Method of improved scatterer size estimation and application to parametric imaging using ultrasound

The frequency dependence of RF signals backscattered from random media (tissues) has been used to describe the microstructure of the media. The frequency dependence of the backscattered RF signal is seen in the power spectrum. Estimates of scatterer properties (average scatterer size) from an interrogated medium are made by minimizing the average squared deviation (MASD) between the measured power spectrum and a theoretical power spectrum over an analysis bandwidth. Estimates of the scatterer properties become increasingly inaccurate as the average signal to noise ratio (SNR) over the analysis bandwidth becomes smaller. Some frequency components in the analysis bandwidth of the measured power spectrum will have smaller SNR than other frequency components. The accuracy of estimates can be improved by weighting the frequency components that have the smallest SNR less than the frequencies with the largest SNR in the MASD. A weighting function is devised that minimizes the noise effects on the estimates of the average scatterer sizes. Simulations and phantom experiments are conducted that show the weighting function gives improved estimates in an attenuating medium. The weighting function is applied to parametric images using scatterer size estimates of a rat that had developed a spontaneous mammary tumor.     

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.     

Anisotropy of the ultrasonic attenuation in soft tissues: measurements in vitro

This study was designed to measure the ultrasonic attenuation within phantoms and tissue samples over a broad bandwidth and at many angles of incidence with respect to intrinsic orientations in order to elucidate both the frequency and angular dependence of the attenuation coefficient. Significant angular dependence, or anisotropy, of the attenuation was observed in canine myocardium (maximum to minimum ratio: 2.2 to 1) and a tissue mimicking phantom of oriented graphite fibers in gelatin (max to min: 2 to 1). In control studies, insignificant anisotropy was observed in the attenuation in canine liver samples and phantoms with graphite powder suspended in gelatin. Comparisons of the magnitude of variations of the oriented-fiber phantom to that predicted by a viscous relative motion model are presented.     

A simulation algorithm for ultrasound liver backscattered signals

In this study, we present a simulation algorithm for the backscattered ultrasound signal from liver tissue. The algorithm simulates backscattered signals from normal liver and three different liver abnormalities. The performance of the algorithm has been tested by statistically comparing the simulated signals with corresponding signals obtained from a previous in vivo study. To verify that the simulated signals can be classified correctly we have applied a classification technique based on an artificial neural network. The acoustic features extracted from the spectrum over a 2.5 MHz bandwidth are the attenuation coefficient and the change of speed of sound with frequency (dispersion). Our results show that the algorithm performs satisfactorily. Further testing of the algorithm is conducted by the use of a data acquisition and analysis system designed by the authors, where several simulated signals are stored in memory chips and classified according to their abnormalities.     

Impact of local attenuation approximations when estimating correlation length from backscattered ultrasound echoes

Estimating the characteristic correlation length of tissue microstructure from the backscattered power spectrum could improve the diagnostic capability of medical ultrasound. Previously, size estimates were obtained after compensating for source focusing, the frequency-dependent attenuation along the propagation path (total attenuation), and the frequency-dependent attenuation in the scattering region (local attenuation). In this study, the impact of approximations of the local attenuation on the scatterer size estimate was determined using computer simulations and theoretical analysis. The simulations used Gaussian impedance distributions with an effective radius of 25 microm randomly positioned in a homogeneous half-space sonified by a spherically focused source (f/1 to f/4). The approximations of the local attenuation that were assessed neglected local attenuation (i.e., assume 0 dB/cm-MHz) neglected frequency dependence of the local attenuation, and assumed a finite frequency dependence (i.e., 0.5 dB/cm-MHz) independent of the true attenuation of the medium. Errors in the scatterer size estimate due to the local attenuation approximations increased with increasing window length, increasing true local attenuation and increasing f number. The most robust estimates were obtained when the local attenuation was approximated by a tissue-independent attenuation value that was greater than 70% of the largest attenuation expected in the tissue region of interest.     

Measurements of cloud contribution to rain millimeter wave attenuation by using a radar and radiometers

The measurement technique of cloud contribution to rain attenuation and the equipment consisted of the coherent pulse Doppler radar at wavelength =3.2 cm, the radiometers at=0.4; 0.8 and 1.35 cm and apparatus for signal recording and processing is described. The results of such measurements are given. The Doppler spectrum of the rain backscattered radar signal was used for determination of rain drop size distribution height profile then rain attenuation was calculated and cloud attenuation was determined as the difference between the total attenuation measured by using the radiometers and rain attenuation. The results of this work gave possibility to improve the known rain model of P.Misme for prediction of rain attenuation statistics for Earth-satellite links at millimeter wave.     

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

The nonreciprocal effect under low- and high-frequency collinear acousto-optic interactions

The nonreciprocal effect under collinear acousto-optic interaction in the low- and high-frequency regimes is studied theoretically. The magnitudes of nonreciprocity determined from the ultrasonic frequency and from the wavelength of light are shown to be quantitatively identical. An expression that governs the magnitude of the nonreciprocity and that is valid for both low- and high-frequency regimes of the collinear acousto-optic interaction is obtained. The shape and width of the frequency characteristic of the collinear acousto-optic interaction calculated in the low diffraction efficiency approximation are shown to be the same in the low- and high-frequency regimes. The dependence of the frequency bandwidth of the collinear acousto-optic interaction on the ultrasonic-wave attenuation and diffraction efficiency is obtained. The magnitude of the nonreciprocal effect in some of the crystals used in acousto-optics is estimated numerically. The nonreciprocity of the collinear interaction is shown to be substantially stronger in the high-frequency regime relative to the low-frequency regime. Sapphire is proved to be an optimal material for experimental realization of the nonreciprocal effect in the high-frequency regime.     

Negative dispersion in bone: the role of interference in measurements of the apparent phase velocity of two temporally overlapping signals

In this study the attenuation coefficient and dispersion (frequency dependence of phase velocity) are measured using a phase sensitive (piezoelectric) receiver in a phantom in which two temporally overlapping signals are detected, analogous to the fast and slow waves typically found in measurements of cancellous bone. The phantom consisted of a flat and parallel Plexiglas plate into which a step discontinuity was milled. The phase velocity and attenuation coefficient of the plate were measured using both broadband and narrowband data and were calculated using standard magnitude and phase spectroscopy techniques. The observed frequency dependence of the phase velocity and attenuation coefficient exhibit significant changes in their frequency dependences as the interrogating ultrasonic field is translated across the step discontinuity of the plate. Negative dispersion is observed at specific spatial locations of the plate at which the attenuation coefficient rises linearly with frequency, a behavior analogous to that of bone measurements reported in the literature. For all sites investigated, broadband and narrowband data (3-7 MHz) demonstrate excellent consistency. Evidence suggests that the interference between the two signals simultaneously reaching the phase sensitive piezoelectric receiver is responsible for this negative dispersion.     

Calculation of the frequency response in step-index plastic optical fibers using the time-dependent power flow equation

The time-dependent power flow equation, which is reduced to its time-independent counterpart is employed to calculate frequency response and bandwidth in addition to mode coupling and mode-dependent attenuation in a step-index plastic optical fiber. The frequency response is specified as a function of distance from the input fiber end. This is compared to reported measurements. Mode-dependent attenuation and mode dispersion and coupling are known to be strong in plastic optical fibers, leading to major implications for their frequency response in data transmission systems.     

Contraction-related variation in frequency dependence of acoustic properties of canine myocardium

Results of experiments performed in several laboratories indicate that contracting myocardium exhibits a cyclic variation of the magnitude of ultrasonic backscatter, with maxima occurring at end-diastole and minima at end-systole. The mechanisms responsible for this variation are not well understood. The purpose of the present study was to determine whether the frequency dependence of backscatter exhibits systematic variation throughout the cardiac cycle, analysis of which may facilitate improved understanding of biologic factors responsible for the cyclic variation of the magnitude of backscatter. In this study, the myocardial backscatter coefficient, as a function of frequency, was measured throughout the cardiac cycle in nine open-chest dogs. The frequency dependence of the backscatter coefficient was computed from a least-squares linear fit to log backscatter coefficient versus log frequency data. A cyclic variation of frequency dependence of backscatter was found with maximum near end-diastole (f2.6 +/- 0.1) and minimum near end-systole (f2.2 +/- 0.1), a significant variation (p less than 0.01). These results suggest that mechanisms responsible for the cyclic variation of backscatter may include changes in the effective size of the dominant scatterers throughout the cardiac cycle. An alternative explanation for the observed variation is an increase in the myocardial attenuation coefficient during systole followed by a decrease in diastole.     

典型大气窗口太赫兹波传输特性和信道分析

在已有大气传输模型的基础上,发展了新的太赫兹波大气传输衰减与色散模型,对宽频太赫兹波在真实大气中传输的衰减和色散特性进行了数值模拟研究.改进太赫兹时域光谱技术,对0.3—2.0 THz频段太赫兹波的大气传输特性进行了透射光谱测量,并得到了一组连续吸收参数.比对发现实验窗口区强度和吸收峰的位置都与计算结果符合得很好.据此选取了三个可行的信道:340,410和667 GHz窗口区,利用线性色散理论和无线通信原理分别从物理上精确地计算了这些信道的群速色散参数和信道容量,并分析了影响最大传输数据率的因素-天线增益.研究结果表明:太赫兹波大气传输1 km时,这三个信道群速色散很小,信号不易被展宽;最大传输速率达十几Gbps,高于单模光纤,但需要更高的天线增益.     

Broadband performance of an active headrest.

This paper presents a study of the attenuation of broadband random acoustic disturbances, when using a feedback active headrest system, as originally suggested by Olson and May. Previous studies showed that a practical active headrest can be designed for tonal disturbances using feedforward controllers. However, many applications, such as jet aircraft and cars, require feedback systems to control random disturbances over a wide frequency bandwidth. In this work, robust feedback controllers are designed to control broadband random disturbances in the low-frequency range based on measured data from a laboratory headrest system. The results show that a practically useful performance can be achieved, but only if the controller is designed to minimize the pressure at a "virtual microphone" close to the listener's ears, and that the performance is maintained reasonably well with movements of the listener's head. The paper emphasizes the importance of both the acoustics and the control in the design of broadband active headrest systems.     

Surface plasmon polaritons frequency-blue shift in low confinement factor excitation region

Surface plasmon polaritons' (SPPs') frequency blue shift is observed in finite-difference time-domain (FDTD) simulation of parallel electron excitation Au bulk structure. Comparing with cold dispersion of SPPs, an obvious frequency blue shift is obtained in low confinement region excitation simulation results. Then, according to SPPs' transverse attenuation characteristics, the excited frequency mode instead of cold dispersion corresponding frequency mode matches it. Thence, this excited mode is confirmed to be SPPs' mode. As is well known the lower the frequency, the smaller the confinement factor is and the lower the excitation efficiency, the wider the bandwidth of excited SPPs is. And considering the attenuation in whole structure, the excited surface field contains attenuation signal. In a low confinement factor region, the higher the SPPs' frequency, the higher the excitation efficiency is, while broadband frequency information obtained in attenuation signal provides high frequency information in stimulation signal. Thence, in the beam-wave interaction, as the signal oscillation time increases, the frequency of the oscillation field gradually increases. Thus, compared with cold dispersion, the frequency of excited SPP is blueshifted This hypothesis is verified by monitoring the time domain signal of excited field in low and high confinement factor regions and comparing them. Then, this frequency-blue shift is confirmed to have commonality of SPPs, which is independent of SPPs' material and structure. Finally, this frequency-blue shift is confirmed in an attenuated total reflection (ATR) experiment. Owing to frequency dependence of most of SPPs' devices, such as coherent enhancement radiation and enhancement transmission devices, the frequency-blue shift presented here is of great influence in the SPPs applications.     

Theoretical modelling of frequency dependent elastic loss in composite piezoelectric transducers

The large number of degrees of freedom in the design of piezoelectric transducers requires a theoretical model that is computationally efficient so that a large number of iterations can be performed in the design optimisation. The materials used are often lossy, and indeed loss can be used to enhance the operational characteristics of these designs. Motivated by these needs, this paper extends the one-dimensional linear systems model to incorporate frequency dependent elastic loss. The reception sensitivity, electrical impedance and electromechanical coupling coefficient of a 1–3 composite transducer, with frequency dependent loss in the polymer filler, are investigated. By plotting these operating characteristics as a function of the volume fraction of piezoelectric ceramic an optimum design is obtained. A device with a non-standard, high shear attenuation polymer is also simulated and this leads to an increase in the electromechanical coupling coefficient. A comparison with finite element simulations is then performed. This shows that the two methods are in reasonable agreement in their electrical impedance profiles in all the cases considered. The plots are almost identical away from the main resonant peak where the frequency location of the peaks are comparable but there is in some cases a 20% discrepancy in the magnitude of the peak value and in its bandwidth. The finite element model also shows that the use of a high shear attenuation polymer filler damps out the unwanted, low frequency modes whilst maintaining a reasonable impedance magnitude.     

In vivo measurement of attenuation

We propose a new technique for the in vivo measurement of attenuation. The method is conceptually simple and can also be easily implemented on a real-time ultrasound unit. The technique is suggested by an analysis of the propagation of a Gaussian pulse in a medium which has frequency-dependent attenuation as well as dispersion (frequency-dependent velocity). If the medium has a loss factor which can be described by H(f) = exp(-eta[f]pX), where f is the frequency and O less than or equal to p less than or equal to 2 (valid for tissues and other objects of interest), then the pulse retains its Gaussian shape, shifting only its centre frequency and bandwidth. This suggests that by measuring the mean frequency of the reflected rf waveform in a window which is moved in depth we can obtain an estimate of the attenuation. Here we describe a particular hardware implementation of this technique which we have completed (based on measurement of zero-crossings) and present some preliminary in vivo measurements.     

Application of time delay spectrometry for rough surface characterization

This paper describes the design and performance of an ultrasound measurement system, utilizing a swept frequency excitation signal, for analyzing the backscattered signal from planar rough surfaces. The implementation is in the form of a time delay spectrometry (TDS) system operating in reflection mode whose advantages are improved signal-to-noise ratio even with low peak power relative to conventional pulse-echo methods. Because of simultaneous transmission and reception, the TDS system requires two transducers. The TDS measurement system uses a swept frequency spectrum analyzer as the central analog processing unit. Both planar piston and focused transducers in the low MHz range were used for the measurements. Due to the statistical nature of rough surface backscatter, the mean of several statistically uncorrelated measurements is required to characterize the scattering behavior of a given rough surface. Backscatter data are obtained for a series of planar rough surfaces, in the form of scattering magnitude vs. frequency and vs. incident (=backscattered) angle. Analysis of the results reveals a good correlation between the root-mean-square (RMS) height and mean backscatter magnitude at 0 degrees incident angle, and between the ratio of RMS height to correlation length and the difference in mean backscatter magnitude between 0 degrees and 5 degrees.     

On the effect of backscattering of γ quanta and statistics in positron-annihilation lifetime measurements

The contribution of backscattered, 1.27-MeV quanta to the coincidence counts in positron-annihilation lifetime measurements has been investigated. Depending on the energy window settings and geometry, as much as 20% of the coincidence counts was found to arise from backscattered events. Computer analysis of such spectra leads to erroneous results. Analysis of computer-generated lifetime spectra shows that good statistics is more important than good resolution power for the quality of the analysis.On leave of absence at Danfoss, DK-6430 Nordborg, Denmark     

Non-Gaussian statistics and temporal variations of the ultrasound signal backscattered by blood at frequencies between 10 and 58 MHz

Very little is known about the blood backscattering behavior and signal statistics following flow stoppage at frequencies higher than 10 MHz. Measurements of the radio frequency (rf) signals backscattered by normal human blood (hematocrit = 40%, temperature = 37 degrees C) were performed in a tube flow model at mean frequencies varying between 10 and 58 MHz. The range of increase of the backscattered power during red blood cell (RBC) rouleau formation was close to 15 dB at 10 and 36 MHz, and dropped, for the same blood samples, below 8 dB at 58 MHz. Increasing the frequency from 10 to 58 MHz raised the slope of the power changes at the beginning of the kinetics of aggregation, and could emphasize the non-Gaussian behavior of the rf signals interpreted in terms of the K and Nakagami statistical models. At 36 and 58 MHz, significant increases of the kurtosis coefficient, and significant reductions of the Nakagami parameter were noted during the first 30 s of flow stoppage. In conclusion, increasing the transducer frequency reduced the magnitude of the backscattered power changes attributed to the phenomenon of RBC aggregation, but improved the detection of rapid growth in aggregate sizes and non-Gaussian statistical behavior.