Jonathan Porée

Stolt's f-k migration for plane wave ultrasound imaging

Ultrafast ultrasound is an emerging modality that offers new perspectives and opportunities in medical imaging. Plane wave imaging (PWI) allows one to attain very high frame rates by transmission of planar ultrasound wavefronts. As a plane wave reaches a given scatterer, the latter becomes a secondary source emitting upward spherical waves and creating a diffraction hyperbola in the received RF signals. To produce an image of the scatterers, all the hyperbolas must be migrated back to their apexes. To perform beamforming of plane wave echo RFs and return high-quality images at high frame rates, we propose a new migration method carried out in the frequency-wavenumber (f-k) domain. The f-k migration for PWI has been adapted from the Stolt migration for seismic imaging. This migration technique is based on the exploding reflector model (ERM), which consists in assuming that all the scatterers explode in concert and become acoustic sources. The classical ERM model, however, is not appropriate for PWI. We showed that the ERM can be made suitable for PWI by a spatial transformation of the hyperbolic traces present in the RF data. In vitro experiments were performed to outline the advantages of PWI with Stolts f-k migration over the conventional delay-and-sum (DAS) approach. The Stolts f-k migration was also compared with the Fourier-based method developed by J.-Y. Lu. Our findings show that multi-angle compounded f-k migrated images are of quality similar to those obtained with a stateof- the-art dynamic focusing mode. This remained true even with a very small number of steering angles, thus ensuring a highly competitive frame rate. In addition, the new FFT-based f-k migration provides comparable or better contrast-to-noise ratio and lateral resolution than the Lus and DAS migration schemes. Matlab codes for the Stolts f-k migration for PWI are provided.

High-Frame-Rate Echocardiography Using Coherent Compounding With Doppler-Based Motion-Compensation

High-frame-rate ultrasonography based on coherent compounding of unfocused beams can potentially transform the assessment of cardiac function. As it requires successive waves to be combined coherently, this approach is sensitive to high-velocity tissue motion. We investigated coherent compounding of tilted diverging waves, emitted from a 2.5 MHz clinical phased array transducer. To cope with high myocardial velocities, a triangle transmit sequence of diverging waves is proposed, combined with tissue Doppler imaging to perform motion compensation (MoCo). The compound sequence with integrated MoCo was adjusted from simulations and was tested in vitro and in vivo. Realistic myocardial velocities were analyzed in an in vitro spinning disk with anechoic cysts. While a 8 dB decrease (no motion versus high motion) was observed without MoCo, the contrast-to-noise ratio of the cysts was preserved with the MoCo approach. With this method, we could provide high-quality in vivo B-mode cardiac images with tissue Doppler at 250 frames per second. Although the septum and the anterior mitral leaflet were poorly apparent without MoCo, they became well perceptible and well contrasted with MoCo. The septal and lateral mitral annulus velocities determined by tissue Doppler were concordant with those measured by pulsed-wave Doppler with a clinical scanner (r2 = 0.7, y = 09.x + 0.5, N = 60). To conclude, high-contrast echo-cardiographic B-mode and tissue Doppler images can be obtained with diverging beams when motion compensation is integrated in the coherent compounding process.

Noninvasive Vascular Elastography With Plane Strain Incompressibility Assumption Using Ultrafast Coherent Compound Plane Wave Imaging

Plane strain tensor estimation using non-invasive vascular ultrasound elastography (NIVE) can be difficult to achieve using conventional focus beamforming due to limited lateral resolution and frame rate. Recent developments in compound plane wave (CPW) imaging have led to high speed and high resolution imaging. In this study, we present the performance of NIVE using coherent CPW. We show the impact of CPW beamforming on strain estimates compared to conventional focus sequences. To overcome the inherent variability of lateral strains, associated with the low lateral resolution of linear array transducers, we use the plane strain incompressibility to constrain the estimator. Taking advantage of the approximate tenfold increase in frame rate of CPW compared with conventional focus imaging, we introduce a time-ensemble estimation approach to further improve the elastogram quality. By combining CPW imaging with the constrained Lagrangian speckle model estimator, we observe an increase in elastography quality (~10 dB both in signal-to-noise and contrast-to-noise ratios) over a wide range of applied strains (0.02 to 3.2%).

ESTIMATION METHOD OF THE HOMODYNED K-DISTRIBUTION BASED ON THE MEAN INTENSITY AND TWO LOG-MOMENTS.

The homodyned K-distribution appears naturally in the context of random walks and provides a useful model for the distribution of the received intensity in a wide range of non-Gaussian scattering configurations, including medical ultrasonics. An estimation method for the homodyned K-distribution based on the first moment of the intensity and two log-moments (XU method), namely the X and U-statistics previously studied in the special case of the K-distribution, is proposed as an alternative to a method based on the first three moments of the intensity (MI method) or the amplitude (MA method), and a method based on the signal-to-noise ratio (SNR), the skewness and the kurtosis of two fractional orders of the amplitude (labeled RSK method). Properties of the X and U statistics for the homodyned K-distribution are proved, except for one conjecture. Using those properties, an algorithm based on the bisection method for monotonous functions was developed. The algorithm has a geometric rate of convergence. Various tests were performed to study the behavior of the estimators. It was shown with simulated data samples that the estimations of the parameters 1/α and 1/(κ + 1) of the homodyned K-distribution are preferable to the direct estimations of the clustering parameter α and the structure parameter κ (with respective relative root mean squared errors (RMSEs) of 0.63 and 0.13 as opposed to 1.04 and 4.37, when N = 1000). Tests on simulated ultrasound images with only diffuse scatterers (up to 10 per resolution cell) indicated that the XU estimator is overall more reliable than the other three estimators for the estimation of 1/α, with relative RMSEs of 0.79 (MI), 0.61 (MA), 0.53 (XU) and 0.67 (RSK). For the parameter 1/(κ + 1), the relative RMSEs were equal to 0.074 (MI), 0.075 (MA), 0.069 (XU) and 0.100 (RSK). In the case of a large number of scatterers (11 to 20 per resolution cell), the relative RMSEs of 1/α were equal to 1.43 (MI), 1.27 (MA), 1.25 (XU) and 1.33 (RSK), and the relative RMSEs of 1/(κ + 1) were equal to 0.14 (MI), 0.16 (MA), 0.17 (XU) and 0.20 (RSK). The four methods were also tested on simulated ultrasound images with a variable density of periodic scatterers to test images with a coherent component. The addition of noise on ultrasound images was also studied. Results showed that the XU estimator was overall better than the three other ones. Finally, on the simulated ultrasound images, the average computation times per image were equal to 6.0 ms (MI), 8.0 ms (MA), 6.8 ms (XU) and 500 ms (RSK). Thus, a fast, reliable, and novel algorithm for the estimation of the homodyned K-distribution was proposed.

Staggered Multiple-PRF Ultrafast Color Doppler

Color Doppler imaging is an established pulsed ultrasound technique to visualize blood flow non-invasively. High-frame-rate (ultrafast) color Doppler, by emissions of plane or circular wavefronts, allows severalfold increase in frame rates. Conventional and ultrafast color Doppler are both limited by the range-velocity dilemma, which may result in velocity folding (aliasing) for large depths and/or large velocities. We investigated multiple pulse-repetition-frequency (PRF) emissions arranged in a series of staggered intervals to remove aliasing in ultrafast color Doppler. Staggered PRF is an emission process where time delays between successive pulse transmissions change in an alternating way. We tested staggered dual- and triple-PRF ultrafast color Doppler, 1) in vitro in a spinning disc and a free jet flow, and 2) in vivo in a human left ventricle. The in vitro results showed that the Nyquist velocity could be extended to up to 6 times the conventional limit. We found coefficients of determination r2 ≥ 0.98 between the de-aliased and ground-truth velocities. Consistent de-aliased Doppler images were also obtained in the human left heart. Our results demonstrate that staggered multiple-PRF ultrafast color Doppler is efficient for high-velocity high-frame-rate blood flow imaging. This is particularly relevant for new developments in ultrasound imaging relying on accurate velocity measurements.

A local angle compensation method based on kinematics constraints for non-invasive vascular axial strain computations on human carotid arteries

Non invasive vascular elastography (NIVE) was developed to highlight atherosclerotic plaque constituents. However, NIVE motion estimates are affected by artifacts, such as an underestimation of deformations due to projected movement angles with respect to the ultrasound beam, movements of the operator or of the patient during image acquisition. The main objective of this work was to propose a local angle compensation method within small measurement windows for the axial strain based on kinematics constraints, and to introduce a filtering process on the strain time-varying curve to reduce as much as possible the impact of motion artifacts. With such preprocessing, we successfully quantified the strain behavior of near and far walls in longitudinal images of internal carotid arteries without (n=30) and with (n=21) significant atherosclerotic disease (greater than 50% stenosis). Maximum strain rates of 4.49% s(-1) for the healthy group and of 2.29% s(-1) for the atherosclerotic group were calculated on the far wall of internal carotid arteries; significant differences were found between these values (p=0.001). The minimum strain rates, also on the far wall of internal carotid arteries, of -3.68% s(-1) for the healthy group and of -1.89% s(-1) for the atherosclerotic group were significantly different as well (p=8×10(-4)). The mean systolic, diastolic and cumulated axial strains could also distinguish the two groups after normalization by the pressure gradient between acquired images. To conclude, the proposed techniques allowed to differentiate healthy and atherosclerotic carotid arteries and may help to diagnose vulnerable plaques.

A sequential Bayesian based method for tracking and strain palpography estimation of arteries in intravascular ultrasound images

This paper investigates the task of tracking and strain estimation of arteries in intravascular ultrasound images. A tracking method is proposed to extract the inner and the outer contours of the vessel wall (lumen/intima-media and intima-media/adventitia interfaces, respectively), and the deformations along them. This estimation is carried out by a non parametric sequential Bayesian method. The Bayesian modeling holds three ingredients: the prior, which is given by a manually defined segmentation of the contours on the first image; the transition, which is assumed to follow a Markovian random walk; and the likelihood, which is a distance between patches distributed along the contours. The underlying Bayesian posterior distribution is approximated using a sequential Monte Carlo approach. Experiments on three PVA-C phantoms present direct readings of the deformations along the lumen/intima-media contour.

High-frame-rate velocity vector imaging echocardiography: an in vitro evaluation

High-frame-rate ultrasound imaging using diverging waves has demonstrated its potential as a useful cardiac imaging method. It has been shown that the compounding of steered beams improves static images quality. In the presence of high-velocity tissue motion, however, the combination of successive steered diverging waves is incoherent and thus deteriorates the image contrast. Motion compensation (MoCo) integrated in the coherent compounding process has recently shown to be a very promising technique to provide high-contrast B-mode images of the cardiac muscle. Ultrafast cardiac motion estimation based on speckle tracking could greatly benefit from this original method. In this study, Velocity Vector Imaging (VVI) was applied on high-frame-rate envelope images performed with MoCo to estimate the myocardium 2-D motion. The method was investigated in vitro, using a rotating disk. With sequences of steered diverging waves (pulse repetition frequency = 4500 Hz) generated by the full aperture of a 2.5 MHz phased array, high-contrast high-resolution images were constructed at 500 FPS using MoCo. Standard cross-correlation and phase correlation in the Fourier domain were applied to generate VVI on the pre-scanned envelope images at 100 images/s. The estimated in vitro velocity vectors were consistent with the expected values, with an average normalized error of 6.0% +/-0.4% in the radial direction, and 13.1% +/-1.2% in the cross-range direction. These results make us confident to pursue the study with in vivo investigations.

Non-invasive vascular modulography: An inverse problem method for imaging the local elasticity of atherosclerotic carotid plaques

Quantifying biomechanical properties of atherosclerotic plaques may help preventing strokes. Non-invasive vascular elastography (NIVE) in superficial carotid arteries has the potential to assess such properties and to discriminate plaque components (e.g., fibrosis, lipid and calcium) through elastograms (i.e., spatial strain distribution). However, the elasticity and morphology of the vessel wall, cannot be assessed directly from strain maps since the stress distribution remains unknown. In this study, we describe an unsupervised inverse problem for elasticity mapping (non invasive vascular modulography), which is capable of reconstructing a heterogeneous Youngs modulus distribution of a plaque. High resolution elastograms were computed from ultrasound compounded plane wave images using the constrained lagrangian speckle model estimator (constrained LSME). Von mises strain maps were combined with a stress map, evaluated using a parametric finite element model (PFEM), and used to highlight mechanical heterogeneities and compute Young modulus maps (Modulograms).

Two-dimensional affine model-based estimators for principal strain vascular ultrasound elastography with compound plane wave and transverse oscillation beamforming.

HighlightsTwo affine model‐based estimators for ultrafast vascular elastography are evaluated.A phase‐based estimator based on transverse oscillation beamforming is developed.Transverse oscillation beamforming is implemented with the Lagrangian speckle model. ABSTRACT Polar strain (radial and circumferential) estimations can suffer from artifacts because the center of a nonsymmetrical carotid atherosclerotic artery, defining the coordinate system in cross‐sectional view, can be misregistered. Principal strains are able to remove coordinate dependency to visualize vascular strain components (i.e., axial and lateral strains and shears). This paper presents two affine model‐based estimators, the affine phase‐based estimator (APBE) developed in the framework of transverse oscillation (TO) beamforming, and the Lagrangian speckle model estimator (LSME). These estimators solve simultaneously the translation (axial and lateral displacements) and deformation (axial and lateral strains and shears) components that were then used to compute principal strains. To improve performance, the implemented APBE was also tested by introducing a time‐ensemble estimation approach. Both APBE and LSME were tested with and without the plane strain incompressibility assumption. These algorithms were evaluated on coherent plane wave compounded (CPWC) images considering TO. LSME without TO but implemented with the time‐ensemble and incompressibility constraint (Porée et al., 2015) served as benchmark comparisons. The APBE provided better principal strain estimations with the time‐ensemble and incompressibility constraint, for both simulations and in vitro experiments. With a few exceptions, TO did not improve principal strain estimates for the LSME. With simulations, the smallest errors compared with ground true measures were obtained with the LSME considering time‐ensemble and the incompressibility constraint. This latter estimator also provided the highest elastogram signal‐to‐noise ratios (SNRs) for in vitro experiments on a homogeneous vascular phantom without any inclusion, for applied strains varying from 0.07% to 4.5%. It also allowed the highest contrast‐to‐noise ratios (CNRs) for a heterogeneous vascular phantom with a soft inclusion, at applied strains from 0.07% to 3.6%. In summary, the LSME outperformed the implemented APBE, and the incompressibility constraint improved performances of both estimators.