A deconvolution filter for improvement of time-delay estimation in elastography

In elastography, tissue under investigation is compressed, and the resulting strain is estimated from the gradient of displacement estimates. Therefore, it is important to accurately estimate the displacements (time-delay) for good quality elastograms. A principal source of error in time-delay estimation in elastography is the decorrelation of the echo signal due to tissue compression (decorrelation noise). Temporal stretching of the postcompression signals has been shown to reduce the decorrelation noise at small strains. In this article, we present a deconvolution filter that reduces the decorrelation even further when applied in conjunction with signal stretching. The performance of the proposed filter is evaluated using simulated data.     

Estimation and reduction of decorrelation effect due to tissue lateral displacement in elastography

In cross-correlation based elastography, the quality of the strain image is degraded by the distortion of echo waveforms due to tissue axial and lateral displacement. To study the effects of tissue lateral displacement on echo decorrelation, a tissue axial stretching model is developed and a concept called correlation signal-to-noise ratio (CSNR) is introduced to quantify the decorrelation effect due to tissue lateral displacement. A computer simulation based on the tissue stretching model is carried out to study the influence of several important elastographic parameters on echo decorrelation due to tissue lateral displacement. Finally, guided by the CSNR concept, a 2-D spatial comprehensive cross-correlation method is proposed to reduce the decorrelation noise. Results indicate that CSNR can be used as a quality indicator of elastography and the 2-D spatial comprehensive cross-correlation method can effectively reduce the decorrelation noise while slightly decreasing the lateral resolution of the strain image     

An adaptive strain estimator for elastography

Elastography is based on the estimation of strain due to applied tissue compression. In conventional elastography, strain is computed from the gradient of the displacement estimates between gated pre- and postcompression echo signals. Gradient-based estimation methods are known to be susceptible to noise. In elastography, in addition to the electronic noise, a principal source of estimation error is the decorrelation of the echo signal as a result of tissue compression (decorrelation noise). Temporal stretching of postcompression signals previously was shown to reduce the decorrelation noise. In this paper, we introduce a novel estimator that uses the stretch factor itself as an estimator of the strain. It uses an iterative algorithm that adaptively maximises the correlation between the pre- and postcompression echo signals by appropriately stretching the latter. We investigate the performance of this adaptive strain estimator using simulated and experimental data. The estimator has exhibited a vastly superior performance compared with the conventional gradient-based estimator.     

Direct and gradient-based average strain estimation by using weighted nearest neighbor cross-correlation peaks

In this paper, two novel approaches, gradientbased and direct strain estimation techniques, are proposed for high-quality average strain imaging incorporating a cost function maximization. Stiffness typically is a continuous function. Consequently, stiffness of proximal tissues is very close to that of the tissue corresponding to a given data window. Hence, a cost function is defined from exponentially weighted neighboring pre- and post-compression RF echo normalized cross-correlation peaks in the lateral (for displacement estimation) or in both the axial and the lateral (for direct strain estimation) directions. This enforces a controlled continuity in displacement/strain and average displacement/strain is calculated from the corresponding maximized cost function. Axial stress causes lateral shift in the tissue. Therefore, a 1-D post-compression echo segment is selected by incorporating Poisson's ratio. Two stretching factors are considered simultaneously in gradient-based strain estimation that allow imaging the lesions properly. The proposed time-domain gradient-based and direct-strain-estimation-based algorithms demonstrate significantly better performance in terms of elastographic signal-to-noise ratio (SNRe), elastographic contrast-to-noise ratio (CNRe), peak signal-to-noise ratio (PSNR), and mean structural similarity (MSSIM) than the other reported time-domain gradientbased and direct-strain-estimation techniques in finite element modeling (FEM) simulation and phantom experiments. For example, in FEM simulation, it has been found that the proposed direct strain estimation method can improve up to approximately 2.49 to 8.71, 2.2 to 6.63, 1.5 to 5, and 1.59 to 2.45 dB in the SNRe, CNRe, PSNR, and MSSIM compared with the traditional direct strain estimation method, respectively, and the proposed gradient-based algorithm demonstrates 2.99 to 16.26, 18.74 to 23.88, 3 to 9.5, and 0.6 to 5.36 dB improvement in the SNRe, CNRe, PSNR, and MSSIM, respectively, compared with a recently reported time-domain gradient-based technique. The range of improvement as noted above is for low to high applied strains. In addition, the comparative results using the in vivo breast data (including malignant or benign masses) also show that the lesion size is better defined by the proposed gradient-based average strain estimation technique.     

Echo decorrelation from displacement gradients in elasticity and velocity estimation

Several ultrasonic techniques for the estimation of blood velocity, tissue motion and elasticity are based on the estimation of displacement through echo time-delay analysis. A common assumption is that tissue displacement is constant within a short observation time used for time delay estimation (TDE). The precision of TDE is mainly limited by noise sources corrupting the echo signals. In addition to electronic and quantization noise, a substantial source of TDE error is the decorrelation of echo signals because of displacement gradients within the observation time. The authors present a theoretical model that describes the mean changes of the crosscorrelation function as a function of observation time and displacement gradient. The gradient is assumed to be small and uniform within the observation time; the decorrelation introduced by the lateral and elevational displacement components is assumed to be small compared with the decorrelation caused by the axial component. The decorrelation model predicts that the expected value of the crosscorrelation function is a low-pass filtered version of the autocorrelation function (i.e., the crosscorrelation obtained without gradients). The filter is a function of the axial gradient and the observation time. This theoretical finding is corroborated experimentally. Limitations imposed by decorrelation in displacement estimation and potential uses of decorrelation in medical ultrasound are discussed.     

2-D companding for noise reduction in strain imaging

Companding is a signal preprocessing technique for improving the precision of correlation-based time delay measurements. In strain imaging, companding is applied to warp 2-D or 3-D ultrasonic echo fields to improve coherence between data acquired before and after compression. It minimizes decorrelation errors, which are the dominant source of strain image noise. The word refers to a spatially variable signal scaling that compresses and expands waveforms acquired in an ultrasonic scan plane or volume. Temporal stretching by the applied strain is a single-scale (global), 1-D companding process that has been used successfully to reduce strain noise. This paper describes a two-scale (global and local), 2-D companding technique that is based on a sum-absolute-difference (SAD) algorithm for blood velocity estimation. Several experiments are presented that demonstrate improvements in target visibility for strain imaging. The results show that, if tissue motion can be confined to the scan plane of a linear array transducer, displacement variance can be reduced two orders of magnitude using 2-D local companding relative to temporal stretching.     

Visualizing the radial and circumferential strain distribution within vessel phantoms using synthetic-aperture ultrasound elastography

Noninvasive elastography (NIVE) produces elastograms that are difficult to interpret because NIVE visualizes strain in the transducer coordinate system. In this paper, we hypothesized that transforming normal and shear strain elastograms to the vessel coordinate system will produce better strain elastograms. To corroborate this hypothesis, we acquired synthetic-aperture (SA) ultrasound data from simulated and physical vessel phantoms. In both studies, SA echo frames were reconstructed from data acquired with a sparse transducer array. The simulation study was performed with homogeneous and heterogenous phantoms, but in the experimental study we used a modified ultrasound scanner to acquire SA data from homogeneous (n = 1) and heterogeneous (n = 3) vessel phantoms. Axial and lateral displacements were estimated by performing two-dimensional cross-correlation analysis on the beamformed RF echo frames. We generated radial and circumferential strain elastograms by transforming normal and shear strain elastograms to the vessel coordinate system. The results revealed: 1) radial and circumferential strain elastograms acquired from simulated data had a relative root mean squared error on the order of 0.1%; 2) experimentally acquired radial and circumferential strain elastograms had elastographic contrast-to-noise ratio (CNRe) between 10 and 40 dB, and elastographic signal-to-noise ratio (SNRe) between 10 and 35 dB, depending on the number of active transmission elements employed during imaging; 3) radial and circumferential strain elastograms produced with fewer than 8 active transmission elements were inferior to those computed with a greater number of active elements; and 4) plaques were evident in the strain elastograms, except in those obtained with the sparsest transducer array. This study demonstrated that a syntheticaperture ultrasound system could visualize radial and circumferential strain noninvasively.     

Three-dimensional tissue motion and its effect on image noise inelastography

In elastography both high correlation coefficient between pre- and post-compression RF signals and high applied strain are required to achieve the best quality in elastograms. Because the elastogram is computed using a 1-D cross-correlation technique applied to a 1-D ultrasound signal, it is assumed that tissue motion occurs only within the axis of compression (axis of the acoustic wave propagation), or at least that the scatterers remain within the acoustic beam during tissue motion. In practice, soft tissues are incompressible and, therefore, the lateral and elevational (out-of-plane) tissue strains are 50% of the applied strain. Therefore, tissue scatterers may move across the beam due to the applied compression. In this paper we address the degradation of the elastographic quality due to the lateral and elevational motion of the scatterers in uniformly elastic media. A full 3-D model predicting the correlation coefficient as measured using 1-D cross-correlations is proposed. It is shown that the signal-to-noise ratio in elastograms (SNR_e) is nonstationary, and that it depends on the beamwidth and on the applied strain. In order to achieve a higher stationary SNR_e, it is proposed to confine the tissue in the lateral direction. Phantom experiments are used to corroborate the theoretical developments     

Improving accuracy in estimation of artery-wall displacement by referring to center frequency of RF echo

Noninvasive measurement of mechanical properties, such as elasticity, of the arterial wall, is useful for diagnosis of atherosclerosis. The elasticity of the arterial wall can be estimated by combining measurement of displacement of the arterial wall with that of blood pressure. In general, the displacement of the arterial wall is estimated from the phase shift of radio frequency (RF) echoes between two consecutive frames using a correlation estimator with quadrature demodulated complex signals. Recently, digitized data of broadband RF echoes are available in modern diagnostic equipment. The Fourier transform can be used to estimate the phase of the RF echo at each frequency within the RF frequency bandwidth. Therefore, the phase shifts between RF echoes of two consecutive frames can be estimated at multiple frequencies. In this estimation, due to object displacement, the RF echo is time shifted in comparison with that of the previous frame. However, the position of the time window for the Fourier transform is not changed between two consecutive frames. This change in relative position between the RF echo and the time window has a strong influence on the estimation of the artery-wall displacement, resulting in error. To suppress this error, the phase shift should be estimated at the actual RF center frequency. In this paper, this error suppression was investigated through simulation experiments and in vivo experiments on the human carotid artery.     

Correlation analysis for angular compounding in strain imaging

Spatial angular compounding for elastography is a new technique that enables the reduction of noise artifacts in elastograms. This technique is most effective when the angular strain estimates to be averaged or compounded are uncorrelated. In this paper, we present a theoretical analysis of the correlation between pre- and postcompression radio-frequency echo signals acquired from the same location but at different beam insonification angles. The accuracy of the theoretical results is verified using radiofrequency pre- and postcompression echo signals acquired using a real-time clinical scanner on tissue-mimicking uniformly elastic and homogenous phantoms. The theory predicts an increased signal decorrelation with an increase in the beam-steered insonification angle as the applied strain increases and for increasing depths in the medium. Theoretical results provide useful information regarding the correlation of the angular strain estimates obtained from different beam angles that helps in finding optimum compounding schemes for elastography.     

Two-dimensional temperature estimation using diagnostic ultrasound

A two-dimensional temperature estimation method was developed based on the detection of shifts in echo location of backscattered ultrasound from a region of tissue undergoing thermal therapy. The echo shifts are due to the combination of the local temperature dependence of speed of sound and thermal expansion in the heated region. A linear relationship between these shifts and the underlying tissue temperature rise is derived from first principles and experimentally validated. The echo shifts are estimated from the correlation of successive backscattered ultrasound frames, and the axial derivative of the accumulated echo shifts is shown to be proportional to the temperature rise. Sharp lateral gradients in the temperature distribution introduce ripple on the estimates of the echo shifts due to a thermo-acoustic lens effect. This ripple can be effectively reduced by filtering the echo shifts along the axial and lateral directions upon differentiation. However, this is achieved at the expense of spatial resolution. Experimental evaluation of the accuracy (0.5 degrees C) and spatial resolution (2 mm) of the algorithm in tissue mimicking phantoms was conducted using a diagnostic ultrasound imaging scanner and a therapeutic ultrasound unit. The estimated temperature maps were overlaid on the gray-scale ultrasound images to illustrate the applicability of this technique for image guidance of focused ultrasound thermal therapy.     

Enhancement of echo-signal correlation in elastography using temporal stretching

Echo-signal decorrelation due to tissue compression is a significant source of error in tissue displacement estimates obtained using crosscorrelation. Tissue displacement estimates are used to compute strain values for imaging the elasticity of biological soft tissues. The correlation coefficient between the pre- and post-compression echo rf signals reduces rapidly with signal decorrelation due to increased compression. Miniscule reductions in the value of the correlation coefficient can have a significant impact on the performance of the strain estimator as illustrated by the strain filter. Reducing the rate of signal decorrelation using temporal stretching (which improves the value of the correlation coefficient), significantly improves the performance of the strain filter. The reduction in the rate of signal decorrelation with the subsequent increase in the correlation coefficient using temporal stretching is discussed in this paper. Theoretical, simulation and experimental results quantify the enhancement in the value of the correlation coefficient attained with temporal stretching.     

Bandwidth and resolution enhancement through pulse compression

A novel pulse compression technique is developed that improves the axial resolution of an ultrasonic imaging system and provides a boost in the echo signal-to-noise ratio (eSNR). The new technique, called the resolution enhancement compression (REC) technique, was validated with simulations and experimental measurements. Image quality was examined in terms of three metrics: the eSNR, the bandwidth, and the axial resolution through the modulation transfer function (MTF). Simulations were conducted with a weakly-focused, single-element ultrasound source with a center frequency of 2.25 MHz. Experimental measurements were carried out with a single-element transducer (f/3) with a center frequency of 2.25 MHz from a planar reflector and wire targets. In simulations, axial resolution of the ultrasonic imaging system was almost doubled using the REC technique (0.29 mm) versus conventional pulsing techniques (0.60 mm). The -3 dB pulse/echo bandwidth was more than doubled from 48% to 97%, and maximum range sidelobes were -40 dB. Experimental measurements revealed an improvement in axial resolution using the REC technique (0.31 mm) versus conventional pulsing (0.44 mm). The -3 dB pulse/echo bandwidth was doubled from 56% to 113%, and maximum range sidelobes were observed at -45 dB. In addition, a significant gain in eSNR (9 to 16.2 dB) was achieved.     

Elasticity reconstruction from displacement and confidence measures of a multi-compressed ultrasound RF sequence

Ultrasound elasticity imaging shows promise as a new way for early detection of cancers by assessing the elastic characteristics of soft tissue. So far the commonly used approach involves solving the so-called inverse elasticity problem of recovering elastic parameters from displacement measurements. We propose a finite-elementbased nonlinear scheme to estimate the elasticity distribution of soft tissue from multi-compressed ultrasound radio frequency (RF) data. An experimental ultrasound workstation has been developed to acquire multi-compressed data. A composite probe was employed as the compression plate. The contact forces and torques were acquired at the same time as imaging. Axial displacements under different static loads are estimated from the RF data before and after deformation using a cross-correlation technique. The confidence of displacement estimates is employed as a weighting factor in solving the objective function describing the inverse elasticity reconstruction problem. A novel splitand- merge strategy is employed over the image sequence in which strain images are used to provide a priori knowledge of the relative stiffness distribution of the tissue to constrain the inverse problem solution. The experimental study has allowed us to investigate the performance of our approach in the controlled environment of simulated and phantom data. For a simulated single inclusion model with 5% axial displacement estimation error, the L2-error between the target and the reconstructed Young's modulus was found to be about 1%. In vivo validation of the proposed method has been carried out and some preliminary results are presented.     

Noise reduction using spatial-angular compounding for elastography

Ultrasound elastography has developed into an imaging modality suitable for detection and diagnosis of cancers in the breast, prostate, and thyroid and for monitoring ablative therapies in the liver, kidneys, and other sites. In this article, a new approach is described that enables the reduction of noise artifacts in elastography without a significant reduction in either the contrast or spatial resolution. The technique uses angular-weighted compounding of local angular strains estimated from echo signals scanned at different insonification angles. Strain estimated along angular insonification directions can be separated into strain tensor components along the axial (direction of compression) and lateral directions. The mechanical stimulus is applied only along one direction. Angular-weighting factors are derived from the relationship between the axial and lateral strains under the assumption of tissue incompressibility. Experimental results using a uniformly elastic, tissue-mimicking phantom demonstrate the improvement in the signal-to-noise ratio obtained with angular-weighted compounding. Variation in the signal-to-noise ratio obtained using different angular increments also is investigated. Elastograms obtained from an inclusion phantom also demonstrate the improvement in contrast detail resolution obtained using spatial-angular compounding.     

Axial strain calculation using a low-pass digital differentiator in ultrasound elastography

In ultrasound elastography, tissue axial strains are calculated from the gradient of the estimated axial displacements. However, the common differentiation operation amplifies the noises in the displacement estimation, especially at high frequencies. In this paper, a low-pass digital differentiator (LPDD) is proposed to calculate the axial strain from the estimated tissue displacement. Several LPDDs that have been well developed in the field of digital signal processing are presented. The corresponding performances are compared qualitatively and quantitatively in computer simulations and in preliminary phantom and in vitro experiments. The results are consistent with the theoretical analysis of the LPDDs.     

Development and evaluation of a high-frequency ultrasound-based system for in vivo strain imaging of the skin

The elastic properties of skin are of great interest in dermatology because they are affected by many pathological conditions. In this paper, a technique for in vivo mechanical strain imaging of the skin based on high-frequency ultrasound (HFUS) is presented. Elastic skin properties are assessed applying suction to the skin surface with a stepwise increased vacuum and estimating the resulting displacements in a spatially resolved manner. Acquired radio frequency (RF) echo signals and their envelope are analyzed for this purpose. A computer-controlled vacuum system with a digital pressure control loop was developed for precise and reproducible deformation. In a first processing step, the skin surface is segmented. Local axial strains inside the skin are estimated from axial displacements, which are estimated from consecutive echo signal frames analyzing the phase of the complex cross correlation function of analytical echo signals. Furthermore, speckle tracking is applied to estimate axial and lateral displacements and to quantify axial and lateral strains. The correlation coefficient of windowed echo signals compensated for displacements are used as a measure to validate the estimated strains, which is essential to accomplish reliable in vivo measurements. Phantom experiments were performed to validate the proposed technique. Results of in vivo measurements are presented, showing the potential for mechanical strain imaging in the skin in vivo.     

Simple and accurate methods for quantifying deformation,disruption, and development in biological tissues

When mechanical factors underlie growth, development, disease or healing, they often function through local regions of tissue where deformation is highly concentrated. Current optical techniques to estimate deformation can lack precision and accuracy in such regions due to challenges in distinguishing a region of concentrated deformation from an error in displacement tracking. Here, we present a simple and general technique for improving the accuracy and precision of strain estimation and an associated technique for distinguishing a concentrated deformation from a tracking error. The strain estimation technique improves accuracy relative to other state-of-the-art algorithms by directly estimating strain fields without first estimating displacements, resulting in a very simple method and low computational cost. The technique for identifying local elevation of strain enables for the first time the successful identification of the onset and consequences of local strain concentrating features such as cracks and tears in a highly strained tissue. We apply these new techniques to demonstrate a novel hypothesis in prenatal wound healing. More generally, the analytical methods we have developed provide a simple tool for quantifying the appearance and magnitude of localized deformation from a series of digital images across a broad range of disciplines.     

Reduction of influence of variation in center frequencies of RF echoes on estimation of artery-wall strain

Atherosclerotic change of the arterial wall leads to a significant change in its elasticity. For assessment of elasticity, measurement of arterial wall deformation is required. For motion estimation, correlation techniques are widely used, and we have developed a phase-sensitive correlation method, namely, the phased-tracking method, to measure the regional strain of the arterial wall due to the heartbeat. Although phase-sensitive methods using demodulated complex signals require less computation in comparison with methods using the correlation between RF signals or iterative methods, the displacement estimated by such phase-sensitive methods are biased when the center frequency of the RF echo apparently varies. One of the reasons for the apparent change in the center frequency would be the interference of echoes from scatterers within the wall. In the present study, a method was introduced to reduce the influence of variation in the center frequencies of RF echoes on the estimation of the artery-wall strain when using the phase-sensitive correlation technique. The improvement in the strain estimation by the proposed method was validated using a phantom. The error from the theoretical strain profile and the standard deviation in strain estimated by the proposed method were 12.0% and 14.1%, respectively, significantly smaller than those (23.7% and 46.2%) obtained by the conventional phase-sensitive correlation method. Furthermore, in the preliminary in vitro experimental results, the strain distribution of the arterial wall well corresponded with pathology, i.e., the region with calcified tissue showed very small strain, and the region almost homogeneously composed of smooth muscle and collagen showed relatively larger strain and clear strain decay with respect to the radial distance from the lumen.     

In-vivo imaging of skin under stress: potential of high-frequency (20 MHz) static 2-D elastography

The aim of this study was to evaluate the potential of high-frequency static two-dimensional (2-D) elastography for in vivo exploration of the mechanical behavior of skin. Our device was based on the combination of a 20 MHz sonographer and a patented extensiometer device able to apply calibrated uniaxial stretching of the skin. We used a new algorithm to compute elastograms that improve elastographic signal-to-noise ratio (SNRe) without sacrificing resolution. Mechanical behavior was described according to the axial strain and lateral displacements induced in the tissue. The efficacy of the strain anpolyvinyl alcohol first evaluated in polyvinyl alcohol (PVA)-cryogel phantoms. Several in vivo experiments then were conducted, mainly with the multistretching averaging method, and demonstrated the potential of this technique in the evaluation of mechanical behavior of the dermis and the hypodermis under stress.