Finite element prediction of proximal femur fracture pattern based on orthotropic behaviour law coupled to quasi-brittle damage

The purpose of this study was to develop a finite element model based on continuum damage mechanics in order to simulate the profile of the fractured area of proximal femur and the complete force-displacement curve from the beginning until complete fracture. The model was developed in term of anisotropic behaviour law coupled to quasi-brittle damage to describe the progressive crack initiation and propagation within proximal femoral. A damage law was developed and implemented into a finite element code (Abaqus) based on experimental observations. To illustrate the potential of the current approach, the right adult human femur previously investigated by Keyak and Falkinstein (Model B: male, age 61) was simulated until complete fracture under one-legged stance load. The femur fracture profile was predicted and compared to clinical observed results. Good agreements were obtained suggesting that the proposed damage model could be used correctly to simulate the force-displacement curve, the fracture type and to simulate the progressive propagation of the crack paths. Present model can contribute towards the development of diagnostic tool that can detect osteoporotic fracture for aged patients in an early stage and predict bone strength accurately.     

股骨近端溶骨性转移瘤三维有限元模型的力学分析

背景：如何评估股骨近端转移瘤的骨折风险在临床上争议较多。 目的：建立股骨近端不同大小溶骨性转移瘤的三维有限元模型,分析在慢步行走过程中病变局部的应力变化,评估骨折风险。 方法：对志愿者双下肢进行薄层CT扫描获得股骨数据,图像处理软件Mimics11.1进行图像处理后数据导入建模软件UG4.0建立股骨近端3个部位溶骨性病变模型,给予加载缓慢行走时单足落地状态下股骨的载荷,利用有限元软件分析股骨颈区,转子间区及转子下区应力的变化。 结果与结论：①股骨颈水平：皮质完整的髓内缺损破坏直径至相应冠状面直径的90%局部应力突然增长至135.98 MPa,破坏一半内侧皮质的髓内病变至70%局部应力突然增长至92.34 MPa,完全破坏皮质的半球形病变至60%时,局部应力大于屈服应力,增长至101.19 MPa。②转子间水平：内侧皮质完整的髓内球形病变破坏直径至80%局部应力突然增长至131.21 MPa,破坏一半内侧皮质的髓内病变破坏至80%局部应力突然增长至105.19 MPa,完全破坏皮质的半球形病变至70%时,局部应力大于屈服应力,增长至92.21 MPa。③转子下水平：破坏一半内侧皮质的髓内病变破坏至80%局部应力突然增长至92.42 MPa,完全破坏皮质的半球形病变至70%-80%之间,局部应力增长至89.97-105.19 MPa,大于屈服应力。结果表明股骨近端未穿透骨皮质的髓内病变对股骨近端应力变化影响不大。对于破坏单侧骨皮质的病变,在股骨颈水平破坏直径大于60%时存在骨折风险,转子间水平破坏直径大于70%时存在骨折风险,转子下水平破坏直径大于70%时存在骨折风险。     

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.     

Prediction of fracture location in the proximal femur using finite element models.

Finite element (FE) models of the proximal femur are often used to study hip fracture. To interpret the results of these models, it is important to know whether the models accurately predict fracture location and/or type. This study evaluated the ability of automatically generated, CT scan-based linear FE models of the proximal femur to predict fracture location and fracture type. Fracture location was defined as the specific location of the fracture. Fracture type was a categorical variable defined as either a cervical or a trochanteric fracture. FE modeling and mechanical testing of 18 pairs of human femora were performed under two loading conditions, one similar to joint loading during single-limb stance and one simulating impact from a fall. For the stance condition, the predicted and actual fracture locations agreed in 13 of the 18 cases (72% agreement). For the fall condition, the predicted and actual fracture locations agreed in 10 of the 15 cases where the actual fractures could be identified (67% agreement). The FE models correctly predicted that only cervical fractures occurred in the stance configuration. For the fall configuration, FE-predicted and actual fracture types agreed in 11 of the 14 cases that could be compared (9 trochanteric, 2 cervical; 79% agreement). These results provide evidence that CT scan-based FE models of the proximal femur can predict fracture location and fracture type with moderate accuracy.     

儿童股骨近端解剖钢板生物力学及三维有限元分析

背景：以往的三维有限元研究多集中在成人骨科生物力学方面。 目的：以三维有限元方法分析儿童股骨近端解剖钢板固定股骨转子下骨折的生物力学性能。 方法：从6具儿童尸体上取股骨12根,X射线排除骨病后分为2组,实验组采用儿童股骨近端解剖钢板固定,对照组采用重建钢板固定。分别进行生物力学实验,测试其轴向压缩、扭转刚度、弯曲刚度。选取1名健康男性儿童进行螺旋CT扫描技术,获得股骨近端图像数据,建立儿童股骨近端三维有限元模型,并进行三维有限元力学分析。 结果与结论：在轴向压缩刚度、扭转刚度上儿童股骨近端解剖钢板与重建钢板两者比较差异无显著性意义(P > 0.05);在抗弯曲刚度上,两者相比差异有显著性意义(P < 0.05)。结果显示儿童股骨近端解剖钢板的抗压能力、抗扭能力上与重建钢板相当,而在抗弯曲能力上强于重建钢板。生物力学三维有限元分析显示儿童股骨近端解剖型钢板的设计符合生物力学原理,具有较好的强度、刚度和稳定性,能够满足对儿童股骨近端骨折固定的需要。儿童股骨近端解剖型钢板对固定股骨转子下骨折具有良好的生物力学性能。     

应用CT断层图像重建股骨有限元模型

目的寻求一种基于CT断层图像快速且精确地建立全股骨三维有限元模型的方法，并应用有限元分析其力学特性以评价建模方法的优势。方法在Mimics中直接读取符合Dicom3．0标准的股骨原始CT数据，经阂值设定、区域增长及形态学操作等生成股骨初始3D模型，后期结合有限元软件ANSYS生成最终的三维有限元网格模型．然后在ANSYS中分别对应用Mimics得到的模型和统一弹性模量的模型加载200N的垂直载荷，比较两者应力分布的异同。结果获得的股骨有限元模型共含有143780个节点和99650个四面体单元，其弹性模量与CT值（密度）相关分布，取值范围在6．01～15．59GPa之间。与统一弹性模量的模型相比较，应用Mimics得到的模型其应力呈现离散性分布。结论应用Mimics可以建立更符合股骨机械结构和力学性质的三维有限元模型，同时缩短了建模时间，据此模型得到的股骨力学特性分析结果更为可信，以辅助指导临床应用。     

基于CT图像的股骨上段有限元建模及单元尺寸分析

目的基于CT图像构建5个不同的股骨上段有限元模型,并分析模型单元尺寸对股骨模型材料属性分布以及生物力学性能的影响。方法利用螺旋CT扫描股骨上段并以DICOM格式输出图像文件,利用Mimics软件提取三维几何文件,分别使用Mimics、3-Matica、ICEM软件生成体素网格模型、四面体网格模型和3个六面体网格模型(单元尺寸分别为2、1和0.5 mm),在Mimics中对网格文件进行材料赋值,将最终的有限元模型导入ABAQUS中进行力学行为分析。结果单元尺寸对5个模型总质量影响较小,5个模型沿相同路径上节点处Von Mises应力和节点位移整体变化趋势一致,但是各个节点处Von Mises应力误差较大,单元尺寸为0.5 mm的六面体网格模型与体素网格模型各节点处Von Mises应力值接近。结论基于CT灰度值进行材料赋值时,单元尺寸对模型的总质量和节点位移影响较小,但是单元尺寸的减小将导致模型中各材料含量和分布的改变,引起应力分布的变化。当模型单元尺寸与体素尺寸接近时,能较好反映股骨的质量分布和力学行为。     

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.     

采用体绘制方法建立人股骨三维有限元模型及其应力分析

背景：目前股骨三维有限元研究建模方法有多种,而采用体绘制分体建模方法还未曾报道过。 目的：采用体绘制方法建立股骨三维有限元实体模型,对所建实体模型模拟力学载荷得出股骨应力分布,并与既往股骨力学实验比较,评估体绘制方法的可行性。 方法：将CT扫描图像去噪等预处理后,采用体绘制技术,利用Mimics和Ansys软件建立人股骨有限元模型,并在Mimics软件中赋予股骨材质,并模拟人体正常站立位时股骨载荷情况。 结果与结论：采用体绘制方法建立的人股骨三维有限元模型,包括皮质骨、松质骨及髓腔解剖结构,网格化后共生成63 900个节点,43 552个实体单元;模拟载荷显示股骨压应力区域主要集中在股骨内侧、尤其是股骨距部位,张应力主要集中于股骨颈外侧、股骨干外侧。表明体绘制方法可以建立高仿真、接近股骨解剖结构股骨三维有限元模型实体模型,可以探索股骨的内部结构,展现其内部细节,模拟股骨生物力学分布。关键词：体绘制;股骨;实体模型;有限元;力学分布 doi:10.3969/j.issn.1673-8225.2012.17.003     

股骨转子间骨折不同固定方式影响股骨近端应力的有限元分析

BACKGROUND: The mechanical characteristics of intramedullary and intramedullary fixations for treating intertrochanteric fracture were hot research of finite element, but there was few comparative research on tension side and pressure side of proximal femur. In our study, we found that the distribution of the stress zone was important indication to researches on intertrochanteric fracture and internal fixation design.     

人体骨骼有限元几何模型的重建

目的：研究重建人体骨骼结构的有限元几何模型。方法：通过CT扫描、影像边界记录、定标等方法，按照点、线、面、体的顺序重建三维结构，并通过有限元分析验证重建模型的有效性。结果：建立了寰椎骨性结构的有限元模型，分析结果证明其在仿真分析中是可行的。结论：该方法适用于重建人体骨骼结构的有限元几何模型，为数字化虚拟人体仿真研究提供了一种可行的建模方法。     

利用有限元分析股骨颈骨折内固定术后前倾角变化对股骨近端力学的影响

目的探讨股骨颈骨折闭合复位空心螺钉内固定术后不同股骨颈前倾角对股骨近端力学分布的影响,为临床中内固定术解剖复位的重要性提供生物力学依据。方法采用16层螺旋CT扫描正常成人髋关节数据,基于三维重建软件和CAD软件,分别建立Pauwells角为70°的股骨颈骨折空心螺钉内固定术后前倾角为0°、5°、10°、15°、20°的股骨近端三维有限元分析模型,对所有模型施加人体缓慢行走时的载荷和约束,观察不同模型间股骨近端结构应力分布的变化。结果当前倾角未改变时(10°模型),股骨所受应力、产生的位移及发生的等效应变最小,股骨近端最大应力值为1.7 MPa,产生的位移为1.1 mm。随着前倾角的增大或减小,股骨近端所承受的有效应力及产生位移呈逐渐增大趋势。当前倾角为20°时,股骨近端及螺钉所受应力最大;当前倾角为0°时,股骨近端产生的位移及发生的等效应变值最大。股骨近端应力集中的部位由股骨距区域转移至头颈交界处的外上方。3枚空心螺钉承受的应力较周围骨组织高,最下方螺钉承受的应力较上方两枚螺钉明显增高。结论股骨颈骨折闭合复位空心螺钉内固定术中恢复前倾角达到解剖复位至关重要;股骨颈骨折术后生物力学因素的改变可能在术后股骨头坏死中起一定作用。     

A finite element model of heat transport in the human eye

A mathematical model of the human eye based on the bioheat transfer equation is developed. The intraocular temperature distribution is calculated using the Galerkin finite element method. A difficulty associated with the development of an accurate model of the human eye is the lack of reliable biological data available on the constants and parameters that are used in the model. These parameters include the thermal conductivities of the ocular tissues, the heat loss from the anterior corneal surface to the surroundings by convection and evaporation, and the convective heat loss from the sclera to the body core. The different values for the parameters reported in the ophthalmic literature are employed in the model, and the sensitivity of the temperature distribution to uncertainties in the parameters is investigated. A set of control parameter values is suggested for the normal human eye. The effect of the ambient temperature and the body-core temperature on the temperature distribution in the human eye is considered.     

基于CT图像构建的腰椎三维有限元模型

背景：与实验生物力学研究相比,有限元分析方法具有独特的优越性。如何准确地构建腰椎节段有限元模型是有限元分析的关键。 目的：建立人体腰椎三维有限元模型用于生物力学分析。 方法：利用GE 64排螺旋CT对成年男性腰部进行扫描,得到351层DICOM格式断层图像,应用Mimics软件进行三维重建,将所得模型以.stl格式导入Solidworks,生成实体模型,最后导入Ansys赋予材料属性并划分网格,得到便于分析的有限元模型。与体外生物力学实验数据对比,完成模型验证。 结果与结论：成功地建立了表面光滑、外观逼真的腰椎有限元模型。该模型共有144 411个节点,88 742个单元,具有较高的准确性,且可以方便地施加约束和载荷,进行有限元分析。为临床腰椎三维有限元模型建立提供了一种精确而实用的方法,所建模型可以用来模拟腰椎生物力学实验。     

腰椎有限元模型建立方法的研究

目的介绍一种基于CT扫描图像重建腰椎有限元模型的方法。方法通过CT扫描获得人体腰椎断层图片,在Mimics 10.0软件及Patran-Nastran中进行腰椎有限元建模,在此模型的L3椎体上表面加载500N轴向压力以模拟正常人站立时的情况,再分别在15NM力矩下进行屈、伸、侧弯以及扭转四个动作来验证模型的有效性。结果建立的腰椎有限元模型各方向的位移与符合真实情况,并且椎间盘应力分布接近现实。结论利用CT扫描技术建立限元模型的方法精确有效。     

In situ parameter identification of optimal density-elastic modulus relationships in subject-specific finite element models of the proximal femur

Quantitative computed tomography based finite element analysis of the femur is currently being investigated as a method for non-invasive stiffness and strength predictions of the proximal femur. The specific objective of this study was to determine better conversion relationships from QCT-derived bone density to elastic modulus, in order to achieve accurate predictions of the overall femoral stiffness in a fall-on-the-hip loading configuration. Twenty-two femurs were scanned, segmented and meshed for finite element analysis. The elastic moduli of the elements were assigned according to the average density in the element. The femurs were then tested to fracture and force-displacement data were collected to calculate femoral stiffness. Using a training set of nine femurs, finite element analyses were performed and the parameters of the density-elastic modulus relationship were iteratively adjusted to obtain optimal stiffness predictions in a least-squares sense. The results were then validated on the remaining 13 femurs. Our novel procedure resulted in parameter identification of both power and sigmoid functions for density-elastic modulus conversion for this specific loading scenario. Our in situ estimated power law achieved improved predictions compared to published power laws, and the sigmoid function yielded even smaller prediction errors. In the future, these results will be used to further improve the femoral strength predictions of our finite element models.     

基于汽车碰撞损伤的人体胸部有限元模型构建与验证

目的利用胸部有限元模型预测与评估碰撞载荷下胸部生物力响应与损伤机理。方法利用CT和MRI图像数据对胸部骨骼与内部软组织进行几何重建,并划分网格。模型的生物组织材料参数与材料本构模型基于文献尸体实验与组织材料实验。结果对模型进行前碰撞与侧碰撞仿真实验验证,结果表明胸部接触力、胸部位移量、力与位移曲线与尸体实验吻合较好,并利用胸部位移量、黏性准则对仿真过程进行损伤评估。结论模型可满足汽车碰撞安全中胸部损伤机理与防护及医学胸部钝器损伤的仿真研究需要。     

Validation of a finite element model of the human metacarpal

Implant loosening and mechanical failure of components are frequently reported following metacarpophalangeal (MCP) joint replacement. Studies of the mechanical environment of the MCP implant-bone construct are rare. The objective of this study was to evaluate the predictive ability of a finite element model of the intact second human metacarpal to provide a validated baseline for further mechanical studies. A right index human metacarpal was subjected to torsion and combined axial/bending loading using strain gauge (SG) and 3D finite element (FE) analysis. Four different representations of bone material properties were considered. Regression analyses were performed comparing maximum and minimum principal surface strains taken from the SG and FE models. Regression slopes close to unity and high correlation coefficients were found when the diaphyseal cortical shell was modelled as anisotropic and cancellous bone properties were derived from quantitative computed tomography. The inclusion of anisotropy for cortical bone was strongly influential in producing high model validity whereas variation in methods of assigning stiffness to cancellous bone had only a minor influence. The validated FE model provides a tool for future investigations of current and novel MCP joint prostheses.     

A finite element model of the otolith membrane

This paper describes a finite element model of the otolith membrane.The system of differential equations governing the displacement of the membrane is expressed in the equivalent variational form. The region occupied by the membrane is divided into triangles and the computer is used to determine the linear combination of the functions chosen to approximate the displacement, which minimizes the variational problem and hence solves the system of differential equations.It is seen that an arbitrarily close approximation to the actual boundary of the membrane is possible.