Exploration of trabecular bone nonlinear elasticity using time-of-flight modulation

Bone tissue contains microcracks that may affect its mechanical properties as well as the whole trabecular structure. The relationship between crack density and bone strength is nevertheless poorly understood. Linear ultrasound techniques being almost insensitive to the level of damage, we propose a method to measure acoustic non- linearity in trabecular bone using time-of-flight modulation (TOFM) measurements. Ultrasonic short bursts times-of- flight (TOF) are modulated as a result of nonlinear interaction with a low-frequency (LF) wave in the medium. TOF variations are directly related to elastic modulus variations. Classical and nonclassical nonlinear parameters beta, delta, and alpha can be derived from these measurements. The method was validated in materials with classical, quadratic, nonlinear elasticity. In dense trabecular bone region, TOFM related to classical, quadratic, nonlinear elasticity as a function of the LF pressure exhibits tension-compression asymmetry. The TOFM amplitude measured in dense areas of trabecular bone is almost one order of magnitude higher than in a low-density area, but the linear parameters show much smaller variations: 5% for ultrasound propagation velocity and 100% for broadband ultrasonic attenuation (BUA). In high-density trabecular bone regions, beta depends on the LF pressure amplitude and can reach 400 at 50 kPa.     

Mechanical properties and bone densities of canine trabecular bone

The purposes of this study were (1) to evaluate the mechanical properties of canine epiphyseal cancellous bones from adult canine femoral heads, femoral condyles, tibial plateau, and humeral heads, using indentation and compression tests, and (2) to measure bone densities (apparent density and ash density) of these cancellous bones so as to develop a normal data base of mechanical strength and bone density. The correlations between the two mechanical tests and between these tests and bone densities were also considered. The results showed all of the three mechanical parameters, ultimate load, stiffness, and ultimate strength, measured by the indentation test were higher than those measured by the compression test. Correlation analysis showed that the two sets of mechanical values correlated well (r=0.823–0.952, p<0.01). The apparent density and ash density correlated well with the mechanical parameters determined by the two types of mechanical tests (r=0.737–0.966, p<0.05). © 1998 Chapman & Hall     

Numerical analysis of variability in ultrasound propagation properties induced by trabecular microstructure in cancellous bone

The manner by which the trabecular microstructure affects the propagation of ultrasound waves through cancellous bone is numerically investigated by finite difference time-domain (FDTD) simulation. Sixteen 3-D numerical models of 6.45times6.45times6.45 mm with a voxel size of 64.5 mum are reconstructed using a 3-D microcomputed tomographic (muCT) image taken from a bovine cancellous bone specimen of approximately 20times20times9 mm. All cancellous bone models have an oriented trabecular structure, and their trabecular elements are gradually eroded to increase the porosity using an image processing technique. Three erosion procedures are presented to realize various changes in the trabecular microstructure with increasing porosity. FDTD simulations of the ultrasound pulse waves propagating through the cancellous bone models at each eroded step are performed in 2 cases of the propagations parallel and perpendicular to the major trabecular orientation. The propagation properties of the wave amplitudes and propagation speeds are derived as a function of the porosity, and their variability due to the trabecular microstructure is revealed. To elucidate an effect of the microstructure, the mean intercept length (MIL), which is a microstructural parameter, is introduced, and the correlations of the propagation properties with the MILs of the trabecular elements and pore spaces are investigated.     

The correlation between the SOS in trabecular bone and stiffness and density studied by finite-element analysis

For the clinical assessment of osteoporosis (i.e., a degenerative bone disease associated with increased fracture risk), ultrasound has been proposed as an alternative or supplement to the dual-energy X-ray absorptiometry (DEXA) technique. However, the interaction of ultrasound waves with (trabecular) bone remains relatively poorly understood. The present study aimed to improve this understanding by simulating ultrasound wave propagation in 15 trabecular bone samples from the human lumbar spine, using microcomputed tomography-based finite-element modeling. The model included only the solid bone, without the bone marrow. Two structural parameters were calculated: the bone volume fraction (BV/TV) and the structural (apparent) elastic modulus (E_s), and the ultrasound propagation parameter speed of sound (SOS). Relations between BV/TV and E_s were similar to published experimental relations. At 1 MHz, correlations between SOS and the structural parameters BV/TV and E_s were rather weak, but the results can be explained from the specific features of the trabecular structure and the intrinsic material elastic modulus E_i. In particular, the systematic differences between the three main directions provide information on the trabecular structure. In addition, at 1 MHz the correlation found between the simulated SOS values and those calculated from the simple bar equation was poor when the three directions are considered separately. Hence, under these conditions, the homogenization approach - including the bar equation - is not valid. However, at lower frequencies (50-300 kHz) this correlation significantly improved. It is concluded that detailed analysis of ultrasound wave propagation through the solid structure in various directions and with various frequencies, can yield much information on the structural and mechanical properties of trabecular bone.     

Influence of multiple reflections on transmission through a stack of plates

We examine the problem of light transmission along the normal through a stack of flat plates whose thicknesses and separations vary. For a modest number of plates, an exact calculation is straightforward, but then one must address how to average over both the disorder in the stack and the distribution of incident wavelengths. Model calculations are used to show that an average over the light's distribution can suppress most of the fluctuations due to disorder. Our results are in qualitative agreement with experimental data and imply that multiple reflections do contribute significantly to the measurements. Finally we explore the effect of multiple reflections on photometry.     

覆冰输电线结构及载荷对舞动的影响

为深入研究导线结构形式对输电线路系统动力学特性影响,以及导线结构形式及气动扭转载荷对覆冰输电线路舞动规律及幅值的影响,采用ANSYS参数化设计语言编写了计算导线舞动的非线性有限元分析程序,计算得出了系统气动载荷作用下的时间历程曲线。发现：在相同的气象条件下,分裂导线的振幅明显大于单根导线,且分裂数越高,导线越容易在短时间内形成稳态的舞动,应尽量采用单根导线或减少导线分裂数;扭转气动力载荷对面内外舞动的规律及幅值影响不大,对扭转角的幅值有较大影响,因此可忽略扭转气动载荷对断线和倒塔的作用。     

A comparative study of elasticity,shell and boundary layer solutions applied to axially compressed cylinders

Summary This paper deals primarily with a comparative study based on different methods of solution for the problem of axially compressed cylinders. A comprehensive discussion on the range of validity of these types of solutions is also included, and an extensive numerical analysis has been carried out.     

The effects of bovine trabecular bone matrix particulates on cortical bone repair

This paper reports the effects of a synthetic bone substitute and bone allograft on cortical bone repair in an experimental model. To test the hypothesis that bovine trabecular bone matrix, BBM, can enhance the repair rate of cortical bone, osteotomies were created in the rabbit fibula and filled with either allograft or BBM particulates or left empty as controls. At five weeks post-surgery, mechanical tests and histological evaluations were performed. No significant differences were observed in the mechanical properties of the healing bone in the three animal groups (n=6). Histologically, the medullary cavity was obstructed and the cross-sectional area ratio of the osteotomies to intact bone was approximately 3 : 1. Highly significant area differences were observed between the intact bone group and both the BBM and the allograft groups . At the junction between the original bone and the newly formed bone, both woven and lamellar bone microstructures were prevalent. However, in the BBM filled defects, the woven bone microstructure was not ostentatious. It is concluded that failure to demonstrate significantly differences between the treatments were due to the small sample sizes and or the efficacy of the tensile analysis.     

Influence of scattering on transmission through long-period fiber gratings and tunable microstructure fibers

Controlled optical scattering within or around an optical fiber provides a potentially useful mean for adjusting its transmission characteristic. This approach can complement conventional methods based on the establishment of well-defined variations in the index of refraction of the core or the cladding of the fiber. We describe the use of a highly scattering submonolayer of nanoparticles deposited onto the fiber surface for adjusting the resonance wavelength, depth, and width of an in-fiber long-period grating filter. We also introduce a polymer-dispersed liquid-crystal material that has a thermally tunable scattering cross section and can be incorporated into the channels of a microstructure optical fiber; this system may provide the means for a fiber-based scattering switch.     

Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders

An analytical approach to solve plane static non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders is presented. This approach is based upon the direct integration method proposed by Vihak (Vigak). The essence of the method mentioned is in the integration of the original differential equilibrium equations, which are independent of the stress–strain relations. This gives the opportunity to deduce the relations, which are invariant with respect to various properties of the material, for the stress-tensor components. From these relations each of the stress-tensor components have been expressed in terms of the governing one. A solution of the equation for the governing stress in the form of Fourier series is presented. To determine the Fourier coefficients, an integral Volterra-type equation is derived and solved by a simple iteration method with rapid convergence. Other stress-tensor components are expressed through the obtained governing stress in the form of an explicit functional dependence on force and thermal loadings.     

超声波对电镀金刚石工具镀层性能及上砂密度的影响

研究了超声波对电镀金刚石工具制备过程的影响。采用在传统瓦特镀液中引入超声波,研究不同超声波功率对镀层组织、镀层厚度及镀层硬度等性能的影响,确定镀层获得良好的综合性能时超声波功率。利用金相显微镜观察镀层组织结构和测量镀层厚度,利用显微硬度计测量镀层硬度,实验表明超声波功率为200W时,镀层有良好的综合性能。在此基础上利用金相显微镜研究了加厚过程应用超声波对金刚石工具上砂密度的影响。     

Effect of supramolecular structure on polymer nanofibre elasticity

Polymer materials of reduced size and dimensionality, such as thin films, polymer nanofibres and nanotubes, exhibit exceptional mechanical properties compared with those of their macroscopic counterparts. We discuss here the abrupt increase in Young's modulus in polymer nanofibres. Using scaling estimation we show that this effect occurs when, in the amorphous (non-crystalline) part of the nanofibres, the transversal size of regions consisting of orientation-correlated macromolecules is comparable to the nanofibre diameter, thereby resulting in confinement of the supramolecular structure. We suggest that in polymer nanofibres the resulting supramolecular microstructure plays a more dominant role in the deformation process than previously thought, challenging the commonly held view that surface effects are most significant. The concept we develop also provides a way to interpret the observed--but not yet understood--temperature dependence of Young's modulus in nanofibres of different diameters.     

Influence of current density on crystalline structure and magnetic properties of electrodeposited Co-rich CoNiW alloys

The influence of current density, at the interval 5–100 mA cm⁻², on the structural and magnetic properties of electrodeposited (Co_100−xNi_x)_100−yW_y alloys (x = 23–33.5 at. % Ni, y = 1.7–7.3 at. % W) was studied from a glycine-containing bath. W-content decreases with the increase of the current density magnitude. X-ray data have shown stabilization of hexagonal close packed, face centered cubic or a mixture of these structures by modulating the applied cathodic current density, for values lower than 50 mA cm⁻². Two structural phase transitions were observed: one from hexagonal close packed to face centered cubic structural transition occurring for a current density of 20 mA cm⁻², and another one, from cubic crystalline phase to amorphous state, which happens for values higher than 50 mA cm⁻². These structural phase transitions seem to be associated with the W-content as well as average crystalline grain sizes that reduce with increasing the current density value. The grain size effect may explain the face centered cubic stabilization in Co-rich CoNiW alloys, which was initially assumed to be basically due to H-adsorption/incorporation. Magnetic properties of Co-rich CoNiW alloys are strongly modified by the current density value; as a result of the changes on the W-content and their structural properties.     

Hierarchical analysis and multi-scale modelling of rat cortical and trabecular bone

The aim of this study was to explore the hierarchical arrangement of structural properties in cortical and trabecular bone and to determine a mathematical model that accurately predicts the tissue''s mechanical properties as a function of these indices. By using a variety of analytical techniques, we were able to characterize the structural and compositional properties of cortical and trabecular bones, as well as to determine the suitable mathematical model to predict the tissue''s mechanical properties using a continuum micromechanics approach. Our hierarchical analysis demonstrated that the differences between cortical and trabecular bone reside mainly at the micro- and ultrastructural levels. By gaining a better appreciation of the similarities and differences between the two bone types, we would be able to provide a better assessment and understanding of their individual roles, as well as their contribution to bone health overall.     

人体组织弹性的超声检测和应用前景

组织的软硬或弹性反映了组织本身的特性。对于它们的检测所得信息往往有助于对疾病的诊断。本文介绍了运用超声检测人体组织弹性的原理入检测中信息处理和特征提取的几种方法，包括我们的研究工作并就其应用前景作了展望。     

双层板结构中声传播主动控制的仿真分析

文章针对一个具有双层板结构的模型，对于在双层板结构中放置次级声源以达到主动控制低频噪声传播的方法进行了数值计算仿真。在数值计算仿真中采用直接对结构－声耦合运动方程进行傅立叶变换的方法，简单而有效地验证了在封闭空腔中放置次级控制声源可以达到控制低频噪声传播的目的，并且分析了不同控制源策略的差异。     

Microwave transmission amplitude-frequency characteristic of two-dimensional composite electromagnetic crystal based on copper cylinders

The amplitude-frequency characteristic of the coefficient of microwave transmission of a two-dimensional composite electromagnetic crystal comprising gypsum (CaSO₄ · 2H₂O) matrix with a regular structure of conducting cylinders has been experimentally studied.     

Influence of film thickness on the optical transmission through subwavelength single slits in metallic thin films

Silver and gold films with thicknesses in the range of 120-450 nm were evaporated onto glass substrates. A sequence of slits with widths varying between 70 and 270 nm was milled in the films using a focused gallium ion beam. We have undertaken high-resolution measurements of the optical transmission through the single slits with 488.0 nm (for Ag) and 632.8 nm (for Au) laser sources aligned to the optical axis of a microscope. Based on the present experimental results, it was possible to observe that (1) the slit transmission is notably affected by the film thickness, which presents a damped oscillatory behavior as the thickness is augmented, and (2) the transmission increases linearly with increasing slit width for a fixed film thickness.