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

Quantifying the immediate post-implantation strain field of cadaveric tibiae implanted with cementless tibial trays: A time-elapsed micro-CT and digital volume correlation analysis during stair descent

Primary stability, the mechanical fixation between implant and bone prior to osseointegration, is crucial for the long-term success of cementless tibial trays. However, little is known about the mechanical interplay between the implant and bone internally, as experimental studies quantifying internal strain are limited. This study employed digital volume correlation (DVC) to quantify the immediate post-implantation strain field of five cadaveric tibiae implanted with a commercially available cementless titanium tibial tray (Attune, DePuy Synthes). The tibiae were subjected to a five-step loading sequence (0-2.5 bodyweight, BW) replicating stair descent, with concomitant time-elapsed micro-CT imaging. With progressive loads, increased compression of trabecular bone was quantified, with the highest strains directly under the posterior region of the tibial tray implant, dissipating with increasing distance from the bone-implant interface. After load removal of the last load step (2.5BW), residual strains were observed in all of the five tibiae, with residual strains confined within 3.14 mm from the bone-implant interface. The residual strain is reflective of the observed initial migration of cementless tibial trays reported in clinical studies. The presence of strains above the yield strain of bone accepted in literature suggests that inelastic properties should be included within finite element models of the initial mechanical environment. This study provides a means to experimentally quantify the internal strain distribution of human tibia with cementless trays, increasing the understanding of the mechanical interaction between bone and implant.

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.

Experimental DVC validation of heterogeneous micro finite element models applied to subchondral trabecular bone of the humeral head

Subchondral trabecular bone (STB) undergoes adaptive changes during osteoarthritic (OA) disease progression. These changes alter both the mineralization patterns and structure of bone and may contribute to variations in the mechanical properties. Similarly, when images are downsampled - as is often performed in micro finite element model (microFEM) generation - the morphological and mineralization patterns may further alter the mechanical properties due to partial volume effects. MicroFEMs accounting for material heterogeneity can account for these tissue variations, but no studies have validated these with robust full-field testing methods. As such, this study compared homogeneous and heterogeneous microFEMs to experimentally loaded trabecular bone cores from the humeral head combined with digital volume correlation (DVC). These microFEMs were used to compare apparent mechanical properties between normal and OA STB. Morphological and mineralization patterns between groups were also compared. There were no significant differences in tissue or bone mineral density between groups. The only significant differences in morphometric parameters were in trabecular thickness between groups. There were no significant differences in linear regression parameters between normal and OA STB apparent mechanical properties estimated using heterogeneous microFEMs with an element-wise bilinear elastic-plastic constitutive model. Clinical significance: Validated heterogeneous microFEMs applied to STB of the humeral head have the potential to significantly improve our understanding of mechanical variations in the bone that occur during OA progression.

Micro-CT scan optimisation for mechanical loading of tibia with titanium tibial tray: A digital volume correlation zero strain error analysis

Primary stability of press-fit tibial trays is achieved by introducing an interference fit between bone and implant. The internal cancellous bone strains induced during this process and during loading have yet to be quantified experimentally. Advancements in large-gantry micro-CT imaging and digital volume correlation (DVC) allow quantification of such strains. However, before undertaking such a test, experimental requirements and DVC performance need to be examined, particularly considering the presence of a large orthopaedic implant (tibial tray). The aim of this study was to assess the DVC zero-strain accuracy (mean absolute error: MAER) and precision (standard deviation of error: SDER) on a cadaveric human tibia implanted with a titanium press-fit tray across four plausible scanning configurations, using a cabinet micro-CT system (Nikon XT H 225 ST). These varied in rotation step and resulting scanning time (106 min vs. 66 min), presence or absence of a 2 mm-thick aluminium cylinder for mechanical testing, and X-ray tube voltage (150 kVp vs. 215 kVp). One proximal tibia was implanted and micro-CT scanned (42 μm/pixel), with repeated scanning and specimen repositioning in between. DVC (DaVis, LaVision, direct correlation) was performed on nine cubic volumes of interest (VOIs: 13.4 mm-side) and across the entire proximal tibia. Strain errors were comparable across the four scanning configurations and sufficiently low for assessing bone within its elastic region in VOIs (MAER=223-540 με; SDER=88-261 με) and at organ level (MAER=536 με; SDER=473 με). Whilst the investigated experimental conditions, including a large titanium implant, present added complexity for DVC analysis, scans of sufficient quality can be achieved, reaching a compromise between the DVC requirements and the wanted application. The approach used for choosing the X-ray source settings considering the transmitted X-ray signal intensity and source power, is also discussed.

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.

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.

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.

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

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

Glenoid bone strain after anatomical total shoulder arthroplasty: In vitro measurements with micro-CT and digital volume correlation

Glenoid implant loosening remains a major source of failure and concern after anatomical total shoulder arthroplasty (aTSA). It is assumed to be associated with eccentric loading and excessive bone strain, but direct measurement of bone strain after aTSA is not available yet. Therefore, our objective was to develop an in vitro technique for measuring bone strain around a loaded glenoid implant. A custom loading device (1500 N) was designed to fit within a micro-CT scanner, to use digital volume correlation for measuring displacement and calculating strain. Errors were evaluated with three pairs of unloaded scans. The average displacement random error of three pairs of unloaded scans was 6.1 µm. Corresponding systematic and random errors of strain components were less than 806.0 µε and 2039.9 µε, respectively. The average strain accuracy (MAER) and precision (SDER) were 694.3 µε and 440.3 µε, respectively. The loaded minimum principal strain (8738.9 µε) was 12.6 times higher than the MAER (694.3 µε) on average, and was above the MAER for most of the glenoid bone volume (98.1%). Therefore, this technique proves to be accurate and precise enough to eventually compare glenoid implant designs, fixation techniques, or to validate numerical models of specimens under similar loading.

The Application of Digital Volume Correlation (DVC) to Evaluate Strain Predictions Generated by Finite Element Models of the Osteoarthritic Humeral Head

Continuum-level finite element models (FEMs) of the humerus offer the ability to evaluate joint replacement designs preclinically; however, experimental validation of these models is critical to ensure accuracy. The objective of the current study was to quantify experimental full-field strain magnitudes within osteoarthritic (OA) humeral heads by combining mechanical loading with volumetric microCT imaging and digital volume correlation (DVC). The experimental data was used to evaluate the accuracy of corresponding FEMs. Six OA humeral head osteotomies were harvested from patients being treated with total shoulder arthroplasty and mechanical testing was performed within a microCT scanner. MicroCT images (33.5 µm isotropic voxels) were obtained in a pre- and post-loaded state and BoneDVC was used to quantify full-field experimental strains (≈ 1 mm nodal spacing, accuracy = 351 µstrain, precision = 518 µstrain). Continuum-level FEMs with two types of boundary conditions (BCs) were simulated: DVC-driven and force-driven. Accuracy of the FEMs was found to be sensitive to the BC simulated with better agreement found with the use of DVC-driven BCs (slope = 0.83, r² = 0.80) compared to force-driven BCs (slope = 0.22, r² = 0.12). This study quantified mechanical strain distributions within OA trabecular bone and demonstrated the importance of BCs to ensure the accuracy of predictions generated by corresponding FEMs.

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.

Material Mapping of QCT-Derived Scapular Models: A Comparison with Micro-CT Loaded Specimens Using Digital Volume Correlation

Subject- and site-specific modeling techniques greatly improve finite element models (FEMs) derived from clinical-resolution CT data. A variety of density-modulus relationships are used in scapula FEMs, but the sensitivity to selection of relationships has yet to be experimentally evaluated. The objectives of this study were to compare quantitative-CT (QCT) derived FEMs mapped with different density-modulus relationships and material mapping strategies to experimentally loaded cadaveric scapular specimens. Six specimens were loaded within a micro-CT (33.5 μm isotropic voxels) using a custom-hexapod loading device. Digital volume correlation (DVC) was used to estimate full-field displacements by registering images in pre- and post-loaded states. Experimental loads were measured using a 6-DOF load cell. QCT-FEMs replicated the experimental setup using DVC-driven boundary conditions (BCs) and were mapped with one of fifteen density-modulus relationships using elemental or nodal material mapping strategies. Models were compared based on predicted QCT-FEM nodal reaction forces compared to experimental load cell measurements and linear regression of the full-field nodal displacements compared to the DVC full-field displacements. Comparing full-field displacements, linear regression showed slopes ranging from 0.86 to 1.06, r-squared values of 0.82–1.00, and max errors of 0.039 mm for all three Cartesian directions. Nearly identical linear regression results occurred for both elemental and nodal material mapping strategies. Comparing QCT-FEM to experimental reaction forces, errors ranged from − 46 to 965% for all specimens, with specimen-specific errors as low as 3%. This study utilized volumetric imaging combined with mechanical loading to derive full-field experimental measurements to evaluate various density-modulus relationships required for QCT-FEMs applied to whole-bone scapular loading. The results suggest that elemental and nodal material mapping strategies are both able to simultaneously replicate experimental full-field displacements and reactions forces dependent on the density-modulus relationship used.