Local displacement and strain uncertainties in different bone types by digital volume correlation of synchrotron microtomograms

A Comprehensive Mechanical Characterization of Subject-Specific 3D Printed Scaffolds Mimicking Trabecular Bone Architecture Biomechanics

This study presents a polymeric scaffold designed and manufactured to mimic the structure and mechanical compressive characteristics of trabecular bone. The morphological parameters and mechanical behavior of the scaffold were studied and compared with trabecular bone from bovine iliac crest. Its mechanical properties, such as modulus of elasticity and yield strength, were studied under a three-step monotonic compressive test. Results showed that the elastic modulus of the scaffold was 329 MPa, and the one for trabecular bone reached 336 MPa. A stepwise dynamic compressive test was used to assess the behavior of samples under various loading regimes. With microcomputed tomography (µCT), a three-dimensional reconstruction of the samples was obtained, and their porosity was estimated as 80% for the polymeric scaffold and 88% for trabecular bone. The full-field strain distribution of the samples was measured using in situ µCT mechanics and digital volume correlation (DVC). This provided information on the local microdeformation mechanism of the scaffolds when compared to that of the tissue. The comprehensive results illustrate the potential of the fabricated scaffolds as biomechanical templates for in vitro studies. Furthermore, there is potential for extending this structure and fabrication methodology to incorporate suitable biocompatible materials for both in vitro and in vivo clinical applications.

Bone metastases do not affect the measurement uncertainties of a global digital volume correlation algorithm

Introduction: Measurement uncertainties of Digital Volume Correlation (DVC) are influenced by several factors, like input images quality, correlation algorithm, bone type, etc. However, it is still unknown if highly heterogeneous trabecular microstructures, typical of lytic and blastic metastases, affect the precision of DVC measurements.

Methods: Fifteen metastatic and nine healthy vertebral bodies were scanned twice in zero-strain conditions with a micro-computed tomography (isotropic voxel size = 39 μm). The bone microstructural parameters (Bone Volume Fraction, Structure Thickness, Structure Separation, Structure Number) were calculated. Displacements and strains were evaluated through a global DVC approach (BoneDVC). The relationship between the standard deviation of the error (SDER) and the microstructural parameters was investigated in the entire vertebrae. To evaluate to what extent the measurement uncertainty is influenced by the microstructure, similar relationships were assessed within sub-regions of interest.

Results: Higher variability in the SDER was found for metastatic vertebrae compared to the healthy ones (range 91-1030 με versus 222–599 με). A weak correlation was found between the SDER and the Structure Separation in metastatic vertebrae and in the sub-regions of interest, highlighting that the heterogenous trabecular microstructure only weakly affects the measurement uncertainties of BoneDVC. No correlation was found for the other microstructural parameters. The spatial distribution of the strain measurement uncertainties seemed to be associated with regions with reduced greyscale gradient variation in the microCT images.

Discussion: Measurement uncertainties cannot be taken for granted but need to be assessed in each single application of the DVC to consider the minimum unavoidable measurement uncertainty when interpreting the results.

Comparison of linear and nonlinear stepwise μFE displacement predictions to digital volume correlation measurements of trabecular bone biopsies

Digital volume correlation (DVC) enables to evaluate the ability of μFE models in predicting experimental results on the mesoscale. In this study predicted displacement fields of three different linear and materially nonlinear μFE simulation methods were compared to DVC measured displacement fields at specific load steps in the elastic regime (Step_El) and after yield (Step_Ult). Five human trabecular bone biopsies from a previous study were compressed in several displacement steps until failure. At every compression step, μCT images (resolution: 36 μm) were recorded. A global DVC algorithm was applied to compute the displacement fields at all loading steps. The unloaded 3D images were then used to generate homogeneous, isotropic, linear and materially nonlinear μFE models. Three different μFE simulation methods were used: linear (L), nonlinear (NL), and nonlinear stepwise (NLS). Regarding L and NL, the boundary conditions were derived from the interpolated displacement fields at Step_El and Step_Ult, while for the NLS method nonlinear changes of the boundary conditions of the experiments were captured using the DVC displacement field of every available load step until Step_El and Step_Ult. The predicted displacement fields of all μFE simulation methods were in good agreement with the DVC measured displacement fields (individual specimens: R²>0.83 at Step_El and R²>0.59 at Step_Ult; pooled data: R²>0.97 at Step_El and R²>0.92 at Step_Ult). At Step_El, all three simulation methods showed similar intercepts, slopes, and coefficients of determination while the nonlinear μFE models improved the prediction of the displacement fields slightly in all Cartesian directions at Step_Ult (individual specimens: L: R²>0.59 and NL, NLS: R²>0.68; pooled data: L: R²>0.92 and NL, NLS: R²>0.94). Damaged/overstrained elements in L, NL, and NLS occurred at similar locations but the number of overstrained elements was overestimated when using the L simulation method. Considering the increased solving time of the nonlinear μFE models as well as the acceptable performance in displacement prediction of the linear μFE models, one can conclude that for similar use cases linear μFE models represent the best compromise between computational effort and accuracy of the displacement field predictions.

Measurement of bone damage caused by quasi-static compressive loading-unloading to explore dental implants stability: Simultaneous use of in-vitro tests, μ-CT images, and digital volume correlation

Primary stability of dental implants is the initial mechanical engagement of the implant with its adjacent bone. Implantation and the subsequent loading may cause mechanical damage in the peripheral bone, which ultimately reduces the stability of the implant. This study aimed at evaluating primary stability of dental implants through applying stepwise compressive displacement-controlled, loading-unloading cycles to obtain overall stiffness and dissipated energy of the bone-implant structure; and quantifying induced plastic strains in surrounding bone using digital volume correlation (DVC) method, through comparing μCT images in different loading steps. To this end, dental implants were inserted into the cylindrical trabecular bones, then the bone-implant structure was undergone step-wise loading-unloading cycles, and μCT images were taken in some particular steps, then comparison was made between undeformed and deformed configurations using DVC to quantify plastic strain within the trabecular bone. Comparing stiffness reduction and dissipated energy values in different loading steps, obtained from the force-displacement curve in each loading step, revealed that the maximum displacement of 0.16 mm can be deemed as a safe threshold above which damages in peri-implant bone started to increase considerably (p < 0.05). In addition, it was found here that peri-implant bone strain linearly increased with decreasing bone-implant stiffness (p < 0.05). Moreover, strain concentration in peri-implant bone region showed that the plastic strain in trabecular bone spread up to a distance of about 2.5 mm away from the implant surface. Research of this kind can be used to optimize the design of dental implants, with the ultimate goal of improving their stability, also to validate in-silico models, e.g., micro-finite element models, which can help gain a deeper understanding of bone-implant construct behavior.

Effect of radiation-induced damage of trabecular bone tissue evaluated using indentation and digital volume correlation

Exposure to X-ray radiation for an extended amount of time can cause damage to the bone tissue and therefore affect its mechanical properties. Specifically, high-resolution X-ray Computed Tomography (XCT), in both synchrotron and lab-based systems, has been employed extensively for evaluating bone micro-to-nano architecture. However, to date, it is still unclear how long exposures to X-ray radiation affect the mechanical properties of trabecular bone, particularly in relation to lab-XCT systems. Indentation has been widely used to identify local mechanical properties such as hardness and elastic modulus of bone and other biological tissues. The purpose of this study is therefore, to use indentation and XCT-based investigative tools such as digital volume correlation (DVC) to assess the microdamage induced by long exposure of trabecular bone tissue to X-ray radiation and how this affects its local mechanical properties. Trabecular bone specimens were indented before and after X-ray exposures of 33 and 66 h, where variation of elastic modulus was evaluated at every stage. The resulting elastic modulus was decreased, and micro-cracks appeared in the specimens after the first long X-ray exposure and crack formation increased after the second exposure. High strain concentration around the damaged tissue exceeding 1% was also observed from DVC analysis. The outcomes of this study show the importance of designing appropriate XCT-based experiments in lab systems to avoid degradation of the bone tissue mechanical properties due to radiation and these results will help to inform future studies that require long X-ray exposure for in situ experiments or generation of reliable subject-specific computational models.

Open-porous magnesium-based scaffolds withstand in vitro corrosion under cyclic loading: A mechanistic study

The successful application of magnesium (Mg) alloys as biodegradable bone substitutes for critical-sized defects may be comprised by their high degradation rate resulting in a loss of mechanical integrity. This study investigates the degradation pattern of an open-porous fluoride-coated Mg-based scaffold immersed in circulating Hanks' Balanced Salt Solution (HBSS) with and without in situ cyclic compression (30 N/1 Hz). The changes in morphological and mechanical properties have been studied by combining in situ high-resolution X-ray computed tomography mechanics and digital volume correlation. Although in situ cyclic compression induced acceleration of the corrosion rate, probably due to local disruption of the coating layer where fatigue microcracks were formed, no critical failures in the overall scaffold were observed, indicating that the mechanical integrity of the Mg scaffolds was preserved. Structural changes, due to the accumulation of corrosion debris between the scaffold fibres, resulted in a significant increase (p < 0.05) in the material volume fraction from 0.52 ± 0.07 to 0.47 ± 0.03 after 14 days of corrosion. However, despite an increase in fibre material loss, the accumulated corrosion products appear to have led to an increase in Young's modulus after 14 days as well as lower third principal strain (εp3) accumulation (−91000 ± 6361 με and −60093 ± 2414 με after 2 and 14 days, respectively). Therefore, this innovative Mg scaffold design and composition provide a bone replacement, capable of sustaining mechanical loads in situ during the postoperative phase allowing new bone formation to be initially supported as the scaffold resorbs.

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First report on in vitro cyclic loading of MgF₂ coated open-porous Mg scaffolds in HBSS simulating 2–3 months in humans.

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Fluoride-coating slows down corrosion under cyclic loading in vitro.

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Entangled scaffold structure accumulates local corrosion debris which keeps the mechanical integrity over 14 days in vitro.

A practical guide for in situ mechanical testing of musculoskeletal tissues using synchrotron tomography

Musculoskeletal tissues are complex hierarchical materials where mechanical response is linked to structural and material properties at different dimensional levels. Therefore, high-resolution three-dimensional tomography is very useful for assessing tissue properties at different scales. In particular, Synchrotron Radiation micro-Computed Tomography (SR-microCT) has been used in several applications to analyze the structure of bone and biomaterials. In the past decade the development of digital volume correlation (DVC) algorithms applied to SR-microCT images and its combination with in situ mechanical testing (four-dimensional imaging) have allowed researchers to visualise, for the first time, the deformation of musculoskeletal tissues and their interaction with biomaterials under different loading scenarios. However, there are several experimental challenges that make these measurements difficult and at high risk of failure. Challenges relate to sample preparation, imaging parameters, loading setup, accumulated tissue damage for multiple tomographic acquisitions, reconstruction methods and data processing. Considering that access to SR-microCT facilities is usually associated with bidding processes and long waiting times, the failure of these experiments could notably slow down the advancement of this research area and reduce its impact. Many of the experimental failures can be avoided with increased experience in performing the tests and better guidelines for preparation and execution of these complex experiments; publication of negative results could help interested researchers to avoid recurring mistakes. Therefore, the goal of this article is to highlight the potential and pitfalls in the design and execution of in situ SR-microCT experiments, involving multiple scans, of musculoskeletal tissues for the assessment of their structural and/or mechanical properties. The advice and guidelines that follow should improve the success rate of this type of experiment, allowing the community to reach higher impact more efficiently.

Characterizing the Mechanical Behavior of Bone and Bone Surrogates in Compression Using pQCT

Many axial and appendicular skeleton bones are subjected to repetitive loading during daily activities. Until recently, the structural analysis of fractures has been limited to 2D sections, and the dynamic assessment of fracture progression has not been possible. The structural failure was analyzed using step-wise micro-compression combined with time-lapsed micro-computed tomographic imaging. The structural failure was investigated in four different sample materials (two different bone surrogates, lumbar vertebral bodies from bovine and red deer). The samples were loaded in different force steps based on uniaxial compression tests. The micro-tomography images were used to create three-dimensional models from which various parameters were calculated that provide information about the structure and density of the samples. By superimposing two 3D images and calculating the different surfaces, it was possible to precisely analyze which trabeculae failed in which area and under which load. According to the current state of the art, bone mineral density is usually used as a value for bone quality, but the question can be raised as to whether other values such as trabecular structure, damage accumulation, and bone mineralization can predict structural competence better than bone mineral density alone.

Digital volume correlation for the characterization of musculoskeletal tissues: Current challenges and future developments

Biological tissues are complex hierarchical materials, difficult to characterise due to the challenges associated to the separation of scale and heterogeneity of the mechanical properties at different dimensional levels. The Digital Volume Correlation approach is the only image-based experimental approach that can accurately measure internal strain field within biological tissues under complex loading scenarios. In this minireview examples of DVC applications to study the deformation of musculoskeletal tissues at different dimensional scales are reported, highlighting the potential and challenges of this relatively new technique. The manuscript aims at reporting the wide breath of DVC applications in the past 2 decades and discuss future perspective for this unique technique, including fast analysis, applications on soft tissues, high precision approaches, and clinical applications.

MicroFE models of porcine vertebrae with induced bone focal lesions: Validation of predicted displacements with digital volume correlation

The evaluation of the local mechanical behavior as a result of metastatic lesions is fundamental for the characterization of the mechanical competence of metastatic vertebrae. Micro finite element (microFE) models have the potential of addressing this challenge through laboratory studies but their predictions of local deformation due to the complexity of the bone structure compromized by the lesion must be validated against experiments. In this study, the displacements predicted by homogeneous, linear and isotropic microFE models of vertebrae were validated against experimental Digital Volume Correlation (DVC) measurements. Porcine spine segments, with and without mechanically induced focal lesions, were tested in compression within a micro computed tomography (microCT) scanner. The displacement within the bone were measured with an optimized global DVC approach (BoneDVC). MicroFE models of the intact and lesioned vertebrae, including or excluding the growth plates, were developed from the microCT images. The microFE and DVC boundary conditions were matched. The displacements measured by the DVC and predicted by the microFE along each Cartesian direction were compared. The results showed an excellent agreement between the measured and predicted displacements, both for intact and metastatic vertebrae, in the middle of the vertebra, in those cases where the structure was not loaded beyond yield (0.69 < R² < 1.00). Models with growth plates showed the worst correlations (0.02 < R² < 0.99), while a clear improvement was observed if the growth plates were excluded (0.56 < R² < 1.00). In conclusion, these simplified models can predict complex displacement fields in the elastic regime with high reliability, more complex non-linear models should be implemented to predict regions with high deformation, when the bone is loaded beyond yield.

Radiotherapy-induced bone deterioration is exacerbated in diabetic rats treated with streptozotocin

Following radiotherapy, patients have decreased bone mass and increased risk of fragility fractures. Diabetes mellitus (DM) is also reported to have detrimental effects on bone architecture and quality. However, no clinical or experimental study has systematically characterized the bone phenotype of the diabetic patients following radiotherapy. After one month of streptozotocin injection, three-month-old male rats were subjected to focal radiotherapy (8 Gy, twice, at days 1 and 3), and then bone mass, microarchitecture, and turnover as well as bone cell activities were evaluated at 2 months post-irradiation. Micro-computed tomography results demonstrated that DM rats exhibited greater deterioration in trabecular bone mass and microarchitecture following irradiation compared with the damage to bone structure induced by DM or radiotherapy. The serum biochemical, bone histomorphometric, and gene expression assays revealed that DM combined with radiotherapy showed lower bone formation rate, osteoblast number on bone surface, and expression of osteoblast-related markers (ALP, Runx2, Osx, and Col-1) compared with DM or irradiation alone. DM plus irradiation also caused higher bone resorption rate, osteoclast number on bone surface, and expression of osteoclast-specific markers (TRAP, cathepsin K, and calcitonin receptor) than DM or irradiation treatment alone. Moreover, lower osteocyte survival and higher expression of Sost and DKK1 genes (two negative modulators of Wnt signaling) were observed in rats with combined DM and radiotherapy. Together, these findings revealed a higher deterioration of the diabetic skeleton following radiotherapy, and emphasized the clinical importance of health maintenance.

Assessment of Intravertebral Mechanical Strains and Cancellous Bone Texture Under Load Using a Clinically Available Digital Tomosynthesis Modality

Vertebral fractures are the most common osteoporotic fractures, but clinical means for assessment of vertebral bone integrity are limited in accuracy, as they typically use surrogate measures that are indirectly related to mechanics. The objective of this study was to examine the extent to which intravertebral strain distributions and changes in cancellous bone texture generated by a load of physiological magnitude can be characterized using a clinically available imaging modality. We hypothesized that digital tomosynthesis-based digital volume correlation (DTS-DVC) and image texture-based metrics of cancellous bone microstructure can detect development of mechanical strains under load. Isolated cadaveric T11 vertebrae and L2-L4 vertebral segments were DTS imaged in a nonloaded state and under physiological load levels. Axial strain, maximum principal strain, maximum compressive and tensile principal strains, and von Mises equivalent strain were calculated using the DVC technique. The change in textural parameters (line fraction deviation, anisotropy, and fractal parameters) under load was calculated within the cancellous centrum. The effect of load on measured strains and texture variables was tested using mixed model analysis of variance, and relationships of strain and texture variables with donor age, bone density parameters, and bone size were examined using regression models. Magnitudes and heterogeneity of intravertebral strain measures correlated with applied loading and were significantly different from background noise. Image texture parameters were found to change with applied loading, but these changes were not observed in the second experiment testing L2-L4 segments. DTS-DVC-derived strains correlated with age more strongly than did bone mineral density (BMD) for T11.

A novel approach to evaluate the effects of artificial bone focal lesion on the three-dimensional strain distributions within the vertebral body

The spine is the first site for incidence of bone metastasis. Thus, the vertebrae have a high potential risk of being weakened by metastatic tissues. The evaluation of strength of the bone affected by the presence of metastases is fundamental to assess the fracture risk. This work proposes a robust method to evaluate the variations of strain distributions due to artificial lesions within the vertebral body, based on in situ mechanical testing and digital volume correlation. Five porcine vertebrae were tested in compression up to 6500N inside a micro computed tomography scanner. For each specimen, images were acquired before and after the application of the load, before and after the introduction of the artificial lesions. Principal strains were computed within the bone by means of digital volume correlation (DVC). All intact specimens showed a consistent strain distribution, with peak minimum principal strain in the range -1.8% to -0.7% in the middle of the vertebra, demonstrating the robustness of the method. Similar distributions of strains were found for the intact vertebrae in the different regions. The artificial lesion generally doubled the strain in the middle portion of the specimen, probably due to stress concentrations close to the defect. In conclusion, a robust method to evaluate the redistribution of the strain due to artificial lesions within the vertebral body was developed and will be used in the future to improve current clinical assessment of fracture risk in metastatic spines.

Multi-scale mechanical and morphological characterisation of sintered porous magnesium-based scaffolds for bone regeneration in critical-sized defects

Magnesium (Mg) and its alloys are very promising degradable, osteoconductive and osteopromotive materials to be used as regenerative treatment for critical-sized bone defects. Under load-bearing conditions, Mg alloys must display sufficient morphological and mechanical resemblance to the native bone they are meant to replace to provide adequate support and enable initial bone bridging. In this study, unique highly open-porous Mg-based scaffolds were mechanically and morphologically characterised at different scales. In situ X-ray computed tomography (XCT) mechanics, digital volume correlation (DVC), electron microscopy and nanoindentation were combined to assess the influence of material properties on the apparent (macro) mechanics of the scaffold. The results showed that Mg exhibited a higher connected structure (38.4mm^-3 and 6.2mm^-3 for Mg and trabecular bone (Tb), respectively) and smaller spacing (245µm and 629µm for Mg and Tb, respectively) while keeping an overall appropriate porosity of 55% in the range of trabecular bone (30-80%). This fully connected and highly porous structure promoted lower local strain compared to the trabecular bone structure at material level (i.e. -22067 ± 8409µε and -40120 ± 18364µε at 6% compression for Mg and trabecular bone, respectively) and highly ductile mechanical behaviour at apparent level preventing premature scaffold failure. Furthermore, the Mg scaffolds exceeded the physiological strain of bone tissue generated in daily activities such as walking or running (500-2000µε) by one order of magnitude. The yield stress was also found to be close to trabecular bone (2.06MPa and 6.67MPa for Mg and Tb, respectively). Based on this evidence, the study highlights the overall biomechanical suitability of an innovative Mg-based scaffold design to be used as a treatment for bone critical-sized defects. STATEMENT OF SIGNIFICANCE: Bone regeneration remains a challenging field of research where different materials and solutions are investigated. Among the variety of treatments, biodegradable magnesium-based implants represent a very promising possibility. The novelty of this study is based on the characterisation of innovative magnesium-based implants whose structure and manufacturing have been optimised to enable the preservation of mechanical integrity and resemble bone microarchitecture. It is also based on a multi-scale approach by coupling high-resolution X-ray computed tomography (XCT), with in situ mechanics, digital volume correlation (DVC) as well as nano-indentation and electron-based microscopy imaging to define how degradable porous Mg-based implants fulfil morphological and mechanical requirements to be used as critical bone defects regeneration treatment.

In Vivo Deformation and Strain Measurements in Human Bone Using Digital Volume Correlation (DVC) and 3T Clinical MRI

Strains within bone play an important role in the remodelling process and the mechanisms of fracture. The ability to assess these strains in vivo can provide clinically relevant information regarding bone health, injury risk, and can also be used to optimise treatments. In vivo bone strains have been investigated using multiple experimental techniques, but none have quantified 3D strains using non-invasive techniques. Digital volume correlation based on clinical MRI (DVC-MRI) is a non-invasive technique that has the potential to achieve this. However, before it can be implemented, uncertainties associated with the measurements must be quantified. Here, DVC-MRI was evaluated to assess its potential to measure in vivo strains in the talus. A zero-strain test (two repeated unloaded scans) was conducted using three MRI sequences, and three DVC approaches to quantify errors and to establish optimal settings. With optimal settings, strains could be measured with a precision of 200 με and accuracy of 480 με for a spatial resolution of 7.5 mm, and a precision of 133 με and accuracy of 251 με for a spatial resolution of 10 mm. These results demonstrate that this technique has the potential to measure relevant levels of in vivo bone strain and to be used for a range of clinical applications.

Heterogeneous Strain Distribution in the Subchondral Bone of Human Osteoarthritic Femoral Heads, Measured with Digital Volume Correlation

Osteoarthritis (OA) is a chronic disease, affecting approximately one third of people over the age of 45. Whilst the etiology and pathogenesis of the disease are still not well understood, mechanics play an important role in both the initiation and progression of osteoarthritis. In this study, we demonstrate the application of stepwise compression, combined with microCT imaging and digital volume correlation (DVC) to measure and evaluate full-field strain distributions within osteoarthritic femoral heads under uniaxial compression. A comprehensive analysis showed that the microstructural features inherent in OA bone did not affect the level of uncertainties associated with the applied methods. The results illustrate the localization of strains at the loading surface as well as in areas of low bone volume fraction and subchondral cysts. Trabecular thickness and connectivity density were identified as the only microstructural parameters with any association to the magnitude of local strain measured at apparent yield strain or the volume of bone exceeding yield strain. This work demonstrates a novel approach to evaluating the mechanical properties of the whole human femoral head in case of severe OA.

Quantifying 3D Strain in Scaffold Implants for Regenerative Medicine

Regenerative medicine solutions require thoughtful design to elicit the intended biological response. This includes the biomechanical stimulus to generate an appropriate strain in the scaffold and surrounding tissue to drive cell lineage to the desired tissue. To provide appropriate strain on a local level, new generations of scaffolds often involve anisotropic spatially graded mechanical properties that cannot be characterised with traditional materials testing equipment. Volumetric examination is possible with three-dimensional (3D) imaging, in situ loading and digital volume correlation (DVC). Micro-CT and DVC were utilised in this study on two sizes of 3D-printed inorganic/organic hybrid scaffolds (n = 2 and n = 4) with a repeating homogenous structure intended for cartilage regeneration. Deformation was observed with a spatial resolution of under 200 µm whilst maintaining displacement random errors of 0.97 µm, strain systematic errors of 0.17% and strain random errors of 0.031%. Digital image correlation (DIC) provided an analysis of the external surfaces whilst DVC enabled localised strain concentrations to be examined throughout the full 3D volume. Strain values derived using DVC correlated well against manually calculated ground-truth measurements (R2 = 0.98, n = 8). The technique ensures the full 3D micro-mechanical environment experienced by cells is intimately considered, enabling future studies to further examine scaffold designs for regenerative medicine.

Sub-trabecular strain evolution in human trabecular bone

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.

Full-field strain of regenerated bone tissue in a femoral fracture model

The mechanical behaviour of regenerated bone tissue during fracture healing is key in determining its ability to withstand physiological loads. However, the strain distribution in the newly formed tissue and how this influences the way a fracture heals it is still unclear. X-ray Computed Tomography (XCT) has been extensively used to assess the progress of mineralised tissues in regeneration and when combined with in situ mechanics and digital volume correlation (DVC) has been proven a powerful tool to understand the mechanical behaviour and full-field three-dimensional (3D) strain distribution in bone. The purpose of this study is therefore to use in situ XCT mechanics and DVC to investigate the strain distribution and load-bearing capacity in a regenerating fracture in the diaphyseal bone, using a rodent femoral fracture model stabilised by external fixation. Rat femurs with 1 mm and 2 mm osteotomy gaps were tested under in situ XCT step-wise compression in the apparent elastic region. High strain was present in the newly formed bone (ε_p1 and ε_p3 reaching 29 000 µε and -43 000 µε, respectively), with a wide variation and inhomogeneity of the 3D strain distribution in the regenerating tissues of the fracture gap, which is directly related to the presence of unmineralised tissue observed in histological images. The outcomes of this study will contribute in understanding natural regenerative ability of bone and its mechanical behaviour under loading.

Full-Field Strain Uncertainties and Residuals at the Cartilage-Bone Interface in Unstained Tissues Using Propagation-Based Phase-Contrast XCT and Digital Volume Correlation

A deeper understanding of the cartilage-bone mechanics is fundamental to unravel onset and progression of osteoarthritis, enabling better diagnosis and treatment. The aim of this study is therefore to explore the capability of X-ray computed (XCT) phase-contrast imaging in a lab-based system to enable digital volume correlation (DVC) measurements of unstained cartilage-bone plugs from healthy adult bovines. DVC strain uncertainties were computed for both articular cartilage and mineralized tissue (calcified cartilage and subchondral bone) in the specimens at increasing propagation distances, ranging from absorption up to four times (4× such effective distance. In addition, a process of dehydration and rehydration was proposed to improve feature recognition in XCT of articular cartilage and mechanical properties of this tissue during the process were assessed via micromechanical probing (indentation), which was also used to determine the effect of long X-ray exposure. Finally, full-field strain from DVC was computed to quantify residual strain distribution at the cartilage-bone interface following unconfined compression test (ex situ). It was found that enhanced gray-scale feature recognition at the cartilage-bone interface was achieved using phase-contrast, resulting in reduced DVC strain uncertainties compared to absorption. Residual strains up to ~7000 µε in the articular cartilage were transferred to subchondral bone via the calcified cartilage and micromechanics revealed the predominant effect of long phase-contrast X-ray exposure in reducing both stiffness and hardness of the articular cartilage. The results of this study will pave the way for further development and refinement of the techniques, improving XCT-based strain measurements in cartilage-bone and other soft-hard tissue interfaces.

Quantifying deformations and strains in human intervertebral discs using Digital Volume Correlation combined with MRI (DVC-MRI)

Physical disruptions to intervertebral discs (IVDs) can cause mechanical changes that lead to degeneration and to low back pain which affects 75% of us in our lifetimes. Quantifying the effects of these changes on internal IVD strains may lead to better preventative strategies and treatments. Digital Volume Correlation (DVC) is a non-invasive technique that divides volumetric images into subsets, and measures strains by tracking the internal patterns within them under load. Applying DVC to MRIs may allow non-invasive strain measurements. However, DVC-MRI for strain measurements in IVDs has not been used previously. The purpose of this study was to quantify the strain and deformation errors associated with DVC-MRI for measurements in human IVDs. Eight human lumbar IVDs were MRI scanned (9.4 T) for a 'zero-strain study' (multiple unloaded scans to quantify noise within the system), and a loaded study (2 mm axial compression). Three DVC methodologies: Fast-Fourier transform (FFT), direct correlation (DC), and a combination of both FFT and DC approaches were compared with subset sizes ranging from 8 to 88 voxels to establish the optimal DVC methodology and settings which were then used in the loaded study. FFT + DC was the optimal method and a subset size of 56 voxels (2520 µm) was found to be a good compromise between errors and spatial resolution. Displacement and strain errors did not exceed 28 µm and 3000 microstrain, respectively. These findings demonstrate that DVC-MRI can quantify internal strains within IVDs non-invasively and accurately. The method has unique potential for assessing IVD strains within patients.

Prenatal growth map of the mouse knee joint by means of deformable registration technique

Joint morphogenesis is the process during which distinct and functional joint shapes emerge during pre- and post-natal joint development. In this study, a repeatable semi-automatic protocol capable of providing a 3D realistic developmental map of the prenatal mouse knee joint was designed by combining Optical Projection Tomography imaging (OPT) and a deformable registration algorithm (Sheffield Image Registration toolkit, ShIRT). Eleven left limbs of healthy murine embryos were scanned with OPT (voxel size: 14.63μm) at two different stages of development: Theiler stage (TS) 23 (approximately 14.5 embryonic days) and 24 (approximately 15.5 embryonic days). One TS23 limb was used to evaluate the precision of the displacement predictions for this specific case. The remaining limbs were then used to estimate Developmental Tibia and Femur Maps. Acceptable uncertainties of the displacement predictions computed from repeated images were found for both epiphyses (between 1.3μm and 1.4μm for the proximal tibia and between 0.7μm and 1.0μm for the femur, along all directions). The protocol was found to be reproducible with maximum Modified Housdorff Distance (MHD) differences equal to 1.9 μm and 1.5 μm for the tibial and femoral epiphyses respectively. The effect of the initial shape of the rudiment affected the developmental maps with MHD of 21.7 μm and 21.9 μm for the tibial and femoral epiphyses respectively, which correspond to 1.4 and 1.5 times the voxel size. To conclude, this study proposes a repeatable semi-automatic protocol capable of providing mean 3D realistic developmental map of a developing rudiment allowing researchers to study how growth and adaptation are directed by biological and mechanobiological factors.

Preservation of Bone Tissue Integrity with Temperature Control for In Situ SR-MicroCT Experiments

Digital volume correlation (DVC), combined with in situ synchrotron microcomputed tomography (SR-microCT) mechanics, allows for 3D full-field strain measurement in bone at the tissue level. However, long exposures to SR radiation are known to induce bone damage, and reliable experimental protocols able to preserve tissue properties are still lacking. This study aims to propose a proof-of-concept methodology to retain bone tissue integrity, based on residual strain determination using DVC, by decreasing the environmental temperature during in situ SR-microCT testing. Compact and trabecular bone specimens underwent five consecutive full tomographic data collections either at room temperature or 0 °C. Lowering the temperature seemed to reduce microdamage in trabecular bone but had minimal effect on compact bone. A consistent temperature gradient was measured at each exposure period, and its prolonged effect over time may induce localised collagen denaturation and subsequent damage. DVC provided useful information on irradiation-induced microcrack initiation and propagation. Future work is necessary to apply these findings to in situ SR-microCT mechanical tests, and to establish protocols aiming to minimise the SR irradiation-induced damage of bone.

The Effect of Material Heterogeneity, Element Type, and Down-Sampling on Trabecular Stiffness in Micro Finite Element Models

Preclinical and clinical bone strength predictions can be elucidated by understanding bone mechanics at a variety of hierarchical levels. As such, down-sampled micro-CT images are often used to make comparisons across image resolutions or used to reduce computational resources in micro finite element models (µFEMs). Therefore, the objectives of this study were to compare trabecular apparent modulus among (i) hexahedral and tetrahedral µFEMs, (ii) µFEMs generated from 32, 64, and 64 µm down-sampled from 32 µm µCT scans, and (iii) µFEMs with homogeneous and heterogeneous tissue moduli. Trabecular µFEMs were generated from scans at the three spatial resolutions taken from the glenoid vault of 14 cadaveric specimens. Simulated unconstrained compression was performed and used to calculate and compare the apparent modulus of each µFEM. It was found that models derived from high-resolution images that account for material heterogeneity are nearly equivalent whether hexahedral or tetrahedral elements are used. However, translation of stiffness from down-sampled scans are not equivalent to scans performed at the down-sampled resolution, or that account for trabecular material heterogeneity. Material heterogeneity is most representative of in vivo trabecular bone and to accurately model trabecular mechanical properties, material heterogeneity should be considered in future µFEM development.

Variability in strain distribution in the mice tibia loading model: A preliminary study using digital volume correlation

It is well known that bone has an enormous adaptive capacity to mechanical loadings, and to this extent, several in vivo studies on mouse tibia use established cyclic compressive loading protocols to investigate the effects of mechanical stimuli. In these experiments, the applied axial load is well controlled but the positioning of the hind-limb between the loading endcaps may dramatically affect the strain distribution induced on the tibia. In this study, the full field strain distribution induced by a typical in vivo setup on mouse tibiae was investigated through a combination of in situ compressive testing, µCT scanning and a global digital volume correlation (DVC) approach. The precision of the DVC method and the effect of repositioning on the strain distributions were evaluated. Acceptable uncertainties of the DVC approach for the analysis of loaded tibiae (411 ± 58µɛ) were found for nodal spacing of approximately 50 voxels (520 µm). When pairs of in situ preloaded and loaded images were registered, low variability of the strain distributions within the tibia were seen (range of mean differences in principal strains: 585-1800µɛ). On contrary, larger differences were seen after repositioning (range of mean differences in principal strains: 2500-5500µɛ). To conclude, these preliminary results on thee specimens showed that the DVC approach applied to the mouse tibia can be precise enough to evaluate local strain distributions under loads, and that repositioning of the hind-limb within the testing machine can induce large differences in the strain distributions that should be accounted for when modelling this system.

Effect of SR-microCT radiation on the mechanical integrity of trabecular bone using in situ mechanical testing and digital volume correlation

The use of synchrotron radiation micro-computed tomography (SR-microCT) is becoming increasingly popular for studying the relationship between microstructure and bone mechanics subjected to in situ mechanical testing. However, it is well known that the effect of SR X-ray radiation can considerably alter the mechanical properties of bone tissue. Digital volume correlation (DVC) has been extensively used to compute full-field strain distributions in bone specimens subjected to step-wise mechanical loading, but tissue damage from sequential SR-microCT scans has not been previously addressed. Therefore, the aim of this study is to examine the influence of SR irradiation-induced microdamage on the apparent elastic properties of trabecular bone using DVC applied to in situ SR-microCT tomograms obtained with different exposure times. Results showed how DVC was able to identify high local strain levels (> 10,000 µε) corresponding to visible microcracks at high irradiation doses (~ 230 kGy), despite the apparent elastic properties remained unaltered. Microcracks were not detected and bone plasticity was preserved for low irradiation doses (~ 33 kGy), although image quality and consequently, DVC performance were reduced. DVC results suggested some local deterioration of tissue that might have resulted from mechanical strain concentration further enhanced by some level of local irradiation even for low accumulated dose.

Validation of finite element models of the mouse tibia using digital volume correlation

The mouse tibia is a common site to investigate bone adaptation. Micro-Finite Element (microFE) models based on micro-Computed Tomography (microCT) images can estimate bone mechanical properties non-invasively but their outputs need to be validated with experiments. Digital Volume Correlation (DVC) can provide experimental measurements of displacements over the whole bone volume. In this study we applied DVC to validate the local predictions of microFE models of the mouse tibia in compression. Six mouse tibiae were stepwise compressed within a microCT system. MicroCT images were acquired in four configurations with applied compression of 0.5 N (preload), 6.5 N, 13.0 N and 19.5 N. Failure load was measured after the last scan. A global DVC algorithm was applied to the microCT images in order to obtain the displacement field over the bone volume. Homogeneous, isotropic linear hexahedral microFE models were generated from the images collected in the preload configuration with boundary conditions interpolated from the DVC displacements at the extremities of the tibia. Experimental displacements from DVC and numerical predictions were compared at corresponding locations in the middle of the bone. Stiffness and strength were also estimated from each model and compared with the experimental measurements. The magnitude of the displacement vectors predicted by microFE models was highly correlated with experimental measurements (R² >0.82). Higher but still reasonable errors were found for the Cartesian components. The models tended to overestimate local displacements in the longitudinal direction (R² = 0.69-0.90, slope of the regression line=0.50-0.97). Errors in the prediction of structural mechanical properties were 14% ± 11% for stiffness and 9% ± 9% for strength. In conclusion, the DVC approach has been applied to the validation of microFE models of the mouse tibia. The predictions of the models for both structural and local properties have been found reasonable for most preclinical applications.

A review of techniques for visualising soft tissue microstructure deformation and quantifying strain Ex Vivo

Many biological tissues have a complex hierarchical structure allowing them to function under demanding physiological loading conditions. Structural changes caused by ageing or disease can lead to loss of mechanical function. Therefore, it is necessary to characterise tissue structure to understand normal tissue function and the progression of disease. Ideally intact native tissues should be imaged in 3D and under physiological loading conditions. The current published in situ imaging methodologies demonstrate a compromise between imaging limitations and maintaining the samples native mechanical function. This review gives an overview of in situ imaging techniques used to visualise microstructural deformation of soft tissue, including three case studies of different tissues (tendon, intervertebral disc and artery). Some of the imaging techniques restricted analysis to observational mechanics or discrete strain measurement from invasive markers. Full-field local surface strain measurement has been achieved using digital image correlation. Volumetric strain fields have successfully been quantified from in situ X-ray microtomography (micro-CT) studies of bone using digital volume correlation but not in soft tissue due to low X-ray transmission contrast. With the latest developments in micro-CT showing in-line phase contrast capability to resolve native soft tissue microstructure, there is potential for future soft tissue mechanics research where 3D local strain can be quantified. These methods will provide information on the local 3D micromechanical environment experienced by cells in healthy, aged and diseased tissues. It is hoped that future applications of in situ imaging techniques will impact positively on the design and testing of potential tissue replacements or regenerative therapies. LAY DESCRIPTION: The soft tissues in our bodies, such as tendons, intervertebral discs and arteries, have evolved to have complicated structures which deform and bear load during normal function. Small changes in these structures can occur with age and disease which then leads to loss of function. Therefore, it is important to image tissue microstructure in 3D and under functional conditions. This paper gives an overview of imaging techniques used to record the deformation of soft tissue microstructures. Commonly there are compromises between obtaining the best imaging result and retaining the samples native structure and function. For example, invasive markers and dissecting samples damages the tissues natural structure, and staining or clearing (making the tissue more transparent) can distort tissue structure. Structural deformation has been quantified from 2D imaging techniques (digital image correlation) to create surface strain maps which help identify local tissue mechanics. When extended to 3D (digital volume correlation), deformation measurement has been limited to bone samples using X-ray micro-CT. Recently it has been possible to image the 3D structure of soft tissue using X-ray micro-CT meaning that there is potential for internal soft tissue mechanics to be mapped in 3D. Future application of micro-CT and digital volume correlation will be important for soft tissue mechanics studies particularly to understand normal function, progression of disease and in the design of tissue replacements.

Micro Finite Element models of the vertebral body: Validation of local displacement predictions

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.