Axial Strain Estimation Research Articles

Teacher-student guided knowledge distillation for unsupervised convolutional neural network-based speckle tracking in ultrasound strain elastography.

Accurate and efficient motion estimation is a crucial component of real-time ultrasound elastography (USE). However, obtaining radiofrequency ultrasound (RF) data in clinical practice can be challenging. In contrast, although B-mode (BM) data is readily available, elastographic data derived from BM data results in sub-optimal elastographic images. Furthermore, existing conventional ultrasound devices (e.g., portable devices) cannot provide elastography modes, which has become a significant obstacle to the widespread use of traditional ultrasound devices. To address the challenges above, we developed a teacher-student guided knowledge distillation for an unsupervised convolutional neural network (TSGUPWC-Net) to improve the accuracy of BM motion estimation by employing a well-established convolutional neural network (CNN) named modified pyramid warping and cost volume network (MPWC-Net). A pre-trained teacher model based on RF is utilized to guide the training of a student model using BM data. Innovations outlined below include employing spatial attention transfer at intermediate layers to enhance the guidance effect of the model. The loss function consists of smoothness of the displacement field, knowledge distillation loss, and intermediate layer loss. We evaluated our method on simulated data, phantoms, and in vivo ultrasound data. The results indicate that our method has higher signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) values in axial strain estimation than the model trained on BM. The model is unsupervised and requires no ground truth labels during training, making it highly promising for motion estimation applications.

A Novel Poroelastography Method for High-quality Estimation of Lateral Strain, Solid Stress and Fluid Pressure In Vivo.

Assessment of mechanical and transport properties of tissues using ultrasound elasticity imaging requires accurate estimations of the spatiotemporal distribution of volumetric strain. Due to physical constraints such as pitch limitation and the lack of phase information in the lateral direction, the quality of lateral strain estimation is typically significantly lower than the quality of axial strain estimation. In this paper, a novel lateral strain estimation technique based on the physics of compressible porous media is developed, tested and validated. This technique is referred to as "Poroelastography-based Ultrasound Lateral Strain Estimation" (PULSE). PULSE differs from previously proposed lateral strain estimators as it uses the underlying physics of internal fluid flow within a local region of the tissue as theoretical foundation. PULSE establishes a relation between spatiotemporal changes in the axial strains and corresponding spatiotemporal changes in the lateral strains, effectively allowing assessment of lateral strains with comparable quality of axial strain estimators. We demonstrate that PULSE can also be used to accurately track compression-induced solid stresses and fluid pressure in cancers using ultrasound poroelastography (USPE). In this study, we report the theoretical formulation for PULSE and validation using finite element (FE) and ultrasound simulations. PULSE-generated results exhibit less than 5% percentage relative error (PRE) and greater than 90% structural similarity index (SSIM) compared to ground truth simulations. Experimental results are included to qualitatively assess the performance of PULSE in vivo. The proposed method can be used to overcome the inherent limitations of non-axial strain imaging and improve clinical translatability of USPE.

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.

Axial compressive behavior and model assessment of FRP-confined seawater sea-sand concrete-filled stainless steel tubular stub columns

Concrete-filled steel tubular (CFST) columns have corrosion issues in coastal/offshore constructions. Thus, a FRP-confined seawater sea-sand concrete (SSC)-filled stainless steel tubular (SST) column (FRP-SSCFSST) is proposed to mitigate corrosion problems. Meanwhile, the use of SSC can relieve the over-exploitation of river-sands. In the present study, the axial compressive behavior of FRP-SSCFSST columns was investigated through testing 12 pairs of stub columns (two duplicates in a pair) including 6 pairs of FRP-SSCFSST specimens, 4 pairs of SSCFSST specimens, and 2 pairs of unconfined concrete specimens. FRP thickness, wall thickness of stainless steel tubes, and concrete strength are the influencing parameters examined in this study. The experimental results showed that the FRP-SSCFSST specimens exhibited a strain-hardening response with the full activation segment as a second ascending line. The SST confinement was less significant, as doubling the wall thickness of SST only led to a small difference in strength index. However, both strength index and strain enhancement ratio increased almost linearly with the increase of FRP thickness. An increase in the concrete strength could result in a reduction in both strength index and axial strain enhancement ratio due to the brittleness of high strength concrete. In addition, the performances of seven load-capacity prediction models and two ultimate axial strain estimation equations were evaluated by using the test results. With minor modifications, Lam and Teng’s model had the best performance in predicting the load carrying capacities of the specimens with an average absolute error at only 3.9%.

Comparison of ultrasonic motion estimators for vascular applications

One-dimensional (1D) motion estimators based on a phase shift of an ultrasonic echo signal have been used to estimate the axial strain of the artery. However, the lateral motion induced by the heartbeat cannot be neglected. Therefore, we proposed a two-dimensional (2D) phase-sensitive motion estimator previously. In this study, simulation experiments were performed to compare the accuracy of the 1D, 2D phase-sensitive, and speckle tracking methods. Furthermore, those three methods were applied to data obtained from a common carotid artery. The 2D phase-sensitive method showed the best accuracy among three, bias errors of 0.5% and standard deviations of 6.6% were obtained with respect to the estimated axial velocities in the simulation experiments. Meanwhile, the speckle tracking showed the best accuracy on the axial strain estimation, bias errors of 4.4% and standard deviations of 8.5% were obtained. In conclusion, the accuracy in the estimation of motion and strain was improved by considering the lateral motion.

Visualizing Angle-Independent Principal Strains in the Longitudinal View of the Carotid Artery: Phantom and In Vivo Evaluation

Non-invasive vascular elastography can evaluate the stiffness of the carotid artery by visualizing the vascular strain distribution. Axial strain estimates of the longitudinal cross section of the carotid artery are sensitive to the angle between the artery and the transducer. Anatomical variations in branching and arching of the carotid artery can affect the assessment of arterial stiffness. In this study, we hypothesized that principal strain elastograms computed using compounded plane wave imaging can reliably visualize the strain distribution in the carotid artery, independent of the transducer angle. We corroborated this hypothesis by conducting phantom and in vivo studies using a commercial ultrasound scanner (Sonix RP, Ultrasonix Medical Corp., Richmond, BC, Canada). The phantom studies were conducted using a homogeneous cryogel vessel phantom. The goal of the phantom study was to assess the feasibility of visualizing the radial deformation in the longitudinal plane of the vessel phantom, independent of the transducer angle (±30°, ±20°, ±10° and 0°). The in vivo studies were conducted on 20 healthy human volunteers in the age group 50–60 y. All echo imaging was performed at a transmit frequency of 5 MHz and sampling frequency of 40 MHz. The elastograms obtained from the phantom study revealed that for straight vessels, which had their lumen parallel to the transducer, principal strains were similar to axial strains. At non-parallel configurations (angles ±30°, ±20° and ±10°), the magnitudes of the mean principal strains were within 2.5% of the parallel configuration (0° angle) estimates and, thus, were observed to be relatively unaffected by change in angle. However, in comparison, the magnitude of the axial strain decreased with increase in angle because of coordinate dependency. Further, the pilot in vivo study indicated that the principal and axial strain elastograms were similar for subjects with relatively straight arteries. However, for arteries with arched geometry, axial strains were significantly lower (p < 0.01) than the corresponding principal vascular strains, which was consistent with the results obtained from the phantom study. In conclusion, the results of the phantom and in vivo studies revealed that principal strain elastograms computed using CPW imaging could reliably visualize angle-independent vascular strains in the longitudinal plane of the carotid artery.

A Fast Peak-Searching Algorithm for Ultrasonic Elastography.

Tissue axial strain estimation with ultrasound elastography has become a hot field in recent years. However, for keypoints tracking-based elastography algorithms, locating extrema in multimodal ultrasonic radiofrequency signals is still a challenging problem. In this paper, a new method is proposed to locate the local maxima and minima of the RF signals directly without derivation operation. This algorithm can accurately locate extrema even if disturbed peaks resulting from different noise exist. Furthermore, the new algorithm can speed up approximately 79% of the implementation process as compared with the standard cross-correlation method on the same computing platform. In addition, the elastographic signal-to-noise ratio and the contrast-to-noise ratio are also significantly improved with this new method.

Stochastic precision analysis of 2D cardiac strain estimation in vivo

Ultrasonic strain imaging has been applied to echocardiography and carries great potential to be used as a tool in the clinical setting. Two-dimensional (2D) strain estimation may be useful when studying the heart due to the complex, 3D deformation of the cardiac tissue. Increasing the framerate used for motion estimation, i.e. motion estimation rate (MER), has been shown to improve the precision of the strain estimation, although maintaining the spatial resolution necessary to view the entire heart structure in a single heartbeat remains challenging at high MERs. Two previously developed methods, the temporally unequispaced acquisition sequence (TUAS) and the diverging beam sequence (DBS), have been used in the past to successfully estimate in vivo axial strain at high MERs without compromising spatial resolution. In this study, a stochastic assessment of 2D strain estimation precision is performed in vivo for both sequences at varying MERs (65, 272, 544, 815 Hz for TUAS; 250, 500, 1000, 2000 Hz for DBS). 2D incremental strains were estimated during left ventricular contraction in five healthy volunteers using a normalized cross-correlation function and a least-squares strain estimator. Both sequences were shown capable of estimating 2D incremental strains in vivo. The conditional expected value of the elastographic signal-to-noise ratio (E(SNRe|ε)) was used to compare strain estimation precision of both sequences at multiple MERs over a wide range of clinical strain values. The results here indicate that axial strain estimation precision is much more dependent on MER than lateral strain estimation, while lateral estimation is more affected by strain magnitude. MER should be increased at least above 544 Hz to avoid suboptimal axial strain estimation. Radial and circumferential strain estimations were influenced by the axial and lateral strain in different ways. Furthermore, the TUAS and DBS were found to be of comparable precision at similar MERs.

2D myocardial strain assessment in the mouse: A comparison between a synthetic lateral phase approach and block-matching using computer simulation

Estimating myocardial strain in the mouse with clinical equipment remains difficult due to the high heart rate and the small size of the mouse heart. Measuring the strain component perpendicular to the ultrasound beam is especially challenging because of the lack of phase information in that direction and the large speckle width compared to the wall thickness. In this study, the performance of a Synthetic Lateral Phase (SLP) approach was contrasted to a standard and a regularized 2D Speckle Tracking (2D ST) algorithm using simulated data sets. SLP yielded higher rms errors for the lateral strain estimates than the regularized 2D ST (Lateral rms error: 0.087±0.012 vs. 0.052±0.010; p<0.05). No significant difference was found between the standard 2D ST and SLP. For the axial strain estimates, SLP produced higher rms errors than the standard 2D ST (Axial rms error: 0.063±0.012 vs. 0.040±0.008; p<0.05). 2D ST combined with geometric regularization showed thus to be the most accurate method.

A motion estimation refinement framework for real-time tissue axial strain estimation with freehand ultrasound

Ultrasound elastography has become a wellknown optional imaging method for the diagnosis of tissue abnormalities in various body parts. It images the elasticity of compliant tissues by estimating the local displacements and strains using pre- and post-compression RF echo signals. In this paper, taking the RF signal as image intensity and RF samples as pixels, we present a motion estimation framework to compute the axial tissue displacements and strains. This method takes advantage of both the block matching algorithm (BMA) and local optical flow techniques. For two frames of RF signals, coarse motion estimates are first computed using BMA. The motion estimates obtained are then used to warp the first frame toward the second one, thus making the warped frame more spatially correlated to the second one. Next, the Lucas-Kanade optical flow method is employed to compute the residual motion between the warped frame and the original second frame, with inherent sub-pixel precision. Finally, the displacements from the two steps are combined. The warp-and-refine procedure can be iterated if the residual motion is larger than a predefined empirical threshold. To test its feasibility, we first applied the method to simulated data. The results show that our method is robust to relatively large motions and is capable of generating accurate motion estimation with subsample spatial resolution. These methods have been deployed and are being tested on a commercialized ultrasound machine that previously did not have elastography functions. Quality real-time display of elastography along with freehand scanning has been accomplished. The proposed framework provides an alternative method for motion estimation with good performance, and it can potentially be improved using hardware to realize the BMA.

Estimation of the Optimal Maximum Beam Angle and Angular Increment for Normal and Shear Strain Estimation

In the current practice of ultrasound elastography, only the axial component of the displacement vector is estimated and used to produce strain images. A method was recently proposed by our group to estimate both the axial and lateral components of a displacement vector using RF echo signal data acquired along multiple angular insonification directions of the ultrasound beam. Previous work has demonstrated that it is important to choose appropriate values for the maximum beam angle and angular increment to achieve optimal performance with this technique. In this paper, we present error propagation analysis using the least-square fitting process for the optimization of the angular increment and the maximum beam steered angle. Ultrasound simulations are performed to corroborate the theoretical prediction of the optimal values for the maximum beam angle and angular increment. Selection of the optimal parameters depends on system parameters, such as center frequency and aperture size. For typical system parameters, the optimal maximum beam angle is around 10 degrees for axial strain estimation and around 15 degrees for lateral strain estimation. The optimal angular increment is around 4 degrees-6 degrees, which indicates that only five to seven beam angles are required for this strain-tensor estimation technique.

SU‐EE‐A4‐06: Estimation of the Optimal Maximum Beam Angle and Angular Increment for Normal and Shear Strain Estimation

Purpose: In current ultrasound elastography, only the axial component of the displacement vector is estimated and used to produce strain images. Previously we had proposed a method to estimate both the axial and lateral components of a displacement vector using radiofrequency echo signal data acquired along multiple angular insonification directions of the ultrasound beam. In this study, we present error propagation through the least square fitting process for optimization of the angular increment and maximum beam steered angle. Method and Materials: Ultrasound simulations are performed to corroborate theoretical predictions of the optimal values for the maximum beam angle and angular increment. Beam steering characteristics of the linear array were simulated by selecting appropriate time delays for each element which determines the focal point and steering angle for the beam. A uniformly elastic phantom was simulated by modeling a random distribution of 50 μm polystyrene beads with an average concentration of 9.7/mm3 in a medium (to simulate Rayleigh scattering). After computing RF signals for each insonification angle, the phantom was deformed by a uniaxial compression (1% of the phantom height). The displacement of each scatterer in the phantom was calculated using the Finite Element Analysis (FEA) software ANSYS. The new scatterer positions were used for calculating the post compression echo signals at each insonification angle. Results: The theoretical prediction matches well with numerical simulations. For typical system parameters, the optimal maximum beam angle is around 10‐deg for axial strain estimation, and around 15‐deg for lateral strain estimation. The optimal angular increment is around 4∼6 deg, which indicates that only 5∼7 beam angles are required for this strain tensor estimation technique. Conclusion: The theory presented in this study is useful for choosing optimal parameters for the angular data acquisition process for strain tensor estimation.

Dynamics of errors in 3D motion estimation and implications forstrain-tensor imaging in acoustic elastography

For the purpose of quantifying the noise in acoustic elastography, adisplacement covariance matrix is derived analytically for thecross-correlation based 3D motion estimator. Static deformation induced intissue from an external mechanical source is represented by a second-orderstrain tensor. A generalized 3D model is introduced for the ultrasonic echosignals. The components of the covariance matrix are related to the variancesof the displacement errors and the errors made in estimating the elements ofthe strain tensor. The results are combined to investigate the dependences ofthese errors on the experimental and signal-processing parameters as well asto determine the effects of one strain component on the estimation of theother. The expressions are evaluated for special cases of axial strainestimation in the presence of axial, axial-shear and lateral-shear typedeformations in 2D. The signals are shown to decorrelate with any of thesedeformations, with strengths depending on the reorganization and interactionof tissue scatterers with the ultrasonic point spread function following thedeformation. Conditions that favour the improvements in motion estimationperformance are discussed, and advantages gained by signal companding andpulse compression are illustrated.

On the use of a modified optical flow algorithm for the correction of axial strain estimates in ultrasonic elastography in medical diagnosis

Tumors of the prostate exhibit a significant mechanical hardness in comparison to the surrounding tissue. However, they often can not be reliably detected in the B-mode image. For this reason, digital palpation of the prostate is still a major tool in tumor diagnostics. Ultrasonic elastography estimates the tissue elasticity from an image series recorded under increasing axial tissue compression applied by the transrectal probe. As a new imaging modality, it promises to support conventional prostate screening methods. Usually, time delays from two corresponding A-lines are estimated by cross-correlation methods applied to the acquired rf data set assuming a uniform axial compression. However, in clinical in vivo data, especially in data which were acquired with a sector scanner, significant lateral motion of the tissue which deteriorates the elasticity estimate was observed. A method is presented which uses a modified ‘‘optical flow’’ algorithm to determine the global two-dimensional motion of the imaged object. This information is used to correct the corresponding A-lines according to the encountered lateral deformation. It is shown that this method is able to improve the strain estimates on data with low signal-to-noise conditions. Images of phantoms and clinical in vivo data are presented. [Work supported by DFG Grant ER 94/20-1.]

A new elastographic method for estimation and imaging of lateral displacements, lateral strains, corrected axial strains and poisson’s ratios in tissues

A major disadvantage of the current practice of elastography is that only the axial component of the strain is estimated. The lateral and elevational components are basically disregarded, yet they corrupt the axial strain estimation by inducing decorrelation noise. In this paper, we describe a new weighted interpolation method operating between neighboring RF A-lines for high precision tracking of the lateral displacement. Due to this high lateral-tracking precision, quality lateral elastograms are generated that display the lateral component of the strain tensor. These precision lateral-displacement estimates allow a fine correction for the lateral decorrelation that corrupts the axial estimation. Finally, by dividing the lateral elastogram by the axial elastogram, we are able to produce a new image that displays the distribution of Poisson’s ratios in the tissue. Results are presented from finite-element simulations and phantoms as well as in vitro and in vivo experiments.