A Robust 3D Finite Element Simulation of Human Proximal Femur Progressive Fracture Under Stance Load with Experimental Validation

TiNbSn alloy plates with low Young's modulus modulates interfragmentary movement and promote osteosynthesis in rat femur

Orthopedic implants such as arthroplasty prostheses, fracture plates, and intramedullary nails often use materials like Ti6Al4V alloy and commercially pure titanium (CP-Ti), which have Young's modulus significantly higher than that of human cortical bone, potentially causing stress shielding and inhibiting effective fracture healing. TiNbSn alloy, a β-type titanium alloy with a lower Young's modulus (40-49 GPa), has shown promise in reducing stress shielding and enhancing bone healing by promoting effective load sharing with bone. This study used 5-hole plates made from TiNbSn alloy and CP-Ti to investigate their effects on bone healing in a rat femoral fracture model. Micro-CT analysis and mechanical testing were performed six weeks postoperatively to assess bone healing. Additionally, Finite element method (FEM) analysis was employed to evaluate stress shielding and interfragmentary movement (IFM) at the fracture site. Micro-CT analysis revealed significantly higher bone volume and mineral density in the TiNbSn group than in the CP-Ti group. Mechanical testing showed increased maximum load and stiffness in the TiNbSn group (77.2 ± 10.0 N for the TiNbSn alloy plate group versus 53.3 ± 8.5 N for the CP-Ti group (p = 0.002)). FEM analysis indicated that TiNbSn plates reduced stress shielding and allowed for greater displacement and strain, promoting IFM conducive to bone healing. The findings suggest that TiNbSn alloy plates are more effective than CP-Ti plates in promoting bone healing by reducing stress shielding and enhancing IFM. The lower Young's modulus of TiNbSn allows better load distribution, facilitating bone regeneration and strengthening at the fracture site.

Outcomes of Short and Long Tibial Stems for Primary Total Knee Arthroplasty in a Population of Obese Patients at Two-Year Follow-Up: A Clinical and Biomechanical Study

BACKGROUND

Obesity can be a source of higher failure rates and inferior clinical outcomes after total knee arthroplasty (TKA). The aim of this study was to compare outcomes, failure rates, and stress distributions of TKA in obese patients using a short, long, or no tibial stem.

METHODS

A matching process based on the type of stem used and the age allowed included 180 patients who had a body mass index (BMI) > 30 and underwent a TKA between January 2010 and December 2019, with a minimum follow-up of 2 years. They were classified as moderately obese (MO: 30 < BMI < 35, N = 90) and severely obese (SO: BMI > 35, N = 90). For each, 3 subgroups were defined: thirty patients received a 30 mm short stem (SS), thirty received a 100 mm long stem (LS), and thirty received no stem (NS). Patients were assessed preoperatively and postoperatively using the Knee Society Score (KSS). A finite element model was developed to evaluate the biomechanical effects of the tibial stem on stress distribution in the subchondral bone based on BMI.

RESULTS

The SS patients had significantly higher postoperative KSS knee score [MO: 88.9 (SS) versus 79 (LS) versus 80.6 (NS); SO: 84.5 versus 72.4 versus 78.2] (P < .0001) and function score [MO: 90.4 (SS) versus 78.4 (LS) versus 68.5 (NS); SO: 85.5 versus 73 versus 61.8] (P < .0001) compared to LS and NS patients. The biomechanical study demonstrated a BMI-dependent increase in stress in the subchondral bone in contact with the tibial components. These stresses were mainly distributed at the tibial cut for NS and along the stem for SS and LS.

CONCLUSIONS

A short, cemented tibial stem offers better functional outcomes without increasing failure rates compared to a longer stem during primary TKA in a population of obese patients at two-year follow-up. A short tibial stem does not lead to increased stress compared to an LS, at least for certain BMI categories.

The Morphology of the Femur Influences the Fracture Risk during Stumbling and Falls on the Hip-A Computational Biomechanical Study

Proximal femur fracture risk depends on subject-specific factors such as bone mineral density and morphological parameters. Here, we aim to analyze the dependency of the femoral strength on sixteen morphological parameters. Therefore, finite-element analyses of 20 human femurs during stumbling and lateral falls on the hip were conducted. Pearson correlation coefficients were calculated and morphological parameters with significant correlations were examined in principal component analysis and linear regression analysis. The dependency of the fracture strength on morphological parameters was more pronounced during lateral falls on the hip compared to stumbling. Significant correlations were observed between the neck shaft angle (r = -0.474), neck diameter (r = 0.507), the true distance between the femoral head center and femoral shaft axis (r = 0.459), and its projected distance on the frontal plane (r = 0.511), greater trochanter height (r = 0.497), and distance between the femoral head center and a plane parallel to the frontal plane containing the projection of the femoral head center to the femoral neck axis (r = 0.669). Principal component analysis was strongly weighted by parameters defining the lever arm during a lateral fall as well as the loaded cross-section in the femoral neck.

Mapping the Spatial Evolution of Proximal Femur Osteoporosis: A Retrospective Cross-Sectional Study Based on CT Scans

Purpose

The purpose of this study was to quantify the modifications occurring in osteoporosis at the level of the human proximal femur throughout the trabecular structure, along with the identification of certain anatomic regions preferentially affected by osteoporosis. Another goal was to map the evolution of the radiodensity of the trabecular bone as osteoporosis progresses to an advanced stage.

Methods

The study included CT scans (right femur) from 51 patients, out of which 40 had various degrees of osteoporosis, but no other local pathology. Ten regions of interest in two orthogonal slices have been identified and the differences in radiodensity as well as their evolution have been statistically analyzed in terms of relative and absolute changes.

Results

A detailed spatial map showing the evolution of osteoporosis was obtained. As osteoporosis evolved, the relative decrease in radiodensity was inversely correlated to the radiodensity of the healthy bone. In particular, the region covering the Ward triangle decreased the most, by an average 61-62% in osteopenia and 101-106% in advanced osteoporosis, while the principal compressive group was affected the least, showing a decrease by an average 14-15% in osteopenia and 29-32% in advanced osteoporosis. The absolute decrease in radiodensity was not correlated to the radiodensity of the healthy bone and was shifted to the inferior-posterior edge of the femur. Inside the femoral head, the upper region was affected the most in absolute terms, while the greater trochanter was less affected than the femoral neck. The maximum metaphyseal cortical bone density was unaffected by the progression of osteoporosis.

Conclusion

Significant differences were noticed in terms of the absolute and relative osteoporotic changes in radiodensity related to different anatomical regions of the human femoral bone. These differences become more pronounced as the disease progresses.

Human femur fracture by mechanical compression: Towards the repeatability of bone fracture acquisition

The increase in life expectancy combined with greater bone fragility over the years is causing a rise in the bone fracture cases. Femur fractures are the most important due to their high mortality rate. This multidisciplinary work is carried out in this context and focuses on the experimental reproduction of human femur fractures by compression. We describe a sequence of steps supervised by orthopaedic surgeons for the correct arrangement of specimens on the system set up to perform the experiment. The device applies force by compression until the human bone is fractured. All tests performed have been monitored and evaluated from different knowledge perspectives. The results obtained have demonstrated the repeatability of the fracture type in a controlled environment as well as identifying the main features involved in this process. In addition, the fractured bones have been digitized to analyze the fracture zone to recreate and evaluate future simulations.

The influence of equine hoof conformation on the initiation and progression of laminitis

BACKGROUND

The health and performance of horses are significantly affected by diseases associated with the hoof. Laminitis is a critical hoof disease that causes pain and, potentially, severe hoof and bone pathology.

OBJECTIVE

To generate an equine hoof finite element (FE) model to investigate the impact of normal and toe-in hoof conformations on the degeneration (decrease in elastic modulus) of the laminar junction (LJ), as occurs in chronic laminitis.

STUDY DESIGN

Computer software modelling.

METHODS

A hoof FE model was generated to investigate the biomechanics of hoof laminitis. A 3D model, consisting of nine components, was constructed from computed tomography scans of an equine left forelimb hoof. The model was loaded with 100 cycles of trotting. Two different centres of pressure (COP) paths representing normal and toe-in conformations were assigned to the model. LJ injury was modelled by degenerating the tissue's elastic modulus in the presence of excessive maximum principal stresses.

RESULTS

FE models successfully showed findings similar to clinical observations, confirming third phalanx (P3) dorsal rotation, a symmetric distal displacement of the P3 (2 mm at the lateral and medial sides) in the normal model, and an asymmetric distal displacement of the P3 (4 mm at the lateral and 1.5 mm at the medial side) in the toe-in model. The proximal distance between P3 and the ground after LJ degeneration in the current model was significantly different from experimental measurements from healthy hooves (P < 0.01).

MAIN LIMITATIONS

The inability to account for variations in population geometry and approximation of boundary conditions and system relations were the limitations of the current study.

CONCLUSIONS

The distribution of LJ tissue degeneration was symmetric at the quarters in the normal hoof and in comparison, there was a lateral concentration of degeneration in the toe-in model.

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.

Percutaneous balloon calcaneoplasty versus open reduction and internal fixation (ORIF) for intraarticular SANDERS 2B calcaneal fracture: Comparison of primary stability using a finite element method

INTRODUCTION

Fractures of the calcaneus are common, with 65% being intra-articular, which can lead to a major impairment of the patient's quality of life. Open reduction and internal fixation with locking plates can be considered as gold-standard technique but has a high rate of post-operative complications. Minimally invasive calcaneoplasty combined with minimally invasive screw osteosynthesis is largely drawn from the management of depressed lumbar or tibial plateau fractures. The hypothesis of this study is that calcaneoplasty associated with minimally invasive percutaneous screw osteosynthesis presents biomechanical characteristics comparable with conventional osteosynthesis.

MATERIALS AND METHODS

Eight hind feet were collected. A SANDERS 2B fracture was reproduced on each specimen, while four calcanei were reduced by a balloon calcaneoplasty method and fixed with a lateral screw, four others were manually reduced and fixed with conventional osteosynthesis. Each calcaneus was then segmented for 3D finite element modeling. A vertical load was applied to the joint surface in order to measure the displacement fields and the stress distribution according to the type of osteosynthesis.

RESULTS

Analyses of the intra-articular displacement fields showed lower overall displacements in calcaneal joints treated with calcaneoplasty and lateral screw fixation. Better stress distribution was found in the calcaneoplasty group with lower equivalent joint stresses. These results could be explained by the role of the PMMA cement as a strut, enabling better load transfer.

CONCLUSION

Balloon Calcaneoplasty combined with lateral screw osteosynthesis has biomechanical characteristics at least comparable to locking plate fixation in the treatment of SANDERS 2B calcaneal joint fractures in terms of displacement fields and stress distribution under the premise of anatomical reduction.

Biomechanical evaluation of different strain judging criteria on the prediction precision of cortical bone fracture simulation under compression

Introduction: The principal strain or equivalent strain is mainly used in current numerical studies to determine the mechanical state of the element in the cortical bone finite element model and then perform fracture simulation. However, it is unclear which strain is more suitable for judging the element mechanical state under different loading conditions due to the lack of a general strain judging criterion for simulating the cortical bone fracture. Methods: This study aims to explore a suitable strain judging criterion to perform compressive fracture simulation on the rat femoral cortical bone based on continuum damage mechanics. The mechanical state of the element in the cortical bone finite element model was primarily assessed using the principal strain and equivalent strain separately to carry out fracture simulation. The prediction accuracy was then evaluated by comparing the simulated findings with different strain judging criteria to the corresponding experimental data. Results: The results showed that the fracture parameters predicted using the principal strain were closer to the experimental values than those predicted using the equivalent strain. Discussion: Therefore, the fracture simulation under compression was more accurate when the principal strain was applied to control the damage and failure state in the element. This finding has the potential to improve prediction accuracy in the cortical bone fracture simulation.

Predicting fracture in the proximal humerus using phase field models

Proximal humerus impacted fractures are of clinical concern in the elderly population. Prediction of such fractures by CT-based finite element methods encounters several major obstacles such as heterogeneous mechanical properties and fracture due to compressive strains. We herein propose to investigate a variation of the phase field method (PFM) embedded into the finite cell method (FCM) to simulate impacted humeral fractures in fresh frozen human humeri. The force-strain response, failure loads and the fracture path are compared to experimental observations for validation purposes. The PFM (by means of the regularization parameter ℓ₀) is first calibrated by one experiment and thereafter used for the prediction of the mechanical response of two other human fresh frozen humeri. All humeri are fractured at the surgical neck and strains are monitored by Digital Image Correlation (DIC). Experimental strains in the elastic regime are reproduced with good agreement (R²=0.726), similarly to the validated finite element method (Dahan et al., 2022). The failure pattern and fracture evolution at the surgical neck predicted by the PFM mimic extremely well the experimental observations for all three humeri. The maximum relative error in the computed failure loads is 3.8%. To the best of our knowledge this is the first method that can predict well the experimental compressive failure pattern as well as the force-strain relationship in proximal humerus fractures.

Varus malalignment of the lower limb increases the risk of femoral neck fracture: A biomechanical study using a finite element method

INTRODUCTION

The understanding of the stresses and strains and their dependence on loading direction caused by an axial deformity is very important for understanding the mechanism of femural neck fractures. The hypothesis of this study is that lower limb malalignment is correlated with a substantial stress variation on the upper end of the femur. The purpose of this biomechanical trial using the finite element method is to determine the effect of the loading direction on the proximal femur regarding the malalignment of the lower limb, and also enlighten the relation between the lower limb alignment and the risk of a femoral neck fracture.

METHODS

Ten segmentations of CT scans were considered. An axial compression load was applied to the femoral head to digitally simulate the physiological configuration in neutral position as well as in different axial positions in varus/valgus alignment.

RESULTS

The stress at the proximal femur changes as the varus _valgus angle does. It can be observed the smaller absolute stress at angle 10° (valgus) and the higher absolute stress at angle -10° (varus). The mean maximum von Mises stress value was 14.1 (SD=±3.48) MPa for 0°, while the mean maximum von Mises stress value was 17.96 MPa (SD=4.87) for -10° in varus. The fracture risk indicator of the proximal femoral epiphyses changes inversely with angle direction. The FRI was the highest at -10° and the lowest at 10°.

CONCLUSION

Based on the biomechanical findings and the fracture risk indicator determined in this preliminary study, varus malalignment increases the risk of femoral neck fracture. Consideration of other parameters such as bone mineral density and morphological parameters should also help to plan preventive medical strategy in the elderly.

Stochastic failure analysis of proximal femur using an isogeometric analysis based nonlocal gradient-enhanced damage model

BACKGROUND AND OBJECTIVE

Medical imaging-based finite element methods are more accurate tools for fracture risk prediction than the traditional aBMD based methods. However, these methods have drawbacks like geometric errors, high computational cost, mesh-dependent results, etc. In this article, the authors have proposed an isogeometric analysis-based nonlocal gradient-enhanced damage model to overcome some of these issues. Moreover, there are uncertainties in the values of input parameters for such analysis due to various measurement errors. Hence, stochastic analysis is performed to quantify the effect of these parametric uncertainties on the fracture behavior of the proximal femur.

METHODS

Computed Tomography images of a patient are used to create a 2D proximal femur model with a heterogeneous description of material properties. A numerical model based on gradient-enhanced nonlocal continuum damage mechanics is used for fracture analysis of proximal femur to overcome the issues related to mesh dependency in traditional continuum damage mechanics models. Further, a multipatch isogeometric solver is developed to solve the governing equations. Monte Carlo simulations are used to understand the effect of parametric uncertainties on the fracture behavior of the proximal femur.

RESULTS

The developed numerical framework is used to solve the fracture problem of proximal femur under single leg stance loading conditions. The obtained results are validated by comparing the load-displacement response and the crack path with that given in the literature. Stochastic analysis is performed by considering a ±5% variation in the elastic modulus, damage initiation strain, and the neck-shaft angle values.

CONCLUSION

The proposed numerical framework can correctly predict the damage initiation and propagation in a proximal femur. The results reveal that the heterogeneous nature of material properties of bone plays a significant role in determining the fracture characteristics of the proximal femur. Further, the results of the stochastic analysis reveal that the parametric uncertainties in the neck-shaft angle have a much more significant influence on the results of the analysis than the parametric uncertainties in the elastic modulus and damage initiation strain.

Biomechanical analysis of the correlation between mid-shaft atypical femoral fracture (AFF) and axial varus deformation

Background

Atypical femoral fractures (AFF) are diaphyseal fractures of the elderly that occur at the end of a minor trauma. The objective of this biomechanical study, using finite element modelling, was to evaluate the variations of the femoral diaphysis fracture indicator according to the variations of the mechanical axis of the lower limb, which can explain all the different atypical fracture types identified in the literature.

Methods

In order to measure variations in stress and risk factors for fracture of the femoral diaphysis, the distal end of the femur was constrained in all degrees of freedom. An axial compression load was applied to the femoral head to digitally simulate the bipodal support configuration in neutral position as well as in different axial positions in varus/valgus (− 10°/10°).

Results

The maximum stress value of Von Mises was twice as high (17.96 ± 4.87 MPa) at a varus angle of − 10^° as in the neutral position. The fracture risk indicator of the femoral diaphysis varies proportionally with the absolute value of the steering angle. However, the largest simulated varus deformation (− 10°) found a higher risk of diaphysis fracture indicator than in valgus (10°).

Conclusions

Variations in the mechanical axis of the lower limb influence the stress distribution at the femur diaphysis and consequently increase the risk of AFF. The axial deformation in varus is particularly at risk of AFF. The combination of axial deformation stresses and bone fragility consequently contribute to the creation of an environment favorable to the development of AFF.

Trial registration: ‘retrospectively registered’.

Finite element modeling of multiple density materials of bone specimens for biomechanical behavior evaluation

The finite elements method allied with the computerized axial tomography (CT) is a mathematical modeling technique that allows constructing computational models for bone specimens from CT data. The objective of this work was to compare the experimental biomechanical behavior by three-point bending tests of porcine femur specimens with different types of computational models generated through the finite elements’ method and a multiple density materials assignation scheme. Using five femur specimens, 25 scenarios were created with differing quantities of materials. This latter was applied to computational models and in bone specimens subjected to failure. Among the three main highlights found, first, the results evidenced high precision in predicting experimental reaction force versus displacement in the models with larger number of assigned materials, with maximal results being an R2 of 0.99 and a minimum root-mean-square error of 3.29%. Secondly, measured and computed elastic stiffness values follow same trend with regard to specimen mass, and the latter underestimates stiffness values a 6% in average. Third and final highlight, this model can precisely and non-invasively assess bone tissue mechanical resistance based on subject-specific CT data, particularly if specimen deformation values at fracture are considered as part of the assessment procedure.

Mesh-independent damage model for trabecular bone fracture simulation and experimental validation

We propose in this study a two-dimensional constitutive model for trabecular bone combining continuum damage with embedded strong discontinuity. The model is capable of describing the three failure phases of trabecular bone tissue which is considered herein as a quasi-brittle material with strains and rotations assumed to be small and without viscous, thermal or other non-mechanical effects. The finite element implementation of the present model uses constant strain triangle (CST) elements. The displacement jump vector is implicitly solved through a return mapping algorithm at the local (finite element) level, while the global equilibrium equations are dealt with by Newton-Raphson method. The performance, accuracy and applicability of the proposed model for trabecular bone fracture are evaluated and validated against experimental measurements. These comparisons include both global and local aspects through numerical simulations of three-point bending tests performed on 10 single bovine trabeculae in the quasi-static regime.

Finite element analysis informed variable selection for femoral fracture risk prediction

Logistic regression classification (LRC) is widely used to develop models to predict the risk of femoral fracture. LRC models based on areal bone mineral density (aBMD) alone are poor, with area under the receiver operator curve (AUROC) scores reported to be as low as 0.63. This has led to researchers investigating methods to extract further information from the image to increase performance. Recently, the use of active shape (ASM) and appearance models (AAM) have resulted in moderate improvements, but there is a risk that inclusion of too many modes will lead to overfitting. In addition, there are concerns that the effort required to extract the additional information does not justify the modest improvement in fracture risk prediction. This raises the question, are we reaching the limits of the information that can be extracted from an image? Finite element analysis was used in combination with active shape and appearance modelling to select variables to develop LRC models of fracture risk. Active shape and active appearance models were constructed based on a previously reported cohort of 94 post-menopausal Caucasian women (47 with and 47 without a fracture). T-tests were used to identify differences between the two groups for each mode of variation. Femur strength was predicted for two load cases, stance and a fall. Stepwise multi-variate linear regression was used to identify shape and appearance modes that were predictors of strength for the femurs in the training set. Femurs were also synthetically generated to explore the influence of the first 10 modes of the shape and appearance models. Identified modes of variation were then used to generate LRC models to predict fracture risk. Only 6 modes, 4 active appearance and 2 active shape modes, were identified that had a significant influence on predicted fracture strength. Of these, only two active appearance modes were needed to substantially improve the predictive mode performance (ΔAUROC = 0.080). The addition of 3 more modes (1 AAM and two ASM) further improved the performance of the classifier (ΔAUROC = 0.123). Further addition of modes did not result in any further substantial improvements. Based on these findings, it is suggested that we are reaching the limits of the information that can be extracted from an image to predict fracture risk.

Advanced Modeling Methods-Applications to Bone Fracture Mechanics

PURPOSE OF REVIEW

The goal of this review is to summarize recent advances in modeling of bone fracture using fracture mechanics-based approaches at multiple length scales spanning nano- to macroscale.

RECENT FINDINGS

Despite the additional information that fracture mechanics-based models provide over strength-based ones, the application of this approach to assessing bone fracture is still somewhat limited. Macroscale fracture models of bone have demonstrated the potential of this approach in uncovering the contributions of geometry, material property variation, as well as loading mode and rate on whole bone fracture response. Cortical and cancellous microscale models of bone have advanced the understanding of individual contributions of microstructure, microarchitecture, local material properties, and material distribution on microscale fracture resistance of bone. Nano/submicroscale models have provided additional insight into the effect of specific changes in mineral, collagen, and non-collagenous proteins as well as their interaction on energy dissipation and fracture resistance at small length scales. Advanced modeling approaches based on fracture mechanics provide unique information about the underlying multiscale fracture mechanisms in bone and how these mechanisms are influenced by the structural and material constituents of bone at different length scales. Fracture mechanics-based modeling provides a powerful approach that complements experimental evaluations and advances the understanding of critical determinants of fracture risk.

Estimation of mass apparent density and Young's modulus of femoral neck-head region

The purpose of this study is to estimate mass apparent density and Young's modulus to investigate biomechanical properties of the proximal femur bone. In this study eleven specimens of sheep femur bone having age between 1-1.25 years and human femur bone having age between 14 and 81years are used. In the present study, the first technique attempts to estimate the density from the image-based Hounsfield unit which is obtained directly from a computed tomography image. The modulus of elasticity is estimated from density-elasticity relation which is available in the literature. Another technique is used to develop a correlation between computed apparent density and greyscale based coefficient obtained by material mapping method using commercial Simpleware ScanIP software. Estimated mean deviation in apparent mass density and Young's modulus is 4.34% and 4.69% in sheep bone and 4.35% and 4.94% in human bone respectively. It is found that apparent density and Young's modulus obtained shows close agreement with values reported in the literature. Moreover, the study attempts to build up a new material model between human and sheep for orthopaedics clinical trials and research in Indian context. In addition, it is also observed that bone mass density of sheep is 1.60 times human. This method can also be useful to study and analyse biomechanical properties of the human femur bone.

Perspectives on the non-invasive evaluation of femoral strength in the assessment of hip fracture risk

We reviewed the experimental and clinical evidence that hip bone strength estimated by BMD and/or finite element analysis (FEA) reflects the actual strength of the proximal femur and is associated with hip fracture risk and its changes upon treatment.

INTRODUCTION

The risk of hip fractures increases exponentially with age due to a progressive loss of bone mass, deterioration of bone structure, and increased incidence of falls. Areal bone mineral density (aBMD), measured by dual-energy X-ray absorptiometry (DXA), is the most used surrogate marker of bone strength. However, age-related declines in bone strength exceed those of aBMD, and the majority of fractures occur in those who are not identified as osteoporotic by BMD testing. With hip fracture incidence increasing worldwide, the development of accurate methods to estimate bone strength in vivo would be very useful to predict the risk of hip fracture and to monitor the effects of osteoporosis therapies.

METHODS

We reviewed experimental and clinical evidence regarding the association between aBMD and/orCT-finite element analysis (FEA) estimated femoral strength and hip fracture risk as well as their changes with treatment.

RESULTS

Femoral aBMD and bone strength estimates by CT-FEA explain a large proportion of femoral strength ex vivo and predict hip fracture risk in vivo. Changes in femoral aBMD are strongly associated with anti-fracture efficacy of osteoporosis treatments, though comparable data for FEA are currently not available.

CONCLUSIONS

Hip aBMD and estimated femoral strength are good predictors of fracture risk and could potentially be used as surrogate endpoints for fracture in clinical trials. Further improvements of FEA may be achieved by incorporating trabecular orientations, enhanced cortical modeling, effects of aging on bone tissue ductility, and multiple sideway fall loading conditions.

Previous Damage Accumulation Can Influence Femoral Fracture Strength: A Finite Element Study

To manage osteoporotic hip fracture risk, it is necessary to understand failure mechanisms of bone at both the material and organ level. The structural response of bone is dependent on load history. Repeated loading causes progressive microstructural cracking, resulting in reduced apparent-level stiffness and, if damage is significant, reductions to peak load bearing capability. However, the effect of previous damage accumulation has not been well explored at the organ level. It was hypothesized that femoral fracture load and fracture pattern may be sensitive to damage accumulation from previous loading events. Six cadaveric specimens were used to develop patient specific finite element (FE) models from quantitative tomographic (qCT) scans. Material properties were assigned from qCT intensity at each element location, and damage evolution was predicted using a previously validated quasi-brittle FE model. Three scenarios were investigated: stumble followed by another stumble (S-S), fall followed by another fall (F-F), and stumble followed by a fall (S-F). Fracture load and pattern were compared to FE predictions for a single stumble (S) or single fall (F) loading event. Most specimens were resilient to accumulated damage, showing little (<5%) change in fracture load from the multiple-load scenarios (S-S, F-F, and S-F) compared to an equivalent single load scenario (S or F). Only one specimen demonstrated moderate (5-15%) reductions in strength from all three multiple-load scenarios. However, two specimens experienced moderate (20-30%) increase in fracture load in some load cases. In these cases, initial damage caused the load to be more evenly distributed upon subsequent loading events. © 2019 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 37:2197-2203, 2019.

A novel phase field method for modeling the fracture of long bones

A proximal humerus fracture is an injury to the shoulder joint that necessitates medical attention. While it is one of the most common fracture injuries impacting the elder community and those who suffer from traumatic falls or forceful collisions, there are almost no validated computational methods that can accurately model these fractures. This could be due to the complex, inhomogeneous bone microstructure, complex geometries, and the limitations of current fracture mechanics methods. In this paper, we develop a novel phase field method to investigate the proximal humerus fracture. To model the fracture in the inhomogeneous domain, we propose a power-law relationship between bone mineral density and critical energy release rate. The method is validated by an in vitro experiment, in which a human humerus is constrained on both ends while subjected to compressive loads on its head, in the longitudinal direction, that lead to fracture at the anatomical neck. CT scans are employed to acquire the bone geometry and material parameters, from which detailed finite element meshes with inhomogeneous Young modulus distributions are generated. The numerical method, implemented in a high performance computing environment, is used to quantitatively predict the complex 3D brittle fracture of the bone and is shown to be in good agreement with experimental observations. Furthermore, our findings show that the damage is initiated in the trabecular bone-head and propagates outward towards the bone cortex. We conclude that the proposed phase field method is a promising approach to model bone fracture.

Numerical modelling of hip fracture patterns in human femur

BACKGROUND AND OBJECTIVE

Hip fracture morphology is an important factor determining the ulterior surgical repair and treatment, because of the dependence of the treatment on fracture morphology. Although numerical modelling can be a valuable tool for fracture prediction, the simulation of femur fracture is not simple due to the complexity of bone architecture and the numerical techniques required for simulation of crack propagation. Numerical models assuming homogeneous fracture mechanical properties commonly fail in the prediction of fracture patterns. This paper focuses on the prediction of femur fracture based on the development of a finite element model able to simulate the generation of long crack paths.

METHODS

The finite element model developed in this work demonstrates the capability of predicting fracture patterns under stance loading configuration, allowing the distinction between the main fracture paths: intracapsular and extracapsular fractures. It is worth noting the prediction of different fracture patterns for the same loading conditions, as observed during experimental tests.

RESULTS AND CONCLUSIONS

The internal distribution of bone mineral density and femur geometry strongly influences the femur fracture morphology and fracture load. Experimental fracture paths have been analysed by means of micro-computed tomography allowing the comparison of predicted and experimental crack surfaces, confirming the good accuracy of the numerical model.

Optimizing Accuracy of Proximal Femur Elastic Modulus Equations

Quantitative computed tomography-based finite element analysis (QCT/FEA) is a promising tool to predict femoral properties. One of the modeling parameters required as input for QCT/FEA is the elastic modulus, which varies with the location-dependent bone mineral density (ash density). The aim of this study was to develop optimized equations for the femoral elastic modulus. An inverse QCT/FEA method was employed, using an optimization process to minimize the error between the predicted femoral stiffness values and experimental values. We determined optimal coefficients of an elastic modulus equation that was a function of ash density only, and also optimal coefficients for several other equations that included along with ash density combinations of the variables sex and age. All of the optimized models were found to be more accurate than models from the literature. It was found that the addition of the variables sex and age to ash density made very minor improvements in stiffness predictions compared to the model with ash density alone. Even though the addition of age did not remarkably improve the statistical metrics, the effect of age was reflected in the elastic modulus equations as a decline of about 9% over a 60-year interval.

Assessment of hip fracture risk by cross-sectional strain-energy derived from image-based beam model

BACKGROUND

Clinicians have been looking for a simple and effective biomechanical tool for the assessment of hip fracture risk. Dual-energy X-ray absorptiometry (DXA) is currently the primary bone imaging modality in clinic, and the engineering beam is the simplest model for a mechanical analysis. Therefore, we developed a DXA-based beam model for the above purpose.

METHODS

A beam model of the proximal femur was constructed from the subject's hip DXA image and denoted DXA-beam. Femur stiffness was calculated at cross-sections of interest using areal bone-mineral-density profile. Impact force induced in a sideways fall was applied as a critical loading. Fracture risk index at a cross-section was defined as the ratio of strain-energy induced by the impact force to the allowable strain-energy. A clinic cohort was used to study the discriminability of DXA-beam, which was measured by the area under the curve and odds ratio, both with 95% confidential interval.

FINDINGS

Fracture risk measured by DXA-beam model at the femoral neck [odds ratio 2.23, 95% confidence interval (1.83, 2.57)], inter-trochanter [2.49, (2.14, 3.25)] and sub-trochanter [2.82, (2.38, 3.51)] were strongly associated with hip fracture. The area under the curve by DXA-beam at the femoral neck [0.74, 95% confidence interval (0.70, 0.76)], inter-trochanter [0.77, (0.75, 0.82)] and sub-trochanter [0.76, (0.74, 0.81)] were higher than that by femoral neck bone mineral density [0.71, (0.65, 0.78)].

INTERPRETATION

The DXA-beam model is a simple and yet effective mechanical model. It had promising performance in discrimination of fracture cases from controls.

Factors associated with proximal femur fracture determined in a large cadaveric cohort

Many researchers have used cadaveric fracture tests to determine the relationship between proximal femur (hip) fracture strength and a multitude of possible explanatory variables, typically considered one or two at a time. These variables include subject-specific proximal femur variables such as femoral neck areal bone mineral density (aBMD), sex, age, and geometry, as well as physiological hip fracture event variables such as fall speed and angle of impact. However, to our knowledge, no study has included all of these variables simultaneously in the same experimental dataset. To address this gap, the present study simultaneously included all of these subject-specific and fracture event variables in multivariate models to understand their contributions to femoral strength and fracture type. The primary aim of this study was to determine not only whether each of these variables contributed to the prediction of femoral strength, but also to determine the relative importance of each variable in strength prediction. A secondary aim was to similarly characterize the importance of these variables for the prediction of fracture type. To accomplish these aims, we characterized 197 proximal femurs (covering a wide range of subject-specific variables) with DXA and CT scans, and then tested the femurs to fracture in a sideways fall on the hip configuration. Each femur was tested using one of three fall speed conditions and one of four angles of impact (bone orientations). During each test, we acquired measurements of relevant force and displacement data. We then reduced the test data to determine femoral strength, and we used post-fracture CT scans to classify the fracture type (e.g., trochanteric, cervical). Using these results, the explanatory variables were analyzed with mixed statistical models to explain variations in hip fracture strength and fracture type, respectively. Five explanatory variables were statistically significant in explaining the variability in femoral strength: aBMD, sex, age, fall speed, and neck-shaft angle (P ≤ 0.0135). These five variables, including significant interactions, explained 80% of the variability in hip fracture strength. Additionally, when only aBMD, sex, and age (P < 0.0001) were considered in the model, again including significant interactions, these three variables alone explained 79% of the variability in hip fracture strength. So while fall speed (P = 0.0135) and neck-shaft angle (P = 0.0041) were statistically significant, the inclusion of these variables did not appreciably improve the prediction of hip fracture strength compared to the model that considered only aBMD, sex and age. For the variables we included in this study, in the ranges we considered, our findings indicate that the clinically-available information of patient age, sex and aBMD are sufficient for femoral strength assessment. These findings also suggest that there is little value in the extra effort required to characterize the effect of femoral geometry on strength, or to account for the probabilistic nature of fall-related factors such as fall speed and angle of impact. For fracture type, the only explanatory variable found to be significant was aBMD (P ≤ 0.0099). We found that the odds of having intertrochanteric fractures increased by 47% when aBMD decreased by one standard deviation (0.2 g/cm2).

Influence of geometry on proximal femoral shaft strains: Implications for atypical femoral fracture

INTRODUCTION

Atypical femoral fractures (AFF) are characterized as low-energy fractures of the femoral shaft or subtrochanteric region. Femoral geometry is known to play a role in AFF risk; it is hypothesized that high-risk geometries are associated with elevated femoral shaft strain. However, it is not well known which geometric parameters have the greatest effect on strain, or whether interaction between parameters is significant. The purpose of this study was to thoroughly quantify the relationship between femoral geometry and diaphyseal strain, using patient specific finite element (FE) modelling in concert with parametric mesh morphing.

METHODS

Ten FE models were generated from computed tomography (CT) images of cadaveric femora. Heterogeneous material properties were assigned based on average CT intensities at element locations and models were subject to loads and boundary conditions representing the stance phase of gait. Mesh morphing was used to manipulate 8 geometric parameters: neck shaft angle (NSA), neck version angle (NV), neck length (NL), femoral length (FL), lateral bowing angle (L.Bow), anterior bowing angle (A.Bow), shaft diameter (S.Dia), and cortical bone thickness (C·Th). A 2-Level full factorial analysis was used to explore the effect of different combinations of physiologically realistic minimum and maximum values for each parameter. Statistical analysis (Generalized Estimating Equations) was used to assess main effects and first order interactions of each parameter.

RESULTS

Six independent parameters and seven interaction terms had statistically significant (p<0.05) effects on peak strain and strained volume. For both measures, the greatest changes were caused by S.Dia, L.Bow, and A.Bow, and/or first order interactions involving two of these variables.

CONCLUSIONS

As hypothesized, a large number of geometric measures (six) and first order interactions (seven) are associated with changes in femoral shaft strain. These measures can be evaluated radiographically, which may have important implications for future studies investigating AFF risk in clinical populations.

Automation of a DXA-based finite element tool for clinical assessment of hip fracture risk

Finite element analysis of medical images is a promising tool for assessing hip fracture risk. Although a number of finite element models have been developed for this purpose, none of them have been routinely used in clinic. The main reason is that the computer programs that implement the finite element models have not been completely automated, and heavy training is required before clinicians can effectively use them. By using information embedded in clinical dual energy X-ray absorptiometry (DXA), we completely automated a DXA-based finite element (FE) model that we previously developed for predicting hip fracture risk. The automated FE tool can be run as a standalone computer program with the subject's raw hip DXA image as input. The automated FE tool had greatly improved short-term precision compared with the semi-automated version. To validate the automated FE tool, a clinical cohort consisting of 100 prior hip fracture cases and 300 matched controls was obtained from a local community clinical center. Both the automated FE tool and femoral bone mineral density (BMD) were applied to discriminate the fracture cases from the controls. Femoral BMD is the gold standard reference recommended by the World Health Organization for screening osteoporosis and for assessing hip fracture risk. The accuracy was measured by the area under ROC curve (AUC) and odds ratio (OR). Compared with femoral BMD (AUC = 0.71, OR = 2.07), the automated FE tool had a considerably improved accuracy (AUC = 0.78, OR = 2.61 at the trochanter). This work made a large step toward applying our DXA-based FE model as a routine clinical tool for the assessment of hip fracture risk. Furthermore, the automated computer program can be embedded into a web-site as an internet application.

Are DXA/aBMD and QCT/FEA Stiffness and Strength Estimates Sensitive to Sex and Age?

Dual X-ray absorptiometry (DXA) measures areal bone mineral density (aBMD) by simplifying a complex 3D bone structure to a 2D projection and is not equally effective for explaining fracture strength in women and men. Unlike DXA, subject-specific quantitative computed tomography-based finite element analysis (QCT/FEA) estimates fracture strength using 3D bone mineral distribution and geometry. By using experimentally-measured femoral stiffness and strength from a one hundred sample cadaveric cohort that included variations in sex and age, we wanted to determine if QCT/FEA estimates were able to better predict the experimental variations than DXA/aBMD. For each femur, DXA/aBMD was assessed and a QCT/FEA model was developed to estimate femoral stiffness and strength. Then, the femur was mechanically tested to fracture in a sideways fall on the hip position to measure stiffness and strength. DXA/aBMD and QCT/FEA estimates were compared for their sensitivity to sex and age with multivariate statistical analyses. When comparing the measured data with DXA/aBMD predictions, both age and sex were significant (p ≤ 0.0398) for both femoral stiffness and strength. However, QCT/FEA predictions of stiffness and strength showed sex was insignificant (p ≥ 0.23). Age was still significant (p ≤ 0.0072). These results indicate that QCT/FEA, unlike DXA/aBMD, accounted for bone differences due to sex.

A rate-independent continuum model for bone tissue with interaction of compressive and tensile micro-damage

Low bone strength is a major risk factor for osteoporotic fractures and is only partially determined by clinical densitometry. Accumulated micro-damage induces residual strains, degrades elastic modulus and reduces bone strength independently of bone mineral density. Histologically, overloading of bone in compression and tension leads to distinct crack size, distribution and orientation which interact during combined loading scenarios. Statistics of rheological models can describe this process and reproduce experimental stress-strain curves with an unprecedented realism, but are computationally expensive and therefore difficult to generalize to 3D. Accordingly, the aim of this work is to formulate a continuum damage model that describes the key features of bone micro-damage, namely the accumulation of residual strains, the degradation of elastic modulus and the reduction of strength in compression, tension and especially in their sequential application. The promising qualitative agreement of the model with the experiments will motivate a generalization to 3D and allow the biomechanical investigation of bones and bone-implant systems subjected to cyclic overloading in tension and/or compression.

Quantitative Computed Tomography (QCT) derived Bone Mineral Density (BMD) in finite element studies: a review of the literature

BACKGROUND

Finite element modeling of human bone provides a powerful tool to evaluate a wide variety of outcomes in a highly repeatable and parametric manner. These models are most often derived from computed tomography data, with mechanical properties related to bone mineral density (BMD) from the x-ray energy attenuation provided from this data. To increase accuracy, many researchers report the use of quantitative computed tomography (QCT), in which a calibration phantom is used during image acquisition to improve the estimation of BMD. Since model accuracy is dependent on the methods used in the calculation of BMD and density-mechanical property relationships, it is important to use relationships developed for the same anatomical location and using the same scanner settings, as these may impact model accuracy. The purpose of this literature review is to report the relationships used in the conversion of QCT equivalent density measures to ash, apparent, and/or tissue densities in recent finite element (FE) studies used in common density-modulus relationships. For studies reporting experimental validation, the validation metrics and results are presented.

RESULTS

Of the studies reviewed, 29% reported the use of a dipotassium phosphate (K2HPO4) phantom, 47% a hydroxyapatite (HA) phantom, 13% did not report phantom type, 7% reported use of both K2HPO4 and HA phantoms, and 4% alternate phantom types. Scanner type and/or settings were omitted or partially reported in 31% of studies. The majority of studies used densitometric and/or density-modulus relationships derived from different anatomical locations scanned in different scanners with different scanner settings. The methods used to derive various densitometric relationships are reported and recommendations are provided toward the standardization of reporting metrics.

CONCLUSIONS

This review assessed the current state of QCT-based FE modeling with use of clinical scanners. It was found that previously developed densitometric relationships vary by anatomical location, scanner type and settings. Reporting of all parameters used when referring to previously developed relationships, or in the development of new relationships, may increase the accuracy and repeatability of future FE models.

Assessment of compressive failure process of cortical bone materials using damage-based model

The main failure factors of cortical bone are aging or osteoporosis, accident and high energy trauma or physiological activities. However, the mechanism of damage evolution coupled with yield criterion is considered as one of the unclear subjects in failure analysis of cortical bone materials. Therefore, this study attempts to assess the structural response and progressive failure process of cortical bone using a brittle damaged plasticity model. For this reason, several compressive tests are performed on cortical bone specimens made of bovine femur, in order to obtain the structural response and mechanical properties of the material. Complementary finite element (FE) model of the sample and test is prepared to simulate the elastic-to-damage behavior of the cortical bone using the brittle damaged plasticity model. The FE model is validated in a comparative method using the predicted and measured structural response as load-compressive displacement through simulation and experiment. FE results indicated that the compressive damage initiated and propagated at central region where maximum equivalent plastic strain is computed, which coincided with the degradation of structural compressive stiffness followed by a vast amount of strain energy dissipation. The parameter of compressive damage rate, which is a function dependent on damage parameter and the plastic strain is examined for different rates. Results show that considering a similar rate to the initial slope of the damage parameter in the experiment would give a better sense for prediction of compressive failure.

Osteoporosis drug effects on cortical and trabecular bone microstructure: a review of HR-pQCT analyses

With the development of new non-invasive analytical techniques and particularly the advent of high-resolution peripheral quantitative computed tomography (HRpQCT) it is possible to assess cortical and trabecular bone changes under the effects of ageing, diseases and treatments. In the present study, we reviewed the treatment-related effects on bone parameters assessed by HRpQCT imaging. We identified 12 full-length articles published in peer-reviewed journals describing treatment-induced changes assessed by HRpQCT. The design of these studies varied a lot in terms of duration and methodology: some of them were open-labelled, others were double-blind, placebo-controlled or double-blind, double-dummy, active controlled. In addition, the sample size in these studies ranged from 11 to 324 patients. Motion artifacts occurring during data acquisition were sometimes a real challenge particularly at the radius leading sometimes to exclude the analysis at the radius due to the uninterpretability of microstructural parameters. Responses to therapies were treatment-specific and divergent effects in cortical and trabecular bone with antiresorptive or anabolic agents were observed. Standardization of bone microarchitecture parameters (including porosity) and bone strength estimates by finite element analysis (FEA) are mandatory. The additional value of microarchitecture and FEA estimates changes with therapies in terms of improvement in fracture outcomes which have to be adequately assessed in clinical trials with fracture end point. Data from these reviewed studies advance our understanding of the microstructural consequences of osteoporosis and highlight potential differences in bone quality outcomes within therapies.

The influence of the modulus-density relationship and the material mapping method on the simulated mechanical response of the proximal femur in side-ways fall loading configuration

Contributing to slow advance of finite element (FE) simulations for hip fracture risk prediction, into clinical practice, could be a lack of consensus in the biomechanics community on how to map properties to the models. Thus, the aim of the present study was first, to systematically quantify the influence of the modulus-density relationship (E-ρ) and the material mapping method (MMM) on the predicted mechanical response of the proximal femur in a side-ways fall (SWF) loading configuration and second, to perform a model-to-model comparison of the predicted mechanical response within the femoral neck for all the specimens tested in the present study, using three different modelling techniques that have yielded good validation outcome in terms of surface strain prediction and whole bone response according to the literature. We found the outcome to be highly dependent on both the E-ρ relationship and the MMM. In addition, we found that the three modelling techniques that have resulted in good validation outcome in the literature yielded different principal strain prediction both on the surface as well as internally in the femoral neck region of the specimens modelled in the present study. We conclude that there exists a need to carry out a more comprehensive validation study for the SWF loading mode to identify which combination of MMMs and E-ρ relationship leads to the best match for whole bone and local mechanical response. The MMMs tested in the present study have been made publicly available at https://simtk.org/home/mitk-gem.

Prediction of the mechanical response of canine humerus to three-point bending using subject-specific finite element modelling

Subject-specific finite element models could improve decision making in canine long-bone fracture repair. However, it preliminary requires that finite element models predicting the mechanical response of canine long bone are proposed and validated. We present here a combined experimental–numerical approach to test the ability of subject-specific finite element models to predict the bending response of seven pairs of canine humeri directly from medical images. Our results show that bending stiffness and yield load are predicted with a mean absolute error of 10.1% (±5.2%) for the 14 samples. This study constitutes a basis for the forthcoming optimization of canine long-bone fracture repair.

Quantification of Age-Related Tissue-Level Failure Strains of Rat Femoral Cortical Bones Using an Approach Combining Macrocompressive Test and Microfinite Element Analysis

Bone mechanical properties vary with age; meanwhile, a close relationship exists among bone mechanical properties at different levels. Therefore, conducting multilevel analyses for bone structures with different ages are necessary to elucidate the effects of aging on bone mechanical properties at different levels. In this study, an approach that combined microfinite element (micro-FE) analysis and macrocompressive test was established to simulate the failure of male rat femoral cortical bone. Micro-FE analyses were primarily performed for rat cortical bones with different ages to simulate their failure processes under compressive load. Tissue-level failure strains in tension and compression of these cortical bones were then back-calculated by fitting the experimental stress–strain curves. Thus, tissue-level failure strains of rat femoral cortical bones with different ages were quantified. The tissue-level failure strain exhibited a biphasic behavior with age: in the period of skeletal maturity (1–7 months of age), the failure strain gradually increased; when the rat exceeded 7 months of age, the failure strain sharply decreased. In the period of skeletal maturity, both the macro- and tissue-levels mechanical properties showed a large promotion. In the period of skeletal aging (9–15 months of age), the tissue-level mechanical properties sharply deteriorated; however, the macromechanical properties only slightly deteriorated. The age-related changes in tissue-level failure strain were revealed through the analysis of male rat femoral cortical bones with different ages, which provided a theoretical basis to understand the relationship between rat cortical bone mechanical properties at macro- and tissue-levels and decrease of bone strength with age.

Modelling of bone fracture and strength at different length scales: a review

In this paper, we review analytical and computational models of bone fracture and strength. Bone fracture is a complex phenomenon due to the composite, inhomogeneous and hierarchical structure of bone. First, we briefly summarize the hierarchical structure of bone, spanning from the nanoscale, sub-microscale, microscale, mesoscale to the macroscale, and discuss experimental observations on failure mechanisms in bone at these scales. Then, we highlight representative analytical and computational models of bone fracture and strength at different length scales and discuss the main findings in the context of experiments. We conclude by summarizing the challenges in modelling of bone fracture and strength and list open topics for scientific exploration. Modelling of bone, accounting for different scales, provides new and needed insights into the fracture and strength of bone, which, in turn, can lead to improved diagnostic tools and treatments of bone diseases such as osteoporosis.

Comparison of proximal femur and vertebral body strength improvements in the FREEDOM trial using an alternative finite element methodology

Denosumab reduced the incidence of new fractures in postmenopausal women with osteoporosis by 68% at the spine and 40% at the hip over 36 months compared with placebo in the FREEDOM study. This efficacy was supported by improvements from baseline in vertebral (18.2%) strength in axial compression and femoral (8.6%) strength in sideways fall configuration at 36 months, estimated in Newtons by an established voxel-based finite element (FE) methodology. Since FE analyses rely on the choice of meshes, material properties, and boundary conditions, the aim of this study was to independently confirm and compare the effects of denosumab on vertebral and femoral strength during the FREEDOM trial using an alternative smooth FE methodology. Unlike the previous FE study, effects on femoral strength in physiological stance configuration were also examined. QCT data for the proximal femur and two lumbar vertebrae were analyzed by smooth FE methodology at baseline, 12, 24, and 36 months for 51 treated (denosumab) and 47 control (placebo) subjects. QCT images were segmented and converted into smooth FE models to compute bone strength. L1 and L2 vertebral bodies were virtually loaded in axial compression and the proximal femora in both fall and stance configurations. Denosumab increased vertebral body strength by 10.8%, 14.0%, and 17.4% from baseline at 12, 24, and 36 months, respectively (p<0.0001). Denosumab also increased femoral strength in the fall configuration by 4.3%, 5.1%, and 7.2% from baseline at 12, 24, and 36 months, respectively (p<0.0001). Similar improvements were observed in the stance configuration with increases of 4.2%, 5.2%, and 5.2% from baseline (p≤0.0007). Differences between the increasing strengths with denosumab and the decreasing strengths with placebo were significant starting at 12 months (vertebral and femoral fall) or 24 months (femoral stance). Using an alternative smooth FE methodology, we confirmed the significant improvements in vertebral body and proximal femur strength previously observed with denosumab. Estimated increases in strength with denosumab and decreases with placebo were highly consistent between both FE techniques.

An eFace-Template Method for Efficiently Generating Patient-Specific Anatomically-Detailed Facial Soft Tissue FE Models for Craniomaxillofacial Surgery Simulation

Accurate surgical planning and prediction of craniomaxillofacial surgery outcome requires simulation of soft-tissue changes following osteotomy. This can only be accomplished on an anatomically-detailed facial soft tissue model. However, current anatomically-detailed facial soft tissue model generation is not appropriate for clinical applications due to the time intensive nature of manual segmentation and volumetric mesh generation. This paper presents a novel semi-automatic approach, named eFace-template method, for efficiently and accurately generating a patient-specific facial soft tissue model. Our novel approach is based on the volumetric deformation of an anatomically-detailed template to be fitted to the shape of each individual patient. The adaptation of the template is achieved by using a hybrid landmark-based morphing and dense surface fitting approach followed by a thin-plate spline interpolation. This methodology was validated using 4 visible human datasets (regarded as gold standards) and 30 patient models. The results indicated that our approach can accurately preserve the internal anatomical correspondence (i.e., muscles) for finite element modeling. Additionally, our hybrid approach was able to achieve an optimal balance among the patient shape fitting accuracy, anatomical correspondence and mesh quality. Furthermore, the statistical analysis showed that our hybrid approach was superior to two previously published methods: mesh-matching and landmark-based transformation. Ultimately, our eFace-template method can be directly and effectively used clinically to simulate the facial soft tissue changes in the clinical application.