Development of a validated glenoid trabecular density-modulus relationship

Age- and sex-specific normative values of bone mineral density in the adult glenoid

The objective of this study was to determine the normative bone mineral density (BMD) of cortical and trabecular bone regions in the adult glenoid and its dependence on the subject's age and sex. We analyzed computed tomography (CT) scans of 441 shoulders (310 males, 18-69 years) without any signs of glenohumeral joint pathology. Glenoid BMD was automatically quantified in six volumes of interest (VOIs): cortical bone (CO), subchondral cortical plate (SC), subchondral trabecular bone (ST), and three adjacent layers of trabecular bone (T1, T2, and T3). BMD was measured in Hounsfield unit (HU). We evaluated the association between glenoid BMD and sex and age with the Student's t test and Pearson's correlation coefficient (r), respectively. The lambda-mu-sigma method was used to determine age- and sex-specific normative values of glenoid BMD in cortical (CO and SC) and trabecular (ST, T1, T2, and T3) bone. Glenoid BMD was higher in males than females, in most age groups and most VOIs. Before 40 years old, the effect of age on BMD was very weak in both males and females. After 40 years old, BMD declined over time in all VOIs. This BMD decline with age was greater in females (cortical: r = -0.45, trabecular: r = -0.41) than in males (cortical: r = -0.30; trabecular: r = -0.32). These normative glenoid BMD values could prove clinically relevant in the diagnosis and management of patients with various shoulder disorders, in particular glenohumeral osteoarthritis and shoulder arthroplasty or shoulder instability, as well as in related research.

Mechanism and microstructure based concept to predict skull fracture using a hybrid-experimental-modeling-computational approach

Cellular and tissue-scale indent/impact thresholds for different mechanisms of functional impairments to the brain would be the preferred method to predict head injuries, but a comprehensive understanding of the dominant possible injury mechanisms under multiaxial stress-states and rates is currently not available. Until then, skull fracture could serve as an indication of head injury. Therefore the ability to predict the initiation of skull fracture through finite element simulation can serve as an in silico tool for assessing the effectiveness of various head protection scenarios. For this objective, skull fracture initiation was represented with a microstructurally-inspired, mechanism-based (MIMB) failure surface assuming three different dominant mechanisms of skull failure: each element, with deformation and failure properties selected based on its microstructure, was allowed to fail either in tension, compression, or shear, corresponding to clinical linear, depressed or penetrating shear-plug failure (fracture), respectively. Microstructure-inspired a priori values for the initiation threshold of each mechanism, obtained previously from uniaxial and simple-shear experiments, were iterated and optimized for the predicted load-displacement to represent that of the corresponding indentation experiment. Element-level failure enabled the visualization of the evolution of fracture by different mechanisms. The final crack pattern at the time of macroscopic (clinically-identifiable) injury was compared between the simulation and experiment obtained through 3D tomography. Even though the timing was slightly different, the simulated prediction represented remarkably well the experimental crack pattern before the appearance of the catastrophic unstable fast crack in the experiment, thus validating the implemented hybrid-experimental-modeling-computational (HEMC) concept as a tool to predict skull fracture initiation.

Proximal Tibia Bone Stiffness and Strength in HR-pQCT- and QCT-Based Finite Element Models

Injury to the ACL significantly increases the risk of developing post-traumatic osteoarthritis. Following injury, considerable focus is placed on visualizing soft tissue changes using MRI, but there is less emphasis on the alterations to the underlying bone. It has recently been shown using high-resolution peripheral quantitative computed tomography (HR-pQCT) that significant reductions in bone quality occur in the knee post ACL-injury. Despite the ability of HR-pQCT to show these changes, the availability of scanners and computational time requirements required to assess bone stiffness and strength with HR-pQCT limit its widespread clinical use. As such, the objective of this study was to determine if clinical quantitative CT (QCT) finite element models (QCT-FEMs) can accurately replicate HR-pQCT FEM proximal tibial stiffness and strength. From FEMs of 30 participants who underwent both QCT and HR-pQCT bilateral imaging, QCT-FEMs were strongly correlated with HR-pQCT FEM stiffness (R² = 0.79). When QCT-FEM bone strength was estimated using the reaction force at 1% apparent strain, strong correlations were observed (R² = 0.81), with no bias between HR-pQCT FEMs and non-linear QCT-FEMs. These results indicate that QCT-FEMs can accurately replicate HR-pQCT FEM stiffness and strength in the proximal tibia. Although these models are not able to replicate the trabecular structure or tissue-level strains, they require significantly reduced computational time and use widely available clinical-CT images as input, which make them an attractive choice to monitor bone density, stiffness and strength alterations, such as those that occur post ACL-injury.

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.

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.

Morphological and Apparent-Level Stiffness Variations Between Normal and Osteoarthritic Bone in the Humeral Head

Osteoarthritis (OA) is characterized by morphological changes that alter bone structure and mechanical properties. This study compared bone morphometric parameters and apparent modulus between humeral heads excised from end-stage OA patients undergoing total shoulder arthroplasty (n = 28) and non-pathologic normal cadavers (n = 28). Morphometric parameters were determined in central cores, with regional variations compared in four medial to lateral regions. Linear regression compared apparent modulus, morphometric parameters, and age. Micro finite element models estimated trabecular apparent modulus and derived density-modulus relationships. Significant differences were found for bone volume fraction (p < 0.001) and trabecular thickness (p < 0.001) in the most medial regions. No significant differences occurred between morphometric parameters and apparent modulus or age, except in slope between groups for apparent modulus versus trabecular number (p = 0.021), and in intercept for trabecular thickness versus age (p = 0.040). Significant differences occurred in both slope and intercept between density-modulus regression fits for each group (p ≤ 0.001). The normal group showed high correlations in the power-fit (r²  = 0.87), with a lower correlation (r²  = 0.61) and a more linear relationship, in the OA group. This study suggests that alterations in structure and apparent modulus persist mainly in subchondral regions of end-stage OA bone. As such, if pathologic regions are removed during joint replacement, computational models that utilize modeling parameters from non-pathologic normal bone may be applied to end-stage OA bone. An improved understanding of humeral trabecular bone variations has potential to improve the surgical management of end-stage OA patients. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 38:503-509, 2020.

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.

A comparison of density-modulus relationships used in finite element modeling of the shoulder

Subject- and site-specific modeling techniques greatly improve the accuracy of computational models derived from clinical-resolution quantitative computed tomography (QCT) data. The majority of shoulder finite element (FE) studies use density-modulus relationships developed for alternative anatomical locations. As such, the objectives of this study were to compare the six most commonly used density-modulus relationships in shoulder finite element (FE) studies. To achieve this, ninety-eight (98) virtual trabecular bone cores were extracted from uCT scans of scapulae from 14 cadaveric specimens (7 male; 7 female). Homogeneous tissue moduli of 20 GPa, and heterogeneous tissue moduli scaled by CT-intensity were considered. Micro finite element models (µ-FEMs) of each virtual core were compressively loaded to 0.5% apparent strain and apparent strain energy density (SED_app) was collected. Each uCT virtual core was then co-registered to clinical QCT images, QCT-FEMs created, and each of the 6 density-modulus relationships applied (6 × 98 = 588 QCT-FEMs). The loading and boundary conditions were replicated and SED_app was collected and compared to µ-FEM SED_app. When a homogeneous tissue modulus was considered in the µ-FEMs, SED_app was best predicted in QCT-FEMs with the density-modulus relationship developed from pooled anatomical locations (QCT-FEM SED_app = 0.979µ-FEM SED_app + 0.0066, r² = 0.933). A different density-modulus relationship best predicted SED_app (QCT-FEM SED_app = 1.014µ-FEM SED_app + 0.0034, r² = 0.935) when a heterogeneous tissue modulus was considered. This study compared density-modulus relationships used in shoulder FE studies using an independent computational methodology for comparing these relationships.