Single-pulse tissue doppler using synthetic transmit beams

Tissue Doppler imaging (TDI) is a common technique for investigating myocardial function. Typically, B-mode data and TDI data are recorded using separate acquisitions and combined into a single, color overlaid image. In this work, we present a novel method for TDI imaging, where both TDI and B-mode are created from the same acquisition. Velocities are calculated from the phase shift between neighboring transmit events in the B-mode scan; hence the name singlepulse tissue Doppler (SPTD). Using a novel transmit beam interleaving pattern, this method provides TDI and B-mode at the same high frame rate with an adjustable Nyquist velocity limit. Through simulations and measurements, this work investigates the bias and variance of the SPTD velocities and compares the estimates to those of the conventional TDI autocorrelation estimation method. The results showed that the method introduces an additional bias and variance in the velocity estimates compared with conventional TDI. However, by applying bias compensation, the SPTD velocity estimates were close to those of regular TDI. Using SPTD, the whole left ventricle was imaged within a 65-degree sector at a frame rate of 110 frames per second (43 transmissions per frame).     

Theoretical quality assessment of myocardial elastography with in vivo validation

Myocardial elastography (ME), a radio frequency (RF)-based speckle tracking technique with one-dimensional (1-D) cross correlation and novel recorrelation methods in a 2-D search was proposed to estimate and fully image 2-D transmural deformation field and to detect abnormal cardiac function. A theoretical framework was first developed in order to evaluate the performance of 2-D myocardial elastography based on a previously developed 3-D finite-element model of the canine left ventricle. A normal (control) and an ischemic (left-circumflex, LCx) model, which more completely represented myocardial deformation than a kinematic model, were considered. A 2-D convolutional image formation model was first used to generate RF signals for quality assessment of ME in the normal and ischemic cases. A 3-D image formation model was further developed to investigate the effect of the out-of-plane motion on the 2-D, in-plane motion estimation. Both orthogonal, in-plane displacement components (i.e., lateral and axial) between consecutive RF frames were iteratively estimated. All the estimated incremental 2-D displacements from end-diastole (ED) to end-systole (ES) were then accumulated to acquire the cumulative 2-D displacements, which were further used to calculate the cumulative 2-D systolic finite strains. Furthermore, the cumulative systolic radial and circumferential strains, which were angle- and frame-rate independent, were obtained from the 2-D finite-strain components and imaged in full view to detect the ischemic region. We also explored the theoretical understanding of the limitations of our technique for the accurate depiction of disease and validated it in vivo against tagged magnetic resonance imaging (tMRI) in the case of a normal human myocardium in a 2-D short-axis (SA) echocardiographic view. The theoretical framework succeeded in demonstrating that the 2-D myocardial elastography technique was a reliable tool for the complete estimation and depiction of the in-plane myocardial deformation field as well as for accurate identification of pathological mechanical function using established finite-element, left-ventricular canine models. In a preliminary study, the 2-D myocardial elastography was shown capable of imaging myocardial deformation comparable to equivalent tMRI estimates in a clinical setting.     

An elasticity microscope. Part II: Experimental results

For pt.I see ibid., vol.44, no.6, pp.1304-19 (1997). Initial experimental results from a 50 MHz elasticity microscope are shown. Using methods discussed previously, we present measured displacement and normal axial strain fields from a tissue mimicking phantom. Results from this homogenous gel are compared to a finite element simulation of the deformation experiment. The spatial resolution is estimated to be approximately 52 μm for axial displacements, and 71 μm for normal axial strains. These estimates were further tested by imaging a phantom containing a hard cylindrical inclusion with cross-sectional diameter of 265 μm. By examining the strain transition between regions in this image, the spatial resolution of the normal axial strain was verified to be at most 88 μm. A typical experiment produces peak normal axial strain around 3%. These experiments demonstrate the potential of high frequency ultrasound as a means for elasticity microscopy. Preliminary deformation experiments are presented on porcine epidermis     

In vivo validation of a blood vector velocity estimator with MR angiography

Conventional Doppler methods for blood velocity estimation only estimate the velocity component along the ultrasound beam direction. This implies that a Doppler angle under examination close to 90° results in unreliable information about the true blood direction and blood velocity. The novel method transverse oscillation (TO), which combines estimates of the axial and the transverse velocity components in the scan plane, makes it possible to estimate the vector velocity of the blood regardless of the Doppler angle. The present study evaluates the TO method with magnetic resonance phase contrast angiography (MRA) by comparing in vivo measurements of stroke volume. Eleven healthy volunteers were included in this prospective study. From the obtained data sets recorded with the 2 modalities, vector velocity sequences were constructed and stroke volume calculated. Angle of insonation was approximately 90° for TO measurements. The correlation between the stroke volume estimated by TO and MRA was 0.91 (p < 0.01) with the equation for the line of regression: MRA = 1.1?TO-0.4. A Bland-Altman plot was additionally constructed where the mean difference was 0.2 ml with limits of agreement at ?1.4 ml and 1.9 ml. The results indicate that reliable vector velocity estimates can be obtained in vivo using the presented angle-independent 2-D vector velocity method. The TO method can be a useful alternative to conventional Doppler systems by avoiding the angle artifact, thus giving quantitative velocity information.     

Application of Bessel beam for Doppler velocity estimation

Limited-diffraction beams have a large depth of field and could be applied to medical imaging, tissue characterization, and nondestructive evaluation of materials. This paper reports the application of limited-diffraction beams, specifically, the Bessel beam, to Doppler velocity estimation. The Bessel beam has the advantage that velocity estimation is less subject to the depth of moving objects and the Doppler spectrum has distinct shoulders that increase the accuracy of velocity (both magnitude and Doppler angle) estimation in noisy environments. The shoulders of the Doppler spectrum might also help in solving the inverse problem, e.g., estimation of the velocity distribution in vessels     

Transmission of a two-dimensional Gaussian beam into a uniaxial crystal.

We study the transmission of a two-dimensional (2-D) TM Gaussian beam through a plane interface between an isotropic medium (e.g., air) and a uniaxially anisotropic crystal. The optic axis of the crystal is taken to be in the plane of incidence but is arbitrarily oriented relative to the interface normal. We show that, in the paraxial approximation, a nontruncated transmitted 2-D TM Gaussian beam inside a uniaxial crystal can be expressed in a form similar to that of a scalar Gaussian beam that propagates in a homogeneous medium. We also show that the transmitted beam corresponding to an incident 2-D TM Gaussian beam with its main propagation direction along the interface normal is tilted inside the crystal by the same angle as is the transmitted axial ray that corresponds to a normally incident ray.     

Velocity bias and fluctuation in the standard dual beam Doppler reconstruction algorithm

Bias and fluctuation of the standard velocity reconstruction algorithm for dual beam vector Doppler velocity estimation systems are analyzed; both magnitude and angle properties are considered. Bias can arise from any of the error sources known to affect single beam systems in addition to both translation and angle misregistration between the two sample volumes; standard deviation is the result of random temporal fluctuations in Doppler frequency estimates in each beam. Approximate closed-form expressions for both biases and standard deviations of the velocity estimates are derived, and the performance of a typical practical dual beam system is discussed as an illustration of the theory.     

Accurate Doppler angle estimation for vector flow measurements

Traditional Doppler methods measure only the axial component of the velocity vector. The lack of information on the beam-flow angle creates an ambiguity that can lead to large errors in velocity magnitude estimates. Different triangulation techniques so far have been proposed, which basically perform multiple measurements of the Doppler frequency shift originating from the same region. In this work, an original approach is introduced, in which two ultrasound beams with known relative orientation are directed toward the same vessel, but only one of them is committed to perform a Doppler measurement; the second (reference) beam has the specific task of detecting the beam-flow angle. The latter goal is obtained by accurately identifying the achievement of the target 900 reference-beam-to-flow angle through the inspection of the backscattered Doppler signal spectrum. In transverse flow conditions, in fact, such spectrum is expected to be centered on the zero frequency, and even small deviations from the desired 900 orientation cause noticeable losses of spectral symmetry. Validation of the new method has been performed through experimental tests, which show that the beam-flow angle can be estimated with high accuracy (rms errors lower than 1 degree), and repeatable velocity magnitude measurements are possible. A procedure for automatically tracking the desired orientation by the reference beam is also introduced and shown suitable for implementation in steerable linear array transducers.     

Lateral displacement estimation using tissue incompressibility

Using the incompressibility property of soft tissue, lateral displacements can be reconstructed from axial strain measurements. Results of simulations and experiments on gelatin-based tissue equivalent phantoms are compared with theoretical displacements, as well as estimates derived from traditional speckle tracking. Incompressibility processing greatly improves the accuracy and signal-to-noise ratio (SNR) of lateral displacement measurements compared with more traditional speckle tracking     

2-D high-frame-rate dynamic elastography using delay compensated and angularly compounded motion vectors: preliminary results

This paper describes a new ultrasound-based system for high-frame-rate measurement of periodic motion in 2-D for tissue elasticity imaging. Similarly to conventional 2-D flow vector imaging, the system acquires the RF signals from the region of interest at multiple steering angles. A custom sector subdivision technique is used to increase the temporal resolution while keeping the total acquisition time within the range suitable for real-time applications. Within each sector, 1-D motion is estimated along the beam direction. The intra- and inter-sector delays are compensated using our recently introduced delay compensation algorithm. In-plane 2-D motion vectors are then reconstructed from these delay-compensated 1-D motions. We show that Young's modulus images can be reconstructed from these 2-D motion vectors using local inversion algorithms. The performance of the system is validated quantitatively using a commercial flow phantom and a commercial elasticity phantom. At the frame rate of 1667 Hz, the estimated flow velocities with the system are in agreement with the velocity measured with a pulsed-wave Doppler imaging mode of a commercial ultrasound machine with manual angle correction. At the frame rate of 1250 Hz, phantom Young's moduli of 29, 6, and 54 kPa for the background, the soft inclusion, and the hard inclusion, are estimated to be 30, 11, and 53 kPa, respectively.     

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.     

Doppler angle estimation using AR modeling

The transit time spectrum broadening effect has long been explored for Doppler angle estimation. Given acoustic beam geometry, the Doppler angle can be derived based on the mean Doppler frequency and the Doppler bandwidth. Spectral estimators based on the fast Fourier transform (FFT) are typically used. One problem with this approach is that a long data acquisition time is required to achieve adequate spectral resolution, with typically 32-128 flow samples being needed. This makes the method unsuitable for real-time two-dimensional Doppler imaging. This paper proposes using an autoregressive (AR) model to obtain the Doppler spectrum using a small number (e.g., eight) of flow samples. The flow samples are properly selected, then extrapolated to ensure adequate spectral resolution. Because only a small number of samples are used, the data acquisition time is significantly reduced and real-time, two-dimensional Doppler angle estimation becomes feasible. The approach was evaluated using both simulated and experimental data. Flows with various degrees of velocity gradient were simulated, with the Doppler angle ranging from 20° to 75°. The results indicate that the AR method generally provided accurate Doppler bandwidth estimates. In addition, the AR method outperformed the FFT method at smaller Doppler angles. The experimental data for Doppler angles, ranging from 33° to 72°, showed that the AR method using only eight flow samples had an average estimation error of 3.6°, which compares favorably to the average error of 4.7° for the FFT method using 64 flow samples. Because accurate estimates can be obtained using a small number of flow samples, it is concluded that real-time, two-dimensional estimation of the Doppler angle over a wide range of angles is possible using the AR method     

星敏感器模型参数分析与校准方法研究

以星内角统计偏差为校准精度评价指标,分析了高解析度面阵 CMOS 星敏感器模型中主要参数,得出焦距对精度影响最大,畸变次之,主点位置影响最小。由此提出了一种星敏感器校准方案,利用高精度 2 维轴向转台和单星星光模拟器采集数据,采用最小二乘参数估计算法计算主点焦距偏差,并且用 10 参数的二维多项式基函数拟合焦平面畸变。仿真结果表明在 0.03 像素误差的噪声水平下该方案能够达到 1″精度,可以满足现代空间飞行器的高精度姿态测量要求。     

A comparison of three‐dimensional embedded strain transducers,compression tested within the same strain field while offset at an angle with the principal axes

Abstract: The strain tensor and principal strains were derived for a range of different patterns of three‐dimensional strain transducers. The precisions of the estimates of these values were based on the Monte Carlo simulation applied to experimental work that was conducted on strain transducers tested within the same strain field. The estimates of precision were also determined theoretically and compared with results based on experimental findings. Results suggest that the tetrahedron transducers in experimental work do not perform as well as rectangular patterns and that estimates of principal strains, which were not coincident with the axes of the transducer, showed slight discrepancies.     

RF-based two-dimensional cardiac strain estimation: a validation study in a tissue-mimicking phantom

Strain and strain rate imaging have been shown to be useful techniques for the assessment of cardiac function. However, one of the major problems of these techniques is their angle dependency. In order to overcome this problem, a new method for estimating the strain (rate) tensor had previously been proposed by our lab. The aim of this study was to validate this methodology in a phantom setup. A tubular thick-walled tissue-mimicking phantom was fixed in a water tank. Varying the intraluminal pressure resulted in a cyclic radial deformation. The 2D strain was calculated from the 2D velocity estimates, obtained from 2D radio frequency (RF) tracking using a 1D kernel. Additionally, ultrasonic microcrystals were implanted on the outer and inner walls of the tube in order to give an independent measurement of the instantaneous wall thickness. The two methods were compared by means of linear regression, the correlation coefficient, and Bland-Altman statistics. As expected, the strain estimates dominated by the azimuth velocity component were less accurate than the ones dominated by the axial velocity component. Correlation coefficients were found to be r = 0.78 for the former estimates and r = 0.83 was found for the latter. Given that the overall shape and timing of the 2D deformation were very accurate (r = 0.95 and r = 0.84), these results were within acceptable limits for clinical applications. The 2D RF-tracking using a 1D kernel thus allows for 2D, and therefore angle-independent, strain estimation.     

Influence of catheter position on estimated strain in intravascular elastography

In elastography, an erroneous strain estimate is obtained when the radial strain and the probing ultrasound beam are not properly aligned: the "strain projection artifact". In practice, an angle between the strain and the ultrasound beam will be present in most of the cases due to inhomogeneities or nonuniform compression. In this study, a theoretical function describing the strain projection artifact is derived as a function of the angle between the radial strain and the ultrasound beam. Two main factors for an angle between strain and ultrasound beam in intravascular elastographic experiments are eccentricity and tilt of the transducer. The theoretical functions describing these errors are corroborated with strain estimates from an experiment with a circular, homogeneous gel-based vessel phantom. Comparison between the theoretical functions and the experimental results reveals that the strain projection artifact is well described by the theoretical findings. As a result, the experimental data can be corrected for this artifact. The corrected elastograms reveal that correct strain estimates are obtained when the eccentricity of the intravascular catheter is less than 63%. An "off-the-wall" device may be required to advance intravascular elastography to in vivo implementation.     

Quantitative 3-d diagnostic ultrasound imaging using a modified transducer array and an automated image tracking technique

An approach for acquiring dimensionally accurate three-dimensional (3-D) ultrasound data from multiple 2-D image planes is presented. This is based on the use of a modified linear-phased array comprising a central imaging array that acquires multiple, essentially parallel, 2-D slices as the transducer is translated over the tissue of interest. Small, perpendicularly oriented, tracking arrays are integrally mounted on each end of the imaging transducer. As the transducer is translated in an elevational direction with respect to the central imaging array, the images obtained by the tracking arrays remain largely coplanar. The motion between successive tracking images is determined using a minimum sum of absolute difference (MSAD) image matching technique with subpixel matching resolution. An initial phantom scanning-based test of a prototype 8 MHz array indicates that linear dimensional accuracy of 4.6% (2 /spl sigma/) is achievable. This result compares favorably with those obtained using an assumed average velocity [31.5% (2 /spl sigma/) accuracy] and using an approach based on measuring image-to-image decorrelation [8.4% (2 /spl sigma/) accuracy]. The prototype array and imaging system were also tested in a clinical environment, and early results suggest that the approach has the potential to enable a low cost, rapid, screening method for detecting carotid artery stenosis. The average time for performing a screening test for carotid stenosis was reduced from an average of 45 minutes using 2-D duplex Doppler to 12 minutes using the new 3-D scanning approach.     

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