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.     

Accuracy of femur reconstruction from sparse geometric data using a statistical shape model

Sparse geometric information from limited field-of-view medical images is often used to reconstruct the femur in biomechanical models of the hip and knee. However, the full femur geometry is needed to establish boundary conditions such as muscle attachment sites and joint axes which define the orientation of joint loads. Statistical shape models have been used to estimate the geometry of the full femur from varying amounts of sparse geometric information. However, the effect that different amounts of sparse data have on reconstruction accuracy has not been systematically assessed. In this study, we compared shape model and linear scaling reconstruction of the full femur surface from varying proportions of proximal and distal partial femur geometry in combination with morphometric and landmark data. We quantified reconstruction error in terms of surface-to-surface error as well as deviations in the reconstructed femur’s anatomical coordinate system which is important for biomechanical models. Using a partial proximal femur surface, mean shape model-based reconstruction surface error was 1.8 mm with 0.15° or less anatomic axis error, compared to 19.1 mm and 2.7–5.6° for linear scaling. Similar results were found when using a partial distal surface. However, varying amounts of proximal or distal partial surface data had a negligible effect on reconstruction accuracy. Our results show that given an appropriate set of sparse geometric data, a shape model can reconstruct full femur geometry with far greater accuracy than simple scaling.     

A biomechanical model of the lumbosacral joint during lifting activities

A biomechanical model of the lumbosacral region was constructed for the purpose of systematically studying the combined stresses and strains on the local ligaments, muscles and disc tissue during sagittal plane two-handed lifting. The model was validated in two ways. The first validation was a comparison of experimental study results with model predictions. In general predictions compared very reasonably with observed values of several authors with the exception of strain predictions on the articular ligaments. Second, a sensitivity analysis was performed over a wide range of lifting tasks. The predicted stress/strain values followed anticipated patterns and were of reasonable magnitudes. On the basis of the results of the sensitivity analysis it was concluded that typical lifting tasks can lead to excessive disc compressive forces, muscle moment generation requirements, and possibly lumbodorsal fascia strains. Conversely, annulus rupture of a healthy disc due to overstrain appears very unlikely.     

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.     

Automated three-dimensional finite element modelling of bone: a new method

Three-dimensional finite element stress analysis of bone is a key to understanding bone remodelling, assessing fracture risk, and designing prostheses; however, the cost and complexity of predicting the stress field in bone with accuracy has precluded the routine use of this method. A new, automated method of generating patient-specific three-dimensional finite element models of bone is presented — it uses digital computed tomographic (CT) scan data to derive the geometry of the bone and to estimate its inhomogeneous material properties. Cubic elements of a user-specified size are automatically defined and then individually assigned the CT scan-derived material properties. The method is demonstrated by predicting the stress, strain, and strain energy in a human proximal femur in vivo. Three-dimensional loading conditions corresponding to the stance phase of gait were taken from the literature and applied to the model. Maximum principal compressive stresses of 8–23 MPa were computed for the medial femoral neck. Automated generation of additional finite element models with larger numbers of elements was used to verify convergence in strain energy.     

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.     

Comparison of strain measurement in the mouse forearm using subject-specific finite element models,strain gaging,and digital image correlation

Mechanical loading in bone leads to the activation of bone-forming pathways that are most likely associated with a minimum strain threshold being experienced by the osteocyte. To investigate the correlation between cellular response and mechanical stimuli, researchers must develop accurate ways to measure/compute strain both externally on the bone surface and internally at the osteocyte level. This study investigates the use of finite element (FE) models to compute bone surface strains on the mouse forearm. Strains from three FE models were compared to data collected experimentally through strain gaging and digital image correlation (DIC). Each FE model was assigned subject-specific bone properties and consisted of one-dimensional springs representing the interosseous membrane. After three-point bending was performed on the ulnae and radii, moment of inertia was determined from microCT analysis of the bone region between the supports and then used along with standard beam analyses to calculate the Young’s modulus. Non-contact strain measurements from DIC were determined to be more suitable for validating numerical results than experimental data obtained through conventional strain gaging. When comparing strain responses in the three ulnae, we observed a 3–14% difference between numerical and DIC strains while the strain gage values were 37–56% lower than numerical values. This study demonstrates a computational approach for capturing bone surface strains in the mouse forearm. Ultimately, strains from these macroscale models can be used as inputs for microscale and nanoscale FE models designed to analyze strains directly in the osteocyte lacunae.     

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.     

Prospects of implant with locking plate in fixation of subtrochanteric fracture: experimental demonstration of its potential benefits on synthetic femur model with supportive hierarchical nonlinear hyperelastic finite element analysis

Background

Effective fixation of fracture requires careful selection of a suitable implant to provide stability and durability. Implant with a feature of locking plate (LP) has been used widely for treating distal fractures in femur because of its favourable clinical outcome, but its potential in fixing proximal fractures in the subtrochancteric region has yet to be explored. Therefore, this comparative study was undertaken to demonstrate the merits of the LP implant in treating the subtrochancteric fracture by comparing its performance limits against those obtained with the more traditional implants; angle blade plate (ABP) and dynamic condylar screw plate (DCSP).

Materials and Methods

Nine standard composite femurs were acquired, divided into three groups and fixed with LP (n?=?3), ABP (n?=?3) and DCSP (n?=?3). The fracture was modeled by a 20?mm gap created at the subtrochanteric region to experimentally study the biomechanical response of each implant under both static and dynamic axial loading paradigms. To confirm the experimental findings and to understand the critical interactions at the boundaries, the synthetic femur/implant systems were numerically analyzed by constructing hierarchical finite element models with nonlinear hyperelastic properties. The predictions from the analyses were then compared against the experimental measurements to demonstrate the validity of each numeric model, and to characterize the internal load distribution in the femur and load bearing properties of each implant.

Results

The average measurements indicated that the constructs with ABP, DCPS and LP respectively had overall stiffness values of 70.9, 110.2 and 131.4?N/mm, and exhibited reversible deformations of 12.4, 4.9 and 4.1?mm when the applied dynamic load was 400?N and plastic deformations of 11.3, 2.4 and 1.4?mm when the load was 1000?N. The corresponding peak cyclic loads to failure were 1100, 1167 and 1600?N. The errors between the displacements measured experimentally or predicted by the nonlinear hierarchical hyperelastic model were less than 18?%. In the implanted femur heads, the principal stresses were spatially heterogeneous for ABP and DCSP but more homogenous for LP, meaning LP had lower stress concentrations.

Conclusion

When fixed with the LP implant, the synthetic femur model of the subtrochancteric fracture consistently exceeds in the key biomechanical measures of stability and durability. These capabilities suggest increased resistance to fatigue and failure, which are highly desirable features expected of functional implants and hence make the LP implant potentially a viable alternative to the conventional ABP or DCSP in the treatment of subtrochancteric femur fractures for the betterment of clinical outcome.     

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.     

Tendon strain measurements with dynamic ultrasound images: evaluation of digital image correlation

Strain is an essential metric in tissue mechanics. Strains and strain distributions during functional loads can help identify damaged and pathologic regions as well as quantify functional compromise. Noninvasive strain measurement in vivo is difficult to perform. The goal of this in vitro study is to determine the efficacy of digital image correlation (DIC) methods to measure strain in B-mode ultrasound images. The Achilles tendons of eight male Wistar rats were removed and mechanically cycled between 0 and 1% strain. Three cine video images were captured for each specimen: (1) optical video for manual tracking of optical markers; (2) optical video for DIC tracking of optical surface markers; and (3) ultrasound video for DIC tracking of image texture within the tissue. All three imaging modalities were similarly able to measure tendon strain during cyclic testing. Manual/ImageJ-based strain values linearly correlated with DIC (optical marker)-based strain values for all eight tendons with a slope of 0.970. DIC (optical marker)-based strain values linearly correlated with DIC (ultrasound texture)-based strain values for all eight tendons with a slope of 1.003. Strain measurement using DIC was as accurate as manual image tracking methods, and DIC tracking was equally accurate when tracking ultrasound texture as when tracking optical markers. This study supports the use of DIC to calculate strains directly from the texture present in standard B-mode ultrasound images and supports the use of DIC for in vivo strain measurement using ultrasound images without additional markers, either artificially placed (for optical tracking) or anatomically in view (i.e., bony landmarks and/or muscle-tendon junctions).     

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)     

The biomechanical effect of the collar of a femoral stem on total hip arthroplasty

To investigate the biomechanical effect of collars, finite element analyses are carried out through two hip joints that are implanted using collared and collarless stems, respectively, and an intact hip joint model. For the analyses, the sacrum, coxal bone, and the cancellous and cortical bones of a femur are modelled using finite elements based on X-ray computed tomographic images taken from a 27-year-old woman. From the results, it is found that a collar with perfect calcar contact prevents stem subsidence and decreases the proximal–lateral gap and the lateral stem tilting. Therefore, it can impart reasonable biomechanical stability for total hip arthroplasty. However, its low load transmission ability and increased stem tilting effect due to the imperfect contact between the collar and the calcar are found to be serious problems that need to be solved. Results of clinical follow-up are presented for supporting the computational results.     

Strain imaging of the lateral collateral ligament using high frequency and conventional ultrasound imaging: An ex-vivo comparison

Recent first attempts of in situ ultrasound strain imaging in collateral ligaments encountered a number of challenges and illustrated a clear need for additional studies and more thorough validation of the available strain imaging methods. Therefore, in this study we experimentally validated ultrasound strain measurements of ex vivo human lateral collateral ligaments in an axial loading condition. Moreover, the use of high frequency ultrasound (>20 MHz) for strain measurement was explored and its performance compared to conventional ultrasound. The ligaments were stretched up to 5% strain and ultrasound measurements were compared to surface strain measurements from optical digital image correlation (DIC) techniques. The results show good correlations between ultrasound based and DIC based strain measures with R² values of 0.71 and 0.93 for high frequency and conventional ultrasound, subsequently. The performance of conventional ultrasound was significantly higher compared to high frequency ultrasound strain imaging, as the high frequency based method seemed more prone to errors. This study demonstrates that ultrasound strain imaging is feasible in ex vivo lateral collateral ligaments, which are relatively small structures. Additional studies should be designed for a more informed assessment of optimal in vivo strain measurements in collateral knee ligaments.     

Finite element and experimental cortex strains of the intact and implanted tibia

Finite Element (FE) models for the simulation of intact and implanted bone find their main purpose in accurately reproducing the associated mechanical behavior. FE models can be used for preclinical testing of joint replacement implants, where some biomechanical aspects are difficult, if not possible, to simulate and investigate in vitro. To predict mechanical failure or damage, the models should accurately predict stresses and strains. Commercially available synthetic femur models have been extensively used to validate finite element models, but despite the vast literature available on the characteristics of synthetic tibia, numerical and experimental validation of the intact and implant assemblies of tibia are very limited or lacking. In the current study, four FE models of synthetic tibia, intact and reconstructed, were compared against experimental bone strain data, and an overall agreement within 10% between experimental and FE strains was obtained. Finite element and experimental (strain gauge) models of intact and implanted synthetic tibia were validated based on the comparison of cortex bone strains. The study also includes the analysis carried out on standard tibial components with cemented and noncemented stems of the P.F.C Sigma Modular Knee System. The overall agreement within 10% previously established was achieved, indicating that FE models could be successfully validated. The obtained results include a statistical analysis where the root-mean-square-error values were always <10%. FE models can successfully reproduce bone strains under most relevant acting loads upon the condylar surface of the tibia. Moreover, FE models, once properly validated, can be used for preclinical testing of tibial knee replacement, including misalignment of the implants in the proximal tibia after surgery, simulation of long-term failure according to the damage accumulation failure scenario, and other related biomechanical aspects.     

Ex vivo determination of bone tissue strains for an in vivo mouse tibial loading model

Previous studies introduced the digital image correlation (DIC) as a viable technique for measuring bone strain during loading. In this study, we investigated the sensitivity of a DIC system in determining surface strains in a mouse tibia while loaded in compression through the knee joint. Specifically, we examined the effect of speckle distribution, facet size and overlap, initial vertical alignment of the bone into the loading cups, rotation with respect to cameras, and ex vivo loading configurations on the strain contour maps measured with a DIC system.     

Development and testing of a modular strain measurement clip

A novel, multi-use, low-stiffness and low-cost transducer for measuring in vitro strains has been developed and tested. Currently available strain measurement methods are either too expensive, too complicated or too inflexible for multi-use strain measurement. The stainless-steel modular strain measurement clip introduced here was instrumented with four 350 Omega axial strain gauges in a full Wheatstone bridge configuration to take advantage of commonly available strain gauge amplifier equipment. Adjustable extension arms were designed to allow greater application versatility. The clip was calibrated and produced a linear response (R(2)>0.99) over a minimum of 1.04 mm at high amplifier gain. With reduced amplifier settings, testing showed a linear response over a range of 30.5 mm (R(2)>0.99). Clip stiffness was 0.6N/mm of extension arm tip displacement for minimal instrumentation artifact. A validation test was conducted through a comparison of strain clips, surface-mounted strain gauges and theoretical strain in an aluminium rod subjected to axial tensile loading. The two measurement techniques were used to determine the modulus of elasticity of the aluminium rod. Results were within 6% of the known modulus of elasticity for aluminium. A comparative biomechanical test was also performed on an equine third metacarpal specimen. The traditional bonded strain gauging method produced similar results as the new strain clip, but failed to measure ultimate strains since all strain gauges failed prior to specimen failure. Further investigations into the multiple uses of the clip are underway and recommendations for future versions of the clip are given.     

Construction of 3D human distal femoral surface models using a 3D statistical deformable model

Construction of 3D geometric surface models of human knee joint is always a challenge in biomedical engineering. This study introduced an improved statistical shape model (SSM) method that only uses 2D images of a joint to predict the 3D joint surface model. The SSM was constructed using 40 distal femur models of human knees. In this paper, a series validation and parametric analysis suggested that more than 25 distal femur models are needed to construct the SSM; each distal femur should be described using at least 3000 nodes in space; and two 2D fluoroscopic images taken in 45° directions should be used for the 3D surface shape prediction. Using this SSM method, ten independent distal femurs from 10 independent living subjects were predicted using their 2D plane fluoroscopic images. The predicted models were compared to their native 3D distal femur models constructed using their 3D MR images. The results demonstrated that using two fluoroscopic images of the knee, the overall difference between the predicted distal femur surface and the MR image-based surface was 0.16±1.16 mm. These data indicated that the SSM method could be a powerful method for construction of 3D surface geometries of the distal femur.     

Mechanical significance of femoral head trabecular bone structure in Loris and Galago evaluated using micromechanical finite element models

Work on the interspecific and intraspecific variation of trabecular bone in the proximal femur of primates demonstrates important architectural variation between animals with different locomotor behaviors. This variation is thought to be related to the processes of bone adaptation whereby bone structure is optimized to the mechanical environment. Micromechanical finite element models were created for the proximal femur of the leaping Galago senegalensis and the climbing and quadrupedal Loris tardigradus by converting bone voxels from high-resolution X-ray computed tomography scans of the femoral head to eight-noded brick elements. The resulting models had approximately 1.8 million elements each. Loading conditions representing takeoff phase of a leap and more generalized load orientations were applied to the models, and the models were solved using the iterative "row-by-row" matrix-vector multiplication algorithm. The principal strain and Von Mises stress results for the leaping model were similar for both species at each load orientation. Similar hip joint reaction forces in the range of 4.9 x to 12 x body weight were calculated for both species under each loading condition, but the hip reaction values estimated for Loris were higher than predicted based on locomotor behavior. These results suggest that functional adaptation to hip joint loading may not fully explain the differences in femoral head trabecular bone structure in Galago and Loris. The finite element method represents a unique and useful tool for analyzing the functional adaptation of trabecular bone in a diversity of animals and for reconstructing locomotor behavior in extinct taxa.     

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

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