A nonlinear QCT-based finite element model validation study for the human femur tested in two configurations in vitro

Explainable machine-learning-based prediction of QCT/FEA-calculated femoral strength under stance loading configuration using radiomics features

Finite element analysis can provide precise femoral strength assessment. However, its modeling procedures were complex and time-consuming. This study aimed to develop a model to evaluate femoral strength calculated by quantitative computed tomography-based finite element analysis (QCT/FEA) under stance loading configuration, offering an effective, simple, and explainable method. One hundred participants with hip QCT images were selected from the Hong Kong part of the Osteoporotic fractures in men cohort. Radiomics features were extracted from QCT images. Filter method, Pearson correlation analysis, and least absolute shrinkage and selection operator method were employed for feature selection and dimension reduction. The remaining features were utilized as inputs, and femoral strengths were calculated as the ground truth through QCT/FEA. Support vector regression was applied to develop a femoral strength prediction model. The influence of various numbers of input features on prediction performance was compared, and the femoral strength prediction model was established. Finally, Shapley additive explanation, accumulated local effects, and partial dependency plot methods were used to explain the model. The results indicated that the model performed best when six radiomics features were selected. The coefficient of determination (R2), the root mean square error, the normalized root mean square error, and the mean squared error on the testing set were 0.820, 1016.299 N, 10.645%, and 750.827 N, respectively. Additionally, these features all positively contributed to femoral strength prediction. In conclusion, this study provided a noninvasive, effective, and explainable method of femoral strength assessment, and it may have clinical application potential.

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.

Development of a density-based topology optimization of homogenized lattice structures for individualized hip endoprostheses and validation using micro-FE

Prosthetic implants, particularly hip endoprostheses, often lead to stress shielding because of a mismatch in compliance between the bone and the implant material, adversely affecting the implant's longevity and effectiveness. Therefore, this work aimed to demonstrate a computationally efficient method for density-based topology optimization of homogenized lattice structures in a patient-specific hip endoprosthesis. Thus, the root mean square error (RMSE) of the stress deviations between the physiological femur model and the optimized total hip arthroplasty (THA) model compared to an unoptimized-THA model could be reduced by 81 % and 66 % in Gruen zone (GZ) 6 and 7. However, the method relies on homogenized finite element (FE) models that only use a simplified representation of the microstructural geometry of the bone and implant. The topology-optimized hip endoprosthesis with graded lattice structures was synthesized using algorithmic design and analyzed in a virtual implanted state using micro-finite element (micro-FE) analysis to validate the optimization method. Homogenized FE and micro-FE models were compared based on averaged von Mises stresses in multiple regions of interest. A strong correlation (CCC > 0.97) was observed, indicating that optimizing homogenized lattice structures yields reliable outcomes. The graded implant was additively manufactured to ensure the topology-optimized result's feasibility.

QCT-based computational bone strength assessment updated with MRI-derived 'hidden' microporosity

Microdamage accumulated through sustained periods of cyclic loading or single overloading events contributes to bone fragility through a reduction in stiffness and strength. Monitoring microdamage in vivo remains unattainable by clinical imaging modalities. As such, there are no established computational methods for clinical fracture risk assessment that account for microdamage that exists in vivo at any specific timepoint. We propose a method that combines multiple clinical imaging modalities to identify an indicative surrogate, which we term 'hidden porosity', that incorporates pre-existing bone microdamage in vivo. To do so, we use the third metacarpal bone of the equine athlete as an exemplary model for fatigue induced microdamage, which coalesces in the subchondral bone. N = 10 metacarpals were scanned by clinical quantitative computed tomography (QCT) and magnetic resonance imaging (MRI). We used a patch-based similarity method to quantify the signal intensity of a fluid sensitive MRI sequence in bone regions where microdamage coalesces. The method generated MRI-derived pseudoCT images which were then used to determine a pre-existing damage (Dpex) variable to quantify the proposed surrogate and which we incorporate into a nonlinear constitutive model for bone tissue. The minimum, median, and maximum detected Dpex of 0.059, 0.209, and 0.353 reduced material stiffness by 5.9%, 20.9%, and 35.3% as well as yield stress by 5.9%, 20.3%, and 35.3%. Limb-specific voxel-based finite element meshes were equipped with the updated material model. Lateral and medial condyles of each metacarpal were loaded to simulate physiological joint loading during gallop. The degree of detected Dpex correlated with a relative reduction in both condylar stiffness (p = 0.001, R2 > 0.74) and strength (p < 0.001, R2 > 0.80). Our results illustrate the complementary value of looking beyond clinical CT, which neglects the inclusion of microdamage due to partial volume effects. As we use clinically available imaging techniques, our results may aid research beyond the equine model on fracture risk assessment in human diseases such as osteoarthritis, bone cancer, or osteoporosis.

Exploration of the synergistic role of cortical thickness asymmetry ("Trabecular Eccentricity" concept) in reducing fracture risk in the human femoral neck and a control bone (Artiodactyl Calcaneus)

The mechanobiology of the human femoral neck is a focus of research for many reasons including studies that aim to curb age-related bone loss that contributes to a near-exponential rate of hip fractures. Many believe that the femoral neck is often loaded in rather simple bending, which causes net tension stress in the upper (superior) femoral neck and net compression stress in its inferior aspect ("T/C paradigm"). This T/C loading regime lacks in vivo proof. The "C/C paradigm" is a plausible alternative simplified load history that is characterized by a gradient of net compression across the entire femoral neck; action of the gluteus medius and external rotators of the hip are important in this context. It is unclear which paradigm is at play in natural loading due to lack of in vivo bone strain data and deficiencies in understanding mechanisms and manifestations of bone adaptation in tension vs. compression. For these reasons, studies of the femoral neck would benefit from being compared to a 'control bone' that has been proven, by strain data, to be habitually loaded in bending. The artiodactyl (sheep and deer) calcaneus model has been shown to be a very suitable control in this context. However, the application of this control in understanding the load history of the femoral neck has only been attempted in two prior studies, which did not examine the interplay between cortical and trabecular bone, or potential load-sharing influences of tendons and ligaments. Our first goal is to compare fracture risk factors of the femoral neck in both paradigms. Our second goal is to compare and contrast the deer calcaneus to the human femoral neck in terms of fracture risk factors in the T/C paradigm (the C/C paradigm is not applicable in the artiodactyl calcaneus due to its highly constrained loading). Our third goal explores interplay between dorsal/compression and plantar/tension regions of the deer calcaneus and the load-sharing roles of a nearby ligament and tendon, with insights for translation to the femoral neck. These goals were achieved by employing the analytical model of Fox and Keaveny (J. Theoretical Biology 2001, 2003) that estimates fracture risk factors of the femoral neck. This model focuses on biomechanical advantages of the asymmetric distribution of cortical bone in the direction of habitual loading. The cortical thickness asymmetry of the femoral neck (thin superior cortex, thick inferior cortex) reflects the superior-inferior placement of trabecular bone (i.e., "trabecular eccentricity," TE). TE helps the femoral neck adapt to typical stresses and strains through load-sharing between superior and inferior cortices. Our goals were evaluated in the context of TE. Results showed the C/C paradigm has lower risk factors for the superior cortex and for the overall femoral neck, which is clinically relevant. TE analyses of the deer calcaneus revealed important synergism in load-sharing between the plantar/tension cortex and adjacent ligament/tendon, which challenges conventional understanding of how this control bone achieves functional adaptation. Comparisons with the control bone also exposed important deficiencies in current understanding of human femoral neck loading and its potential histocompositional adaptations.

Computation of physiological loading induced interstitial fluid motion in muscle standardized femur: Healthy vs. osteoporotic bone

BACKGROUND AND OBJECTIVES

Physiological loading-induced mechanical environments regulate bone modeling and remodeling. Thus, loading-induced normal strain is typically considered a stimulus to osteogenesis. However, several studies noticed new bone formation near the sites of minimal normal strain, e.g., the neutral axis of bending in long bones, which raises a question on how bone mass is maintained near these sites. Secondary mechanical components such as shear strain and interstitial fluid flow also stimulate bone cells and regulate bone mass. However, the osteogenic potential of these components is not well established. Accordingly, the present study estimates the distribution of physiological muscle loading-induced mechanical environments such as normal strain, shear strain, pore pressure, and interstitial fluid flow in long bones.

METHODS

A poroelastic finite element muscle standardized femur (MuscleSF) model is developed to compute the distribution of the mechanical environment as a function of bone porosities associated with osteoporotic and disuse bone loss.

RESULTS

The results indicate the presence of higher shear strain and interstitial fluid motion near the minimal strain sites, i.e., the neutral axis of bending of femoral cross-sections. This suggests that secondary stimuli may maintain the bone mass at these locations. Pore pressure and interstitial fluid motion reduce with the increased porosity associated with bone disorders, possibly resulting in diminished skeletal mechano-sensitivity to exogenous loading.

CONCLUSIONS

These outcomes present a better understanding of mechanical environment-mediated regulation of site-specific bone mass, which can be beneficial in developing prophylactic exercise to prevent bone loss in osteoporosis and muscle disuse.

Fracture analysis of healthy and osteoporotic femora using clinical CT images, phantomless densitometry, and linear FE method

Computational fracture analysis has become a growing branch of orthopedic research. Particularly, the associated methods provide reliable tools for the analysis of 3D CT-based models of bone. This paper reports the results of such analyses for 15 human femora (healthy and osteoporotic) under different loading orientations (85 different analysis cases). A new method was developed for the calculation of the density distribution in the models from ordinary clinical CT images without calibration phantom. This method, along with a strain-energy-based linear finite element (FE) analysis scheme, was used to predict the fracture strength and pattern of 10 cadaveric femora, for which the mechanical testing results and calibrated FE models were already available. The very good agreement and consistency between different sets of results showed the reliability and accuracy of the new density calibration method, as well as the linear analysis scheme. Accordingly, the method was applied to five new clinical images, gathered from two clinics that used different scanners with different protocols. The strength and fracture pattern of each one of these specimens were analyzed under 15 different loading conditions. A consistent behavior was found for variation of the fracture load and pattern of all specimens with the loading orientations, while very clear contrasts were observed between the strength amplitudes of healthy and osteoporotic specimens. The proposed methods can be easily applied to ordinary daily (even archived) clinical CT scans to conduct fast and reliable fracture analysis of human femora for general bone research and opportunistic studies of osteoporosis and trauma.

The predictive ability of a QCT-FE model of the proximal femoral stiffness under multiple load cases is strongly influenced by experimental uncertainties

Despite significant improvements in terms of the predictive ability of Quantitative Computed Tomography based Finite Element (QCT-FE) models in estimating femoral strength (fracture load and stiffness), no substantial clinical adoption of this method has taken place to date. Narrowing the wide variability of FE results by standardizing the methodology and validation protocols, as well as reducing the uncertainties in the FEA process have been proposed as routes towards improved reliability. The aim of this study was to: First, validate a QCT-FE model of proximal femoral stiffness in multiple stance load cases, and second, using a parametric approach, determine the influence of select experimental and modeling parameters on the predictive ability of our model. Ten fresh frozen human femoral samples were tested in neutral stance, 15° adducted and 15° abducted load cases. Voxel-based linear-elastic QCT-FE models of the samples were generated to predict the models' stiffness values in all load cases. The base FE models were validated against the experimental results using linear regression. Thirty six deviated models were created using the minimum and maximum values of experiment-based "plausible range" for 18 parameters in 4 categories of embedding, loading, material, and segmentation. The predictive ability of the models were compared in terms of the coefficient of determination (R²) of the linear regression between the measured and predicted stiffness values in all load cases. Our model was capable of capturing 90% of the variation in the experimental stiffness of the samples in neutral stance position (R² = 0.9, concordance correlation coefficient (CCC) = 0.93, percent root mean squared error (RMSE%) = 8.4%, slope and intercept not significantly different from unity and zero, respectively). Embedding and loading categories strongly affected the predictive ability of the models with an average percent difference in R² of 4.36% ± 2.77 and 2.96% ± 1.69 for the stance-neutral load case, respectively. The performance of the models were significantly different in adducted and abducted load cases with their R² dropping to 71% and 70%, respectively. Similarly, off-axes load cases were affected by the parameters differently compared to the neutral load case, with the loading parameter category imposing more than 10% difference on their R², larger than all other categories. We also showed that automatically selecting the best performing plausible value for each parameter and each sample would result in a perfectly linear correlation (R²> 0.99) between the "tuned" model's predicted stiffness and experimental results. Based on our results, high sensitivity of the model performance to experimental parameters requires extra diligence in modeling the embedding geometry and the loading angles since these sources of uncertainty could dwarf the effects of material modeling and image processing parameters. The results of this study could help in improving the robustness of the QCT-FE models of proximal femur by limiting the uncertainties in the experimental and modeling steps.

2D-3D reconstruction of the proximal femur from DXA scans: Evaluation of the 3D-Shaper software

Introduction: Osteoporosis is currently diagnosed based on areal bone mineral density (aBMD) computed from 2D DXA scans. However, aBMD is a limited surrogate for femoral strength since it does not account for 3D bone geometry and density distribution. QCT scans combined with finite element (FE) analysis can deliver improved femoral strength predictions. However, non-negligible radiation dose and high costs prevent a systematic usage of this technique for screening purposes. As an alternative, the 3D-Shaper software (3D-Shaper Medical, Spain) reconstructs the 3D shape and density distribution of the femur from 2D DXA scans. This approach could deliver a more accurate estimation of femoral strength than aBMD by using FE analysis on the reconstructed 3D DXA. Methods: Here we present the first independent evaluation of the software, using a dataset of 77 ex vivo femora. We extend a prior evaluation by including the density distribution differences, the spatial correlation of density values and an FE analysis. Yet, cortical thickness is left out of this evaluation, since the cortex is not resolved in our FE models. Results: We found an average surface distance of 1.16 mm between 3D DXA and QCT images, which shows a good reconstruction of the bone geometry. Although BMD values obtained from 3D DXA and QCT correlated well (r ² = 0.92), the 3D DXA BMD were systematically lower. The average BMD difference amounted to 64 mg/cm³, more than one-third of the 3D DXA BMD. Furthermore, the low correlation (r ² = 0.48) between density values of both images indicates a limited reconstruction of the 3D density distribution. FE results were in good agreement between QCT and 3D DXA images, with a high coefficient of determination (r ² = 0.88). However, this correlation was not statistically different from a direct prediction by aBMD. Moreover, we found differences in the fracture patterns between the two image types. QCT-based FE analysis resulted mostly in femoral neck fractures and 3D DXA-based FE in subcapital or pertrochanteric fractures. Discussion: In conclusion, 3D-Shaper generates an altered BMD distribution compared to QCT but, after careful density calibration, shows an interesting potential for deriving a standardized femoral strength from a DXA scan.

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.

The biomechanical behavior of 3D printed human femoral bones based on generic and patient-specific geometries

Background

Bone is a highly complex composite material which makes it hard to find appropriate artificial surrogates for patient-specific biomechanical testing. Despite various options of commercially available bones with generic geometries, these are either biomechanically not very realistic or rather expensive.

Methods

In this work, additive manufacturing was used for the fabrication of artificial femoral bones. These were based on CT images of four different commercially available femoral bone surrogates and three human bones with varying bone density. The models were 3D printed using a low-budget fused deposition modeling (FDM) 3D printer and PLA filament. The infill density was mechanically calibrated and varying cortical thickness was used. Compression tests of proximal femora simulating stance were performed and the biomechanical behavior concerning ultimate force, spring stiffness, and fracture pattern were evaluated as well as compared to the results of commercial and cadaveric bones.

Results

Regarding the ultimate forces and spring stiffness, the 3D printed analogs showed mechanical behavior closer to their real counterparts than the commercially available polyurethan-based surrogates. Furthermore, the increase in ultimate force with increasing bone density observed in human femoral bones could be reproduced well. Also, the fracture patterns observed match well with fracture patterns observed in human hip injuries.

Conclusion

Consequently, the methods presented here show to be a promising alternative for artificial generic surrogates concerning femoral strength testing. The manufacturing is straightforward, cheap, and patient-specific geometries are possible.

A practical guide for in situ mechanical testing of musculoskeletal tissues using synchrotron tomography

Musculoskeletal tissues are complex hierarchical materials where mechanical response is linked to structural and material properties at different dimensional levels. Therefore, high-resolution three-dimensional tomography is very useful for assessing tissue properties at different scales. In particular, Synchrotron Radiation micro-Computed Tomography (SR-microCT) has been used in several applications to analyze the structure of bone and biomaterials. In the past decade the development of digital volume correlation (DVC) algorithms applied to SR-microCT images and its combination with in situ mechanical testing (four-dimensional imaging) have allowed researchers to visualise, for the first time, the deformation of musculoskeletal tissues and their interaction with biomaterials under different loading scenarios. However, there are several experimental challenges that make these measurements difficult and at high risk of failure. Challenges relate to sample preparation, imaging parameters, loading setup, accumulated tissue damage for multiple tomographic acquisitions, reconstruction methods and data processing. Considering that access to SR-microCT facilities is usually associated with bidding processes and long waiting times, the failure of these experiments could notably slow down the advancement of this research area and reduce its impact. Many of the experimental failures can be avoided with increased experience in performing the tests and better guidelines for preparation and execution of these complex experiments; publication of negative results could help interested researchers to avoid recurring mistakes. Therefore, the goal of this article is to highlight the potential and pitfalls in the design and execution of in situ SR-microCT experiments, involving multiple scans, of musculoskeletal tissues for the assessment of their structural and/or mechanical properties. The advice and guidelines that follow should improve the success rate of this type of experiment, allowing the community to reach higher impact more efficiently.

Analysis of loading to the hip joint in fall using whole-body FE model

Hip fractures caused by falls are important health problems for the elderly. Many studies used finite element (FE) models of the femur and its surroundings to evaluate the hip fracture risk during the impact phase in a fall. In this study, the whole-body human FE model (THUMS) of a small female was applied from the descent to the impact phase in a fall to understand the effect of the whole body. Brosh's material model was used for the soft tissue of the hip. A low-BMI and high-BMI model were developed based on THUMS (middle-BMI). For the middle-BMI model, the torso angle and the pelvis impact velocity were 45.2° and 2.62 m/s at the time of pelvis impact. The effective mass changed with time, and was 18.3 kg when the femoral neck force was maximum. The femoral neck force was 2.11 kN for the low-BMI model. The femoral neck forces when wearing a soft and a hard hip protector, and when falling on an energy-absorbing floor were compared for the FE models of human and a hip protector testing system. Though the force attenuation of the protective devices was 32.0-44.3 % in the testing system, the force attenuation in the middle-BMI was 0.1-22.2 %. In the low-BMI model, the attenuation of the soft protector was limited (4.2 %) because the hip protector protruded from the outer surface, so the contact force was concentrated at the hip region. This research suggests the importance of including the whole body to evaluate the hip fracture risk.

Two Cannulated Screws Provide Sufficient Biomechanical Strength for Prophylactic Fixation in Adult Patients With an Aggressive Benign Femoral Neck Lesion

Background: Two cannulated screws were proposed for prophylactic fixation in adult patients with an aggressive benign femoral neck lesion in recent literature. However, the biomechanical properties of this intervention have not yet been investigated.

Methods: After the evaluation of the heterogeneity of bone mineral density and geometry via quantitative computed tomography, 24 embalmed adult human cadaver femurs were randomized into the control, inferior half of the anterior cortical (25%) bone defect, entire anterior cortical (50%) bone defect, and the 50% bone defect and two cannulated screw group. Biomechanical analysis was conducted to compare the stiffness and failure load among the four groups when mimicking a one-legged stance. A CT-based finite element analysis (FEA) was performed to mimic the cortical and cancellous bone defect and the implantation of two cannulated screws of the four groups. Measurements of the maximal displacement and von Mises stress were conducted with the longitudinal load force and boundary conditions being established for a one-leg-standing status.

Results: We noted a significant improvement in the failure load after the insertion of two 6.5 mm cannulated screws in femurs with 50% bone defect (+95%, p = 0.048), and no significant difference was found between the screw group and the intact femur. Similar trends were also found in the measurements of stiffness (+23%, p &gt; 0.05) via biomechanical testing and the von Mises stresses (−71%, p = 0.043) by FEA when comparing the screw group and the 50% bone defect group.

Conclusion: Our findings suggest that two cannulated screws provided sufficient biomechanical strength for prophylactic fixation in adult patients with an aggressive benign femoral neck lesion even when the entire anterior cortical bone is involved.

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

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

Modeling attachment and compressive loading of locking and non-locking plate fixation: a finite element investigation of a supracondylar femur fracture model

This study developed a finite element (FE) model of simulated locking plate fixation to examine the strain response following supracondylar femoral plate attachment and under compressive loading. An implicit FE model of a synthetic femur with a distal fracture gap stabilized with a lateral plate was evaluated following attachment and 500 N loading, considering locking and non-locking proximal screws configurations. Screw pre-tension values of 60 N for both distal and proximal non-locking screws yielded good agreement with plate experimental strain data in attached (unloaded) and loaded conditions. The results highlight the importance of pre-tensioning in modeling plate attachment using non-locking screws.

Finite element derived femoral strength is a better predictor of hip fracture risk than aBMD in the AGES Reykjavik study cohort

Hip fractures associated with a high economic burden, loss of independence, and a high rate of post-fracture mortality, are a major health concern for modern societies. Areal bone mineral density is the current clinical metric of choice when assessing an individual's future risk of fracture. However, this metric has been shown to lack sensitivity and specificity in the targeted selection of individuals for preventive interventions. Although femoral strength derived from computed tomography based finite element models has been proposed as an alternative based on its superior femoral strength prediction ex vivo, such predictions have only shown marginal or no improvement for assessing hip fracture risk. This study compares finite element derived femoral strength to aBMD as a metric for hip fracture risk assessment in subjects (N = 601) from the AGES Reykjavik Study cohort and analyses the dependence of femoral strength predictions and classification accuracy on the material model and femoral loading alignment. We found hip fracture classification based on finite element derived femoral strength to be significantly improved compared to aBMD. Finite element models with non-linear material models performed better at classifying hip fractures compared to finite element models with linear material models and loading alignments with low internal rotation and adduction, which do not correspond to weak femur alignments, were found to be most suitable for hip fracture classification.

On challenges in clinical assessment of hip fracture risk using image-based biomechanical modelling: a critical review

INTRODUCTION

Hip fracture is a common health risk among elderly people, due to the prevalence of osteoporosis and accidental fall in the population. Accurate assessment of fracture risk is a crucial step for clinicians to consider patient-by-patient optimal treatments for effective prevention of fractures. Image-based biomechanical modeling has shown promising progress in assessment of fracture risk, and there is still a great possibility for improvement. The purpose of this paper is to identify key issues that need be addressed to improve image-based biomechanical modeling.

MATERIALS AND METHODS

We critically examined issues in consideration and determination of the four biomechanical variables, i.e., risk of fall, fall-induced impact force, bone geometry and bone material quality, which are essential for prediction of hip fracture risk. We closely inspected: limitations introduced by assumptions that are adopted in existing models; deficiencies in methods for construction of biomechanical models, especially for determination of bone material properties from bone images; problems caused by separate use of the variables in clinical study of hip fracture risk; availability of clinical information that are required for validation of biomechanical models.

RESULTS AND CONCLUSIONS

A number of critical issues and gaps were identified. Strategies for effectively addressing the issues were discussed.

Non-invasive prediction of the mouse tibia mechanical properties from microCT images: comparison between different finite element models

New treatments for bone diseases require testing in animal models before clinical translation, and the mouse tibia is among the most common models. In vivo micro-Computed Tomography (microCT)-based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experimental data. Different modelling techniques can be used to estimate the bone properties, and the accuracy associated with each is unclear. The aim of this study was to evaluate the ability of different microCT-based microFE models to predict the mechanical properties of the mouse tibia under compressive load. Twenty tibiae were microCT scanned at 10.4 µm voxel size and subsequently compressed at 0.03 mm/s until failure. Stiffness and failure load were measured from the load-displacement curves. Different microFE models were generated from each microCT image, with hexahedral or tetrahedral mesh, and homogeneous or heterogeneous material properties. Prediction accuracy was comparable among models. The best correlations between experimental and predicted mechanical properties, as well as lower errors, were obtained for hexahedral models with homogeneous material properties. Experimental stiffness and predicted stiffness were reasonably well correlated (R2 = 0.53-0.65, average error of 13-17%). A lower correlation was found for failure load (R2 = 0.21-0.48, average error of 9-15%). Experimental and predicted mechanical properties normalized by the total bone mass were strongly correlated (R2 = 0.75-0.80 for stiffness, R2 = 0.55-0.81 for failure load). In conclusion, hexahedral models with homogeneous material properties based on in vivo microCT images were shown to best predict the mechanical properties of the mouse tibia.

Femoral strength can be predicted from 2D projections using a 3D statistical deformation and texture model with finite element analysis

Ultimate force of the proximal human femur can be predicted using Finite Element Analysis (FEA), but the models rely on 3D computed tomography images. Landmark-based statistical appearance models (SAM) and B-Spline transformation-based statistical deformation models (SDM) have been used to estimate 3D images from 2D projections, which facilitates model generation and reduces the radiation dose. However, there is no literature on the accuracy of SDM-based FEA models of bones with respect to experimental results. In this study, a methodology for an enhanced SDM with textural information is presented. The statistical deformation and texture models (SDTMs) are based on a set of 37 quantitative CT (QCT) images. They were used to estimate 3D images from two or one projections of the set in a leave-one-out setup. These estimations where then used to create FEA models. The ultimate force predicted by FEA models estimated from two or one projection using the SDTMs were compared to the experimental ultimate force from a previous study on the same femora and to the results of standard QCT-based FEA models. High correlations between predictions and experimental measurements were found for FEA models reconstructed from 2D projections with R²=0.835 when based on two projections and R²=0.724 when using one projection. The correlations were comparable to those reached with standard QCT-based FE-models with the experimental results (R²=0.795). This study shows the high potential of SDTM-based 3D image reconstruction and FEA modelling from 2D projections to predict femoral ultimate force.

Risk assessment of vertebral compressive fracture using bone mass index and strength predicted by computed tomography image based finite element analysis

BACKGROUND

A main purpose of osteoporosis diagnosis is to evaluate the bone fracture risk. Some bone mass indices evaluated using bone mineral density has been utilized clinically to assess the degree of osteoporosis. On the other hand, Computed tomography image based finite element analysis has been developed to evaluate bone strength of vertebral bodies. The strength of a vertebra is defined as the load at the onset of compressive fracture. The objective of this study was therefore to propose a new feasible method to combine the advantages of the two osteoporotic indices such as the bone mass index and the bone strength.

METHODS

Three-dimensional finite element models of 246 vertebral bodies from 88 patients were constructed using the computed tomography images. Finite element analysis was then conducted to evaluate their strength values. The Pearson's correlation analysis was also conducted between the vertebral strength and bone mass indices.

FINDINGS

It was found that relatively weak positive correlations existed between the strength and the bone mass indices. A new assessment method was then proposed by combining the strength and the bone mass index. "high risk zone" corresponding to low strength with normal bone mass was found from the assessment method.

INTERPRETATION

Singe bone mass index cannot predict the fracture risk with high standard. The results of fracture risk assessment conducted by the new method clearly indicated the necessity and effectiveness to take both the strength and the bone mass index into account.

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.

Damage tolerance and toughness of elderly human femora

Observations of elastic instability of trabecular bone cores supported the analysis of cortical thickness for predicting bone fragility of the hip in people over 60 years of age. Here, we falsified the hypothesis that elastic instability causes minimal energy fracture by analyzing, with a micrometric resolution, the deformation and fracture behavior of entire femora. Femur specimens were obtained from elderly women aged between 66 - 80 years. Microstructural images of the proximal femur were obtained under 3 - 5 progressively increased loading steps and after fracture. Bone displacements, strain, load bearing and energy absorption capacity were analyzed. Elastic instability of the cortex appeared at early loading stages in regions of peak compression. No elastic instability of trabecular bone was observed. The subchondral bone displayed local crushing in compression at early loading steps and progressed to 8 - 16% compression before fracture. The energy absorption capacity was proportional to the displacement. Stiffness decreased to near-zero values before fracture. Three-fourth of the fracture energy (10.2 - 20.2 J) was dissipated in the final 25% force increment. Fracture occurred in regions of peak tension and shear, adjacent to the location of peak compression, appearing immediately before fracture. Minimal permanent deformation was visible along the fracture surface. Elastic instability modulates the interaction between cortical and trabecular bone promoting an elastically stable fracture behavior of the femur organ, load bearing capacity, toughness, and damage tolerance. These findings will advance current methods for predicting hip fragility.

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.

Risk assessment of resurfacing implant loosening and femur fracture under low-energy impacts taking into account degenerative changes in bone tissues. Computer simulation

BACKGROUND AND OBJECTIVE

Degenerative diseases of the musculoskeletal system significantly reduce the quality of human life. Hip resurfacing is used to treat degenerative diseases in the later stages. After surgery, there is a risk of endoprosthesis loosening and low-energy fracture during daily physical activity. Computer modeling is a promising way to predict the optimal low-energy loads that do not lead to bone destruction. This paper aims to study numerically the mechanical behavior of the proximal femur, amenable to degenerative changes and subjected to hip resurfacing under low-energy impact equivalent to physiological loads.

METHODS

A numerical model of the mechanical behavior of the femur after hip resurfacing arthroplasty under low-energy impacts equivalent to physiological loads is presented. The model is based on the movable cellular automaton method (discrete elements), where the mechanical behavior of bone tissue is described using the Biot poroelasticity accounting for the presence and transfer of interstitial biological fluid.

RESULTS

For the first time, it is shown that a poroelastic model allows predicting the service life of endoprostheses, taking into account the individual characteristics of the bone tissues amenable to various degenerative diseases. The obtained results indicate that the changes in the bone properties have a significant influence on the critical forces corresponding to the first appearance of microcracks and the fracture formation. At the same time, their effect on the type of fracture is negligible. A much more impact on the type of fracture has the kinematic and dynamic conditions of the exposure.

CONCLUSIONS

The obtained results show the promise of using the proposed model for predicting the operational resource of resurfacing endoprostheses, taking into account the physiological features of the structure of the patient's bone tissues.

Assessment of femoral neck strength and bone mineral density changes following exercise using 3D-DXA images

Physical exercise induces spatially heterogeneous bone changes in the proximal femur. Recent advances have enabled 3D dual-energy X-ray Absorptiometry (DXA)-based finite element (FE) models to estimate bone strength. However, its ability to detect exercise-induced BMD and strength changes is unclear. The aim of this study was to quantify the repeatability of vBMD and femoral neck strength obtained from 3D-DXA images and determine the changes due an exercise intervention. The DXA scans included pairs of same-day repeated scans from ten healthy females and pre- and post-exercise intervention scans of 26 males. FE models with element-by-element correspondence were generated by morphing a template mesh to each bone. BMD and femoral strength under single-leg-stance and sideways fall loading configurations were obtained for both groups and compared. In the repeated images, the total hip vBMD difference was 0.5 ± 2.5%. Element-by-element BMD differences reached 30 ± 50%. The strength difference in single-leg stance was 2.8 ± 13% and in sideways fall was 4.5% ± 19%. In the exercise group, strength changes were 6 ± 19% under single-leg stance and 1 ± 18% under sideways fall. vBMD parameters were weakly correlated to strength (R² < 0.31). The exercise group had a mean bone accrual exceeding repeatability values in the femoral head and cortical regions. The case with the highest vBMD change (6.4%) caused 18% and -7% strength changes under single-leg stance and sideways fall. 3D-DXA technology can assess the effect of exercise interventions in large cohorts but its validity in individual cases should be interpreted with caution.

Paggiosi M, McCloskey EV, Viceconti M, Mazzà C, Li X. Femoral neck strain prediction during level walking using a combined musculoskeletal and finite element model approach

Recently, coupled musculoskeletal-finite element modelling approaches have emerged as a way to investigate femoral neck loading during various daily activities. Combining personalised gait data with finite element models will not only allow us to study changes in motion/movement, but also their effects on critical internal structures, such as the femur. However, previous studies have been hampered by the small sample size and the lack of fully personalised data in order to construct the coupled model. Therefore, the aim of this study was to build a pipeline for a fully personalised multiscale (body-organ level) model to investigate the strain levels at the femoral neck during a normal gait cycle. Five postmenopausal women were included in this study. The CT and MRI scans of the lower limb, and gait data were collected for all participants. Muscle forces derived from the body level musculoskeletal models were used as boundary constraints on the finite element femur models. Principal strains were estimated at the femoral neck region during a full gait cycle. Considerable variation was found in the predicted peak strain among individuals with mean peak first principal strain of 0.24% ± 0.11% and mean third principal strain of -0.29% ± 0.24%. For four individuals, two overall peaks of the maximum strains were found to occur when both feet were in contact with the floor, while one individual had one peak at the toe-off phase. Both the joint contact forces and the muscular forces were found to substantially influence the loading at the femoral neck. A higher correlation was found between the predicted peak strains and the gluteus medius (R² ranged between 0.95 and 0.99) than the hip joint contact forces (R² ranged between 0.63 and 0.96). Therefore, the current findings suggest that personal variations are substantial, and hence it is important to consider multiple subjects before deriving general conclusions for a target population.

Numerical analysis of hip fracture due to a sideways fall

The primary purpose of this paper is to outline a methodology for evaluating the likelihood of cortical bone fracture in the proximal femur in the event of a sideways fall. The approach includes conducting finite element (FE) analysis in which the cortical bone is treated as an anisotropic material, and the admissibility of the stress field is validated both in tension and compression regime. In assessing the onset of fracture, two methodologies are used, namely the Critical Plane approach and the Microstructure Tensor approach. The former is employed in the tension regime, while the latter governs the conditions at failure in compression. The propagation of localized damage is modeled using a constitutive law with embedded discontinuity (CLED). In this approach, the localized deformation is described by a homogenization procedure in which the average properties of cortical tissue intercepted by a macrocrack are established. The key material properties governing the conditions at failure are specified from a series of independent material tests conducted on cortical bone samples tested at different orientations relative to the loading direction. The numerical analysis deals with simulations of experiments involving the sideways fall, and the results are compared with the experimental data. This includes both the evolution of fracture pattern and the local load-displacement characteristics. The proposed approach is numerically efficient, and the results do not display a pathological mesh-dependency. Also, in contrast to the XFEM approach, the analysis does not require any extra degrees of freedom.

Body Anthropometry and Bone Strength Conjointly Determine the Risk of Hip Fracture in a Sideways Fall

We hypothesize that variations of body anthropometry, conjointly with the bone strength, determine the risk of hip fracture. To test the hypothesis, we compared, in a simulated sideways fall, the hip impact energy to the energy needed to fracture the femur. Ten femurs from elderly donors were tested using a novel drop-tower protocol for replicating the hip fracture dynamics during a fall on the side. The impact energy was varied for each femur according to the donor’s body weight, height and soft-tissue thickness, by adjusting the drop height and mass. The fracture pattern, force, energy, strain in the superior femoral neck, bone morphology and microarchitecture were evaluated. Fracture patterns were consistent with clinically relevant hip fractures, and the superior neck strains and timings were comparable with the literature. The hip impact energy (11 – 95 J) and the fracture energy (11 – 39 J) ranges overlapped and showed comparable variance (CV = 69 and 61%, respectively). The aBMD-based definition of osteoporosis correctly classified 7 (70%) fracture/non-fracture cases. The incorrectly classified cases presented large impact energy variations, morphology variations and large subcortical voids as seen in microcomputed tomography. In conclusion, the risk of osteoporotic hip fracture in a sideways fall depends on both body anthropometry and bone strength.

Optimization of the failure criterion in micro-Finite Element models of the mouse tibia for the non-invasive prediction of its failure load in preclinical applications

New treatments against osteoporosis require testing in animal models and the mouse tibia is among the most common studied anatomical sites. In vivo micro-Computed Tomography (microCT) based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experiments. The aim of this study was to evaluate the ability of different microCT-based bone parameters and microFE models to predict tibial structural mechanical properties in compression. Twenty tibiae were scanned at 10.4 μm voxel size and subsequently tested in uniaxial compression at 0.03 mm/s until failure. Stiffness and failure load were measured from the load-displacement curves. Standard morphometric parameters were measured from the microCT images. The spatial distribution of bone mineral content (BMC) was evaluated by dividing the tibia into 40 regions. MicroFE models were generated by converting each microCT image into a voxel-based mesh with homogeneous isotropic material properties. Failure load was estimated by using different failure criteria, and the optimized parameters were selected by minimising the errors with respect to experimental measurements. Experimental and predicted stiffness were moderately correlated (R² = 0.65, error = 14% ± 8%). Normalized failure load was best predicted by microFE models (R² = 0.81, error = 9% ± 6%). Failure load was not correlated to the morphometric parameters and weakly correlated with some geometrical parameters (R² < 0.37). In conclusion, microFE models can improve the current estimation of the mouse tibia structural properties and in this study an optimal failure criterion has been defined. Since it is a non-invasive method, this approach can be applied longitudinally for evaluating temporal changes in the bone strength.

Subject-specific FE models of the human femur predict fracture path and bone strength under single-leg-stance loading

Hip fractures are a major health problem with high socio-economic costs. Subject-specific finite element (FE) models have been suggested to improve the fracture risk assessment, as compared to clinical tools based on areal bone mineral density, by adding an estimate of bone strength. Typically, such FE models are limited to estimate bone strength and possibly the fracture onset, but do not model the fracture process itself. The aim of this study was to use a discrete damage approach to simulate the full fracture process in subject-specific femur models under stance loading conditions. A framework based on the partition of unity finite element method (PUFEM), also known as XFEM, was used. An existing PUFEM framework previously used on a homogeneous generic femur model was extended to include a heterogeneous material description together with a strain-based criterion for crack initiation. The model was tested on two femurs, previously mechanically tested in vitro. Our results illustrate the importance of implementing a subject-specific material distribution to capture the experimental fracture pattern under stance loading. Our models accurately predicted the fracture pattern and bone strength (1% and 5% error) in both investigated femurs. This is the first study to simulate complete fracture paths in subject-specific FE femur models and it demonstrated how discrete damage models can provide a more complete picture of fracture risk by considering both bone strength and fracture toughness in a subject-specific fashion.

Cortical thinning and accumulation of large cortical pores in the tibia reflect local structural deterioration of the femoral neck

INTRODUCTION

Cortical bone thinning and a rarefaction of the trabecular architecture represent possible causes of increased femoral neck (FN) fracture risk. Due to X-ray exposure limits, the bone microstructure is rarely measurable in the FN of subjects but can be assessed at the tibia. Here, we studied whether changes of the tibial cortical microstructure, which were previously reported to be associated with femur strength, are also associated with structural deteriorations of the femoral neck.

METHODS

The cortical and trabecular architectures in the FN of 19 humans were analyzed ex vivo on 3D microcomputed tomography images with 30.3 μm voxel size. Cortical thickness (Ct.Th_tibia), porosity (Ct.Po_tibia) and pore size distribution in the tibiae of the same subjects were measured using scanning acoustic microscopy (12 μm pixel size). Femur strength during sideways falls was simulated with homogenized voxel finite element models.

RESULTS

Femur strength was associated with the total (vBMD_tot; R² = 0.23, p < 0.01) and trabecular (vBMD_trab; R² = 0.26, p < 0.01) volumetric bone mineral density (vBMD), with the cortical thickness (Ct.Th_FN; R² = 0.29, p < 0.001) and with the trabecular bone volume fraction (Tb.BV/TV_FN; R² = 0.34, p < 0.001), separation (Tb.Sp_FN; R² = 0.25, p < 0.01) and number (Tb.N_FN; R² = 0.32, p < 0.001) of the femoral neck. Moreover, smaller Ct.Th_tibia was associated with smaller Ct.Th_FN (R² = 0.31, p < 0.05), lower Tb.BV/TV_FN (R² = 0.29, p < 0.05), higher Tb.Sp_FN (R² = 0.33, p < 0.05) and lower Tb.N_FN (R² = 0.42, p < 0.01). A higher prevalence of pores with diameter > 100 μm in tibial cortical bone (relCt.Po_100μm-tibia) indicated higher Tb.Sp_FN (R² = 0.36, p < 0.01) and lower Tb.N_FN (R² = 0.45, p < 0.01).

CONCLUSION

Bone resorption and structural decline of the femoral neck may be identified in vivo by measuring cortical bone thickness and large pores in the tibia.

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.

Empirical relationships between bone density and ultimate strength: A literature review

INTRODUCTION

Ultimate strength-density relationships for bone have been reported with widely varying results. Reliable bone strength predictions are crucial for many applications that aim to assess bone failure. Bone density and bone morphology have been proposed to explain most of the variance in measured bone strength. If this holds true, it could lead to the derivation of a single ultimate strength-density-morphology relationship for all anatomical sites.

METHODS

All relevant literature was reviewed. Ultimate strength-density relationships derived from mechanical testing of human bone tissue were included. The reported relationships were translated to ultimate strength-apparent density relationships and normalized with respect to strain rate. Results were grouped based on bone tissue type (cancellous or cortical), anatomical site, and loading mode (tension vs. compression). When possible, the relationships were compared to existing ultimate strength-density-morphology relationships.

RESULTS

Relationships that considered bone density and morphology covered the full spectrum of eight-fold inter-study difference in reported compressive ultimate strength-density relationships for trabecular bone. This was true for studies that tested specimens in different loading direction and tissue from different anatomical sites. Sparse data was found for ultimate strength-density relationships in tension and for cortical bone properties transverse to the main loading axis of the bone.

CONCLUSIONS

Ultimate strength-density-morphology relationships could explain measured strength across anatomical sites and loading directions. We recommend testing of bone specimens in other directions than along the main trabecular alignment and to include bone morphology in studies that investigate bone material properties. The lack of tensile strength data did not allow for drawing conclusions on ultimate strength-density-morphology relationships. Further studies are needed. Ideally, these studies would investigate both tensile and compressive strength-density relationships, including morphology, to close this gap and lead to more accurate evaluation of bone failure.

Modelling Human Locomotion to Inform Exercise Prescription for Osteoporosis

PURPOSE OF REVIEW

We review the literature on hip fracture mechanics and models of hip strain during exercise to postulate the exercise regimen for best promoting hip strength.

RECENT FINDINGS

The superior neck is a common location for hip fracture and a relevant exercise target for osteoporosis. Current modelling studies showed that fast walking and stair ambulation, but not necessarily running, optimally load the femoral neck and therefore theoretically would mitigate the natural age-related bone decline, being easily integrated into routine daily activity. High intensity jumps and hopping have been shown to promote anabolic response by inducing high strain in the superior anterior neck. Multidirectional exercises may cause beneficial non-habitual strain patterns across the entire femoral neck. Resistance knee flexion and hip extension exercises can induce high strain in the superior neck when performed using maximal resistance loadings in the average population. Exercise can stimulate an anabolic response of the femoral neck either by causing higher than normal bone strain over the entire hip region or by causing bending of the neck and localized strain in the superior cortex. Digital technologies have enabled studying interdependences between anatomy, bone distribution, exercise, strain and metabolism and may soon enable personalized prescription of exercise for optimal hip strength.

Biomechanical Computed Tomography analysis (BCT) for clinical assessment of osteoporosis

The surgeon general of the USA defines osteoporosis as "a skeletal disorder characterized by compromised bone strength, predisposing to an increased risk of fracture." Measuring bone strength, Biomechanical Computed Tomography analysis (BCT), namely, finite element analysis of a patient's clinical-resolution computed tomography (CT) scan, is now available in the USA as a Medicare screening benefit for osteoporosis diagnostic testing. Helping to address under-diagnosis of osteoporosis, BCT can be applied "opportunistically" to most existing CT scans that include the spine or hip regions and were previously obtained for an unrelated medical indication. For the BCT test, no modifications are required to standard clinical CT imaging protocols. The analysis provides measurements of bone strength as well as a dual-energy X-ray absorptiometry (DXA)-equivalent bone mineral density (BMD) T-score at the hip and a volumetric BMD of trabecular bone at the spine. Based on both the bone strength and BMD measurements, a physician can identify osteoporosis and assess fracture risk (high, increased, not increased), without needing confirmation by DXA. To help introduce BCT to clinicians and health care professionals, we describe in this review the currently available clinical implementation of the test (VirtuOst), its application for managing patients, and the underlying supporting evidence; we also discuss its main limitations and how its results can be interpreted clinically. Together, this body of evidence supports BCT as an accurate and convenient diagnostic test for osteoporosis in both sexes, particularly when used opportunistically for patients already with CT. Biomechanical Computed Tomography analysis (BCT) uses a patient's CT scan to measure both bone strength and bone mineral density at the hip or spine. Performing at least as well as DXA for both diagnosing osteoporosis and assessing fracture risk, BCT is particularly well-suited to "opportunistic" use for the patient without a recent DXA who is undergoing or has previously undergone CT testing (including hip or spine regions) for an unrelated medical condition.

Comparison study of bone strength of the proximal femur with and without hip osteoarthritis by computed tomography-based finite element analysis

Proximal femoral fractures are common in elderly osteoporosis patients; however, its prevalence is clinically rare in hip fracture patients with hip osteoarthritis (OA). This study aimed to evaluate bone strength of the proximal femur with or without hip OA and proximal femoral fracture risk using computed tomography (CT)-based finite element analysis (FEA). A retrospective analysis was done on CT data of 20 patients who underwent total hip arthroplasty for unilateral hip OA. Furthermore, the fracture load between OA and contralateral sides was compared and the association between fracture load and risk factor was analyzed. The fracture load was significantly higher in the OA side than that in the contralateral side (3819.5 ± 1557.8 N vs. 3224.5 ± 943.7 N, respectively; P = 0.0405). There was no significant difference in fracture load between OA and the contralateral side in Kellgren-Lawrence (KL)-3 and KL-4 grade, but the KL-4 fracture load tends to be high (P = 0.2461 and P = 0.0527, respectively). Moreover, there was no significant association between fracture load and OA severity or age. The study findings may assist in predicting bone strength and proximal femur fracture risk. The results of this FEA study indicate the bone strength of the proximal femur was affected by the severity of the osteoarthritis.

Femur strength predictions by nonlinear homogenized voxel finite element models reflect the microarchitecture of the femoral neck

In the human femoral neck, the contribution of the cortical and trabecular architecture to mechanical strength is known to depend on the load direction. In this work, we investigate if QCT-derived homogenized voxel finite element (hvFE) simulations of varying hip loading conditions can be used to study the architecture of the femoral neck. The strength of 19 pairs of human femora was measured ex vivo using nonlinear hvFE models derived from high-resolution peripheral QCT scans (voxel size: 30.3 µm). Standing and side-backwards falling loads were modeled. Quasi-static mechanical tests were performed on 20 bones for comparison. Associations of femur strength with volumetric bone mineral density (vBMD) or microstructural parameters of the femoral neck obtained from high-resolution QCT were compared between mechanical tests and simulations and between standing and falling loads. Proximal femur strength predictions by hvFE models were positively associated with the vBMD of the femoral neck (R² > 0.61, p < 0.001), as well as with its cortical thickness (R² > 0.27, p < 0.001), trabecular bone volume fraction (R² = 0.42, p < 0.001) and with the first two principal components of the femoral neck architecture (R² > 0.38, p < 0.001). Associations between femur strength and femoral neck microarchitecture were stronger for one-legged standing than for side-backwards falling. For both loading directions, associations between structural parameters and femur strength from hvFE models were in good agreement with those from mechanical tests. This suggests that hvFE models can reflect the load-direction-specific contribution of the femoral neck microarchitecture to femur strength.

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.

Enhancing hip fracture risk prediction by statistical modeling and texture analysis on DXA images

Each year in the US more than 300,000 older adults suffer from hip fractures. While protective measures exist, identification of those at greatest risk by DXA scanning has proved inadequate. This study proposed a new technique to enhance hip fracture risk prediction by accounting for many contributing factors to the strength of the proximal femur. Twenty-two isolated cadaveric femurs were DXA scanned, 16 of which had been mechanically tested to failure. A function consisting of the calculated modes from the statistical shape and appearance modeling (to consider the shape and BMD distribution), homogeneity index (representing trabecular quality), BMD, age and sex of the donor was created in a training set and used to predict the fracture load in a test group. To classify patients as "high risk" or "low risk", fracture load thresholds were investigated. Hip fracture load estimation was significantly enhanced using the new technique in comparison to using t-score or BMD alone (average R² of 0.68, 0.32, and 0.50, respectively) (P < 0.05). Using a fracture cut-off of 3400 N correctly predicted risk in 94% of specimens, a substantial improvement over t-score classification (38%). Ultimately, by identifying patients at high risk more accurately, devastating hip fractures can be prevented through applying protective measures.

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis-A Survey

This paper provides a starting point for researchers and practitioners from biology, medicine, physics and engineering who can benefit from an up-to-date literature survey on patient-specific bone fracture modelling, simulation and risk analysis. This survey hints at a framework for devising realistic patient-specific bone fracture simulations. This paper has 18 sections: Section 1 presents the main interested parties; Section 2 explains the organzation of the text; Section 3 motivates further work on patient-specific bone fracture simulation; Section 4 motivates this survey; Section 5 concerns the collection of bibliographical references; Section 6 motivates the physico-mathematical approach to bone fracture; Section 7 presents the modelling of bone as a continuum; Section 8 categorizes the surveyed literature into a continuum mechanics framework; Section 9 concerns the computational modelling of bone geometry; Section 10 concerns the estimation of bone mechanical properties; Section 11 concerns the selection of boundary conditions representative of bone trauma; Section 12 concerns bone fracture simulation; Section 13 presents the multiscale structure of bone; Section 14 concerns the multiscale mathematical modelling of bone; Section 15 concerns the experimental validation of bone fracture simulations; Section 16 concerns bone fracture risk assessment. Lastly, glossaries for symbols, acronyms, and physico-mathematical terms are provided.

Predicting bone strength from CT data: Clinical applications

In this review we summarise over 15 years of research and development around the prediction of whole bones strength from Computed Tomography data, with particular reference to the prediction of the risk of hip fracture in osteoporotic patients. We briefly discuss the theoretical background, and then provide a summary of the laboratory and clinical validation of these modelling technologies. We then discuss the three current clinical applications: in clinical research, in clinical trials, and in clinical practice. On average the strength predicted with finite element models (QCT-FE) based on computed tomography is 7% more accurate that that predicted with areal bone mineral density from Dual X-ray Absorptiometry (DXA-aBMD), the current standard of care, both in term of laboratory validation on cadaver bones and in terms of stratification accuracy on clinical cohorts of fractured and non-fractured women. This improved accuracy makes QCT-FE superior to DXA-aBMD in clinical research and in clinical trials, where the its use can cut in half the number of patients to be enrolled to get the same statistical power. For routine clinical use to decide who to treat with antiresorptive drugs, QCT-FE is more accurate but less cost-effective than DXA-aBMD, at least when the decision is on first line treatment like bisphosphonates. But the ability to predict skeletal strength from medical imaging is now opening a number of other applications, for example in paediatrics and oncology.

The effect of boundary and loading conditions on patient classification using finite element predicted risk of fracture

BACKGROUND

Osteoporotic proximal femoral fractures associated to falls are a major health burden in the ageing society. Recently, bone strength estimated by finite element models emerged as a feasible alternative to areal bone mineral density as a predictor of fracture risk. However, previous studies showed that the accuracy of patients' classification under their risk of fracture using finite element strength when simulating posterolateral falls is only marginally better than that of areal bone mineral density. Patients tend to fall in various directions: since the predicted strength is sensitive to the fall direction, a prediction based on certain fall directions might not be fully representative of the physical event. Hence, side fall boundary conditions may not be completely representing the physical event.

METHODS

The effect of different side fall boundary and loading conditions on a retrospective cohort of 98 postmenopausal women was evaluated to test models' ability to discriminate fracture and control cases. Three different boundary conditions (Linear, Multi-point constraints and Contact model) were investigated under various anterolateral and posterolateral falls.

FINDINGS

The stratification power estimated by the area under the receiver operating characteristic curve was highest for Contact model (0.82), followed by Multi-point constraints and Linear models with 0.80. Both Contact and MPC models predicted high strains in various locations of the proximal femur including the greater trochanter, which has rarely reported previously.

INTERPRETATION

A full range of fall directions and less restrictive displacement constraints can improve the finite element strength ability to classify patients under their risk of fracture.

Subject-specific ex vivo simulations for hip fracture risk assessment in sideways falls

The risk of hip fracture of a patient due to a fall can be described from a mechanical perspective as the capacity of the femur to withstand the force that it experiences in the event of a fall. So far, impact forces acting on the lateral aspect of the pelvic region and femur strength have been investigated separately. This study used inertia-driven cadaveric impact experiments that mimic falls to the side from standing in order to evaluate the subject-specific force applied to the hip during impact and the fracture outcome in the same experimental model. Eleven fresh-frozen pelvis-femur constructs (6 female, 5 male, age = 77 years (SD = 13 years), BMI = 22.8 kg/m² (SD = 7.8 kg/m²), total hip aBMD = 0.734 g/cm² (SD = 0.149 g/cm²)), were embedded into soft tissue surrogate material that matched subject-specific mass and body shape. The specimens were attached to metallic lower-limb constructions with subject-specific masses and subjected to an inverted pendulum motion. Impact forces were recorded with a 6-axis force plate at 10,000 Hz and three dimensional deflections in the pelvic region were tracked with two high-speed cameras at 5000 Hz. Of the 11 specimens, 5 femur fractures and 3 pelvis fractures were observed. Three specimens did not fracture. aBMD alone did not reliably separate femur fractures from non-fractures. However, a mechanical risk ratio, which was calculated as the impact force divided by aBMD, classified specimens reliably into femur fractures and non-fractures. Single degree of freedom models, based on specimen kinetics, were able to predict subject-specific peak impact forces (RMSE = 2.55% for non-fractures). This study provides direct evidence relating subject-specific impact forces and subject-specific strength estimates and improves the assessment of the mechanical risk of hip fracture for a specific femur/pelvis combination in a sideways fall.

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.