腰椎椎间植骨融合有限元分析

为了评估植骨融合术对腰椎运动和应力分布的影响, 利用影像诊断技术(CT扫描) 和CAD三维重建技术获得人体腰椎三维模型, 椎间盘纤维环采用各向异 性纤维加强超弹性本构模型, 建立了包括椎体、椎间盘和韧带的正常有限元模型以 及L3-L4融合的腰椎L2-L4节段有限元模型, 并通过对比模拟和实验结果验证其有效 性. 利用商业有限元软件ABAQUS/Standard 进行前屈、后伸和轴向旋转载荷情况下 的模拟分析, 对比两种模型在不同状态下的运动范围及应力分布情况. 模拟结果显 示: 在相同的载荷情况下, 融合模型的运动范围和正常模型相比明显偏小; 相邻椎 体的应力分布与正常模型明显不同, 但植骨融合对相邻椎间盘的影响相对较小. 此 外, 小关节对维持脊椎正常生理功能起着重要作用, 小关节功能丧失会使相应节 段的椎间盘髓核压力增大.     

A semi-experimental stress analysis of the human intervertebral disk in compression

The intervertebral disk is a heavily loaded component of the human body. In the lumbar region, in vivo measurements by Nachemson (1966, 1970)^4–5 show compressive loads in the range of 1000–3000 Newton under normal living conditions. Determination of stresses in intervertebral disks is, thus, a relevant biomechanical problem that has been studied experimentally and from a clinical point of view by Nachemson (1960, 1963, 1966, 1970).^2–5 Galante (1967)¹ investigated tensile properties of the lumbar annulus fibrosus. Nachemson found the state of stress in the nucleus pulposus to be hydrostatic, and Galante's investigation revealed a considerable inhomogeneity of the material in the annulus fibrosus. In this paper, the effect of material inhomogeneity on the distribution of stress in annulus fibrosus is studied. On the basis of previous experimental findings and complementary measurements of the lateral pressure distribution through the disk, the tangenital and radial stress distributions are determined theoretically. The results of the theoretical analysis show that inhomogeneity influences the distribution of tangential stress considerably, whereas only heavy lateral pressure gradients disturb this same stress distribution to any significant extent. Experimental results show that high pressure gradients may well be present in annulus. Only pure compression of the disk is considered.     

基于多孔弹性模型的脊椎关节生物力学特性和体液流动特性研究

建立了L4/L5段人体腰椎关节的非线性多孔弹性有限元模型,并对其施加1000N振动载荷1h,考察在不同的振动频率(1Hz、4Hz、8Hz、11.5Hz、15Hz)下腰椎关节的变形、应力分布和体液流动情况;并对不同频率作用下脊椎组织的生物力学特性进行了对比分析。结果表明,在不同频率振动载荷下,脊椎模型的应力分配、体液流量都呈现与振动载荷不同的周期性波动变化。振动载荷频率等于腰椎关节的固有频率11.5Hz时,椎间盘应力分配和体液流量波动的幅值最短;而振动频率为4Hz、8Hz、15Hz时各项指标波动的幅值比11.5Hz时小。振动过程中,椎间盘内外压力梯度的变化引起体液的流动,振动时间越长,总流失量越大。     

瞬态载荷下L4/L5椎间盘内流固耦合效应

中医正脊治疗通过对腰椎施加瞬态拉伸和旋转来治疗腰椎间盘退变, 本文采用考虑流固耦合效应的数值模拟研究其生物力学机制. 通过实验测量和文献调研, 确定了合理的拉伸和旋转的载荷参数; 发展了使用人体断层扫描图像结合解剖学数据建立详细腰椎几何模型的方法; 将松质骨、终板、椎间盘考虑为多孔弹性介质, 其他组织考虑为线性弹性介质, 进而建立了考虑生物组织中流固耦合效应的物理模型; 通过数值模拟得到了不同瞬态载荷及其组合作用下椎间盘内应力?应变与流体流动的变化规律. 研究发现, 瞬态载荷通过改变L4/L5椎间盘基质应力和髓核内外压力梯度, 在髓核中产生流体流动; 拉伸加载引起流体先流出髓核、再流入髓核, 产生含水量变化; 顺时针旋转加载在髓核左右产生相反的流动, 髓核右侧的含水量变化较左侧大. 本研究所采用的方法为流动过程相关的人体椎间盘退变病理生理机制研究提供了新的方法, 为中医正脊研究提供科学化思路, 也为相关的力学-生物学耦合研究和髓核再生的基础研究提供了一个切入点.      

<Emphasis Type="Italic">Ex Vivo</Emphasis> Intervertebral Disc Bulging Measurement Using a Fibre Bragg Grating Sensor

Advances using optical fibres as sensors may represent an important contribution for development of minimally invasive techniques in biomedical and biomechanical applications. Concerning spine injuries, intervertebral disc (IVD) degeneration is a major clinical issue since it represents gross structural disruption and it is irreversible. Measuring biomechanical parameters of the IVD should contribute for better understanding on its mechanical response to external applied forces. The purpose of this study was to explore the potential of a Fibre Bragg Grating (FBG) sensor to measure strain caused by bulging of the intervertebral disc under axial compression. Disc bulging is a consequence of IVD compression and a technique to register this behaviour is addressed in this study. Needle-mounted sensors were already used to measure IVD pressure in cadaveric material. In this study we also explored the possibility of using needles only for sensor guiding and positioning leaving sensor directly in contact with the IVD material. An ex vivo porcine dorsal functional spinal unit was instrumented with a FBG sensor and submitted to axial compression. Results suggest the sensor’s ability to measure strain response to load. Bulging of the annulus fibrosus as a consequence of axial compression was confirmed using the FBG sensor. Hysteresis and viscoelastic behaviour were observable suggesting that energy is dissipated by the deformation of the annulus and that unloading time was insufficient for disc recovery. Nevertheless the relatively low strain sensitivity of the sensor as well as signal artefacts caused by transverse loading may constitute a problem in the analysis and interpretation of strain data. The technique may not be suitable for measurement of physiologic bulging being more indicative of the radial force exerted by the annulus.     

腰椎力学分析的数值模拟与实验研究

采用数值模拟和实验测试技术对两种不同内固定法的腰椎模型进行应力和变形分析,基于CT图像建立L4-S1的三维数值模型,经ANSYS计算分析得出五种工况下的终板应力值;在实验中采用了一种薄膜压力测试传感器结合图像处理的方法,提高测试椎间盘压力分布的精度;同时采用数字图像相关技术对腰椎骨上下关节突在承载情况下的空间位移进行了测量,获得了腰椎间盘（L3-L4）在承受轴压、前屈后伸和侧弯情况下的压力分布,以及对应的关节突的位移迹线。结果表明：本研究采用的数值分析技术和实验开发的测试技术可操作性强,精度满足要求,有望在类似的生物力学分析中得到应用。     

A non-linear finite element model of human L4-L5 lumbar spinal segment with three-dimensional solid element ligaments

This paper establishes a non-linear finite element model (NFEM) of L4-L5 lumbar spinal segment with accurate three-dimensional solid ligaments and intervertebral disc. For the purpose, the intervertebral disc and surrounding ligaments are modeled with four-nodal three-dimensional tetrahedral elements with hyper-elastic material properties. Pure moment of 10 N·m without preload is applied to the upper vertebral body under the loading conditions of lateral bending, backward extension, torsion, and forward flexion, respectively. The simulate relationship curves between generalized forces and generalized displacement of the NFEM are compared with the in vitro experimental result curves to verify NFEM. The verified results show that: (1) The range of simulated motion is a good agreement with the in vitro experimental data; (2) The NFEM can more effectively reflect the actual mechanical properties than the FE model using cable and spring elements ligaments; (3) The NFEM can be used as the basis for further research on lumbar degenerative diseases.     

Deduction of Spinal Loading from Vertebral Body Surface Strain Measurements

The lumbar intervertebral disc, the apparent nexus of low back pain, undergoes biomechanical changes during its degeneration which are as yet poorly understood. In an effort to ultimately examine in vivo daily activity loads across intervertebral discs, we engaged in the following methodological study. The aim of this research was to correlate vertebral body surface strains with the loads across a lumbar spine segment. Rosette strain gages were affixed anterolaterally on L4 and L5 in a macaque monkey model. These tissues were loaded axially and with sagittal plane moments and the principal strains were compared with the applied loads. Predictable axial and sagittal plane loading profiles were found for similar strain measurements and the system was found to be robust through freezing and thawing. These results support future research aimed at quantifying the in vivo disc mechanics of healthy and degenerate tissues in an attempt to develop prevention or intervention strategies to ease those afflicted with low back pain.     

A microstructure-based model for time-dependent mechanics of multi-layered soft tissues and its application to intervertebral disc annulus

Meccanica - In recent experimental studies an unusual time-dependent transversal behavior of the annulus fibrosus of the intervertebral disc mainly caused by the coupling between mechanics and...     

人体腰椎生物力学的某些基本问题

本文就人体腰段脊柱生物力学的某些基本问题的研究现状与进展进行述评。介绍了腰椎各组成部分包括椎体、椎间盘、椎弓、韧带以及脊髓的力学性能,对其运动学和运动力学进行了讨论,最后就腰椎的力学模型主要是有限元模型的研究作了简单的回顾。      

Rate effect on sharing of passive lumbar motion segment under load-controlled sagittal flexion: viscoelastic finite element analysis

Industrial epidemiological studies have shown that jobs requiring a higher speed of trunk motion contribute to a higher risk of industrial low back disorders. Consideration of the loading dynamic characteristics, such as lifting at different speeds, requires modeling of the viscoelastic behavior of passive tissues. Detailed systematic analysis of the effects of loading rate has been lacking in the literature. A validated viscoelastic finite element model of a L2–L3 motion segment was used to identify the load sharing among the passive elements at different loading rates. Force controlled complex flexion movement was simulated by applying load at the top of the upper vertebra without constraining any coupled sagittal rotation, whereas the lower vertebra was fixed at the bottom. The load reached its maximum values of 2000 N compression, 400 N anterior shear, and 20 Nm flexion in three different durations of 0.3, 3 and 30 s to represent fast, medium and slow movement. The global force–displacement response of the motion segment, forces in facet joints and ligaments, stresses and strains in anulus fibrosus, and intradiscal pressure were compared across different rates. The higher rate of loading while reaching a prescribed complex forward flexion loading increased the intradiscal pressure and the stress in the anulus fibers at the posterolateral innermost layers, but reduced the global displacements, ligament forces and facet joint forces. The distribution of stress and strain was markedly affected by the loading rate. Consideration of the time-dependent material properties of passive elements is essential to improve our understanding of the responses of the motion segment to dynamic loading conditions. Speed of the manual materials handling (MMH) tasks should be included as a risk factor in the biomechanical and epidemiological studies and guidelines for safe lifting.     

Development and validation of a viscoelastic finite element model of an L2/L3 motion segment

The prediction of the time dependent response of the spine to dynamic loading conditions is essential in understanding the injury mechanisms leading to occupationally related low back disorders (OLBD). Many previous finite element (FE) models of the lumbar spine have over-simplified the geometry and the material properties of their elements, yielding results limited generalizability. This study reports on the development and validation of a nonlinear viscoelastic FE model that can quantify the mechanical responses of the L2/L3 motion segment to time varying external loads. This model was developed by consideration of the intrinsic material properties of its individual constituents. A piecewise parameter identification method was adopted due to the inherent complexity in determining the role and contribution of each element to the overall behavior of the motion segment. The results of simulation of four loading conditions (quasistatic, constant loading rate, creep and cyclic relaxation) showed a satisfactory agreement with experimental observations in the literature. The detailed estimates of the state of stress/strain of this validated FE model can be used to test the role of epidemiological risk factors such as prolonged awkward posture, speed of lift (strain rate effect) and complex repetitive loading in OLBD.     

Simulating the sensitivity of cell nutritive environment to composition changes within the intervertebral disc

Altered nutrition in the intervertebral disc affects cell viability and can generate catabolic cascades contributing to extracellular matrix (ECM) degradation. Such degradation is expected to affect couplings between disc mechanics and nutrition, contributing to accelerate degenerative processes. However, the relation of ECM changes to major biophysical events within the loaded disc remains unclear. A L4-L5 disc finite element model including the nucleus (NP), annulus (AF) and endplates was used and coupled to a transport-cell viability model. Solute concentrations and cell viability were evaluated along the mid-sagittal plane path. A design of experiment (DOE) was performed. DOE parameters corresponded to AF and NP biochemical tissue measurements in discs with different degeneration grades. Cell viability was not affected by any parameter combinations defined. Nonetheless, the initial water content was the parameter that affected the most the solute contents, especially glucose. Calculations showed that altered NP composition could negatively affect AF cell nutrition. Results suggested that AF and NP tissue degeneration are not critical to nutrition-related cell viability at early-stage of disc degeneration. However, small ECM degenerative changes may alter significantly disc nutrition under mechanical loads. Coupling disc mechano-transport simulations and enzyme expression studies could allow identifying spatiotemporal sequences related to tissue catabolism.     

A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus

This paper presents a composites-based hyperelastic constitutive model for soft tissue. Well organized soft tissue is treated as a composite in which the matrix material is embedded with a single family of aligned fibers. The fiber is modeled as a generalized neo-Hookean material in which the stiffness depends on fiber stretch. The deformation gradient is decomposed multiplicatively into two parts: a uniaxial deformation along the fiber direction and a subsequent shear deformation. This permits the fiber-matrix interaction caused by inhomogeneous deformation to be estimated by using effective properties from conventional composites theory based on small strain linear elasticity and suitably generalized to the present large deformation case. A transversely isotropic hyperelastic model is proposed to describe the mechanical behavior of fiber-reinforced soft tissue. This model is then applied to the human annulus fibrosus. Because of the layered anatomical structure of the annulus fibrosus, an orthotropic hyperelastic model of the annulus fibrosus is developed. Simulations show that the model reproduces the stress-strain response of the human annulus fibrosus accurately. We also show that the expression for the fiber-matrix shear interaction energy used in a previous phenomenological model is compatible with that derived in the present paper.     

Irreversible deformation with subsequent unloading of a spherical viscoelastoplastic layer

Analytic solutions are obtained for a sequence of one-dimensional quasistatic problems describing viscoelastic deformation processes in the material of a hollow ball and the plastic flow nucleation and evolution processes occurring in the ball as the pressure on the outer boundary increases. The unloading process under slow removal of the loading pressure is considered as well. The stress fields and the elastic and plastic strain fields in the spherical layer material, the law of motion of the elastoplastic boundary, and the residual stress level and distribution are computed. It is assumed that at the stage preceding the plastic flow the material obeys the viscoelastic Voigt model and the loading surface is determined by the von Mises plastic flow condition.     

Bulging intervertebral disc: an asymptotic elasticity solution

A bulging intervertebral disc (IVD) occurs when pressure on a spinal disc damages the once healthy disc, causing it to compress or change its normal shape. In medicine, most attention has been paid clinically to diagnosis of and treatment for such problems, which little effect has been made to understand such issues from a mechanics perspective, i.e., the bulging deformation of the soft IVD induced by excessive compressive load. We report herein a simple elasticity solution to understand the bulging disc issue. For simplicity, the soft IVD is modeled as an incompressible circular composite layer consisting of an inner nucleus and outer annulus, sandwiched between two vertebral segments which are much stiffer than the IVD and can be treated as rigid bodies. Without adopting any assumptions regarding prescribed displacements or stresses, we obtained the stress and displacement fields within the composite layer when a certain compressive stain is applied via an asymptotic approach. This asymptotic approach is very simple and accurate enough for prediction of the bugling profile of the IVD. We also performed finite-element modeling (FEM) to validate our solutions; the predicted stress and displacement fields inside the composite are in good agreement with the FEM results.     

加筋土地基模型试验边界效应与承载性能分析

为进一步探讨边界效应对加筋土地基的影响,基于室内方形基础下加筋土地基大模型试验,采用ABAQUS有限元软件建立加筋土地基数值模型,主要分析了模型宽度L和加载板宽度B对加筋土地基承载性能、地基内部土体应力应变及筋材变形的影响。结果表明:无筋地基与加筋土地基极限承载力均随L/B的减小而增大,当L/B>5时,可忽略边界效应对加筋土地基的影响;当L/B<2.67时,边界效应对加筋土地基的影响最大;当L/B>4时,边界效应对无筋地基的影响可忽略不计;加筋能够显著改善地基土体的不均匀沉降和减小基础两侧土体隆起高度;竖向应力分布区域随着B的增大而增大,加筋土地基受竖向荷载的影响宽度为5B,影响深度为2.57B~4B;当L/B>5时,不同L/B工况下土体变形、应力分布及格栅变形曲线基本重合,此时加筋土地基受边界效应的影响可忽略不计。     

脊柱L3-L5段机械模型的力学特性分析

借助计算机辅助设计软件SolidEdge,根据人体解剖学数据建立了人体脊柱L3-L5段近似三维几何模型,并利用有限元分析软件ANSYS进行赋值,模拟了脊柱L3-L5段的结构特性、材料特性、接触特性。将椎骨划分为皮质骨、松质骨等结构,用接触连接的方法模拟了椎骨与椎间盘之间、小关节之间的连接情况,采用实体单元Solid187对其进行网格划分。对该三维有限元模型进行加载分析,得到其在200N轴向力作用下和100N侧向力作用下的应力和变形数据,该数据可以为脊柱生物力学的研究和侧凸脊柱的病因及矫正提供一定的参考依据。     

Cyclic plasticity modeling with the distribution of non-linear relaxations approach

Motivated by the distribution of non-linear relaxation (DNLR) approach, a phenomenological model is proposed in order to describe the cyclic plasticity behavior of metals under proportional and non-proportional loading paths with strain-controlled conditions. Such a model is based on the generalization of the Gibbs's relationship outside the equilibrium of uniform system and the use of the fluctuation theory to analyze the material dissipation due to its internal reorganization. The non-linear cyclic stress–strain behavior of metals notably under complex loading is of particular interest in this study. Since the hardening effects are described appropriately and implicitly by the model, thus, a host of inelastic behavior of metals under uniaxial and multiaxial cyclic loading paths are successfully predicted such as, Bauschinger, strain memory effects as well as additional hardening. After calibrating the model parameters for two metallic materials, the model has demonstrated obviously its ability to describe the cyclic elastic-inelastic behavior of the nickel base alloy Waspaloy and the stainless steel 316L. The model is then implemented in a commercial finite element code simulating the cyclic stress–strain response of a thin-walled tube specimen. The numerical responses are in good agreement with experimental results.     

An alternative analytic approach to the Brazilian disc test with friction at the disc-jaw interface

The role of the tangential (friction) stresses developed at the disc-jaw interface during the standardized realization of the Brazilian disc test is quantified. Sinusoidal variation of both the radial pressure and the friction stresses is considered. The pressure is maximized at the symmetry axis of the load distribution while friction is maximized at the mid-point of the contact semi-arc. Both load distributions (radial and frictional) are exerted along the actual contact length as it is developed during the loading procedure. The stress field all over the disc due to friction stresses is determined in closed form using the complex potentials technique. The solution obtained is applied for two materials both of brittle nature and of different relative deformability compared to steel (i.e. the material of the jaw). The stress field due to friction is compared for both materials with that due to radial pressure, and then, the two solutions are superimposed in order to quantify the total stress field. It is concluded that as one approaches the loading platens, non-ignorable tensile stresses are developed that could lead the disc to premature failure far from the disc’s center. The magnitude of these stresses strongly depends among others on the relative deformability of the disc’s and jaw’s materials since the latter dictates the extent of the loading rim.