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.     

Stress analysis and failure prediction in the proximal femur before and after total hip replacement

An investigation was performed to determine the effects of the presence of two lengths of proximal Müller prosthesis on predicted failure loads, as compared to those for an intact femur. Three-dimensional stresses in a bone/cement/prosthesis system were determined using finite element methods, with both isotropic and transversely isotropic material properties used for the diaphyseal cortex. Significant increases in prosthesis stem stresses were found when the transversely isotropic material properties were employed in the diaphyseal cortex. This leads to the conclusion that accurate anisotropic material properties for bone are essential for precise stress determination and optimum design in prosthetic implants. Failure loads were also predicted for vertical compression and axial torque, similar to available experimental conditions, and were within the range of the experimental failure data found in the literature. The technique developed herein can be used to systematically assess existing as well as future implant designs, taking into account the complex three-dimensional interaction effects of the overall bone/cement/prosthesis system.     

Activity intensity,assistive devices and joint replacement influence predicted remodelling in the proximal femur

Bone morphology and density changes are commonly observed following joint replacement, may contribute to the risks of implant loosening and periprosthetic fracture and reduce the available bone stock for revision surgery. This study was presented in the ‘Bone and Cartilage Mechanobiology across the scales’ WCCM symposium to review the development of remodelling prediction methods and to demonstrate simulation of adaptive bone remodelling around hip replacement femoral components, incorporating intrinsic (prosthesis) and extrinsic (activity and loading) factors. An iterative bone remodelling process was applied to finite element models of a femur implanted with a cementless total hip replacement (THR) and a hip resurfacing implant. Previously developed for a cemented THR implant, this modified process enabled the influence of pre- to post-operative changes in patient activity and joint loading to be evaluated. A control algorithm used identical pre- and post-operative conditions, and the predicted extents and temporal trends of remodelling were measured by generating virtual X-rays and DXA scans. The modified process improved qualitative and quantitative remodelling predictions for both the cementless THR and resurfacing implants, but demonstrated the sensitivity to DXA scan region definition and appropriate implant–bone position and sizing. Predicted remodelling in the intact femur in response to changed activity and loading demonstrated that in this simplified model, although the influence of the extrinsic effects were important, the mechanics of implantation were dominant. This study supports the application of predictive bone remodelling as one element in the range of physical and computational studies, which should be conducted in the preclinical evaluation of new prostheses.     

pQCT provides better prediction of canine femur breaking load than does DXA

Our study was designed to examine the validity of dual energy X-ray absorptiometry (DXA) and peripheral quantitative computed tomography (pQCT) measurements as predictors of whole bone breaking strength in beagle femora. DXA was used to determine the bone mineral content, bone area, and 'areal' bone mineral density. PQCT was used to determine the cross-sectional moments of inertia, volumetric densities of the bone, and to calculate bone strength indices based on bone geometry and density. A three-point bending mechanical test was used to determine maximal load. Three variables from the pQCT data set explained 88% of the variance in maximal load, with the volumetric bone mineral density explaining 32% of the variance. The addition of the volumetric cortical density increased the adjusted r(2) to 0.601 (p=0.001) and the addition of an index created by multiplying volumetric cortical bone density by the maximum cross-sectional moment of inertia made further significant (p<0.001) improvements to an adjusted r(2) of 0.877. In comparison, when only the DXA variables were considered in a multiple regression model, areal bone mineral density was the only variable entered and explained only 51% (p<0.001) of the variance in maximal load. These results suggest that pQCT can better predict maximal load in whole beagle femora since pQCT provides information on the bone's architecture in addition to its volumetric density.     

Familial comparison of bone mineral density at the proximal femur and lumbar spine

Familial resemblance of bone mineral density (BMD) was studied in the lumbar spine and three regions of the proximal femur in 41 biological mother-daughter (M-D), 42 mother-son (M-S), 24 mother-grandmother (M-G) pairs and 18 mother-grandmother-daughter (M-G-D) triads. Children were placed into three maturity categories based on an assessment of secondary sex characteristics and growth velocities. Two sets of standardized BMD Z-scores were derived for the children based on either their chronological age or their maturational status. These scores were compared with maternal Z-scores derived from age-specific norms. Similar comparisons were made between the Z-scores of the mothers and grandmothers. For all three regions of the proximal femur and for the total AP lumbar spine the correlations between Z-score values were similar and significant (P < 0.05) between the M-G and M-D pairs ranging from 0.41 to 0.57. In general, the familial correlations improved when maturity-status based Z-scores were used for comparison. The absolute BMD values measured in the grandmothers and the three maturity groups of the children — expressed as a percentage of the BMD of the mothers — showed that at the neck and the trochanteric regions of the proximal femur the late-pubescent girls and boys had a significantly (P < 0.05) greater bone density than their mothers (115–123%), whereas at the AP spine these groups averaged only 88% of their mothers BMD. This site differential was not apparent when comparing the post-menopausal grandmothers with the pre-menopausal mothers (80% at both sites). Three generation comparisons demonstrated a strong familial resemblance in bone mineral density. The value of incorporating maturity-based versus chronological-based parameters for comparison with adult measures in studies that involve growing children at different stages of development was also demonstrated.     

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)     

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.     

Mechanical properties of metaphyseal bone in the proximal femur

We used a three-point bending test to investigate the structural behavior of 123 rectangular flat plate specimens harvested from the metaphyseal shell of the cervical and intertrochanteric regions of five fresh/frozen human proximal femora. For comparison purposes, 36 specimens of similar geometry were also fabricated from bone of the femoral diaphysis. All specimens were oriented in either the local longitudinal or transverse directions. The mean longitudinal elastic modulus was 9650 +/- 2410 (SD) MPa and demonstrated a 24% decrease from that measured for the diaphysis (12500 +/- 2140 MPa) using the same testing technique. However, the transverse elastic moduli did not differ significantly between the proximal (5470 +/- 1720 MPa) and diaphyseal (5990 +/- 1520 MPa) specimens. The globally averaged values for the ultimate tensile strengths of the metaphyseal shell were 101 +/- 26 MPa in the longitudinal and 50 +/- 12 MPa in the transverse directions. These compared with diaphyseal values of 128 +/- 16 MPa and 47 +/- 12 MPa, respectively. While these differences were largely due to the reduced density of the proximal specimens, a slight decrease in transverse anisotropy for the proximal specimens was also noted by comparing the ratio of longitudinal to transverse moduli (1.76) and tensile strength (2.02) to the diaphyseal values (2.09 and 2.71, respectively). Use of these data should lead to improved performance of analytical models for the proximal femur, and thus help focus increased attention on the structural contribution of trabecular bone to the strength and rigidity of the proximal femur.     

Comparison of micro-level and continuum-level voxel models of the proximal femur

Continuum-level finite element (FE) models became standard computational tools for the evaluation of bone mechanical behavior from in vivo computed tomography scans. Such scans do not account for the anisotropy of the bone. Instead, local mechanical properties in the continuum-level FE models are assumed isotropic and are derived from bone density, using statistical relationships. Micro-FE models, on the other hand, incorporate the anisotropic structure in detail. This study aimed to quantify the effects of assumed isotropy, by comparing continuum-level voxel models of a healthy and a severely osteoporotic proximal femur with recently analyzed micro-FE models of the same bones. The micro-model element size was coarsened to generate continuum FE models with two different element sizes (0.64 and 3.04 mm) and two different density–modulus relationships found in the literature for wet and ash density. All FE models were subjected to the same boundary conditions that simulated a fall to the side, and the stress and strain distributions, model stiffness and yield load were compared. The results indicated that the stress and strain distributions could be reproduced well with the continuum models. The smallest differences between the continuum-level model and micro-level model predictions of the stiffness and yield load were obtained with the coarsest element size. Better results were obtained for both continuum-element sizes when isotropic moduli were based on ash density rather than wet density.     

Radiographic changes in the clavicle and proximal femur and their use in the determination of skeletal age at death

Visually seriated radiographs of the proximal femur, proximal humerus, clavicle, and calcaneus from 130 individuals from the Hamann-Todd collection were examined as indicators of skeletal age at death. The clavicle demonstrated the most consistent relationship to age in both sexes. The same radiographs were also seriated by size-normalized optical density as a means of establishing relative radiolucency. In this context, visual seriation proved superior. The four sites studied showed strong divergence in response to age. Since each was sampling bone response from the same individual, it is concluded that bone loss is highly site specific. This demonstrates the individual character of specific skeletal sites. Visual inspection of clavicular radiographs, seriated on a populational basis, provides age estimates that are comparable to anatomical age indicators and provides independent estimates of skeletal age when included in the summary age method (1985: Am. J. Phys. Anthropol. 68:1–14).     

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.     

Statistical shape and appearance models for fast and automated estimation of proximal femur fracture load using 2D finite element models

Estimating the risk of osteoporotic fractures is an important diagnostic step that needs to be taken before medicinal treatment. Densitometry-based criteria are normally used in clinical practice for this purpose. However, densitometry-based techniques could not explain all low-energy fractures. As patient-specific finite element (FE) models allow for consideration of other parameters (e.g. load conditions) that are known to be associated with fracture, they are considered promising candidates for more accurate fracture risk estimation. Nevertheless, they are often time consuming, expensive, and complex to build and may need the type of expertise that is not normally available in clinical settings. In this study, we report the development of an automated platform for estimating proximal femur fracture loads using patient-specific 2D FE models generated using dual-energy x-ray absorptiometry (DXA) scans. First, a statistical shape and appearance model (SSAM) is built using DXA scans of patients screened for osteoporosis following a low energy fracture. SSAM is then used together with Active Appearance Models (AAM) for automated segmentation of the proximal femur from new unseen DXA scans. The mean point-to-curve error of the automated procedure, i.e. 1.2–1.4 mm, is shown to be only slightly larger than the intra-observer variability of manual segmentation, i.e. 1.0 mm. Moreover, the developed platform automatically meshes the segmented shape, assigns density-based mechanical properties, assigns loads and boundary conditions, submits the 2D FE model for solution, and performs post-processing of the 2D FE simulation data to determine fracture loads. The fracture loads predicted using the manually generated and automatically generated 2D FE models are shown to be very close with a mean difference of around 8.8%. Repeated measures ANOVA showed no significant differences between the fracture loads calculated using FE models manually generated by three independent observers and those calculated using the automatically generated FE models (p>0.05).     

Validation of subject-specific automated p-FE analysis of the proximal femur

Background: The use of subject-specific finite element (FE) models in clinical practice requires a high level of automation and validation. In Yosibash et al. [2007a. Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations. J. Biomechanics 40, 3688–3699] a novel method for generating high-order finite element (p-FE) models from CT scans was presented and validated by experimental observations on two fresh frozen femurs (harvested from a 30 year old male and 21 year old female). Herein, we substantiate the validation process by enlarging the experimental database (54 year old female femur), improving the method and examine its robustness under different CT scan conditions.Approach: A fresh frozen femur of a 54 year old female was scanned under two different environments: in air and immersed in water (dry and wet CT). Thereafter, the proximal femur was quasi-statically loaded in vitro by a 1000 N load. The two QCT scans were manipulated to generate p-FE models that mimic the experimental conditions. We compared p-FE displacements and strains of the wet CT model to the dry CT model and to the experimental results. In addition, the material assignment strategy was reinvestigated. The inhomogeneous Young's modulus was represented in the FE model using two different methods, directly extracted from the CT data and using continuous spatial functions as in Yosibash et al. [2007a. Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations. J. Biomechanics 40, 3688–3699].Results: Excellent agreement between dry and wet FE models was found for both displacements and strains, i.e. the method is insensitive to CT conditions and may be used in vivo. Good agreement was also found between FE results and experimental observations. The spatial functions representing Young's modulus are local and do not influence strains and displacements prediction. Finally, the p-FE results of all three fresh frozen human femurs compare very well to experimental observations exemplifying that the presented method may be in a mature stage to be used in clinical computer-aided decision making.     

Densitometric, morphometric and mechanical distributions in the human proximal femur

With the prevalent use of DXA-measured BMD to assess pathologic hip fractures and its recently reported lack of reliability to predict fracture or account for efficacy of anti-resorptive therapy, it is reasonable to assess whether variations in the primary and secondary tensile and compressive trabecular microstructure can account for variations in proximal femur strength in comparison to DXA-measured BMD. To that end, microstructural and densitometric measures of trabecular bone specimens, from discrete sites within the proximal femur, were correlated with their mechanical properties. We hypothesize that accounting for regional variations in trabecular microstructure will improve predictions of proximal femur strength and stiffness compared to bone density measured by DXA. Forty-seven samples (seven donors) from seven distinct sites of human proximal femur underwent DXA and muCT imaging and mechanical testing. The results revealed significant variations in BMC, morphometric indices and mechanical properties within the proximal femur. This work has demonstrated that the mechanical performance of each sub-region is highly dependent on the corresponding trabecular microstructure. BMD measured by DXA at standard regions of interest cannot resolve the variations in trabecular density and microstructure that govern the mechanical behavior of the proximal femur. This work suggests that a quantitative Singh index that uses high resolution QCT to monitor the trabecular microstructure at specific sub-regions of the proximal femur may allow better predictions of hip fracture risk in individual patients and an improved assessment of changing bone structure in response to pharmacological interventions.     

Concept and development of an orthotropic FE model of the proximal femur

PURPOSE: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE "model femur" to realistically simulate three-dimensional bone remodelling. METHODS: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known "density-determined" bony material properties (Young's modulus; Poisson's ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same "CT-density-characterized" volumetric group.In order to fix the principal directions of stiffness in FE areas with the same "density characterization", the cadaveric femurs were cut in 2mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the "CT-density characterized" three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter's criterion. RESULTS: In the constructed "model femur", each FE is characterized by the principal directions of the stiffness and the "CT-density-determined" material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. CONCLUSIONS: With the orthotropic "model femur", the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc).