Comparison of the Linear Finite Element Prediction of Deformation and Strain of Human Cancellous Bone to 3D Digital Volume Correlation Measurements

Digital wrist tomosynthesis (DWT)-based finite element analysis of ultra-distal radius differentiates patients with and without a history of osteoporotic fracture

Despite effective therapies for those at risk of osteoporotic fracture, low adherence to screening guidelines and limited accuracy of bone mineral density (BMD) in predicting fracture risk preclude identification of those at risk. Because of high adherence to routine mammography, bone health screening at the time of mammography using a digital breast tomosynthesis (DBT) scanner has been suggested as a potential solution. BMD and bone microstructure can be measured from the wrist using a DBT scanner. However, the extent to which biomechanical variables can be derived from digital wrist tomosynthesis (DWT) has not been explored. Accordingly, we measured stiffness from a DWT based finite element (DWT-FE) model of the ultra-distal (UD) radius and ulna, and correlate these to reference microcomputed tomography image based FE (μCT-FE) from five cadaveric forearms. Further, this method is implemented to determine in vivo reproducibility of FE derived stiffness of UD radius and demonstrate the in vivo utility of DWT-FE in bone quality assessment by comparing two groups of postmenopausal women with and without a history of an osteoporotic fracture (Fx; n = 15, NFx; n = 51). Stiffness obtained from DWT and μCT had a strong correlation (R2 = 0.87, p < 0.001). In vivo repeatability error was <5 %. The NFx and Fx groups were not significantly different in DXA derived minimum T-scores (p > 0.3), but stiffness of the UD radius was lower for the Fx group (p < 0.007). Logistic regression models of fracture status with stiffness of the nondominant arm as the predictor were significant (p < 0.01). In conclusion this study demonstrates the feasibility of fracture risk assessment in mammography settings using DWT imaging and FE modeling in vivo. Using this approach, bone and breast screening can be performed in a single visit, with the potential to improve both the prevalence of bone health screening and the accuracy of fracture risk assessment.

Stiffness and Strain Properties Derived From Digital Tomosynthesis-Based Digital Volume Correlation Predict Vertebral Strength Independently From Bone Mineral Density

Vertebral fractures are the most common osteoporotic fractures, but their prediction using standard bone mineral density (BMD) measurements from dual energy X-ray absorptiometry (DXA) is limited in accuracy. Stiffness, displacement, and strain distribution properties derived from digital tomosynthesis-based digital volume correlation (DTS-DVC) have been suggested as clinically measurable metrics of vertebral bone quality. However, the extent to which these properties correlate to vertebral strength is unknown. To establish this relationship, two independent experiments, one examining isolated T11 and the other examining L3 vertebrae within the L2-L4 segments from cadaveric donors were utilized. Following DXA and DTS imaging, the specimens were uniaxially compressed to fracture. BMD, bone mineral content (BMC), and bone area were recorded for the anteroposterior and lateromedial views from DXA, stiffness, endplate to endplate displacement and distribution statistics of intravertebral strains were calculated from DTS-DVC and vertebral strength was measured from mechanical tests. Regression models were used to examine the relationships of strength with the other variables. Correlations of BMD with vertebral strength varied between experimental groups (R2adj = 0.19-0.78). DTS-DVC derived properties contributed to vertebral strength independently from BMD measures (increasing R2adj to 0.64-0.95). DTS-DVC derived stiffness was the best single predictor (R2adj = 0.66, p < 0.0001) and added the most to BMD in models of vertebral strength for pooled T11 and L3 specimens (R2adj = 0.95, p < 0.0001). These findings provide biomechanical relevance to DTS-DVC calculated properties of vertebral bone and encourage further efforts in the development of the DTS-DVC approach as a clinical tool.

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.

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.

Nonlinear micro finite element models based on digital volume correlation measurements predict early microdamage in newly formed bone

Bone regeneration in critical-sized defects is a clinical challenge, with biomaterials under constant development aiming at enhancing the natural bone healing process. The delivery of bone morphogenetic proteins (BMPs) in appropriate carriers represents a promising strategy for bone defect treatment but optimisation of the spatial-temporal release is still needed for the regeneration of bone with biological, structural, and mechanical properties comparable to the native tissue. Nonlinear micro finite element (μFE) models can address some of these challenges by providing a tool able to predict the biomechanical strength and microdamage onset in newly formed bone when subjected to physiological or supraphysiological loads. Yet, these models need to be validated against experimental data. In this study, experimental local displacements in newly formed bone induced by osteoinductive biomaterials subjected to in situ X-ray computed tomography compression in the apparent elastic regime and measured using digital volume correlation (DVC) were used to validate μFE models. Displacement predictions from homogeneous linear μFE models were highly correlated to DVC-measured local displacements, while tissue heterogeneity capturing mineralisation differences showed negligible effects. Nonlinear μFE models improved the correlation and showed that tissue microdamage occurs at low apparent strains. Microdamage seemed to occur next to large cavities or in biomaterial-induced thin trabeculae, independent of the mineralisation. While localisation of plastic strain accumulation was similar, the amount of damage accumulated in these locations was slightly higher when including material heterogeneity. These results demonstrate the ability of the nonlinear μFE model to capture local microdamage in newly formed bone tissue and can be exploited to improve the current understanding of healing bone and mechanical competence. This will ultimately aid the development of BMPs delivery systems for bone defect treatment able to regenerate bone with optimal biological, mechanical, and structural properties.

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.

Microstructure and mechanical behaviors of tibia for collagen-induced arthritic mice treated with gingiva-derived mesenchymal stem cells

Rheumatoid arthritis (RA) is a systemic polyarticular arthritis that primarily affects the small joints but also causes bone erosion in large joints. None of the currently existing treatment approaches is curable. In this study, the effects of human gingiva-derived mesenchymal stem cells (GMSCs) on collagen-induced arthritis (CIA) mice are examined by experimentally assessing the microstructure and mechanical behaviors of tibia. Bone morphology and mineral density of mouse tibiae were assessed using micro-X-ray computed tomography (micro-CT). Compression testing was performed on mouse tibia to access its stiffness. The deformation and strain localized inside proximal tibia were mapped using mechanical testing coupled with micro-CT and digital volume correlation of micro-CT images. The results show that CIA disease caused bone erosion in epiphyseal cortical bone, which manifested into the adjacent epiphyseal trabecular bone, and also affected the metaphyseal cortical bone. CIA disease also weakened the load-bearing function of proximal tibia. GMSC treatment interfered with the progress of CIA, attenuated the bone erosion in epiphyseal and metaphyseal trabecular bone and resulted in improved load-bearing function of proximal tibia. GMSCs provide a promising potential treatment of autoimmune arthritis.

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.

Digital volume correlation using a spherical shell template and cubic element for large rotation measurement

The displacement hypothesis of eight-node cubic elements is selected as the shape function of digital volume correlation (DVC), and the Newton-Raphson iterative method is selected to solve the partial differential equation to measure the displacement field. In order to ensure that the DVC algorithm is usable under the large rotation condition, the spherical shell template matching technique is presented to perform the integer-voxel displacement searching for nodes, which can provide the optimal initial values for the Newton-Raphson iterative method due to the rotation and translation invariance of the spherical shell template. Simulated volume images are used to verify the reliability of the proposed method, and the results show that the proposed DVC method can be used to measure the deformation with an arbitrary rigid body rotation angle. This work is expected to be useful to measure deformation with large rotation of the internal structure of materials.

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.

Vertebral stiffness measured via tomosynthesis-based digital volume correlation is strongly correlated with reference values from micro-CT-based DVC

Digital tomosynthesis (DTS) is a clinically available modality that allows imaging of a patient's spine in supine and standing positions. The purpose of this study was to establish the extent to which vertebral displacement and stiffness derived from DTS-based digital volume correlation (DTS-DVC) are correlated with those from a reference method, i.e., microcomputed tomography-based DVC (μCT-DVC). T11 vertebral bodies from 11 cadaveric donors were DTS imaged twice in a nonloaded state and once under a fixed load level approximating upper body weight. The same vertebrae were µCT imaged in nonloaded and loaded states (40 μm voxel size). Vertebral displacements were calculated at each voxel using DVC with pairs of nonloaded and loaded images, from which endplate-to-endplate axial displacement (D_DVC) and vertebral stiffness (S_DVC) were calculated. Both D_DVC and S_DVC demonstrated strong positive correlations between DTS-DVC and μCT-DVC, with correlations being stronger when vertebral displacement was calculated using the median (R²=0.80; p<0.0002 and R²=0.93; p<0.0001, respectively) rather than average displacement (R²=0.63; p<0.004 and R²=0.69; p<0.002, respectively). In conclusion, the demonstrated relationship of DTS-DVC with the μCT standard supports further development of a biomechanics-based clinical assessment of vertebral bone quality using the DTS-DVC technique.

3D full-field strain in bone-implant and bone-tooth constructs and their morphological influential factors

The biomechanics of bone-tooth and bone-implant interfaces affects the outcomes of several dental treatments, such as implant placement, because bone, tooth and periodontal ligament are living tissues that adapt to the changes in mechanical stimulations. In this work, mechanical testing coupled with micro-CT was performed on human cadaveric mandibular bone-tooth and bone-implant constructs. Using digital volume correlation, the 3D full-field strain in bone under implant loading and tooth loading was measured. Concurrently, bone morphology and bone-implant and bone-tooth contact were also measured through the analysis of micro-CT images. The results show that strain in bone increased when a tooth was replaced by a dental implant. Strain concentration was observed in peri-implant bone, as well as in the buccal bone plate, which is also the clinically-observed bone resorption area after implant placement. Decreasing implant stability measurements (resonance frequency analysis and torque test) indicated increased peri-implant strain, but their relationships may not be linear. Peri-implant bone strain linearly increased with decreasing bone-implant contact (BIC) ratio. It also linearly decreased with increasing bone-tooth/bone-implant contact ratio. The high strain in the buccal bone plate linearly increased with decreasing buccal bone plate thickness. The results of this study revealed 3D full-field strain in bone-tooth and bone-implant constructs, as well as their several morphological influential factors.

A new finite element based parameter to predict bone fracture

Dual Energy X-Ray Absorptiometry (DXA) is currently the most widely adopted non-invasive clinical technique to assess bone mineral density and bone mineral content in human research and represents the primary tool for the diagnosis of osteoporosis. DXA measures areal bone mineral density, BMD, which does not account for the three-dimensional structure of the vertebrae and for the distribution of bone mass. The result is that longitudinal DXA can only predict about 70% of vertebral fractures. This study proposes a complementary tool, based on Finite Element (FE) models, to improve the DXA accuracy. Bone is simulated as elastic and inhomogeneous material, with stiffness distribution derived from DXA greyscale images of density. The numerical procedure simulates a compressive load on each vertebra to evaluate the local minimum principal strain values. From these values, both the local average and the maximum strains are computed over the cross sections and along the height of the analysed bone region, to provide a parameter, named Strain Index of Bone (SIB), which could be considered as a bone fragility index. The procedure is initially validated on 33 cylindrical trabecular bone samples obtained from porcine lumbar vertebrae, experimentally tested under static compressive loading. Comparing the experimental mechanical parameters with the SIB, we could find a higher correlation of the ultimate stress, σULT, with the SIB values (R2adj = 0.63) than that observed with the conventional DXA-based clinical parameters, i.e. Bone Mineral Density, BMD (R2adj = 0.34) and Trabecular Bone Score, TBS (R2adj = -0.03). The paper finally presents a few case studies of numerical simulations carried out on human lumbar vertebrae. If our results are confirmed in prospective studies, SIB could be used-together with BMD and TBS-to improve the fracture risk assessment and support the clinical decision to assume specific drugs for metabolic bone diseases.

Fully experiment-based evaluation of few digital volume correlation techniques

Digital Volume Correlation (DVC) is a powerful set of techniques used to compute the local shifts of 3D images obtained, for instance, in tomographic experiments. It is utilized to analyze the geometric changes of the investigated object as well as to correct the corresponding image misalignments for further analysis. It can therefore be used to evaluate the local density changes of the same regions of the inspected specimens, which might be shifted between measurements. In recent years, various approaches and corresponding pieces of software were introduced. Accuracies for the computed shift vectors of up to about 1‰ of a single voxel size have been reported. These results, however, were based either on synthetic datasets or on an unrealistic setup. In this work, we propose two simple methods to evaluate the accuracy of DVC-techniques using more realistic input data and apply them to several DVC programs. We test these methods on three materials (tuff, sandstone, and concrete) that show different contrast and structural features.

Three-dimensional static optical coherence elastography based on inverse compositional Gauss-Newton digital volume correlation

The three-dimensional (3D) mechanical properties characterization of tissue is essential for physiological and pathological studies, as biological tissue is mostly heterogeneous and anisotropic. A digital volume correlation (DVC)-based 3D optical coherence elastography (OCE) method is developed to measure the 3D displacement and strain tensors. The DVC algorithm includes a zero-mean normalized cross-correlation criterion-based coarse search regime, an inverse compositional Gauss-Newton fine search algorithm and a local ternary quadratic polynomial fitting strain calculation method. A 3D optical coherence tomography (OCT) scanning protocol is proposed through theoretical analysis and experimental verification. Measurement errors of the DVC-based 3D OCE method are evaluated to be less than 2.0 μm for displacements and 0.30% for strains by rigid body motion experiments. The 3D displacements and strains of a phantom and a specimen of chicken breast tissue under compression are measured. Results of the phantom show a good agreement with theoretical analysis and tensile testing. The strains of the chicken breast tissue indicate anisotropic biomechanical properties. This study provides an effective method for 3D biomechanical property studies of soft tissue and improves the development of 3D OCE techniques.

Digital tomosynthesis based digital volume correlation: A clinically viable noninvasive method for direct measurement of intravertebral displacements using images of the human spine under physiological load

PURPOSE

We have developed a clinically viable method for measurement of direct, patient-specific intravertebral displacements using a novel digital tomosynthesis based digital volume correlation technique. These displacements may be used to calculate vertebral stiffness under loads induced by a patient's body weight; this is particularly significant because, among biomechanical variables, stiffness is the strongest correlate of bone strength. In this proof of concept study, we assessed the feasibility of the method through a preliminary evaluation of the accuracy and precision of the method, identification of a range of physiological load levels for which displacements are measurable, assessment of the relationship of measured displacements with microcomputed tomography based standards, and demonstration of the in vivo application of the technique.

METHODS

Five cadaveric T11 vertebrae were allocated to three groups in order to study (a) the optimization of digital volume correlation algorithm input parameters, (b) accuracy and precision of the method and the ability to measure displacements at a range of physiological load levels, and (c) the correlation between displacements measured using tomosynthesis based digital volume correlation vs. high resolution microcomputed tomography based digital volume correlation and large scale finite element models. Tomosynthesis images of one patient (Female, 60 yr old) were used to calculate displacement maps, and in turn stiffness, using images acquired in both standing and standing-with-weight (8 kg) configurations.

RESULTS

We found that displacements were accurate (2.28 µm total error) and measurable at physiological load levels (above 267 N) with a linear response to applied load. Calculated stiffness among three tested vertebral bodies was within an acceptable range relative to reported values for vertebral stiffness (5651-13260 N/mm). Displacements were in good qualitative and quantitative agreement with both microcomputed tomography based finite element (r²  = 0.762, P < 0.001) and digital volume correlation (r²  = 0.799, P < 0.001) solutions. For one patient tested twice, once standing and once holding weights, results demonstrated excellent qualitative reproducibility of displacement distributions with superior endplate displacements increasing by 22% with added weight.

CONCLUSIONS

The results of this work collectively suggest the feasibility of the method for in vivo measurement of intravertebral displacements and stiffness in humans. These findings suggest that digital volume correlation using digital tomosynthesis imaging may be useful in understanding the mechanical response of bone to disease and may further enhance our ability to assess fracture risk and treatment efficacy for the spine.

3D Strain and Elasticity Measurement of Layered Biomaterials by Optical Coherence Elastography based on Digital Volume Correlation and Virtual Fields Method

The three-dimensional (3D) mechanical property characterization of biological tissues is essential for physiological and pathological studies. A digital volume correlation (DVC) and virtual fields method (VFM) based 3D optical coherence elastography (OCE) method is developed to quantitatively measure the 3D full-field displacements, strains and elastic parameters of layered biomaterials assuming the isotropy and homogeneity of each layer. The integrated noise-insensitive DVC method can obtain the 3D strain tensor with an accuracy of 10%. Automatic segmentation of the layered materials is realized based on the full field strain and strain gradient. With the strain tensor as input, and in combination with the segmented geometry, the Young’s modulus and Poison’s ratio of each layer of a double-layered material and a pork specimen are obtained by the VFM. This study provides a powerful experimental method for the differentiation of various components of heterogeneous biomaterials, and for the measurement of biomechanics.

Voxel-based micro-finite element analysis of dental implants in a human cadaveric mandible: Tissue modulus assignment and sensitivity analyses

The success of dental implant treatment is related to the complex 3-dimensional (3D) biomechanics of the implant-bone interaction. In this work, 3D numerical models are built based on micro X-ray computed tomography (micro-CT) images of a cadaveric mandible specimen with implants placed in it. The simulation results show that the computed strain values in bone are sensitive to the uncertainties in trabecular tissue modulus and fairly insensitive to the modulus of implants and teeth and the detailed geometry of the fixed boundary condition. A bone-volume-fraction (BV/TV) based method is proposed to assign the tissue moduli of bone elements based on their BV/TV to increase the connectivity of the mesh and to improve the accuracy of the models. These models are potentially powerful for calculating the 3D full-field bone strain under implant loading, enabling in silico testing of different implant designs, but demand validation of the models. The computed results reveal high strain concentration at bone-implant contact areas and, more importantly, in the buccal (lip-side) bone that is not making contact with the implant. The computed strain concentration patterns are found to be in good agreement with the observations from our prior experiments using 3D full-field mechanical testing coupled with micro-CT and digital volume correlation. The buccal bone is thinner and less stiff than other areas of bone and is also the commonly observed area of bone resorption after dental implant treatment.

Mechanical simulation study of postoperative displacement of trochanteric fractures using the finite element method

BACKGROUND

Femoral trochanteric fractures are common among older adults. In the reduction of trochanteric fractures, acquiring the support of the anterior cortex at the fracture site on lateral view immediately after surgery is important. However, even if the cortical support is acquired, postoperative displacement due to the loss of this support often occurs. This study aimed to investigate local stress distribution in several trochanteric fracture models and to evaluate risk factors for postoperative displacement using the finite element (FE) method.

METHODS

Displaced two-fragment fracture models with an angulation deformity at the fracture site and a non-displaced two-fragment fracture model were constructed. The models with an angulation deformity were of two types, one with the proximal fragment directed backward (type A) and the other with the proximal fragment rotated forward from the femoral neck axis (type B). Thereafter, FE models of the femur and a sliding hip screw mounted on a 135° three-hole side-plate were constructed. A 2010-N load was applied to the femoral head, and a 1086-N load was applied to the greater trochanter. Under this condition, the maximum value of the von Mises stress distribution and the amount of displacement of the femoral head vertex in the distal direction were investigated.

RESULTS

A larger maximum stress value at the medial femoral neck cortex and a higher amount of displacement in the distal direction were particularly recognized in type A models. These results indicate that microstructural damage was larger in type A models and that type A fracture alignment may be particularly related to fracture collapse and subsequent postoperative displacement.

CONCLUSION

Even if support of the anterior cortex at the fracture site on lateral view is acquired immediately after surgery, caution is necessary for cases in which the proximal fragment is directed backward in the postoperative displacement from the viewpoint of the biomechanics of the FE method.

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.

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 three-dimensional strain measurement method in elastic transparent materials using tomographic particle image velocimetry

Background

The mechanical interaction between blood vessels and medical devices can induce strains in these vessels. Measuring and understanding these strains is necessary to identify the causes of vascular complications. This study develops a method to measure the three-dimensional (3D) distribution of strain using tomographic particle image velocimetry (Tomo-PIV) and compares the measurement accuracy with the gauge strain in tensile tests.

Methods and findings

The test system for measuring 3D strain distribution consists of two cameras, a laser, a universal testing machine, an acrylic chamber with a glycerol water solution for adjusting the refractive index with the silicone, and dumbbell-shaped specimens mixed with fluorescent tracer particles. 3D images of the particles were reconstructed from 2D images using a multiplicative algebraic reconstruction technique (MART) and motion tracking enhancement. Distributions of the 3D displacements were calculated using a digital volume correlation. To evaluate the accuracy of the measurement method in terms of particle density and interrogation voxel size, the gauge strain and one of the two cameras for Tomo-PIV were used as a video-extensometer in the tensile test. The results show that the optimal particle density and interrogation voxel size are 0.014 particles per pixel and 40 × 40 × 40 voxels with a 75% overlap. The maximum measurement error was maintained at less than 2.5% in the 4-mm-wide region of the specimen.

Conclusions

We successfully developed a method to experimentally measure 3D strain distribution in an elastic silicone material using Tomo-PIV and fluorescent particles. To the best of our knowledge, this is the first report that applies Tomo-PIV to investigate 3D strain measurements in elastic materials with large deformation and validates the measurement accuracy.

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.

The pressure-induced deformation response of the human lamina cribrosa: Analysis of regional variations

The objective of this study was to measure the pressure-induced deformation response of the human lamina cribrosa (LC) and analyze for variations with age and anatomical region. The posterior scleral cup of 8 eyes from 6 human donors was mounted onto a custom inflation chamber. A laser-scanning microscope was used for second harmonic generation (SHG) imaging of the collagen structure in the posterior volume of the LC at pressures from 5mmHg to 45mmHg. The SHG volumes were analyzed by the Fast-Fourier Iterative Digital Volume Correlation (DVC) algorithm for the three dimensional (3D) displacement field. The components of the Green-Lagrange strain tensor and the in-plane principal and maximum shear strains were evaluated from the DVC displacement field for the central and peripheral regions of the LC and the nasal, temporal, inferior, and superior quadrants surrounding the central retinal artery and vein. Among the major findings were that older age was associated with lower strains, the maximum shear strain was larger in the peripheral than central region, and the maximum principal strain was lower in the nasal quadrant. The elliptical shape of the LC was also predictive of the biaxial strain ratio. Age-related and structure-related variations in the pressure-induced strains of the LC may contribute to the susceptibility and severity of optic nerve damage in glaucoma, and regional variations may explain the progression of axonal damage and tissue remodeling observed in the LC in glaucoma.

STATEMENT OF SIGNIFICANCE

Glaucoma causes vision loss through progressive damage of the retinal ganglion axons at the lamina cribrosa (LC), the connective tissue structure that supports the axons as they leave the eye. Mechanical characterization of the LC is challenging because of the complex 3D shape and inaccessibility of the tissue. We present a new method using digital volume correlation to map the 3D displacement and strain fields in the LC under inflation. We report for the first time significant regional variations in the strains that are consistent with the pattern of optic nerve damage in early glaucoma. Thus regional strain variations may be predictive of the progression of axonal damage in glaucoma.

Application of digital volume correlation to study the efficacy of prophylactic vertebral augmentation

BACKGROUND

Prophylactic augmentation is meant to reinforce the vertebral body, but in some cases it is suspected to actually weaken it. Past studies only investigated structural failure and the surface strain distribution. To elucidate the failure mechanism of the augmented vertebra, more information is needed about the internal strain distribution. This study aims to measure, for the first time, the full-field three-dimensional strain distribution inside augmented vertebrae in the elastic regime and to failure.

METHODS

Eight porcine vertebrae were prophylactically-augmented using two augmentation materials. They were scanned with a micro-computed tomography scanner (38.8μm voxel resolution) while undeformed, and loaded at 5%, 10%, and 15% compressions. Internal strains (axial, antero-posterior and lateral-lateral components) were computed using digital volume correlation.

FINDINGS

For both augmentation materials, the highest strains were measured in the regions adjacent to the injected cement mass, whereas the cement-interdigitated-bone was less strained. While this was already visible in the elastic regime (5%), it was a predictor of the localization of failure, which became visible at higher degrees of compression (10% and 15%), when failure propagated across the trabecular bone. Localization of high strains and failure was consistent between specimens, but different between the cement types.

INTERPRETATION

This study indicated the potential of digital volume correlation in measuring the internal strain (elastic regime) and failure in augmented vertebrae. While the cement-interdigitated region becomes stiffer (less strained), the adjacent non-augmented trabecular bone is affected by the stress concentration induced by the cement mass. This approach can help establish better criteria to improve vertebroplasty.

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 (U_X: y=1.07x-0.002, RMSE: 0.001mm; U_Y: y=1.03x-0.001, RMSE: 0.001mm; U_Z: 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.

Strain mapping and correlative microscopy of the alveolar bone in a bone-periodontal ligament-tooth fibrous joint

This study details a method to calculate strains within interradicular alveolar bone using digital volume correlation on X-ray tomograms of intact bone-periodontal ligament-tooth fibrous joints. The effects of loading schemes (concentric and eccentric) and optical magnification on the resulting strain in alveolar bone will be investigated with an intent to correlate deformation gradients with data sets from other complementary techniques. Strain maps will be correlated with structural and site-specific mechanical properties obtained on the same specimen using atomic force microscopy and atomic force microscopy-based nanoindentation technique. Specimens include polydimethylsiloxane as a standard material and intact hemi-mandibles harvested from rats. X-ray tomograms were taken at no-load and loaded conditions using an in situ load cell coupled to a micro X-ray computed tomography unit. Digital volume correlation was used to calculate deformations within alveolar bone. Comparison of strain maps was made as a result of different loading schemes (concentric vs eccentric) and at different magnifications (4× vs 10×). Virtual sections and strain maps from digital volume correlation solutions were aligned with structure and reduced elastic modulus to correlate datasets of the same region within a specimen. Strain distribution between concentrically and eccentrically loaded complexes was different but illustrated a similar range. Strain maps of homogeneous materials (polydimethylsiloxane) resulting from digital volume correlation at different magnifications were similar. However, strain maps of heterogeneous materials at lower and higher magnification differed. The digital volume correlation technique illustrated a dependence on optical magnification specifically for heterogeneous materials such as bone. The results at a higher optical magnification highlight the potential for extracting deformation at higher resolutions. Correlation of data spaces from different complementary techniques is plausible and could provide insights into biological and physicochemical processes that lead to functional adaptation of tissues and joints.

Phase-Contrast Micro-Computed Tomography Measurements of the Intraocular Pressure-Induced Deformation of the Porcine Lamina Cribrosa

The lamina cribrosa (LC) is a complex mesh-like tissue in the posterior eye. Its biomechanical environment is thought to play a major role in glaucoma, the second most common cause of blindness. Due to its small size and relative inaccessibility, high-resolution measurements of LC deformation, important in characterizing LC biomechanics, are challenging. Here we present a novel noninvasive imaging method, which enables measurement of the three-dimensional deformation of the LC caused by acute elevation of intraocular pressure (IOP). Posterior segments of porcine eyes were imaged using synchrotron radiation phase contrast micro-computed tomography (PC μCT) at IOPs between 6 and 37 mmHg. The complex trabecular architecture of the LC was reconstructed with an isotropic spatial resolution of 3.2 μm. Scans acquired at different IOPs were analyzed with digital volume correlation (DVC) to compute full-field deformation within the LC. IOP elevation caused substantial tensile, shearing and compressive devformation within the LC, with maximum tensile strains at 30 mmHg averaging 5.5%, and compressive strains reaching 20%. We conclude that PC μCT provides a novel high-resolution method for imaging the LC, and when combined with DVC, allows for full-field 3D measurement of ex vivo LC biomechanics at high spatial resolution.

Spatial resolution and measurement uncertainty of strains in bone and bone-cement interface using digital volume correlation

The measurement uncertainty of strains has been assessed in a bone analogue (sawbone), bovine trabecular bone and bone-cement interface specimens under zero load using the Digital Volume Correlation (DVC) method. The effects of sub-volume size, sample constraint and preload on the measured strain uncertainty have been examined. There is generally a trade-off between the measurement uncertainty and the spatial resolution. Suitable sub-volume sizes have been be selected based on a compromise between the measurement uncertainty and the spatial resolution of the cases considered. A ratio of sub-volume size to a microstructure characteristic (Tb.Sp) was introduced to reflect a suitable spatial resolution, and the measurement uncertainty associated was assessed. Specifically, ratios between 1.6 and 4 appear to give rise to standard deviations in the measured strains between 166 and 620 με in all the cases considered, which would seem to suffice for strain analysis in pre as well as post yield loading regimes. A microscale finite element (μFE) model was built from the CT images of the sawbone, and the results from the μFE model and a continuum FE model were compared with those from the DVC. The strain results were found to differ significantly between the two methods at tissue level, consistent in trend with the results found in human bones, indicating mainly a limitation of the current DVC method in mapping strains at this level.

Inverse finite element modeling for characterization of local elastic properties in image-guided failure assessment of human trabecular bone

The local interpretation of microfinite element (μFE) simulations plays a pivotal role for studying bone structure–function relationships such as failure processes and bone remodeling.In the past μFE simulations have been successfully validated on the apparent level,however, at the tissue level validations are sparse and less promising. Furthermore,intra trabecular heterogeneity of the material properties has been shown by experimental studies. We proposed an inverse μFE algorithm that iteratively changes the tissue level Young's moduli such that the μFE simulation matches the experimental strain measurements.The algorithm is setup as a feedback loop where the modulus is iteratively adapted until the simulated strain matches the experimental strain. The experimental strain of human trabecular bone specimens was calculated from time-lapsed images that were gained by combining mechanical testing and synchrotron radiation microcomputed tomography(SRlCT). The inverse μFE algorithm was able to iterate the heterogeneous distribution of moduli such that the resulting μFE simulations matched artificially generated and experimentally measured strains.

Novel Method to Track Soft Tissue Deformation by Micro-Computed Tomography: Application to the Mitral Valve

Increasing availability of micro-computed tomography (µCT) as a structural imaging gold-standard is bringing unprecedented geometric detail to soft tissue modeling. However, the utility of these advances is severely hindered without analogous enhancement to the associated kinematic detail. To this end, labeling and following discrete points on a tissue across various deformation states is a well-established approach. Still, existing techniques suffer limitations when applied to complex geometries and large deformations and strains. Therefore, we herein developed a non-destructive system for applying fiducial markers (minimum diameter: 500 µm) to soft tissue and tracking them through multiple loading conditions by µCT. Using a novel applicator to minimize adhesive usage, four distinct marker materials were resolvable from both tissue and one another, without image artifacts. No impact on tissue stiffness was observed. µCT addressed accuracy limitations of stereophotogrammetry (inter-method positional error 1.2 ± 0.3 mm, given marker diameter 1.9 ± 0.1 mm). Marker application to ovine mitral valves revealed leaflet Almansi areal strains (45 ± 4%) closely matching literature values, and provided radiographic access to previously inaccessible regions, such as the leaflet coaptation zone. This system may meaningfully support mechanical characterization of numerous tissues or biomaterials, as well as tissue-device interaction studies for regulatory standards purposes.

Biomechanics and strain mapping in bone as related to immediately-loaded dental implants

The effects of alveolar bone socket geometry and bone-implant contact on implant biomechanics, and resulting strain distributions in bone were investigated. Following extraction of lateral incisors on a cadaver mandible, implants were placed immediately and bone-implant contact area, stability implant biomechanics and bone strain were measured. In situ biomechanical testing coupled with micro X-ray microscopy (µ-XRM) illustrated less stiff bone-implant complexes (701-822 N/mm) compared with bone-periodontal ligament (PDL)-tooth complexes (791-913 N/mm). X-ray tomograms illustrated that the cause of reduced stiffness was due to limited bone-implant contact. Heterogeneous elemental composition of bone was identified by using energy dispersive X-ray spectroscopy (EDS). The novel aspect of this study was the application of a new experimental mechanics method, that is, digital volume correlation, which allowed mapping of strains in volumes of alveolar bone in contact with a loaded implant. The identified surface and subsurface strain concentrations were a manifestation of load transferred to bone through bone-implant contact based on bone-implant geometry, quality of bone, implant placement, and implant design. 3D strain mapping indicated that strain concentrations are not exclusive to the bone-implant contact regions, but also extend into bone not directly in contact with the implant. The implications of the observed strain concentrations are discussed in the context of mechanobiology. Although a plausible explanation of surgical complications for immediate implant treatment is provided, extrapolation of results is only warranted by future systematic studies on more cadaver specimens and/or in vivo models.

The importance of intrinsic damage properties to bone fragility: a finite element study

As the average age of the population has increased, the incidence of age-related bone fracture has also increased. While some of the increase of fracture incidence with age is related to loss of bone mass, a significant part of the risk is unexplained and may be caused by changes in intrinsic material properties of the hard tissue. This investigation focused on understanding how changes to the intrinsic damage properties affect bone fragility. We hypothesized that the intrinsic (μm) damage properties of bone tissue strongly and nonlinearly affect mechanical behavior at the apparent (whole tissue, cm) level. The importance of intrinsic properties on the apparent level behavior of trabecular bone tissue was investigated using voxel based finite element analysis. Trabecular bone cores from human T12 vertebrae were scanned using microcomputed tomography (μCT) and the images used to build nonlinear finite element models. Isotropic and initially homogenous material properties were used for all elements. The elastic modulus (E(i)) of individual elements was reduced with a secant damage rule relating only principal tensile tissue strain to modulus damage. Apparent level resistance to fracture as a function of changes in the intrinsic damage properties was measured using the mechanical energy to failure per unit volume (apparent toughness modulus, W(a)) and the apparent yield strength (σ(ay), calculated using the 0.2% offset). Intrinsic damage properties had a profound nonlinear effect on the apparent tissue level mechanical response. Intrinsic level failure occurs prior to apparent yield strength (σ(ay)). Apparent yield strength (σ(ay)) and toughness vary strongly (1200% and 400%, respectively) with relatively small changes in the intrinsic damage behavior. The range of apparent maximum stresses predicted by the models was consistent with those measured experimentally for these trabecular bone cores from the experimental axial compressive loading (experimental: σ(max) = 3.0-4.3 MPa; modeling: σ(max) = 2-16 MPa). This finding differs significantly from previous studies based on nondamaging intrinsic material models. Further observations were that this intrinsic damage model reproduced important experimental apparent level behaviors including softening after peak load, microdamage accumulation before apparent yield (0.2% offset), unload softening, and sensitivity of the apparent level mechanical properties to variability of the intrinsic properties.

Torsional properties of distal femoral cortical defects

The optimal management of pathologic long bone lesions remains a challenge in orthopedic surgery. The goal of the current study was to investigate the effect of defect depth on the torsional properties of the distal femur. A laterally placed distal metaphyseal cylindrical defect was milled in the cortex of the distal femur in 20 composite models. The proximal extent of the defects was constant. By decreasing the radius of the cylinder that intersected this predefined cord, 4 different radii defining 4 different depths of resection of the distal femur were created for testing: 17%, 33%, 50%, and 67% cortical defects, when normalized to the width of the femur at the level of resection. Each femur was mounted into a hydraulic axial/torsion materials testing machine and each specimen underwent torsional stiffness testing and torsional failure in external rotation. The specimens with less than a 33% cortical loss consistently demonstrated a superiorly oriented spiral fracture pattern, while the specimens with greater than a 50% cortical loss consistently demonstrated an inferiorly oriented transverse fracture pattern. The cortical defects were all statistically (P<.05) less stiff in torsion as the defect grew larger. There was a strong linear correlation between the mean torsional stiffness and cortical defect size (r(2)=0.977). This observation is supported by finite element analysis. The amount of femur remaining is crucial to stability. This biomechanical analysis predicts a critical loss of torsional integrity when a cortical defect approaches 50% of the width of the femur.

μFEA successfully exhibits higher stresses and strains in microdamaged regions of whole vertebrae

Micro-finite element (μFE) modeling has shown promise in evaluating the structural integrity of trabecular bone. Histologic microcrack analyses have been compared to μFE models of trabecular bone cores to demonstrate the potential of this technique. To date this has not been achieved in whole bone structures, and comparisons of histologic microcrack and μFE results have been limited due to challenges in alignment of 2D sections with 3D data sets. The goal of this study was to ascertain if image registration can facilitate determination of a relationship between stresses and strains generated from μFE models of whole vertebrae and histologically identified microdamage. μFE models of three whole vertebrae, stained sequentially with calcein and fuchsin, were generated with accurate integration of element sets representing the histologic sections based on volumetric image registration. Displacement boundary conditions were applied to the μFE models based on registration of loaded and unloaded μCT images. Histologically labeled damaged regions were found to have significantly higher von Mises stresses and principle strains in the μFE models, as compared to undamaged regions. This work provides a new robust method for generating and histologically validating μFE models of whole bones that can represent trabecular damage resulting from complex physiologic loading.

Evaluation of the performance of a motion capture system for small displacement recording and a discussion for its application potential in bone deformation in vivo measurements

The aim of this study is to evaluate the performance of a motion capture system and discuss the application potential of the proposed system in in vivo bone-segment deformation measurements. In this study, the effects of the calibration procedure, camera distance and marker size on the accuracy and precision of the motion capture system have been investigated by comparing the captured movement of the markers with reference movement. The results indicated that the system resolution is at least 20 microm in a capture volume of 400 X 300 X 300 mm3, which mostly covers the range of motion of the tibia during the stance phase of one gait cycle. Within this volume, the system accuracy and precision decreased following the increase of camera distance along the optical axis of the cameras. With the best configuration, the absolute error and precision for the range of 20 microm displacement were 1.2-1.8 microm and 1.5-2.5 microm, respectively. Small markers (Ø3-8 mm) yielded better accuracy and repeatability than the larger marker (Ø10.5 mm). We conclude that the proposed system is capable of recording minor displacements in a relative large volume.

Quantification of the effect of osteolytic metastases on bone strain within whole vertebrae using image registration

The vertebral column is the most frequent site of metastatic involvement of the skeleton with up to 1/3 of all cancer patients developing spinal metastases. Longer survival times for patients, particularly secondary to breast cancer, have increased the need for better understanding the impact of skeletal metastases on structural stability. This study aims to apply image registration to calculate strain distributions in metastatically involved rodent vertebrae utilizing µCT imaging. Osteolytic vertebral lesions were developed in five rnu/rnu rats 2-3 weeks post intracardiac injection with MT-1 human breast cancer cells. An image registration algorithm was used to calculate and compare strain fields due to axial compressive loading in metastatically involved and control vertebrae. Tumor-bearing vertebrae had greatly increased compressive strains, double the magnitude of strain compared to control vertebrae (p=0.01). Qualitatively strain concentrated within the growth plates in both tumor bearing and control vertebrae. Most interesting was the presence of strain concentrations at the dorsal wall in metastatically involved vertebrae, suggesting structural instability. Strain distributions, quantified by image registration were consistent with known consequences of lytic involvement. Metastatically involved vertebrae had greater strain magnitude than control vertebrae. Strain concentrations at the dorsal wall in only the metastatic vertebrae, were consistent with higher incidence of burst fracture secondary to this pathology. Future use of image registration of whole vertebrae will allow focused examination of the efficacy of targeted and systemic treatments in reducing strains and the related risk of fracture in pathologic bones under simple and complex loading.

Digital Volume Correlation for Study of the Mechanics of Whole Bones

Full-field measurement of deformation in biological structures such as bones is a promising experimental approach for study of the spatial heterogeneity in mechanical behavior. With the advent of high-resolution, 3-D imaging, digital volume correlation (DVC) allows for the measurement of spatially heterogeneous, 3-D deformation fields throughout entire volumes. For bones such as the vertebra, use of DVC to detect the onset and progression of failure is of direct relevance to the study of osteoporotic fractures. Application of DVC to whole bones, as opposed to machined specimens of bone tissue, involves additional challenges such as the irregular geometry, large data sets, and decreased signal-to-noise ratio. These challenges are addressed in this paper, and the DVC method that results is used to examine yield and post-yield deformations in vertebral compression experiments.