A theoretical comparison of attenuation measurement techniques from backscattered ultrasound echoes

Accurate characterization of tissue pathologies using ultrasonic attenuation is strongly dependent on the accuracy of the algorithm that is used to obtain the attenuation coefficient estimates. In this paper, computer simulations were used to compare the accuracy and the precision of the three methods that are commonly used to estimate the local ultrasonic attenuation within a region of interest (ROI) in tissue; namely, the spectral log difference method, the spectral difference method, and the hybrid method. The effects of the inhomgeneities within the ROI on the accuracy of the three algorithms were studied, and the optimal ROI size (the number of independent echoes laterally and the number of pulse lengths axially) was quantified for each method. The three algorithms were tested for when the ROI was homogeneous, the ROI had variations in scatterer number density, and the ROI had variations in effective scatterer size. The results showed that when the ROI was homogeneous, the spectral difference method had the highest accuracy and precision followed by the spectral log difference method and the hybrid method, respectively. Also, when the scatterer number density varied, the spectral difference method completely failed, while the log difference method and hybrid method still gave good results. Lastly, when the scatterer size varied, all of the methods failed.     

Ultrasound attenuation estimation using backscattered echoes from multiple sources

The objective of this study was to devise an algorithm that can accurately estimate the attenuation along the propagation path (i.e., the total attenuation) from backscattered echoes. It was shown that the downshift in the center frequency of the backscattered ultrasound echoes compared to echoes obtained in a water bath was calculated to have the form Deltaf=mf(o)+b after normalizing with respect to the source bandwidth where m depends on the correlation length, b depends on the total attenuation, and f(o) is the center frequency of the source as measured from a reference echo. Therefore, the total attenuation can be determined independent of the scatterer correlation length by measuring the downshift in center frequency from multiple sources (i.e., different f(o)) and fitting a line to the measured shifts versus f(o). The intercept of the line gives the total attenuation along the propagation path. The calculations were verified using computer simulations of five spherically focused sources with 50% bandwidths and center frequencies of 6, 8, 10, 12, and 14 MHz. The simulated tissue had Gaussian scattering structures with effective radii of 25 mum placed at a density of 250 mm(3). The attenuation of the tissue was varied from 0.1 to 0.9 dB / cm-MHz. The error in the attenuation along the propagation path ranged from -3.5+/-14.7% for a tissue attenuation of 0.1 dB / cm-MHz to -7.0+/-3.1% for a tissue attenuation of 0.9 dB / cm-MHz demonstrating that the attenuation along the propagation path could be accurately determined using backscattered echoes from multiple sources using the derived algorithm.     

A model for estimating ultrasound attenuation along the propagation path to the fetus from backscattered waveforms

Accurate estimates of the ultrasound pressure and/or intensity incident on the developing fetus on a patient-specific basis could improve the diagnostic potential of medical ultrasound by allowing the clinician to increase the transmit power while still avoiding the potential for harmful bioeffects. Neglecting nonlinear effects, the pressure/intensity can be estimated if an accurate estimate of the attenuation along the propagation path (i.e., total attenuation) can be obtained. Herein, a method for determining the total attenuation from the backscattered power spectrum from the developing fetus is proposed. The boundaries between amnion and either the fetus' skull or soft tissue are each modeled as planar impedance boundaries at an unknown orientation with respect to the sound beam. A mathematical analysis demonstrates that the normalized returned voltage spectrum from this model is independent of the planes orientation. Hence, the total attenuation can be estimated by comparing the location of the spectral peak in the reflection from the fetus to the location of the spectral peak in a reflection obtained from a rigid plane in a water bath. The independence of the attenuation estimate and plane orientation is then demonstrated experimentally using a Plexiglas plate, a rat's skull, and a tissue-mimicking phantom.     

Wavelet transforms in estimating scatterer spacing from ultrasound echoes

Ultrasound echoes from organs such as the liver display resolvable periodicity due to regular scattering centers within tissue. The spacing among such scattering centers has been proposed as a signature to characterize diffuse and focal diseases of the liver. Even though it is highly desirable to be able to estimate an inter-scatterer-spacing (ISS) distribution, current methods can estimate only the mean value of scatterer spacing (MSS) over a tissue length. In this paper, we propose a wavelet transform-based technique that is capable of estimating the location of each scattering center, making it possible to obtain the ISS distribution. We represent liver tissue with a point scatterer model, and show, via computer simulations, that the use of multi-scale information in the wavelet scale-space allows us to estimate the locations of regular scattering centers. We show that both the observation noise and random ultrasound returns from unresolvable tissue microstructure can be removed successfully in the wavelet domain via the properties of the modulus maxima sequence of observation across different scales.     

Improved algorithm for estimation of attenuation along propagation path using backscattered echoes from multiple sources

Accurately determining the attenuation along the propagation path leading to a region of interest could significantly improve diagnostic ultrasound tissue characterization since tissue characterization requires exact compensation for the frequency-dependent attenuation along the propagation path. In a previous study (JASA, 124:1367, 2008), it was shown that the total attenuation can be determined by using the backscattered echoes from multiple sources. The preliminary computer simulation results, had an average error between ?0.3 and +0.2 dB/MHz for the cases tested with a trend towards increasing error with increasing correlation length (i.e., characteristic size of the tissue microstructure of the scattering medium) and attenuation along the propagation path. Therefore, the goal of this study was to improve the accuracy of previously derived algorithm and reduce the dependence of the algorithm on correlation length and attenuation. In this study, the previous derivations were redone and the assumptions made by the algorithm regarding the scattering properties of the medium and the shape of the backscattered power spectrum were relaxed. The revised algorithm was then verified using computer simulations of five sources (6, 8, 10, 12, and 14 MHz, 50% bandwidth) exposing a homogeneous tissue region. The simulated tissue had microstructure following a Gaussian spatial correlation function (i.e., exp (?0.827(ka_eff)²) where k is the wavenumber) with effective radii, a_eff, of 5–55 μm (one size per simulated case) placed at a density of 250/mm³ (～5 scatterers/resolution cell for 14 MHz transducer). The attenuation of the tissue was also varied from 0.1 to 0.9 dB/cm-MHz. The computer simulations demonstrated that the modifications significantly improved the accuracy of the algorithm resulting in average errors between ?0.04 and 0.1 dB/MHz which is three times better than the error performance of the original algorithm.     

Time domain attenuation estimation method from ultrasonic backscattered signals

Ultrasonic attenuation is important not only as a parameter for characterizing tissue but also for compensating other parameters that are used to classify tissues. Several techniques have been explored for estimating ultrasonic attenuation from backscattered signals. In the present study, a technique is developed to estimate the local ultrasonic attenuation coefficient by analyzing the time domain backscattered signal. The proposed method incorporates an objective function that combines the diffraction pattern of the source/receiver with the attenuation slope in an integral equation. The technique was assessed through simulations and validated through experiments with a tissue mimicking phantom and fresh rabbit liver samples. The attenuation values estimated using the proposed technique were compared with the attenuation estimated using insertion loss measurements. For a data block size of 15 pulse lengths axially and 15 beamwidths laterally, the mean attenuation estimates from the tissue mimicking phantoms were within 10% of the estimates using insertion loss measurements. With a data block size of 20 pulse lengths axially and 20 beamwidths laterally, the error in the attenuation values estimated from the liver samples were within 10% of the attenuation values estimated from the insertion loss measurements.     

Effective length of filaments measurement using backscattered fluorescence from nitrogen molecules

The effective length of self-induced long (100 meters) plasma filaments, generated by intense femtosecond near IR laser pulses in air, was measured remotely using a lidar technique. This technique is based on detecting the backscattered fluorescence signal from nitrogen molecules excited along the intense laser pulse propagation path. This opens up the possibility of measuring remotely long filaments extending over hundreds of meters in the atmosphere. PACS 42.65.Jx; 42.68.Ay; 42.68.Wt     

Semi-empirical bone model for determination of trabecular structure properties from backscattered ultrasound

A novel semi-empirical scattering model of trabecular bone facilitating its characterization and allowing optimization of the interrogating pulse-echo transducer performance was developed. The model accounts for spatial density distribution of the trabeculae and includes measurement conditions such as pressure–time waveform of the probing ultrasound wave, the emitted field structure, and the transfer function and limited bandwidth of the acoustic source operating in pulse-echo mode. These measurement conditions are of importance as they modify the scattered echoes, which in turn are linked to the micro-architecture of the bone. The bone was modeled by a random distribution of long and thin cylindrical scatterers having randomly varying diameters and mechanical properties, and oriented perpendicularly to the ultrasound beam axis. To mimic clinically encountered conditions the relevant empirical data obtained at 1 MHz were input to the model. The data included pulse-echo source pressure field distribution in the focal zone and the above mentioned transfer function. With these data the model allowed frequency dependent backscattering coefficient of the simulated bone structure and its statistical properties to be determined. The results obtained indicated that the computer simulation is of particular relevance in studying scattering properties of the cancellous bone and holds promise as a tool to determine the relationship between the physical dimensions and shape of the scatterers and for monitoring of osteoporosis. The results of simulations also indicated that the new bone model proposed is well suited to mimic clinically relevant conditions. In contrast to the existing bone models, which usually assume scatterers to be randomly distributed as infinitely long identical cylinders with a cross-section much smaller than the probing ultrasound wave, the new model includes two populations of scatterers having different physical dimensions and also allows the mechanical properties of the scatterers to be varied.     

Dynamical effects of electron-hole correlation and giant quantum attenuation of ultrasound in semimetals

The giant quantum attenuation of ultrasound in bismuth and other semimetals is noticeably enhanced when certain pair of Landau subbands of electrons and holes participate simultaneously in an attenuation peak. A theoretical analysis is presented which emphasizes importance of dynamical effects of the electron-hole correlation. In the temperature range between 1 K and 4 K covered by most experiments, the correlation effect is found to be weak on the real part of the relevant response function which gives changes in sound velocity. This implies that equilibrium properties of the system are not much influenced by the correlation effect. Nonetheless, the electron-hole correlation is shown to have a drastic consequence on the imaginary part of the response function probed by the ultrasonic attenuation. Proposal for experiment is advanced to discriminate relative importance of this exciton-like correlation from that of republsive correlation between carriers with the same charge.     

Gluonic correlation length from spin-dependent potentials

The vacuum gluonic correlation length is extracted from recent lattice data on spin-dependent interquark potentials in heavy quarkonia. It is shown that the data are consistent with extremely small values of the correlation length, T _g ? 0.1 fm.

     

Gluonic correlation length from spin-dependent potentials

The vacuum gluonic correlation length is extracted from recent lattice data on spin-dependent interquark potentials in heavy quarkonia. It is shown that the data are consistent with extremely small values of the correlation length, T _g ≲ 0.1 fm. The article is published in the original.     

Material property estimates from ultrasound attenuation in fibre suspensions

An investigation of a new method for measuring fibre material properties from ultrasonic attenuation in a dilute suspension of synthetic fibres of uniform geometry is presented. The method is based on inversely solving an ultrasound scattering and absorption model of suspended fibres in water for the material properties of the fibres. Experimental results were obtained from three suspensions of nylon 66 fibres each with different fibre diameters. A forward solution to the model with reference material values is compared to experimental data to verify the model’s behaviour. Estimates of the shear and Young’s modulus, the compressional wave velocity, Poisson’s ratio and loss tangent from nylon 66 fibres are compared to data available from other sources. Experimental data confirms that the model successfully predicts that the resonance features in the frequency response of the attenuation are a function of diameter. Consistent estimated values for the compressional wave velocity and the Poisson’s ratio were found to be difficult to obtain but in combination gave values of shear modulus within previously reported values and with low sensitivity to noise. Young’s modulus was underestimated by 54% but was consistent and had low sensitivity to noise. The underestimation is believed to be caused by the assumption of isotropic material used in the model. Additional tests on isotropic fibre would confirm this. Further analysis of the model sensitivity and the reasons for the resonance features are required.     

Impact of large-angle scattering on diffusively backscattered halos

We discuss the impact of large-angle scattering events in highly forward-scattering media on the spatial distribution of the diffusively reflected light. We show that, even for highly forward-scattering media, the reflected light near the incident beam axis is strongly dependent on the small number of large-angle scattering events. Reliable modeling of near-axis reflection thus requires accurate knowledge of the scattering phase function's behavior at large angles.     

Intensity correlation function of field backscattered by two isotropic atoms

It is shown that the temporal intensity correlation function of laser light backscattered by two isotropic atoms displays the photon antibunching property in a helicity-conserving polarization channel. A simple qualitative explanation to this effect is given, results of numerical calculations that support the qualitative analysis are presented, and possibilities of the experimental observation of this effect are discussed.     

Multiexponential attenuation of the CPMG spin echoes due to a geometrical confinement

The CPMG multi-echo technique is often used to investigate the translational motion of diffusing nuclei in a confining medium. Henceforth, periodically repeated RF pulses with a diffusion-sensitizing gradient yield a formation of spin echoes of gradually decreasing amplitudes. The parameters of their exponential fits may characterize the structure of porous materials or biological tissue. In this paper, a multiexponential character of the CPMG measurements is rigorously demonstrated, once a geometrical confinement is present. Based on the multiple propagator approach, we derived a spectral representation for the echo amplitudes under external magnetic field of an arbitrary gradient profile. The multiple relaxation times and their spectral weights were found in a general form. The study of simple restrictive media allowed to obtain a quantitative condition under which the multiexponential attenuation is reduced to a monoexponential one.     

Decaying turbulence: What happens when the correlation length varies spatially in two adjacent zones

We have imagined a numerical experiment to explore the onset of turbulent intermittency associated with a spatial perturbation of the correlation length. We place two isotropic regions, with different integral scales, inside a volume where the turbulent kinetic energy is initially uniform and leave them to interact and evolve in time. The different length scales produce different decay rates in the two regions. Since the smaller-scale region decays faster, a transient turbulent energy gradient is generated at the interface between the two regions. The transient is characterized by three phases in which the kinetic energy gradient across the interface grows, peaks and then slowly decays. The transient lifetime is almost proportional to the initial ratio of the correlation lengths. The direct numerical simulations also show that the interface width grows in time. The velocity moments inside this interaction zone are seen to depart from their initial isotropic values and, with a certain lag, the anisotropy is seen to spread to small scales. The longitudinal derivative moments also become anisotropic after a few eddy turnover times. This anisotropic behaviour is different from that observed in sheared homogeneous turbulent flows, where high transverse derivative moments are generated, but longitudinal moments almost maintain the isotropic turbulence values. Apart from the behaviour of the energy gradient transients, the results also show the timescaling of the interface diffusion width, and data on the anisotropy of the large and small scales, observed through one-point statistics determined inside the intermittency sublayer, which is associated with the interaction zone.     

Automated measurement of ultrasound velocity and attenuation

A fully-automated system has been developed to measure changes in ultrasonic velocity and the attenuation coefficient resulting from changes in temperature and magnetic field. Accuracy and sensitivity comparable to the pulse-echo overlap technique have been achieved together with an increase in temperature resolution and sample throughput as a result of the automation. All components of the instrumentation are commercially available.     

Accurate local approximations to the triples correlation energy: formulation,implementation and tests of 5th-order scaling models

Local models for the triples part of the MP4 or CCSD(T) energy are formulated in terms of atom-labelled functions to describe the occupied and virtual orbital spaces. These models retain triple substitutions in which at most one of the three orbital replacements involves a change of atom. This reduces the number of triple substitutions from scaling with the 6th power of molecule size to scaling with the 4th power, and reduces the computational cost from 7th order to 5th order. Non-locality in the triple substitutions is dominated by terms in which an electron is scattered twice, while the other two singly scattered electrons exhibit non-locality that is similar to that seen in double substitutions. Two non-iterative computational models are designed around this observation. The first, ionic2, allows for non-locality only in the doubly-scattered electron, and recovers around 95% of the triples correlation energy (in the large-molecule limit). The second, ionic*, also approximately accounts for the effect of simultaneous non-locality of the doubly-scattered electron and the singly scattered electrons, and recovers over 99% of the triples energy. The latter yields a maximum error of 0.23?kcal?mol^?1 and an RMS error of 0.05?kcal?mol^?1 in the MP4/6-31G* triples energies of 179 closed shell molecules from the G3 database. A one-parameter empirical local model is introduced which recovers typically 99.7% of the MP4 triples correlation energy, and reduces the maximum error to 0.03?kcal?mol^?1 and the RMS error to 0.01?kcal?mol^?1. An implementation of these models is described which manifests the 5th-order scaling of cost with molecule size, without requiring storage of the local triples or the vvvo integrals.     

Lifshitz-point correlation length exponents from the large-n expansion

The large-n expansion is applied to the calculation of thermal critical exponents describing the critical behavior of spatially anisotropic d-dimensional systems at m  -axial Lifshitz points. We derive the leading non-trivial 1/n$1/n$ correction for the perpendicular correlation-length exponent _νL2${\nu }_{L2}$ and hence several related thermal exponents to order O(1/n)$O(1/n)$. The results are consistent with known large-n expansions for d  -dimensional critical points and isotropic Lifshitz points, as well as with the second-order epsilon expansion about the upper critical dimension d^?=4+m/2$d^{?}=4+m/2$ for generic m∈[0,d]$m\in [0,d]$. Analytical results are given for the special case d=4$d=4$, m=1$m=1$. For uniaxial Lifshitz points in three dimensions, 1/n$1/n$ coefficients are calculated numerically. The estimates of critical exponents at d=3$d=3$, m=1$m=1$ and n=3$n=3$ are discussed.     

Neutralization of helium ions backscattered from tungsten

Measurements and computer simulations of the energy spectra of helium ions backscattered from clean, polycrystalline tungsten at 138° have been combined to obtain estimates of the probability of survival against neutralization. For incident ion energies of 300, 1180 and 2600 eV, the estimated survival probabilities for ions backscattered near the surface are 0.05%, 0.2% and 1%, respectively. The estimated survival probability for subsurface backscattered ions has been found to range from a value of 1% at 2600 eV, comparable to that of near-surface backscattered ions, down to near zero at 300 eV incident ion energy. Evidence is presented that the final charge state of ions which backscatter from beneath the surface is not controlled by their emergence speed but by their previous history in the solid.