The effects of frequency-dependent attenuation and dispersion on sound speed measurements: applications in human trabecular bone

Sound speed may be measured by comparing the transit time of a broadband ultrasonic pulse transmitted through an object with that transmitted through a reference water path. If the speed of sound in water and the thickness of the sample are known, the speed of sound in the object may be computed. To measure the transit time differential, a marker such as a zero-crossing, may be used. A sound speed difference between the object and water shifts all markers backward or forward. Frequency-dependent attenuation and dispersion may alter the spectral characteristics of the waveform, thereby distorting the locations of markers and introducing variations in sound-speed estimates. Theory is derived to correct for this distortion for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The theory is validated using numerical analysis, measurements on a tissue mimicking phantom, and on 24 human calcaneus samples in vitro. Variations in soft tissue-like media are generally not exceptionally large for most applications but can be substantial, particularly for high bandwidth pulses propagating through media with high attenuation coefficients. At 500 kHz, variations in velocity estimates in bone can be very substantial, on the order of 40 to 50 m/s because of the high attenuation coefficient of bone. In trabecular bone, the effects of frequency-dependent attenuation are considerable, and the effects of dispersion are negligible.     

Relative measurements of the velocity and attenuation of ultrasound in highly absorbing liquids

It is shown that it is possible to use a continuous sinusoidal signal to make relative measurements of the velocity and absorption coefficient of ultrasound in highly absorbing liquids such as liquid crystals. Compared with the traditional variable-frequency pulse-phase method, the technique described has the advantage of giving a direct reading of the results under dynamic measurement conditions. A block diagram and the characteristics of the equipment for measuring the anisotropy of acoustic parameters by both pulse and continuous methods are presented.Translated from Izmeritel'naya Tekhnika, No. 1, pp. 66–67, January, 1995.     

A device for in vivo measurements of quantitative ultrasound variables at the human proximal femur

Quantitative ultrasound (QUS) at the calcaneus has similar power as a bone mineral density (BMD)- measurement using DXA for the prediction of osteoporotic fracture risk. Ultrasound equipment is less expensive than DXA and free of ionizing radiation. As a mechanical wave, QUS has the potential of measuring different bone properties than dual X-ray absorptiometry (DXA,) which depends on X-ray attenuation and might be developed into a tool of comprehensive assessment of bone strength. However, site- specific DXA at the proximal femur shows best performance in the prediction of hip fractures. To combine the potential of QUS with measurements directly at the femur, we developed a device for in vivo QUS measurements at this site. Methods comprise ultrasound transmission through the bone, reflection from the bone surface, and backscat- ter from the inner trabecular structure. The complete area of the proximal femur can be scanned except at the femoral head, which interferes with the ilium. To avoid edge artifacts, a subregion of the proximal femur in the trochanteric region was selected as measurement region. First, in vivo measurements demonstrate a good signal to noise ratio and proper depiction of the proximal femur on an attenuation image. Our results demonstrate the feasibility of in vivo measurements. Further improvements can be expected by refinement of the scanning technique and data evaluation method to enhance the potential of the new method for the estimation of bone strength.     

Sound velocity and sound attenuation measurements by dynamic light scattering

Dynamic light scattering (photon correlation spectroscopy) has been applied to the determination of sound velocity and sound attenuation from the Brillouin component of the frequency spectrum scattered from a fluid sample transversed by a laser beam. In this paper the time-resolved determination of the Brillouin component is described. The measurement of the linewidth allows an accurate determination of the sound attenuation, while the central frequency is connected to the adiabatic sound velocity. Sound attenuation and sound velocity measurements are presented for the new refrigerant pentafluorethane (R125). The accuracy and possible systematic errors of this technique are discussed and compared to those obtained from other spectroscopic and acoustic techniques.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado. U.S.A.     

Ultrasonic velocity and attenuation measurements at the metamagnetic transition in UPt3

The longitudinal ultrasonic attenuation and velocity were measured on a single crystal of UPt₃ in a high magnetic field of up to 23T. Earlier ultrasonic measurements had seen a softening of the lattice as evidenced by a huge drop in the velocity at a field of 20T. Both the attenuation and velocity have been measured in field sweeps. Accompanying the large dip in the velocity is a large attenuation peak at this metamagnetic transition. Measurements were also done at several frequencies.     

Wavelength-dependent measurements of optical-fiber transit time, material dispersion, and attenuation

A new, to our knowledge, method for measuring the wavelength dependence of the transit time, material dispersion, and attenuation of an optical fiber is described. We inject light from a 4-ns rise-time pulsed broadband flash lamp into fibers of various lengths and record the transmitted signals with a time-resolved spectrograph. Segments of data spanning a range of approximately 3000 A are recorded from a single flash-lamp pulse. Comparison of data acquired with short and long fibers enables the determination of the transit time and the material dispersion as functions of wavelength dependence for the entire recorded spectrum simultaneously. The wavelength-dependent attenuation is also determined from the signal intensities. The method is demonstrated with experiments using a step-index 200-mum-diameter SiO(2) fiber. The results agree with the transit time determined from the bulk glass refractive index to within ?0.035% for the visible (4000-7200-A) spectrum and 0.12% for the UV (2650-4000-A) spectrum and with the attenuation specified by the fiber manufacturer to within ?10%.     

Magnetic field dependence of ultrasound attenuation and sound velocity in superfluid3He-A

In the presence of a magnetic field the gap amplitude of the axial state is found to split atall temperatures if particle-hole asymmetry is taken into account. The relative gap splitting is of the order of the relative splitting of the transition temperature and leads to splittings of the frequencies of the clapping and flapping modes. The ultrasonic attenuation and sound velocity are calculated for different sound frequencies, fields, and orientations of the wave vectorq with respect to the axisl of the energy gap. The predicted splittings of the clapping and flapping mode peaks and of the cusp in the attenuation and of the step in the sound velocity at=2₀(T) should become observable at sufficiently high fields. The results are discussed in connection with ultrasonic impedance, attenuation, and velocity measurements in the A₂ and A₁ phases.     

The effect of phase cancellation on estimates of broadband ultrasound attenuation and backscatter coefficient in human calcaneus in vitro

Broadband ultrasound attenuation (BUA) is a clinically proven indicator of osteoporotic fracture risk. BUA measurements are typically performed in through- transmission with single-element phase sensitive (PS) receivers and therefore can be compromised by phase cancellation artifact. Phase-insensitive (PI) receivers suppress phase cancellation artifact. To study the effect of phase cancellation on BUA measurements, through-transmission measurements were performed on 16 human calcaneus samples in vitro using a two-dimensional receiver array that enabled PS and PI BUA estimation. The means plus or minus standard deviations for BUA measurements were 22.1 plusmn 15.8 dB/MHz (PS) and 17.6 plusmn 7.2 dB/MHz (PI), suggesting that, on the average, approximately 20% of PS BUA values in vitro can be attributed to phase cancellation artifact. Therefore, although cortical plates are often regarded as the primary source of phase cancellation artifact, the heterogeneity of cancellous bone in the calcaneal interior may also be a significant source. Backscatter coefficient estimates in human calcaneus that are based on PS attenuation compensation overestimate 1) average magnitude of backscatter coefficient at 500 kHz by a factor of about 1.6 plusmn 0.3 and 2) average exponent (n) of frequency dependence by about 0.34 plusmn 0.12 (where backscatter coefficient is fit to a power law form proportional to frequency to the nth power).     

The effect of frequency-dependent attenuation and the frequency characteristic of the converters on the error of measurements in ultrasonic flaw detection

The error in measuring the distance to a defect, due to white noise, is estimated. Distortions of the signal spectrum due to frequency-dependent attenuation of ultrasound and the nonuniformity of the frequency characteristics of the converters are taken into account. Translated from Izmeritel'naya Tekhnika, No. 11, pp. 64–66, November, 2008.     

A Gaussian framework for modeling effects of frequency-dependent attenuation,frequency-dependent scattering,and gating

For a wide range of applications in medical ultrasound, power spectra of received signals are approximately Gaussian. It has been established previously that an ultrasound beam with a Gaussian spectrum propagating through a medium with linear attenuation remains Gaussian. In this paper, Gaussian transformations are derived to model the effects of scattering (according to a power law, as is commonly applicable in soft tissues, especially over limited frequency ranges) and gating (with a Hamming window, a commonly used gate function). These approximations are shown to be quite accurate even for relatively broad band systems with fractional bandwidths approaching 100%. The theory is validated by experiments in phantoms consisting of glass particles suspended in agar.     

Singular spectrum analysis applied to backscattered ultrasound signals from in vitro human cancellous bone specimens

Mean scatterer spacing (MSS) holds particular promise for the detection of changes in quasiperiodic tissue microstructures such as may occur during development of disease in the liver, spleen, or bones. Many techniques that may be applied for MSS estimation (temporal and spectral autocorrelation, power spectrum and cepstrum, higher order statistics, and quadratic transformation) characterize signals that contain a mixture of periodic and nonperiodic contributions. In contrast, singular spectrum analysis (SSA), a method usually applied in nonlinear dynamics, first identifies components of signals corresponding to periodic structures and, second, identifies dominant periodicity. Thus, SSA may better separate periodic structures from nonperiodic structures and noise. Using an ultrasound echo simulation model, we previously demonstrated SSA's potential to identify MSS of structures in quasiperiodic scattering media. The current work aims to observe the behavior of MSS estimation by SSA using ultrasound measurements in phantom materials (two parallel, nylon-line phantoms and four foam phantoms of different densities). The SSA was able to estimate not only the nylon-line distances but also nylon-line thickness. The method also was sensitive to the average pore-size differences of the four sponges. The algorithms then were applied to characterize human cancellous bone microarchitectures. Using 1-MHz center-frequency, radio-frequency ultrasound signals, MSS was measured in 24 in vitro bone samples and ranged from 1.0 to 1.7 mm. The SSA MSS estimates correlate significantly to MSS measured independently from synchrotron microtomography, r2 = 0.68. Thus, application of SSA to backscattered ultrasound signals seems to be useful for providing information linked to tissue microarchitecture that is not evident from clinical images.     

Compressibility of nano inclusions in complex fluids by ultrasound velocity measurements

We present a high precision ultrasonic velocimeter for a small volume sample (1 cm/sup 3/) for a path length of 1 cm achieved. The method used is based on the time of flight measurement with an original signal processing technique: the barycenter method. With our system, we have measured the sound velocity with an accuracy of 10/sup -5/. The detection of a difference in velocity between two liquids of about 2 cm/s is achieved. The compressibility of the reference liquid can then be deduced with an accuracy better than 0.2%. Using this custom-made system, we have studied and characterized complex fluids, systems biomimetic of biological membranes, as well as proteins included in nanometric water droplets. Under these experimental conditions, we have reached the value of protein compressibilities with an accuracy better than 10%.     

The effect of frequency dependent scattering and attenuation on the estimation of blood velocity using ultrasound

A comprehensive theoretical performance comparison of the wideband maximum-likelihood (WMLE) and cross-correlation strategies, previously proposed and evaluated for the estimation of blood velocity using ultrasound is presented. It is based on evaluation of the bias, local and global accuracy, and signal-to-noise ratio (SNR) performance. The results show that the intervening medium does not bias either wideband estimation, due to the effect of tracking the scattering target. The presence of intervening tissue actually improves the global accuracy of both wideband estimators, without a significant change in the local accuracy of either wideband estimator. After the transmission of P pulses, a comparison of the performance of the two strategies shows that the cross-correlation estimator requires P(2 ) correlations to achieve performance similar to that of the WMLE with P operations. In addition, the WMLE can increase the effective SNR in comparison with cross correlation.     

Characterization of solutionizing behavior in VT14 titanium alloy using ultrasonic velocity and attenuation measurements

VT14 titanium alloy (Ti–4.5Al–3Mo–1V) was subjected to a series of heat treatments consisting of solutionizing for 1 h at the selected temperatures in range of 923–1323 K at an interval of 50 K, followed by water quenching. Hardness and optical microscopy results are correlated with ultrasonic longitudinal and shear wave velocities and attenuation in these specimens. Ultrasonic velocities and hardness decrease with solution annealing temperature (SAT) in the 923–1123 K range. Beyond 1123 up to 1223 K, they increase slightly. Beyond 1223 K, ultrasonic velocities become constant, whereas hardness increases up to 1323 K. Ultrasonic attenuation exhibits an opposite behavior to velocity and hardness. Further, for the first time, authors have shown that ultrasonic velocity can be used to identify the β-transus temperature in this alloy. Because of non-monotonous variation of velocity and attenuation with solutionizing temperature, it was not possible to identify the SAT using any one of these parameters. Hence, a new parameter, ratio of normalized differential of ultrasonic attenuation to normalized differential of ultrasonic velocity (RNDAV) has been used, which is found to increase monotonously with SAT and hence enabling unambiguous characterization of SAT in solution annealed VT14 alloy.     

Ultrasonic velocity and attenuation in glass

Ultrasonic velocity and attenuation in glasses exhibit anomalous properties and the current theory most successful in explaining these anomalous properties in the high temperature range has been presented. The model considers that the disorder inherent in amorphous network results in a double well potential corresponding to two equilibrium configurations and a particle is ascribed to move in the double-well potential. Acoustic behaviours in glasses have been interpreted in terms of a thermally activated relaxation process. Improvement of this basic model has also been discussed. Mention has also been made of some behaviours at high temperature that need further research for convincing explanation.     

Wave dispersion and attenuation in fiber composites

 This work deals with the dispersion and attenuation of elastic plane waves propagating in a single layer fiber reinforced composite, in a direction which is perpendicular to the fibers. An iterative effective medium model, based on single scattering considerations, for the quantitative estimation of wave dispersion and attenuation is proposed. The single scattering problem is solved numerically by means of a 2-D boundary element methodology. Numerical results concerning the plane velocity and the attenuation coefficient of longitudinal or transverse SH, SV waves propagating in two types of fiber reinforced composite materials, are presented. The obtained results are compared to those taken either experimentaly or numericaly by other investigators.