A new approach to determine the accuracy of morphology–elasticity relationships in continuum FE analyses of human proximal femur

Accuracy of osseointegrated screw-bone construct stiffness and peri-implant loading predicted by homogenized FE models relative to micro-FE models

Computational predictions of stiffness and peri-implant loading of screw-bone constructs are highly relevant to investigate and improve bone fracture fixations. Homogenized finite element (hFE) models have been used for this purpose in the past, but their accuracy has been questioned given the numerous simplifications, such as neglecting screw threads and modelling the trabecular bone structure as a continuum. This study aimed to investigate the accuracy of hFE models of an osseointegrated screw-bone construct when compared to micro-FE models considering the simplified screw geometry and different trabecular bone material models. Micro-FE and hFE models were created from 15 cylindrical bone samples with a virtually inserted, osseointegrated screw (fully bonded interface). Micro-FE models were created including the screw with threads (=reference models) and without threads to quantify the error due to screw geometry simplification. In the hFE models, the screws were modelled without threads and four different trabecular bone material models were used, including orthotropic and isotropic material derived from homogenization with kinematic uniform boundary conditions (KUBC), as well as from periodicity-compatible mixed uniform boundary conditions (PMUBC). Three load cases were simulated (pullout, shear in two directions) and errors in the construct stiffness and the volume average strain energy density (SED) in the peri-implant region were evaluated relative to the micro-FE model with a threaded screw. The pooled error caused by only omitting screw threads was low (max: 8.0%) compared to the pooled error additionally including homogenized trabecular bone material (max: 92.2%). Stiffness was predicted most accurately using PMUBC-derived orthotropic material (error: -0.7 ± 8.0%) and least accurately using KUBC-derived isotropic material (error: +23.1 ± 24.4%). Peri-implant SED averages were generally well correlated (R² ≥ 0.76), but slightly over- or underestimated by the hFE models and SED distributions were qualitatively different between hFE and micro-FE models. This study suggests that osseointegrated screw-bone construct stiffness can be predicted accurately using hFE models when compared to micro-FE models and that volume average peri-implant SEDs are well correlated. However, the hFE models are highly sensitive to the choice of trabecular bone material properties. PMUBC-derived isotropic material properties represented the best trade-off between model accuracy and complexity in this study.

Bone remodelling in implanted proximal femur using topology optimization and parameterized cellular model

The clinical relevance of bone remodelling predictions calls for accurate finite element (FE) modelling of implant-bone structure and musculoskeletal loading conditions. However, simplifications in muscle loading, material properties, has often been used in FE simulations. Bone adaptation induces changes in bone apparent density and its microstructure. Multiscale simulations, involving optimization methods and biomimetic microstructural models, have proven to be promising for predicting changes in bone morphology. The objective of the study is to develop a novel computational framework to predict bone remodelling around an uncemented femoral implant, using multiscale topology optimization and a parameterized cellular model. The efficacy of the scheme was evaluated by comparing the remodelling predictions with those of isotropic strain energy density (SED) and orthotropy based formulations. The characteristic functional groups and low-density regions of Ward's triangle, predicted by the optimization scheme, were comparable to micro-CT images of the proximal femur. Although the optimization scheme predicted well comparable material distribution in the 2D femur models, the obscured material orientations in some planes of the 3D model indicate the need for a more robust modelling of the boundary conditions. Regression analysis revealed a higher correlation (0.6472) between the topology optimization and SED models than the orthotropic predictions (0.4219). Despite higher bone apposition of 10-20% around the distal tip of the implant, the bone density distributions were well comparable to clinical observations towards the proximal femur. The proposed computational scheme appears to be a viable method for including bone anisotropy in the remodelling formulation.

Orthotropic bone remodelling around uncemented femoral implant: a comparison with isotropic formulation

Peri-prosthetic bone adaptation has usually been predicted using subject-specific finite element analysis in combination with remodelling algorithms and assuming isotropic bone material property. The objective of the study is to develop an orthotropic bone remodelling algorithm for evaluation of peri-prosthetic bone adaptation in the uncemented implanted femur. The simulations considered loading conditions from a variety of daily activities. The orthotropic algorithm was tested on 2D and 3D models of the intact femur for verification of predicted results. The predicted orthotropic directionality, based on principal stress directions, was in agreement with the trabecular orientation in a micro-CT data of proximal femur. The validity of the proposed strain-based algorithm was assessed by comparing the predicted results of the orthotropic model with those of the strain-energy-density-based isotropic formulation. Despite agreement in cortical densities [Formula: see text], the isotropic remodelling algorithm tends to predict relatively higher values around the distal tip of the implant as compared to the orthotropic model. Both formulations predicted 4-8% bone resorption in the proximal femur. A linear regression analysis revealed a significant correlation [Formula: see text] between the stresses and strains on the cortex of the proximal femur, predicted by the isotropic and orthotropic formulations. Despite reasonable agreement in peri-prosthetic bone density distributions, the quantitative differences with isotropic model predictions highlight the combined influences of bone orthotropy and mechanical stimulus in the adaptation process.

Bone Density Micro-CT Assessment during Embedding of the Innovative Multi-Spiked Connecting Scaffold in Periarticular Bone to Elaborate a Validated Numerical Model for Designing Biomimetic Fixation of Resurfacing Endoprostheses

Our team has been working for some time on designing a new kind of biomimetic fixation of resurfacing endoprostheses, in which the innovative multi-spiked connecting scaffold (MSC-Scaffold) that mimics the natural interface between articular cartilage and periarticular trabecular bone in human joints is the crucial element. This work aimed to develop a numerical model enabling the design of the considered joint replacement implant that would reflect the mechanics of interacting biomaterials. Thus, quantitative micro-CT analysis of density distribution in bone material during the embedding of MSC-Scaffold in periarticular bone was applied. The performed numerical studies and corresponding mechanical tests revealed, under the embedded MSC-Scaffold, the bone material densification affecting its mechanical properties. On the basis of these findings, the built numerical model was modified by applying a simulated insert of densified bone material. This modification led to a strong correlation between the re-simulation and experimental results (FVU = 0.02). The biomimetism of the MSC-Scaffold prototype that provided physiological load transfer from implant to bone was confirmed based on the Huber–von Mises–Hencky (HMH) stress maps obtained with the validated finite element (FE) model of the problem. The micro-CT bone density assessment performed during the embedding of the MSC-Scaffold prototype in periarticular bone provides insight into the mechanical behaviour of the investigated implant-bone system and validates the numerical model that can be used for the design of material and geometric features of a new kind of resurfacing endoprostheses fixation.

Finite element analysis of bone strength in osteogenesis imperfecta

As a dedicated experimentalist, John Currey praised the high potential of finite element (FE) analysis but also recognized its critical limitations. The application of the FE methodology to bone tissue is reviewed in the light of his enthusiastic and colorful statements. In the past decades, FE analysis contributed substantially to the understanding of structure-function properties in the hierarchical organization of bone and to the simulation of bone adaptation. The systematic experimental validation of FE analysis of bone strength in anatomical locations at risk of fracture led to its application in clinical studies to evaluate efficacy of antiresorptive or anabolic treatment of bone fragility. Beyond the successful analyses of healthy or osteoporotic bone, FE analysis becomes increasingly involved in the investigation of other fragility-related bone diseases. The case of osteogenesis imperfecta (OI) is exposed, the multiscale alterations of the bone tissue and the effect of treatment summarized. A few FE analyses attempting to answer open questions in OI are then reported. An original study is finally presented that explored the structural properties of the Brtl/+ murine model of OI type IV subjected to sclerostin neutralizing antibody treatment using microFE analysis. The use of identical material properties in the four-point bending FE simulations of the femora reproduced not only the experimental values but also the statistical comparisons examining the effect of disease and treatment. Further efforts are needed to build upon the extraordinary legacy of John Currey and clarify the impact of different bone diseases on the hierarchical mechanical properties of bone.

Effect of fabric on the accuracy of computed tomography-based finite element analyses of the vertebra

Quantitative computed tomography (QCT)-based finite element (FE) models of the vertebra are widely used in studying spine biomechanics and mechanobiology, but their accuracy has not been fully established. Although the models typically assign material properties based only on local bone mineral density (BMD), the mechanical behavior of trabecular bone also depends on fabric. The goal of this study was to determine the effect of incorporating measurements of fabric on the accuracy of FE predictions of vertebral deformation. Accuracy was assessed by using displacement fields measured via digital volume correlation-applied to time-lapse microcomputed tomography (μCT)-as the gold standard. Two QCT-based FE models were generated from human L1 vertebrae (n = 11): the entire vertebral body and a cuboid-shaped portion of the trabecular centrum [dimensions: (20-30) × (15-20) × (15-20) mm3]. For axial compression boundary conditions, there was no difference (p = 0.40) in the accuracy of the FE-computed displacements for models using material properties based on local values of BMD versus those using material properties based on local values of fabric and volume fraction. However, when using BMD-based material properties, errors were higher for the vertebral-body models (8.4-50.1%) than cuboid models (1.5-19.6%), suggesting that these properties are inaccurate in the peripheral regions of the centrum. Errors also increased when assuming that the cuboid region experienced uniaxial loading during axial compression of the vertebra. These findings indicate that a BMD-based constitutive model is not sufficient for the peripheral region of the vertebral body when seeking accurate QCT-based FE modeling of the vertebra.

Comparative Study of Femur Bone Having Different Boundary Conditions and Bone Structure Using Finite Element Method

Background:

Femur bone is an important part in human which basically gives stability and support to carry out all day to day activities. It carries loads from upper body to lower abdomen.

Objective:

In this work, the femur having composite structure with cortical, cancellous and bone marrow cavity is bisected from condyle region with respect to 25%, 50% and 75% of its height. There is considerable difference in the region chosen for fixing all degrees of freedom in the analysis of femur.

Methods:

The CT scans are taken, and 3D model is developed using MIMICS. The developed model is used for static structural analysis by varying the load from 500N to 3000N.

Results:

The findings for 25% bisected femur model report difference in directional deformation less than 5% for loads 2000N and less. In the study comparing fully solid bone and the composite bone, the total deformation obtained for a complete solid bone was 3.5 mm which was 18.7% less than that determined for the composite bone.

Conclusion:

The standardization for fixing the bone is developed. And it is required to fix the distal end always with considering full femur bone.

Mapping anisotropy improves QCT-based finite element estimation of hip strength in pooled stance and side-fall load configurations

Hip fractures are one of the most severe consequences of osteoporosis. Compared to the clinical standard of DXA-based aBMD at the femoral neck, QCT-based FEA delivers a better surrogate of femoral strength and gains acceptance for the calculation of hip fracture risk when a CT reconstruction is available. Isotropic, homogenised voxel-based, finite element (hvFE) models are widely used to estimate femoral strength in cross-sectional and longitudinal clinical studies. However, fabric anisotropy is a classical feature of the architecture of the proximal femur and the second determinant of the homogenised mechanical properties of trabecular bone. Due to the limited resolution, fabric anisotropy cannot be derived from clinical CT reconstructions. Alternatively, fabric anisotropy can be extracted from HR-pQCT images of cadaveric femora. In this study, fabric anisotropy from HR-pQCT images was mapped onto QCT-based hvFE models of 71 human proximal femora for which both HR-pQCT and QCT images were available. Stiffness and ultimate load computed from anisotropic hvFE models were compared with previous biomechanical tests in both stance and side-fall configurations. The influence of using the femur-specific versus a mean fabric distribution on the hvFE predictions was assessed. Femur-specific and mean fabric enhance the prediction of experimental ultimate force for the pooled, i.e. stance and side-fall, (isotropic: r²=0.81, femur-specific fabric: r²=0.88, mean fabric: r²=0.86,p<0.001) but not for the individual configurations. Fabric anisotropy significantly improves bone strength prediction for the pooled configurations, and mapped fabric provides a comparable prediction to true fabric. The mapping of fabric anisotropy is therefore expected to help generate more accurate QCT-based hvFE models of the proximal femur for personalised or multiple load configurations.

A novel in silico method to quantify primary stability of screws in trabecular bone

Insufficient primary stability of screws in bone leads to screw loosening and failure. Unlike conventional continuum finite-element models, micro-CT based finite-element analysis (micro-FE) is capable of capturing the patient-specific bone micro-architecture, providing accurate estimates of bone stiffness. However, such in silico models for screws in bone highly overestimate the apparent stiffness. We hypothesized that a more accurate prediction of primary implant stability of screws in bone is possible by considering insertion-related bone damage. We assessed two different screw types and loading scenarios in 20 trabecular bone specimens extracted from 12 cadaveric human femoral heads (N = 5 for each case). In the micro-FE model, we predicted specimen-specific Young's moduli of the peri-implant bone damage region based on morphometric parameters such that the apparent stiffness of each in silico model matched the experimentally measured stiffness of the corresponding in vitro specimen as closely as possible. The standard micro-FE models assuming perfectly intact peri-implant bone overestimated the stiffness by over 330%. The consideration of insertion related damaged peri-implant bone corrected the mean absolute percentage error down to 11.4% for both loading scenarios and screw types. Cross-validation revealed a mean absolute percentage error of 14.2%. We present the validation of a novel micro-FE modeling technique to quantify the apparent stiffness of screws in trabecular bone. While the standard micro-FE model overestimated the bone-implant stiffness, the consideration of insertion-related bone damage was crucial for an accurate stiffness prediction. This approach provides an important step toward more accurate specimen-specific micro-FE models. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:2415-2424, 2017.

Direct Bio-printing with Heterogeneous Topology Design

Bio-additive manufacturing is a promising tool to fabricate porous scaffold structures for expediting the tissue regeneration processes. Unlike the most traditional bulk material objects, the microstructures of tissue and organs are mostly highly anisotropic, heterogeneous, and porous in nature. However, modelling the internal heterogeneity of tissues/organs structures in the traditional CAD environment is difficult and oftentimes inaccurate. Besides, the de facto STL conversion of bio-models introduces loss of information and piles up more errors in each subsequent step (build orientation, slicing, tool-path planning) of the bio-printing process plan. We are proposing a topology based scaffold design methodology to accurately represent the heterogeneous internal architecture of tissues/organs. An image analysis technique is used that digitizes the topology information contained in medical images of tissues/organs. A weighted topology reconstruction algorithm is implemented to represent the heterogeneity with parametric functions. The parametric functions are then used to map the spatial material distribution. The generated information is directly transferred to the 3D bio-printer and heterogeneous porous tissue scaffold structure is manufactured without STL file. The proposed methodology is implemented to verify the effectiveness of the approach and the designed example structure is bio-fabricated with a deposition based bio-additive manufacturing system.

A patient-specific model of total knee arthroplasty to estimate patellar strain: A case study

BACKGROUND

Inappropriate patellar cut during total knee arthroplasty can lead to patellar complications due to increased bone strain. In this study, we evaluated patellar bone strain of a patient who had a deeper patellar cut than the recommended.

METHODS

A patient-specific model based on patient preoperative data was created. The model was decoupled into two levels: knee and patella. The knee model predicted kinematics and forces on the patella during squat movement. The patella model used these values to predict bone strain after total knee arthroplasty. Mechanical properties of the patellar bone were identified with micro-finite element modeling testing of cadaveric samples. The model was validated with a robotic knee simulator and postoperative X-rays. For this patient, we compared the deeper patellar cut depth to the recommended one, and evaluated patellar bone volume with octahedral shear strain above 1%.

FINDINGS

Model predictions were consistent with experimental measurements of the robotic knee simulator and postoperative X-rays. Compared to the recommended cut, the deeper cut increased the critical strain bone volume, but by less than 3% of total patellar volume.

INTERPRETATION

We thus conclude that the predicted increase in patellar strain should be within an acceptable range, since this patient had no complaints 8 months after surgery. This validated patient-specific model will later be used to address other questions on groups of patients, to eventually improve surgical planning and outcome of total knee arthroplasty.

Predicting the stiffness and strength of human femurs with real metastatic tumors

BACKGROUND

Predicting patient specific risk of fracture in femurs with metastatic tumors and the need for surgical intervention are of major clinical importance. Recent patient-specific high-order finite element methods (p-FEMs) based on CT-scans demonstrated accurate results for healthy femurs, so that their application to metastatic affected femurs is considered herein.

METHODS

Radiographs of fresh frozen proximal femur specimens from donors that died of cancer were examined, and seven pairs with metastatic tumor were identified. These were CT-scanned, instrumented by strain-gauges and loaded in stance position at three inclination angles. Finally the femurs were loaded until fracture that usually occurred at the neck. Histopathology was performed to determine whether metastatic tumors are present at fractured surfaces. Following each experiment p-FE models were created based on the CT-scans mimicking the mechanical experiments. The predicted displacements, strains and yield loads were compared to experimental observations.

RESULTS

The predicted strains and displacements showed an excellent agreement with the experimental observations with a linear regression slope of 0.95 and a coefficient of regression R(2)=0.967. A good correlation was obtained between the predicted yield load and the experimental observed yield, with a linear regression slope of 0.80 and a coefficient of regression R(2)=0.78.

DISCUSSION

CT-based patient-specific p-FE models of femurs with real metastatic tumors were demonstrated to predict the mechanical response very well. A simplified yield criterion based on the computation of principal strains was also demonstrated to predict the yield force in most of the cases, especially for femurs that failed at small loads. In view of the limited capabilities to predict risk of fracture in femurs with metastatic tumors used nowadays, the p-FE methodology validated herein may be very valuable in making clinical decisions.

Locally measured microstructural parameters are better associated with vertebral strength than whole bone density

Whole vertebrae areal and volumetric bone mineral density (BMD) measurements are not ideal predictors of vertebral fractures. We introduce a technique which enables quantification of bone microstructural parameters at precisely defined anatomical locations. Results show that local assessment of bone volume fraction at the optimal location can substantially improve the prediction of vertebral strength.

INTRODUCTION

Whole vertebrae areal and volumetric BMD measurements are not ideal predictors of vertebral osteoporotic fractures. Recent studies have shown that sampling bone microstructural parameters in smaller regions may permit better predictions. In such studies, however, the sampling location is described only in general anatomical terms. Here, we introduce a technique that enables the quantification of bone volume fraction and microstructural parameters at precisely defined anatomical locations. Specific goals of this study were to investigate at what anatomical location within the vertebrae local bone volume fraction best predicts vertebral-body strength, whether this prediction can be improved by adding microstructural parameters and to explore if this approach could better predict vertebral-body strength than whole bone volume fraction and finite element (FE) analyses.

METHODS

Eighteen T12 vertebrae were scanned in a micro-computed tomography (CT) system and FE meshes were made using a mesh-morphing tool. For each element, bone microstructural parameters were measured and correlated with vertebral compressive strength as measured experimentally. Whole bone volume fraction and FE-predicted vertebral strength were also compared to the experimental measurements.

RESULTS

A significant association between local bone volume fraction measured at a specific central region and vertebral-body strength was found that could explain up to 90% of the variation. When including all microstructural parameters in the regression, the predictive value of local measurements could be increased to 98%. Whole bone volume fraction could explain only 64% and FE analyses 76% of the variation in bone strength.

CONCLUSIONS

A local assessment of volume fraction at the optimal location can substantially improve the prediction of bone strength. Local assessment of other microstructural parameters may further improve this prediction but is not clinically feasible using current technology.

Inter-individual variability of bone density and morphology distribution in the proximal femur and T12 vertebra

Bone geometry, density and microstructure can vary widely between subjects. Knowledge about this variation in a population is of interest in particular for the design of orthopedic implants and interventions. The goal of this study is to investigate the local variability of bone density and microstructural parameters between subjects using a novel inter-subject image registration approach. Human proximal femora of 29 and T12 vertebrae of 20 individuals were scanned using a HR-pQCT and a micro-CT system, respectively. A pre-defined iso-anatomic mesh template was morphed to each micro-CT scan. For each element bone volume fraction and other morphological parameters (Tb.Th, Tb.N, Tb.Sp, SMI, DA) were determined and assigned to the element. A coefficient of variation (CV) was calculated for each parameter at each element location of the 29 femora and 20 T12 vertebrae. Contour plots of the CV distribution revealed very detailed information about the inter-individual variation in bone density and morphology. It is also shown that analyzing large sub-volumes, as commonly done in previous studies, would miss much of this variation. Detailed quantitative information of bone morphological parameters for each sample in the femur and the T12 database and their inter-individual variability are available from the mesh templates as supplementary data (http://w3.bmt.tue.nl/nl/fe_database/). We expect that these results can help to optimize implants and orthopedic procedures by taking local bone morphological parameter variations into account.

A novel approach to estimate trabecular bone anisotropy using a database approach

Continuum finite element (FE) models of bones have become a standard pre-clinical tool to estimate bone strength. These models are usually based on clinical CT scans and material properties assigned are chosen as isotropic based only on the density distribution. It has been shown, however, that trabecular bone elastic behavior is best described as orthotropic. Unfortunately, the use of orthotropic models in FE analysis derived from CT scans is hampered by the fact that the measurement of a trabecular orientation (fabric) is not possible from clinical CT images due to the low resolution of such images. In this study, we explore the concept of using a database (DB) of high-resolution bone models to derive the fabric information that is missing in clinical images. The goal of this study was to investigate if models with fabric derived from a relatively small database can already produce more accurate results than isotropic models. A DB of 33 human proximal femurs was generated from micro-CT scans with a nominal isotropic resolution of 82 µm. Continuum FE models were generated from the images using a pre-defined mesh template in combination with an iso-anatomic mesh morphing tool. Each element within the mesh template is at a specific anatomical location. For each element within the cancellous bone, a spherical region around the element centroid with a radius of 2mm was defined. Bone volume fraction and the mean-intercept-length fabric tensor were analyzed for that region. Ten femurs were used as test cases. For each test femur, four different models were generated: (1) an orthotropic model based on micro-CT fabric measurements (gold standard), (2) an orthotropic model based on the fabric derived from the best-matched database model, (3) an isotropic-I model in which the fabric tensor was set to the identity tensor, and (4) a second isotropic-II model with its total bone stiffness fitted to the gold standard. An elastic-plastic damage model was used to simulate failure and post failure behavior during a fall to the side. The results show that all models produce a similar stress distribution. However, compared to the gold standard, both isotropic-I and II models underestimated the stress/damage distributions significantly. We found no significant difference between DB-derived and gold standard models. Compared to the gold standard, the isotropic-I models further underestimated whole bone stiffness by 26.3% and ultimate load by 14.5%, while these differences for the DB-derived orthotropic models were only 4.9% and 3.1% respectively. The results indicate that the concept of using a DB to estimate patient-specific anisotropic material properties can considerably improve the results. We expect that this approach can lead to more accurate results in particular for cases where bone anisotropy plays an important role, such as in osteoporotic patients and around implants.

The heterogeneity in femoral neck structure and strength

Most measures of femoral neck strength derived using dual-energy X-ray absorptiometry or computed tomography (CT) assume the femoral neck is a cylinder with a single cortical thickness. We hypothesized that these simplifications introduce errors in estimating strength and that detailed analyses will identify new parameters that more accurately predict femoral neck strength. High-resolution CT data were used to evaluate 457 cross-sectional slices along the femoral neck of 12 postmortem specimens. Cortical morphology was measured in each cross-section. The distribution of cortical thicknesses was evaluated to determine whether the mean or median better estimated central tendency. Finite-element models were used to calculate the stresses in each cross-section resulting from the peak hip joint forces created during a sideways fall. The relationship between cortical morphology and peak bone stress along the femoral neck was analyzed using multivariate regression analysis. In all cross-sections, cortical thicknesses were non-normally distributed and skewed toward smaller thicknesses (p < 0.0001). The central tendency of cortical thickness was best estimated by the median, not the mean. Stress increased as the median cortical thickness decreased along the femoral neck. The median, not mean, cortical thickness combined with anterior-posterior diameter best predicted peak bone stress generated during a sideways fall (R(2) = 0.66, p < 0.001). Heterogeneity in the structure of the femoral neck determines the diversity of its strength. The median cortical thickness best predicted peak femoral neck stress and is likely to be a relevant predictor of femoral neck fragility.