Subject-specific finite element model of the pelvis: development, validation and sensitivity studies

A better understanding of the three-dimensional mechanics of the pelvis, at the patient-specific level, may lead to improved treatment modalities. Although finite element (FE) models of the pelvis have been developed, validation by direct comparison with subject-specific strains has not been performed, and previous models used simplifying assumptions regarding geometry and material properties. The objectives of this study were to develop and validate a realistic FE model of the pelvis using subject-specific estimates of bone geometry, location-dependent cortical thickness and trabecular bone elastic modulus, and to assess the sensitivity of FE strain predictions to assumptions regarding cortical bone thickness as well as bone and cartilage material properties. A FE model of a cadaveric pelvis was created using subject-specific computed tomography image data. Acetabular loading was applied to the same pelvis using a prosthetic femoral stem in a fashion that could be easily duplicated in the computational model. Cortical bone strains were monitored with rosette strain gauges in ten locations on the left hemipelvis. FE strain predictions were compared directly with experimental results for validation. Overall, baseline FE predictions were strongly correlated with experimental results (r2=0.824), with a best-fit line that was not statistically different than the line y=x (experimental strains = FE predicted strains). Changes to cortical bone thickness and elastic modulus had the largest effect on cortical bone strains. The FE model was less sensitive to changes in all other parameters. The methods developed and validated in this study will be useful for creating and analyzing patient-specific FE models to better understand the biomechanics of the pelvis.     

The biomechanics of human femurs in axial and torsional loading: comparison of finite element analysis, human cadaveric femurs, and synthetic femurs

To assess the performance of femoral orthopedic implants, they are often attached to cadaveric femurs, and biomechanical testing is performed. To identify areas of high stress, stress shielding, and to facilitate implant redesign, these tests are often accompanied by finite element (FE) models of the bone/implant system. However, cadaveric bone suffers from wide specimen to specimen variability both in terms of bone geometry and mechanical properties, making it virtually impossible for experimental results to be reproduced. An alternative approach is to utilize synthetic femurs of standardized geometry, having material behavior approximating that of human bone, but with very small specimen to specimen variability. This approach allows for repeatable experimental results and a standard geometry for use in accompanying FE models. While the synthetic bones appear to be of appropriate geometry to simulate bone mechanical behavior, it has not, however, been established what bone quality they most resemble, i.e., osteoporotic or osteopenic versus healthy bone. Furthermore, it is also of interest to determine whether FE models of synthetic bones, with appropriate adjustments in input material properties or geometric size, could be used to simulate the mechanical behavior of a wider range of bone quality and size. To shed light on these questions, the axial and torsional stiffness of cadaveric femurs were compared to those measured on synthetic femurs. A FE model, previously validated by the authors to represent the geometry of a synthetic femur, was then used with a range of input material properties and change in geometric size, to establish whether cadaveric results could be simulated. Axial and torsional stiffnesses and rigidities were measured for 25 human cadaveric femurs (simulating poor bone stock) and three synthetic "third generation composite" femurs (3GCF) (simulating normal healthy bone stock) in the midstance orientation. The measured results were compared, under identical loading conditions, to those predicted by a previously validated three-dimensional finite element model of the 3GCF at a variety of Young's modulus values. A smaller FE model of the 3GCF was also created to examine the effects of a simple change in bone size. The 3GCF was found to be significantly stiffer (2.3 times in torsional loading, 1.7 times in axial loading) than the presently utilized cadaveric samples. Nevertheless, the FE model was able to successfully simulate both the behavior of the 3GCF, and a wide range of cadaveric bone data scatter by an appropriate adjustment of Young's modulus or geometric size. The synthetic femur had a significantly higher stiffness than the cadaveric bone samples. The finite element model provided a good estimate of upper and lower bounds for the axial and torsional stiffness of human femurs because it was effective at reproducing the geometric properties of a femur. Cadaveric bone experiments can be used to calibrate FE models' input material properties so that bones of varying quality can be simulated.     

Validation and application of an intervertebral disc finite element model utilizing independently constructed tissue-level constitutive formulations that are nonlinear,anisotropic, and time-dependent

Finite element (FE) models are advantageous in the study of intervertebral disc mechanics as the stress–strain distributions can be determined throughout the tissue and the applied loading and material properties can be controlled and modified. However, the complicated nature of the disc presents a challenge in developing an accurate and predictive disc model, which has led to limitations in FE geometry, material constitutive models and properties, and model validation. The objective of this study was to develop a new FE model of the intervertebral disc, to validate the model?s nonlinear and time-dependent responses without tuning or calibration, and to evaluate the effect of changes in nucleus pulposus (NP), cartilaginous endplate (CEP), and annulus fibrosus (AF) material properties on the disc mechanical response. The new FE disc model utilized an analytically-based geometry. The model was created from the mean shape of human L4/L5 discs, measured from high-resolution 3D MR images and averaged using signed distance functions. Structural hyperelastic constitutive models were used in conjunction with biphasic-swelling theory to obtain material properties from recent tissue tests in confined compression and uniaxial tension. The FE disc model predictions fit within the experimental range (mean±95% confidence interval) of the disc?s nonlinear response for compressive slow loading ramp, creep, and stress-relaxation simulations. Changes in NP and CEP properties affected the neutral-zone displacement but had little effect on the final stiffness during slow-ramp compression loading. These results highlight the need to validate FE models using the disc?s full nonlinear response in multiple loading scenarios.     

The influence of material property and morphological parameters on specimen-specific finite element models of porcine vertebral bodies

The use of finite element (FE) methods in spinal research is increasing, but there is only limited information available on the influence of different input parameters on the model predictions. The aim of this study was to investigate the role of these parameters in FE models of the vertebral body. Experimental tests were undertaken on porcine lumbar vertebral bodies and scans of the specimens were used to create specimen-specific FE models. Three models were created for each specimen with combinations of generic and specimen-specific parameters. Stiffness and strength predictions were also made directly from the specimen trabecular bone volume fraction (BVF) and cross-sectional area (CSA). The agreement between the experimental results and the FE models with generic morphology was poorer (concordance coefficients = 0.058, 0.125 for stiffness, strength) than those made from the BVF and CSA (concordance coefficients = 0.638, 0.609). The greatest levels of agreement were found with the morphologically specific models including element-specific material properties (concordance coefficients = 0.881, 0.752). This indicates that highly specific models, both in terms of morphology and bone quality, are necessary if the FE tool is to be used effectively for spinal research and clinical practice.     

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.     

Finite element model development of a child pelvis with optimization-based material identification

A finite element (FE) model of a 10-years-old child pelvis was developed and validated against experimental data from lateral impacts of pediatric pelves. The pelvic bone geometry was reconstructed from a set of computed tomography images, and a hexahedral mesh was generated using a new octree-based hexahedral meshing technique. Lateral impacts to the greater trochanter and iliac wing of the seated pelvis were simulated. Sensitivity analysis was conducted to identify material parameters that substantially affected the model response. An optimization-based material identification method was developed to obtain the most favorable material property set by minimizing differences in biomechanical responses between experimental and simulation results. This study represents a pilot effort in the development and validation of age-dependent musculoskeletal FE models for children, which may ultimately serve to evaluate injury mechanisms and means of protection for the pediatric population.     

Quantifying nonlinear anisotropic elastic material properties of biological tissue by use of membrane inflation

Determination of material parameters for soft tissue frequently involves regression of material parameters for nonlinear, anisotropic constitutive models against experimental data from heterogeneous tests. Here, parameter estimation based on membrane inflation is considered. A four parameter nonlinear, anisotropic hyperelastic strain energy function was used to model the material, in which the parameters are cast in terms of key response features. The experiment was simulated using finite element (FE) analysis in order to predict the experimental measurements of pressure versus profile strain. Material parameter regression was automated using inverse FE analysis; parameter values were updated by use of both local and global techniques, and the ability of these techniques to efficiently converge to a best case was examined. This approach provides a framework in which additional experimental data, including surface strain measurements or local structural information, may be incorporated in order to quantify heterogeneous nonlinear material properties.     

Model sensitivity and use of the comparative finite element method in mammalian jaw mechanics: mandible performance in the gray wolf

Finite Element Analysis (FEA) is a powerful tool gaining use in studies of biological form and function. This method is particularly conducive to studies of extinct and fossilized organisms, as models can be assigned properties that approximate living tissues. In disciplines where model validation is difficult or impossible, the choice of model parameters and their effects on the results become increasingly important, especially in comparing outputs to infer function. To evaluate the extent to which performance measures are affected by initial model input, we tested the sensitivity of bite force, strain energy, and stress to changes in seven parameters that are required in testing craniodental function with FEA. Simulations were performed on FE models of a Gray Wolf (Canis lupus) mandible. Results showed that unilateral bite force outputs are least affected by the relative ratios of the balancing and working muscles, but only ratios above 0.5 provided balancing-working side joint reaction force relationships that are consistent with experimental data. The constraints modeled at the bite point had the greatest effect on bite force output, but the most appropriate constraint may depend on the study question. Strain energy is least affected by variation in bite point constraint, but larger variations in strain energy values are observed in models with different number of tetrahedral elements, masticatory muscle ratios and muscle subgroups present, and number of material properties. These findings indicate that performance measures are differentially affected by variation in initial model parameters. In the absence of validated input values, FE models can nevertheless provide robust comparisons if these parameters are standardized within a given study to minimize variation that arise during the model-building process. Sensitivity tests incorporated into the study design not only aid in the interpretation of simulation results, but can also provide additional insights on form and function.     

Comparison of deformable and elastic foundation finite element simulations for predicting knee replacement mechanics

Rigid body total knee replacement (TKR) models with tibiofemoral contact based on elastic foundation (EF) theory utilize simple contact pressure-surface overclosure relationships to estimate joint mechanics, and require significantly less computational time than corresponding deformable finite element (FE) methods. However, potential differences in predicted kinematics between these representations are currently not well understood, and it is unclear if the estimates of contact area and pressure are acceptable. Therefore, the objectives of the current study were to develop rigid EF and deformable FE models of tibiofemoral contact, and to compare predicted kinematics and contact mechanics from both representations during gait loading conditions with three different implant designs. Linear and nonlinear contact pressure-surface overclosure relationships based on polyethylene material properties were developed using EF theory. All other variables being equal, rigid body FE models accurately estimated kinematics predicted by fully deformable FE models and required only 2% of the analysis time. As expected, the linear EF contact model sufficiently approximated trends for peak contact pressures, but overestimated the deformable results by up to 30%. The nonlinear EF contact model more accurately reproduced trends and magnitudes of the deformable analysis, with maximum differences of approximately 15% at the peak pressures during the gait cycle. All contact area predictions agreed in trend and magnitude. Using rigid models, edge-loading conditions resulted in substantial overestimation of peak pressure. Optimal nonlinear EF contact relationships were developed for specific TKR designs for use in parametric or repetitive analyses where computational time is paramount. The explicit FE analysis method utilized here provides a unique approach in that both rigid and deformable analyses can be run from the same input file, thus enabling simple selection of the most appropriate representation for the analysis of interest.     

Finite element modelling approaches for well-ordered porous metallic materials for orthopaedic applications: cost effectiveness and geometrical considerations

The mechanical properties of well-ordered porous materials are related to their geometrical parameters at the mesoscale. Finite element (FE) analysis is a powerful tool to design well-ordered porous materials by analysing the mechanical behaviour. However, FE models are often computationally expensive. This article aims to develop a cost-effective FE model to simulate well-ordered porous metallic materials for orthopaedic applications. Solid and beam FE modelling approaches are compared, using finite size and infinite media models considering cubic unit cell geometry. The model is then applied to compare two unit cell geometries: cubic and diamond. Models having finite size provide similar results than the infinite media model approach for large sample sizes. In addition, these finite size models also capture the influence of the boundary conditions on the mechanical response for small sample sizes. The beam FE modelling approach showed little computational cost and similar results to the solid FE modelling approach. Diamond unit cell geometry appeared to be more suitable for orthopaedic applications than the cubic unit cell geometry.     

MRI-based finite-element analysis of left ventricular aneurysm

Tagged MRI and finite-element (FE) analysis are valuable tools in analyzing cardiac mechanics. To determine systolic material parameters in three-dimensional stress-strain relationships, we used tagged MRI to validate FE models of left ventricular (LV) aneurysm. Five sheep underwent anteroapical myocardial infarction (25% of LV mass) and 22 wk later underwent tagged MRI. Asymmetric FE models of the LV were formed to in vivo geometry from MRI and included aneurysm material properties measured with biaxial stretching, LV pressure measurements, and myofiber helix angles measured with diffusion tensor MRI. Systolic material parameters were determined that enabled FE models to reproduce midwall, systolic myocardial strains from tagged MRI (630 +/- 187 strain comparisons/animal). When contractile stress equal to 40% of the myofiber stress was added transverse to the muscle fiber, myocardial strain agreement improved by 27% between FE model predictions and experimental measurements (RMS error decreased from 0.074 +/- 0.016 to 0.054 +/- 0.011, P < 0.05). In infarct border zone (BZ), end-systolic midwall stress was elevated in both fiber (24.2 +/- 2.7 to 29.9 +/- 2.4 kPa, P < 0.01) and cross-fiber (5.5 +/- 0.7 to 11.7 +/- 1.3 kPa, P = 0.02) directions relative to noninfarct regions. Contrary to previous hypotheses but consistent with biaxial stretching experiments, active cross-fiber stress development is an integral part of LV systole; FE analysis with only uniaxial contracting stress is insufficient. Stress calculations from these validated models show 24% increase in fiber stress and 115% increase in cross-fiber stress at the BZ relative to remote regions, which may contribute to LV remodeling.     

Development and validation of a subject-specific finite element model of a human clavicle

This study aimed to develop and validate a finite element (FE) model of a human clavicle which can predict the structural response and bone fractures under both axial compression and anterior–posterior three-point bending loads. Quasi-static non-injurious axial compression and three-point bending tests were first conducted on a male clavicle followed by a dynamic three-point bending test to fracture. Then, two types of FE models of the clavicle were developed using bone material properties which were set to vary with the computed tomography image density of the bone. A volumetric solid FE model comprised solely of hexahedral elements was first developed. A solid-shell FE model was then created which modelled the trabecular bone as hexahedral elements and the cortical bone as quadrilateral shell elements. Finally, simulations were carried out using these models to evaluate the influence of variations in cortical thickness, mesh density, bone material properties and modelling approach on the biomechanical responses of the clavicle, compared with experimental data. The FE results indicate that the inclusion of density-based bone material properties can provide a more accurate reproduction of the force–displacement response and bone fracture timing than a model with uniform bone material properties. Inclusion of a variable cortical thickness distribution also slightly improves the ability of the model to predict the experimental response. The methods developed in this study will be useful for creating subject-specific FE models to better understand the biomechanics and injury mechanism of the clavicle.     

Validation of an efficient method of assigning material properties in finite element analysis of pelvic bone

Bone in the pelvis is a composite material with a complex anatomical structure that is difficult to model computationally. Rather than assigning material properties to increasingly smaller elements to capture detail in three-dimensional finite element (FE) models, properties can be assigned to Gauss points within larger elements. As part of a validation process, we compared experimental and analytical results from a composite beam under four-point load to FE models with material properties assigned to refined elements and Gauss points within larger elements. Both FE models accurately predicted deformation and the analytical predictions of internal shear stress.     

A novel methodology for generating 3D finite element models of the hip from 2D radiographs

Finite element (FE) modelling has been proposed as a tool for estimating fracture risk and patient-specific FE models are commonly based on computed tomography (CT). Here, we present a novel method to automatically create personalised 3D models from standard 2D hip radiographs. A set of geometrical parameters of the femur were determined from seven a–p hip radiographs and compared to the 3D femoral shape obtained from CT as training material; the error in reconstructing the 3D model from the 2D radiographs was assessed. Using the geometry parameters as the input, the 3D shape of another 21 femora was built and meshed, separating a cortical and trabecular compartment. The material properties were derived from the homogeneity index assessed by texture analysis of the radiographs, with focus on the principal tensile and compressive trabecular systems. The ability of these FE models to predict failure load as determined by experimental biomechanical testing was evaluated and compared to the predictive ability of DXA. The average reconstruction error of the 3D models was 1.77 mm (±1.17 mm), with the error being smallest in the femoral head and neck, and greatest in the trochanter. The correlation of the FE predicted failure load with the experimental failure load was r²=64% for the reconstruction FE model, which was significantly better (p<0.05) than that for DXA (r²=24%). This novel method for automatically constructing a patient-specific 3D finite element model from standard 2D radiographs shows encouraging results in estimating patient-specific failure loads.     

Effects of idealized joint geometry on finite element predictions of cartilage contact stresses in the hip

Computational models may have the ability to quantify the relationship between hip morphology, cartilage mechanics and osteoarthritis. Most models have assumed the hip joint to be a perfect ball and socket joint and have neglected deformation at the bone-cartilage interface. The objective of this study was to analyze finite element (FE) models of hip cartilage mechanics with varying degrees of simplified geometry and a model with a rigid bone material assumption to elucidate the effects on predictions of cartilage stress. A previously validated subject-specific FE model of a cadaveric hip joint was used as the basis for the models. Geometry for the bone-cartilage interface was either: (1) subject-specific (i.e. irregular), (2) spherical, or (3) a rotational conchoid. Cartilage was assigned either a varying (irregular) or constant thickness (smoothed). Loading conditions simulated walking, stair-climbing and descending stairs. FE predictions of contact stress for the simplified models were compared with predictions from the subject-specific model. Both spheres and conchoids provided a good approximation of native hip joint geometry (average fitting error ～0.5 mm). However, models with spherical/conchoid bone geometry and smoothed articulating cartilage surfaces grossly underestimated peak and average contact pressures (50% and 25% lower, respectively) and overestimated contact area when compared to the subject-specific FE model. Models incorporating subject-specific bone geometry with smoothed articulating cartilage also underestimated pressures and predicted evenly distributed patterns of contact. The model with rigid bones predicted much higher pressures than the subject-specific model with deformable bones. The results demonstrate that simplifications to the geometry of the bone-cartilage interface, cartilage surface and bone material properties can have a dramatic effect on the predicted magnitude and distribution of cartilage contact pressures in the hip joint.     

Sensitivity of the tibio-femoral response to finite element modeling parameters

A generic finite element (FE) model of the lower limb was used to study the knee response in-vivo during a one-legged hop. The approach uses an explicit FE code and a combination of estimated muscle forces and measured three-dimensional tibio-femoral kinematics and ground reaction force as input to the FE model. The sensitivity of the simulated tibio-femoral response to variations of key geometric and material parameters was investigated by performing a total of 38 different simulations. The amplitudes of both kinematic and kinetic responses were affected by the change of these parameters. For the current approach, the results suggest that while cartilage mechanical and geometric properties are very important for the estimation of tibio-femoral cartilage pressure, they have limited effects on the overall kinematic response. The study may help to better define the relative importance of modeling parameters for the development of subject-specific models.     

Development of a Finite Element Model of Decompressive Craniectomy

Decompressive craniectomy (DC), an operation whereby part of the skull is removed, is used in the management of patients with brain swelling. While the aim of DC is to reduce intracranial pressure, there is the risk that brain deformation and mechanical strain associated with the operation could damage the brain tissue. The nature and extent of the resulting strain regime is poorly understood at present. Finite element (FE) models of DC can provide insight into this applied strain and hence assist in deciding on the best surgical procedures. However there is uncertainty about how well these models match experimental data, which are difficult to obtain clinically. Hence there is a need to validate any modelling approach outside the clinical setting. This paper develops an axisymmetric FE model of an idealised DC to assess the key features of such an FE model which are needed for an accurate simulation of DC. The FE models are compared with an experimental model using gelatin hydrogel, which has similar poro-viscoelastic material property characteristics to brain tissue. Strain on a central plane of the FE model and the front face of the experimental model, deformation and load relaxation curves are compared between experiment and FE. Results show good agreement between the FE and experimental models, providing confidence in applying the proposed FE modelling approach to DC. Such a model should use material properties appropriate for brain tissue and include a more realistic whole head geometry.     

Comparison of analytical and inverse finite element approaches to estimate cell viscoelastic properties by micropipette aspiration

The viscoelastic properties of cells are important in predicting cell deformation under mechanical loading and may reflect cell phenotype or pathological transition. Previous studies have demonstrated that viscoelastic parameters estimated by finite element (FE) analyses of micropipette aspiration (MA) data differ from those estimated by the analytical half-space model. However, it is unclear whether these differences are statistically significant, as previous studies have been based on average cell properties or parametric analyses that do not reflect the inherent experimental and biological variability of real experimental data. To determine whether cell material parameters estimated by the half-space model are significantly different from those predicted by the FE method, we implemented an inverse FE method to estimate the viscoelastic parameters of a population of primary porcine aortic valve interstitial cells tested by MA. We found that inherent differences between the analytical and inverse FE estimation methods resulted in statistically significant differences in individual cell properties. However, in cases with small pipette to cell radius ratios and short loading periods, model-dependent differences were masked by experimental and cell-to-cell variability. Analytical models that account for finite cell-size and loading rate further relaxed the experimental conditions for which accurate cell material parameter estimates could be obtained. These data provide practical guidelines for analysis of MA data that account for the wide range of conditions encountered in typical experiments.     

Evaluating a suitable level of model complexity for finite element analysis of the intact acetabulum

To enable large-scale multi-factorial finite element (FE) studies, the FE models used must be as computationally efficient as is feasible, while maintaining a suitable level of definition. The present study seeks to find an optimum level of model complexity for use in such large-scale studies by investigating which model attributes are most influential over the chosen model outputs of principal stress and strain in the intact acetabulum. A multi-factorial sensitivity study was carried out using 128 FE models, representing combinations of the following variables: bone stiffness distribution, imposed muscle loading, boundary condition location, hip joint contact conditions and patient's bone anatomy. The relative sensitivity of each input factor was analysed, and it was concluded that the optimum level of model definition must include CT-dependent trabecular bone properties and a sliding interface at the hip joint. It was found that it was not essential to describe the ligamentous sacroiliac and pubic symphysis joints; these could be rigidly fixed in space; and for the normal walking load case, muscle forces may be neglected. It was also concluded that a variety of bone anatomies should be included in a multi-factorial analysis if results are to be inferred for a wider population.