A Systematic Investigation of Lateral Estimation Using Various Interpolation Approaches in Conventional Ultrasound Imaging

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.

Influence of key parameters on motion artifacts in lateral strain estimation with spatial angular compounding

Strain imaging can reveal the changes in tissue mechanical properties related to pathological alterations by estimating tissue strains in the lateral and axial directions of ultrasound imaging. The estimation performance in the lateral direction is usually worse than that in the axial direction. Spatial angular compounding (SAC) has been demonstrated to improve the quality of lateral estimation by deriving the lateral displacements using axial displacements obtained from multi-angle transmissions. However, motion and deformation of tissues during multiple transmissions may cause motion artifacts, and thus deteriorate the quality of strain estimation. These artifacts can be reduced by choosing appropriate imaging parameters. However, few studies have been conducted to evaluate the influences of key parameters in strain estimation, such as the pulse repetition frequency (PRF), the number of steering angles (NSA), and the maximum steering angles (MSA), in terms of performance optimization. Therefore, this study aims to investigate the effects of these parameters through simulations and phantom experiments. The performance of strain estimation is evaluated by measuring the root-mean-square error (RMSE) and the standard deviation (SD) in the simulations and phantom experiments, respectively. The contrast-to-noise ratio (CNR) of strain images is calculated in both the simulations and phantom experiments. The results show that motion artifacts in strain estimation can be reduced by increasing the PRF to 1 kHz. When the PRF reaches 1 kHz, further increase of the PRF shows little obvious improvement in strain estimation. An increase in the NSA can cause larger motion artifacts and deteriorate the quality of strain images, and the improvement of strain estimation is limited when the NSA is increased from 3 to 7. An NSA of 3 is thus recommended to balance the influences of motion artifacts and the improvement for strain estimation. The MSA has little influence on the motion artifacts, while increased MSA can achieve improved lateral estimation performance at the cost of a smaller imaging region. In light of the lateral strain estimation performance and imaging region, an MSA of 15° is recommended. The influences of these key parameters obtained from this study may provide insights for parameter optimization in strain estimation with SAC to minimize the effects of motion artifacts.

Separated Respiratory Phases for In Vivo Ultrasonic Thermal Strain Imaging

Thermal strain imaging (TSI) uses echo shifts in ultrasonic B-scan images to estimate changes in temperature which is of great values for thermotherapies. However, for in vivo applications, it is difficult to overcome the artifacts and errors arising from physiological motions. Here, a respiration separated TSI (RS-TSI) method is proposed, which can be considered as carrying out TSI in each of the exhalation and inhalation phases and then combining the results. Normalized cross correlation (NXcorr) coefficient between RF images along the timeline are used to extract the respiratory frequency, after which reference frames are selected to identify the exhalation and inhalation phases, and the two phases are divided quasi-periodically. RF images belonging to both phases are selected by applying NXcorr thresholds, and motion compensation together with a second frame selection helps to obtain two finely matched image sequences. After TSI calculations for each phase, the two processes are merged into one through extrapolation and interphase averaging. Compared to TSI based on dynamic frame selection (DFS), RS-TSI ensures that frames are selected during both the exhalation and inhalation phases while setting the frame selection range according to the respiratory frequency helps to improve motion compensation. The temporal intervals of TSI output are approximately half that employing DFS.

Hadamard-Encoded Synthetic Transmit Aperture Imaging for Improved Lateral Motion Estimation in Ultrasound Elastography

Lateral motion estimation has been a challenge in ultrasound elastography mainly due to the low resolution, low sampling frequency, and lack of phase information in the lateral direction. Synthetic transmit aperture (STA) can achieve high resolution due to two-way focusing and can beamform high-density image lines for improved lateral motion estimation with the disadvantages of low signal-to-noise ratio (SNR) and limited penetration depth. In this study, Hadamard-encoded STA (Hadamard-STA) is proposed for the improvement of lateral motion estimation in elastography, and it is compared with STA and conventional focused wave (CFW) imaging. Simulations, phantom, and in vivo experiments were conducted to make the comparison. The normalized root mean square error (NRMSE) and the contrast-to-noise ratio (CNR) were calculated as the evaluation criteria in the simulations. The results show that, at a noise level of -10 dB and an applied strain of -1% (compression), Hadamard-STA decreases the NRMSEs of lateral displacements by 46.92% and 35.35%, decreases the NRMSEs of lateral strains by 52.34% and 39.75%, and increases the CNRs by 9.70 and 9.75 dB compared with STA and CFW, respectively. In the phantom experiments performed on a heterogeneous tissue-mimicking phantom, the sum of squared differences (SSD) between the reference and the motion-compensated RF data, and the CNR were calculated as the evaluation criteria. At an applied strain of -1.80%, Hadamard-STA is found to decrease the SSDs by 20.91% and 30.99% and increase the CNRs by 14.15 and 24.66 dB compared with STA and CFW, respectively. In the experiments performed on a breast phantom, Hadamard-STA achieves better visualization of the breast inclusion with a clearer boundary between the inclusion and the background than STA and CFW. The in vivo experiments were performed on a patient with a breast tumor, and the tumor could also be better visualized with a more homogeneous background in the strain image obtained by Hadamard-STA than by STA and CFW. These results demonstrate that Hadamard-STA achieves a substantial improvement in lateral motion estimation and maybe a competitive method for quasi-static elastography.

Virtual Source Synthetic Aperture for Accurate Lateral Displacement Estimation in Ultrasound Elastography

Ultrasound elastography (USE) is an emerging noninvasive imaging technique in which pathological alterations can be visualized by revealing the mechanical properties of the tissue. Estimating tissue displacement in all directions is required to accurately estimate the mechanical properties. Despite capabilities of elastography techniques in estimating displacement in both axial and lateral directions, estimation of axial displacement is more accurate than lateral direction due to higher sampling frequency, higher resolution, and having a carrier signal propagating in the axial direction. Among different ultrasound imaging techniques, synthetic aperture (SA) has better lateral resolution than others, but it is not commonly used for USE due to its limitation in imaging depth of field. Virtual source synthetic aperture (VSSA) imaging is a technique to implement SA beamforming on the focused transmitted data to overcome the limitation of SA in depth of field while maintaining the same lateral resolution as SA. Besides lateral resolution, VSSA has the capability of increasing sampling frequency in the lateral direction without interpolation. In this article, we utilize VSSA to perform beamforming to enable higher resolution and sampling frequency in the lateral direction. The beamformed data are then processed using our recently published elastography technique, OVERWIND. Simulation and experimental results show substantial improvement in the estimation of lateral displacements.

A Novel Normalized Cross-Correlation Speckle-Tracking Ultrasound Algorithm for the Evaluation of Diaphragm Deformation

Objectives: To develop a two-dimensional normalized cross-correlation (NCC)-based ultrasonic speckle-tracking algorithm for right diaphragm deformation analysis.

Methods: Six healthy and eight mechanical ventilation patients were enrolled in this study. Images were acquired by a portable ultrasound system in three sections. DICOM data were processed with NCC to obtain the interframe/cumulative vertical and horizontal displacements, as well as the global strain of the right diaphragm, with continuous tracking and drift correction.

Results: The NCC algorithm can track the contraction and relaxation of the right diaphragm by following the respiratory movement continuously. For all three sections, the interframe and accumulated horizontal displacements were both significantly larger than the corresponding vertical displacements (interframe p values: 0.031, 0.004, and 0.000; cumulative p values: 0.039, 0.001, and <0.0001). For the global strain of the right diaphragm, there was no significant difference between each pair of sections (all p > 0.05), regardless of whether the horizontal interval of the initial diaphragm point was 1, 3, 5, or 10 times in the sampling interval.

Conclusions: This study developed a novel diaphragm deformation ultrasound imaging method. This method can be used to estimate the diaphragm interframe/accumulated displacement in the horizontal and vertical directions and the global strain on three different imaging planes, and it was found that the strain was not sensitive to the imaging plane.

Shear Induced Non-Linear Elasticity Imaging: Elastography for Compound Deformations

The goal of non-linear ultrasound elastography is to characterize tissue mechanical properties under finite deformations. Existing methods produce high contrast non-linear elastograms under conditions of pure uni-axial compression, but exhibit bias errors of 10-50% when the applied deformation deviates from the uni-axial condition. Since freehand transducer motion generally does not produce pure uniaxial compression, a motion-agnostic non-linearity estimator is desirable for clinical translation. Here we derive an expression for measurement of the Non-Linear Shear Modulus (NLSM) of tissue subject to combined shear and axial deformations. This method gives consistent nonlinear elasticity estimates irrespective of the type of applied deformation, with a reduced bias in NLSM values to 6-13%. The method combines quasi-static strain imaging with Single-Track Location-Shear Wave Elastography (STL-SWEI) to generate local estimates of axial strain, shear strain, and Shear Wave Speed (SWS). These local values were registered and non-linear elastograms reconstructed with a novel nonlinear shear modulus estimation scheme for general deformations. Results on tissue mimicking phantoms were validated with mechanical measurements and multiphysics simulations for all deformation types with an error in NLSM of 6-13%. Quantitative performance metrics with the new compound-motion tracking strategy reveal a 10-15 dB improvement in Signal-to-Noise Ratio (SNR) for simple shear versus pure compressive deformation for NLSM elastograms of homogeneous phantoms. Similarly, the Contrast-to-Noise Ratio (CNR) of NLSM elastograms of inclusion phantoms improved by 25-30% for simple shear over pure uni-axial compression. Our results show that high fidelity NLSM estimates may be obtained at ~30% lower strain under conditions of shear deformation as opposed axial compression. The reduction in strain required could reduce sonographer effort and improve scan safety.

Improving Ultrasound Lateral Strain Estimation Accuracy using Log Compression of Regularized Correlation Function

Normalized cross-correlation (NCC) function used in ultrasound strain imaging can get corrupted due to signal decorrelation inducing large displacement errors. Bayesian regularization has been applied in an iterative manner to regularize the NCC function and to reduce estimation variance and peak-hopping errors. However, incorrect choice of the number of iterations can lead to over-regularization errors. In this paper, we propose the use of log compression of regularized NCC function to improve subsample estimation. Performance of parabolic interpolation before and after log compression of the regularized NCC function were compared in numerical simulations of uniform and inclusion phantoms. Significant improvement was achieved with the proposed scheme for lateral estimation results. For example, lateral signal-to-noise ratio (SNR) was 10 dB higher after log compression at 3% strain in a uniform phantom. Lateral contrast-to-noise ratio (CNR) was 1.81 dB higher with proposed method at 3% strain in inclusion phantom. No significant difference was observed in axial estimation due to presence of phase information and high sampling frequency. Our results suggest that this simple approach makes Bayesian regularization robust to over-regularization artifacts.

Locally optimized correlation-guided Bayesian adaptive regularization for ultrasound strain imaging

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 (CNR _e ) 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 CNR _e 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.

Spatial Angular Compounding With Affine-Model-Based Optical Flow for Improvement of Motion Estimation

Tissue motion estimation is an essential step for ultrasound elastography. Our previous study has shown that the affine-model-based optical flow (OF) method outperforms the normalized cross-correlation-based block matching (BM) method in motion estimation. However, the quality of lateral estimation using OF is still low due to inherent limitation of ultrasound imaging. BM-based spatial angular compounding (SAC) has been developed to obtain better motion estimation. In this paper, OF-based SAC (OF-SAC) is proposed to further improve the performance of lateral (and axial) estimation, and it is compared with BM-based SAC (BM-SAC). Plane wave as well as focused wave is transmitted in both simulations and phantom experiments on a linear array. In order to compare the performance quantitatively, the root-mean-square error (RMSE) of axial/lateral displacement and strain, and signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) of axial/lateral strain are used as the evaluation criteria in the simulations. In the phantom experiments, the SNR and CNR are used to assess the quality of axial/lateral strain. The results show that for both OF and BM, SAC improves the performance of motion estimation, regardless of using plane or focused wave transmission. More importantly, OF-SAC is shown to outperform BM-SAC with lower RMSE, higher SNR, and higher CNR. In addition, preliminary in vivo experiments on the carotid artery of a healthy human subject also prove the superiority of OF-SAC. These results suggest that OF-SAC is preferred for both axial and lateral motion estimation to BM-SAC.

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.

Assessment of Mechanical Properties of Tissue in Breast Cancer-Related Lymphedema Using Ultrasound Elastography

Breast cancer-related lymphedema is a consequence of a malfunctioning lymphatic drainage system resulting from surgery or some other form of treatment. In the initial stages, minor and reversible increases in the fluid volume of the arm are evident. As the stages progress over time, the underlying pathophysiology dramatically changes with an irreversible increase in arm volume most likely due to a chronic local inflammation leading to adipose tissue hypertrophy and fibrosis. Clinicians have subjective ways to stage the degree and severity such as the pitting test which entails manually comparing the elasticity of the affected and unaffected arms. Several imaging modalities can be used but ultrasound appears to be the most preferred because it is affordable, safe, and portable. Unfortunately, ultrasonography is not typically used for staging lymphedema, because the appearance of the affected and unaffected arms is similar in B-mode ultrasound images. However, novel ultrasound techniques have emerged, such as elastography, which may be able to identify changes in mechanical properties of the tissue related to detection and staging of lymphedema. This paper presents a novel technique to compare the mechanical properties of the affected and unaffected arms using quasi-static ultrasound elastography to provide an objective alternative to the current subjective assessment. Elastography is based on time delay estimation (TDE) from ultrasound images to infer displacement and mechanical properties of the tissue. We further introduce a novel method for TDE by incorporating higher order derivatives of the ultrasound data into a cost function and propose a novel optimization approach to efficiently minimize the cost function. This method works reliably with our challenging patient data. We collected radio frequency ultrasound data from both arms of seven patients with stage 2 lymphedema, at six different locations in each arm. The ratio of strain in skin, subcutaneous fat, and skeletal muscle divided by strain in the standoff gel pad was calculated in the unaffected and affected arms. The p -values using a Wilcoxon sign-rank test for the skin, subcutaneous fat, and skeletal muscle were 1.24×10^-5 , 1.77×10^-8 , and 8.11×10^-7 respectively, showing differences between the unaffected and affected arms with a very high level of significance.

Comparison of Displacement Tracking Algorithms for in Vivo Electrode Displacement Elastography

Hepatocellular carcinoma and liver metastases are common hepatic malignancies presenting with high mortality rates. Minimally invasive microwave ablation (MWA) yields high success rates similar to surgical resection. However, MWA procedures require accurate image guidance during the procedure and for post-procedure assessments. Ultrasound electrode displacement elastography (EDE) has demonstrated utility for non-ionizing imaging of regions of thermal necrosis created with MWA in the ablation suite. Three strategies for displacement vector tracking and strain tensor estimation, namely coupled subsample displacement estimation (CSDE), a multilevel 2-D normalized cross-correlation method, and quality-guided displacement tracking (QGDT) have previously shown accurate estimations for EDE. This paper reports on a qualitative and quantitative comparison of these three algorithms over 79 patients after an MWA procedure. Qualitatively, CSDE presents sharply delineated, clean ablated regions with low noise except for the distal boundary of the ablated region. Multilevel and QGDT contain more visible noise artifacts, but delineation is seen over the entire ablated region. Quantitative comparison indicates CSDE with more consistent mean and standard deviations of region of interest within the mass of strain tensor magnitudes and higher contrast, while Multilevel and QGDT provide higher CNR. This fact along with highest success rates of 89% and 79% on axial and lateral strain tensor images for visualization of thermal necrosis using the Multilevel approach leads to it being the best choice in a clinical setting. All methods, however, provide consistent and reproducible delineation for EDE in the ablation suite.

3-D Single Breath-Hold Shear Strain Estimation for Improved Breast Lesion Detection and Classification in Automated Volumetric Ultrasound Scanners

Automated breast volume scanner (ABVS) is an ultrasound imaging modality used in breast cancer screening. It has high sensitivity but limited specificity as it is hard to discriminate between benign and malignant lesions by echogenic properties. Specificity might be improved by shear strain imaging as malignant lesions, firmly bonded to its host tissue, show different shear patterns compared to benign lesions, often loosely bonded. Therefore, 3-D quasi-static elastography was implemented in an ABVS-like system. Plane wave instead of conventional focused transmissions were used to reduce scan times within a single breath hold. A 3-D strain tensor was obtained and shear strains were reconstructed in phantoms containing firmly and loosely bonded lesions. Experiments were also simulated in finite-element models (FEMs). Experimental results, confirmed by FEM-results, indicated that loosely bonded lesions showed increased maximal shear strains (~2.5%) and different shear patterns compared to firmly bonded lesions (~0.9%). To conclude, we successfully implemented 3-D elastography in an ABVS-like system to assess lesion bonding by shear strain imaging.

2D myocardial deformation imaging based on RF-based non-rigid image registration

Myocardial deformation imaging is a well-established echocardiographic technique for the assessment of myocardial function. Although some solutions make use of speckle tracking of the reconstructed B-mode images, others apply block matching on the underlying radio-frequency (RF) data in order to increase sensitivity to small inter-frame motion and deformation. However, for both approaches, lateral motion estimation remains a challenge due to the relatively poor lateral resolution of the ultrasound image in combination with the lack of phase information in this direction. Hereto, non-rigid image registration (NRIR) of B-mode images has previously been proposed as an attractive solution. However, hereby, the advantages of RF-based tracking were lost. The aim of this study was therefore to develop an NRIR motion estimator adopted to RF data sets. The accuracy of this estimator was quantified using synthetic data and was contrasted against a state of the art block matching solution. The results show that RF-based NRIR outperforms BM in terms of tracking accuracy particularly, as hypothesized, in the lateral direction. Finally, this RF-based NRIR algorithm was applied clinically, illustrating its ability to estimate both in-plane velocity components in-vivo.