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.     

Femoral strength is better predicted by finite element models than QCT and DXA.

Clinicians and patients would benefit if accurate methods of predicting and monitoring bone strength in-vivo were available. A group of 51 human femurs (age range 21-93; 23 females, 28 males) were evaluated for bone density and geometry using quantitative computed tomography (QCT) and dual energy X-ray absorptiometry (DXA). Regional bone density and dimensions obtained from QCT and DXA were used to develop statistical models to predict femoral strength ex vivo. The QCT data also formed the basis of a three-dimensional finite element (FE) models to predict structural stiffness. The femurs were separated into two groups; a model training set (n = 25) was used to develop statistical models to predict ultimate load, and a test set (n = 26) was used to validate these models. The main goal of this study was to test the ability of DXA, QCT and FE techniques to predict fracture load non-invasively, in a simple load configuration which produces predominantly femoral neck fractures. The load configuration simulated the single stance phase portion of normal gait; in 87% of the specimens, clinical appearing sub-capital fractures were produced. The training/test study design provided a tool to validate that the predictive models were reliable when used on specimens with "unknown" strength characteristics. The FE method explained at least 20% more of the variance in strength than the DXA models. Planned refinements of the FE technique are expected to further improve these results. Three-dimensional FE models are a promising method for predicting fracture load, and may be useful in monitoring strength changes in vivo.     

Use of a statistical model of the whole femur in a large scale,multi-model study of femoral neck fracture risk

Interpatient variability is often overlooked in orthopaedic computational studies due to the substantial challenges involved in sourcing and generating large numbers of bone models. A statistical model of the whole femur incorporating both geometric and material property variation was developed as a potential solution to this problem. The statistical model was constructed using principal component analysis, applied to 21 individual computer tomography scans. To test the ability of the statistical model to generate realistic, unique, finite element (FE) femur models it was used as a source of 1000 femurs to drive a study on femoral neck fracture risk. The study simulated the impact of an oblique fall to the side, a scenario known to account for a large proportion of hip fractures in the elderly and have a lower fracture load than alternative loading approaches. FE model generation, application of subject specific loading and boundary conditions, FE processing and post processing of the solutions were completed automatically. The generated models were within the bounds of the training data used to create the statistical model with a high mesh quality, able to be used directly by the FE solver without remeshing. The results indicated that 28 of the 1000 femurs were at highest risk of fracture. Closer analysis revealed the percentage of cortical bone in the proximal femur to be a crucial differentiator between the failed and non-failed groups. The likely fracture location was indicated to be intertrochantic. Comparison to previous computational, clinical and experimental work revealed support for these findings.     

Development of a surrogate model based on patient weight,bone mass and geometry to predict femoral neck strains and fracture loads

Osteoporosis and related bone fractures are an increasing global burden in our ageing society. Areal bone mineral density assessed through dual energy X-ray absorptiometry (DEXA), the clinically accepted and most used method, is not sufficient to assess fracture risk individually. Finite element (FE) modelling has shown improvements in prediction of fracture risk, better than aBMD from DEXA, but is not practical for widespread clinical use. The aim of this study was to develop an adaptive neural network (ANN)-based surrogate model to predict femoral neck strains and fracture loads obtained from a previously developed population-based FE model. The surrogate model performance was assessed in simulating two loading conditions: the stance phase of gait and a fall.The surrogate model successfully predicted strains estimated by FE (r² = 0.90–0.98 for level gait load case, r² = 0.92–0.96 for the fall load case). Moreover, an ANN model based on three measurements obtainable in clinics (femoral neck length (level gait) or maximum femoral neck diameter (fall), femoral neck bone mass, body weight) was able to give reasonable predictions (r² = 0.84–0.94) for all of the strain metrics and the estimated femoral neck fracture load. Overall, the surrogate model has potential for clinical applications as they are based on simple measures of geometry and bone mass which can be derived from DEXA images, accurately predicting FE model outcomes, with advantages over FE models as they are quicker and easier to perform.     

Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur

Functional adaptation of the femur has been investigated in several studies by embedding bone remodelling algorithms in finite element (FE) models, with simplifications often made to the representation of bone’s material symmetry and mechanical environment. An orthotropic strain-driven adaptation algorithm is proposed in order to predict the femur’s volumetric material property distribution and directionality of its internal structures within a continuum. The algorithm was applied to a FE model of the femur, with muscles, ligaments and joints included explicitly. Multiple load cases representing distinct frames of two activities of daily living (walking and stair climbing) were considered. It is hypothesised that low shear moduli occur in areas of bone that are simply loaded and high shear moduli in areas subjected to complex loading conditions. In addition, it is investigated whether material properties of different femoral regions are stimulated by different activities. The loading and boundary conditions were considered to provide a physiological mechanical environment. The resulting volumetric material property distribution and directionalities agreed with ex vivo imaging data for the whole femur. Regions where non-orthogonal trabecular crossing has been documented coincided with higher values of predicted shear moduli. The topological influence of the different activities modelled was analysed. The influence of stair climbing on the properties of the femoral neck region is highlighted. It is recommended that multiple load cases should be considered when modelling bone adaptation. The orthotropic model of the complete femur is released with this study.     

Influence of the change in stem length on the load transfer and bone remodelling for a cemented resurfaced femur

The effect of a short-stem femoral resurfacing component on load transfer and potential failure mechanisms has rarely been studied. The stem length has been reduced by approximately 50% as compared to the current long-stem design. Using 3-D FE models of natural and resurfaced femurs, the study is aimed at investigating the influence of a short-stem resurfacing component on load transfer and bone remodelling. Applied loading conditions include normal walking and stair climbing. The mechanical role of the stem along with implant–cement and stem–bone contact conditions was observed to be crucial. Shortening the stem length to half of the current length (long-stem) led to several favourable effects, even though the stress distributions in the implant and the cement were similar in both the cases. The short-stem implant led not only to a more physiological stress distribution but also to bone apposition (increase of 20–70% bone density) in the superior resurfaced head, when the stem–bone contact prevailed. This also led to a reduction in strain concentration in the cancellous bone around the femoral neck–component junction. The normalised peak strain in this region was lower for the short-stem design as compared to that of the long-stem one, thereby reducing the initial risk of neck fracture. The effect of strain shielding (50–75% reduction) was restricted to a small bone volume underlying the cement, which was approximately half of that of the long-stem design. Consequently, bone resorption was considerably less for the short-stem design. The short-stem design offers better prospects than the long-stem resurfacing component.     

Sensitivity of periprosthetic stress-shielding to load and the bone density-modulus relationship in subject-specific finite element models

Subject-specific finite element (FE) computer models of the proximal femur in hip replacement could potentially predict stress-shielding and subsequent bone loss in individual patients. Before such predictions can be made, it is important first to determine if between subject differences in stress-shielding are sensitive to poorly defined parameters such as the load and the bone material properties. In this study we investigate if subject-specific FE models provide consistent stress-shielding patterns in the bone, independent of the choice of the loading conditions and the bone density-modulus relationship used in the computer model. FE models of two right canine femurs with and without implants were constructed based on contiguous computed tomography (CT) scans so that subject-specific estimates of stress-shielding could be calculated. Four different loading conditions and two bone density-modulus relationships were tested. Stress-shielding was defined as the decrease of strain energy per gram bone mass in the femur with the implant in place relative to the intact femur.The analyses showed that for the four loading conditions and two bone density-modulus relationships the difference in stress-shielding between the two subjects was essentially constant (1% variation) when the same loading condition and density-modulus relationship was used for both subjects. The severity of stress-shielding within a subject was sensitive to these input parameters, varying up to 20% in specific regions with a change in loading conditions and up to 10% for a change in the assumed density-modulus relationship. We conclude that although the choice of input parameters can substantially affect stress-shielding in an individual, this choice had virtually no effect on the relative differences in femoral periprosthetic stress-shielding between individuals. Thus, while care should be taken in the interpretation of the absolute value of stress-shielding calculated with these type of models, subject-specific FE models may be useful for explaining the variation in bone adaptation responsiveness between different subjects in experimental or clinical studies.     

Prediction of femoral strength using 3D finite element models reconstructed from DXA images: validation against experiments

Computed tomography (CT)-based finite element (FE) models may improve the current osteoporosis diagnostics and prediction of fracture risk by providing an estimate for femoral strength. However, the need for a CT scan, as opposed to the conventional use of dual-energy X-ray absorptiometry (DXA) for osteoporosis diagnostics, is considered a major obstacle. The 3D shape and bone mineral density (BMD) distribution of a femur can be reconstructed using a statistical shape and appearance model (SSAM) and the DXA image of the femur. Then, the reconstructed shape and BMD could be used to build FE models to predict bone strength. Since high accuracy is needed in all steps of the analysis, this study aimed at evaluating the ability of a 3D FE model built from one 2D DXA image to predict the strains and fracture load of human femora. Three cadaver femora were retrieved, for which experimental measurements from ex vivo mechanical tests were available. FE models were built using the SSAM-based reconstructions: using only the SSAM-reconstructed shape, only the SSAM-reconstructed BMD distribution, and the full SSAM-based reconstruction (including both shape and BMD distribution). When compared with experimental data, the SSAM-based models predicted accurately principal strains (coefficient of determination >0.83, normalized root-mean-square error <16%) and femoral strength (standard error of the estimate 1215 N). These results were only slightly inferior to those obtained with CT-based FE models, but with the considerable advantage of the models being built from DXA images. In summary, the results support the feasibility of SSAM-based models as a practical tool to introduce FE-based bone strength estimation in the current fracture risk diagnostics.     

The effect of boundary condition on the biomechanics of a human pelvic joint under an axial compressive load: a three-dimensional finite element model

The finite element (FE) model of the pelvic joint is helpful for clinical diagnosis and treatment of pelvic injuries. However, the effect of an FE model boundary condition on the biomechanical behavior of a pelvic joint has not been well studied. The objective of this study was to study the effect of boundary condition on the pelvic biomechanics predictions. A 3D FE model of a pelvis using subject-specific estimates of intact bone structures, main ligaments and bone material anisotropy by computed tomography (CT) gray value was developed and validated by bone surface strains obtained from rosette strain gauges in an in vitro pelvic experiment. Then three FE pelvic models were constructed to analyze the effect of boundary condition, corresponding to an intact pelvic joint, a pelvic joint without sacroiliac ligaments and a pelvic joint without proximal femurs, respectively. Vertical load was applied to the same pelvis with a fixed prosthetic femoral stem and the same load was simulated in the FE model. A strong correlation coefficient (R(2)=0.9657) was calculated, which indicated a strong correlation between the FE analysis and experimental results. The effect of boundary condition changes on the biomechanical response depended on the anatomical location and structure of the pelvic joint. It was found that acetabulum fixed in all directions with the femur removed can increase the stress distribution on the acetabular inner plate (approximately double the original values) and decrease that on the superior of pubis (from 7 MPa to 0.6 MPa). Taking sacrum and ilium as a whole, instead of sacroiliac and iliolumber ligaments, can influence the stress distribution on ilium and pubis bone vastly. These findings suggest pelvic biomechanics is very dependent on the boundary condition in the FE model.     

Load transfer analysis of the distal radius from in-vivo high-resolution CT-imaging.

Prevention of osteoporotic bone fractures requires accurate diagnostic methods to detect the increase in bone fragility at an early stage of osteoporosis. However, today's bone fracture risk prediction, primarily based on bone density measurement, is not sufficiently precise. There is increasing evidence that, in addition to bone density, also the bone microarchitecture and its mechanical loading conditions are important factors determining the fracture risk. Recently, it has been shown that new high-resolution imaging techniques in combination with new computer modeling techniques based on the finite-element (FE) method can account for these additional factors. These techniques might provide information that is more relevant for the prediction of bone fracture risk. So far, however, these new imaged-based FE techniques have not been feasible in-vivo. The objectives of this study were to quantify the load transfer through the trabecular network in a distal radius using a computer model based on in-vivo high-resolution images and to determine if common regions of fractures can be explained as a result of high tissue loading in these regions. The left distal radius and the two adjacent carpal bones of a healthy volunteer were imaged using a high-resolution three-dimensional CT system providing an isotropic resolution of 165 microm. The bone representation was converted into a FE-model that was used to calculate stresses and strains in the trabecular network. The two carpal bones were loaded using different load ratios (for each load case 1000 N in total) representing impact forces on the hand either in near-neutral position or ulnar/radial deviation. The load transfer through the trabecular network of the radius was characterized by the tissue strain energy density (SED) distribution for all load cases. It was found that the distribution of the tissue loading depends on the ratio of the forces acting on the carpal bones. For all load cases the higher SED values (on average: 0.02 +/- 0.08 (S.D.) N mm(-2)) are found in a 10 mm region adjacent to the articular surface which corresponds well with the region where Colles- or Chauffeur-fractures occur. We expect that, eventually, this new approach can lead to a better prediction of the fracture risk than methods based on bone density alone since it accounts for the bone microstructure as well as its loading conditions.     

Stiffening of the femoral head due to inter-trabecular fluid and intraosseous pressure

The mechanical properties of cancellous bone, as measured from bone plug samples have been widely documented. However, few tests have been attempted to explore the effects the intertrabecular contents may have on the load bearing capabilities. In this study, canine femoral heads were subjected to dynamic compressive strain cycles. The femoral heads were tested intact, as well as with disrupted boundary conditions of the continuous, intraosseous fluid space. A significant reduction in mechanical stiffness was observed when the fluid compartment boundary was disrupted by drilling a hole part way into the femoral neck. A finite element model of a typical femoral head showed that the stiffness change was not due to removal of material from the neck, hydraulic effects notwithstanding. Refilling the hole in the neck with saline solution and sealing the boundary restored the stiffness to the intact baseline level. However, an increase in the fluid pressure did not cause a statistically significant increase in the stiffness of the femoral head.     

Off-axis loads cause failure of the distal radius at lower magnitudes than axial loads: a finite element analysis

Distal radius (Colles') fractures are a common fall-related injury in older adults and frequently result in long-term pain and reduced ability to perform activities of daily living. Because the occurrence of a fracture during a fall depends on both the strength of the bone and upon the kinematics and kinetics of the impact itself, we sought to understand how changes in bone mineral density (BMD) and loading direction affect the fracture strength and fracture initiation location in the distal radius. A three-dimensional finite element model of the radius, scaphoid, and lunate was used to examine changes of +/-2% and +/-4% BMD, and both axial and physiologically relevant off-axis loads on the radius. Changes in BMD resulted in similar percent changes in fracture strength. However, modifying the applied load to include dorsal and lateral components (assuming a dorsal view of the wrist, rather than an anatomic view) resulted in a 47% decrease in fracture strength (axial failure load: 2752N, off-axis: 1448N). Loading direction also influenced the fracture initiation site. Axially loaded radii failed on the medial surface immediately proximal to the styloid process. In contrast, off-axis loads, containing dorsal and lateral components, caused failure on the dorsal-lateral surface. Because the radius appears to be very sensitive to loading direction, the results suggest that much of the variability in fracture strength seen in cadaver studies may be attributed to varying boundary conditions. The results further suggest that interventions focused on reducing the incidence of Colles' fractures when falls onto the upper extremities are unavoidable may benefit from increasing the extent to which the radius is loaded along its axis.     

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.     

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.     

Trabecular Bone Adaptation to Low-Magnitude High-Frequency Loading in Microgravity

Exposure to microgravity causes loss of lower body bone mass in some astronauts. Low-magnitude high-frequency loading can stimulate bone formation on earth. Here we hypothesized that low-magnitude high-frequency loading will also stimulate bone formation under microgravity conditions. Two groups of six bovine cancellous bone explants were cultured at microgravity on a Russian Foton-M3 spacecraft and were either loaded dynamically using a sinusoidal curve or experienced only a static load. Comparable reference groups were investigated at normal gravity. Bone structure was assessed by histology, and mechanical competence was quantified using μCT and FE modelling; bone remodelling was assessed by fluorescent labelling and secreted bone turnover markers. Statistical analyses on morphometric parameters and apparent stiffness did not reveal significant differences between the treatment groups. The release of bone formation marker from the groups cultured at normal gravity increased significantly from the first to the second week of the experiment by 90.4% and 82.5% in response to static and dynamic loading, respectively. Bone resorption markers decreased significantly for the groups cultured at microgravity by 7.5% and 8.0% in response to static and dynamic loading, respectively. We found low strain magnitudes to drive bone turnover when applied at high frequency, and this to be valid at normal as well as at microgravity. In conclusion, we found the effect of mechanical loading on trabecular bone to be regulated mainly by an increase of bone formation at normal gravity and by a decrease in bone resorption at microgravity. Additional studies with extended experimental time and increased samples number appear necessary for a further understanding of the anabolic potential of dynamic loading on bone quality and mechanical competence.     

Development of a finite element model of the tibia for short-duration high-force axial impact loading

Finite element (FE) models can allow computer simulations of impact loading, providing a useful companion to cadaveric testing. These models allow injury evaluations to be conducted under a variety of conditions, but must be validated against experimental data. An FE model of a cadaveric tibia was developed using geometry from CT scans, and the quality of the mesh was evaluated. Loading and boundary conditions from experimental tests were simulated, and the model was optimised to best represent the response of natural bone to impacts. The model was shown to have good agreement for impact force, duration, impulse and strain during simulation of three non-injurious and one injurious axial impact when compared with experimental test data for the specimen. Failure criteria were evaluated for their ability to predict fracture. This model of the tibia can be used for future injury prediction assessment studies.     

Personalized loading conditions for homogenized finite element analysis of the distal sections of the radius

The microstructure of trabecular bone is known to adapt its morphology in response to mechanical loads for achieving a biomechanical homeostasis. Based on this form–function relationship, previous investigators either simulated the remodeling of bone to predict the resulting density and architecture for a specific loading or retraced physiological loading conditions from local density and architecture. The latter inverse approach includes quantifying bone morphology using computed tomography and calculating the relative importance of selected load cases by minimizing the fluctuation of a tissue loading level metric. Along this concept, the present study aims at identifying an optimal, personalized, multiaxial load case at the distal section of the human radius using in vivo HR-pQCT-based isotropic, homogenized finite element (hFE) analysis. The dataset consisted of HR-pQCT reconstructions of the 20 mm most distal section of 21 human fresh-frozen radii. We simulated six different unit canonical load cases (FX palmar–dorsal force, FY ulnar–radial force, FZ distal–proximal force, MX moment about palmar–dorsal, MY moment about ulnar–radial, MZ moment about distal–proximal) using a simplified and efficient hFE method based on a single isotropic bone phase. Once we used a homogeneous mean density (shape model) and once the original heterogeneous density distribution (shape + density model). Using an analytical formulation, we minimized the deviation of the resulting strain tensors ε(x) to a hydrostatic compressive reference strain ε₀, once for the 6 degrees of freedom (DOF) optimal (OPT) load case and for all individual 1 DOF load cases (FX, FY, FZ, MX, MY, MZ). All seven load cases were then extended in the nonlinear regime using the scaled displacements of the linear load cases as loading boundary conditions (MAX). We then compared the load cases and models for their objective function (OF) values, the stored energies and their ultimate strength using a specific torsor norm. Both shape and shape + density linear-optimized OPT models were dominated by a positive force in the z-direction (FZ). Transversal force DOFs were close to zero and mean moment DOFs were different depending on the model type. The inclusion of density distribution increased the influence and changed direction of MX and MY, while MZ was small in both models. The OPT load case had 12–15% lower objective function (OF) values than the FZ load case, depending on the model. Stored energies at the optimum were consistently 142–178% higher for the OPT load case than for the FZ load case. Differences in the nonlinear response maximum torsor norm ‖t‖ were heterogeneous, but consistently higher for OPT_MAX than FZ_MAX. We presented the proof of concept of an optimization procedure to estimate patient-specific loading conditions for hFE methods. In contrast to similar models, we included canonical load cases in all six DOFs and used a strain metric that favors hydrostatic compression. Based on a biomechanical analysis of the distal joint surfaces at the radius, the estimated load directions are plausible. For our dataset, the resulting OPT load case is close to the standard axial compression boundary conditions, usually used in HR-pQCT-based FE analysis today. But even using the present simplified hFE model, the optimized linear six DOF load case achieves a more homogeneous tissue loading and can absorb more than twice the energy than the standard uniaxial load case. The ultimate strength calculated with a torsor norm was consistently higher for the 6-DOF nonlinear model (OPT_MAX) than for the 1-DOF nonlinear uniaxial model (FZ_MAX). Defining patient-specific boundary conditions may decrease angulation errors during CT measurements and improve repeatability as well as reproducibility of bone stiffness and strength estimated by HR-pQCT-based hFE analysis. These results encourage the extension of the present method to anisotropic hFE models and their application to repeatability data sets to test the hypothesis of reduced angulation errors during measurement.

     

Incorporating uncertainty in mechanical properties for finite element-based evaluation of bone mechanics

Finite element (FE) models of bone, developed from computed tomography (CT) scan data, are used to evaluate stresses and strains, load transfer and fixation of implants, and potential for fracture. The experimentally derived relationships used to transform CT scan data in Hounsfield unit to modulus and strength contain substantial scatter. The scatter in these relationships has potential to impact the results and conclusions of bone studies. The objectives of this study were to develop a computationally efficient probabilistic FE-based platform capable of incorporating uncertainty in bone property relationships, and to apply the model to a representative analysis; variability in stresses and fracture risk was predicted in five proximal femurs under stance loading conditions. Based on published variability in strength and modulus relationships derived in the proximal femur, the probabilistic analysis predicted the distributions of stress and risk. For the five femurs analyzed, the 1 and 99 percentile bounds varied by an average of 17.3 MPa for stress and by 0.28 for risk. In each femur, the predicted variability in risk was greater than 50% of the mean risk calculated, with obvious implications for clinical assessment. Results using the advanced mean value (AMV) method required only seven analysis trials (1h) and differed by less than 2% when compared to a 1000-trial Monte-Carlo simulation (400 h). The probabilistic modeling platform developed has broad applicability to bone studies and can be similarly implemented to investigate other loading conditions, structures, sources of uncertainty, or output measures of interest.     

Physiologically based boundary conditions in finite element modelling

Finite element analysis has been used extensively in the study of bone loading and implant performance, such as in the femur. The boundary conditions applied vary widely, generally producing excessive femoral deformation, and although it has been shown that the muscle forces influence femoral deflections and loading, little consideration has been given to the displacement constraints. It is hypothesised that careful application of physiologically based constraints can produce physiological deformation, and therefore straining, of the femur. Joint contact forces and a complete set of muscle forces were calculated based on the geometry of the Standardised Femur using previously validated musculoskeletal models. Five boundary condition cases were applied to a finite element model of the Standardised Femur: (A) diaphyseally constrained with hip contact and abductor forces; (B) case A plus vasti forces; (C) case A with complete set of muscle forces; (D) distally constrained with all muscle forces; (E) physiological constraints with all muscle forces. It was seen that only the physiological boundary conditions, case E, produced physiological deflections (< 2.0mm) of the femoral head in both the coronal and sagittal planes, which resulted in minimal reaction forces at the constrained nodes. Strains in the mid-diaphysis varied by up to 600 micro-strain under walking loads and 1000 micro-strain under stair climbing loads. The mode of loading, as indicated by the strain profiles on the cortex also varied substantially under these boundary conditions, which has important consequences for studies that examine localised bone loading such as fracture or bone remodelling simulations.     

Embedding of human vertebral bodies leads to higher ultimate load and altered damage localisation under axial compression

Computer tomography (CT)-based finite element (FE) models of vertebral bodies assess fracture load in vitro better than dual energy X-ray absorptiometry, but boundary conditions affect stress distribution under the endplates that may influence ultimate load and damage localisation under post-yield strains. Therefore, HRpQCT-based homogenised FE models of 12 vertebral bodies were subjected to axial compression with two distinct boundary conditions: embedding in polymethylmethalcrylate (PMMA) and bonding to a healthy intervertebral disc (IVD) with distinct hyperelastic properties for nucleus and annulus. Bone volume fraction and fabric assessed from HRpQCT data were used to determine the elastic, plastic and damage behaviour of bone. Ultimate forces obtained with PMMA were 22% higher than with IVD but correlated highly (R² = 0.99). At ultimate force, distinct fractions of damage were computed in the endplates (PMMA: 6%, IVD: 70%), cortex and trabecular sub-regions, which confirms previous observations that in contrast to PMMA embedding, failure initiated underneath the nuclei in healthy IVDs. In conclusion, axial loading of vertebral bodies via PMMA embedding versus healthy IVD overestimates ultimate load and leads to distinct damage localisation and failure pattern.