Evaluation of the generality and accuracy of a new mesh morphing procedure for the human femur

Various papers described mesh morphing techniques for computational biomechanics, but none of them provided a quantitative assessment of generality, robustness, automation, and accuracy in predicting strains. This study aims to quantitatively evaluate the performance of a novel mesh-morphing algorithm. A mesh-morphing algorithm based on radial-basis functions and on manual selection of corresponding landmarks on template and target was developed. The periosteal geometries of 100 femurs were derived from a computed tomography scan database and used to test the algorithm generality in producing finite element (FE) morphed meshes. A published benchmark, consisting of eight femurs for which in vitro strain measurements and standard FE model strain prediction accuracy were available, was used to assess the accuracy of morphed FE models in predicting strains. Relevant parameters were identified to test the algorithm robustness to operative conditions. Time and effort needed were evaluated to define the algorithm degree of automation. Morphing was successful for 95% of the specimens, with mesh quality indicators comparable to those of standard FE meshes. Accuracy of the morphed meshes in predicting strains was good (R(2)>0.9, RMSE%<10%) and not statistically different from the standard meshes (p-value=0.1083). The algorithm was robust to inter- and intra-operator variability, target geometry refinement (p-value>0.05) and partially to the number of landmark used. Producing a morphed mesh starting from the triangularized geometry of the specimen requires on average 10 min. The proposed method is general, robust, automated, and accurate enough to be used in bone FE modelling from diagnostic data, and prospectively in applications such as statistical shape modelling.     

Mesh morphing for finite element analysis of implant positioning in cementless total hip replacements

Finite element (FE) analysis of the effect of implant positioning on the performance of cementless total hip replacements (THRs) requires the generation of multiple meshes to account for positioning variability. This process can be labour intensive and time consuming as CAD operations are needed each time a specific orientation is to be analysed. In the present work, a mesh morphing technique is developed to automate the model generation process. The volume mesh of a baseline femur with the implant in a nominal position is deformed as the prosthesis location is varied. A virtual deformation field, obtained by solving a linear elasticity problem with appropriate boundary conditions, is applied. The effectiveness of the technique is evaluated using two metrics: the percentages of morphed elements exceeding an aspect ratio of 20 and an angle of 165° between the adjacent edges of each tetrahedron. Results show that for 100 different implant positions, the first and second metrics never exceed 3% and 3.5%, respectively. To further validate the proposed technique, FE contact analyses are conducted using three selected morphed models to predict the strain distribution in the bone and the implant micromotion under joint and muscle loading. The entire bone strain distribution is well captured and both percentages of bone volume with strain exceeding 0.7% and bone average strains are accurately computed. The results generated from the morphed mesh models correlate well with those for models generated from scratch, increasing confidence in the methodology. This morphing technique forms an accurate and efficient basis for FE based implant orientation and stability analysis of cementless hip replacements.     

Comprehensive evaluation of PCA-based finite element modelling of the human femur

Computed tomography (CT)-based finite element (FE) reconstructions describe shape and density distribution of bones. Both shape and density distribution, however, can vary a lot between individuals. Shape/density indexation (usually achieved by principal component analysis—PCA) can be used to synthesize realistic models, thus overcoming the shortage of CT-based models, and helping e.g. to study fracture determinants, or steer prostheses design. The aim of this study was to describe a PCA-based statistical modelling algorithm, and test it on a large CT-based population of femora, to see if it can accurately describe and reproduce bone shape, density distribution, and biomechanics.To this aim, 115 CT-datasets showing normal femoral anatomy were collected and characterized. Isotopological FE meshes were built. Shape and density indexation procedures were performed on the mesh database. The completeness of the database was evaluated through a convergence study. The accuracy in reconstructing bones not belonging to the indexation database was evaluated through (i) leave-one-out tests (ii) comparison of calculated vs. in-vitro measured strains.Fifty indexation modes for shape and 40 for density were necessary to achieve reconstruction errors below pixel size for shape, and below 10% for density. Similar errors for density, and slightly higher errors for shape were obtained when reconstructing bones not belonging to the database. The in-vitro strain prediction accuracy of the reconstructed FE models was comparable to state-of-the-art studies.In summary, the results indicate that the proposed statistical modelling tools are able to accurately describe a population of femora through finite element models.     

A new method for the automatic mesh generation of bone segments from CT data.

A new procedure for the automatic generation of finite element meshes of bone segments from computed tomography (CT) data sets is described. The new method allows a direct automatic generation from the CT data and produces a very accurate unstructured hexahedral mesh. The accuracy of the method was established using the CT images of an artificial femur showing range of attenuation values comparable to those of a human femur. To establish the optimal values for the parameters controlling the mesh a sensitivity analysis was carried out using mesh-conditioning indicators. Some of the best meshes, with increasing levels of refinement, were used to analyse the stresses induced in the proximal femur by single leg stance posture. The accuracy of the meshes was evaluated using an implicit a posteriori residual-based error estimates. The number of elements with stress residuals larger than 10% of the peak stress was 7.8% using the coarsest mesh and only 1.8% with the finest mesh. The proposed method has been proved able to conjugate full automation with high-quality finite element meshes. The stress predictions obtained using these hexahedral-only meshes have been more accurate than those obtained by any other automatic mesh generation algorithm. Once properly integrated in an easy-to-use application, the described method could finally make feasible many clinical applications of finite element analysis.     

Comparison of an inhomogeneous orthotropic and isotropic material models used for FE analyses

Finite element (FE) analysis has been widely used to study the behaviour of bone or implants in many clinical applications. One of the main factors in analyses is the realistic behaviour of the bone model, because the behaviour of the bone is strongly dependent on a realistic bone material property assignment. The objective of this study was to compare isotropic and orthotropic inhomogeneous material models used for FE analyses of the "global" proximal femur and "small" specimens of the bone (cancellous and cortical). Our hypothesis was that realistic material property assignment (orthotropy) is very important for the FE analyses of small bone specimens, whereas in global FE analyses of the proximal femur, this assignment can be omitted, if the inhomogeneous material model was used. The three-dimensional geometry of the "global" proximal femur was reconstructed using CT scans of a cadaveric femur. This model was implemented into an FE simulation tool and various bone material properties, dependant on bone density, were assigned to each element in the models. The "small" specimens of cortical and cancellous bone were created in the same way as the model of the proximal femur. The results obtained from FE analyses support our above described hypothesis.     

Statistical modelling of the whole human femur incorporating geometric and material properties

When analysing the performance of orthopaedic implants the vast majority of computational studies use either a single or limited number of bone models. The results are then extrapolated to the population as a whole, overlooking the inherent and large interpatient variability in bone quality and geometry. This paper describes the creation of a three dimensional, statistical, finite element analysis (FEA) ready model of the femur using principal component analysis. To achieve this a registration scheme based on elastic surface matching and a mesh morphing algorithm has been developed. This method is fully automated enabling registration and generation of high resolution models. The variation in both geometry and material properties was extracted from 46 computer tomography scans and captured by the statistical model. Analysis of mesh quality showed this was maintained throughout the model generation and sampling process. Reconstruction of the training femurs showed 35 eigenmodes were required for accurate reproduction. A set of unique, anatomically realistic femur models were generated using the statistical model, with a variation comparable to that seen in the population. This study illustrates a methodology with the potential to generate femur models incorporating material properties for large scale multi-femur finite element studies.     

An improved method for the automatic mapping of computed tomography numbers onto finite element models

The assignment of bone tissue material properties is a fundamental step in the generation of subject-specific finite element models from computed tomography data. Aim of the present work is to investigate the influence of the material mapping algorithm on the results predicted by the finite element analysis. Two models, a coarse and a refined one, of a human ileum, femur and tibia, were generated from CT data and used for the tests. In addition a convergence analysis was carried out for the femur model, using six refinement levels, to verify whether the inclusion of the material properties would significantly alter the convergence behaviour of the mesh. The results showed that the choice of the mapping algorithm influences the material distribution. However, this did not always propagate into the finite element results. The difference between the maximum Von Mises stress remained always lower than 10%, apart one case when it reached the 13%. However, the global behaviour of the meshes showed more marked differences between the two algorithms: in the finer meshes of the two long bones 20-30% of the bone volume showed differences in the predicted Von Mises stresses greater than 10%. The convergence behaviour of the model was not worsened by the introduction of inhomogeneous material properties. The software was made available in the public domain.     

基于CT数据的人体L3-L4腰椎节段的三维有限元建模和分析

目的 建立一个精确的人体L3-L4腰椎节段有限元模型,用于腰椎生物力学的研究.方法 基于可视人计划(visible human project,VHP)男性冷冻CT数据,通过Marchingcubes算法三维重建L3和L4椎骨的几何模型并转换为有限元网格,然后结合椎间盘和韧带的网格建立L3-L4节段的有限元网格.根据CT值设定材料特性建立有限元模型,施加压缩的边界条件进行有限元分析,并和参考模型的结果比较分析.结果 基于CT的L3-L4节段有限元模型比参考模型更符合腰椎的解剖结构.结论 基于CT的L3-L4节段有限元模型能够精确的描述腰椎解剖结构,保证有限元分析的准确性.     

Methods for high-resolution anisotropic finite element modeling of the human head: automatic MR white matter anisotropy-adaptive mesh generation

This study proposes an advanced finite element (FE) head modeling technique through which high-resolution FE meshes adaptive to the degree of tissue anisotropy can be generated. Our adaptive meshing scheme (called wMesh) uses MRI structural information and fractional anisotropy maps derived from diffusion tensors in the FE mesh generation process, optimally reflecting electrical properties of the human brain. We examined the characteristics of the wMeshes through various qualitative and quantitative comparisons to the conventional FE regular-sized meshes that are non-adaptive to the degree of white matter anisotropy. We investigated numerical differences in the FE forward solutions that include the electrical potential and current density generated by current sources in the brain. The quantitative difference was calculated by two statistical measures of relative difference measure (RDM) and magnification factor (MAG). The results show that the wMeshes are adaptive to the anisotropic density of the WM anisotropy, and they better reflect the density and directionality of tissue conductivity anisotropy. Our comparison results between various anisotropic regular mesh and wMesh models show that there are substantial differences in the EEG forward solutions in the brain (up to RDM=0.48 and MAG=0.63 in the electrical potential, and RDM=0.65 and MAG=0.52 in the current density). Our analysis results indicate that the wMeshes produce different forward solutions that are different from the conventional regular meshes. We present some results that the wMesh head modeling approach enhances the sensitivity and accuracy of the FE solutions at the interfaces or in the regions where the anisotropic conductivities change sharply or their directional changes are complex. The fully automatic wMesh generation technique should be useful for modeling an individual-specific and high-resolution anisotropic FE head model incorporating realistic anisotropic conductivity distributions towards more accurate analysis of bioelectromagnetic problems.     

Single-trabecula building block for large-scale finite element models of cancellous bone

Recent development of high-resolution imaging of cancellous bone allows finite element (FE) analysis of bone tissue stresses and strains in individual trabeculae. However, specimen-specific stress/strain analyses can include effects of anatomical variations and local damage that can bias the interpretation of the results from individual specimens with respect to large populations. This study developed a standard (generic) ‘building-block’ of a trabecula for large-scale FE models. Being parametric and based on statistics of dimensions of ovine trabeculae, this building block can be scaled for trabecular thickness and length and be used in commercial or custom-made FE codes to construct generic, large-scale FE models of bone, using less computer power than that currently required to reproduce the accurate micro-architecture of trabecular bone. Orthogonal lattices constructed with this building block, after it was scaled to trabeculae of the human proximal femur, provided apparent elastic moduli of ∼ 150 MPa, in good agreement with experimental data for the stiffness of cancellous bone from this site. Likewise, lattices with thinner, osteoporotic-like trabeculae could predict a reduction of ∼30% in the apparent elastic modulus, as reported in experimental studies of osteoporotic femora. Based on these comparisons, it is concluded that the single-trabecula element developed in the present study is well-suited for representing cancellous bone in large-scale generic FE simulations.     

个性化全骨盆三维有限元建模及骶髂关节骨折脱位模拟

目的建立高度仿真的个性化的完整骨盆三维有限元模型,并在此基础上进行骶髂关节骨折脱位的模拟。方法从CT精确重建独立的左、右髋骨和骶骨实体模型,根据髋骨和骶骨的外形特征,利用专门的流线型生物力学有限元网格划分器生成规则的体网格模型,并进一步建立骶髂关节的终板、软骨、关节接触面,和骨盆上的主要韧带组织及耻骨间盘。在建立的完整模型上去掉一侧的骶髂关节韧带群进行骨折脱位模拟,并与正常的情况进行对比。结果建立了高精度的个性化全骨盆的三维有限元模型,包括左右髋骨和骶骨的皮质骨、松质骨,骶髂关节的终板、软骨和带摩擦的关节接触面,韧带包括骶髂骨间韧带、骶髂前韧带、骶髂后韧带、骶棘韧带、骶结节韧带、耻骨上韧带和耻骨弓状韧带,以及耻骨间盘。正常模型的加载模拟和骶髂关节骨折脱位模拟的预测结果均与文献试验生物力学结果相符合。结论利用专门的生物力学有限元建模工具能建立更复杂更精确的三维有限元模型,成为全骨盆生物力学分析研究的平台和基础。     

Methods and evaluations of MRI content-adaptive finite element mesh generation for bioelectromagnetic problems

In studying bioelectromagnetic problems, finite element analysis (FEA) offers several advantages over conventional methods such as the boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropic conductivity. For FEA, mesh generation is the first critical requirement and there exist many different approaches. However, conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes (cMeshes), resulting in numerous nodes and elements in modelling the conducting domain, and thereby increasing computational load and demand. In this work, we present efficient content-adaptive mesh generation schemes for complex biological volumes of MR images. The presented methodology is fully automatic and generates FE meshes that are adaptive to the geometrical contents of MR images, allowing optimal representation of conducting domain for FEA. We have also evaluated the effect of cMeshes on FEA in three dimensions by comparing the forward solutions from various cMesh head models to the solutions from the reference FE head model in which fine and equidistant FEs constitute the model. The results show that there is a significant gain in computation time with minor loss in numerical accuracy. We believe that cMeshes should be useful in the FEA of bioelectromagnetic problems.     

X-Ray Image Review of the Bone Remodeling Around an Osseointegrated Trans-femoral Implant and a Finite Element Simulation Case Study

The insertion of an implant into a bone leads to stress/strain redistribution, hence bone remodeling occurs adjacent to the implant. The study of the bone remodeling around the osseointegration implants can predict the long-term clinical success of the implant. The clinical medial–lateral X-rays of 11 patients were reviewed. To eliminate geometrical distortion of different X-rays, they were converted into a digital format and geometrical correction was carried out. Furthermore, the finite element (FE) method was used to investigate how the bone remodeling was affected by the stress/strain distribution in the femur. The review of clinical X-rays showed cortical bone growth around the proximal end of the implant and absorbtion at the distal end of the femur. The FE simulation revealed the stress/strain distribution in the femur of a selected patient. This provided a biomechanical interpretation of the bone remodeling. The existing bone remodeling theories such as minimal strain and strain rate theories were unable to offer satisfactory explanation for the cortical bone growth at the implant side of the proximal femur, where the stress/strain level was much lower than the one in the intact side of the femur. The study established the correlation between stress/strain distribution obtained from FE simulations and the bone remodeling of the clinical review. The cortical bone growth was initiated by the stress/strain gradient in the bone. Through the review of clinical X-rays and FE simulations, the study confirmed that the bone remodeling in a femur with an implant was influenced by the stress/strain redistribution. The strain level and stress gradient hypothesis is presented to offer an explanation for the implanted cortical bone remodeling observed in this study.     

Establishment of an architecture-specific experimental validation approach for finite element modeling of bone by rapid prototyping and high resolution computed tomography

A new experimental validation method for assessing the accuracy of large-scale finite element (FE) models of bone micro-structure at the apparent and tissue level was developed. Augmented scaled bone replicas were built using rapid prototype machines based on micro-computed tomography (micro-CT) data. The geometric accuracy of the model was evaluated by comparing experimental tests with the replicas to the FE solution based on the same micro-CT data. A new version of the large-scale FE solver was developed to incorporate orthotropic material properties, hence the experimentally determined properties of the rapid prototype material were input into the FE models. The modified FE solver predicted the experimental apparent level stiffness within less than 1%, and the difference between experimental strain gauge measurements and FE-calculated surface stresses was 7% and 49% on a flat and curved surface region, respectively. While absolute error estimates of surface stresses were limited due to strain gauge errors, the relatively larger difference on the curved surface is indicative of the limitations of a hexahedron FE model for representing such geometries. Although the validation approach is applied here for hexahedron based meshes, the method is flexible for varying bone architectures and will be important for validation of future large-scale FE modeling developments that utilize techniques such as mesh smoothing and tetrahedron elements.     

Morphology based anisotropic finite element models of the proximal femur validated with experimental data

Finite element analysis (FEA) of bones scanned with Quantitative Computed Tomography (QCT) can improve early detection of osteoporosis. The accuracy of these models partially depends on the assigned material properties, but anisotropy of the trabecular bone cannot be fully captured due to insufficient resolution of QCT. The inclusion of anisotropy measured from high resolution peripheral QCT (HR-pQCT) could potentially improve QCT-based FEA of the femur, although no improvements have yet been demonstrated in previous experimental studies.This study analyzed the effects of adding anisotropy to clinical resolution femur models by constructing six sets of FE models (two isotropic and four anisotropic) for each specimen from a set of sixteen femurs that were experimentally tested in sideways fall loading with a strain gauge on the superior femoral neck. Two different modulus–density relationships were tested, both with and without anisotropy derived from mean intercept length analysis of HR-pQCT scans.Comparing iso- and anisotropic models to the experimental data resulted in nearly identical correlation and highly similar linear regressions for both whole bone stiffness and strain gauge measurements. Anisotropic models contained consistently greater principal compressive strains, approximately 14% in magnitude, in certain internal elements located in the femoral neck, greater trochanter, and femoral head.In summary, anisotropy had minimal impact on macroscopic measurements, but did alter internal strain behavior. This suggests that organ level QCT-based FE models measuring femoral stiffness have little to gain from the addition of anisotropy, but studies considering failure of internal structures should consider including anisotropy to their models.     

基于图像处理的个性化建模：从医学扫描到高精度计算模型的转换

目的　对于生物力学领域的研究者来说，计算仿真技术已成为一种不可或缺的工具。对于这种工具的性能，至关重要的一点在于其有效模拟个性化问题方面的能力。本文将阐述能将三维数字图像（由CT、超声机或MRI扫描仪生成的）直接转换生成高精度计算模型的一种独特的非常有效的方法。方法　采用的方法主要涉及：基于扫描的数据生成可输出到商业网格器中的表面模型－这种方法非常费时并且不是很精确，事实上对于复杂拓扑结构的影像数据这种方法很难处理：另外一种更加直接的方法是将几何模型的生成和网格划分一次性完成－这种方法先对感兴趣区域（三维图像分割）进行识别分割，然历直接生成基于一种由定义的边界分割的体素的体网格，这种方法被用来在整个体模型生成四面体和／或六面体单元，从而直接划分网格。结果　采用一种基于图像的网格方法来处理问题是非常先进的，也是非常精确有效的。这种基于图像自动生成的网格，其有限元单元模型区域边界正好在等值面上因此其考虑了局部体效应从而能保证局部体素的精确度。结论　对影像数据进行网格化是挑战也是机遇，这种与以往方法思想不一样的方法，在很多例子中，获得了更好的结果。这种能简易生成精确模型的方法，对于当前很多数值分析难以处理的问题诸如血液流体和病人个性化假体设计等提供了新的解决方案。     

Validation of statistical shape model based reconstruction of the proximal femur—A morphology study

Seventeen bones (sixteen cadaveric bones and one plastic bone) were used to validate a method for reconstructing a surface model of the proximal femur from 2D X-ray radiographs and a statistical shape model that was constructed from thirty training surface models. Unlike previously introduced validation studies, where surface-based distance errors were used to evaluate the reconstruction accuracy, here we propose to use errors measured based on clinically relevant morphometric parameters. For this purpose, a program was developed to robustly extract those morphometric parameters from the thirty training surface models (training population), from the seventeen surface models reconstructed from X-ray radiographs, and from the seventeen ground truth surface models obtained either by a CT-scan reconstruction method or by a laser-scan reconstruction method. A statistical analysis was then performed to classify the seventeen test bones into two categories: normal cases and outliers. This classification step depends on the measured parameters of the particular test bone. In case all parameters of a test bone were covered by the training population's parameter ranges, this bone is classified as normal bone, otherwise as outlier bone.Our experimental results showed that statistically there was no significant difference between the morphometric parameters extracted from the reconstructed surface models of the normal cases and those extracted from the reconstructed surface models of the outliers. Therefore, our statistical shape model based reconstruction technique can be used to reconstruct not only the surface model of a normal bone but also that of an outlier bone.     

A Robust 3D Finite Element Simulation of Human Proximal Femur Progressive Fracture Under Stance Load with Experimental Validation

Clinical implementation of quantitative computed tomography-based finite element analysis (QCT/FEA) of proximal femur (hip) fractures requires (i) to develop a bone material behavior able to describe the progressive fracturing process until complete failure of the hip. And (ii) to validate the model with realistic test data that represent typical hip fractures. The objective of the current study was to develop and experimentally validate an accurate 3D finite element (FE) model coupled to a quasi-brittle damage law to simulate human proximal femur fracture considering the initiation and progressive propagation of multiple cracks phases under quasi-static load. The model is based on continuum damage mechanics that can predict hip fracture in more adequate physical terms than criteria-based fracture models. In order to validate the model, ten human proximal femurs were tested until complete fracture under one-legged stance quasi-static load. QCT/FE models were generated and FE simulations were performed on these femurs with the same applied loads and boundary conditions than in the stance experiments. The proposed FE model leads to excellent agreement (R ² = 0.9432) between predicted and measured results concerning the shape of the force–displacement curve (yielding and fracturing) and the profile of the fractured edge. The motivation of this work was to propose a FE model for possible clinical use with a good compromise between complexity and capability of the simulation.