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

Alternating direction method of multipliers for displacement estimation in ultrasound strain elastography

BACKGROUND

Ultrasound strain imaging, which delineates mechanical properties to detect tissue abnormalities, involves estimating the time delay between two radio-frequency (RF) frames collected before and after tissue deformation. The existing regularized optimization-based time-delay estimation (TDE) techniques suffer from at least one of the following drawbacks: (1) The regularizer is not aligned with the tissue deformation physics due to taking only the first-order displacement derivative into account; (2) TheL 2 $L2$ -norm of the displacement derivatives, which oversmooths the estimated time-delay, is utilized as the regularizer; (3) The modulus function defined mathematically should be approximated by a smooth function to facilitate the optimization ofL 1 $L1$ -norm.

PURPOSE

Our purpose is to develop a novel TDE technique that resolves the aforementioned shortcomings of the existing algorithms.

METHODS

Herein, we propose employing the alternating direction method of multipliers (ADMM) for optimizing a novel cost function consisting ofL 2 $L2$ -norm data fidelity term andL 1 $L1$ -norm first- and second-order spatial continuity terms. ADMM empowers the proposed algorithm to use different techniques for optimizing different parts of the cost function and obtain high-contrast strain images with smooth backgrounds and sharp boundaries. We name our technique ADMM for totaL variaTion RegUlarIzation in ultrasound STrain imaging (ALTRUIST). ALTRUIST's efficacy is quantified using absolute error (AE), Structural SIMilarity (SSIM), signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and strain ratio (SR) with respect to GLUE, OVERWIND, andL 1 $L1$ -SOUL, three recently published energy-based techniques, and UMEN-Net, a state-of-the-art deep learning-based algorithm. Analysis of variance (ANOVA)-led multiple comparison tests and paired t $t$ -tests at5 % $5\%$ overall significance level were conducted to assess the statistical significance of our findings. The Bonferroni correction was taken into account in all statistical tests. Two simulated layer phantoms, three simulated resolution phantoms, one hard-inclusion simulated phantom, one multi-inclusion simulated phantom, one experimental breast phantom, and three in vivo liver cancer datasets have been used for validation experiments. We have published the ALTRUIST code at http://code.sonography.ai.

RESULTS

ALTRUIST substantially outperforms the four state-of-the-art benchmarks in all validation experiments, both qualitatively and quantitatively. ALTRUIST yields up to573 % ∗ ${573\%}^{*}$ ,41 % ∗ ${41\%}^{*}$ , and51 % ∗ ${51\%}^{*}$ SNR improvements and443 % ∗ ${443\%}^{*}$ ,53 % ∗ ${53\%}^{*}$ , and15 % ∗ ${15\%}^{*}$ CNR improvements overL 1 $L1$ -SOUL, its closest competitor, for simulated, phantom, and in vivo liver cancer datasets, respectively, where the asterisk (*) indicates statistical significance. In addition, ANOVA-led multiple comparison tests and paired t $t$ -tests indicate that ALTRUIST generally achieves statistically significant improvements over GLUE, UMEN-Net, OVERWIND, andL 1 $L1$ -SOUL in terms of AE, SSIM map, SNR, and CNR.

CONCLUSIONS

A novel ultrasonic displacement tracking algorithm named ALTRUIST has been developed. The principal novelty of ALTRUIST is incorporating ADMM for optimizing anL 1 $L1$ -norm regularization-based cost function. ALTRUIST exhibits promising performance in simulation, phantom, and in vivo experiments.

Exploiting Mechanics-Based Priors for Lateral Displacement Estimation in Ultrasound Elastography

Tracking the displacement between the pre- and post-deformed radio-frequency (RF) frames is a pivotal step of ultrasound elastography, which depicts tissue mechanical properties to identify pathologies. Due to ultrasound's poor ability to capture information pertaining to the lateral direction, the existing displacement estimation techniques fail to generate an accurate lateral displacement or strain map. The attempts made in the literature to mitigate this well-known issue suffer from one of the following limitations: 1) Sampling size is substantially increased, rendering the method computationally and memory expensive. 2) The lateral displacement estimation entirely depends on the axial one, ignoring data fidelity and creating large errors. This paper proposes exploiting the effective Poisson's ratio (EPR)-based mechanical correspondence between the axial and lateral strains along with the RF data fidelity and displacement continuity to improve the lateral displacement and strain estimation accuracies. We call our techniques MechSOUL (Mechanically-constrained Second-Order Ultrasound eLastography) and L1 -MechSOUL ( L1 -norm-based MechSOUL), which optimize L2 - and L1 -norm-based penalty functions, respectively. Extensive validation experiments with simulated, phantom, and in vivo datasets demonstrate that MechSOUL and L1 -MechSOUL's lateral strain and EPR estimation abilities are substantially superior to those of the recently-published elastography techniques. We have published the MATLAB codes of MechSOUL and L1 -MechSOUL at https://code.sonography.ai.

Ultrafast Myocardial Principal Strain Ultrasound Elastography During Stress Tests: In Vitro Validation and In Vivo Feasibility

Objective myocardial contractility assessment during stress tests aims to improve the diagnosis of myocardial ischemia. Tissue Doppler imaging (TDI) or optical flow (OF) speckle tracking echocardiography (STE) has been used to quantify myocardial contractility at rest. However, this is more challenging during stress tests due to image decorrelation at high heart rates. Moreover, stress tests imply a high frame rate which leads to a limited lateral field of view. Therefore, a large lateral field-of-view robust ultrafast myocardial regularized OF-TDI principal strain estimator has been developed for high-frame-rate echocardiography of coherently compounded transmitted diverging waves. The feasibility and accuracy of the proposed estimator were validated in vitro (using sonomicrometry as the gold standard) and in vivo stress experiments. Compared with OF strain imaging, the proposed estimator improved the accuracy of principal major and minor strains during stress tests, with an average contrast-to-noise ratio improvement of 4.4 ± 2.7 dB ( p -value < 0.01). Moreover, there was a significant correlation and a very close agreement between the proposed estimator and sonomicrometry for tested heart rates between 60 and 180 beats per minute (bpm). The averages ± standard deviations (STD) of R² and biases ± STD between them were 0.96 ± 0.04 ( p -value < 0.01) and 0.01 ± 0.03% in the axial direction, respectively; and 0.94 ± 0.02 ( p -value < 0.01) and 0.04 ± 0.06% in the lateral direction, respectively. These results suggest that the proposed estimator could be useful clinically to provide an accurate and quantitative 2-D large lateral field-of-view myocardial strain assessment at high heart rates during stress echocardiography.

Deep learning in ultrasound elastography imaging: A review

It is known that changes in the mechanical properties of tissues are associated with the onset and progression of certain diseases. Ultrasound elastography is a technique to characterize tissue stiffness using ultrasound imaging either by measuring tissue strain using quasi-static elastography or natural organ pulsation elastography, or by tracing a propagated shear wave induced by a source or a natural vibration using dynamic elastography. In recent years, deep learning has begun to emerge in ultrasound elastography research. In this review, several common deep learning frameworks in the computer vision community, such as multilayer perceptron, convolutional neural network, and recurrent neural network are described. Then, recent advances in ultrasound elastography using such deep learning techniques are revisited in terms of algorithm development and clinical diagnosis. Finally, the current challenges and future developments of deep learning in ultrasound elastography are prospected. This article is protected by copyright. All rights reserved.

Second-Order Ultrasound Elastography With L1-Norm Spatial Regularization

Time delay estimation (TDE) between two radio-frequency (RF) frames is one of the major steps of quasi-static ultrasound elastography, which detects tissue pathology by estimating its mechanical properties. Regularized optimization-based techniques, a prominent class of TDE algorithms, optimize a nonlinear energy functional consisting of data constancy and spatial continuity constraints to obtain the displacement and strain maps between the time-series frames under consideration. The existing optimization-based TDE methods often consider the L2 -norm of displacement derivatives to construct the regularizer. However, such a formulation over-penalizes the displacement irregularity and poses two major issues to the estimated strain field. First, the boundaries between different tissues are blurred. Second, the visual contrast between the target and the background is suboptimal. To resolve these issues, herein, we propose a novel TDE algorithm where instead of L2 -, L1 -norms of both first- and second-order displacement derivatives are taken into account to devise the continuity functional. We handle the non-differentiability of L1 -norm by smoothing the absolute value function's sharp corner and optimize the resulting cost function in an iterative manner. We call our technique Second-Order Ultrasound eLastography (SOUL) with the L1 -norm spatial regularization ( L1 -SOUL). In terms of both sharpness and visual contrast, L1 -SOUL substantially outperforms GLobal Ultrasound Elastography (GLUE), tOtal Variation rEgulaRization and WINDow-based time delay estimation (OVERWIND), and SOUL, three recently published TDE algorithms in all validation experiments performed in this study. In cases of simulated, phantom, and in vivo datasets, respectively, L1 -SOUL achieves 67.8%, 46.81%, and 117.35% improvements of contrast-to-noise ratio (CNR) over SOUL. The L1 -SOUL code can be downloaded from http://code.sonography.ai.

Recent advances in vascular ultrasound imaging technology and their clinical implications

In this paper recent advances in vascular ultrasound imaging technology are discussed, including three-dimensional ultrasound (3DUS), contrast-enhanced ultrasound (CEUS) and strain- (SE) and shear-wave-elastography (SWE). 3DUS imaging allows visualisation of the actual 3D anatomy and more recently of flow, and assessment of geometrical, morphological and mechanical features in the carotid artery and the aorta. CEUS involves the use of microbubble contrast agents to estimate sensitive blood flow and neovascularisation (formation of new microvessels). Recent developments include the implementation of computerised tools for automated analysis and quantification of CEUS images, and the possibility to measure blood flow velocity in the aorta. SE, which yields anatomical maps of tissue strain, is increasingly being used to investigate the vulnerability of the carotid plaque, but is also promising for the coronary artery and the aorta. SWE relies on the generation of a shear wave by remote acoustic palpation and its acquisition by ultrafast imaging, and is useful for measuring arterial stiffness. Such advances in vascular ultrasound technology, with appropriate validation in clinical trials, could positively change current management of patients with vascular disease, and improve stratification of cardiovascular risk.

Deformability of ascending thoracic aorta aneurysms assessed using ultrafast ultrasound and a principal strain estimator: In vitro evaluation and in vivo feasibility

BACKGROUND

Noninvasive vascular strain imaging under conventional line-by-line scanning has a low frame rate and lateral resolution, and depends on the coordinate system. It is thus affected by high deformations due to image decorrelation between frames.

PURPOSE

To develop an ultrafast time-ensemble regularized tissue-Doppler optical-flow principal strain estimator for aorta deformability assessment in a long-axis view.

METHODS

This approach alleviated the impact of lateral resolution using image compounding and that of the coordinate system dependency using principal strain. Accuracy and feasibility were evaluated in two aorta-mimicking phantoms first, and then in four age-matched individuals with either a normal aorta or a pathological ascending thoracic aorta aneurysm (TAA).

RESULTS

Instantaneous aortic maximum and minimum principal strain maps and regional accumulated strains during each cardiac cycle were estimated at systolic and diastolic phases to characterize the normal aorta and TAA. In vitro, principal strain results matched sonomicrometry measurements. In vivo, a significant decrease in maximum and minimum principal strains was observed in TAA cases, whose range was respectively 7.9 ± 6.4% and 8.2 ± 2.6% smaller than in normal aortas.

CONCLUSIONS

The proposed principal strain estimator showed an ability to potentially assess TAA deformability, which may provide an individualized and reliable evaluation method for TAA rupture risk assessment. This article is protected by copyright. All rights reserved.

Parameterized Strain Estimation for Vascular Ultrasound Elastography With Sparse Representation

Ultrasound vascular strain imaging has shown its potential to interrogate the motion of the vessel wall induced by the cardiac pulsation for predicting plaque instability. In this study, a sparse model strain estimator (SMSE) is proposed to reconstruct a dense strain field at a high resolution, with no spatial derivatives, and a high computation efficiency. This sparse model utilizes the highly-compacted property of discrete cosine transform (DCT) coefficients, thereby allowing to parameterize displacement and strain fields with truncated DCT coefficients. The derivation of affine strain components (axial and lateral strains and shears) was reformulated into solving truncated DCT coefficients and then reconstructed with them. Moreover, an analytical solution was derived to reduce estimation time. With simulations, the SMSE reduced estimation errors by up to 50% compared with the state-of-the-art window-based Lagrangian speckle model estimator (LSME). The SMSE was also proven to be more robust than the LSME against global and local noise. For in vitro and in vivo tests, residual strains assessing cumulated errors with the SMSE were 2 to 3 times lower than with the LSME. Regarding computation efficiency, the processing time of the SMSE was reduced by 4 to 25 times compared with the LSME, according to simulations, in vitro and in vivo results. Finally, phantom studies demonstrated the enhanced spatial resolution of the proposed SMSE algorithm against LSME.

Contractile Fronts In The Interventricular Septum: A Case For High Frame Rate Echocardiographic Imaging

The real time high frame rate (HFR) 2-dimensional ultrasound system, T5, at Duke University is capable of imaging at up to 1000 images per second for adult cardiac imaging. A method for detecting and visualizing the mechanical contraction fronts using HFR echocardioagraphy-derived Strain Rate Image (SRI) was described in 26 patients. The Tissue Shortening Onset front durations for echocardiographic normal patients were significantly shorter than conduction disorder patients with left bundle branch block (LBBB) with intrinsic conduction and conduction disorder patients without LBBB (non-LBBB) with simulated LBBB (sLBBB). Echocardiographic normal patients had significantly higher correlation coefficients between their SRIs and spatially inverted versions of themselves compared to non-LBBB patients with intrinsic conduction and sLBBB. In conclusion, SRIs could spatially resolve contractile event fronts in patients.

Interoperator Reproducibility of Carotid Elastography for Identification of Vulnerable Atherosclerotic Plaques

Ultrasound-based carotid elastography has been developed to evaluate the vulnerability of carotid atherosclerotic plaques. The aim of this study was to investigate the in vivo interoperator reproducibility of carotid elastography for the identification of vulnerable plaques, with high-resolution magnetic resonance imaging (MRI) as reference. Ultrasound radio-frequency data of 45 carotid arteries (including 53 plaques) from 32 volunteers were acquired separately by two experienced operators in the longitudinal view and then were used to estimate the interframe axial strain rate (ASR) with a two-step optical flow method. The maximum 99th percentile of absolute ASR of all plaques in a carotid artery was used as the elastographic index. MRI scanning was also performed on each volunteer to identify the vulnerable plaque. The results showed no systematic bias in the Bland-Altman plot and an intraclass correlation coefficient of 0.66 between the two operators. In addition, no statistical significance was found between the receiver operating characteristic (ROC) curves from the two operators ( ), and their areas under the ROC curves were 0.83 and 0.77, respectively. Using the mean measurements of the two operators as the classification criterion, a sensitivity of 71.4%, a specificity of 87.1%, and an accuracy of 82.2% were obtained with a cutoff value of 1.37 [Formula: see text]. This study validates the interoperator reproducibility of ultrasound-based carotid elastography for identifying vulnerable carotid plaques.

Investigation of out-of-plane motion artifacts in 2D noninvasive vascular ultrasound elastography

Ultrasound noninvasive vascular elastography (NIVE) has shown its potential to measure strains of carotid arteries to predict plaque instability. When two-dimensional (2D) strain estimation is performed, either in longitudinal or cross-sectional view, only in-plane motions are considered. The motions in elevation direction (i.e. perpendicular to the imaging plane), can induce estimation artifacts affecting the accuracy of 2D NIVE. The influence of such out-of-plane motions on the performance of axial strain and axial shear strain estimations has been evaluated in this study. For this purpose, we designed a diseased carotid bifurcation phantom with a 70% stenosis and an in vitro experimental setup to simulate orthogonal out-of-plane motions of 1 mm, 2 mm and 3 mm. The Lagrangian speckle model estimator (LSME) was used to estimate axial strains and shears under pulsatile conditions. As anticipated, in vitro results showed more strain estimation artifacts with increasing magnitudes of motions in elevation. However, even with an out-of-plane motion of 2.0 mm, strain and shear estimations having inter-frame correlation coefficients higher than 0.85 were obtained. To verify findings of in vitro experiments, a clinical LSME dataset obtained from 18 participants with carotid artery stenosis was used. Deduced out-of-plane motions (ranging from 0.25 mm to 1.04 mm) of the clinical dataset were classified into three groups: small, moderate and large elevational motions. Clinical results showed that pulsatile time-varying strains and shears remained reproducible for all motion categories since inter-frame correlation coefficients were higher than 0.70, and normalized cross-correlations (NCC) between radiofrequency (RF) images were above 0.93. In summary, the performance of LSME axial strain and shear estimations appeared robust in the presence of out-of-plane motions (<2 mm) as encountered during clinical ultrasound imaging.