Material mapping strategy to improve the predicted response of the proximal femur to a sideways fall impact

A convolutional neural network-based method for the generation of super-resolution 3D models from clinical CT images

BACKGROUND AND OBJECTIVE

The accurate evaluation of bone mechanical properties is essential for predicting fracture risk based on clinical computed tomography (CT) images. However, blurring and noise in clinical CT images can compromise the accuracy of these predictions, leading to incorrect diagnoses. Although previous studies have explored enhancing trabecular bone CT images to super-resolution (SR), none of these studies have examined the possibility of using clinical CT images from different instruments, typically of lower resolution, as a basis for analysis. Additionally, previous studies rely on 2D SR images, which may not be sufficient for accurate mechanical property evaluation, due to the complex nature of the 3D trabecular bone structures. The objective of this study was to address these limitations.

METHODS

A workflow was developed that utilizes convolutional neural networks to generate SR 3D models across different clinical CT instruments. The morphological and finite-element-derived mechanical properties of these SR models were compared with ground truth models obtained from micro-CT scans.

RESULTS

A significant improvement in analysis accuracy was demonstrated, where the new SR models increased the accuracy by up to 700 % compared with the low-resolution data, i.e. clinical CT images. Additionally, we found that the mixture of different CT image datasets may improve the SR model performance.

CONCLUSIONS

SR images, generated by convolutional neural networks, outperformed clinical CT images in the determination of morphological and mechanical properties. The developed workflow could be implemented for fracture risk prediction, potentially leading to improved diagnoses and subsequent clinical decision making.

The efficacy of femoral augmentation for hip fracture prevention using ceramic-based cements: A preliminary experimentally-driven finite element investigation

Femoral fractures due to sideways falls continue to be a major cause of concern for the elderly. Existing approaches for the prevention of these injuries have limited efficacy. Prophylactic femoral augmentation systems, particularly those involving the injection of ceramic-based bone cements, are gaining more attention as a potential alternative preventative approach. We evaluated the mechanical effectiveness of three variations of a bone cement injection pattern (basic ellipsoid, hollow ellipsoid, small ellipsoid) utilizing finite element simulations of sideways fall impacts. The basic augmentation pattern was tested with both high- and low-strength ceramic-based cements. The cement patterns were added to the finite element models (FEMs) of five cadaveric femurs, which were then subject to simulated sideways falls at seven impact velocities ranging from 1.0 m/s to 4.0 m/s. Peak impact forces and peak acetabular forces were examined, and failure was evaluated using a strain-based criterion. We found that the basic HA ellipsoid provided the highest increases in both the force at the acetabulum of the impacted femur ("acetabular force", 55.0% ± 22.0%) and at the force plate ("impact force", 37.4% ± 15.8%). Changing the cement to a weaker material, brushite, resulted in reduced strengthening of the femur (45.2% ± 19.4% acetabular and 30.4% ± 13.0% impact). Using a hollow version of the ellipsoid appeared to have no effect on the fracture outcome and only a minor effect on the other metrics (54.1% ± 22.3% acetabular force increase and 35.3% ± 16.0% impact force increase). However, when the outer two layers of the ellipsoid were removed (small ellipsoid), the force increases that were achieved were only 9.8% ± 5.5% acetabular force and 8.2% ± 4.1% impact force. These results demonstrate the importance of supporting the femoral neck cortex to prevent femoral fractures in a sideways fall, and provide plausible options for prophylactic femoral augmentation. As this is a preliminary study, the surgical technique, the possible effects of trabecular bone damage during the augmentation process, and the effect on the blood supply to the femoral head must be assessed further.

Effect of fall direction on the lower hip fracture risk in athletes with different loading histories: A finite element modeling study in multiple sideways fall configurations

Physical loading makes bones stronger through structural adaptation. Finding effective modes of exercise to improve proximal femur strength has the potential to decrease hip fracture risk. Previous proximal femur finite element (FE) modeling studies have indicated that the loading history comprising impact exercises is associated with substantially higher fracture load. However, those results were limited only to one specified fall direction. It remains thus unclear whether exercise-induced higher fracture load depends on the fall direction. To address this, using magnetic resonance images of proximal femora from 91 female athletes (mean age 24.7 years with >8 years competitive career) and their 20 non-athletic but physically active controls (mean age 23.7 years), proximal femur FE models were created in 12 different sideways fall configurations. The athletes were divided into five groups by typical loading patterns of their sports: high-impact (H-I: 9 triple- and 10 high-jumpers), odd-impact (O-I: 9 soccer and 10 squash players), high-magnitude (H-M: 17 powerlifters), repetitive-impact (R-I: 18 endurance runners), and repetitive non-impact (R-NI: 18 swimmers). Compared to the controls, the FE models showed that the H-I and R-I groups had significantly (p < 0.05) higher fracture loads, 11-17% and 22-28% respectively, in all fall directions while the O-I group had significantly 10-11% higher fracture loads in four fall directions. The H-M and R-NI groups did not show significant benefit in any direction. Also, the analyses of the minimum fall strength (MFS) among these multiple fall configurations confirmed significantly 15%, 11%, and 14% higher MFSs in these impact groups, respectively, compared to the controls. These results suggest that the lower hip fracture risk indicated by higher fracture loads in athletes engaged in high impact or repetitive impact sports is independent of fall direction whereas the lower fracture risk attributed to odd-impact exercise is more modest and specific to the fall direction. Moreover, in concordance with the literature, the present study also confirmed that the fracture risk increases if the impact is imposed on the more posterolateral aspect of the hip. The present results highlight the importance of engaging in the impact exercises to prevent hip fractures and call for retrospective studies to investigate whether specific impact exercise history in adolescence and young adulthood is also associated with lower incidence of hip fractures in later life.

Effect of osteoporosis-related reduction in the mechanical properties of bone on the acetabular fracture during a sideways fall: A parametric finite element approach

Purpose

The incidence of acetabular fractures due to low-energy falls is increasing among the geriatric population. Studies have shown that several biomechanical factors such as body configuration, impact velocity, and trochanteric soft-tissue thickness contribute to the severity and type of acetabular fracture. The effect of reduction in apparent density and elastic modulus of bone as well as other bone mechanical properties due to osteoporosis on low-energy acetabular fractures has not been investigated.

Methods

The current comprehensive finite element study aimed to study the effect of reduction in bone mechanical properties (trabecular, cortical, and trabecular + cortical) on the risk and type of acetabular fracture. Also, the effect of reduction in the mechanical properties of bone on the load-transferring mechanism within the pelvic girdle was examined.

Results

We observed that while the reduction in the mechanical properties of trabecular bone considerably affects the severity and area of trabecular bone failure, reduction in mechanical properties of cortical bone moderately influences both cortical and trabecular bone failure. The results also indicated that by reducing bone mechanical properties, the type of acetabular fracture turns from elementary to associated, which requires a more extensive intervention and rehabilitation period. Finally, we observed that the cortical bone plays a substantial role in load transfer, and by increasing reduction in the mechanical properties of cortical bone, a greater share of load is transmitted toward the pubic symphysis.

Conclusion

This study increases our understanding of the effect of osteoporosis progression on the incidence of low-energy acetabular fractures. The osteoporosis-related reduction in the mechanical properties of cortical bone appears to affect both the cortical and trabecular bones. Also, during the extreme reduction in the mechanical properties of bone, the acetabular fracture type will be more complicated. Finally, during the final stages of osteoporosis (high reduction in mechanical properties of bone) a smaller share of impact load is transferred by impact-side hemipelvis to the sacrum, therefore, an osteoporotic pelvis might mitigate the risk of sacral fracture.

The Influence of Fall Direction and Hip Protector on Fracture Risk: FE Model Predictions Driven by Experimental Data

Hip fractures in older adults, which often lead to lasting impairments and an increased risk of mortality, are a major public health concern. Hip fracture risk is multi-factorial, affected by the risk of falling, the load acting on the femur, and the load the femur can withstand. This study investigates the influence of impact direction on hip fracture risk and hip protector efficacy. We simulated falls for 4 subjects, in 7 different impact directions (15° and 30° anterior, lateral, and 15°, 30°, 60°, and 90° posterior) at two different impact velocities (2.1 and 3.1 m/s), all with and without hip protector, using previously validated biofidelic finite element models. We found the highest number of fractures and highest fragility ratios in lateral and 15° posterior impacts. The hip protector attenuated femur forces by 23–49 % for slim subjects under impact directions that resulted in fractures (30° anterior to 30° posterior). The hip protector prevented all fractures (6/6) for 2.1 m/s impacts, but only 10% of fractures for 3.1 m/s impacts. Our results provide evidence that, regarding hip fracture risk, posterior-lateral impacts are as dangerous as lateral impacts, and they support the efficacy of soft-shell hip protectors for anterior- and posterior-lateral impacts.

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.

Prophylactic augmentation implants in the proximal femur for hip fracture prevention: An in silico investigation of simulated sideways fall impacts

Femoral fractures from sideways falls in the elderly are associated with significant rates of morbidity and mortality. Approaches to prevent these catastrophic injuries include pharmacological treatments, which have limited efficacy. Prophylactic femoral augmentation systems are a promising alternative that are gaining prominence by addressing the most debilitating osteoporosis-related fracture. We have developed finite element models (FEMs) of a novel experimental sideways fall simulator for cadavers. By virtue of the range of specimens and injury outcomes, these FEMs are well-suited to the evaluation of such implants. The purpose of this study was to use the FEMs to evaluate the mechanical effectiveness of three different prophylactic femoral augmentation systems. Models of the Y-Strut® (Hyprevention®, Pessac, France), Gamma Nail® (Stryker, Kalamazoo, USA), and a simple lag screw femoral fracture implant systems were placed into FEMs of five cadaveric pelvis-femur constructs embedded in a soft tissue surrogate, which were then subject to simulated sideways falls at seven impact velocities. Femur-only FEMs were also evaluated. Peak impact forces and peak acetabular forces were examined, and failure was evaluated using a strain-based criterion. We found that the femoral augmentation systems increased the peak forces prior to fracture, but were unable to prevent fracture for severe impacts. The Gamma Nail® system consistently produced the largest strength increases relative to the unaugmented femur for all five specimens in both the pendulum-drop FEMs and the femur-only simulations. In some cases, the same implant appeared to cause fractures in the acetabulum. The femur-only FEMs showed larger force increases than the pendulum-drop simulations, which suggests that the results of the femur-only simulations may not represent sideways falls as accurately as the soft tissue-embedded pendulum-drop simulations. The results from this study demonstrate the ability to simulate a high energy phenomenon and the effect of implants in an in silico environment. The results also suggest that implants could increase the force applied to the proximal femur during impact. Fracture outcomes from the tested implants can be used to inform the design of future devices, which reaffirms the value of modelling with biofidelic considerations in the implant design process. To the authors' knowledge, this is the first paper to use more complex biofidelic FEMs to assess prophylactic femoral augmentation methods.

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

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

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

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

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.

Validation of 3D finite element models from simulated DXA images for biofidelic simulations of sideways fall impact to the hip

Computed tomography (CT)-derived finite element (FE) models have been proposed as a tool to improve the current clinical assessment of osteoporosis and personalized hip fracture risk by providing an accurate estimate of femoral strength. However, this solution has two main drawbacks, namely: (i) 3D CT images are needed, whereas 2D dual-energy x-ray absorptiometry (DXA) images are more generally available, and (ii) quasi-static femoral strength is predicted as a surrogate for fracture risk, instead of predicting whether a fall would result in a fracture or not. The aim of this study was to combine a biofidelic fall simulation technique, based on 3D computed tomography (CT) data with an algorithm that reconstructs 3D femoral shape and BMD distribution from a 2D DXA image. This approach was evaluated on 11 pelvis-femur constructs for which CT scans, ex vivo sideways fall impact experiments and CT-derived biofidelic FE models were available. Simulated DXA images were used to reconstruct the 3D shape and bone mineral density (BMD) distribution of the left femurs by registering a projection of a statistical shape and appearance model with a genetic optimization algorithm. The 2D-to-3D reconstructed femurs were meshed, and the resulting FE models inserted into a biofidelic FE modeling pipeline for simulating a sideways fall. The median 2D-to-3D reconstruction error was 1.02 mm for the shape and 0.06 g/cm³ for BMD for the 11 specimens. FE models derived from simulated DXAs predicted the outcome of the falls in terms of fracture versus non-fracture with the same accuracy as the CT-derived FE models. This study represents a milestone towards improved assessment of hip fracture risk based on widely available clinical DXA images.

Implicit and explicit finite element models predict the mechanical response of calcium phosphate-titanium cranial implants

The structural integrity of cranial implants is of great clinical importance, as they aim to provide cerebral protection after neurosurgery or trauma. With the increased use of patient-specific implants, the mechanical response of each implant cannot be characterized experimentally in a practical way. However, computational models provide an excellent possibility for efficiently predicting the mechanical response of patient-specific implants. This study developed finite element models (FEMs) of titanium-reinforced calcium phosphate (CaP-Ti) implants. The models were validated with previously obtained experimental data for two different CaP-Ti implant designs (D1 and D2), in which generically shaped implant specimens were loaded in compression at either quasi-static (1 mm/min) or impact (5 kg, 1.52 m/s) loading rates. The FEMs showed agreement with experimental data in the force-displacement response for both implant designs. The implicit FEMs predicted the peak load with an underestimation for D1 (9%) and an overestimation for D2 (11%). Furthermore, the shape of the force-displacement curves were well predicted. In the explicit FEMs, the first part of the force-displacement response showed 5% difference for D1 and 2% difference for D2, with respect to the experimentally derived peak loads. The explicit FEMs efficiently predicted the maximum displacements with 1% and 4% difference for D1 and D2, respectively. Compared to the CaP-Ti implant, an average parietal cranial bone FEM showed a stiffer response, greater energy absorption and less deformation under the same impact conditions. The framework developed for modelling the CaP-Ti implants has a potential for modelling CaP materials in other composite implants in future studies since it only used literature based input and matched boundary conditions. Furthermore, the developed FEMs make an important contribution to future evaluations of patient-specific CaP-Ti cranial implant designs in various loading scenarios.

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.

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.

Individualized prediction of pedicle screw fixation strength with a finite element model

Pedicle screws are used for the treatment of a wide variety of spinal pathologies. A good screw holding power in bone is required for treatment success, but has so far not been predictable computationally. The goal of this study was to develop an automated tool able to predict patient-specific screw fixation strength through finite element simulation. We compared the simulation results with results from biomechanical pull-out tests performed on animal lumbar specimens. Experimental and simulation pull-out strengths were highly correlated [Formula: see text] and the mean error was 20.25%. The fixation strength was also associated to great extent with pull-out stiffness and strain energy, as well as the screw size and mean vertebral density.

An exclusion approach for addressing partial volume artifacts with quantititive computed tomography-based finite element modeling of the proximal tibia

INTRODUCTION

Quantitative computed tomography based finite element modeling (QCT-FE) has potential to clarify the role of subchondral bone stiffness in osteoarthritis. The limited spatial resolution of clinical QCT systems, however, results in partial volume (PV) artifacts and low contrast between cortical and trabecular bone, which adversely affects the accuracy of QCT-FE models. The objective of this research was to evaluate the agreement between stiffness predictions offered by QCT-FE models of proximal tibial subchondral bone (constructed with and without a new voxel-exclusion algorithm) with experimentally-derived local subchondral bone structural stiffness.

METHODS

Thirteen proximal tibial compartments were obtained and imaged using QCT. Two types of QCT-FE models were developed: (1) standard model, which employed the standard procedure for QCT-FE modeling; and (2) "voxel exclusion (VE)" model, which addressed PV artifacts by excluding low density voxels during the material mapping stage of construction. We assessed agreement between QCT-FE stiffness estimates (using standard and VE approaches) with experimental stiffness by reporting predicted variance from linear regression and mean bias with 95% Limits of Agreement (LOA).

RESULTS

The standard and VE models explained 81% and 84% of the variance in experimentally measured stiffness, respectively. The standard model showed a mean bias of -268 N/mm (LOA -1210 to 679 N/mm); the VE model showed a mean bias of +59 N/mm (LOA -762 to 910 N/mm).

INTERPRETATION

The VE model explained more variance in subchondral bone stiffness with less bias. Our findings indicate that the VE method has potential to improve QCT-FE models of bone affected by PV artifacts.

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.

Explicit Finite Element Models Accurately Predict Subject-Specific and Velocity-Dependent Kinetics of Sideways Fall Impact

The majority of hip fractures in the elderly are the result of a fall from standing or from a lower height. Current injury models focus mostly on femur strength while neglecting subject-specific loading. This article presents an injury modeling strategy for hip fractures related to sideways falls that takes subject-specific impact loading into account. Finite element models (FEMs) of the human body were used to predict the experienced load and the femoral strength in a single model. We validated these models for their predicted peak force, effective pelvic stiffness, and fracture status against matching ex vivo sideways fall impacts (n = 11) with a trochanter velocity of 3.1 m/s. Furthermore, they were compared to sideways impacts of volunteers with lower impact velocities that were previously conducted by other groups. Good agreement was found between the ex vivo experiments and the FEMs with respect to peak force (root mean square error [RMSE] = 10.7%, R² = 0.85) and effective pelvic stiffness (R² = 0.92, RMSE = 12.9%). The FEMs were predictive of the fracture status for 10 out of 11 specimens. Compared to the volunteer experiments from low height, the FEMs overestimated the peak force by 25% for low BMI subjects and 8% for high BMI subjects. The effective pelvic stiffness values that were derived from the FEMs were comparable to those derived from impacts with volunteers. The force attenuation from the impact surface to the femur ranged between 27% and 54% and was highly dependent on soft tissue thickness (R² = 0.86). The energy balance in the FEMS showed that at the time of peak force 79% to 93% of the total energy is either kinetic or was transformed to soft tissue deformation. The presented FEMs allow for direct discrimination between fracture and nonfracture outcome for sideways falls and bridge the gap between impact testing with volunteers and impact conditions representative of real life falls. © 2019 American Society for Bone and Mineral Research.

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

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

Automated segmentation of cortical and trabecular bone to generate finite element models for femoral bone mechanics

Finite element (FE) models based on quantitative computed tomography (CT) images are better predictors of bone strength than conventional areal bone mineral density measurements. However, FE models require manual segmentation of the femur, which is not clinically applicable. This study developed a method for automated FE analyses from clinical CT images. Clinical in-vivo CT images of 13 elderly female subjects were collected to evaluate the method. Secondly, proximal cadaver femurs were harvested and imaged with clinical CT (N = 17). Of these femurs, 14 were imaged with µCT and three had earlier been tested experimentally in stance-loading, while collecting surface deformations with digital image correlation. Femurs were segmented from clinical CT images using an automated method, based on the segmentation tool Stradwin. The method automatically distinguishes trabecular and cortical bone, corrects partial volume effect and generates input for FE analysis. The manual and automatic segmentations agreed within about one voxel for in-vivo subjects (0.99 ± 0.23 mm) and cadaver femurs (0.21 ± 0.07 mm). The strains from the FE predictions closely matched with the experimentally measured strains (R² = 0.89). The method can automatically generate meshes suitable for FE analysis. The method may bring us one step closer to enable clinical usage of patient-specific FE analyses.

Biofidelic finite element models for accurately classifying hip fracture in a retrospective clinical study of elderly women from the AGES Reykjavik cohort

Clinical retrospective studies have only reported limited improvements in hip fracture classification accuracy using finite element (FE) models compared to conventional areal bone mineral density (aBMD) measurements. A possible explanation is that state-of-the-art quasi-static models do not estimate patient-specific loads. A novel FE modeling technique was developed to improve the biofidelity of simulated impact loading from sideways falling. This included surrogate models of the pelvis, lower extremities, and soft tissue that were morphed based on subject anthropometrics. Hip fracture prediction models based on aBMD and FE measurements were compared in a retrospective study of 254 elderly female subjects from the AGES-Reykjavik study. Subject fragility ratio (FR) was defined as the ratio between the ultimate forces of paired biofidelic models, one with linear elastic and the other with non-linear stress-strain relationships in the proximal femur. The expected end-point value (EEV) was defined as the FR weighted by the probability of one sideways fall over five years, based on self-reported fall frequency at baseline. The change in maximum volumetric strain (ΔMVS) on the surface of the femoral neck was calculated between time of ultimate femur force and 90% post-ultimate force in order to assess the extent of tensile tissue damage present in non-linear models. After age-adjusted logistic regression, the area under the receiver-operator curve (AUC) was highest for ΔMVS (0.72), followed by FR (0.71), aBMD (0.70), and EEV (0.67), however the differences between FEA and aBMD based prediction models were not deemed statistically significant. When subjects with no history of falling were excluded from the analysis, thus artificially assuming that falls were known a priori with no uncertainty, a statistically significant difference in AUC was detected between ΔMVS (0.85), and aBMD (0.74). Multivariable linear regression suggested that the variance in maximum elastic femur force was best explained by femoral head radius, pelvis width, and soft tissue thickness (R² = 0.79; RMSE = 0.46 kN; p < 0.005). Weighting the hip fracture prediction models based on self-reported fall frequency did not improve the models' sensitivity, however excluding non-fallers lead to significant differences between aBMD and FE based models. These findings suggest that an accurate assessment of fall probability is necessary for accurately identifying individuals predisposed to hip fracture.

On the internal reaction forces, energy absorption, and fracture in the hip during simulated sideways fall impact

The majority of hip fractures have been reported to occur as a result of a fall with impact to the greater trochanter of the femur. Recently, we developed a novel cadaveric pendulum-based hip impact model and tested two cadaveric femur-pelvis constructs, embedded in a soft tissue surrogate. The outcome was a femoral neck fracture in a male specimen while a female specimen had no fracture. The aim of the present study was, first, to develop a methodology for constructing and assessing the accuracy of explicit Finite Element Models (FEMs) for simulation of sideways falls to the hip based on the experimental model. Second, to use the FEMs for quantifying the internal reaction forces and energy absorption in the hip during impact. Third, to assess the potential of the FEMs in terms of separating a femoral fracture endpoint from a non-fracture endpoint. Using a non-linear, strain rate dependent, and heterogeneous material mapping strategy for bone tissue in these models, we found the FEM-derived results to closely match the experimental test results in terms of impact forces and displacements of pelvic video markers up to the time of peak impact force with errors below 10%. We found the internal reaction forces in the femoral neck on the impact side to be approximately 35% lower than the impact force measured between soft tissue and ground for both specimens. In addition, we found the soft tissue to be the component that absorbed the largest part of the energy of the tissue types in the hip region. Finally, we found surface strain patterns derived from FEM results to match the fracture location and extent based on post testing x-rays of the specimens. This is the first study with quantitative data on the energy absorption in the pelvic region during a sideways fall.