Effects Of Frequency-dependent Attenuation Research Articles

Effect of Frequency-Dependent Attenuation on Predicted Histotripsy Waveforms in Tissue-Mimicking Phantoms

Tissue-mimicking phantoms are employed for the assessment of shocked histotripsy pulses in vitro. These broadband shock waves are critical for tissue ablation and are influenced by the frequency-dependent attenuation of the medium. The density, sound speed and attenuation spectra (2–25 MHz) were measured for phantoms that mimic key histotripsy targets. The influence of non-linear propagation relative to the attenuation was described in terms of Gol'dberg number. An expression was derived to estimate the bandwidth of shocked histotripsy pulses for power law-dependent attenuation. The expression is independent of the fundamental frequency of the histotripsy pulse for linear frequency-dependent attenuation.

Epistemic uncertainty and limitations of theκ0model for near-surface attenuation at hard rock sites

The determination of near-surface attenuation for hard rock sites is an important issue in a wide range of seismological applications, particularly seismic hazard analysis. In this article we choose six hard to very-hard rock sites (Vs30 1030–3000ms–1) and apply a range of analysis methods to measure the observed attenuation at distance based on a simple exponential decay model with whole-path attenuation operator κr. The κr values are subsequently decoupled from path attenuation (Q) so as to obtain estimates of near-surface attenuation (κ0). Five methods are employed to measure κr which can be split into two groups: broad-band methods and high-frequency methods. Each of the applied methods has advantages and disadvantages, which are explored and discussed through the comparison of results from common data sets. In our first step we examine the variability of the individual measured κr values. Some variation between methods is expected due to simplifications of source, path, and site effects. However, we find that significant differences arise between attenuation measured on individual recordings, depending on the method employed or the modelling decisions made during a particular approach. Some of the differences can be explained through site amplification effects: although usually weak at rock sites, amplification may still lead to bias of themeasured κr due to the chosen fitting frequency bandwidth, which often varies between methods. At some sites the observed high-frequency spectral shape was clearly different to the typical κr attenuation model, with curved or bi-linear rather than linear decay at high frequencies. In addition to amplification effects this could be related to frequency-dependent attenuation effects [e.g. Q( f )]: since the κr model is implicitly frequency independent, κr will in this case be dependent on the selected analysis bandwidth. In our second step, using thewhole-path κr data sets from the five approaches, we investigate the robustness of the near-surface attenuation parameter κ0 and the influence of constraints, such as assuming a value for the regional crustal attenuation (Q).We do this by using a variety of fitting methods: least squares, absolute amplitude and regressions with and without fixing Q to an a priori value. We find that the value to which we fix Q strongly influences the near-surface attenuation term κ0. Differences in Q derived from the data at the six sites under investigation could not be reconciled with the average values found previously over the wider Swiss region. This led to starkly different κ0 values, depending on whether we allowed for a data-driven Q, or whether we forced Q to be consistent with existing simulation models or ground motion prediction equations valid for the wider region. Considering all the possible approaches we found that the contribution to epistemic uncertainty for κ0 determination at the six hard-rock sites in Switzerland could be represented by a normal distribution with standard deviation σκ0 = 0.0083 ± 0.0014 s.

Acoustic Nonlinearity of Surface Wave in a Fatigued Aluminum Alloy Specimen

This paper reports a case study for the evaluation of surface fatigue damage by using the acoustic nonlinearity of surface waves. A measurement system using contact angle beam transducers was constructed to measure the acoustic nonlinearity of surface waves based on the harmonic measurement. In order to prove the general properties of acoustic nonlinearity, dependencies of the second harmonic amplitude on the fundamental frequency amplitude and the propagation distance were tested first, where the effect of frequency-dependent attenuation was compensated for. The results showed good agreement with the theoretical expectations. Next, an aluminum 6061 T6 specimen, of which the surface was damaged by a three-point bending fatigue test, was experimented on and magnitudes of nonlinear parameter, measured before and after the fatigue test, were compared. We could see a clear increase in the nonlinear parameter after the fatigue test at the central position of the specimen, where the surface fatigue damage was expected to be concentrated. [doi:10.2320/matertrans.I-M2011846]

A numerical comparison of the Westervelt equation with viscous attenuation and a causal propagation operator

The Westervelt wave equation can be used to describe non-linear propagation of finite amplitude sound. If one assumes that the medium can be treated as a thermoviscous fluid, a loss mechanism can be incorporated, but such a loss mechanism is not adequate if the medium is dispersive. In order to accurately describe pulse propagation in a dispersive medium the Westervelt equation must incorporate attenuation and dispersion correctly. Szabo has shown that the effects of frequency dependent attenuation and dispersion can be included by the use of a causal time-domain propagation factor (TDPF) which is obtained from a corresponding time domain convolution operator. In previous work the TDPF has been successfully employed in the linear wave equation for both isotropic and non-isotropic media, and the authors recently carried out a comparison of numerical solutions, in one dimension, to the Westervelt equation using the TDPF with those obtained using a traditional loss mechanism for a themoviscous fluid. These computations showed that the TDPF correctly incorporated the full dispersive characteristics of the media, and that the results may differ significantly from those obtained using the traditional loss term. In this work the problem of propagation of ultrasonic acoustic energy through human tissue in two dimensions is solved numerically using the Westervelt equation with the TDPF, and comparisons are made with computations treating the human tissue as a thermoviscous fluid. The equations are solved using the method of finite differences.

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.

Simulation of ultrasound two-dimensional array transducers using a frequency domain model

Ultrasound imaging with two-dimensional (2D) arrays has garnered broad interest from scanner manufacturers and researchers for real time three-dimensional (3D) applications. Previously the authors described a frequency domain B-mode imaging model applicable for linear and phased array transducers. In this paper, the authors extend this model to incorporate 2D array transducers. Further approximations can be made based on the fact that the dimensions of the 2D array element are small. The model is compared with the widely used ultrasound simulation program FIELD II, which utilizes an approximate form of the time domain impulse response function. In a typical application, errors in simulated RF waveforms are less than 4% regardless of the steering angle for distances greater than 2 cm, yet computation times are on the order of 1/35 of those incurred using FIELD II. The 2D model takes into account the effects of frequency-dependent attenuation, backscattering, and dispersion. Modern beam-forming techniques such as apodization, dynamic aperture, dynamic receive focusing, and 3D beam steering can also be simulated.

Partial Discharge Pulse Propagation in Shielded Power Cable and Implications for Detection Sensitivity

Boggs and Stone (1982) defined the fundamental limits to the electrical detection of corona and partial discharge (PD), i.e., wideband detection of a PD-induced pulse in the presence of thermal noise. This paper treated the effect of frequency-dependent attenuation in shielded power cable in that context. However, most of the plots in that paper were the result of numerical computations. In the same year, Stone and Boggs set out a theory for high-frequency attenuation of shielded power cable. They showed good agreement between attenuation predicted from measured material properties and measured, high-frequency attenuation of shielded power cable. Since 1982, measurements of high-frequency cable attenuation have been reported by a number of authors for a variety of cables. In addition, software tools have become available that facilitate an analytic solution for the parameters of interest. This article summarizes the theory for PD propagation in shielded power cable for both symmetric (Gaussian) and asymmetric PD-pulse waveforms, based on the assumption that the attenuation constant (dB/m or Nepers/m) of the cable is proportional to frequency. This appears to be the most complete possible analytic exposition of PD attenuation in shielded-power cable, which has obvious applications to field PD measurements of such cable.

The dependence of time-domain speed-of-sound measurements on center frequency, bandwidth, and transit-time marker in human calcaneusin vitro

Time-domain speed-of-sound (SOS) measurements in calcaneus are effective predictors of osteoporotic fracture risk. High attenuation and dispersion in bone, however, produce severe distortion of transmitted pulses that leads to ambiguity of time-domain SOS measurements. An equation to predict the effects of system parameters (center frequency and bandwidth), algorithm parameters (pulse arrival-time marker), and bone properties (attenuation coefficient and thickness) on time-domain SOS estimates is derived for media with attenuation that varies linearly with frequency. The equation is validated using data from a bone-mimicking phantom and from 30 human calcaneus samples in vitro. The data suggest that the effects of dispersion are small compared with the effects of frequency-dependent attenuation. The equation can be used to retroactively compensate data. System-related variations in SOS are shown to decrease as the pulse-arrival-time marker is moved toward the pulse center. Therefore, compared with other time-domain measures of SOS, group velocity exhibits the minimum system dependence.

Effects of frequency-dependent attenuation and velocity dispersion on in vitro ultrasound velocity measurements in intact human femur specimens

Numerous studies have shown that ultrasonic velocity measured in bone provides a good assessment of osteoporotic fracture risk. However, a lack of standardization of signal processing techniques used to compute the speed of sound (SOS) complicates the comparison between data obtained with different commercial devices. In this study, 38 intact femurs were tested using a through-transmission technique and SOS determined using different techniques. The resulting difference in measured SOS was determined as functions of the attenuation and the velocity dispersion. A numerical simulation was used to explain how attenuation and dispersion impact two different SOS measurements (group velocity, velocity based on the first zero crossing of the signal). A new method aimed at compensating for attenuation was devised and led to a significant reduction in the difference between SOS obtained with both signal processing techniques. A comparison between SOS and X-ray density measurements indicated that the best correlation was reached for SOS based on the first zero crossing apparently because it used a marker located in the early part of the signal and was less sensitive to multipath interference. The conclusion is that first zero crossing velocity may be preferred to group velocity for ultrasonic assessment at this potential fracture site.

Full wave modeling of therapeutic ultrasound: Efficient time-domain implementation of the frequency power-law attenuation

For the simulation of therapeutic ultrasound applications, a method including frequency-dependent attenuation effects directly in the time domain is highly desirable. This paper describes an efficient numerical time-domain implementation of the power-law attenuation model presented by Szabo [Szabo, J. Acoust. Soc. Am. 96, 491-500 (1994)]. Simulations of therapeutic ultrasound applications are feasible in conjunction with a previously presented finite differences time-domain (FDTD) algorithm for nonlinear ultrasound propagation [Ginter et al., J. Acoust. Soc. Am. 111, 2049-2059 (2002)]. Szabo implemented the empirical frequency power-law attenuation using a causal convolutional operator directly in the time-domain equation. Though a variety of time-domain models has been published in recent years, no efficient numerical implementation has been presented so far for frequency power-law attenuation models. Solving a convolutional integral with standard time-domain techniques requires enormous computational effort and therefore often limits the application of such models to 1D problems. In contrast, the presented method is based on a recursive algorithm and requires only three time levels and a few auxiliary data to approximate the convolutional integral with high accuracy. The simulation results are validated by comparison with analytical solutions and measurements.

A numerical method to predict the effects of frequency-dependent attenuation and dispersion on speed of sound estimates in cancellous bone.

Many studies have demonstrated that time-domain speed-of-sound (SOS) measurements in calcaneus are predictive of osteoporotic fracture risk. However, there is a lack of standardization for this measurement. Consequently, different investigators using different measurement systems and analysis algorithms obtain disparate quantitative values for calcaneal SOS, impairing and often precluding meaningful comparison and/or pooling of measurements. A numerical method has been developed to model the effects of frequency-dependent attenuation and dispersion on transit-time-based SOS estimates. The numerical technique is based on a previously developed linear system analytic model for Gaussian pulses propagating through linearly attenuating, weakly dispersive media. The numerical approach is somewhat more general in that it can be used to predict the effects of arbitrary pulse shapes and dispersion relationships. The numerical technique, however, utilizes several additional assumptions (compared with the analytic model) which would be required for the practical task of correcting existing clinical databases. These include a single dispersion relationship for all calcaneus samples, a simple linear model relating phase velocity to broadband ultrasonic attenuation, and a constant calcaneal thickness. Measurements on a polycarbonate plate and 30 human calcaneus samples were in good quantitative agreement with numerical predictions. In addition, the numerical approach predicts that in cancellous bone, frequency-dependent attenuation tends to be a greater contributor to variations in transit-time-based SOS estimates than dispersion. This approach may be used to adjust previously acquired individual measurements so that SOS data recorded with different devices using different algorithms may be compared in a meaningful fashion.

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.

A frequency domain model for generating B-mode images with array transducers

A frequency domain B-mode imaging model applicable to linear and phased array transducers was developed for simulating ultrasound images of random media. Computations are based on an approximation that is less restrictive than the Fresnel approximation. The model is compared with the exact time domain impulse response method, regarded as the "gold standard". In a typical application, errors in simulated rf waveforms are less than 1% regardless of the steering angle for distances greater than 2 cm, yet computation times are on the order of 1/150 of those using the exact method. This model takes into account the effects of frequency-dependent attenuation, backscattering, and dispersion. Modern beam-forming techniques such as apodization, dynamic aperture, elevational focusing, multiple transmit focusing and dynamic receiving focusing also can be simulated.

Responses of captive African elephants to playback of low-frequency calls

We conducted a series of playback trials with captive African elephants to identify behaviors that might indicate perception of calls by conspecifics. Our findings were as follows. (i) The elephants responded clearly to playbacks of prerecorded low-frequency elephant calls. Responses included, in rough sequence, lifting and stiffening of ears, vocalization, walking or running towards the concealed speaker, clustering in a tight group, and remaining motionless ("freezing"), with occasional scanning movements of the head. The occurrence of each of these behaviors increased substantially immediately after the playbacks. (ii) Elephants responded both to full-bandwidth playbacks and to playbacks of calls in which most of the energy above 25 Hz was filtered out, simulating the effect of frequency-dependent attenuation over distance. (iii) Elephants did not respond to a pure-tone control stimulus similar in frequency and intensity to the filtered elephant calls. Thus, the observed responses to elephant calls were not merely responses to an unexpected stimulus, but probably indicate recognition of a biologically meaningful signal.

Kirchhoff-Helmholtz reflection seismograms in a laterally inhomogeneous multi-layered elastic medium - II. Computations

Summary. In a medium consisting of elastic layers with irregular interfaces, Kirchhoff-Helmholtz (KH) theory can be extended to synthesize the motion due to various generalized rays. An exact elastic form of the KH integral is first derived, then various asymptotic approximations are used to convert this integral into one which can be rapidly evaluated to give the motion of a single generalized ray. The approximations used are those of geometrical optics, for propagation across layers, and the Kirchhoff or tangent-plane approximation for propagation across boundaries. It is shown how the KH method leads naturally to a generalization of our usual notion of elastic reflection and transmission coefficients. The new coefficients are functions of both angle of incidence and angle of reflection or transmission and they are derived so as to obtain coordinate-free formulae that show clearly their relation to the conventional Snell’s law coefficients. The elastic KH method is applied first to the problem of a single interface, where its performance is compared to that of the Gaussian beam and Maslov methods. (For synthesizing reflections from irregular interfaces the KH method is superior because it includes signals diffracted from corners. However, when the interface is very smooth on the scale of a wavelength the Maslov and Gaussian beam methods are superior because they do not break down when there is a caustic on the reflector.) KH theory is then applied to a multilayered elastic medium and it is shown how the effects of frequency-dependent attenuation and dispersion can be incorporated into the theory by taking advantage of the approximately logarithmic variation of slowness with frequency in most earth materials. The limitations of the KH theory are discussed and some recent attempts to overcome these difficulties are reviewed. A new method for overcoming the problem of a caustic on the reflector becomes apparent when the KH integral is regarded as a member of a larger family of equivalent 1-fold integrals all of which are derivable from the same multifold path integral. Refracted or diving rays can be treated within the same formalism with equal benefit. For velocity models that are independent of one spatial direction (strike) a method is given for approximately converting 2-D results into 3-D results.

Kirchhoff?Helmholtz reflection seismograms in a laterally inhomogeneous multi-layered elastic medium ? I. Theory

Summary. In a medium consisting of elastic layers with irregular interfaces, Kirchhoff-Helmholtz (KH) theory can be extended to synthesize the motion due to various generalized rays. An exact elastic form of the KH integral is first derived, then various asymptotic approximations are used to convert this integral into one which can be rapidly evaluated to give the motion of a single generalized ray. The approximations used are those of geometrical optics, for propagation across layers, and the Kirchhoff or tangent-plane approximation for propagation across boundaries. It is shown how the KH method leads naturally to a generalization of our usual notion of elastic reflection and transmission coefficients. The new coefficients are functions of both angle of incidence and angle of reflection or transmission and they are derived so as to obtain coordinate-free formulae that show clearly their relation to the conventional Snell’s law coefficients. The elastic KH method is applied first to the problem of a single interface, where its performance is compared to that of the Gaussian beam and Maslov methods. (For synthesizing reflections from irregular interfaces the KH method is superior because it includes signals diffracted from corners. However, when the interface is very smooth on the scale of a wavelength the Maslov and Gaussian beam methods are superior because they do not break down when there is a caustic on the reflector.) KH theory is then applied to a multilayered elastic medium and it is shown how the effects of frequency-dependent attenuation and dispersion can be incorporated into the theory by taking advantage of the approximately logarithmic variation of slowness with frequency in most earth materials. The limitations of the KH theory are discussed and some recent attempts to overcome these difficulties are reviewed. A new method for overcoming the problem of a caustic on the reflector becomes apparent when the KH integral is regarded as a member of a larger family of equivalent 1-fold integrals all of which are derivable from the same multifold path integral. Refracted or diving rays can be treated within the same formalism with equal benefit. For velocity models that are independent of one spatial direction (strike) a method is given for approximately converting 2-D results into 3-D results.

A Coaxial Cable Delay System for a Synthesis Radio Telescope

A switchable coaxial cable delay system for path compensation in a synthesis radio telescope operates over the frequency band 15-45 MHz. The requirements of continuum and spectral line observations determine the system specifications. Diode switches include or exclude cables whose lengths form a binary sequence from 0.625 to 320 m. Cables are equalized to compensate for the effects of frequency dependent attenuation and of dispersion. A simple technique for dispersion equalization is described.

The effects of frequency-dependent attenuation and noise on the improvement of ultrasonic echo resolution using a deconvolution technique: T. Mochizuki, T. Itoh, and C. Kasai, Research Institute, Aloka Co., Ltd., 6-22-1, Mure, Mitaka, Tokyo 181, Japan

The effects of frequency-dependent attenuation and noise on the improvement of ultrasonic echo resolution using a deconvolution technique: T. Mochizuki, T. Itoh, and C. Kasai, Research Institute, Aloka Co., Ltd., 6-22-1, Mure, Mitaka, Tokyo 181, Japan

Fundamental Limitations in the Measurement of Corona and Partial Discharge

The theoretical sensitivity of conventional partial discharge detectors is compared with that obtained from ultra wideband (UWB) (up to l GHz) detection systems. The comparison indicates that for relatively lossfree distributed systems, such as SF6 insulated bus, the UWB system is up to two orders of magnitude more sensitive. UWB detection also embodies additional advantages such as facilitating the location of discharge sites and the rejection of external electrical noise. For discharge detection in plastic-insulated cables, true UWB detection is not practical because of frequency-dependent attenuation effects, although certain gains in sensitivity can be achieved with a detector bandwidth of up to 10 MHz.

The effect of electrical gradients on current fluctuations and impedance recorded from Necturus gallbladder.

Transepithelial current fluctuations were recorded inNecturus gallbladder, clamped at negative as well as positive potentials up to 64 mV. With NaCl-Ringer's (+10mm TAP) on both sides a mucosa-negative potential enhanced the relaxation noise component, present at zero potential, and produced peaking in the power spectrum at potentials above −36mV. Concomitantly at these potentials an inductive as well as a capacitive low-frequency feature appeared in the impedance locus. Clamping at positive potentials of 18 mV suppressed the relaxation noise component. At potentials above 51mV the spectral values increased predominantly at low frequencies. In this case the power spectrum showed only a 1/fα noise component. The experiments confirm the previous finding that a K+ efflux through fluctuating apical K+ channels exists under normal conditions. With serosal KCl-Ringer's the initial Lorentzian component was enhanced at negative but suppressed at positive potentials. The increase at negative potentials was less pronounced than in experiments with NaCl-Ringer's on both sides, indicating saturation of the fluctuating K+ current component. With mucosal KCl-Ringer's a negative potential depressed the initial relaxation noise component, whereas it was enhanced at +18 mV clamp potential. In the latter case an additional Lorentzian component became apparent at higher frequencies. At potentials of 36 mV and above the low-frequency Lorentzian disappeared whereas the corner frequency of the high-frequency component increased. The latter experiments demonstrate that the relaxation noise component inNecturus gallbladder consists of two superimposed Lorentzians. As the relaxation times of these two components behave differently under an electrical field, there may exist two different types of K+ channels. It is demonstrated that peaking in the plateau of power spectra can be explained by frequency-dependent attenuation effects, caused by a polarization impedance.