An autocorrelation-based method for improvement of sub-pixel displacement estimation in ultrasound strain imaging

In ultrasound strain and elasticity imaging, an accurate and cost-effective sub-pixel displacement estimator is required because strain/elasticity imaging quality relies on the displacement SNR, which can often be higher if more computational resources are provided. In this paper, we introduce an autocorrelation-based method to cost-effectively improve subpixel displacement estimation quality. To quantitatively evaluate the performance of the autocorrelation method, simulated and tissue-mimicking phantom experiments were performed. The computational cost of the autocorrelation method is also discussed. The results of our study suggest the autocorrelation method can be used for a real-time elasticity imaging system.     

Speckle tracking methods for ultrasonic elasticity imaging using short-time correlation

In ultrasound elasticity imaging, strain decorrelation is a major source of error in displacements estimated using correlation techniques. This error can be significantly decreased by reducing the correlation kernel. Additional gains in signal-to-noise ratio (SNR) are possible by filtering the correlation functions prior to displacement estimation. Tradeoffs between spatial resolution and estimate variance are discussed, and estimation in elasticity imaging is compared to traditional time-delay estimation. Simulations and experiments on gel-based phantoms are presented. The results demonstrate that high resolution, high SNR strain estimates can be computed using small correlation kernels (on the order of the autocorrelation width of the ultrasound signal) and correlation filtering.     

Frequency-locked pulse sequencer for high-frame-rate monochromatic tissue motion imaging

To overcome the inherent low frame rate of conventional ultrasound, we have previously presented a system that can be implemented on conventional ultrasound scanners for high-frame-rate imaging of monochromatic tissue motion. The system employs a sector subdivision technique in the sequencer to increase the acquisition rate. To eliminate the delays introduced during data acquisition, a motion phase correction algorithm has also been introduced to create in-phase displacement images. Previous experimental results from tissue- mimicking phantoms showed that the system can achieve effective frame rates of up to a few kilohertz on conventional ultrasound systems. In this short communication, we present a new pulse sequencing strategy that facilitates high-frame-rate imaging of monochromatic motion such that the acquired echo signals are inherently in-phase. The sequencer uses the knowledge of the excitation frequency to synchronize the acquisition of the entire imaging plane to that of an external exciter. This sequencing approach eliminates any need for synchronization or phase correction and has applications in tissue elastography, which we demonstrate with tissue-mimicking phantoms.     

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.     

Comparison of template-matching and singular-spectrum-analysis methods for imaging implanted brachytherapy seeds

Brachytherapy using small implanted radioactive seeds is becoming an increasingly popular method for treating prostate cancer, in which a radiation oncologist implants seeds in the prostate transperineally under ultrasound guidance. Dosimetry software determines the optimal placement of seeds for achieving the prescribed dose based on ultrasonic determination of the gland boundaries. However, because of prostate movement and distortion during the implantation procedure, some seeds may not be placed in the desired locations; this causes the delivered dose to differ from the prescribed dose. Current ultrasonic imaging methods generally cannot depict the implanted seeds accurately. We are investigating new ultrasonic imaging methods that show promise for enhancing the visibility of seeds and thereby enabling real-time detection and correction of seed-placement errors during the implantation procedure. Real-time correction of seed-placement errors will improve the therapeutic radiation dose delivered to target tissues. In this work, we compare the potential performance of a template-matching method and a previously published method based on singular spectrum analysis for imaging seeds. In particular, we evaluated how changes in seed angle and position relative to the ultrasound beam affect seed detection. The conclusion of the present study is that singular spectrum analysis has better sensitivity but template matching is more resistant to false positives; both perform well enough to make seed detection clinically feasible over a relevant range of angles and positions. Combining the information provided by the two methods may further reduce ambiguities in determining where seeds are located.     

Noninvasive thermometry assisted by a dual-function ultrasound transducer for mild hyperthermia

Mild hyperthermia is increasingly important for the activation of temperature-sensitive drug delivery vehicles. Noninvasive ultrasound thermometry based on a 2-D speckle tracking algorithm was examined in this study. Here, a commercial ultrasound scanner, a customized co-linear array transducer, and a controlling PC system were used to generate mild hyperthermia. Because the co-linear array transducer is capable of both therapy and imaging at widely separated frequencies, RF image frames were acquired during therapeutic insonation and then exported for off-line analysis. For in vivo studies in a mouse model, before temperature estimation, motion correction was applied between a reference RF frame and subsequent RF frames. Both in vitro and in vivo experiments were examined; in the in vitro and in vivo studies, the average temperature error had a standard deviation of 0.7°C and 0.8°C, respectively. The application of motion correction improved the accuracy of temperature estimation, where the error range was 1.9 to 4.5°C without correction compared with 1.1 to 1.0°C following correction. This study demonstrates the feasibility of combining therapy and monitoring using a commercial system. In the future, real-time temperature estimation will be incorporated into this system.     

Temperature estimation using ultrasonic spatial compound imaging

The feasibility of temperature estimation during high-intensity focused ultrasound therapy using pulse-echo diagnostic ultrasound data has been demonstrated. This method is based upon the measurement of thermally-induced modifications in backscattered RF echoes due to thermal expansion and local changes in the speed of sound. It has been shown that strong ripple artifacts due to the thermo-acoustic lens effect severely corrupt the temperature estimates behind the heated region. We propose here a new imaging technique that improves the temperature estimation behind the heated region and reduces the variance of the temperature estimates in the entire image. We replaced the conventional beamforming on transmit with multiple steered plane wave insonifications using several subapertures. A two-dimensional temperature map is estimated from axial displacement maps between consecutive RF images of identically steered plane wave insonifications. Temperature estimation is then improved by averaging the two-dimensional maps from the multiple steered plane wave insonifications. Experiments were conducted in a tissue-mimicking gelatin-based phantom and in fresh bovine liver.     

Strain imaging using conventional and ultrafast ultrasound imaging: numerical analysis

In elasticity imaging, the ultrasound frames acquired during tissue deformation are analyzed to estimate the internal displacements and strains. If the deformation rate is high, high-frame-rate imaging techniques are required to avoid the severe decorrelation between the neighboring ultrasound images. In these high-frame-rate techniques, however, the broader and less focused ultrasound beam is transmitted and, hence, the image quality is degraded. We quantitatively compared strain images obtained using conventional and ultrafast ultrasound imaging methods. The performance of the elasticity imaging was evaluated using custom-designed, numerical simulations. Our results demonstrate that signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR) and spatial resolutions in displacement and strain images acquired using conventional and ultrafast ultrasound imaging are comparable. This study suggests that the high-frame-rate ultrasound imaging can be reliably used in elasticity imaging if frame rate is critical     

Comparison of 2-D speckle tracking and tissue Doppler imaging in an isolated rabbit heart model

Ultrasound strain imaging has been proposed to quantitatively assess myocardial contractility. Cross-correlation-based 2-D speckle tracking (ST) and auto-correlation-based tissue Doppler imaging (TDI) [often called Doppler tissue imaging (DTI)] are competitive ultrasound techniques for this application. Compared with 2-D ST, TDI, as a 1-D method, is sensitive to beam angle and suffers from low strain signal-to-noise ratio because a high pulse repetition frequency is required to avoid aliasing in velocity estimation. In addition, ST and TDI are fundamentally different in the way that physical parameters such as the mechanical strain are derived, resulting in different estimation accuracy and interpretation. In this study, we directly compared the accuracy of TDI and 2-D ST estimates of instantaneous axial normal strain and accumulated axial normal strain using a simulated heart. We then used an isolated rabbit heart model of acute ischemia produced by left descending anterior artery ligation to evaluate the performance of the two methods in detecting abnormal motion. Results showed that instantaneous axial normal strains derived using TDI (0.36% error) were less accurate with larger variance than those derived from 2-D ST (0.08% error) given the same spatial resolution. In addition to poorer accuracy, accumulated axial normal strain estimates derived using TDI suffered from bias, because the accumulation method for TDI cannot trace along the actual tissue displacement path. Finally, we demonstrated the advantage 2-D ST has over TDI to reduce dependency on beam angle for lesion detection by estimating strains based on the principal stretches and their corresponding principal axes.     

Ultrasound attenuation measurement in the presence of scatterer variation for reduction of shadowing and enhancement

Pulse-echo ultrasound display relies on many assumptions that are known to be incorrect. Departure from these makes interpretation of conventional ultrasound images difficult, and three-dimensional (3-D) visualizations harder still. For instance, shadowing and enhancement are the result of an incorrect assumption that sound attenuation is a function only of depth. Attempts to reduce such artefacts by estimating attenuation locally have been frustrated by large statistical variations and the influence of scatterer type. We address the latter by examining the influence of scatterer type on two existing attenuation estimation algorithms. This analysis is novel for one of the algorithms, and contains a correction to previously published work for the other. We then propose a novel algorithm that is less sensitive to scatterer variation. We also present a novel technique for handling large statistical variations based on combined assumptions of monotonicity and smoothness. We then assess the performance of each algorithm for correcting shadowing and enhancement in in vitro data, using a real time 3-D radio frequency (RF) ultrasound acquisition system developed for this purpose. The results show visible differences in attenuation estimates from each technique, which are supported by the theoretical analysis. The novel attenuation estimation algorithm does show less sensitivity to scatterer variation, though it results in a more noisy estimate. Nevertheless, the novel technique for reducing statistical variations is sufficient to allow some degree of correction of shadowing and enhancement in each case.     

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.     

Uniform precision ultrasound strain imaging

Ultrasound strain imaging is becoming increasingly popular as a way to measure stiffness variation in soft tissue. Almost all techniques involve the estimation of a field of relative displacements between measurements of tissue undergoing different deformations. These estimates are often high resolution, but some form of smoothing is required to increase the precision, either by direct filtering or as part of the gradient estimation process. Such methods generate uniform resolution images, but strain quality typically varies considerably within each image, hence a trade-off is necessary between increasing precision in the low-quality regions and reducing resolution in the high-quality regions. We introduce a smoothing technique, developed from the nonparametric regression literature, which can avoid this trade-off by generating uniform precision images. In such an image, high resolution is retained in areas of high strain quality but sacrificed for the sake of increased precision in low-quality areas. We contrast the algorithm with other methods on simulated, phantom, and clinical data, for both 2-D and 3-D strain imaging. We also show how the technique can be efficiently implemented at real-time rates with realistic parameters on modest hardware. Uniform precision nonparametric regression promises to be a useful tool in ultrasound strain imaging.     

Elasticity imaging using conventional and high-frame rate ultrasound imaging: experimental study

High-frame rate ultrasound imaging is necessary to track fast deformation in ultrasound elasticity imaging, but the image quality may be degraded. Previously, we investigated the performance of strain imaging using numerical models of conventional and ultrafast ultrasound imaging techniques. In this paper, we performed experimental studies to quantitatively evaluate the strain images and elasticity maps obtained using conventional and high frame rate ultrasound imaging methods. The experiments were carried out using point target and tissue mimicking phantoms. The experimental results were compared with the results of numerical simulation. Our experimental studies confirm that the signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and axial/lateral resolution of the displacement and strain images acquired using high-frame rate ultrasound imaging are slightly lower but comparable with those obtained using conventional imaging. Furthermore, the quality of elasticity images also exhibits similar trends. Thus, high-frame rate ultrasound imaging can be used reliably for static elasticity imaging to capture the internal tissue motion if the frame rate is critical.     

Improving IVUS palpography by incorporation of motion compensation based on block matching and optical flow

Intravascular ultrasound (IVUS) strain imaging of the luminal layer in coronary arteries, coined as IVUS palpography, utilizes conventional radio frequency (RF) signals acquired at 2 different levels of a compressional load. The signals are cross-correlated to obtain the microscopic tissue displacements, which can be directly translated into local strain of the vessel wall. However, (apparent) tissue motion and nonuniform deformation of the vessel wall, due to catheter wiggling, reduce signal correlation and result in invalid strain estimates. Implications of probe motion were studied on the tissue-mimicking phantom. The measured circumferential tissue displacement and level of the speckle decorrelation amounted to 12° and 0.58, respectively, for the catheter displacement of 456 μm. To compensate for the motion artifacts in IVUS palpography, a novel method based on the feature-based scale-space optical flow (OF), and classical block matching (BM) algorithm, were employed. The computed OF vector and BM displacement fields quantify the amount of local tissue misalignment in consecutive frames. Subsequently, the extracted circumferential displacements are used to realign the signals before strain computation. Motion compensation reduces the RF signal decorrelation and increases the number of valid strain estimates. The advantage of applying the motion correction in IVUS palpography was demonstrated in a midscale validation study on 14 in vivo pullbacks. Both methods substantially increase the number of valid strain estimates in the partial and compounded palpograms. Mean relative improvement in the number of valid strain estimates with motion compensation in comparison to one without motion compensation amounts to 28% and 14%, respectively. Implementation of motion compensation methods boosts the diagnostic value of IVUS palpography.     

Frequency-domain-based strain estimation and high-frame-rate imaging for quasi-static elastography

In freehand elastography, quasi-static tissue compression is applied through the ultrasound probe, and the corresponding axial strain is estimated by calculating the time shift between consecutive echo signals. This calculation typically suffers from a poor signal-to-noise ratio or from the decorrelation between consecutive echoes resulting from an erroneous axial motion impressed by the operator. This paper shows that the quality of elastograms can be improved through the integration of two distinct techniques in the strain estimation procedure. The first technique evaluates the displacement of the tissue by analyzing the phases of the echo signal spectra acquired during compression. The second technique increases the displacement estimation robustness by averaging multiple displacement estimations in a high-frame-rate imaging system, while maintaining the typical elastogram frame-rate. The experimental results, obtained with the Ultrasound Advanced Open Platform (ULA-OP) and a cyst phantom, demonstrate that each of the proposed methods can independently improve the quality of elastograms, and that further improvements are possible through their combination.     

A benchmark study of reduced‐strain shell finite elements: quadratic schemes

We study experimentally the accuracy and reliability of some low‐order shell finite element schemes based on modifying the standard displacement formulation by reduced‐strain expressions. We focus on quadrilateral elements with a quadratic displacement approximation. Three benchmark problems with different asymptotic behaviour in the limit of zero shell thickness is used in the experiments. Following the error analysis of a reduced‐strain scheme, we study two components of the total error, the approximation error and the consistency error. We demonstrate that the performance of the methods is both case and mesh dependent. When a bending dominated problem is solved, none of the methods studied can avoid the usual worst‐case locking effect of the approximation error on general meshes. For a membrane dominated problem the total error is typically dominated by the consistency error which often convergences slowly. Copyright © 2000 John Wiley & Sons, Ltd.     

Angular strain estimation method for elastography

In the conventional cross-correlation-based strain estimation, there is a trade-off between the interpolation accuracy and the computational requirement. On the other hand, the autocorrelation-based method does not need interpolation, but it cannot estimate the wide range of displacements for elastography. We have developed a new strain estimator, called the angular strain estimation method, which does not need any interpolation and can estimate strain without restricting the range of displacements. The new method estimates strain utilizing complex correlation between correlated ultrasound signals from pre-and post-compression frames. From simulation and experiments, we found that the angular strain estimation method improves the accuracy and strain image quality compared to the conventional strain estimator using cross correlation with interpolation. Furthermore, it is computationally efficient and can be readily incorporated in ultrasound machines for rea -time elastography.     

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.     

Phase-based ultrasonic deformation estimation

Deformation estimation is the foundation of emerging techniques for imaging the mechanical properties of soft tissues. We present theoretical analysis and experimental results from an investigation of phase-based ultrasonic deformation estimators. Numerous phase-based algorithm variants were tested quantitatively on simulated RF data from uniform scatterer fields, subject to a range of uniform strain deformations. Particular attention is paid to a new algorithm, weighted phase separation, the performance of which is demonstrated in application to in vivo freehand strain imaging. Good results support the theory that underlies the new algorithm, and more generally highlight the factors that should be considered in the design of high performance deformation estimators for practical applications. For context, note that this represents progress with an algorithm class that is suitable for real-time applications, yet has already been shown quantitatively to offer greater accuracy over a wide range of scanning conditions than adaptive companding methods based on correlation coefficient or sum of absolute differences.