Biomechanical analysis of lumbar interbody fusion with an anisotropic hyperelastic model for annulus fibrosis

Based on computed tomography scanning images, this paper developed a detailed finite element model for the human L2–L4 lumbar spine segment with or without L3–L4 fusion. The model included vertebrae, intervertebral disc, facet articulating surfaces and various ligaments. A previously developed hyperelastic fibre-reinforced constitutive model was used to characterize the material property of annulus fibrosus. Numerical results of L3–L4 motion unit such as load–displacement curves and nucleus pressure were compared with experimental data to validate the FE model. The normal and fused lumbar spine segments under various loading conditions, such as flexion, extension and axial rotation, were analysed. The motion range and stress distribution of the L2–L4 models under different loading conditions were then obtained to investigate the effect of lumbar fusion operation. It was shown that under the same loading condition, the fused model had a much smaller body motion range. Interbody fusion brought out obviously different stress distribution in adjacent intervertebral disc annulus fibrosus. And it also increased the intradiscal pressure of adjacent intervertebral disc significantly.     

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。     

<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.     

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。     

Shock response of the commercial high explosive Detasheet

The mechanical and chemical response of the flexible commercial high explosive Detasheet^R is studied under controlled impact and plane-wave, high explosive loading. Results on nonreactive material behavior, sound speed, shock-initiation sensitivity and detonation pressure are presented. The material is found to respond in a viscous manner reminiscent of viscoelastic response of polymeric materials. Time-resolved pressure and pressure-rate measurements with PVDF piezoelectric polymer gauges are presented along with Manganin pressure and plate-dent test measurements of detonation pressure. Detonation pressures of 18GPa are indicated. Pressure measurements show initiation of reaction between 3 and 8 mm for an impact stress of 3.1 GPa. Plane wave loading wedge tests show run distances to detonation consistent with the pressure measurements, and with behavior like that of XTX8003 (80 % PETN/20 % Sylgard 182^R).This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

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.     

Detonation propagation in hydrogen–air mixtures with transverse concentration gradients

The influence of transverse concentration gradients on detonation propagation in \(\hbox {H}_2\)–air mixtures is investigated experimentally in a wide parameter range. Detonation fronts are characterized by means of high-speed shadowgraphy, OH* imaging, pressure measurements, and soot foils. Steep concentration gradients at low average \(\hbox {H}_2\) concentrations lead to single-headed detonations. A maximum velocity deficit compared to the Chapman–Jouguet velocity of 9 % is observed. Significant amounts of mixture seem to be consumed by turbulent deflagration behind the leading detonation. Wall pressure measurements show high local pressure peaks due to strong transverse waves caused by the concentration gradients. Higher average \(\hbox {H}_2\) concentrations or weaker gradients allow for multi-headed detonation propagation.     

Analysis of vibrations in a nonhomogeneous thermoelastic thin annular disk under dynamic pressure

The forced vibration analysis of nonhomogeneous thermoelastic, isotropic, thin annular disk under periodic and exponential types of axisymmetric dynamic pressures applied on its inner boundary has been performed and analytical benchmark solution has been obtained. The material has been assumed to have inhomogeneity according to a simple power law in the radial coordinate. The present analysis has been worked out in the context of generalized theory of thermoelasticity with one relaxation time. The two coupled partial differential equations have been clubbed and solved by employing Laplace transform technique to obtain the solution for radial displacement and temperature change in the space domain. In order to obtain the solution in physical domain, the inversion of the transform has been carried out by using residue calculus. The radial displacement, radial stress, circumferential stress, and temperature change have been computed numerically for copper material annular disk. The numerically computed results have been presented graphically to demonstrate the effect of two different types of dynamic pressure in reference to homogeneous and nonhomogeneous material disk. The results for homogeneous material disk have been deduced and validated with that available in literature. The closed-form solution obtained here is interesting and allows further parametric studies of nonhomogeneous structures.     

A Pressurized Functionally Graded Hollow Cylinder with Arbitrarily Varying Material Properties

The elastic analysis of a pressurized functionally graded material (FGM) annulus or tube is made in this paper. Different from existing studies, this study deals with an axisymmetrical FGM hollow cylinder or disk with arbitrarily varying material properties. A simple and efficient approach is suggested, which reduces the associated problem to solving a Fredholm integral equation. The resulting equation is approximately solved by expanding the solution as series of Legendre polynomials. The stresses and displacements can be represented in terms of the solution to the equation. For radius-dependent Young’s modulus, numerical results of the distribution of the radial and circumferential stresses are presented graphically. Our results indicate that change in the gradient of the FGM tube does not produce a substantial variation of the radial stress, but strongly affects the distribution of the hoop stress. In particular, the hoop stress may reach its maximum at an internal position or at the outer surface when the tube is internally pressurized. The results obtained are helpful in designing FGM cylindrical vessels to prevent failure.      

Die Volumenretardation des Polystyrols nach Druck- und Temperatursprüngen

Summary Measurements of the isothermal-isobaric volume retardation in crosslinked and non-crosslinked polystyrene are reported.The measurements have been carried out applying the temperature-jump method, and, for the first time, also the pressure-jump method. For the measurements using the temperature-jump method a quartz-glassdilatometer has been used which allows the registration of volume changes of ±7·10⁶ cm³. A pressure dilatometer has been developed for the measurements according to the pressure-jump method which permits volumemeasurments of the same precision in the pressure-range between 1 and 60 atmospheres.The experimental results show that for the volume retardation of polystyrene a measurable linear region exists. For this case of linear retardation behaviour various kinetic theories predict an exponential time dependence of the deviation of the volume from the equilibrium value, which is due to the existence of a single retardation time. This result is not confirmed by our experiments. The volume retardation in the linear region — at least for polystyrene — can in no case be described in terms of a single retardation time, but only by a distribution of retardation times. It turns out, that the retardation function (distribution function of retardation times) in the linear region differs after a previous temperature change from that after a previous pressure change. This result can be confirmed by theoretical considerations which follow fromMeixner's thermodynamic theory of linear relaxation phenomena.

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Vorgetragen vonG. Goldbach auf dem Symposium der Nederländischen Rheologischen Gesellschaft in Valkenburg (Niederlande), am 17. Mai 1966. Kurzfassung in Rheologica Acta 5, 302 (1966) erschienen.     

Direct measurements of local bed shear stress in the presence of pressure gradients

This paper describes the development of a shear plate sensor capable of directly measuring the local mean bed shear stress in small-scale and large-scale laboratory flumes. The sensor is capable of measuring bed shear stress in the range \(\pm\) 200 Pa with an accuracy up to \(\pm\) 1 %. Its size, 43 mm in the flow direction, is designed to be small enough to give spatially local measurements, and its bandwidth, 75 Hz, is high enough to resolve time-varying forcing. Typically, shear plate sensors are restricted to use in zero pressure gradient flows because secondary forces on the edge of the shear plate caused by pressure gradients can introduce large errors. However, by analysis of the pressure distribution at the edges of the shear plate in mild pressure gradients, we introduce a new methodology for correcting for the pressure gradient force. The developed sensor includes pressure tappings to measure the pressure gradient in the flow, and the methodology for correction is applied to obtain accurate measurements of bed shear stress under solitary waves in a small-scale wave flume. The sensor is also validated by measurements in a turbulent flat plate boundary layer in open channel flow.     

The Pressurized Hollow Cylinder or Disk Problem for Functionally Graded Isotropic Linearly Elastic Materials

The purpose of this research is to investigate the effects of material inhomogeneity on the response of linearly elastic isotropic hollow circular cylinders or disks under uniform internal or external pressure. The work is motivated by the recent research activity on functionally graded materials (FGMs), i.e., materials with spatially varying properties tailored to satisfy particular engineering applications. The analog of the classic Lamé problem for a pressurized homogeneous isotropic hollow circular cylinder or disk is considered. The special case of a body with Young"s modulus depending on the radial coordinate only, and with constant Poisson"s ratio, is examined. It is shown that the stress response of the inhomogeneous cylinder (or disk) is significantly different from that of the homogeneous body. For example, the maximum hoop stress does not, in general, occur on the inner surface in contrast with the situation for the homogeneous material. The results are illustrated using a specific radially inhomogeneous material model for which explicit exact solutions are obtained. This revised version was published online in August 2006 with corrections to the Cover Date.     

Stress disturbances caused by the inhomogeneity in an elastic half-space subjected to contact loading

Inhomogeneities can increase localized stress and cause microstructural alterations to initiate fatigue failures in rolling elements under cyclic contact loading. To study the stress disturbances created by the inhomogeneity, a two-dimensional contact stress analysis is presented for a cylindrical indenter sliding on an elastic half-space containing an inhomogeneity of arbitrary shape. The boundary element method is used to analyze the contact problem, where actual contact boundary, contact pressure as well as tractions and displacements at inhomogeneity–substrate interface are determined by solving a set of integral equations numerically. Numerical results are presented to investigate effects and the stress disturbances caused by the inhomogeneity with various locations, sizes and material properties of inhomogeneity. The results also show that hard inclusions are more detrimental than soft deformable particles in rolling contact elements.     

An experimental investigation of the combined effects of surface curvature and streamwise pressure gradients both in laminar and turbulent flows

Flow and heat transfer characteristics over flat, concave and convex surfaces have been investigated in a low speed wind tunnel in the presence of adverse and favourable pressure gradients (k), for a range of –3.6 × 10^–6 ≤ k ≤ +3.6 × 10^–6. The laminar near zero pressure gradient flow, with an initial momentum thickness Reynolds number of 200, showed that concave wall boundary layer was thinner and heat transfer coefficients were almost 2 fold of flat plate values. Whereas for the same flow condition, thicker boundary layer and 35% less heat transfer coefficients of the convex wall were recorded with an earlier transition. Accelerating laminar flows caused also thinner boundary layers and an augmentation in heat transfer values by 28%, 35% and 16% for the flat, concave and convex walls at k = 3.6 × 10^–6. On the other hand decelerating laminar flows increased the boundary layer thickness and reduced Stanton numbers by 31%, 26% and 22% on the flat surface, concave and convex walls respectively. Turbulent flow measurements at k = 0, with an initial momentum thickness Reynolds number of 1100, resulted in 30% higher and 25% lower Stanton numbers on concave and convex walls, comparing to flat plate values. Moreover the accelerating turbulent flow of k = 0.6 × 10^–6 brought about 29%, 30% and 24% higher Stanton numbers for the flat, concave and convex walls and the decelerating turbulent flow of k = –0.6 × 10^–6 caused St to decrease up to 27%, 25% and 29% for the same surfaces respectively comparing to zero pressure gradient values. An empirical equation was also developed and successfully applied, for the estimation of Stanton number under the influence of pressure gradients, with an accuracy of better than 4%.     

Transitionally rough zero pressure gradient turbulent boundary layers

Near-wall measurements are performed to study the effects of surface roughness and viscous shear stresses on the transitionally rough regime (5 < k ⁺ < 70) of a zero pressure gradient turbulent boundary layer. The x-dependence is known from the eleven consecutive measurements in the streamwise direction, which allows for the computation of the streamwise gradients in the boundary layer equations. Thus, the skin friction is computed from the integrated boundary layer equation with errors of 3 and 5% for smooth and rough, respectively. It is found that roughness destroys the viscous layer near the wall, thus, reducing the contribution of the viscous stress in the wall region. As a result, the contribution in the wall shear stress due to form drag increases, while the viscous stress decreases. This yields Reynolds number invariance in the skin friction as k ⁺ increases into the fully rough regime. Furthermore, the roughness at the wall reduces the high peak of the streamwise component of the Reynolds stress in the near-wall region. However, for the Reynolds wall-normal and shear stress components, its contribution is not significantly altered for sand grain roughness.     

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.      

Measurements on scaled models of thrust pads

Reasons for use of scaled models in lubrication are put forward. It is shown how such models of thrust pads having a stepped surface can be used and how pressures, thrust and friction can be measured. In the family of pads chosen for experimentation, the lateral steps make an angle of cot^?12 with the free-stream direction, and the position of step which is at right angles to the oil flow and which joins the lateral steps is assumed to be at both optimum and non-optimum conditions with respect to the thrust/friction ratio. The mean experimental results for thrust load lie within +10 percent of the theory when obtained from pressure distribution and within +20 percent when obtained from direct-force measurements. For friction, the appropriate departures when obtained from pressure and direct-force measurements are ±2 percent and +8 percent.     

Two-phase flow simulations at 0−4o inclination in an eccentric annulus

Co-current two-phase simulations of gas-liquid flow with mixture velocities from 1.2 to 4.2 m/s were run in a partially eccentric annulus and compared with entirely eccentric and concentric experimental data collected at the Institute for Energy Technology in Norway. The gas-phase was sulphur hexafluoride (SF₆) for all cases, while the liquid-phase was Exxsol D60 for the horizontal cases and a mixture of Exxsol D60 and Marcol 82 for the inclined case. The outer diameter of the annulus was 0.1 m for all cases, while the inner diameter was 0.05 m in the horizontal configuration and 0.04 m for the inclined configuration. The purpose of this paper is to explore the effect of the holdup fraction, mixture velocity, and interior pipe’s position on the pressure gradient and flow regime, in effect a study of the pressure gradient and holdup fraction transients. The comparisons between simulations and experiments indicate that moving the pipe from an entirely eccentric to the partially eccentric configuration has a drastic impact on the pressure gradient. In all 4 cases where the inner pipe was changed from a completely eccentric geometry in the experiments to a less eccentric configuration in the simulations, we notice an increase of 48–303% of the mean pressure gradient. Comparatively, the 4 cases where the pipe was moved from a concentric experimental configuration to a more eccentric configuration in the simulations result in less drastic pressure gradient changes. Two cases were within 22% of the experimental results for mean, maximum, and minimum pressure gradient, while the last two cases exceeded the minimum and mean pressure gradients by 25–250%, respectively. The flow regime is rarely significantly affected by a change in eccentricity; 2 out of the 8 horizontal cases indicate either a transition from wavy flow to slug flow or significantly larger waves. The most prominent and frequent discrepancies identified were altered slug and wave frequencies. The last case, a 4^o inclined, partially eccentric simulation was compared to an entirely eccentric experiment and results in a 0.2 Hz increase in wave frequency, up from the experimental 0.56 Hz and a 49% increase in the mean pressure gradient.     

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.     

Thermoelastic analysis of functionally graded annulus with arbitrary gradient

A thermoelastic problem of a circular annulus made of functionally graded materials with an arbitrary gradient is investigated. Different from previous works, our analysis neither requires a special form of the gradient of material properties nor demands partitioning the entire structure into a multilayered homogeneous structure. Instead, we propose a new method for solving the thermoelastic problem of a functionally graded circular annulus by transforming it to a Fredholm integral equation. The distribution of thermal stresses and radial displacement can be obtained by solving the resulting equation. Illustrative examples are given to show the effects of varying gradients on the thermal stresses and radial displacement for given temperature changes at the inner and outer surfaces. The results indicate that the thermal stresses can be relaxed for specified gradients, which is beneficial to design an inhomogeneous annulus to maintain structural integrity.