Cortical bone mapping improves finite element strain prediction accuracy at the proximal femur

Dual-zone material assignment method for correcting partial volume effects in image-based bone models

In image-based finite element analysis of bone, partial volume effects (PVEs) arise from image blur at tissue boundaries and as a byproduct of geometric reconstruction and meshing during model creation. In this study, we developed and validated a material assignment approach to mitigate partial volume effects. Our validation data consisted of physical torsion testing of intact tibiae from N = 20 Swiss alpine sheep. We created finite element models from micro-CT scans of these tibiae using three popular element types (10-node tetrahedral, 8-node hexahedral, and 20-node hexahedral). Without partial volume management, the models over-predicted the torsional rigidity compared to physical biomechanical tests. To address this problem, we implemented a dual-zone material model to treat elements that overlap low-density surface voxels as soft tissue rather than bone. After in situ inverse optimization, the dual-zone material model produced strong correlations and high absolute agreement between the virtual and physical tests. This suggests that with appropriate partial volume management, virtual mechanical testing can be a reliable surrogate for physical biomechanical testing. For maximum flexibility in partial volume management regardless of element type, we recommend the use of the following dual-zone material model for ovine tibiae: soft-tissue cutoff density of 665 mgHA/cm3 with a soft tissue modulus of 50 MPa (below cutoff) and a density-modulus conversion slope of 10,225 MPa-cm3/mgHA for bone (above cutoff).

The application of an isotropic crushable foam model to predict the femoral fracture risk

For biomechanical simulations of orthopaedic interventions, it is imperative to implement a material model that can realistically reproduce the nonlinear behavior of the bone structure. However, a proper material model that adequately combines the trabecular and cortical bone response is not yet widely identified. The current paper aims to investigate the possibility of using an isotropic crushable foam (ICF) model dependent on local bone mineral density (BMD) for simulating the femoral fracture risk. The elastoplastic properties of fifty-nine human femoral trabecular cadaveric bone samples were determined and combined with existing cortical bone properties to characterize two forms of the ICF model, a continuous and discontinuous model. Subsequently, the appropriateness of this combined material model was evaluated by simulating femoral fracture experiments, and a comparison with earlier published results of a softening Von-Mises (sVM) material model was made. The obtained mechanical properties of the trabecular bone specimens were comparable to previous findings. Furthermore, the ultimate failure load predicted by the simulations of femoral fractures was on average 79% and 90% for the continuous and discontinuous forms of the ICF model and 82% of the experimental value for the sVM material model. Also, the fracture locations predicted by ICF models were comparable to the experiments. In conclusion, a nonlinear material model dependent on BMD was characterized for human femoral bone. Our findings indicate that the ICF model could predict the femoral bone strength and reproduce the variable fracture locations in the experiments.

Applying a homogeneous pressure distribution to the upper vertebral endplate: Validation of a new loading system, pilot application to human vertebral bodies, and finite element predictions of DIC measured displacements and strains

Image-based personalized Finite Element Models (pFEM) could detect alterations in physiological deformation of human vertebral bodies, but their accuracy has been seldom reported. Meaningful validation experiments should allow vertebral endplate deformability and ensure well-controlled boundary conditions. This study aimed to (i) validate a new loading system to apply a homogeneous pressure on the vertebral endplate during vertebral body compression regardless of endplate deformation; (ii) perform a pilot study on human vertebral bodies measuring surface displacements and strains with Digital Image Correlation (DIC); (iii) determine the accuracy of pFEM of the vertebral bodies. Homogeneous pressure application was achieved by pressurizing a fluid silicone encased in a rubber silicone film acting on the cranial endplate. The loading system was validated by comparing DIC-measured longitudinal strains and lower-end contact pressures, measured on three homogeneous pseudovertebrae of constant transversal section at 2.0 kN, against theoretically calculated values. Longitudinal strains and contact pressures were rather homogeneous, and their mean values close to theoretical calculations (5% underestimation). DIC measurements of surface longitudinal and circumferential displacements and strains were obtained on three human vertebral bodies at 2.0 kN. Complete displacement and strain maps were achieved for anterolateral aspects with random errors ≤0.2 μm and ≤30 μstrain, respectively. Venous plexus and double curvatures limited the completeness and accuracy of DIC data in posterior aspects. pFEM of vertebral bodies, including cortical bone mapping, were built from computed tomography images. In anterolateral aspects, pFEM accuracy of the three vertebrae was: (i) comparable to literature in terms of longitudinal displacements (R2>0.8); (ii) extended to circumferential displacements (pooled data: R2>0.9) and longitudinal strains (zero median error, 95% error: <27%). Circumferential strains were overestimated (median error: 39%). The new methods presented may permit to study how physiological and pathologic conditions influence the ability of vertebral endplates/bodies to sustain loads.

Fracture risk assessment and evaluation of femoroplasty in metastatic proximal femurs. An in vivo CT-based finite element study

The goal of this study was twofold. First, we aimed to evaluate the accuracy of a finite element (FE) model to predict bone fracture in cancer patients with proximal femoral bone metastases. Second, we evaluated whether femoroplasty could effectively reduce fracture risk. A total of 89 patients were included, with 101 proximal femurs affected with bone metastases. The accuracy of the model to predict fracture was evaluated by comparing the FE failure load, normalized for body weight, against the actual occurrence of fracture during a 6-month follow-up. Using a critical threshold, the model could identify whether femurs underwent fracture with a sensitivity of 92% and a specificity of 66%. A virtual treatment with femoroplasty was simulated in a subset of 34 out of the 101 femurs; only femurs with one or more well-defined lytic lesions were considered eligible for femoroplasty. We modeled their lesions, as well as the surrounding 4 mm of trabecular bone, to be augmented with bone cement. The simulation of femoroplasty increased the median failure load of the FE model by 57% for lesions located in the head/neck of the femur. At this lesion location, all high risk femurs that had fractured during follow-up effectively moved from a failure load below the critical threshold to a value above. For lesions located in the trochanteric region, no definite improvement in failure load was found. Although additional validation studies are required, our results suggest that femoroplasty can effectively reduce fracture risk for several osteolytic lesions in the femoral head/neck.

Can neck fractures in proximal humeri be predicted by CT-based FEA?

BACKGROUND

Proximal humeri fractures at anatomical and surgical neck (∼5% and ∼50% incidence respectively) are frequent in elderly population. Yet, neither in-vitro experiments nor CT-based finite element analyses (CTFEA) have investigated these in depth. Herein we enhance (Dahan et al., 2019) (addressing anatomical neck fractures) by more experiments and specimens, accounting for surgical neck fractures and explore CTFEA's prediction of humeri mechanical response and yield force.

METHODS

Four fresh frozen human humeri were tested in a new experimental configuration inducing surgical neck fractures. Digital image correlation (DIC) provided strains and displacements on humeri surfaces and used to validate CTFEA predictions. CTFEA were enhanced herein to improve the accuracy at the proximal neck: A cortical bone mapping (CBM) algorithm was implemented to overcome insufficient scanning resolution, and a new trabecular material mapping was investigated.

RESULTS

The new experimental setting induced impacted surgical neck fractures in all humeri. Excellent DIC to CTFEA correlation in strains was obtained at the shaft (slope 0.984, R²=0.99) and a fair agreement (slope 0.807, R²=0.73) at the neck. CBM algorithm had worsened the correlation, whereas the new material mapping had a negligible influence. Yield loads predictions improved considerably when trabecular yielding (maximum principal strain criterion) was considered instead of surface cortical yielding.

DISCUSSION

CTFEA well predicts strains on the shaft and reasonably well on the neck. This enhances former conclusions by past studies conducted using SGs, now also evident by DIC. Yield load prediction for surgical neck fractures (involving crushing of trabecular bone) is predicted better by trabecular failure laws rather than cortex ones. Further FEA studies using trabecular orthotropic constitutive models and failure laws are warrant.

Finite Element Assessment of Bone Fragility from Clinical Images

PURPOSE OF REVIEW

We re-evaluated clinical applications of image-to-FE models to understand if clinical advantages are already evident, which proposals are promising, and which questions are still open.

RECENT FINDINGS

CT-to-FE is useful in longitudinal treatment evaluation and groups discrimination. In metastatic lesions, CT-to-FE strength alone accurately predicts impending femoral fractures. In osteoporosis, strength from CT-to-FE or DXA-to-FE predicts incident fractures similarly to DXA-aBMD. Coupling loads and strength (possibly in dynamic models) may improve prediction. One promising MRI-to-FE workflow may now be tested on clinical data. Evidence of artificial intelligence usefulness is appearing. CT-to-FE is already clinical in opportunistic CT screening for osteoporosis, and risk of metastasis-related impending fractures. Short-term keys to improve image-to-FE in osteoporosis may be coupling FE with fall risk estimates, pool FE results with other parameters through robust artificial intelligence approaches, and increase reproducibility and cross-validation of models. Modeling bone modifications over time and bone fracture mechanics are still open issues.

Heterogeneous material mapping methods for patient-specific finite element models of pelvic trabecular bone: A convergence study

Patient-specific finite element (FE) models of bone require the assignment of heterogeneous material properties extracted from the subject's computed tomography (CT) images. Though node-based (NB) and element-based (EB) material mapping methods (MMMs) have been proposed, the sensitivity and convergence of FE models to MMM for varying mesh sizes are not well understood. In this work, CT-derived and synthetic bone material data were used to evaluate the effect of MMM on results from FE analyses. Pelvic trabecular bone data was extracted from CT images of six subjects, while synthetic data were created to resemble trabecular bone properties. The numerical convergence of FE bone models using different MMMs were evaluated for strain energy, von-Mises stress, and strain. NB and EB MMMs both demonstrated good convergence regarding total strain energy, with the EB method having a slight edge over the NB. However, at the local level (e.g., maximum stress and strain), FE results were sensitive to the field type, MMM, and the FE mesh size. The EB method exhibited superior performance in finer meshes relative to the voxel size. The NB method converged better than did the EB method for coarser meshes. These findings may lead to higher-fidelity patient-specific FE bone models.

A novel specimen shape for measurement of linear strain fields by means of digital image correlation

Strains on the surface of engineering structures or biological tissues are non-homogeneous. These strain fields can be captured by means of Digital Image Correlation (DIC). However, DIC strain field measurements are prone to noise and filtering of these fields influences measured strain gradients. This study aims to design a novel tensile test specimen showing two linear gradients, to measure full-field linear strain measurements on the surface of test specimens, and to investigate the accuracy of DIC strain measurements globally (full-field) and locally (strain gauges' positions), with and without filtering of the DIC strain fields. Three materials were employed for this study: aluminium, polymer, and bovine bone. Normalized strain gradients were introduced that are load independent and evaluated at two local positions showing 3.6 and 6.9% strain change per mm. Such levels are typically found in human bones. At these two positions, two strain gauges were applied to check the experimental strain magnitudes. A third strain gauge was applied to measure the strain in a neutral position showing no gradient. The accuracy of the DIC field measurement was evaluated at two deformation stages (at [Formula: see text] 500 and 1750 μstrain) using the root mean square error (RMSE). The RMSE over the two linear strain fields was less than 500 μstrain for both deformation stages and all materials. Gaussian low-pass filter (LPF) reduced the DIC noise between 25% and 64% on average. As well, filtering improved the accuracy of the local normalized strain gradients measurements with relative difference less than 20% and 12% for the high- and low-gradient, respectively. In summary, a novel specimen shape and methodological approach are presented which are useful for evaluating and improving the accuracy of the DIC measurement where non-homogeneous strain fields are expected such as on bone tissue due to their hierarchical structure.

Effect of Model Parameters on the Biomechanical Behavior of the Finite Element Cervical Spine Model

Finite element (FE) models have frequently been used to analyze spine biomechanics. Material parameters assigned to FE spine models are generally uncertain, and their effect on the characterization of the spinal components is not clear. In this study, we aimed to analyze the effect of model parameters on the range of motion, stress, and strain responses of a FE cervical spine model. To do so, we created a computed tomography-based FE model that consisted of C2-C3 vertebrae, intervertebral disc, facet joints, and ligaments. A total of 32 FE analyses were carried out for two different elastic modulus equations and four different bone layer numbers under four different loading conditions. We evaluated the effects of elastic modulus equations and layer number on the biomechanical behavior of the FE spine model by taking the range of angular motion, stress, and strain responses into account. We found that the angular motions of the one- and two-layer models had a greater variation than those in the models with four and eight layers. The angular motions obtained for the four- and eight-layer models were almost the same, indicating that the use of a four-layer model would be sufficient to achieve a stress value converging to a certain level as the number of layers increases. We also observed that the equation proposed by Gupta and Dan (2004) agreed well with the experimental angular motion data. The outcomes of this study are expected to contribute to the determination of the model parameters used in FE spine models.

A systematic approach to the scale separation problem in the development of multiscale models

Throughout engineering there are problems where it is required to predict a quantity based on the measurement of another, but where the two quantities possess characteristic variations over vastly different ranges of time and space. Among the many challenges posed by such 'multiscale' problems, that of defining a 'scale' remains poorly addressed. This fundamental problem has led to much confusion in the field of biomedical engineering in particular. The present study proposes a definition of scale based on measurement limitations of existing instruments, available computational power, and on the ranges of time and space over which quantities of interest vary characteristically. The definition is used to construct a multiscale modelling methodology from start to finish, beginning with a description of the system (portion of reality of interest) and ending with an algorithmic orchestration of mathematical models at different scales within the system. The methodology is illustrated for a specific but well-researched problem. The concept of scale and the multiscale modelling approach introduced are shown to be easily adaptable to other closely related problems. Although out of the scope of this paper, we believe that the proposed methodology can be applied widely throughout engineering.

Femoral strength and strains in sideways fall: Validation of finite element models against bilateral strain measurements

Low impact falls to the side are the main cause of hip fractures in elderly. Finite element (FE) models of the proximal femur may help in the assessment of patients at high risk for a hip fracture. However, extensive validation is essential before these models can be used in a clinical setting. This study aims to use strain measurements from bilateral digital image correlation to validate an FE model against ex vivo experimental data of proximal femora under a sideways fall loading condition. For twelve subjects, full-field strain measurements were available on the medial and lateral side of the femoral neck. In this study, subject-specific FE models were generated based on a consolidated procedure previously validated for stance loading. The material description included strain rate dependency and separate yield and fracture strain limits in tension and compression. FE predicted fracture force and experimentally measured peak forces showed a strong correlation (R² = 0.92). The FE simulations predicted the fracture initiation within 3 mm distance of the experimental fracture line for 8/12 subjects. The predicted and measured strains correlated well on both the medial side (R² = 0.87) and the lateral side (R² = 0.74). The lower correlation on the lateral side is attributed to the irregularity of the cortex and presence of vessel holes in this region. The combined validation against bilateral full-field strain measurements and peak forces has opened the door for a more elaborate qualitative and quantitative validation of FE models of femora under sideways fall loading.

Design and Fabrication of a Customized Partial Hip Prosthesis Employing CT-Scan Data and Lattice Porous Structures

As a larger elderly human population is expected worldwide in the next 30 years, the occurrence of aging-associated illnesses will also be increased. The use of prosthetic devices by this population is currently important and will be even more dramatic in the near future. Hence, the design of prosthetic devices able to reduce some of the problems associated with the use of current components, such as stress shielding, reduced mobility, infection, discomfort, etc., becomes relevant. The use of additive manufacturing (AM) and the design fabrication of self-supported cellular structures in the biomedical area have opened up important opportunities for controlling the physical and mechanical properties of hip implants, resulting in specific benefits for the patients. Different studies have reported the development of hip prosthetic designs employing AM, although there are still opportunities for improvement when it comes to customized design and tuning of the physical and mechanical properties of such implants. This work shows the design and manufacture by AM of a personalized stainless-steel partial hip implant using tomography data and self-supported triply periodic minimal surface (TPMS) cell structures; the design considers dimensional criteria established by international standards. By employing tomography data, the external dimensions of the implant were established and the bone density of a specific patient was calculated; the density and mechanical properties in compression of the implant were modulated by employing an internal gyroid-type cell structure. Using such a cell structure, the patient's bone density was emulated; also, the mechanical properties of the implant were fine-tuned in order to make them comparable to those reported for the bone tissue replaced by the prosthesis. The implant design and manufacturing methodology developed in this work considered the clinical condition of a specific patient and can be reproduced and adjusted for different types of bone tissue qualities for specific clinical requirements.

Image-based finite-element modeling of the human femur

Fracture is considered a critical clinical endpoint in skeletal pathologies including osteoporosis and bone metastases. However, current clinical guidelines are limited with respect to identifying cases at high risk of fracture, as they do not account for many mechanical determinants that contribute to bone fracture. Improving fracture risk assessment is an important area of research with clear clinical relevance. Patient-specific numerical musculoskeletal models generated from diagnostic images are widely used in biomechanics research and may provide the foundation for clinical tools used to quantify fracture risk. However, prior to clinical translation, in vitro validation of predictions generated from such numerical models is necessary. Despite adopting radically different models, in vitro validation of image-based finite element (FE) models of the proximal femur (predicting strains and failure loads) have shown very similar, encouraging levels of accuracy. The accuracy of such in vitro models has motivated their application to clinical studies of osteoporotic and metastatic fractures. Such models have demonstrated promising but heterogeneous results, which may be explained by the lack of a uniform strategy with respect to FE modeling of the human femur. This review aims to critically discuss the state of the art of image-based femoral FE modeling strategies, highlighting principal features and differences among current approaches. Quantitative results are also reported with respect to the level of accuracy achieved from in vitro evaluations and clinical applications and are used to motivate the adoption of a standardized approach/workflow for image-based FE modeling of the femur.