Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations

Background: The mechanical response of patient-specific bone to various load conditions is of major clinical importance in orthopedics. Herein we enhance the methods presented in Yosibash et al. [2007. A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments. ASME Journal of Biomechanical Engineering 129(3), 297–309.] for the reliable simulations of the human proximal femur by high-order finite elements (FEs) and validate the simulations by experimental observations.

Method of approach: A fresh-frozen human femur was scanned by quantitative computed tomography (QCT) and thereafter loaded (in vitro experiments) by a quasi-static force of up to 1250 N. QCT scans were manipulated to generate a high-order FE bone model with distinct cortical and trabecular regions having inhomogeneous isotropic elastic properties with Young's modulus represented by continuous spatial functions. Sensitivity analyses were performed to quantify parameters that mostly influence the mechanical response. FE results were compared to displacements and strains measured in the experiments.

Results: Young moduli correlated to QCT Hounsfield Units by relations in Keyak and Falkinstein [2003. Comparison of in situ and in vitro CT scan-based finite element model predictions of proximal femoral fracture load. Medical Engineering and Physics 25, 781–787.] were found to provide predictions that match the experimental results closely. Excellent agreement was found for both the displacements and strains. The presented study demonstrates that reliable and validated high-order patient-specific FE simulations of human femurs based on QCT data are achievable for clinical computer-aided decision making.     

Prediction of strength and strain of the proximal femur by a CT-based finite element method

Hip fractures are the most serious complication of osteoporosis and have been recognized as a major public health problem. In elderly persons, hip fractures occur as a result of increased fragility of the proximal femur due to osteoporosis. It is essential to precisely quantify the strength of the proximal femur in order to estimate the fracture risk and plan preventive interventions. CT-based finite element analysis could possibly achieve precise assessment of the strength of the proximal femur. The purpose of this study was to create a simulation model that could accurately predict the strength and surface strains of the proximal femur using a CT-based finite element method and to verify the accuracy of our model by load testing using fresh frozen cadaver specimens. Eleven right femora were collected. The axial CT scans of the proximal femora were obtained with a calibration phantom, from which the 3D finite element models were constructed. Materially nonlinear finite element analyses were performed. The yield and fracture loads were calculated, while the sites where elements failed and the distributions of the principal strains were determined. The strain gauges were attached to the proximal femoral surfaces. A quasi-static compression test of each femur was conducted. The yield loads, fracture loads and principal strains of the prediction significantly correlated with those measured (r=0.941, 0.979, 0.963). Finite element analysis showed that the solid elements and shell elements in undergoing compressive failure were at the same subcapital region as the experimental fracture site.     

Mapping anisotropy of the proximal femur for enhanced image based finite element analysis

Finite element (FE) models of bone derived from quantitative computed tomography (QCT) rely on realistic material properties to accurately predict bone strength. QCT cannot resolve bone microarchitecture, therefore QCT-based FE models lack the anisotropy apparent within the underlying bone tissue. This study proposes a method for mapping femoral anisotropy using high-resolution peripheral quantitative computed tomography (HR-pQCT) scans of human cadaver specimens. Femur HR-pQCT images were sub-divided into numerous overlapping cubic sub-volumes and the local anisotropy was quantified using a ‘direct-mechanics’ method. The resulting directionality reflected all the major stress lines visible within the trabecular lattice, and provided a realistic estimate of the alignment of Harvesian systems within the cortical compartment. QCT-based FE models of the proximal femur were constructed with isotropic and anisotropic material properties, with directionality interpolated from the map of anisotropy. Models were loaded in a sideways fall configuration and the resulting whole bone stiffness was compared to experimental stiffness and ultimate strength. Anisotropic models were consistently less stiff, but no statistically significant differences in correlation were observed between material models against experimental data. The mean difference in whole bone stiffness between model types was approximately 26%, suggesting that anisotropy can still effect considerable change in the mechanics of proximal femur models. The under prediction of whole bone stiffness in anisotropic models suggests that the orthotropic elastic constants require further investigation. The ability to map mechanical anisotropy from high-resolution images and interpolate information into clinical-resolution models will allow testing of new anisotropic material mapping strategies.     

Accuracy of finite element predictions in sideways load configurations for the proximal human femur

Subject-specific finite element models have been used to predict stress-state and fracture risk in individual patients. While many studies analysed quasi-axial loading configurations, only few works simulated sideways load configurations, such as those arising in a fall. The majority among these latter directly predicted bone strength, without assessing elastic strain prediction accuracy. The aim of the present work was to evaluate if a subject-specific finite element modelling technique from CT data that accurately predicted strains in quasi-axial loading configurations is suitable to accurately predict strains also when applying low magnitude loads in sideways configurations. To this aim, a combined numerical-experimental study was performed to compare finite element predicted strains with strain-gauge measurements from three cadaver proximal femurs instrumented with sixteen strain rosettes and tested non-destructively under twelve loading configurations, spanning a wide cone (0-30° for both adduction and internal rotation angles) of sideways fall scenarios. The results of the present study evidenced a satisfactory agreement between experimentally measured and predicted strains (R(2) greater than 0.9, RMSE% lower than 10%) and displacements. The achieved strain prediction accuracy is comparable to those obtained in state of the art studies in quasi-axial loading configurations. Still, the presence of the highest strain prediction errors (around 30%) in the lateral neck aspect would deserve attention in future studies targeting bone failure.     

Combined finite element model of human proximal femur behaviour considering remodeling and fracture

The purpose of this work was to develop a combined remodeling-to-fracture finite element model allowing for the combined simulation of human proximal femur remodeling under a given boundary conditions followed by the simulation of its fracture behaviour under quasi-static load. The combination of remodeling and fracture simulation into one unified model consists in considering that the femur properties resulting from the remodeling simulation correspond to the initial state for the fracture prediction. The remodeling model is based on a coupled strain and fatigue damage stimulus approach. The fracture model is based on continuum damage mechanics in order to predict the progressive fracturing process, which allows to predict the fracture pattern and the complete force-displacement curve under quasi-static load. To investigate the potential of the proposed unified remodeling-to-fracture model, we performed remodeling simulations on a 3D proximal femur model for a duration of 365 days followed by a side fall fracture simulation reproducing.     

Fracture prediction for the proximal femur using finite element models: Part II--Nonlinear analysis.

In Part I we reported the results of linear finite element models of the proximal femur generated using geometric and constitutive data collected with quantitative computed tomography. These models demonstrated excellent agreement with in vitro studies when used to predict ultimate failure loads. In Part II, we report our extension of those finite element models to include nonlinear behavior of the trabecular and cortical bone. A highly nonlinear material law, originally designed for representing concrete, was used for trabecular bone, while a bilinear material law was used for cortical bone. We found excellent agreement between the model predictions and in vitro fracture data for both the onset of bone yielding and bone fracture. For bone yielding, the model predictions were within 2 percent for a load which simulated one-legged stance and 1 percent for a load which simulated a fall. For bone fracture, the model predictions were within 1 percent and 17 percent, respectively. The models also demonstrated different fracture mechanisms for the two different loading configurations. For one-legged stance, failure within the primary compressive trabeculae at the subcapital region occurred first, leading to load transfer and, ultimately, failure of the surrounding cortical shell. However, for a fall, failure of the cortical and trabecular bone occurred simultaneously within the intertrochanteric region. These results support our previous findings that the strength of the subcapital region is primarily due to trabecular bone whereas the strength of the intertrochanteric region is primarily due to cortical bone.     

Fracture prediction for the proximal femur using finite element models: Part I--Linear analysis.

Over 90 percent of the more than 250,000 hip fractures that occur annually in the United States are the result of falls from standing height. Despite this, the stresses associated with femoral fracture from a fall have not been investigated previously. Our objectives were to use three-dimensional finite element models of the proximal femur (with geometries and material properties based directly on quantitative computed tomography) to compare predicted stress distributions for one-legged stance and for a fall to the lateral greater trochanter. We also wished to test the correspondence between model predictions and in vitro strain gage data and failure loads for cadaveric femora subjected to these loading conditions. An additional goal was to use the model predictions to compare the sensitivity of several imaging sites in the proximal femur which are used for the in vivo prediction of hip fracture risk. In this first of two parts, linear finite element models of two unpaired human cadaveric femora were generated. In Part II, the models were extended to include nonlinear material properties for the cortical and trabecular bone. While there was poor correspondence between strain gage data and model predictions, there was excellent agreement between the in vitro failure data and the linear model, especially using a von Mises effective strain failure criterion. Both the onset of structural yielding (within 22 and 4 percent) and the load at fracture (within 8 and 5 percent) were predicted accurately for the two femora tested. For the simulation of one-legged stance, the peak stresses occurred in the primary compressive trabeculae of the subcapital region.(ABSTRACT TRUNCATED AT 250 WORDS)     

A round-robin finite element analysis of human femur mechanics between seven participating laboratories with experimental validation

Finite element analysis is a common tool that has been used for the past few decades to predict the mechanical behavior of bone. However, to our knowledge, there are no round-robin finite element analyses of long human bones with more than two participating biomechanics laboratories published yet, where the results of the experimental tests were not known in advance. We prepared a fresh-frozen human femur for a compression test in a universal testing machine measuring the strains at 10 bone locations as well as the deformation of the bone in terms of the displacement of the loading point at a load of 2?kN. The computed tomography data of the bone with a calibration phantom as well as the orientation of the bone in the testing machine with the according boundary conditions were delivered to seven participating laboratories. These were asked to perform a finite element analysis simulating the experimental setup and deliver their results to the coordinator without knowing the experimental results. Resultantly, four laboratories had deviations from the experimentally measured strains of less than 40%, and three laboratories had deviations of their numerically determined values compared to the experimental data of more than 120%. These deviations are thought to be based on different material laws and material data, as well as different material mapping methods. Investigations will be conducted to clarify and assess the reasons for the large deviations in the numerical data. It was shown that the precision of finite element models of the human femur is not yet as developed as desired by the biomechanics community.     

A B-spline based heterogeneous modeling and analysis of proximal femur with graded element

Bone is a complex biological tissue and natural heterogeneous object. The main objective of this study is to simulate quasi-static loading of bio-objects like human femur with B-spline based modeling and its 3D finite element analysis with graded element. B-spline surface representation method is extended to represent material composition to develop heterogeneous solid model of proximal femur. Lagrangian graded element is used to assign inhomogeneous isotropic elastic properties in finite element model to improve the performance. Convergence study is carried out with finite element model in single leg stance load condition. To test the feasibility of the model, sensitivity of simulation is investigated. To validate the model, numerical results are compared with those of an experimental work for the same specimen in simple stance load condition obtained from one of the reference paper. Good agreement is achieved for vertical displacement and strains in most of the locations.     

A comparative analysis of different treatments for distal femur fractures using the finite element method

The main objective of this work is the evaluation, by means of the finite element method (FEM) of the mechanical stability and long-term microstructural modifications in bone induced to three different kinds of fractures of the distal femur by three types of implants: the Condyle Plate, the less invasive stabilization system plate (LISS) and the distal femur nail (DFN). The displacement and the stress distributions both in bone and implants and the internal bone remodelling process after fracture and fixation are obtained and analysed by computational simulation. The main conclusions of this work are that distal femoral fractures can be treated correctly with the Condyle Plate, the LISS plate and the DFN. The stresses both in LISS and DFN implant are high especially around the screws. When respect to remodelling, the LISS produces an important resorption in the fractured region, while the other two implants do not strongly modify bone tissue microstructure.     

Development of a parametric finite element model of the proximal femur using statistical shape and density modelling

Skeletal fractures associated with bone mass loss are a major clinical problem and economic burden, and lead to significant morbidity and mortality in the ageing population. Clinical image-based measures of bone mass show only moderate correlative strength with bone strength. However, engineering models derived from clinical image data predict bone strength with significantly greater accuracy. Currently, image-based finite element (FE) models are time consuming to construct and are non-parametric. The goal of this study was to develop a parametric proximal femur FE model based on a statistical shape and density model (SSDM) derived from clinical image data. A small number of independent SSDM parameters described the shape and bone density distribution of a set of cadaver femurs and captured the variability affecting proximal femur FE strength predictions. Finally, a three-dimensional FE model of an 'unknown' femur was reconstructed from the SSDM with an average spatial error of 0.016 mm and an average bone density error of 0.037 g/cm(3).     

Trabecular structure compared to stress trajectories in the proximal femur and the calcaneus

The theory that the trabecular structure within bones follows the principal stress trajectories, is investigated by two-dimensional finite element models of increasing complexity. This is done for the proximal femur of the human and for the calcaneus of the horse. In both cases, a simple model with well-chosen loading and boundary conditions gives good agreement between the observed trabecular structure and the calculated stress trajectories. It is shown that this stress trajectory theory has a mechanically founded explanation.     

Impact loading history modulates hip fracture load and location: A finite element simulation study of the proximal femur in female athletes

Sideways falls impose high stress on the thin superolateral cortical bone of the femoral neck, the region regarded as a fracture-prone region of the hip. Exercise training is a natural mode of mechanical loading to make bone more robust. Exercise-induced adaptation of cortical bone along the femoral neck has been previously demonstrated. However, it is unknown whether this adaption modulates hip fracture behavior. The purpose of this study was to investigate the influence of specific exercise loading history on fall-induced hip fracture behavior by estimating fracture load and location with proximal femur finite element (FE) models created from magnetic resonance images (MRI) of 111 women with distinct exercise histories: 91 athletes (aged 24.7 ± 6.1 years, >8 years competitive career) and 20 women as controls (aged 23.7 ± 3.8 years). The athletes were divided into five groups based on typical loading patterns of their sports: high-impact (H-I: 9 triple-jumpers and 10 high jumpers), odd-impact (O-I: 9 soccer and 10 squash players), high-magnitude (H-M: 17 power-lifters), repetitive-impact (R-I: 18 endurance runners), and repetitive non-impact (R-NI: 18 swimmers). Compared to the controls, the H-I, O-I, and R-I groups had significantly higher (11–26%, p < 0.05) fracture loads. Also, the fracture location in the H-I and O-I groups was significantly more proximal (7–10%) compared to the controls. These results suggest that an exercise loading history of high impacts, impacts from unusual directions, or repetitive impacts increases the fracture load and may lower the risk of fall-induced hip fracture.     

Trabecular bone ontogeny in the human proximal femur

Ontogenetic changes in the human femur associated with the acquisition of bipedal locomotion, especially the development of the bicondylar angle, have been well documented. The purpose of this study is to quantify changes in the three-dimensional structure of trabecular bone in the human proximal femur in relation to changing functional and external loading patterns with age. High-resolution X-ray computed tomography scan data were collected for 15 juvenile femoral specimens ranging in age from prenatal to approximately nine years of age. Serial slices were collected for the entire proximal femur of each individual with voxel resolutions ranging from 0.017 to 0.046 mm depending on the size of the specimen. Spherical volumes of interest were defined within the proximal femur, and the bone volume fraction, trabecular thickness, trabecular number, and fabric anisotropy were calculated in three dimensions. Bone volume fraction, trabecular number, and degree of anisotropy decrease between the age of 6 months and 12 months, with the lowest values for these parameters occurring in individuals near 12 months of age. By age 2-3 years, the bone volume, thickness, and degree of anisotropy increase slightly, and regions in the femoral neck become more anisotropic corresponding to the thickening of the inferior cortical bone of the neck. These results suggest that trabecular structure in the proximal femur reflects the shift in external loading patterns associated with the initiation of unassisted walking in infants.     

Experimental validation of a finite element model of the proximal femur using digital image correlation and a composite bone model

Computational biomechanical models are useful tools for supporting orthopedic implant design and surgical decision making, but because they are a simplification of the clinical scenario they must be carefully validated to ensure that they are still representative. The goal of this study was to assess the validity of the generation process of a structural finite element model of the proximal femur employing the digital image correlation (DIC) strain measurement technique. A finite element analysis model of the proximal femur subjected to gait loading was generated from a CT scan of an analog composite femur, and its predicted mechanical behavior was compared with an experimental model. Whereas previous studies have employed strain gauging to obtain discreet point data for validation, in this study DIC was used for full field quantified comparison of the predicted and experimentally measured strains. The strain predicted by the computational model was in good agreement with experimental measurements, with R(2) correlation values from 0.83 to 0.92 between the simulation and the tests. The sensitivity and repeatability of the strain measurements were comparable to or better than values reported in the literature for other DIC tests on tissue specimens. The experimental-model correlation was in the same range as values obtained from strain gauging, but the DIC technique produced more detailed, full field data and is potentially easier to use. As such, the findings supported the validity of the model generation process, giving greater confidence in the model's predictions, and digital image correlation was demonstrated as a useful tool for the validation of biomechanical models.     

A finite element analysis of hollow stemmed hip prostheses as a means of reducing stress shielding of the femur.

Stress shielding of the femur is known to be a principal factor in aseptic loosening of hip replacements. This paper considers the use of a hollow stemmed hip implant for reducing the effects of stress shielding, while maintaining acceptably low levels of stress in the cement. Using finite element modelling, the stresses in the proximal femur using different shapes of hollow stem were compared with those produced using comparable sizes of solid stem with different values of elastic modulus. A reduction in stress shielding could be achieved with a hollow stem. A cylindrical hollow stem design was then optimised in order to control the maximum allowable stress in the cement, the minimum allowable stresses in the bone, and a combination of the two. The resulting stems achieved an increase in proximal bone stress of about 15% for the first case and 32% for a model using high strength cement, compared with solid stems of the same nominal outside diameter. The gains of these theoretically optimised designs dropped off rapidly further down the stem. Linearly tapered hollow stems reached a 22% gain, which could be a good compromise between acceptable cement stresses and ease of manufacture.