时频方法分析长骨中的超声导波及皮质骨厚度

超声导波在长骨中传播时,接收信号中含有相互叠加的多个导波模式。本文提出将希尔伯特-黄变换(HHT)用于分析叠加的多模式导波信号,将其分解成许多单个独立的模式,然后对分解出的模式求得其对应频率下的群速度,并与短时傅里叶变换所得的结果进行比较。通过与理论计算结果比较,可得到长骨皮质骨的厚度。研究结果表明,实验得到的厚度与实际厚度一致。说明通过测量导波模式的速度可以评价皮质骨的厚度,也说明HHT方法是一种识别叠加多模式导波信号的有效方法。      

Diagnosis of osteoporosis based on multi-scale wavelet parameters of ultrasonic guided waves

Evaluating bone regularly is important to prevent and control the disease of osteoporosis. Impact of osteoporosis on ultrasonic guided waves propagating in human long bones is studied in this paper. Multi-scale wavelet transform is proposed to process the received guided waves, and by analyzing energy changes in detail components of high order wavelet at different propagating distance to assess if osteoporosis happened. The guided waves signals are collected from the tibias of 13 volunteers. Based on the analysis of multi-scale wavelet transform, the high order detail components d6 and d5 changed dramatically with the propagation of ultrasonic guided waves along long bones, which means these 7 volunteers are diagnosed with osteoporosis. Compared with X-ray diagnosis, the effectiveness of this method can reach 92.3% in 13 volunteers. This suggests the multi-scale wavelet transform method is potential in ultrasonic assessment of bone quality.     

采用超声导波特征参量的骨质疏松识别方法

骨质的定期检测对骨质疏松的防治至关重要。本文研究了骨质疏松对超声导波在人体长骨中传播的影响。提出采用多尺度小波变换方法对接收到的导波信号进行处理,通过分析在不同传播距离下高阶小波细节分量所占信号总能量的变化,来判断是否患有骨质疏松症。在13位志愿者的小腿胫骨上进行超声测量,得到导波信号。经多尺度小波变换方法的分析处理结果显示在13位志愿者中,有7位志愿者的超声导波信号随着传播距离的改变,其主要频率成分发生了明显的变化,显示这7位志愿者患有骨质疏松症。这一诊断结果与X射线技术诊断结果相比,准确率可以达到92.3%,表明本文所提出的利用小波多尺度变换方法对长骨进行超声诊断具有较好的潜力。      

Nonlinear inversion of ultrasonic guided waves for in vivo evaluation of cortical bone properties

Ultrasonic guided waves (UGWs), which propagate throughout the entire thickness of cortical bone, are attractive for the early diagnosis of osteoporosis. However, this is challenging due to the impact of soft tissue and the inherent difficulties related to multiparametric inversion of cortical bone quality factors, such as cortical thickness and bulk wave velocity. Therefore, in this research, a UGW-based multi-parameter inversion algorithm is developed to predict strength-related factors. In simulation, a free plate (cortical bone) and a bilayer plate (soft tissue and cortical bone) are used to validate the proposed method. The inversed cortical thickness (CTh), longitudinal velocity (V_L) and transverse velocity (V_T) are in accordance with the true values. Then four bovine cortical bone plates were used in in vitro experiments. Compared with the reference values, the relative errors for cortical thickness were 3.96%, 0.83%, 2.87%, and 4.25%, respectively. In the in vivo measurements, UGWs are collected from the tibias of 10 volunteers. The theoretical dispersion curves depicted by the estimated parameters (V_T, V_L, CTh) match well with the extracted experimental ones. In comparison with dual-energy x-ray absorptiometry, our results show that the estimated transverse velocity and cortical thickness are highly sensitive to osteoporosis. Therefore, these two parameters (CTh and V_T) of long bones have potential to be used for diagnosis of bone status in clinical applications.     

Multi-frequency axial transmission bone ultrasonometer

The last decade has seen a surge in the development of axial transmission QUS (Quantitative UltraSound) technologies for the assessment of long bones using various modes of acoustic waves. The condition of cortical bones and the development of osteoporosis are determined by numerous mechanical, micro-structural, and geometrical or macro-structural bone properties like hardness, porosity and cortical thickness. Such complex manifestations of osteoporosis require the evaluation of multiple parameters with different sensitivities to the various properties of bone that are affected by the disease. This objective may be achieved by using a multi-frequency ultrasonic examination The ratio of the acoustic wavelength to the cortical thickness can be changed by varying the frequency of the ultrasonic pulse propagating through the long bone that results in the change in composition of the induced wave comprised of a set of numerous modes of guided, longitudinal, and surface acoustic waves. The multi-frequency axial transmission QUS method developed at Artann Laboratories (Trenton, NJ) is implemented in the Bone Ultrasonic Scanner (BUSS). In the current version of the BUSS, a train of ultrasonic pulses with 60, 100, 400, 800, and 1200 kHz frequencies is used. The developed technology was tested on a variety of bone phantoms simulating normal, osteopenic, and osteoporotic bones. The results of this study confirm the feasibility of the multi-frequency approach for the assessment of the processes leading to osteoporosis.     

Comment on "Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones," [J. Acoust. Soc. Am. 121(6), 3907-3921 (2007)

Protopappas et al. performed finite element (FE) studies on the propagation of guided ultrasound waves in intact and healing long bones, and found that the dispersion of guided modes was significantly influenced by the irregularity and anisotropy of the bone. A time-frequency (t-f) method was applied to the obtained signals and several wave modes were identified. However, this technique was unable to quantify their observations and provide monitoring capabilities. One possible reason of this shortcoming may come from the inherent disadvantage of the t-f method. The objective of this comment is to demonstrate that it is necessary to combine other techniques with FE simulations for the extraction of significant quantitative ultrasonic features. Individual guided modes in an isotropic pipe have been theoretically examined using the normal mode expansion (NME) method, and many modes that are missed by the t-f analysis have been identified. It is concluded that in order to extract quantitative ultrasonic features, FE simulations should be supplemented by other techniques such as the NME.     

Three-dimensional finite element modeling of guided ultrasound wave propagation in intact and healing long bones

The use of guided waves has recently drawn significant interest in the ultrasonic characterization of bone aiming at supplementing the information provided by traditional velocity measurements. This work presents a three-dimensional finite element study of guided wave propagation in intact and healing bones. A model of the fracture callus was constructed and the healing course was simulated as a three-stage process. The dispersion of guided modes generated by a broadband 1-MHz excitation was represented in the time-frequency domain. Wave propagation in the intact bone model was first investigated and comparisons were then made with a simplified geometry using analytical dispersion curves of the tube modes. Then, the effect of callus consolidation on the propagation characteristics was examined. It was shown that the dispersion of guided waves was significantly influenced by the irregularity and anisotropy of the bone. Also, guided waves were sensitive to material and geometrical changes that take place during healing. Conversely, when the first-arriving signal at the receiver corresponded to a nondispersive lateral wave, its propagation velocity was almost unaffected by the elastic symmetry and geometry of the bone and also could not characterize the callus tissue throughout its thickness. In conclusion, guided waves can enhance the capabilities of ultrasonic evaluation.     

Guided wave dispersion curves for a bar with an arbitrary cross-section,a rod and rail example

Theoretical and experimental issues of acquiring dispersion curves for bars of arbitrary cross-section are discussed. Since a guided wave can propagate over long distances in a structure, guided waves have great potential for being applied to the rapid non-destructive evaluation of large structures such as rails in the railroad industry. Such fundamental data as phase velocity, group velocity, and wave structure for each guided wave mode is presented for structures with complicated cross-sectional geometries as rail. Phase velocity and group velocity dispersion curves are obtained for bars with an arbitrary cross-section using a semi-analytical finite element method. Since a large number of propagating modes with close phase velocities exist, dispersion curves consisting of only dominant modes are obtained by calculating the displacement at a received point for each mode. These theoretical dispersion curves agree in characteristic parts with the experimental dispersion curves obtained by a two-dimensional Fourier transform technique.     

Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

We investigate the guided waves in a multi-layered cylindrical elastic solid medium. The dispersion function of guided waves is usually complex and the dispersion curves of all modes are not conveniently obtained. Here we present an effective method to obtain the dispersion curves of all modes. First, the dispersion function of the guided waves is transformed into a real function. The dispersion curves are then calculated for all the modes of the guided waves by the bisection method. The modes with the orders n = 0, 1, and 2 are analysed in two- and three-layer media. The existence condition of Stoneley wave is discussed. The modes of the guided waves are also investigated in a two-layer medium, in which the velocity of shear wave in the outer layer is less than that in the inner layer.     

Influence of the slow wave on the relation between the angular resonances and the leaky guided modes properties for a poroelastic plate embedded in water

A numerical study of the guided modes in a water-saturated poroelastic plate that obeys the Biot theory is presented. In the first part, we study the leaky guided modes and the angular resonances when the slow wave does not propagate. Two types of guided modes exist. The first ones occur from coupling of the fast longitudinal wave with the shear wave; most of them propagate whatever the frequency is, provided that it is not close to their cut-off frequencies. The leaky guided modes of the second type occur from coupling of the two longitudinal waves and the shear wave. These modes do not propagate (they are highly damped) as long as the slow wave remains diffusive. We show that the characteristics of the angular resonances can be linked to the leaky guided waves of the first type in the same way as for an elastic plate. The guided modes of the second type may not be associated to angular resonances. In the second part, we consider a thinner plate in a higher frequency range so that the slow wave can propagate. Once again its influence is studied both on the leaky guided modes and on the angular resonances.     

A numerical study on the propagation of Rayleigh and guided waves in cortical bone according to Mindlin's Form II gradient elastic theory

Cortical bone is a multiscale heterogeneous natural material characterized by microstructural effects. Thus guided waves propagating in cortical bone undergo dispersion due to both material microstructure and bone geometry. However, above 0.8 MHz, ultrasound propagates rather as a dispersive surface Rayleigh wave than a dispersive guided wave because at those frequencies, the corresponding wavelengths are smaller than the thickness of cortical bone. Classical elasticity, although it has been largely used for wave propagation modeling in bones, is not able to support dispersion in bulk and Rayleigh waves. This is possible with the use of Mindlin's Form-II gradient elastic theory, which introduces in its equation of motion intrinsic parameters that correlate microstructure with the macrostructure. In this work, the boundary element method in conjunction with the reassigned smoothed pseudo Wigner-Ville transform are employed for the numerical determination of time-frequency diagrams corresponding to the dispersion curves of Rayleigh and guided waves propagating in a cortical bone. A composite material model for the determination of the internal length scale parameters imposed by Mindlin's elastic theory is exploited. The obtained results demonstrate the dispersive nature of Rayleigh wave propagating along the complex structure of bone as well as how microstructure affects guided waves.     

Propagation of time-reversed Lamb waves in acrylic cylindrical tubes as cortical-bone-mimicking phantoms

The present study aims to investigate the propagation of time-reversed Lamb waves in acrylic cylindrical tubes as cortical-bone-mimicking phantoms. Time-reversed Lamb waves could be successfully launched in 6 acrylic tubes with wall thicknesses from 2 to 12 mm by using a modified time reversal method. The group velocities of the time-reversed Lamb waves in the acrylic tubes were measured by using the axial transmission technique. They decreased very slightly with increasing wall thickness, showing good agreement with the theoretical group velocity of the A0 Lamb wave in the acrylic plate. These results suggest that the time-reversed Lamb waves in the acrylic tubes would essentially behave as the A0 Lamb wave, consistent with the behavior of the slow guided wave in long cortical bones. It is expected that the application of the time-reversed Lamb waves in long bones would enhance clinical potential of ultrasonic technologies for the diagnosis of osteoporosis.     

Barker码激励超声导波在长骨检测中的应用

单脉冲激励的超声导波在长骨中传播时,信号的衰减大,导致接收信号的幅度很小,且噪声严重。Barker码激励能有效增大接收信号幅度,提高信噪比(SNR)。将其应用到超声导波长骨检测中,进行仿真和长骨实验,得到的信号分别用加权匹配滤波器和有限冲激响应-最小均方误差(FIR-LS)逆滤波器进行压缩,并与单脉冲激励的结果进行了对比。结果表明,对于13位的Barker码,采用加权匹配滤波器进行解码时,压缩信号幅度是单脉冲激励接收信号的13倍;而FIR-LS逆滤波器则达到-63.59 dB的峰值旁瓣水平(PSL),更好地抑制噪声。说明可以将Barker码激励超声导波应用于长骨的检测中。      

Investigation of the phase velocities of guided acoustic waves in soft porous layers

A new experimental method for measuring the phase velocities of guided acoustic waves in soft poroelastic or poroviscoelastic plates is proposed. The method is based on the generation of standing waves in the material and on the spatial Fourier transform of the displacement profile of the upper surface. The plate is glued on a rigid substrate so that it has a free upper surface and a nonmoving lower surface. The displacement is measured with a laser Doppler vibrometer along a line corresponding to the direction of propagation of plane surface waves. A continuous sine with varying frequencies was chosen as excitation signal to maximize the precision of the measurements. The spatial Fourier transform provides the wave numbers, and the phase velocities are obtained from the relationship between wave number and frequency. The phase velocities of several guided modes could be measured in a highly porous foam saturated by air. The modes were also studied theoretically and, from the theoretical results, the experimental results, and a fitting procedure, it was possible to determine the frequency behavior of the complex shear modulus and of the complex Poisson ratio from 200 Hz to 1.4 kHz, in a frequency range higher than the traditional methods.     

液态金属快堆主管道中超声导波传播特性研究

讨论了钠冷快堆(Sodium-cooled Fast Reactor,SFR)主管道的整体温度和内部液态金属钠流动速度的变化对管道导波传播特性的影响。推导了充液管道中导波频散方程的一般形式,并给出了管道内液态金属钠处于流动状态下的导波频散方程。采用数值计算方法获得了管内液态金属钠处于不同温度和不同流速时的导波纵向模式频散曲线和导波时域波形。结果表明,温度变化对基阶纵向模式的影响较小,但对高阶纵向模式的影响较大;液态钠流速增大会使导波频散曲线向高频轻微移动,但在实际检测中可以忽路管内液体流动速度的影响。通过对时域接收波形的模拟计算,进一步考察了液态金属钠的温度及流动速度变化对导波传播的影响,并通过对比不同模态的激发特点和不同频段的导波时域波形特点,结合导波频散曲线,给出了适用于SFR管道超声无损检测的导波模态和声源激发频段选择方案。      

Characterization of circumferential guided waves in a cylindrical cortical bone-mimicking phantom

The femoral neck cortical shell was recently demonstrated to act like a waveguide for circumferential waves. Femoral neck assessment with ultrasound could be enhanced by guided waves measurement. In this study, the decomposition of the time reversal operator (DORT) method is used to measure the phase velocities of circumferential guided modes in a circular tube with dimensions characteristic of femoral neck. The tube is made of a bone-mimicking material. Five guided modes are obtained and compared to theoretical predictions. The work substantiates the feasibility of measuring guided waves in a relatively thick tube of attenuating material with the DORT method.     

Guided elastic waves in a pre-stressed compressible interlayer

The propagation of guided elastic waves in a pre-stressed elastic compressible layer embedded in a different compressible material is examined. The waves propagate parallel to the planar layer interfaces as a superposed dynamic stress state on the statically pre-stressed layer and host material. The underlying stress condition in the two materials is characterized by equibiaxial in-plane deformations with common principal axes of strain, one of the axes being perpendicular to the layering. Both materials have arbitrary strain energy functions. The dispersion equation is derived in explicit form. Analysis of the dispersion equation reveals the propagation characteristics and their dependence on frequency, material parameters and stress parameters. Combinations of these parameters are also defined for which guided waves cannot propagate.     

Impact of attenuation on guided mode wavenumber measurement in axial transmission on bone mimicking plates

Robust signal processing methods adapted to clinical measurements of guided modes are required to assess bone properties such as cortical thickness and porosity. Recently, an approach based on the singular value decomposition (SVD) of multidimensional signals recorded with an axial transmission array of emitters and receivers has been proposed for materials with negligible absorption, see Minonzio et al. [J. Acoust. Soc. Am. 127, 2913-2919 (2010)]. In presence of absorption, the ability to extract guided mode degrades. The objective of the present study is to extend the method to the case of absorbing media, considering attenuated plane waves (complex wavenumber). The guided mode wavenumber extraction is enhanced and the order of magnitude of the attenuation of the guided mode is estimated. Experiments have been carried out on 2 mm thick plates in the 0.2-2 MHz bandwidth. Two materials are inspected: polymethylacrylate (PMMA) (isotropic with absorption) and artificial composite bones (Sawbones, Pacific Research Laboratory Inc, Vashon, WA) which is a transverse isotropic absorbing medium. Bulk wave velocities and bulk attenuation have been evaluated from transmission measurements. These values were used to compute theoretical Lamb mode wavenumbers which are consistent with the experimental ones obtained with the SVD-based approach.     

Use of multiple acoustic wave modes for assessment of long bones: model study

Multiple acoustic wave mode method has been proposed as a new modality in axial bone QUS. The new method is based on measurement of ultrasound velocity at different ratio of wavelength to the bone thickness, and taking into account both bulk and guided waves. It allows assessment of changes in both the material properties related to porosity and mineralization as well as the cortical thickness influenced by resorption from inner layers, which are equally important in diagnostics of osteoporosis and other bone osteopenia. Developed method was validated in model studies using a dual-frequency (100 and 500 kHz) ultrasound device. Three types of bone phantoms for long bones were developed and tested: (1) tubular specimens from polymer materials to model combined changes of material stiffness and cortical wall thickness; (2) layered specimens to model porosity in compact bone progressing from endosteum towards periosteum; (3) animal bone specimens with both cortical and trabecular components. Observed changes of the ultrasound velocity of guided waves at 100 kHz followed gradual changes in the thickness of the intact cortical layer. On the other hand, the bulk velocity at 500 kHz remained nearly constant at the different cortical layer thickness but was affected by the material stiffness. Similar trends were observed in phantoms and in fragments of animal bones.     

无限流体中孔隙介质圆柱周向导波的传播特性

为研究无限大流体约束的孔隙圆柱中周向导波的传播规律,分析孔隙参数对导波传播特性的影响,建立了无限流体中孔隙介质圆柱的理论模型,利用孔隙介质弹性波动理论,建立了周向导波频散方程,通过数值模拟计算得到无限流体中孔隙介质圆柱的频散曲线,探讨了圆柱半径和孔隙参数对导波传播特性的影响,并对导波的衰减特性进行了分析;通过数值计算,得到了周向导波的时域波形,讨论了孔隙参数对波形的影响.结果表明,孔隙介质圆柱半径的改变影响圆柱尺度,孔隙度的改变影响孔隙介质中体声波的波速,都对周向导波频散曲线产生一定的影响,所得到的频散曲线特征及衰减曲线与时域波形吻合.研究结果对开展无限流体中孔隙介质圆柱的超声无损评价提供了一定的理论参考.