Experimental validation of finite element models of intact and implanted composite hemipelvises using digital image correlation

A detailed understanding of the changes in load transfer due to implantation is necessary to identify potential failure mechanisms of orthopedic implants. Computational finite element (FE) models provide full field data on intact and implanted bone structures, but their validity must be assessed for clinical relevance. The aim of this study was to test the validity of FE predicted strain distributions for the intact and implanted pelvis using the digital image correlation (DIC) strain measurement technique. FE models of an in vitro hemipelvis test setup were produced, both intact and implanted with an acetabular cup. Strain predictions were compared to DIC and strain rosette measurements. Regression analysis indicated a strong linear relationship between the measured and predicted strains, with a high correlation coefficient (R?=?0.956 intact, 0.938 implanted) and a low standard error of the estimate (SE?=?69.53?με, 75.09?με). Moreover, close agreement between the strain rosette and DIC measurements improved confidence in the validity of the DIC technique. The FE model therefore was supported as a valid predictor of the measured strain distribution in the intact and implanted composite pelvis models, confirming its suitability for further computational investigations.     

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

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

Experimental validation of intact and implanted distal femur finite element models

Four finite element (FE) models of intact and distal femur of knee replacements were validated relative to measured bone strains. FE models of linear tetrahedrons were used. Femoral replacements with cemented stemless, cemented and noncemented femoral stems of the PFC Sigma Modular Knee System were analyzed. Bone strains were recorded at ten locations on the cortex. The magnitude of the FE bone strains corresponded to the mean measured strains, with an overall agreement of 10%. Linear regression between the FE and mean experimental strains produced slopes between 0.94 and 1.06 and R(2) values between 0.92 and 0.99. RSME values were less than 12%. The FE models were able to adequately replicate the mechanical behavior of distal femur reconstructions.     

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

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

Experimental validation of a finite element model of a human cadaveric tibia

Finite element (FE) models of long bones are widely used to analyze implant designs. Experimental validation has been used to examine the accuracy of FE models of cadaveric femurs; however, although convergence tests have been carried out, no FE models of an intact and implanted human cadaveric tibia have been validated using a range of experimental loading conditions. The aim of the current study was to create FE models of a human cadaveric tibia, both intact and implanted with a unicompartmental knee replacement, and to validate the models against results obtained from a comprehensive set of experiments. Seventeen strain rosettes were attached to a human cadaveric tibia. Surface strains and displacements were measured under 17 loading conditions, which consisted of axial, torsional, and bending loads. The tibia was tested both before and after implantation of the knee replacement. FE models were created based on computed tomography (CT) scans of the cadaveric tibia. The models consisted of ten-node tetrahedral elements and used 600 material properties derived from the CT scans. The experiments were simulated on the models and the results compared to experimental results. Experimental strain measurements were highly repeatable and the measured stiffnesses compared well to published results. For the intact tibia under axial loading, the regression line through a plot of strains predicted by the FE model versus experimentally measured strains had a slope of 1.15, an intercept of 5.5 microstrain, and an R(2) value of 0.98. For the implanted tibia, the comparable regression line had a slope of 1.25, an intercept of 12.3 microstrain, and an R(2) value of 0.97. The root mean square errors were 6.0% and 8.8% for the intact and implanted models under axial loads, respectively. The model produced by the current study provides a tool for simulating mechanical test conditions on a human tibia. This has considerable value in reducing the costs of physical testing by pre-selecting the most appropriate test conditions or most favorable prosthetic designs for final mechanical testing. It can also be used to gain insight into the results of physical testing, by allowing the prediction of those variables difficult or impossible to measure directly.     

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

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

Maxillary expansion treatment using bone anchors: development and validation of a 3D finite element model

OBJECTIVE: Develop a finite element (FE) model of a skull to perform biomechanical studies of maxillary expansion using bone anchors (BA). MATERIALS AND METHODS: A skull model was developed and assigned material properties based on Hounsfield unit (HU) values of cone-beam computerized tomography (CBCT) images. A 3 mm diameter cylindrical BA was modelled and inserted in the palatal bone. A 4 mm transverse displacement was applied on the anchor. An evaluation on the effect on local stresses of BA implantation inclination angle was performed. RESULTS: Proper displacement results and strain-stress trends for the expansion process were present. Stress distribution patterns were similar as reported in the literature. No significant difference between BA inclination angles was found. CONCLUSION: This work leads to a better understanding and prediction of craniofacial and maxillary bone remodelling during ME with BA treatments and is a first step towards the development of patient specific treatments.     

Maxillary expansion treatment using bone anchors: development and validation of a 3D finite element model

Objective: Develop a finite element (FE) model of a skull to perform biomechanical studies of maxillary expansion using bone anchors (BA).

Materials and methods: A skull model was developed and assigned material properties based on Hounsfield unit (HU) values of cone-beam computerized tomography (CBCT) images. A 3 mm diameter cylindrical BA was modelled and inserted in the palatal bone. A 4 mm transverse displacement was applied on the anchor. An evaluation on the effect on local stresses of BA implantation inclination angle was performed.

Results: Proper displacement results and strain–stress trends for the expansion process were present. Stress distribution patterns were similar as reported in the literature. No significant difference between BA inclination angles was found.

Conclusion: This work leads to a better understanding and prediction of craniofacial and maxillary bone remodelling during ME with BA treatments and is a first step towards the development of patient specific treatments.     

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)     

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

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

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

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

A finite element model of myocardial infarction using a composite material approach

Computational models are effective tools to study cardiac mechanics under normal and pathological conditions. They can be used to gain insight into the physiology of the heart under these conditions while they are adaptable to computer assisted patient-specific clinical diagnosis and therapeutic procedures. Realistic cardiac mechanics models incorporate tissue active/passive response in conjunction with hyperelasticity and anisotropy. Conventional formulation of such models leads to mathematically-complex problems usually solved by custom-developed non-linear finite element (FE) codes. With a few exceptions, such codes are not available to the research community. This article describes a computational cardiac mechanics model developed such that it can be implemented using off-the-shelf FE solvers while tissue pathologies can be introduced in the model in a straight-forward manner. The model takes into account myocardial hyperelasticity, anisotropy, and active contraction forces. It follows a composite tissue modeling approach where the cardiac tissue is decomposed into two major parts: background and myofibers. The latter is modelled as rebars under initial stresses mimicking the contraction forces. The model was applied in silico to study the mechanics of infarcted left ventricle (LV) of a canine. End-systolic strain components, ejection fraction, and stress distribution attained using this LV model were compared quantitatively and qualitatively to corresponding data obtained from measurements as well as to other corresponding LV mechanics models. This comparison showed very good agreement.     

Effect of round curvature of anterior implant-supported zirconia frameworks: finite element analysis and in vitro study using digital image correlation

Two groups of 4-unit zirconia frameworks were produced by CAD/CAM to simulate the restoration of an anterior edentulous gap supported by 2 implant-abutment assemblies. Group 1 comprised straight configuration frameworks and group 2 consisted of arched frameworks. Specimens were made with the same connector cross-section area and were cemented and submitted to static loads. Displacements were captured with two high-speed photographic cameras and analysed with video correlation system. Frameworks and the implant-abutment assembly were scanned and converted to 3DCAD objects by reverse engineering process. A specimen of each group was veneered and the corresponding 3D geometry was similarly obtained after scanning. Numerical models were created from the CAD objects and the FE analysis was performed on the zirconia frameworks and on the FPDs bi-layered with porcelain (veneered frameworks). Displacements were higher for the curved frameworks group, under any load. The predicted displacements correlated well with the experimental values of the two framework groups, but on the straight framework the experimental vertical displacements were superior to those predicted by the FEA. The results showed that the round curvature of zirconia anterior implant-supported FPDs plays a significant role on the deformation/stress of FPDs that cannot be neglected neither in testing nor in simulation and should be considered in the clinical setting.     

Assessment of the 3-D shape and mechanics of the proximal femur using a shape template and a bone mineral density image

Measurement of bone mineral density (BMD) by DXA (dual-energy X-ray absorptiometry) is generally considered to be the clinical golden standard technique to diagnose osteoporosis. However, BMD alone is only a moderate predictor of fracture risk. Finite element analyses of bone mechanics can contribute to a more accurate prediction of fracture risk. In this study, we applied a method to estimate the 3D geometrical shape of bone based on a 2D BMD image and a femur shape template. Proximal femurs of eighteen human cadavers were imaged with computed tomography (CT) and divided into two groups. Image data from the first group (N = 9) were applied to create a shape template by using the general Procrustes analysis and thin plate splines. This template was then applied to estimate the shape of the femurs in the second group (N = 9), using the 2D BMD image projected from the CT image, and the geometrical errors of the shape estimation method were evaluated. Finally, finite element analysis with stance loading condition was conducted based on the original CT and the estimated geometrical shape to evaluate the effect of the geometrical errors on the outcome of the simulations. The volumetric errors induced by the shape estimation method itself were low (<0.6%). Increasing the number of bone specimens used for the template decreased the geometrical errors. When nine bones were used for the template, the mean distance difference (±SD) between the estimated and the CT shape surfaces was 1.2 ± 0.3 mm, indicating that the method was feasible for estimating the shape of the proximal femur. Small errors in geometry led systematically to larger errors in the mechanical simulations. The method could provide more information of the mechanical characteristics of bone based on 2D BMD radiography and could ultimately lead to more sensitive diagnosis of osteoporosis.     

Validating a voxel-based finite element model of a human mandible using digital speckle pattern interferometry

Finite element analysis is a powerful tool for predicting the mechanical behaviour of complex biological structures like bones, but to be confident in the results of an analysis, the model should be validated against experimental data. In such validation experiments, the strains in the loaded bones are usually measured with strain gauges glued to the bone surface, but the use of strain gauges on bone can be difficult and provides only very limited data regarding surface strain distributions. This study applies the full-field strain measurement technique of digital speckle pattern interferometry to measure strains in a loaded human mandible and compares the results with the predictions of voxel-based finite element models of the same specimen. It is found that this novel strain measurement technique yields consistent, reliable measurements. Further, strains predicted by the finite element analysis correspond well with the experimental data. These results not only confirm the usefulness of this technique for future validation studies in the field of bone mechanics, but also show that the modelling approach used in this study is able to predict the experimental results very accurately.     

Physical validation of a patient-specific contact finite element model of the ankle

A validation study was conducted to determine the extent to which computational ankle contact finite element (FE) results agreed with experimentally measured tibio-talar contact stress. Two cadaver ankles were loaded in separate test sessions, during which ankle contact stresses were measured with a high-resolution (Tekscan) pressure sensor. Corresponding contact FE analyses were subsequently performed for comparison. The agreement was good between FE-computed and experimentally measured mean (3.2% discrepancy for one ankle, 19.3% for the other) and maximum (1.5% and 6.2%) contact stress, as well as for contact area (1.7% and 14.9%). There was also excellent agreement between histograms of fractional areas of cartilage experiencing specific ranges of contact stress. Finally, point-by-point comparisons between the computed and measured contact stress distributions over the articular surface showed substantial agreement, with correlation coefficients of 90% for one ankle and 86% for the other. In the past, general qualitative, but little direct quantitative agreement has been demonstrated with articular joint contact FE models. The methods used for this validation enable formal comparison of computational and experimental results, and open the way for objective statistical measures of regional correlation between FE-computed contact stress distributions from comparison articular joint surfaces (e.g., those from an intact versus those with residual intra-articular fracture incongruity).     

Development and validation of an atlas-based finite element brain model

Traumatic brain injury is a leading cause of disability and injury-related death. To enhance our ability to prevent such injuries, brain response can be studied using validated finite element (FE) models. In the current study, a high-resolution, anatomically accurate FE model was developed from the International Consortium for Brain Mapping brain atlas. Due to wide variation in published brain material parameters, optimal brain properties were identified using a technique called Latin hypercube sampling, which optimized material properties against three experimental cadaver tests to achieve ideal biomechanics. Additionally, falx pretension and thickness were varied in a lateral impact variation. The atlas-based brain model (ABM) was subjected to the boundary conditions from three high-rate experimental cadaver tests with different material parameter combinations. Local displacements, determined experimentally using neutral density targets, were compared to displacements predicted by the ABM at the same locations. Error between the observed and predicted displacements was quantified using CORrelation and Analysis (CORA), an objective signal rating method that evaluates the correlation of two curves. An average CORA score was computed for each variation and maximized to identify the optimal combination of parameters. The strongest relationships between CORA and material parameters were observed for the shear parameters. Using properties obtained through the described multiobjective optimization, the ABM was validated in three impact configurations and shows good agreement with experimental data. The final model developed in this study consists of optimized brain material properties and was validated in three cadaver impacts against local brain displacement data.     

Development and experimental validation of a finite element model of total ankle replacement

Total ankle replacement remains a less satisfactory solution compared to other joint replacements. The goal of this study was to develop and validate a finite element model of total ankle replacement, for future testing of hypotheses related to clinical issues. To validate the finite element model, an experimental setup was specifically developed and applied on 8 cadaveric tibias. A non-cemented press fit tibial component of a mobile bearing prosthesis was inserted into the tibias. Two extreme anterior and posterior positions of the mobile bearing insert were considered, as well as a centered one. An axial force of 2 kN was applied for each insert position. Strains were measured on the bone surface using digital image correlation. Tibias were CT scanned before implantation, after implantation, and after mechanical tests and removal of the prosthesis. The finite element model replicated the experimental setup. The first CT was used to build the geometry and evaluate the mechanical properties of the tibias. The second CT was used to set the implant position. The third CT was used to assess the bone-implant interface conditions. The coefficient of determination (R-squared) between the measured and predicted strains was 0.91. Predicted bone strains were maximal around the implant keel, especially at the anterior and posterior ends. The finite element model presented here is validated for future tests using more physiological loading conditions.     

A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments

The prediction of patient-specific proximal femur mechanical response to various load conditions is of major clinical importance in orthopaedics. This paper presents a novel, empirically validated high-order finite element method (FEM) for simulating the bone response to loads. A model of the bone geometry was constructed from a quantitative computerized tomography (QCT) scan using smooth surfaces for both the cortical and trabecular regions. Inhomogeneous isotropic elastic properties were assigned to the finite element model using distinct continuous spatial fields for each region. The Young's modulus was represented as a continuous function computed by a least mean squares method. p-FEMs were used to bound the simulation numerical error and to quantify the modeling assumptions. We validated the FE results with in-vitro experiments on a fresh-frozen femur loaded by a quasi-static force of up to 1500 N at four different angles. We measured the vertical displacement and strains at various locations and investigated the sensitivity of the simulation. Good agreement was found for the displacements, and a fair agreement found in the measured strain in some of the locations. The presented study is a first step toward a reliable p-FEM simulation of human femurs based on QCT data for clinical computer aided decision making.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1–L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.