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)     

Specimen-specific modeling of hip fracture pattern and repair

Hip fracture remains a major health problem for the elderly. Clinical studies have assessed fracture risk based on bone quality in the aging population and cadaveric testing has quantified bone strength and fracture loads. Prior modeling has primarily focused on quantifying the strain distribution in bone as an indicator of fracture risk. Recent advances in the extended finite element method (XFEM) enable prediction of the initiation and propagation of cracks without requiring a priori knowledge of the crack path. Accordingly, the objectives of this study were to predict femoral fracture in specimen-specific models using the XFEM approach, to perform one-to-one comparisons of predicted and in vitro fracture patterns, and to develop a framework to assess the mechanics and load transfer in the fractured femur when it is repaired with an osteosynthesis implant. Five specimen-specific femur models were developed from in vitro experiments under a simulated stance loading condition. Predicted fracture patterns closely matched the in vitro patterns; however, predictions of fracture load differed by approximately 50% due to sensitivity to local material properties. Specimen-specific intertrochanteric fractures were induced by subjecting the femur models to a sideways fall and repaired with a contemporary implant. Under a post-surgical stance loading, model-predicted load sharing between the implant and bone across the fracture surface varied from 59%:41% to 89%:11%, underscoring the importance of considering anatomic and fracture variability in the evaluation of implants. XFEM modeling shows potential as a macro-level analysis enabling fracture investigations of clinical cohorts, including at-risk groups, and the design of robust implants.     

Rib fractures under anterior–posterior dynamic loads: Experimental and finite-element study

The purpose of this study was to investigate whether using a finite-element (FE) mesh composed entirely of hexahedral elements to model cortical and trabecular bone (all-hex model) would provide more accurate simulations than those with variable thickness shell elements for cortical bone and hexahedral elements for trabecular bone (hex–shell model) in the modeling human ribs. First, quasi-static non-injurious and dynamic injurious experiments were performed using the second, fourth, and tenth human thoracic ribs to record the structural behavior and fracture tolerance of individual ribs under anterior–posterior bending loads. Then, all-hex and hex–shell FE models for the three ribs were developed using an octree-based and multi-block hex meshing approach, respectively. Material properties of cortical bone were optimized using dynamic experimental data and the hex–shell model of the fourth rib and trabecular bone properties were taken from the literature. Overall, the reaction force–displacement relationship predicted by both all-hex and hex–shell models with nodes in the offset middle-cortical surfaces compared well with those measured experimentally for all the three ribs. With the exception of fracture locations, the predictions from all-hex and offset hex–shell models of the second and fourth ribs agreed better with experimental data than those from the tenth rib models in terms of reaction force at fracture (difference <15.4%), ultimate failure displacement and time (difference <7.3%), and cortical bone strains. The hex–shell models with shell nodes in outer cortical surfaces increased static reaction forces up to 16.6%, compared to offset hex–shell models. These results indicated that both all-hex and hex–shell modeling strategies were applicable for simulating rib responses and bone fractures for the loading conditions considered, but coarse hex–shell models with constant or variable shell thickness were more computationally efficient and therefore preferred.     

The susceptibility of the femoral neck to fracture: an assessment incorporating the effects of age-remodeling and stress reduction

Age-related bone remodeling may cause fragility of the femoral neck, thereby increasing fracture risk in elderly populations. We investigated the effects of age-remodeling and stress-reduction on the femoral neck region using the Finite Strip Method (FSM). We verified the possibility that the femoral neck is likely to undergo fracture through two mechanisms: yielding and local buckling. We hypothesized that the femoral necks of young subjects are more prone to fracture by yielding, whereas those of elderly subjects are more susceptible to fracture initiated by local buckling. The slices from the CT-scans of 15 subjects corresponding to the lowest area moment of inertia were segregated into cortex and trabeculae. Geometric and material properties for each strip were obtained from the CT-scans. The FSM, proposed here as an approximation to the better-known Finite Element Method (FEM), was implemented on a model comprising both cortex and trabeculae. Finite strip (FS) analyses were performed on models that incorporated the effects of age-related bone remodeling, as well as a reduction in physiological stress on the bone (as a result of weight loss). Comparisons were made with similar FS analyses performed on only the cortical shell, in order to ascertain the contributions of the trabeculae to femoral neck strength. We observed that the femoral necks of simulated young subjects manifested a marked predisposition to undergo yielding, whereas the femoral neck models of simulated elderly subjects were more prone to buckling before yielding. The trabecular degradation and cortical thinning involved in aging render the femoral neck more susceptible to failure by buckling.     

Experimental and probabilistic analysis of distal femoral periprosthetic fracture: a comparison of locking plate and intramedullary nail fixation. Part A: experimental investigation

The following is a two-part study. Part A evaluates biomechanically intramedullary (IM) nails vs. locking plates for fixation of femoral fractures in osteoporotic bone. Part B of this study introduces a deterministic finite element model of each construct type and investigates the probability of periprosthetic fracture of the locking plate compared with the retrograde IM nail using Monte Carlo simulation. For Part A, an extra-articular, metaphyseal wedge fracture pattern was created in 11 osteoporotic fourth-generation composite femurs. Fixation was performed with a locking plate or a retrograde IM nail. Axial, torsion and bending cyclic loading to simulate post-operative damage accumulation were performed followed by ramped load to failure. Locking plates proved to be more stable (using stiffness as the determining factor) in osteoporotic bone as observed under low load cycle conditions. However, some of these advantages were offset by a greater incidence of sudden periprosthetic fracture observed under ramped loading conditions. Cadaveric, osteoporotic femurs included as a case study also exhibited periprosthetic fracture, but failure was accompanied by catastrophic comminution of the cortex. Periprosthetic failure at the implant end including bone comminution is difficult to salvage with revision fixation. The weakened trabecular matrix and thinned cortex of osteoporotic bone may increase the incidence of periprosthetic fracture. It is, therefore, essential for the surgeon to consider all possible loading scenarios when recommending an ideal implant for the osteoporotic patient.     

Pathological fractures of the femoral neck

In a review of subcapital fractures due to metastases in the femoral neck it was found that in the majority of cases pain in the region of the hip developed a few days prior to fracture. While the majority of subcapital fractures are sustained as the result of a single incident of trauma, in cases with metastases trabecular stress fractures occur in increasing numbers until finally femoral neck fracture occurs. It would seem that once a critical number of trabecular stress fractures has been reached the patient develops pain. Immediate radiologic examination should be performed, and if there is evidence of bone destruction approaching 50% of the cortex, prophylactic hip pinning is strongly indicated.     

A structural model for the mechanical behavior of trabecular bone

A quantitative model is developed for trabecular bone by approximating the trabecular geometry with a hypothetical network of compact bone. For the region immediately beneath the articular cartilage in the distal end of the femur, finite element analyses were performed with a high speed computer, assuming a physiological static load. The results indicate that bending and buckling of trabeculae are considerable in any elastic deformation of the bone; that fatigue fracture in some fraction of suitably oriented trabeculae is inevitable in normal ambulation; and that the stiffness varies considerably with lateral position across the subchondral plate. The latter depends totally on trabecular arrangement and may play a role in joint function and degeneration. The adjustments necessary to bring the gross stiffness into agreement with experiment imply that the intertrabecular soft tissues are of no consequence to the mechanical properties and that the compact bone of which trabeculae are made is probably not as stiff as cortical bone.     

Predicting the failure response of cement-bone constructs using a non-linear fracture mechanics approach

A non-linear fracture mechanics approach was used to predict the failure response of complex cement-bone constructs. A series of eight mechanical tests with a combination of tensile and shear loading along the cement-bone interface was performed. Each experiment was modeled using the finite element method with non-linear constitutive models at the cement-bone interface. Interface constitutive parameters were assigned based on the quantity of bone interdigitated with the cement. There was a strong correlation (r2 = 0.80) between experimentally measured and finite element predicted ultimate loads. The average error in predicted ultimate load was 23.9 percent. In comparison to the ultimate load predictions, correlations and errors for total energy to failure (r2 = 0.24, avg. error = 38.2 percent) and displacement at 50 percent of the ultimate load (r2 = 0.27, avg. error = 52.2 percent) were poor The results indicate that the non-linear constitutive laws could be useful in predicting the initiation and progression of interface failure of cemented bone-implant systems. However improvements in the estimation of post-yield interface properties from the quantity of bone interdigitated with cement are needed to enhance predictions of the overall failure response.     

A cellular solid criterion for predicting the axial-shear failure properties of bovine trabecular bone.

In a long-term effort to develop a complete multi-axial failure criterion for human trabecular bone, the overall goal of this study was to compare the ability of a simple cellular solid mechanistic criterion versus the Tsai-Wu, Principal Strain, and von Mises phenomenological criteria--all normalized to minimize effects of interspecimen heterogeneity of strength--to predict the on-axis axial-shear failure properties of bovine trabecular bone. The Cellular Solid criterion that was developed here assumed that vertical trabeculae failed due to a linear superposition of axial compression/tension and bending stresses, induced by the apparent level axial and shear loading, respectively. Twenty-seven bovine tibial trabecular bone specimens were destructively tested on-axis without end artifacts, loaded either in combined tension-torsion (n = 10), compression-torsion (n = 11), or uniaxially (n = 6). For compression-shear, the mean (+/- S.D.) percentage errors between measured values and criterion predictions were 7.7 +/- 12.6 percent, 19.7 +/- 23.2 percent, 22.8 +/- 18.9 percent, and 82.4 +/- 64.5 percent for the Cellular Solid, Tsai-Wu, Principal Strain, and von Mises criteria, respectively; corresponding mean errors for tension-shear were -5.2 +/- 11.8 percent, 14.3 +/- 12.5 percent, 6.9 +/- 7.6 percent, and 57.7 +/- 46.3 percent. Statistical analysis indicated that the Cellular Solid criterion was the best performer for compression-shear, and performed as well as the Principal Strain criterion for tension-shear. These data should substantially improve the ability to predict axial-shear failure of dense trabecular bone. More importantly, the results firmly establish the importance of cellular solid analysis for understanding and predicting the multiaxial failure behavior of trabecular bone.     

Biaxial failure behavior of bovine tibial trabecular bone

Multiaxial failure properties of trabecular bone are important for modeling of whole bone fracture and can provide insight into structure-function relationships. There is currently no consensus on the most appropriate form of multiaxial yield criterion for trabecular bone. Using experimentally validated, high-resolution, non-linear finite element models, biaxial plain strain boundary conditions were applied to seven bovine tibial specimens. The dependence of multiaxial yield properties on volume fraction was investigated to quantify the interspecimen heterogeneity in yield stresses and strains. Two specimens were further analyzed to determine the yield properties for a wide range of biaxial strain loading conditions. The locations and quantities of tissue level yielding were compared for on-axis, transverse, and biaxial apparent level yielding to elucidate the micromechanical failure mechanisms. As reported for uniaxial loading of trabecular bone, the yield strains in multiaxial loading did not depend on volume fraction, whereas the yield stresses did. Micromechanical analysis indicated that the failure mechanisms in the on-axis and transverse loading directions were mostly independent. Consistent with this, the biaxial yield properties were best described by independent curves for on-axis and transverse loading. These findings establish that the multiaxial failure of trabecular bone is predominantly governed by the strain along the loading direction, requiring separate analytical expressions for each orthotropic axis to capture the apparent level yield behavior.     

Prediction of femoral fracture load using finite element models: an examination of stress- and strain-based failure theories

Finite element (FE) models are often used to model bone failure. However, no failure theory for bone has been validated at this time. In this study, we examined the performance of nine stress- and strain-based failure theories, six of which could account for differences in tensile and compressive material strengths. The distortion energy, Hoffman and a strain-based Hoffman analog, maximum normal stress, maximum normal strain, maximum shear strain, maximum shear stress (tau(max)), Coulomb-Mohr, and modified Mohr failure theories were evaluated using automatically generated, computed tomographic scan-based FE models of the femur. Eighteen matched pairs of proximal femora were examined in two load configurations, one approximating joint loading during single-limb stance and one simulating impact from a fall. Mechanical testing was performed to assess model and failure theory performance in the context of predicting femoral fracture load. Measured and FE-computed fracture load were significantly correlated for both loading conditions and all failure criteria (p < or = 0.001). The distortion energy and tau(max) failure theories were the most robust of those examined, providing the most consistently strong FE model performance for two very different loading conditions. The more complex failure theories and the strain-based theories examined did not improve performance over the simpler distortion energy and tau(max) theories, and often degraded performance, even when differences between tensile and compressive failure properties were represented. The relatively strong performance of the distortion energy and tau(max) theories supports the hypothesis that shear/distortion is an important failure mode during femoral fracture.     

Sensitivity of damage predictions to tissue level yield properties and apparent loading conditions

High-resolution finite element models of trabecular bone failure could be used to augment current techniques for measuring damage in trabecular bone. However, the sensitivity of such models to the assumed tissue yield properties and apparent loading conditions is unknown. The goal of this study was to assess the sensitivity of the amount and mode (tension vs. compression) of tissue level yielding in trabecular bone to these factors. Linear elastic, high-resolution finite element models of nine bovine tibial trabecular bone specimens were used to calculate the fraction of the total tissue volume that exceeded each criterion for apparent level loading to the reported elastic limit in both on-axis and transverse compression and tension, and in shear. Four candidate yield criteria were studied, based on values suggested in the literature. Both the amount and the failure mode of yielded tissue were sensitive to the magnitudes of the tissue yield strains, the degree of tension-compression asymmetry of the yield criterion, and the applied apparent loads. The amount of yielded tissue was most sensitive to the orientation of the applied apparent loading, with the most tissue yielding for loading along the principal trabecular orientation and the least for loading perpendicular to it, regardless of the assumed tissue level yield criterion. Small changes in the magnitudes and the degree of asymmetry of the tissue yield criterion resulted in much larger changes in the amount of yielded tissue in the model. The results indicate that damage predictions based on high-resolution finite element models are highly sensitive to the assumed tissue yield properties. As such, good estimates of these values are needed before high-resolution finite element models can be applied to the study of trabecular bone damage. Regardless of the assumed tissue yield properties, the amount and type of damage that occurs in trabecular bone depends on the relative orientations of the applied apparent loads to the trabecular architecture, and this parameter should be controlled for both experimental and computational damage studies.     

Testing two predictions for fracture load using computer models of trabecular bone

Aging induces several types of architectural changes in trabecular bone including thinning, increased levels of anisotropy, and perforation. It has been determined, on the basis of analysis of mathematical models, that reduction in fracture load caused by perforation is significantly higher than those due to equivalent levels of thinning or anisotropy. The analysis has also provided an expression which relates the fractional reduction of strength tau to the fraction of elements nu that have been removed from a network. Further, it was proposed that the ratio Gamma of the elastic constant of a sample and its linear response at resonance can be used as a surrogate for tau. Experimental validation of these predictions requires following architectural changes in a given sample of trabecular bone; techniques to study such changes using microcomputed tomography are only beginning to be available. In the present study, we use anatomically accurate computer models constructed from digitized images of bone samples for the purpose. Images of healthy bone are subjected to successive levels of synthetic degradation via surface erosion. Computer models constructed from these images are used to calculate their fracture load and other mechanical properties. Results from these computations are shown to be consistent with predictions derived from the analysis of mathematical models. Although the form of tau(nu) is known, parameters in the expression are expected to be sample-specific, and hence nu is not a reliable predictor of strength. We provide an example to demonstrate this. In contrast, analysis of model networks shows that the linear part of tau(Gamma) depends only on the structure of trabecular bone. Computations on models constructed from samples of iliac crest trabecular bone are shown to be in agreement with this assertion. Since Gamma can be computed from a vibrational assessment of bone, we argue that the latter can be used to introduce new surrogates for bone strength and hence diagnostic tools for osteoporosis.     

Bone Strength in Growing Rats Treated with Fluoride: a Multi-dose Histomorphometric,Biomechanical and Densitometric Study

Bone deformation and fragility are common signs of skeletal fluorosis. Disorganisation of bone tissue and presence of inflammatory foci were observed after fluoride (F^?) administration. Most information about F^? effects on bone has been obtained in adult individuals. However, in fluorosis areas, children are a population very exposed to F^? and prone to develop not only dental but also skeletal fluoroses. The aim of this work was to evaluate the bone parameters responsible for the effect of different doses of F^? on fracture load of the trabecular and cortical bones using multivariate analysis in growing rats. Twenty-four 21-day-old Sprague-Dawley rats were divided into four groups: F0, F20, F40 and F80, which received orally 0, 20, 40 or 80 μmol F^?/100 g bw/day, respectively, for 30 days. After treatment, tibiae were used for measuring bone histomorphometric and connectivity parameters, bone mineral density (BMD) and bone cortical parameters. The femurs were used for biomechanical tests and bone F^? content. Trabecular bone volume was significantly decreased by F^?. Consistently, we observed a significant decrease in fracture load and Young’s modulus (YM) of the trabecular bone in F^?-treated groups. However, cortical bone parameters were not significantly affected by F^?. Moreover, there were no significant differences in cortical nor trabecular BMD. Multivariate analysis revealed a significant correlation between the trabecular fracture load and YM but not with bone volume or BMD. It is concluded that when F^? is administered as a single daily dose, it produces significant decrease in trabecular bone strength by changing the elasticity of the trabecular bone.     

Quantification of a rat tail vertebra model for trabecular bone adaptation studies

A feedback controlled loading apparatus for the rat tail vertebra was developed to deliver precise mechanical loads to the eighth caudal vertebra (C8) via pins inserted into adjacent vertebrae. Cortical bone strains were recorded using strain gages while subjecting the C8 in four cadaveric rats to mechanical loads ranging from 25 to 100 N at 1 Hz with a sinusoidal waveform. Finite element (FE) models, based on micro computed tomography, were constructed for all four C8 for calculations of cortical and trabecular bone tissue strains. The cortical bone strains predicted by FE models agreed with strain gage measurements, thus validating the FE models. The average measured cortical bone strain during 25-100 N loading was between 298 +/- 105 and 1210 +/- 297 microstrain (muepsilon). The models predicted average trabecular bone tissue strains ranging between 135 +/- 35 and 538 +/- 138 mu epsilon in the proximal region, 77 +/- 23-307 +/- 91 muepsilon in the central region, and 155 +/- 36-621 +/- 143 muepsilon in the distal region for 25-100 N loading range. Although these average strains were compressive, it is also interesting that the trabecular bone tissue strain can range from compressive to tensile strains (-1994 to 380 mu epsilon for a 100 N load). With this novel approach that combines an animal model with computational techniques, it could be possible to establish a quantitative relationship between the microscopic stress/strain environment in trabecular bone tissue, and the biosynthetic response and gene expression of bone cells, thereby study bone adaptation.     

Relationships between femoral fracture loads for two load configurations

Studies of proximal femoral strength usually involve one of two types of loading conditions, loading similar to joint loading during single-limb stance or loading simulating impact from a fall. When interpreting the results of studies involving only one of these load configurations, the question arises as to their applicability to the other configuration. In addition, it is desirable to know whether, for an individual bone, fracture load for one load configuration is indicative of fracture load for the other configuration. In this study, the relationship between proximal femoral fracture loads for single-limb stance loading and loading simulating impact from a type of fall was determined from mechanical testing of 17 matched pairs of human proximal femora. Fracture loads for these two configurations were found to be linearly related (r = 0.901, p < 0.001). However, the correlation between fracture loads is not notably stronger than correlations currently available between fracture load and measures of bone density and geometry. In addition, the regression results indicate that 81% of the variance in fracture load for one loading condition is accounted for by fracture load for the other loading condition. Thus, 19% of the variance remains unexplained, indicating that the results of studies involving only one load configuration are not necessarily indicative of those that would be found for another configuration.     

What humeri are suitable for comparative testing of suture anchors? An ultrastructural bone analysis and biomechanical study of ovine,bovine and human humeri and four different anchor types

For testing of fixation devices such as suture anchors used in rotator cuff repair often animal bones are used. They are easily obtained, inexpensive and some have been found to be similar to human bone. But can we rely on the results drawn from these studies in our daily surgical practice?The purpose of this study was to compare the trabecular bone mineral density, the trabecular bone volume fraction and the cortical layer thickness in the greater tubercle in different species to evaluate their influence on primary stability of suture anchors under a cyclic loading protocol representing the physiologic forces placed on rotator cuff repairs in vivo.Bovine and ovine humeri are not suitable for suture anchor testing. The statistical significances for pullout forces between the anchors varied from species to species. Therefore, no very applicable information can be obtained from testing suture anchors in ovine or bovine humeri with regard to ultimate failure loads in human humeri. The ultimate failure load seems to depend mainly on the cortical thickness and on the subcortical trabecular bone quality.     

An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

Interbody fusion device subsidence has been reported clinically. An enhanced understanding of the mechanical behaviour of the surrounding bone would allow for accurate predictions of vertebral subsidence. The multiaxial inelastic behaviour of trabecular bone is investigated at a microscale and macroscale level. The post-yield behaviour of trabecular bone under hydrostatic and confined compression is investigated using microcomputed tomography-derived microstructural models, elucidating a mechanism of pressure-dependent yielding at the macroscopic level. Specifically, microstructural trabecular simulations predict a distinctive yield point in the apparent stress–strain curve under uniaxial, confined and hydrostatic compression. Such distinctive apparent stress–strain behaviour results from localised stress concentrations and material yielding in the trabecular microstructure. This phenomenon is shown to be independent of the plasticity formulation employed at a trabecular level. The distinctive response can be accurately captured by a continuum model using a crushable foam plasticity formulation in which pressure-dependent yielding occurs. Vertebral device subsidence experiments are also performed, providing measurements of the trabecular plastic zone. It is demonstrated that a pressure-dependent plasticity formulation must be used for continuum level macroscale models of trabecular bone in order to replicate the experimental observations, further supporting the microscale investigations. Using a crushable foam plasticity formulation in the simulation of vertebral subsidence, it is shown that the predicted subsidence force and plastic zone size correspond closely with the experimental measurements. In contrast, the use of von Mises, Drucker–Prager and Hill plasticity formulations for continuum trabecular bone models lead to over prediction of the subsidence force and plastic zone.     

Failure modelling of trabecular bone using a non-linear combined damage and fracture voxel finite element approach

Trabecular bone tissue failure can be considered as consisting of two stages: damage and fracture; however, most failure analyses of 3D high-resolution trabecular bone samples are confined to damage mechanisms only, that is, without fracture. This study aims to develop a computational model of trabecular bone consisting of an explicit representation of complete failure, incorporating damage criteria, fracture criteria, cohesive forces, asymmetry and large deformation capabilities. Following parameter studies on a test specimen, and experimental testing of bone sample to complete failure, the asymmetric critical tissue damage and fracture strains of ovine vertebral trabecular bone were calibrated and validated to be compression damage ?1.16 %, tension damage 0.69 %, compression fracture ?2.91 % and tension fracture 1.98 %. Ultimate strength and post–ultimate strength softening were captured by the computational model, and the failure of individual struts in bending and shear was also predicted. This modelling approach incorporated a cohesive parameter that provided a facility to calibrate ductile–brittle behaviour of bone tissue in this non-linear geometric and non-linear constitutive property analyses tool. Finally, the full accumulation of tissue damage and tissue fracture has been monitored from range of small magnitude (normal daily loading) through to specimen yielding, ultimate strength and post–ultimate strength softening.