Time-varying autoregressive spectral estimation for ultrasound attenuation in tissue characterization

In the field of biological tissue characterization, fundamental acoustic attenuation properties have been demonstrated to have diagnostic importance. Attenuation caused by scattering and absorption shifts the instantaneous spectrum to the lower frequencies. Due to the time-dependence of the spectrum, the attenuation phenomenon is a time-variant process. This downward shift may be evaluated either by the maximum energy frequency of the spectrum or by the center frequency. In order to improve, in strongly attenuating media, the results given by the short-time Fourier analysis and the short-time parametric analysis, we propose two approaches adapted to this time-variant process: an adaptive method and a time-varying method. Signals backscattered by an homogeneous medium of scatterers are modeled by a computer algorithm with attenuation values ranging from 1 to 5 dB/cm MHz and a 45 MHz transducer center frequency. Under these conditions, the preliminary results obtained with the proposed time-variant methods, compared with the classical short-time Fourier analysis and the short-time auto-regressive (AR) analysis, are superior in terms of standard deviation (SD) of the attenuation coefficient estimate. This study, based on nonstationary AR spectral estimation, promises encouraging perspectives for in vitro and in vivo applications both in weakly and highly attenuating media.     

WOLD decomposition of the backscatter echo in ultrasound images of soft tissue organs

Deals with a method of detecting and estimating the scatterer spacing between the regularly spaced resolvable coherent scatterers in tissue. Scatterer spacing has been successfully used in classifying tissue structure, in differentiating between normal and cirrhotic liver, and in detecting diffuse liver disease. This paper presents a WOLD decomposition of the radio frequency (RF) field into its diffused and coherent components from which maximum likelihood estimates (MLE) or minimum mean square error (MMSE) estimates of the scattering spacing are easily computed. The MLE are efficient and for relatively long record are unbiased. They result in accurate estimates in low signal-to-noise (SNR) ratios. Unfortunately, they require nonlinear minimization and knowledge of the probability density associated with the RF backscatter echo. The MMSE estimates, on the other hand, are computationally simple, yield unique closed form solutions, do not require a-priori knowledge of the probability distribution function of the backscatter echo, and result in accurate estimates in low SNR ratios. This paper also presents an unbiased decision rule to detect whether or not an RF echo exhibits any specular scattering relative to the wavelength of the interrogating ultrasonic pulse. The approach has been tried on simulations as well as on in-vivo scans of liver data, and appears to perform well.     

Stable and unbiased flow turbulence estimation from pulse echo ultrasound

A new method for stable and unbiased flow turbulence estimation has been developed for medical ultrasonic color flow imaging. Conventional turbulence estimates from a finite number of transmitted pulses could be biased, unreliable, and erroneous. We found that a conventional method cannot provide quantitative estimates of variance of flow velocity. We propose a new approach for flow turbulence estimation that is based on analysis of the flow velocity vectors. The new method estimates the variance of the flow velocity and provides reliable estimates for flow turbulence. Numerical examples, computer simulations, and experiments using a flow phantom demonstrate that the new method can estimate variance of flow velocity accurately and without bias. This work also reports a complete derivation in the time domain for both unbiased velocity and turbulence estimations. The results include two velocity estimation equations agreeing with the 1-D and 2-D autocorrelation methods derived from the frequency domain. The results indicate that the new method for flow turbulence is particularly useful when the 2-D autocorrelation method is used for color flow imaging. The new method also appears to be able to detect low turbulence; therefore, it may be useful for diagnosing abnormalities such as minor stenoses and valvular jets.     

Intervening attenuation affects first-order statistical properties of ultrasound echo signals

Previous studies show that first-order statistical properties of ultrasound echo signals are related to the effective number of scatterers in the "resolution cell" of a pulse-echo ultrasound system. When the effective number of scatterers is large (~10 or more) this results in echo signals whose amplitude follows a Rayleigh distribution, with the RF echo signal obeying Gaussian statistics; deviation from Rayleigh or Gaussian statistics yields information on scatterer number densities. In this paper, the influence of the medium's attenuation on non-Gaussian properties of the echo signal is considered. Preferential attenuation of higher frequency components of a pulsed ultrasound beam effectively broadens the beam and increases the resolution cell size. Thus, the resultant non-Gaussian parameter for broad bandwidth excitation of the transducer depends not only on the scatterer number density but also on the attenuation in the medium. These effects can be reduced or eliminated by using narrow-band experiments.     

Heating of bone and soft tissue by ultrasound

Abstract

The absorption of ultrasound in human tissue always causes some local increase in temperature. In the case of ultrasound imaging, the power is usually much less than that used therapeutically and is unlikely to produce any significant physiological effect. However, a reliable means of calculating the maximum temperature rise to be expected in any given case will assist in both the development and the safe use of new ultrasound devices. To validate earlier work on ultrasonic tissue heating, including both experiment and finite element modelling (FEM), an analytical method is described for calculating the steady-state temperature rise along the axis of an axially symmetrical beam of ultrasound incident through water on a two-layer phantom consisting of agar gel and a bone mimic, the practical beam profile being modelled by a pair of coaxial Gaussian functions. It is shown that, in the absence of perfusion, the steady-state temperature distribution for the extended heat source generated by the ultrasound absorption can be obtained by integrating the point-source solution to the Bioheat transfer equation (BHTE). The boundary conditions associated with the difference in thermal properties of the mimic materials are satisfied by introducing images of the extended heat source in the gel/bone–mimic interface.     

Effect of resonant impurity scattering on collective mode peaks in the ultrasound attenuation of heavy fermion superconductors

We have calculated the attenuation of longitudinal ultrasound due to real order parameter fluctuations in impure polar and planarp-wave superconductors. The quasiparticle self-energy and the corresponding vertex corrections have been included in thet-matrix approximation for arbitrary scattering rate =1/2_N and all scattering phase shifts _N (0 _N/2). We obtain sound attenuation peaks belowT _c whose heights, positions, and shapes depend on ₀ (sound frequency), (₀), _N, and (coupling strength due to particle-hole asymmetry). The peaks become much more distinct and sharper for _N =/2 (resonant scattering by impurities) than for _N=0 (Born approximation). By choosing , _N, and suitably, qualitative agreement between calculated and observed peaks in UBe₁₃ and UPt₃ can be achieved.     

PSF dedicated to estimation of displacement vectors for tissue elasticity imaging with ultrasound

This paper investigates a new approach devoted to displacement vector estimation in ultrasound imaging. The main idea is to adapt the image formation to a given displacement estimation method to increase the precision of the estimation. The displacement is identified as the zero crossing of the phase of the complex cross-correlation between signals extracted from the lateral direction of the ultrasound RF image. For precise displacement estimation, a linearity of the phase slope is needed as well as a high phase slope. Consequently, a particular point spread function (PSF) dedicated to this estimator is designed. This PSF, showing oscillations in the lateral direction, leads to synthesis of lateral RF signals. The estimation is included in a 2-D displacement vector estimation method. The improvement of this approach is evaluated quantitatively by simulation studies. A comparison with a speckle tracking technique is also presented. The lateral oscillations improve both the speckle tracking estimation and our 2-D estimation method. Using our dedicated images, the precision of the estimation is improved by reducing the standard deviation of the lateral displacement error by a factor of 2 for speckle tracking and more than 3 with our method compared to using conventional images. Our method performs 7 times better than speckle tracking. Experimentally, the improvement in the case of a pure lateral translation reaches a factor of 7. Finally, the experimental feasibility of the 2-D displacement vector estimation is demonstrated on data acquired from a Cryogel phantom.     

Estimation of ultrasound attenuation from broadband echo-signals using bandpass filtering

A problem with video signal analysis for estimating frequency-dependent ultrasonic attenuation is that relative echogenicity versus depth curves are distorted when broadband pulses are used. In this correspondence, we present results that demonstrate improved accuracy of attenuation estimates computed from B-mode or envelope data derived after narrowband (1 MHz BW) filtering at different frequencies around the center frequency of the broadband echo signal. Based on the premise that transducer center frequencies are selected in part on penetration or imaging depth requirements, simulation and experimental results for a typical ultrasound imaging system show that narrowband video signal analysis for frequencies lower than or at the center frequency of the broadband pulse provide unbiased attenuation estimation over this depth. Filtered signals above the center frequency of the pulse yield accurate results only at shallow depths.     

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.     

Scattering of ultrasound from skeletal muscle tissue

The purpose of this work was to explore the mechanisms which are responsible for the scattering of ultrasound from skeletal muscle tissue. It was undertaken in response to an interesting phenomenon observed in the authors' laboratory whereby scattering power from avian skeletal muscle changed in concordance with passive stretch. Ultrasonic scattering from skeletal muscle samples was measured as they were stretched passively in increments of 10% of their original length up to 40%. The samples were illuminated with an ultrasound beam from a transducer which was oriented orthogonally to and at 20 degrees from the normal to the long axis of the muscle sample. It was found that the integrated backscatter increased significantly over the strain range for the orthogonal orientation, but it changed very little after the initial stretch when the orientation was 20 degrees . It is postulated that this phenomenon may be caused by reorientation of the endomysial collagen fibers surrounding each muscle fiber.     

FLASH correlation: a new method for 3-D ultrasound tissue motion tracking and blood velocity estimation

We report a new method for tracking tissue motion and blood flow in three dimensions (3-D) using successive volumetric ultrasound scans. The method is based on combining the concepts of feature tracking and 3-D correlation search to achieve a compromise between accuracy and computational efficiency. This paper introduces the new method and the experimental setup used for its evaluation in a tissue-mimicking material. Results are presented demonstrating that the new method has both satisfactory tracking performance and the potential for practical real-time implementation.     

A novel envelope detector for high-frame rate, high-frequency ultrasound imaging

This paper proposes a novel design of envelope detectors capable of supporting a small animal cardiac imaging system requiring a temporal resolution of more than 150 frames per second. The proposed envelope detector adopts the quadrature demodulation and the lookup table (LUT) method to compute the magnitude of the complex baseband components of received echo signals. Because the direct use of the LUT method for a square root function is not feasible due to a large memory size, this paper presents a new LUT strategy dramatically reducing its size by using binary logarithmic number system (BLNS). Due to the nature of BLNS, the proposed design does not require an individual LOG-compression functional block. In the implementation using a field programmable gate array (FPGA), a total of 166.56 Kbytes memories were used for computing the magnitude of 16-bit in-phase and quadrature components instead of 4 Gbytes in the case of the direct use of the LUT method. The experimental results show that the proposed envelope detector is capable of generating LOG-compressed envelope data at every clock cycle after 32 clock cycle latency, and its maximum error is less than 0.5 (i.e., within the rounding error), compared with the arithmetic results of square root function and LOG compression.     

Thermal dose optimization for ultrasound tissue ablation

A formal and general thermal dose optimisation method is developed and tested. Prior methods require brute force searches wherein the temperature and dose distributions must be computed at each iteration by solving the bioheat transfer equation (BHTE) numerically. This is extremely time-consuming and can only be used to compare a few prespecified strategies instead of obtaining a more general optimal result. With the method developed here, dose distribution can be calculated without solving the BHTE numerically. This can be done in a matter of a few minutes compared with many hours. Moreover, general thermal dose optimization can now be performed to find the optimal strength and location of each focus so that an optimal dose distribution is obtained while the specified constraint is satisfied. The algorithm developed here consists of a closed-form solution to the BHTE, a Gaussian model for parameterizing a temperature distribution created by a power deposition pattern, and a two-step optimization technique for obtaining the model parameters that optimize the thermal dose distribution. Several examples are given to demonstrate the effectiveness of the algorithm and its robustness under different initial conditions and under assumptions of different sizes of the target region and different numbers of foci. The algorithm developed here provides an efficient and effective tool for treatment planning in ultrasound tissue ablation.     

A review of attenuation correction techniques for tissue fluorescence.

Fluorescence intensity measurements have the potential to facilitate the diagnoses of many pathological conditions. However, accurate interpretation of the measurements is complicated by the distorting effects of tissue scattering and absorption. Consequently, different techniques have been developed to attempt to compensate for these effects. This paper reviews currently available correction techniques with emphasis on clinical application and consideration given to the intrinsic accuracy and limitations of each technique.     

Novel three-dimensional cocoon-like hydrogels for soft tissue regeneration

Large three-dimensional hydrogels (> 150 cm³) of bacterial cellulose (BC) were synthesized by using Gluconacetobacter hansenii ATCC 23769 under controlled agitated culture conditions. The macroscopic cocoon-like structures are gelatinous and translucent and may find applications in several areas, particularly in tissue and organ engineering. Internal microstructure was investigated by scanning electron microscopy (SEM) and field emission scanning electron microscopy (FESEM), which revealed that the cocoons are composed of cellulosic nanofibres randomly and three-dimensionally dispersed. The macroscopic bodies are delimited by a dense semi-permeable membrane with thickness between 0.2 and 2 mm, also composed of cellulosic nanofibres. Endothelial cells were seeded on the hydrogels and incubated for 7 days. HUVECs grew and migrated into the inner part of the structure. The three-dimensional BC hydrogel structures can be directly implanted in tissue deficient regions as scaffolds containing the appropriate cultured cells.     

Coded ultrasound for blood flow estimation using subband processing

This paper investigates the use of coded excitation for blood flow estimation in medical ultrasound. Traditional autocorrelation estimators use narrow-band excitation signals to provide sufficient signal-to-noise-ratio (SNR) and velocity estimation performance. In this paper, broadband coded signals are used to increase SNR, followed by subband processing. The received broadband signal is filtered using a set of narrow-band filters. Estimating the velocity in each of the bands and averaging the results yields better performance compared with what would be possible when transmitting a narrow-band pulse directly. Also, the spatial resolution of the narrow-band pulse would be too poor for brightness-mode (B-mode) imaging, and additional transmissions would be required to update the B-mode image. For the described approach in the paper, there is no need for additional transmissions, because the excitation signal is broadband and has good spatial resolution after pulse compression. This means that time can be saved by using the same data for B-mode imaging and blood flow estimation. Two different coding schemes are used in this paper, Barker codes and Golay codes. The performance of the codes for velocity estimation is compared with a conventional approach transmitting a narrow-band pulse. The study was carried out using an experimental ultrasound scanner and a commercial linear array 7 MHz transducer. A circulating flow rig was scanned with a beam-to-flow angle of 60 degrees. The flow in the rig was laminar and had a parabolic flow-profile with a peak velocity of 0.09 m/s. The mean relative standard deviation of the velocity estimate using the reference method with an 8-cycle excitation pulse at 7 MHz was 0.544% compared with the peak velocity in the rig. Two Barker codes were tested with a length of 5 and 13 bits, respectively. The corresponding mean relative standard deviations were 0.367% and 0.310%, respectively. For the Golay coded experiment, two 8-bit codes were used, and the mean relative standard deviation was 0.335%.     

A compound scattering pdf for the ultrasonic echo envelope and its relationship to K and Nakagami distributions

A compound probability density function (pdf) is presented to describe the envelope of the backscattered echo from tissue. This pdf allows local and global variation in scattering cross sections in tissue. The ultrasonic backscattering cross sections are assumed to be gamma distributed. The gamma distribution also is used to model the randomness in the average cross sections. This gamma-gamma model results in the compound scattering pdf for the envelope. The relationship of this compound pdf to the Rayleigh, K, and Nakagami distributions is explored through an analysis of the signal-to-noise ratio of the envelopes and random number simulations. The three parameter compound pdf appears to be flexible enough to represent envelope statistics giving rise to Rayleigh, K, and Nakagami distributions.     

Current time-domain methods for assessing tissue motion by analysis from reflected ultrasound echoes-a review

The Doppler technique has traditionally been the method used to extract motion information from ultrasonic echoes reflected by moving tissues. The Doppler technique has been around for a long time, and has been extensively reviewed and analyzed in the literature. Recently, time-domain methodologies for estimating tissue motion have gained in popularity. Time-domain methods have advantages over Doppler methods in many applications, and as of yet have not been comprehensively reviewed. An overview of time-domain techniques that have appeared in the literature over the past few years is presented. Their potential advantages over Doppler are examined, and the individual techniques are compared.     

Acoustic waves in hydrogels: A bi-phasic model for ultrasound tissue-mimicking phantom

In the present paper a continuum poroelastic model for high frequency acoustic waves in hydrogels has been developed. The model has been used to obtain the acoustic longitudinal wave equation for ultrasound.In order to obtain a satisfactory model for hydrogels, a viscoelastic force describing the interaction between the polymer network of the matrix and the bounded water is introduced.The model is validated by means of ultrasound (US) wave speed and attenuation measurements in polyvinylalcohol (PVA) hydrogel samples as a function of their water volume fraction “β” and polymer matrix cross-linking.The model predicts that the law ∝ ν^(1 + δ) for ultrasound attenuation can be applied as a function of the frequency ν, where δ is the frequency exponent of the polymer-bounded water viscosity. This outcome can well explain the attenuation of the US frequency in natural gels where δ is typically about 0.25÷0.50 while the value for pure water is 1.The theory and experiments show that US attenuation in hydrogels decreases steadily with the increase of its water volume fraction β in a linear.The new proposed dissipative mechanism leads to a US wave speed c that follows the law: c = c_w(β ? ?)^? 3/2, where c_w is the US wave speed in water and ? is the volume fraction of the bounded water.Since 0 < β < 1 and ? > 0, the hydrogel US velocity is always higher than that of pure water.If β tends to 1 (100% water), then the US speed in hydrogels converges to a higher value than that of pure water.The US speed gap at β = 1, between hydrogels and water, is the direct consequence of the introduction of the polymer network-bounded water interaction. This is in line with the experimental results that show that the US speed gap at β = 1 decreases in the gel samples with a more cross-linked polymer matrix that has a lower bounded water volume fraction.On the contrary, if the water content is very low (i.e., β < 0.4), the measured US speed converges to that of the dry hydrogel matrix which increases in the samples with a higher degree of network cross-linking with greater elastic moduli.