Distribution of longitudinal wave properties in bovine cortical bone in vitro

The detailed spatial distributions of longitudinal ultrasonic velocity in cortical bone specimens obtained from three bovine femoral diaphysis were experimentally investigated using a pulse-echo system. The relationship between velocity, density, bone mineral density (BMD) and microstructure was investigated. Velocity was found to vary as a function of the direction of propagation and the location of the measured specimens in the bone diaphysis. A significant correlation was found between density and velocity, and between density and BMD. In some parts with plexiform structure, clear variations in velocity anisotropy were found despite no significant difference in density, BMD and microstructure.     

Effect of anisotropy on acoustoelastic birefringence in wood

The ultrasonic velocity of shear waves propagating through radial direction of a wood plate specimen, transversely to the loading direction, was measured. By rotating an ultrasonic sensor, the oscillation direction of the shear waves was varied with respect to the wood plate axis and loading direction. The relationship between shear wave velocity and oscillation direction was examined to discuss the effect of anisotropy on the acoustoelastic birefringence in wood. The results obtained were summarized as follows. When the oscillation direction of the shear wave corresponded to the tangential direction of the wood specimen regardless of the stress direction, shear wave velocity decreased markedly and the relationship between shear wave velocity and rotation angle tended to become discontinuous. That is, when the shear waves oscillated in the anisotropic axis of the wood, the shear wave velocity peaked unlike in the case of oscillation in the stress direction. In an isotropic material (acrylic, aluminum 5052), on the contrary, when the shear waves oscillated in the stress direction of the specimen, the shear wave velocity peaked regardless of the main-axis direction of the specimen. On the basis of the discussion of these results, the ultrasonic shear wave propagating in wood under stress is confirmed to be polarized in the anisotropic axis of the wood.     

Ultrasonic slow waves in air-saturated cancellous bone

This paper describes preliminary observations of ultrasonic wave propagation in air-saturated defatted cancellous bone from the human vertebra. Using a broadband pulse transmission system, attenuation and phase velocity were measured over a wide frequency range (100 kHz-1 MHz). The observed behaviour was consistent with that expected for the decoupled slow wave predicted by Biot's theory. Velocity was lower than that of free air, and there was marked frequency-dependent attenuation and velocity dispersion. The tortuosity (alpha) of the trabecular microstructure was estimated from the high frequency limit of the dispersion curve, with a mean value of alpha = 1.040 +/- 0.004 obtained in five specimens. Ultrasonic measurements in air represent a valuable new approach, capable of yielding parameters that directly characterise bone structure. Furthermore, they may give useful insights into wave propagation in bone in vivo, where the trabecular framework is saturated with marrow fat rather than air.     

Influence of cancellous bone microstructure on two ultrasonic wave propagations in bovine femur: an in vitro study

The influence of cancellous bone microstructure on the ultrasonic wave propagation of fast and slow waves was experimentally investigated. Four spherical cancellous bone specimens extracted from two bovine femora were prepared for the estimation of acoustical and structural anisotropies of cancellous bone. In vitro measurements were performed using a PVDF transducer (excited by a single sinusoidal wave at 1 MHz) by rotating the spherical specimens. In addition, the mean intercept length (MIL) and bone volume fraction (BV/TV) were estimated by X-ray micro-computed tomography. Separation of the fast and slow waves was clearly observed in two specimens. The fast wave speed was strongly dependent on the wave propagation direction, with the maximum speed along the main trabecular direction. The fast wave speed increased with the MIL. The slow wave speed, however, was almost constant. The fast wave speeds were statistically higher, and their amplitudes were statistically lower in the case of wave separation than in that of wave overlap.     

Anisotropy of ultrasonic velocity and elastic properties in normal human myocardium.

Measurements of ultrasonic quasilongitudinal velocity were made in the muscle fiber plane of excised human myocardium. Multiple adjacent planes across the left ventricular wall were interrogated to assess the transmural dependence of velocity. For each measurement plane, data were obtained in 2-deg increments through the full 360 deg relative to the myofibers. An approximate 1.3% magnitude of anisotropy was observed with maximum velocity along the muscle fibers and minimum velocity perpendicular to the muscle fibers. The known transmural shift in myofiber orientation was evidenced in the anisotropy of velocity as angular shifts between plots obtained from adjacent transmural planes within the same specimen. Measured values of velocity and density were used to estimate the effective C33 and C11 elastic constants of a thin layer of normal myocardium.     

Ultrasonic pulse waves in cancellous bone analyzed by finite-difference time-domain methods

The trabecular frame of cancellous bone has a high degree of porosity, anisotropy and inhomogeneity. The propagation of ultrasonic waves in cancellous bone is significantly affected by the trabecular structure. In this paper, two two-dimensional finite-difference time-domain (FDTD) methods, which were the popular viscoelastic FDTD method for a viscoelastic medium and Biot's FDTD method for a fluid-saturated porous medium, have been applied to numerically analyze the ultrasonic pulse waves propagating through bovine cancellous bone in the directions parallel and perpendicular to the trabecular alignment. The Biot's fast and slow longitudinal waves, which were identified in previous experiments for the propagation parallel to the trabecular orientation, could be analyzed using Biot's FDTD method rather than the viscoelastic FDTD method. For the single wave propagation in the perpendicular direction, on the other hand, the viscoelastic FDTD result was found to be in more good agreement with the experimental result.     

Effect of texture and grain shape on ultrasonic backscattering in polycrystals

An ultrasonic backscattering model is developed for textured polycrystalline materials with orthotropic or trigonal grains of ellipsoidal shape. The model allows us to simulate realistic microstructures and orthotropic macroscopic material textures resulting from thermomechanical processing for a broad variety of material symmetries. The 3-D texture is described by a modified Gaussian orientation distribution function (ODF) of the crystallographic orientation of the grains along the macroscopic texture direction. The preferred texture directions are arbitrary relative to the axes of the ellipsoidal grains. The averaged elastic covariance and the directional anisotropy of the backscattering coefficient are obtained for a wave propagation direction arbitrary relative to the texture and grain elongation directions. One particular application of this analysis is the backscattering solution for cubic crystallites with common textures such as Cube, Goss, Brass and Copper. In our analysis, in the texture-defined coordinates the matrix of elastic constants for cubic crystallites takes the form of orthotropic or trigonal symmetry. Numerical results are presented, discussed and compared to the experimental data available in the literature illustrating the dependence of the backscattering coefficient on texture and grain shape.     

In vitro estimation of fast and slow wave parameters of thin trabecular bone using space-alternating generalized expectation-maximization algorithm

In testing cancellous bone using ultrasound, two types of longitudinal Biot’s waves are observed in the received signal. These are known as fast and slow waves and their appearance depend on the alignment of bone trabeculae in the propagation path and the thickness of the specimen under test (SUT). They can be used as an effective tool for the diagnosis of osteoporosis because wave propagation behavior depends on the bone structure. However, the identification of these waves in the received signal can be difficult to achieve.In this study, ultrasonic wave propagation in a 4 mm thick bovine cancellous bone in the direction parallel to the trabecular alignment is considered. The observed Biot’s fast and slow longitudinal waves are superimposed; which makes it difficult to extract any information from the received signal. These two waves can be separated using the space alternating generalized expectation maximization (SAGE) algorithm. The latter has been used mainly in speech processing.In this new approach, parameters such as, arrival time, center frequency, bandwidth, amplitude, phase and velocity of each wave are estimated. The B-Scan images and its associated A-scans obtained through simulations using Biot’s finite-difference time-domain (FDTD) method are validated experimentally using a thin bone sample obtained from the femoral-head of a 30 months old bovine.     

Parameters influencing the sonic velocity in compact calcified tissues of various species

Compact calcified tissues from a wide variety of species were used in a study of the dependence of sonic plesio-velocity on physical parameters. A linear dependence of velocity on wet density has been found for each of three categories of wet mineralized tissue: compact long bone measured in the axial direction, compact long bone measured in the radial direction, and hyperpycnotic mineralized tissues. A similar linear dependency was found for dry calcified tissue using the dry density. In addition to these three parameters (density, orientation, and water content) two other factors were identified. The bone fibers in long bone matrix are ordered with respect to the bone axis and the anisotropy of long bone matches that of its matrix. There is no corresponding order to the fibers in hyperpycnotic tissue matrix. The fifth parameter is believed to be the porosity. Fish bone is much more porous than other compact bone from long bone and the sonic velocity in fish bone is much lower than for other bone. These parameters are not independent.     

Attenuation of ultrasonic waves in rolled metals

Scattering of ultrasonic waves in polycrystals with texture is studied in this article. The attenuations of the three wave modes are determined as a function of dimensionless frequency and propagation direction, respectively, for given orientation distribution coefficients (ODCs). The calculation is done in the case of a statistically orthorhombic sample made up of cubic crystallites. The wave propagation and scattering model is formulated by the Dyson equation using an anisotropic Green's function approach. Within the limits of the first-order smoothing approximation, the Dyson equation is solved in the spatial Fourier transform domain. The results presented are shown to be directional dependent, frequency dependent, and especially dependent on the texture coefficients (ODCs) for the quasilongitudinal and two quasishear waves. The theoretical results presented may be used to improve the understanding of the microstructure during recrystallization processes.     

Determination of crystallographic orientation of large grain metals with surface acoustic waves

A previously described laser ultrasonic technique known as spatially resolved acoustic spectroscopy (SRAS) can be used to image surface microstructure, using the local surface acoustic wave (SAW) velocity as a contrast mechanism. It is shown here that measuring the SAW velocity in multiple directions can be used to determine the crystallographic orientation of grains. The orientations are determined by fitting experimentally measured velocities to theoretical velocities. Using this technique the orientations of 12 nickel and 3 aluminum single crystal samples have been measured, and these are compared with x-ray Laue backreflection (LBR) measurements with good agreement. The root mean square difference between SRAS and LBR measurements in terms of an R-value is less than 4.1°. The influence of systematic errors in the SAW velocity determination due to instrument miscalibration, which affects the accurate determination of the planes, is discussed. SRAS has great potential for complementary measurements or even for replacing established orientation determination and imaging techniques.     

Structure and mechanical properties of nylon 6.12 prepared by temperature slope crystallization. I. Crystallization of oriented spherulitic textures

Oriented spherulitic textures of a rod-shaped nylon 6.12 sample were crystallized by the temperature slope method. Crystallization conditions were compared by changing temperatures and growth rates. Three types of textures (negative spherulites, positive spherulites, and spherulitic aggregates) were observed by this method. The negative textures appeared when the growth rate was less than 0.1 mm/h. Crystalline orientation and mechanical properties of the textures were investigated by x-ray diffraction and micro-hardness measurements, respectively. The hydrogen-bonded (010) planes were perpendicular to the growth direction in the negative spherulite, while they were parallel to the growth direction in the positive spherulite. In the spherulitic aggregates, the b axis was parallel to the growth direction, while the (010) planes formed roughly an angle of 45° with the growth direction. Due to the orientation of the hydrogen-boned planes, the negative texture exhibited an anisotropy, with hardness values of 106 MPa and 137 Mpa when measured perpendicular or parallel to the growth direction, respectively.     

Investigation of an anisotropic tortuosity in a biot model of ultrasonic propagation in cancellous bone

The modeling of ultrasonic propagation in cancellous bone is relevant to the study of clinical bone assessment. Historical experiments revealed the importance of both the viscous effects of bone marrow and the anisotropy of the porous microstructure. Of those propagation models previously applied to cancellous bone, Biot's theory incorporates viscosity, but has only been applied in isotropic form, while Schoenberg's anisotropic model does not include viscosity. In this paper we present an approach that incorporates the merits of both models, by utilizing the tortuosity, a key parameter describing pore architecture. An angle-dependent tortuosity for a layered structure is used in Biot's theory to generate the "Stratified Biot Model" for cancellous bone, which is compared with published bone data. While the Stratified Biot model was inferior to Schoenberg's model for slow wave velocity prediction, the proposed model improved agreement fast wave velocity at high propagation angles, particularly when sorted for porosity. An attempt was made to improve the fast wave agreement at low angles by introducing an angle-dependent Young's Modulus, which, while improving the agreement of predicted fast wave velocity at low angles, degraded agreement at high angles. In this paper the utility of the tortuosity in characterizing the architecture of cancellous bone is highlighted.     

Application of a micro-Brillouin scattering technique to characterize bone in the GHz range

The evaluation of elastic properties of bone matrix has been investigated using several techniques such as nanoindentation and scanning acoustic microscopy (SAM). These techniques make use of good spatial resolution, which can prevent effects due to microstructures at the level of several hundreds of microns. In this paper, micro-Brillouin scattering (μ-BR) is introduced as another possible technique to characterize the elastic properties of bone. This technique is well known as a non-contact and non-destructive method to evaluate viscoelastic properties of transparent materials in the GHz range. Using thin, translucent bone specimens with thicknesses of around 100 μm, and the reflection induced optical geometry, ultrasonic wave velocities in the GHz range were obtained. Because this technique optically measures thermal phonons in the specimen, we can easily measure in-plane anisotropy of wave velocities by rotating the specimen. In a single trabecula, the site matched data between SAM and μ-BR showed good correlation, revealing the applicability of this technique to characterize material properties of bone. Some recent results on the anisotropy in a trabecula and the elasticity evaluation of newly and matured bones are also introduced.     

Ultrasonic measurement of the elastic properties of benzoyl glycine single crystals

Certain organic crystals are found to possess high non-linear optical coefficients, often one to two orders of magnitude higher than those of the well-known inorganic non-linear optical materials. Benzoyl glycine is one such crystal whose optical second-harmonic generation efficiency is much higher than that of potassium dihydrogen phosphate. Single crystals of benzoyl glycine are grown by solvent evaporation technique usingN, N-dimethyl formamide as the solvent. All the nine second-order elastic stiffness constants of this orthorhombic crystal are determined from ultrasonic wave velocity measurements employing the pulse echo overlap technique. The anisotropy of elastic wave propagation in this crystal is demonstrated by plotting the phase velocity, slowness, Young’s modulus and linear compressibility surfaces along symmetry planes. The volume compressibility, bulk modulus and relevant Poisson’s ratios are also determined. Variation of the diagonal elastic stiffness constants with temperature over a limited range are measured and reported.     

Two-wave behavior under various conditions of transition area from cancellous bone to cortical bone

The two-wave phenomenon, the wave separation of a single ultrasonic pulse in cancellous bone, is expected to be a useful tool for the diagnosis of osteoporosis. However, because actual bone has a complicated structure, precise studies on the effect of transition conditions between cortical and cancellous parts are required. This study investigated how the transition condition influenced the two-wave generation using three-dimensional X-ray CT images of an equine radius and a three-dimensional simulation technique. As a result, any changes in the boundary between cortical part and trabecular part, which gives the actual complex structure of bone, did not eliminate the generation of either the primary wave or the secondary wave at least in the condition of clear trabecular alignment. The results led us to the possibility of using the two-wave phenomenon in a diagnostic system for osteoporosis in cases of a complex boundary.     

Effects of wave propagation anisotropy on the wave focusing by negative refractive sonic crystal flat lenses

<正>In this study,wave propagation anisotropy in a triangular lattice crystal structure and its associated waveform shaping in a crystal structure are investigated theoretically.A directional variation in wave velocity inside a crystal structure is shown to cause bending wave envelcpes.The authors report that a triangular lattice sonic crystal possesses six numbers of a high symmetry direction,which leads to a wave convergence caused by wave velocity anisotropy inside the crystal.However,two of them are utilized mostly in wave focusing by an acoustic flat lens.Based on wave velocity anisotropy,the pseudo ideal imaging effect obtained in the second band of the flat lens is discussed.     

Acoustic inspection of bond strength of steel-reinforced mortar after exposure to elevated temperatures

In order to evaluate the bond strength between the reinforcement and concrete after fire damage, a combination of acoustic through-transmission and pull-out tests were used. Previous studies have shown a 25% decrease in the ultrasonic pulse velocity at 90% of the maximum load at room temperature. The specimens were kept in the oven at an elevated temperature for 1, 2, or 3 h. They were then removed and cooled to room temperature. Inspection was conducted using a high-power ultrasonic pulse velocity system while a pull-out load was applied. The correlation between preheated temperature, acoustic wave velocity, and the applied load was analyzed. Initial results show that bond strength and pulse velocity decreased substantially as the temperature or the heating time increased.     

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.     

A STUDY ON THE ULTRASONIC VELOCITY AND ATTENU-ATION IN NdFeB MAGNET WITHIN THE TEMPERATURE RANGE OF 80-300K(Ⅰ)

The ultrasonic velocity V and attenuation A of both longitudinal and shear waves in an anisotropic NdFeB magnet were measured over the temperature range from 80K to 300 K by the pulse echo method. The anisotropy of the ultrasonic wave propagating in a NdFeB magnet was observed. Anomalous changes in both V-T and A-T curves in the temperature range of 110-160 K were found, which might be due to the spin reorientation phase transition of Nd2Fe14B.