HR-pQCT-based homogenised finite element models provide quantitative predictions of experimental vertebral body stiffness and strength with the same accuracy as μFE models

This study validated two different high-resolution peripheral quantitative computer tomography (HR-pQCT)-based finite element (FE) approaches, enhanced homogenised continuum-level (hFE) and micro-finite element (μFE) models, by comparing them with compression test results of vertebral body sections. Thirty-five vertebral body sections were prepared by removing endplates and posterior elements, scanned with HR-pQCT and tested in compression up to failure. Linear hFE and μFE models were created from segmented and grey-level CT images, and apparent model stiffness values were compared with experimental stiffness as well as strength results. Experimental and numerical apparent elastic properties based on grey-level/segmented CT images (N=35) correlated well for μFE (r2=0.748/0.842) and hFE models (r2=0.741/0.864). Vertebral section stiffness values from the linear μFE/hFE models estimated experimental ultimate apparent strength very well (r2=0.920/0.927). Calibrated hFE models were able to predict quantitatively apparent stiffness with the same accuracy as μFE models. However, hFE models needed no back-calculation of a tissue modulus or any kind of fitting and were computationally much cheaper.     

Biofidelic white matter heterogeneity decreases computational model predictions of white matter strains during rapid head rotations

The finite element (FE) brain model is used increasingly as a design tool for developing technology to mitigate traumatic brain injury. We developed an ultra high-definition FE brain model (>4 million elements) from CT and MRI scans of a 2-month-old pre-adolescent piglet brain, and simulated rapid head rotations. Strain distributions in the thalamus, coronal radiata, corpus callosum, cerebral cortex gray matter, brainstem and cerebellum were evaluated to determine the influence of employing homogeneous brain moduli, or distinct experimentally derived gray and white matter property representations, where some white matter regions are stiffer and others less stiff than gray matter. We find that constitutive heterogeneity significantly lowers white matter deformations in all regions compared with homogeneous properties, and should be incorporated in FE model injury prediction.     

A new approach for assigning bone material properties from CT images into finite element models

Generation of subject-specific finite element (FE) models from computed tomography (CT) datasets is of significance for application of the FE analysis to bone structures. A great challenge that remains is the automatic assignment of bone material properties from CT Hounsfield Units into finite element models. This paper proposes a new assignment approach, in which material properties are directly assigned to each integration point. Instead of modifying the dataset of FE models, the proposed approach divides the assignment procedure into two steps: generating the data file of the image intensity of a bone in a MATLAB program and reading the file into ABAQUS via user subroutines. Its accuracy has been validated by assigning the density of a bone phantom into a FE model. The proposed approach has been applied to the FE model of a sheep tibia and its applicability tested on a variety of element types. The proposed assignment approach is simple and illustrative. It can be easily modified to fit users’ situations.     

The use of sparse CT datasets for auto-generating accurate FE models of the femur and pelvis

The finite element (FE) method when coupled with computed tomography (CT) is a powerful tool in orthopaedic biomechanics. However, substantial data is required for patient-specific modelling. Here we present a new method for generating a FE model with a minimum amount of patient data. Our method uses high order cubic Hermite basis functions for mesh generation and least-square fits the mesh to the dataset. We have tested our method on seven patient data sets obtained from CT assisted osteodensitometry of the proximal femur. Using only 12 CT slices we generated smooth and accurate meshes of the proximal femur with a geometric root mean square (RMS) error of less than 1 mm and peak errors less than 8 mm. To model the complex geometry of the pelvis we developed a hybrid method which supplements sparse patient data with data from the visible human data set. We tested this method on three patient data sets, generating FE meshes of the pelvis using only 10 CT slices with an overall RMS error less than 3 mm. Although we have peak errors about 12 mm in these meshes, they occur relatively far from the region of interest (the acetabulum) and will have minimal effects on the performance of the model. Considering that linear meshes usually require about 70-100 pelvic CT slices (in axial mode) to generate FE models, our method has brought a significant data reduction to the automatic mesh generation step. The method, that is fully automated except for a semi-automatic bone/tissue boundary extraction part, will bring the benefits of FE methods to the clinical environment with much reduced radiation risks and data requirement.     

结合薄层CT技术建立下颌第一前磨牙三维有限元模型

目的结合薄层CT技术建立下颌第一前磨牙三维有限元模型。方法对正常人下颌第一前磨牙进行薄层CT扫描及图像处理,通过Matlab和ANSYS软件建立三维有限元模型,并加载验证模型力学分析的可行性。结果建立了包含髓腔的下颌第一前磨牙的三维有限元模型,得到101564个单元,144053个节点。载荷后的应力分布主要集中在颊尖部位和根尖部位,牙颈部受力较小。结论薄层CT技术与Matlab和ANSYS软件相结合,建立包含髓腔的下颌第一前磨牙的三维有限元模型,精度高、速度快,使用灵活,为后期的楔缺模型建立和分析奠定了基础。     

Computer aided stress analysis of long bones utilizing computed tomography

A computer aided analysis method has been developed which utilizes computed tomography (CT) and a finite element (FE) computer program to determine the stress-displacement pattern in a long bone section. The CT data file provides the geometry, the apparent density and the elastic properties for the three-dimensional FE model. A developed pre-processor generates the FE model of a human diaphyseal tibia section which is then analyzed by the SAP IV finite element program. The results obtained are sorted and displayed by a developed post-processor and compared with stresses and deformations from the literature. The model generation method was verified by applying it to a model of simple geometry and boundary conditions, then comparing the results with the analytical solution of the same problem. The convergence behavior of nodal displacements was tested as a function of mesh refinement. This method provides an automatic, versatile, non-invasive and accurate tool of long bone modeling for finite element stress analysis.     

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

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

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.     

Smooth surface meshing for automated finite element model generation from 3D image data

Finite element (FE) modelling based on data from three-dimensional high-resolution computed tomography (CT) imaging systems provides a non-invasive method to assess structural mechanics. Automated mesh generation from these voxel based image data can be achieved by direct conversion to hexahedron elements, however these model representations have jagged edges. This paper proposes an automated method to generate smoothed FE meshes from voxel-based image data. Mesh fairing processes are utilized that allow constraints that control the smoothing process, and are computationally efficient. Surfaces of the mesh on the exterior, as well as interfaces between two tissues, can be smoothed by varying fairing parameters and constraint criteria. The method was tested on a variety of real and simulated three-dimensional data sets, resulting in both hexahedron and tetrahedron meshes. It was shown that the fairing process is linearly related to the number of smoothing iterations, and that peak stresses are reduced in FE simulations of the smoothed models. Although developed for micro-CT data sets, this fast and reliable mesh smoothing method could be applied to any three-dimensional image data where node and element connectivity have been defined.     

Determination of orthotropic bone elastic constants using FEA and modal analysis

Finite element models have been widely employed in an effort to quantify the stress and strain distribution around implanted prostheses and to explore the influence of these distributions on their long-term stability. In order to provide meaningful predictions, such models must contain an appropriate reflection of mechanical properties. Detailed geometrical and density information is now readily available from CT scanning. However, despite the use of phantoms, a method of determining mechanical properties (or elastic constants) from bone density has yet to be made available in a usable form.In this study, a cadaveric bone was CT scanned and its natural frequencies were measured using modal analysis. Using the geometry obtained from the CT scan data, a finite element mesh was created with the distribution of density established by matching the mass of the FE bone model with the mass of the cadaveric bone. The maximum values of the orthotropic elastic constants were then established by matching the predictions from FE modal analyses to the experimental natural frequencies, giving a maximum error of 7.8% over 4 modes of vibration. Finally, the elastic constants of the bone derived from the analyses were compared with those measured using ultrasound techniques. This produced a difference of <1% for both the maximum density and axial Young's Modulus. This study has thereby produced an orthotropic finite element model of a human femur. More importantly, however, is the implication that it is possible to create a valid FE model by simply comparing the FE results with the measured resonant frequency of the CT scanned bone.     

Identification of the material parameters of soft tissues in the compressed leg

Elastic compression is recommended in prophylaxis and the treatment of venous disorder of the human leg. However, the mechanisms of compression are not completely understood and the response of internal tissues to the external pressure is partially unknown. To address this later issue, a 3D FE model of a human leg is developed. The geometry is derived from 3D CT scans. The FE model is made up of soft tissues and rigid bones. An inverse method is applied to identify the properties of soft tissues which are modelled as hyperelastic, near-incompressible, homogeneous and isotropic materials. The principle is to calibrate the constitutive properties using CT scans carried out with and without the presence of a compression sock. The deformed geometry computed by the calibrated FE model is in agreement with the geometry deduced from the CT scans. The model also provides the internal pressure distribution, which may lead to medical exploitation in the future.     

Concept and development of an orthotropic FE model of the proximal femur

PURPOSE: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE "model femur" to realistically simulate three-dimensional bone remodelling. METHODS: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known "density-determined" bony material properties (Young's modulus; Poisson's ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same "CT-density-characterized" volumetric group.In order to fix the principal directions of stiffness in FE areas with the same "density characterization", the cadaveric femurs were cut in 2mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the "CT-density characterized" three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter's criterion. RESULTS: In the constructed "model femur", each FE is characterized by the principal directions of the stiffness and the "CT-density-determined" material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. CONCLUSIONS: With the orthotropic "model femur", the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc).     

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

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

Validation of 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.     

Development and validation of subject-specific finite element models for blunt trauma study

This study developed and validated finite element (FE) models of swine and human thoraxes and abdomens that had subject-specific anatomies and could accurately and efficiently predict body responses to blunt impacts. Anatomies of the rib cage, torso walls, thoracic, and abdominal organs were reconstructed from X-ray computed tomography (CT) images and extracted into geometries to build FE meshes. The rib cage was modeled as an inhomogeneous beam structure with geometry and bone material parameters determined directly from CT images. Meshes of soft components were generated by mapping structured mesh templates representative of organ topologies onto the geometries. The swine models were developed from and validated by 30 animal tests in which blunt insults were applied to swine subjects and CT images, chest wall motions, lung pressures, and pathological data were acquired. A comparison of the FE calculations of animal responses and experimental measurements showed a good agreement. The errors in calculated response time traces were within 10% for most tests. Calculated peak responses showed strong correlations with the experimental values. The stress concentration inside the ribs, lungs, and livers produced by FE simulations also compared favorably to the injury locations. A human FE model was developed from CT images from the Visible Human project and was scaled to simulate historical frontal and side post mortem human subject (PMHS) impact tests. The calculated chest deformation also showed a good agreement with the measurements. The models developed in this study can be of great value for studying blunt thoracic and abdominal trauma and for designing injury prevention techniques, equipments, and devices.     

Strategies towards rapid generation of forefoot model incorporating realistic geometry of metatarsals encapsulated into lumped soft tissues for personalized finite element analysis

Use of finite element (FE) foot model as a clinical diagnostics tool is likely to improve the specificity of foot injury predictions in the diabetic population. Here we proposed a novel workflow for rapid construction of foot FE model incorporating realistic geometry of metatarsals encapsulated into lumped forefoot’s soft tissues. Custom algorithms were implemented to perform unsupervised segmentation and mesh generation to directly convert CT data into a usable FE model. The automatically generated model provided higher efficiency and comparable numerical accuracy when compared to the model constructed using a traditional solid-based mesh process. The entire procedure uses MATLAB as the main platform, and makes the present approach attractive for creating personalized foot models to be used in clinical studies.     

Reliable simulations of the human proximal femur by high-order finite element analysis validated by experimental observations

Background: The mechanical response of patient-specific bone to various load conditions is of major clinical importance in orthopedics. Herein we enhance the methods presented in Yosibash et al. [2007. A CT-based high-order finite element analysis of the human proximal femur compared to in-vitro experiments. ASME Journal of Biomechanical Engineering 129(3), 297–309.] for the reliable simulations of the human proximal femur by high-order finite elements (FEs) and validate the simulations by experimental observations.

Method of approach: A fresh-frozen human femur was scanned by quantitative computed tomography (QCT) and thereafter loaded (in vitro experiments) by a quasi-static force of up to 1250 N. QCT scans were manipulated to generate a high-order FE bone model with distinct cortical and trabecular regions having inhomogeneous isotropic elastic properties with Young's modulus represented by continuous spatial functions. Sensitivity analyses were performed to quantify parameters that mostly influence the mechanical response. FE results were compared to displacements and strains measured in the experiments.

Results: Young moduli correlated to QCT Hounsfield Units by relations in Keyak and Falkinstein [2003. Comparison of in situ and in vitro CT scan-based finite element model predictions of proximal femoral fracture load. Medical Engineering and Physics 25, 781–787.] were found to provide predictions that match the experimental results closely. Excellent agreement was found for both the displacements and strains. The presented study demonstrates that reliable and validated high-order patient-specific FE simulations of human femurs based on QCT data are achievable for clinical computer-aided decision making.     

A new cell-based FE model for the mechanics of embryonic epithelia

In order to overcome a significant stiffening artefact associated with current finite element (FE) models for the mechanics of embryonic epithelia, two new FE formulations were developed. Cell–cell interfacial tensions γ are represented by constant-force rod elements as in previous models. However, the viscosity of the cytoplasm with its embedded organelles and filament networks is modeled using viscous triangular elements, it is modeled using either radial and circumferential dashpots or an orthogonal dashpot system rather than the viscous triangular elements typical of previous two-dimensional FE models. The models are tested against tissue (epithelium) stretching because it gives rise to significant changes in cell shape and against cell sorting because it involves high rates of cell rearrangement. The orthogonal dashpot system is found to capture cell size and shape effects well, give the model cells characteristics that are consistent with those of real cells, provide high computational efficiency and hold promise for future three-dimensional analyses.     

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.     

A new cell-based FE model for the mechanics of embryonic epithelia

In order to overcome a significant stiffening artefact associated with current finite element (FE) models for the mechanics of embryonic epithelia, two new FE formulations were developed. Cell-cell interfacial tensions gamma are represented by constant-force rod elements as in previous models. However, the viscosity of the cytoplasm with its embedded organelles and filament networks is modeled using viscous triangular elements, it is modeled using either radial and circumferential dashpots or an orthogonal dashpot system rather than the viscous triangular elements typical of previous two-dimensional FE models. The models are tested against tissue (epithelium) stretching because it gives rise to significant changes in cell shape and against cell sorting because it involves high rates of cell rearrangement. The orthogonal dashpot system is found to capture cell size and shape effects well, give the model cells characteristics that are consistent with those of real cells, provide high computational efficiency and hold promise for future three-dimensional analyses.