized-force BCs.The results of this study demonstrate that scapula QCT-FEMs can accurately predict local experimental full-field displacements if the BCs are derived from DVC measurements.

Effect of Fragile Speckle Patterns on Accuracy of Digital Volume Correlation

Due to challenges in generating high-quality 3D speckle patterns for Digital Volume Correlation (DVC) strain measurements, DVC experiments often utilize the intrinsic texture and contrast of composite microstructures. One common deficiency of these natural speckle patterns is their poor durability under large deformations, which can lead to decorrelation and inaccurate strain measurements. Using syntactic foams as a model material, the effects of speckle pattern degradation on the accuracy of DVC displacement and strain measurements are assessed with both experimentally-acquired and numerically-generated images. It is shown that measurement error can be classified into two regimes as a function of the percentage of markers that have disappeared from the speckle pattern. For minor levels of damage beneath a critical level of damage, displacement and strain error remained near the noise floor of less than 0.05 voxels and 100 μe, respectively; above this level, error rapidly increased to unacceptable levels above 0.2 voxels and 10,000 μe. This transition occurred after 30%–40% of the speckles disappeared, depending on characteristics of the speckle pattern and its degradation mechanisms. These results suggest that accurate DVC measurements can be obtained in many types of fragile materials despite severe damage to the speckle pattern.

Self-Adaptive Digital Volume Correlation for Unknown Deformation Fields

Digital volume correlation (DVC) has evolved into a powerful tool for quantifying full-field internal deformation. In existing subvolume-based local DVC, subvolume size and shape function are two key user-defined parameters closely related to the DVC measurement errors. In routine implementation, the user must define fixed subvolume size and shape function according to prior experience and intuition, which cannot ensure accurate measurements, particularly for unknown complex heterogeneous deformation fields. Self-adaptive selection of optimal subvolume size and the best shape function is therefore highly desirable to realize full-automatic and quality DVC measurements. In this work, we first establish theoretical error models that relate total displacement errors to subvolume sizes and shape functions. By minimizing the V-shaped models of theoretically predicted total errors, optimal subvolume size and the best shape function can be identified as inputs for self-adaptive DVC analysis at each calculation point. The accuracy advantage of the presented self-adaptive DVC approach over classic one using fixed subvolume size and shape function is demonstrated through numerically simulated three-point bending tests.

On the calibration of elastoplastic parameters at the microscale via X-ray microtomography and digital volume correlation for the simulation of ductile damage

Abstract An identification framework is introduced herein to calibrate material parameters at the microscale in order to analyze ductile damage. It is applied to study a dog-bone sample, which is made of spheroidal graphite cast iron, loaded in tension and imaged via in situ microtomography. The region of interest is analyzed via Digital Volume Correlation (DVC) to measure kinematic fields. Finite Element (FE) simulations, which account for the studied microstructure that is explicitly meshed thanks its 3D image, are driven by Dirichlet boundary conditions extracted from DVC measurements. The plastic behavior of the ferritic matrix is calibrated via integrated DVC. The three mechanisms of ductile damage are then analyzed in view of the predictions of numerical simulations at the microscopic scale .

Systematic errors in digital volume correlation due to the self-heating effect of a laboratory x-ray CT scanner

The use of digital volume correlation (DVC) in combination with a laboratory x-ray computed tomography (CT) for full-field internal 3D deformation measurement of opaque materials has flourished in recent years. During x-ray tomographic imaging, the heat generated by the x-ray tube changes the imaging geometry of x-ray scanner, and further introduces noticeable errors in DVC measurements. In this work, to provide practical guidance high-accuracy DVC measurement, the errors in displacements and strains measured by DVC due to the self-heating for effect of a commercially available x-ray scanner were experimentally investigated. The errors were characterized by performing simple rescan tests with different scan durations. The results indicate that the maximum strain errors associated with the self-heating of the x-ray scanner exceed 400 µε. Possible approaches for minimizing or correcting these displacement and strain errors are discussed. Finally, a series of translation and uniaxial compression tests were performed, in which strain errors were detected and then removed using pre-established artificial dilatational strain-time curve. Experimental results demonstrate the efficacy and accuracy of the proposed strain error correction approach.

Research progress in digital volume correlation method

Full-field displacement and strain measurements of materials, structures and biological tissues subjected to various external (i.e. mechanical or thermal) loading is a primary task of experimental solid mechanics. For nearly a century, benefiting from the rapid development of different branches of physics, various new techniques for whole-field displacement and strain measurements have been developed, advocated and widely used. However, most of these techniques only allows for surface deformation measurement, while in most cases the surface deformation is very different from the actual deformation throughout the interior of a test object. To quantify full-field internal 3D deformation of various opaque materials or biologic tissues subjected to external loading, digital volume correlation (DVC) was developed at the end of last century. Thanks to the increasing popularity and constant emergence of various volumetric imaging devices (e.g., X-ray computed tomography), internal microstructure of a tested sample arising from natural texture or embedded particles can be recorded as digital volume image with distinct random grayscale distribution. By comparing the volume images recorded at different configurations, the internal kinematic filed of the sample can be accurately retrieved by DVC algorithm with the assistance of advanced 3D image registration algorithms and modern computational facilities. Benefiting from constant emergence of new 3D imaging facilities, continual refinement of image registration algorithms, and rapid development of high-performance parallel computing technologies, DVC has gained numerous successful applications in biomedicine, solid mechanics, rock and geo mechanics, material science and biomedicines etc. Basically, as an image-based experimental technique, the implementation of DVC for internal deformation measurement comprises two consecutive steps: volume image acquisition using a certain 3D imaging device and image processing using 3D image registration algorithm. Thus, the accuracy and precision of DVC measurements depend on two primary components: the quality of the recorded volumetric images and the performance of DVC algorithms. In order to satisfy the increasing requirement of measurement accuracy in practical applications, many researchers have contributed to investigate the algorithm improvement and imaging error calibration. In the past decade, plenty of methodologies and algorithmic details have been developed to realize higher measurement accuracy and computational efficiency. Although both the image quality and algorithm performance have gain significant improvement in recent years, systematic and random errors inevitably occur during DVC analyses due to the influence of internal microstructure, image acquirement system, loading environment and algorithm details, thus posing important challenge to accurate DVC measurement in practical applications. In this review, the basic principles and procedures of DVC approach and the concept of the algorithmic details are briefly described first. Then, various methodologies and algorithmic details employed in DVC for internal 3D displacement and strain measurement are systematically described and commented. Limitations and potential developments of the technique are also summarized in terms of material microstructure, volumetric imaging and algorithm performance. Despite facing several challenges such as highly dependence on internal microstructure and large data processing with relatively lower computational efficiency, it is foreseen that DVC method will play an increasingly important role in the field of experimental mechanics and definitely expect more potential applications in broad areas especially in material science and biological engineering.

Numerical validation framework for micromechanical simulations based on synchrotron 3D imaging

A combined computational–experimental framework is introduced herein to validate numerical simulations at the microscopic scale. It is exemplified for a flat specimen with central hole made of cast iron and imaged via in-situ synchrotron laminography at micrometer resolution during a tensile test. The region of interest in the reconstructed volume, which is close to the central hole, is analyzed by digital volume correlation (DVC) to measure kinematic fields. Finite element (FE) simulations, which account for the studied material microstructure, are driven by Dirichlet boundary conditions extracted from DVC measurements. Gray level residuals for DVC measurements and FE simulations are assessed for validation purposes.

Micro-CT based finite element models of cancellous bone predict accurately displacement once the boundary condition is well replicated: A validation study

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 (UX: y=1.07x−0.002, RMSE: 0.001mm; UY: y=1.03x−0.001, RMSE: 0.001mm; UZ: 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.

Computation of full-field displacements in a scaffold implant using digital volume correlation and finite element analysis

Measurements of three-dimensional displacements in a scaffold implant under uniaxial compression have been obtained by two digital volume correlation (DVC) methods, and compared with those obtained from micro-finite element models. The DVC methods were based on two approaches, a local approach which registers independent small volumes and yields discontinuous displacement fields; and a global approach where the registration is performed on the whole volume of interest, leading to continuous displacement fields. A customised mini-compression device was used to perform in situ step-wise compression of the scaffold within a micro-computed tomography (μCT) chamber, and the data were collected at steps of interest. Displacement uncertainties, ranging from 0.006 to 0.02 voxel (i.e. 0.12–0.4μm), with a strain uncertainty between 60 and 600μɛ, were obtained with a spatial resolution of 32 voxels using both approaches, although the global approach has lower systematic errors. Reduced displacement and strain uncertainties may be obtained using the global approach by increasing the element size; and using the local approach by increasing the number of intermediary sub-volumes. Good agreements between the results from the DVC measurements and the FE simulations were obtained in the primary loading direction as well as in the lateral directions. This study demonstrates that volumetric strain measurements can be obtained successfully using DVC, which may be a useful tool to investigate mechanical behaviour of porous implants.