Lateral Strain Imaging Using Self-Supervised and Physically Inspired Constraints in Unsupervised Regularized Elastography

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.

Ultrasound Viscoelastography by Acoustic Radiation Force: A State-of-the-Art Review

Ultrasound elastography (USE) is a promising tool for tissue characterization as several diseases result in alterations of tissue structure and composition, which manifest as changes in tissue mechanical properties. By imaging the tissue response to an applied mechanical excitation, USE mimics the manual palpation performed by clinicians to sense the tissue elasticity for diagnostic purposes. Next to elasticity, viscosity has recently been investigated as an additional, relevant, diagnostic biomarker. Moreover, since biological tissues are inherently viscoelastic, accounting for viscosity in the tissue characterization process enhances the accuracy of the elasticity estimation. Recently, methods exploiting different acquisition and processing techniques have been proposed to perform ultrasound viscoelastography. After introducing the physics describing viscoelasticity, a comprehensive overview of the currently available USE acquisition techniques is provided, followed by a structured review of the existing viscoelasticity estimators classified according to the employed processing technique. These estimators are further reviewed from a clinical usage perspective, and current outstanding challenges are discussed.

Ultrafast Cardiac Imaging Using Deep Learning for Speckle-Tracking Echocardiography

High-quality ultrafast ultrasound imaging is based on coherent compounding from multiple transmissions of plane waves (PW) or diverging waves (DW). However, compounding results in reduced frame rate, as well as destructive interferences from high-velocity tissue motion if motion compensation (MoCo) is not considered. While many studies have recently shown the interest of deep learning for the reconstruction of high-quality static images from PW or DW, its ability to achieve such performance while maintaining the capability of tracking cardiac motion has yet to be assessed. In this article, we addressed such issue by deploying a complex-weighted convolutional neural network (CNN) for image reconstruction and a state-of-the-art speckle-tracking method. The evaluation of this approach was first performed by designing an adapted simulation framework, which provides specific reference data, i.e., high-quality, motion artifact-free cardiac images. The obtained results showed that, while using only three DWs as input, the CNN-based approach yielded an image quality and a motion accuracy equivalent to those obtained by compounding 31 DWs free of motion artifacts. The performance was then further evaluated on nonsimulated, experimental in vitro data, using a spinning disk phantom. This experiment demonstrated that our approach yielded high-quality image reconstruction and motion estimation, under a large range of velocities and outperforms a state-of-the-art MoCo-based approach at high velocities. Our method was finally assessed on in vivo datasets and showed consistent improvement in image quality and motion estimation compared to standard compounding. This demonstrates the feasibility and effectiveness of deep learning reconstruction for ultrafast speckle-tracking echocardiography.

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.

A Data-Efficient Deep Learning Strategy for Tissue Characterization via Quantitative Ultrasound: Zone Training

Deep learning (DL) powered biomedical ultrasound imaging is an emerging research field where researchers adapt the image analysis capabilities of DL algorithms to biomedical ultrasound imaging settings. A major roadblock to wider adoption of DL powered biomedical ultrasound imaging is that acquisition of large and diverse datasets is expensive in clinical settings, which is a requirement for successful DL implementation. Hence, there is a constant need for developing data-efficient DL techniques to turn DL powered biomedical ultrasound imaging into reality. In this work, we develop a data-efficient DL training strategy for classifying tissues based on the ultrasonic backscattered RF data, i.e., quantitative ultrasound (QUS), which we named zone training. In zone training, we propose to divide the complete field of view of an ultrasound image into multiple zones associated with different regions of a diffraction pattern and then, train separate DL networks for each zone. The main advantage of zone training is that it requires less training data to achieve high accuracy. In this work, three different tissue-mimicking phantoms were classified by a DL network. The results demonstrated that zone training can require a factor of 2-3 less training data in low data regime to achieve similar classification accuracies compared to a conventional training strategy.

Convolutional Neural Network-Based Speckle Tracking for Ultrasound Strain Elastography: An Unsupervised Learning Approach

Accurate and computationally efficient motion estimation is a critical component of real-time ultrasound strain elastography (USE). With the advent of deep-learning neural network models, a growing body of work has explored supervised convolutional neural network (CNN)-based optical flow in the framework of USE. However, the above-said supervised learning was often done using simulated ultrasound data. The research community has questioned whether simulated ultrasound data containing simple motion can train deep-learning CNN models that can reliably track complex in vivo speckle motion. In parallel with other research groups' efforts, this study developed an unsupervised motion estimation neural network (UMEN-Net) for USE by adapting a well-established CNN model named PWC-Net. Our network's input is a pair of predeformation and postdeformation radio frequency (RF) echo signals. The proposed network outputs both axial and lateral displacement fields. The loss function consists of a correlation between the predeformation signal and the motion-compensated postcompression signal, smoothness of the displacement fields, and tissue incompressibility. Notably, an innovative correlation method known as the globally optimized correspondence (GOCor) volumes module developed by Truong et al. was used to replace the original Corr module to enhance our evaluation of signal correlation. The proposed CNN model was tested using simulated, phantom, and in vivo ultrasound data containing biologically confirmed breast lesions. Its performance was compared against other state-of-the-art methods, including two deep-learning-based tracking methods (MPWC-Net++ and ReUSENet) and two conventional tracking methods (GLUE and BRGMT-LPF). In summary, compared with the four known methods mentioned above, our unsupervised CNN model not only obtained higher signal-to-noise ratios (SNRs) and contrast-to-noise ratios (CNRs) for axial strain estimates but also improved the quality of the lateral strain estimates.