Finite Element Analysis of the Multiple Drilling Technique for Early Osteonecrosis of the Femoral Head

We used finite element (FE) method to investigate the effect of the drilling number and entry location of holes used in the multiple drilling technique on the stress and strain state in femur. Different three-dimensional FE models of a human hip joint with or without multiple drilling were fabricated using computed tomographic images obtained from the hip joint of a cadaver. The analysis technique was evaluated in a compression test using the cadaver specimen and FE analysis for the test using an FE model of the specimen. Von Mises stresses, principal stresses, and principal strains in the cancellous and cortical bone were calculated by using the different models, and changes in these values in relation to drilling number and entry hole locations were evaluated. Calculated peak values were much smaller than the yield strength, tensile strength, and yield strain of the cancellous and cortical bone for all cases of multiple drilling. Our results support that the multiple drilling technique for osteonecrosis of the femoral head is a stable operation technique.     

An experimentally validated micromechanical model of a rat vertebra under compressive loading

In recent years, finite element analysis (FEA) has been increasingly applied to examine and predict the mechanical behaviour of craniofacial and other bony structures. Traditional methods used to determine material properties and validate finite element models (FEMs) have met with variable success, and can be time‐consuming. An implicit assumption underlying many FE studies is that relatively high localized stress/strain magnitudes identified in FEMs are likely to predict material failure. Here we present a new approach that may offer some advantages over previous approaches. Recently developed technology now allows us to both image and conduct mechanical tests on samples in situ using a materials testing stage (MTS) fitted inside the microCT scanner. Thus, micro‐finite element models can be created and validated using both quantitative and qualitative means. In this study, a rat vertebra was tested under compressive loading until failure using an MTS. MicroCT imaging of the vertebra before mechanical testing was used to create a high resolution finite element model of the vertebra. Load‐displacement data recorded during the test were used to calculate the effective Young’s modulus of the bone (found to be 128 MPa). The microCT image of the compressed vertebra was used to assess the predictive qualities of the FE model. The model showed the highest stress concentrations in the areas that failed during the test. Clearly, our analyses do not directly address biomechanics of the craniofacial region; however, the methodology adopted here could easily be applied to examine the properties and behaviour of specific craniofacial structures, or whole craniofacial regions of small vertebrates. Experimentally validated micro‐FE analyses are a powerful method in the study of materials with complex microstructures such as bone.     

侧向冲击载荷作用下股骨-骨盆复合体的生物力学响应

目的利用三维有限元分析方法研究股骨-骨盆复合体在人体侧向摔倒时冲击载荷作用下的生物力学行为特性。方法基于中国力学虚拟人模型库建立股骨-骨盆-软组织复合体的三维有限元模型,包括皮质骨、松质骨和软组织;同时,构建一个刚体平面仿真地面。约束地面刚体,对整个股骨-骨盆-软组织复合体模型施加侧向2 m/s的速度载荷,整个仿真分析时间设定为20 ms。通过三维有限元分析计算获得股骨-骨盆侧摔冲击过程中应力应变变化特性。结果在13 ms时,股骨大转子处软组织与地面的接触力达到最大值7 656 N,对应的骨盆软组织上的最大等效应力值为2.64 MPa。冲击过程中,耻骨联合处骨皮质上等效应力出现极大值,为142.64 MPa,接近其屈服强度;股骨颈和大转子处应力水平较高,股骨颈处皮质骨上的最大等效应力值为76.49 MPa;股骨颈处松质骨上的最大等效应力值为8.44 MPa,最大压缩应变值为0.94%;股骨大转子处松质骨上的最大等效应力值为8.50 MPa,最大压缩应变值为0.93%。结论人体股骨-骨盆复合体在侧摔减速冲击载荷作用下股骨颈、大转子及耻骨联合处易出现骨折。     

腰椎椎体有限元建模的最优单元尺寸和材料属性分布及建模方法

目的研究人体腰椎椎体有限元建模中有限元的单元尺寸和类型、松质骨材料属性分配方式以及皮质骨结构模拟方法对有限元结果的影响。方法基于定量CT扫描人体腰椎的影像,采用6种不同的单元尺寸(0.5、1.0、1.5、2.0、2.5、3.0 mm)、2种松质骨材料属性分配方法、2种松质骨非均匀材料属性分配梯度(150、300)、2种皮质骨结构建模方法,建立22个去除后部结构的腰椎L2段椎体有限元模型,计算获得22个有限元模型的最大位移、应变能、平均应力、轴向刚度,并对这些结果进行统计分析和验证。结果单元尺寸为0.5 mm时,10、150、300三种非均匀材料属性分配梯度下,模型的轴向刚度值出现明显差异;不同单元尺寸下,松质骨在150种非均匀材料属性分配梯度下,模型的平均应力波动变化平缓;利用最外层六面体单元模拟皮质骨结构方法,其平均应力大于利用在最外层添加蒙皮(skin)模拟皮质骨结构方法。结论在进行腰椎椎体有限元建模时,选取0.5 mm尺寸的六面体单元、为椎体松质骨分配150种非均匀材料属性、利用最外层六面体单元模拟椎体皮质骨结构的建模方法,建立的有限元模型更加合理和有效。研究结果为后续大批量、个体化腰椎椎体模型的建立奠定基础。     

Three-Dimensional Finite Element Modeling of Human Ear for Sound Transmission

An accurate, comprehensive finite element model of the human ear can provide better understanding of sound transmission, and can be used for assessing the influence of diseases on hearing and the treatment of hearing loss. In this study, we proposed a three-dimensional finite element model of the human ear that included the external ear canal, tympanic membrane (eardrum), ossicular bones, middle ear suspensory ligaments/muscles, and middle ear cavity. This model was constructed based on a complete set of histological section images of a left ear temporal bone. The finite element (FE) model of the human ear was validated by comparing model-predicted ossicular movements at the stapes footplate and tympanic membrane with published experimental measurements on human temporal bones. The FE model was employed to predict the effects of eardrum thickness and stiffness, incudostapedial joint material, and cochlear load on acoustic-mechanical transmission through the human ossicular chain. The acoustic-structural coupled FE analysis between the ear canal air column and middle ear ossicles was also conducted and the results revealed that the peak responses of both tympanic membrane and stapes footplate occurred between 3000 and 4000 Hz.     

单髁膝关节置换胫骨元件不同固定柱形状的有限元分析

目的针对单髁膝关节置换后胫骨前内侧疼痛、胫骨元件松动以及对侧关节炎恶化的问题,通过有限元方法比较分析胫骨元件固定柱的不同几何形状对胫骨应力分布的影响。方法建立有效的单髁膝关节置换有限元模型,对胫骨元件固定柱的形状进行设计。在相同的加载条件下,分别对双柱形、单脊形、双脊形和十字星形胫骨元件进行有限元分析,并与完整膝关节模型进行对比,评估胫骨元件固定柱不同形状设计对胫骨前内侧皮质骨应力、胫骨截骨面松质骨应力、胫骨对侧软骨应力的影响。结果单髁置换后胫骨前内侧皮质骨应力峰值均增大。与完整膝关节相比,在双柱形、单脊形、双脊形和十字星形胫骨元件固定柱的模型中,胫骨前内侧皮质骨应力峰值分别增加56.1%、55.9%、54.5%和68.4%。单脊形和双脊形胫骨元件松质骨截骨面应力峰值比完整胫骨分别减小8.1%和15.6%,而双柱形和十字星形则分别增大67.9%和121.5%,超过松质骨的疲劳屈服应力。双柱形、单脊形、双脊形和十字星形胫骨固定柱对应的胫骨对侧软骨应力峰值相比于完整胫骨分别减小42.1%、26.6%、24.2%和28.5%。结论单髁膝关节置换改变了胫骨内外侧的载荷分布,使置换侧承受更大的载荷。单脊形和双脊形胫骨元件在降低胫骨前内侧皮质骨和截骨面松质骨应力方面效果更好,其中单脊形胫骨元件更接近完整膝关节胫骨的应力分布。研究结果可为设计更符合膝关节力学性能的单髁膝关节假体提供理论依据。     

各向异性松质骨弹性性能有限元分析

骨质疏松会导致松质骨细化从而降低松质骨力学性能。为了评估椎体松质骨的力学特性,文中采用有限元参数化建模,利用十四面体模型模拟棒状小梁骨的微结构,对各向异性松质骨的弹性性能进行了计算分析。通过控制输入参数Tb.Th、Tb.Sp、E0模拟不同骨质疏松程度的松质骨。计算结果表明,松质骨模量与骨体积分数呈平方律关系;随着各向异性比的增加,松质骨纵、横向模量间的比值呈线性增加,而横向两个模量保持基本一致。结果说明该微结构模型较好地反映了松质骨的横观各向同性性质,并能较好地反映受载松质骨的应力分布。     

A parametric analysis of fixation post shape in tibial knee prostheses

A primary concern of total knee replacement (TKR) is aseptic loosening of the tibial component, which may be caused by shielding of mechanical stresses in the bone and may require subsequent revision surgery. A three-dimensional (3D) finite element (FE) model has been developed to study bone and interface stresses for four different tibial prosthesis designs. The model described here incorporates orthotropic and heterogeneous bone properties with physiologically representative loading conditions. Results from this model indicate that stress distribution is affected by the incorporation of anisotropy and spatial variation of bone properties. All bone properties were mapped from published data to characterize their anisotropy and heterogeneity. Physiological loading was incorporated by mapping experimentally determined contact patterns. Convergence testing was performed to ensure model accuracy. In terms of interface forces, a tapered post decreased post shear while slightly increasing post compression compared to a cylindrical post; a post of elliptical cross-section increased post shear and decreased post compression. In terms of cancellous bone stress, tapered and elliptical posts both relieved compression compared to a cylindrical post, while a tapered post also produced increased peripheral stress. The inclusion of medial and lateral pegs in addition to a central fixation post caused localized stress shielding in the periphery of the pegs. In general, all implant models caused a reduction of cancellous bone stress plus high compression beneath the central fixation posts.     

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.     

面向个性化椎间融合器生物力学评价的有限元建模因素影响分析

目的有限元分析已广泛应用于个性化椎间融合器生物力学的评价和优化。针对有限元建模过程中存在的耗时长、计算要求高、参数选择依赖主观经验的问题,本文研究有限元建模因素对仿真结果的影响,为提高个性化椎间融合器生物力学评价中有限元建模效率提供科学依据。方法以L3、L4节段腰椎融合器设计与优化为例,选择韧带模拟方式、模型网格大小、椎体皮质骨厚度、椎体松质骨材料赋值、椎体小关节摩擦系数、融合器与椎体连接方式六种不同建模因素作为分析对象,根据相关文献中对不同因素的处理方法,采用正交实验设计建立18个有限元模型,比较不同因素对计算结果影响。结果采用融合器上的最大von Mises应力为分析指标时,韧带模拟方法、椎体小关节摩擦系数、融合器与椎体连接方式对计算结果有显著影响;采用椎间融合器最大沉降位移为分析指标时,韧带模拟方式、融合器与椎体连接方式对计算结果有显著影响;在满足一定条件下,网格大小、皮质骨厚度、松质骨材料属性对上述两种指标的影响不显著。结论在本文所研究的腰椎融合器有限元建模的6个因素中,韧带的模拟类型、椎体小关节间摩擦系数、融合器与椎体连接方式是需要重点考虑的因素。本文提出的基于正交实验设计的评价建模因素影响的方法,可以为个性化植入介入器械有限元建模过程的参数优化选择提供参考。     

Validity and sensitivity of a human cranial finite element model: implications for comparative studies of biting performance

Finite element analysis (FEA) is a modelling technique increasingly used in anatomical studies investigating skeletal form and function. In the case of the cranium this approach has been applied to both living and fossil taxa to (for example) investigate how form relates to function or infer diet or behaviour. However, FE models of complex musculoskeletal structures always rely on simplified representations because it is impossible completely to image and represent every detail of skeletal morphology, variations in material properties and the complexities of loading at all spatial and temporal scales. The effects of necessary simplifications merit investigation. To this end, this study focuses on one aspect, model geometry, which is particularly pertinent to fossil material where taphonomic processes often destroy the finer details of anatomy or in models built from clinical CTs where the resolution is limited and anatomical details are lost. We manipulated the details of a finite element (FE) model of an adult human male cranium and examined the impact on model performance. First, using digital speckle interferometry, we directly measured strains from the infraorbital region and frontal process of the maxilla of the physical cranium under simplified loading conditions, simulating incisor biting. These measured strains were then compared with predicted values from FE models with simplified geometries that included modifications to model resolution, and how cancellous bone and the thin bones of the circum‐nasal and maxillary regions were represented. Distributions of regions of relatively high and low principal strains and principal strain vector magnitudes and directions, predicted by the most detailed FE model, are generally similar to those achieved in vitro. Representing cancellous bone as solid cortical bone lowers strain magnitudes substantially but the mode of deformation of the FE model is relatively constant. In contrast, omitting thin plates of bone in the circum‐nasal region affects both mode and magnitude of deformation. Our findings provide a useful frame of reference with regard to the effects of simplifications on the performance of FE models of the cranium and call for caution in the interpretation and comparison of FEA results.     

人体膝关节有限元动力学分析模型的建立与验证

根据乘员碰撞事故中人体膝关节的生物力学响应特性,应用有限元(FE)方法和碰撞模拟技术,构建了一个人体膝关节模型。模型按人体解剖学结构构建,由股骨内、外侧髁,胫骨内、外侧髁,腓骨小头、髌骨、软骨、半月板以及主要韧带构成。通过比较模型仿真和尸体碰撞实验在轴向载荷条件下膝关节受刚性碰撞的响应结果,验证了模型的有效性。该模型为研究人体膝关节损伤机理提供了可靠的基础数据,并可应用于乘员损伤防护装置的设计和开发。     

Experimental and computational models to investigate the effect of adhesion on the mechanical properties of bone-cement composites

A generic finite element approach was developed to study the effect of adhesion on the mechanical response of bone cement composites and validated against literature data. The results showed that a zero friction bone-cement (PMMA) interface conditions captured the results of the experimental testing better than assuming a fully bonded interface. An experimental model for studying the effect of interface adhesion in a bone-cement like composite was also developed in the present study. The results using this model indicate that the difference in Young's modulus and ultimate strength between a fully bonded interface and unbonded interface is approximately 30% for bone volume fraction similar to what can be found in osteoporotic vertebrae. Apart from concluding that bone to cement adhesion is a major contributor to the mechanical response of bone-cement composites, our studies based on the generic FE approach also indicate that the mechanical properties of the cement is the most important contributor to the resulting mechanical properties of the composite at bone volume fraction relevant in terms of vertebroplasty treatment.     

Prediction of structural failure of tibial bone models under physiological loads: Effect of CT density–modulus relationships

Although finite element (FE) models can provide distinct benefits in understanding knee biomechanics, in particular the response of the knee to implants, their usefulness is limited by the modelling assumptions and input parameters. This study highlights the uncertainty of material input parameters derived from the literature and its limitation on the accuracy and usefulness of FE models of the tibia. An FE model of the intact human knee and a database of knee forces (muscles, ligaments and medial and lateral tibio-femoral contacts) were developed for walking and stair-descent activities. Ten models were constructed from ten different combinations of apparent bone density to elastic modulus material property relationships, published in the literature. Some of the published material property relationships led to predictions of bone strains in the proximal tibia which exceeded published failure criteria under loads imposed by normal activities. These relationships appear not to be applicable for the human tibia. There is a large discrepancy in proposed relationships that cover the cancellous bone density range. For FE models of the human tibia, the material relationship proposed by Morgan et al., which assumed species and anatomic site dependence, produced the most believable results for cancellous bone. In addition to casting doubt on the use of some of the published density–modulus relationships for analysis of the human proximal tibia, this study highlights the need for further experimental work to characterise the behaviour of bone with intermediate densities.     

Finite element analysis of a three-dimensional model of a proximal femur-cemented femoral THJR component construct: influence of assigned interface conditions on strain energy density

A finite element analysis of the stresses in a construct, comprising a three-dimensional model of the proximal human femur in which the stem of a total hip joint replacement was cemented, was performed. The one-legged standing condition was used, with all applied forces on the proximal femur being considered. These forces were the resultant hip joint reaction force and the forces due to the activation of the abductor, ilio-psoas, and ilio-tibialis muscles. The cortical and cancellous bones were assigned anisotropic elastic properties. It was found that the mean value of the strain energy density at each of the regions considered was considerably higher when debonding was considered at both the cancellous bone-acrylic bone cement and bone cement-stem interfaces (represented using surface-to-surface Coulomb friction, coefficient of friction = 0.22) compared to when perfect bonding conditions were taken to exist at these interfaces. The significance of this finding, together with the study limitations, is discussed.     

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.     

基于CT图像的长管骨有限元材料属性研究及实验验证

目的探讨经酒精处理的新鲜人体长管骨个性化材料属性定义的方法,以及骨骼材料数目对有限元结果的影响。方法利用断层扫描CT图片,在Mimics中建立股骨干三维实体模型,然后导入Hypermesh中分割成皮质骨、松质骨以及骨髓;根据相关经验公式分别赋于皮质骨和松质骨的材料参数,设置5组材料数目的不同仿真组;在Abaqus中进行线弹性阶段的压缩实验仿真,并进行体外验证实验。结果端部位移在0～1 mm时,松质骨材料数目为1种,皮质骨材料数目大于10种的整体力-位移有限元仿真结果与实测数据平均相对误差在10%左右;骨干的测量点变形量的有限元结果与实测数据相对误差为14.6%。在小位移下0～0.5 mm时1,种皮质骨材料的整体力-位移的仿真结果与实测数据误差为2.83%。结论 (1)利用CT图片灰度值,可以精确定义骨骼各成份的材料属性;(2)皮质骨材料数目设定对有限元仿真结果影响较大,将皮质骨设定10种即可满足有限元分析需要;(3)小变形时,1种材料的皮质骨就能满足分析要求。     

How to select the elastic modulus for cancellous bone in patient-specific continuum models of the spine

Patient-specific finite element (FE) modelling is a promising technology that is expected to support clinical assessment of the spine in the near future. To allow rapid, robust and economic patient-specific modelling of the whole spine or of large spine segments, it is practicable to consider vertebral cancellous bone in the spine as a continuum material, but the elastic modulus of that continuum material must reflect the quality of the individual vertebral bone. A numerical parametric model of lattice trabecular architecture has been developed for determining the apparent elastic modulus of cancellous bone E_cb in vertebrae. The model inputs were apparent morphological parameters (trabecular thickness Tb_Th and trabecular separation Tb_Sp) and the bone mineral density (BMD), which can all be measuredin vivo, using the spatial resolution of current clinical quantitative computed tomography (QCT) commercial whole-body scanners. The model predicted that E_cb values between 30 and 110 MPa represent normal morphology and BMD of human spinal cancellous bone. The present E_cb to Tb_Th, Tb_Sp and BMD relationships pave the way for automatic generation of patientspecific continuum FE spine models that consider the individual's osteoporotic or other degenerative condition of cancellous bone.     

Compressive behaviour of bovine cancellous bone and bone analogous materials, microCT characterisation and FE analysis

Compressive behaviour of bovine cancellous bone and three open-cell metallic foams (AlSi7Mg (30 ppi and 45 ppi); CuSn12Ni2 (30 ppi)) has been studied using mechanical testing, micro-focus computed tomography and finite element modelling. Whilst the morphological parameters of the foams and the bone appear to be similar, the mechanical properties vary significantly between the foams and the bone. Finite element models were built from the CT images of the samples and multi-linear constitutive relations were used for modelling of the bone and the foams. The global responses of the bone and foam samples were reasonably well captured by the FE models, whilst the percentage of yielded elements as a measure of damage evolution during compression seems to be indicative of the micro-mechanical behaviour of the samples. The damage evolution and distribution patterns across the bone and the foams are broadly similar for the strain range studied, suggesting possible substitution of trabecular bones with appropriate foams for biomechanical studies.     

Image-based vs. mesh-based statistical appearance models of the human femur: Implications for finite element simulations

Statistical appearance models have recently been introduced in bone mechanics to investigate bone geometry and mechanical properties in population studies. The establishment of accurate anatomical correspondences is a critical aspect for the construction of reliable models. Depending on the representation of a bone as an image or a mesh, correspondences are detected using image registration or mesh morphing. The objective of this study was to compare image-based and mesh-based statistical appearance models of the femur for finite element (FE) simulations. To this aim, (i) we compared correspondence detection methods on bone surface and in bone volume; (ii) we created an image-based and a mesh-based statistical appearance models from 130 images, which we validated using compactness, representation and generalization, and we analyzed the FE results on 50 recreated bones vs. original bones; (iii) we created 1000 new instances, and we compared the quality of the FE meshes. Results showed that the image-based approach was more accurate in volume correspondence detection and quality of FE meshes, whereas the mesh-based approach was more accurate for surface correspondence detection and model compactness. Based on our results, we recommend the use of image-based statistical appearance models for FE simulations of the femur.