Performance of Two Dimensional Displacement and Strain Estimation Techniques Using a Phased Array Transducer

Ultrasound strain imaging utilizes radio-frequency (RF) ultrasound echo signals to estimate the relative elasticity of tissue under deformation. Due to the diagnostic value inherent in tissue elasticity, ultrasound strain imaging has found widespread clinical and preclinical applications. Accurate displacement estimation using pre and post-deformation RF signals is a crucial first step to derive high quality strain tensor images. Incorporating regularization into the displacement estimation framework is a commonly employed strategy to improve estimation accuracy and precision. In this work, we propose an adaptive variation of the iterative Bayesian regularization scheme utilizing RF similarity metric signal-to-noise ratio previously proposed by our group. The regularization scheme is incorporated into a 2D multi-level block matching (BM) algorithm for motion estimation. Adaptive nature of our algorithm is attributed to the dynamic variation of iteration number based on the normalized cross-correlation (NCC) function quality and a similarity measure between pre-deformation and motion compensated post-deformation RF signals. The proposed method is validated for either quasi-static and cardiac elastography or strain imaging applications using uniform and inclusion phantoms and canine cardiac deformation simulation models. Performance of adaptive Bayesian regularization was compared to conventional NCC and Bayesian regularization with fixed number of iterations. Results from uniform phantom simulation study show significant improvement in lateral displacement and strain estimation accuracy. For instance, at 1.5% lateral strain in a uniform phantom, Bayesian regularization with five iterations incurred a lateral strain error of 104.49%, which was significantly reduced using our adaptive approach to 27.51% (p < 0.001). Contrast-to-noise (CNRe) ratios obtained from inclusion phantom indicate improved lesion detectability for both axial and lateral strain images. For instance, at 1.5% lateral strain, Bayesian regularization with five iterations had lateral CNRe of −0.31 dB which was significantly increased using the adaptive approach to 7.42 dB (p < 0.001). Similar results are seen with cardiac deformation modelling with improvement in myocardial strain images. In vivo feasibility was also demonstrated using data from a healthy murine heart. Overall, the proposed method makes Bayesian regularization robust for clinical and preclinical applications.

Ultrasound strain imaging maps the tissue stiffness in the region of interest by estimating strain when the tissue is stressed. Prestress and poststress ultrasound echoes are processed to estimate the displacements, and the strain image is computed by a spatial derivative of the estimated displacement. Due to the nature of derivative operations, smaller errors in displacement estimation can cause large noise in the computed strain image. When tissue displacements are estimated using the phase of the autocorrelation between the prestress and poststress data (i.e., 1D autocorrelation method), it has been previously reported that local variations in ultrasonic center frequency due to speckle can introduce errors in the estimated displacement. We have developed a new method to compute strain based on two-dimensional autocorrelation. By estimating the local ultrasound frequency, we can improve the accuracy of displacement estimates and hence reduce the noise in strain images. We have analyzed the effect of local frequency changes on noise in strain images and the improvement in the strain signal-to-noise ratio with the 2D autocorrelation method. The simulation results are supported by experiments with homogenous gelatin phantoms and show that strain signal-to-noise ratio with 2D autocorrelation is consistently higher than that with 1D autocorrelation. The 2D autocorrelation can increase the strain signal-to-noise ratio by up to 200%, which leads us to believe that our estimation method can significantly improve the quality of strain images.

The common process of window-based ultrasound elastography (USE) is based on estimating the displacement fields and calculating the strain images by differentiating them. The displacement fields can be obtained using operators such as normalized cross-correlation (NCC). However, the provided displacements suffer from the artifacts caused by two dominant sources, the decorrelation, and amplitude modulation (AM) error. The main contribution of this study is to obtain strain images of higher quality and reduce the effect of artifacts. To this end, a weighted displacement estimation method is proposed. The proposed method consists of two steps. Some changes are applied to the windowing process, speeding up displacement estimation using the NCC method and filtering the provided displacements in two stages using median and weighted windows. We have assessed the performance of different weighted windows in conjunction with NCC on simulation and phantom data. This evaluation has not been implemented on the displacement fields yet. Thus, we tried to represent their improving effects on the estimated strains compared to the simple NCC approach and suggest the best window. The quantitative evaluation is performed in terms of elastographic signal to noise ratio (SNRe) and elastographic contrast to noise ratio (CNRe) on simulation and phantom data. The root mean square error (RMSE) comparison is also implemented for the simulation data. The visual and quantitative comparisons reveal that the proposed method substantially reduces artifacts, improves the strain image quality, and outperforms the NCC method.

In this paper, two novel approaches, gradient-based 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 gradient-based 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.

With the rapid development of computer vision, vision cameras have been used as noncontact sensors for structural displacement measurements. However, vision-based techniques are limited to short-term displacement measurements because of their degraded performance under varying illumination and inability to operate at night. To overcome these limitations, this study developed a continuous structural displacement estimation technique by combining measurements from an accelerometer with vision and infrared (IR) cameras collocated at the displacement estimation point of a target structure. The proposed technique enables continuous displacement estimation for both day and night, automatic optimization of the temperature range of an infrared camera to ensure a region of interest (ROI) with good matching features, and adaptive updating of the reference frame to achieve robust illumination–displacement estimation from vision/IR measurements. The performance of the proposed method was verified through lab-scale tests on a single-story building model. The displacements were estimated with a root-mean-square error of less than 2 mm compared with the laser-based ground truth. In addition, the applicability of the IR camera for displacement estimation under field conditions was validated using a pedestrian bridge test. The proposed technique eliminates the need for a stationary sensor installation location by the on-site installation of sensors and is therefore attractive for long-term continuous monitoring. However, it only estimates displacement at the sensor installation location, and cannot simultaneously estimate multi-point displacements which can be achieved by installing cameras off-site.

We present the split-merge displacement estimation algorithm as a bridge between the standard, block matching, displacement estimation technique and the semantic motion estimation techniques. We review this new technique and its applications in video compression and show how it can be used to maintain two different segmentation of the current visual field: a spatial segmentation identifying the objects that are present in the scene and a classification of the visual field into moving areas, that keeps track over time of the relationships between the objects.

This research project examines the applicability of novel spectral domain strain estimation algorithms to improve the clinical value of tissue elasticity images. Pathological changes can be frequently correlated to changes in soft tissue stiffness. Despite the fact that many cancers, including those found in the breast and prostate, often manifest themselves as stiff focal lesions, there location and shape can make them difficult, if not impossible, to detect during a palpation-based physical examination. The mechanical properties of tissue cannot be measured directly using any current imaging modality. However, an ultrasound-based technique known as elastography has evolved over the last fifteen years which is capable of estimating relative strain distributions in soft tissue. Under certain conditions, these strain images (elastograms) can give a clear depiction of the underlying tissue stiffness distributions, and thus, can be used as a clinical tool for the detection of pathological lesions. Conventionally elastographic techniques estimate tissue strain by tracking spatial features found in congruent pairs of ultrasonic echo backscattered signals before and after a small, quasistatic compression is applied to the tissue surface via the ultrasound transducer. Although this technique has shown promise from a clinical perspective in detecting both benign and malignant lesions of the breast and prostate, it is sensitive to extraneous motions that ultimately compromise the strain estimation procedure. To alleviate this problem, the applicability of spectral-domain strain estimation algorithms and techniques were examined. Both simulation and experimental (in vitro) results obtained using an elastographic phantom indicate that this approach holds promise to improve the clinical value of the images produced. Also, initial results obtained using a novel elastographic animal model further support the efficacy of spectral-based strain imaging in vivo.

Strain imaging has been performed using 1D, 2D and 3D ultrasound data. Usually, strain is only estimated in the beam direction, because of the availability of phase information. However, strain estimates in other directions are also desired, since most tissues are anisotropic. Beam steering enables measurement of different projections of the 2D displacement field while using phase information. The full 2D displacement field and strain tensor can be derived using multiple projections. This study aims at deriving the full 2D strain tensor by estimating only displacement along the beam while steering the beam at three angles, i.e. 0?, a positive, and a negative beam steering angle. Displacements were iteratively estimated using 2D cross-correlations. The 0? acquisition yielded the vertical displacement vector. Projection of the other measured displacements yielded the horizontal (lateral) vector. The full 2D strain tensor was derived using 1D least squares strain estimators. Since horizontal displacements and strains are usually the least accurate, these were first focused on. Horizontal displacements were estimated for simulated radiofrequency (rf) data of a block with a four times stiffer cylindrical inclusion before and after application of 2% vertical compression. Root mean squared error (RMSE) of the horizontal displacements were calculated for every symmetric pair of beam steering angles in the range of -30 to 30? with angular increments of 5?. The RMSE analysis was performed for signal-to-noise (SNR) levels of 5, 10, 20 and 50 dB. Beam steering combinations of about -25? and 25? were found to be most optimal. The technique's performance was maintained regardless of the SNR level. For an SNR of 5 dB a reduction in RMSE of up to 70% was observed. In analogy with the simulations, experiments were performed with a similar inclusion phantom made of polyvinyl alcohol. Using data from beam steering angles of -25?, 0? and 25? strain images were constructed for all strain components and compared to strain images constructed without beam steering. The horizontal and shear strain images improved clearly with beam steering. Finally, the technique was also applied to derive radial and circumferential strain images for a homogeneous vessel phantom made of gelatin. Radially, SNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> and CNR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">e</sub> increased with 2.2 dB and 8 dB and circumferentially with 2.6 dB and 9.2 dB compared to non steered strain estimates. To conclude, the full 2D strain tensor can be accurately measured by using three beam steering angles.

We demonstrate the feasibility of ultrasound saline infused sonohysterography based strain imaging, for the determination of variations in the stiffness of uterine masses in-vivo. Strain images are estimated using a two-dimensional multilevel hybrid algorithm developed for ultrasound sector array transducers. Coarse displacements are initially estimated using envelope data, followed by guided finer displacement estimation using window lengths on the order of 4 wavelengths and 5A-lines on RF data. Strain images are obtained by estimating displacement slopes using least squares estimation. The strain images provide additional new information that may supplement current clinical B-mode imaging, used for diagnosis of uterine abnormalities. Stiffer masses such as fibroids are clearly differentiated on the strain images, which appear to be darker on the strain images with the characteristic decorrelation "halo" when compared to the normal uterine tissue. In addition, uterine polyps are visualized with a lighter grayscale when compared to the background myometrium, indicating the presence of a softer mass. Our results demonstrate the feasibility of improving clinical diagnosis based on strain imaging.

Elastography holds great promises for the additional characterization of lesions especially in the domain of breast cancer diagnosis. Most ultrasound based approaches have so far been limited to a one dimensional (1D) or at most two dimensional (2D) displacement estimation in one plane. This leads for the general case to sparse data which cannot be used to solve the full three dimensional (3D) wave equation in an unbiased manner. For instance contributions from the compressional wave cannot be removed via application of the curl operator. In order to overcome this limitation we developed an ultrasound based elastography system which uses the concept of computed tomography for data acquisition in combination with 2D vector displacement estimation within the plane of the ultrasound beam. The vector displacement estimation is achieved using the concept of adaptive subapertures during the receive beamforming process. The object of interest is scanned using a conventional ultrasonic probe (4 MHz, 128 elements) from different directions on a circular orbit. The transducer is translated perpendicular to the orbit (~10 times) for each angle which leads to several block datasets (~30 blocks) each containing 2D displacement information. Thereby, the displacement of each voxel within the object is measured several times from different directions. This provides high resolution volumic 3D displacement fields after regridding each dataset from polar to Cartesian coordinates. The data acquisition system is contained within a water tank underneath a standard breast biopsy table. This enables in vivo measurements with the patient in prone position. Thereby, the 3D acquisition as already developed in the area of magnetic resonance elastography (MRE), is brought to the ultrasonic field. Initial phantom experiments were conducted with steady state mechanical excitation at 150 Hz. Inclusions are clearly visible in the complex shear modulus as reconstructed from inverting the full 3D wave equation. Taking benefit of the ultrafast acquisition speed of our ultrasound system, the proposed method allows to measure volumic datasets within clinically acceptable time. The method provides for each voxel of the 3D volume the frequency dependence of the complex shear modulus which in turn is linked to the underlying rheology of the material. This represents the proof of concept for a spectroscopic approach of elastography suitable for clinical application. The system enables the study of rheological properties of tumors which should further extend the diagnostic gain of elastography

Echocardiography is the most prevalent imaging modalities in clinical cardiology. However, current diagnostic techniques rely on qualitative image analysis, ignoring the quantitative data inherent to this modality. We seek to develop a quantitative system for analyzing echocardiographic images. In this study, the performance of myocardial elastography was tested under motion-induced decorrelation noise using a tissue- mimicking phantom of the human left ventricle (LV) that underwent physiologic, cardiac motion configurations. A Terason system (Teratech Corp., Burlington, MA, USA.) with a phased array transducer (128 elements, 3.5 MHz) was utilized to acquire radiofrequency (RF) data in a short-axis view of a cylindrical polyacrylamide phantom with geometric (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> = 28 mm, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> = 15 mm, L = 15 cm) and mechanical properties (E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">wall</sub> = 50 kPa + agar scatterers; E <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">core</sub> = 10 kPa) similar to those of an adult, healthy LV. The phantom underwent two motion configurations - either pure rotation, with the non-rotating end of the phantom being free, or torsion with the non-rotating end being fixed; the latter in order to simulate the "wringing" action of the LV. This provided a realistic motion pattern for decorrelation noise and rotational motion analysis. RF data were acquired at multiple slices to assess differential displacements under these motion configurations. In-plane (lateral and axial) displacements were iteratively estimated using a 1D cross-correlation and recorrelation technique in a 2D search (4.10 mm window with 75% overlap) and then radial, circumferential, and angular displacements were calculated via a coordinate transformation. Second, in-plane strains were calculated using a least-squares strain estimator. Radial and circumferential strains were then computed based on a similar coordinate transformation. The observed displacement estimates were in accordance with the theoretically predicted results. During pure rotation, all regions of the phantom exhibited similar displacements and minute strains. In the case of torsion, in-plane strains were again insignificant, but analysis of multiple slices revealed differential motion resulting from the imposed constraint on rotation. Ongoing studies aim at investigating the reproducibility of the measurements as well as studying more complex motion configurations, including simultaneous radial deformation and flow.

Atherosclerotic plaque rupture can initiate stroke or myocardial infarction. Lipid-rich plaques with thin fibrous caps have a higher risk to rupture than fibrotic plaques. Elastic moduli differ for lipid-rich and fibrous tissue and can be reconstructed using tissue displacements estimated from intravascular ultrasound radiofrequency (RF) data acquisitions. This study investigated if modulus reconstruction is possible for noninvasive RF acquisitions of vessels in transverse imaging planes using an iterative 2D cross-correlation based displacement estimation algorithm. Furthermore, since it is known that displacements can be improved by compounding of displacements estimated at various beam steering angles, we compared the performance of the modulus reconstruction with and without compounding. For the comparison, simulated and experimental RF data were generated of various vessel-mimicking phantoms. Reconstruction errors were less than 10%, which seems adequate for distinguishing lipid-rich from fibrous tissue. Compounding outperformed single-angle reconstruction: the interquartile range of the reconstructed moduli for the various homogeneous phantom layers was approximately two times smaller. Additionally, the estimated lateral displacements were a factor of 2–3 better matched to the displacements corresponding to the reconstructed modulus distribution. Thus, noninvasive elastic modulus reconstruction is possible for transverse vessel cross sections using this cross-correlation method and is more accurate with compounding.

The cardiac elastography aims at identification of non-transmural infarctions. Two displacement estimation methods in such an application using synthetic ultrasonic data are studied. Reference was obtained from Finite Element Modelling. Models had the form of half of an ellipsoid with 15 mm wall thickness. The homogenous model, models with transmural and nontransmural inclusion were designed. Deformation of the models was simulated using Abaqus. Ultrasonic data of LAX and SAX views were generated using Field II. Radial (dR) and lateral (dL) displacements were estimated using a 2D correlation search with 2D stretching (2DCS) and B-spline (BS) method. Strains were estimated using least squares estimator. Mean Absolute Error (MAE) of the dR in the LAX view was approx. 6[μm] for 2DCS and 8[μm] for BS, that of the dL 30 and 24[&mu;m] respectively. MAE of the second component of the principal strain (epsilon)₂ was 0.10 and 0.14[%], respectively. Corresponding values for SAX view were 7, 10, 42, 52[&mu;m] and 0.47 and 1.08[%]. In the LAX view both estimation methods result in the (epsilon)₂ behavior coherent with the presence of the inclusion, with the 2DCS results closer to the reference. In the SAX view the BS approach results in high errors of the estimate. The (epsilon)₂ profiles, LAX view, show minor discrepancies with respect to the reference and show the effect of the inclusion. The (epsilon)₂ profiles, SAX view, obtained from displacements estimated using the BS method strongly deviate from the reference. Block matching performs better in application to the local strain estimation.

Los desarrollos ocurridos en las últimas décadas, tanto en los métodos numéricos de solución de problemas de ingeniería geo-sísmica, como licuación y sus efectos, así como en la tecnología computacional, ha permitido que el uso de técnicas rigurosas de modelado matemático sean más frecuentes en ingeniería aplicada. Sin embargo, para el caso particular de la estimación de desplazamientos laterales inducidos por sismos, (asociados a la licuación de áreas extensas de terreno), resulta complicado para llevar a cabo análisis detallados que involucren modelos bi y tridimensionales. Es común el recurrir a estimaciones estadísticas, o inclusive a predicciones obtenidas con sistemas neurodifusos. En este artículo, se introduce un enfoque simplificado para calcular los desplazamientos laterales inducidos por sismos cuando se presenta licuación. La respuesta dinámica de un perfil de suelo es simulada a través de elementos finitos unidimensionales acoplados a un esquema de generación de presiones de poro. La ecuación de movimiento se resuelve en el dominio del tiempo y con base en cada incremento de presión de poro. Los parámetros de resistencia y dinámicos del suelo se modifican, permitiendo la estimación de los desplazamientos del suelo que ocurren durante el evento dinámico. La formulación propuesta se aplica al análisis de varios casos de estudio en donde se realizaron mediciones de desplazamientos laterales.

Structural displacement estimation by fusing vision camera and accelerometer using hybrid computer vision algorithm and adaptive multi-rate Kalman filter