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

Neural-network-based Motion Tracking for Breast Ultrasound Strain Elastography: An Initial Assessment of Performance and Feasibility

Accurate tracking of tissue motion is critically important for several ultrasound elastography methods. In this study, we investigate the feasibility of using three published convolution neural network (CNN) models built for optical flow (hereafter referred to as CNN-based tracking) by the computer vision community for breast ultrasound strain elastography. Elastographic datasets produced by finite element and ultrasound simulations were used to retrain three published CNN models: FlowNet-CSS, PWC-Net, and LiteFlowNet. After retraining, the three improved CNN models were evaluated using computer-simulated and tissue-mimicking phantoms, and in vivo breast ultrasound data. CNN-based tracking results were compared with two published two-dimensional (2D) speckle tracking methods: coupled tracking and GLobal Ultrasound Elastography (GLUE) methods. Our preliminary data showed that, based on the Wilcoxon rank-sum tests, the improvements due to retraining were statistically significant (p < 0.05) for all three CNN models. We also found that the PWC-Net model was the best neural network model for data investigated, and its overall performance was on par with the coupled tracking method. CNR values estimated from in vivo axial and lateral strain elastograms showed that the GLUE algorithm outperformed both the retrained PWC-Net model and the coupled tracking method, though the GLUE algorithm exhibited some biases. The PWC-Net model was also able to achieve approximately 45 frames/second for 2D speckle tracking data investigated.

Slip elastography: a novel method for visualising and characterizing adherence between two surfaces in contact

Identification of the anatomical location and mechanical properties such as adherence at the tissue tumour interface may be of clinical benefit in determination of tumour resectability and prognosis. There are currently no imaging modalities in routine clinical practice that can provide this information. This paper presents the development of a new imaging technique based on ultrasound elastography, called slip elastography, for determination of the anatomical location and measurement of the adherence between two surfaces. The theoretical basis of slip and its definition in relation to shear are described. In vitro testing with gelatine phantoms to determine the optimal parameters for shear strain estimation and slip boundary measurement and to test reliability are also described. The results suggest that slip elastography can reliably identify the anatomical location of a slip boundary and can measure the externally applied axial force required to initiate slip at that boundary in vitro. The vector based shear strain estimator was the most robust and worked with minimal angular dependence with minimal non-slip shearing artefact.

Recent results in nonlinear strain and modulus imaging

We report a summary of recent developments and current status of our team's efforts to image and quantify in vivo nonlinear strain and tissue mechanical properties. Our work is guided by a focus on applications to cancer diagnosis and treatment using clinical ultrasound imaging and quasi-static tissue deformations. We review our recent developments in displacement estimation from ultrasound image sequences. We discuss cross correlation approaches, regularized optimization approaches, guided search methods, multiscale methods, and hybrid methods. Current implementations can return results of high accuracy in both axial and lateral directions at several frames per second.We compare several strain estimators. Again we see a benefit from a regularized optimization approach. We then discuss both direct and iterative methods to reconstruct tissue mechanical property distributions from measured strain and displacement fields. We review the formulation, discretization, and algorithmic considerations that come into play when attempting to infer linear and nonlinear elastic properties from strain and displacement measurements. Finally we illustrate our progress with example applications in breast disease diagnosis and tumor ablation monitoring. Our current status shows that we have demonstrated quantitative determination of nonlinear parameters in phantoms and in vivo, in the context of 2D models and data. We look forward to incorporating 3D data from 2D transducer arrays to noninvasively create calibrated 3D quantitative maps of nonlinear elastic properties of breast tissues in vivo.

Sub-sample displacement estimation from digitized ultrasound RF signals using multi-dimensional polynomial fitting of the cross-correlation function

A widely used time-domain technique for motion or delay estimation between digitized ultrasound RF signals involves the maximization of a discrete pattern-matching function, usually the cross-correlation. To achieve sub-sample accuracy, the discrete pattern-matching function is interpolated using the values at the discrete maximizer and adjacent samples. In prior work, only 1-D fit, applied separately along the axial, lateral, and elevational axes, has been used to estimate the sub-sample motion in 1-D, 2-D, and 3-D. In this paper, we explore the use of 2-D and 3-D polynomial fitting for this purpose. We quantify the estimation error in noise-free simulations using Field II and experiments with a commercial ultrasound machine. In simulated 2-D translational motions, function fitting with quartic spline polynomials leads to maximum bias of 0.2% of the sample spacing in the axial direction and 0.4% of the sample spacing in the lateral direction, corresponding to 38 nm and 1.31 μm, respectively. The maximum standard deviations were approximately 1% of the sample spacing in both the axial and the lateral directions, corresponding to 193 nm axially and 4.43 μm laterally. In simulated 1% axial strain, the same function fitting leads to mean absolute displacement estimation errors of 255 nm in the axial direction and 4.77 μm in the lateral direction. In experiments with a linear array transducer, 2-D quartic spline fitting leads to maximum bias of 458 nm and 6.27 μm in the axial and the lateral directions, respectively. These results are more than one order of magnitude smaller than those obtained with separate 1-D fit when applied to the same data set. Simulations and experiments in 3-D yield similar results when comparing 3-D polynomial fitting with 1-D fitting along the axial, lateral, and elevational directions.

Assisted-freehand ultrasound elasticity imaging

Good-quality elasticity imaging requires highly controlled compressions of the breast, which are often challenging to obtain with freehand, even by an experienced radiologist. This paper presents assisted-freehand ultrasound (AFUSON): a fusion of freehand and automated ultrasound systems designed to assisted elasticity imaging acquisition while remaining as flexible as freehand. In the form of a hand-held device, this semi-automatic solution delivers both increased acquisition precision and control. Compared with freehand acquisitions, it reduces out-of-plane motion decorrelation by one-half and lateral motion by one-third, increases within-scan repeatability by 50%, and does so across operators.

Correlation analysis of three-dimensional strain imaging using ultrasound two-dimensional array transducers

Two-dimensional (2D) transducer arrays represent a promising solution for implementing real time three-dimensional (3D) ultrasound elastography. 2D arrays enable electronic steering and focusing of ultrasound beams throughout a 3D volume along with improved slice thickness performance when compared to one-dimensional (1D) transducer arrays. Therefore, signal decorrelation caused by tissue motion in the elevational (out-of-plane) direction needs to be considered. In this paper, a closed form expression is derived for the correlation coefficient between pre- and postdeformation ultrasonic radio frequency signals. Signal decorrelation due to 3D motion of scatterers within the ultrasonic beam has been considered. Computer simulations are performed to corroborate the theoretical results. Strain images of a spherical inclusion phantom generated using 1D and 2D array transducers are obtained using a frequency domain simulation model. Quantitative image quality parameters, such as the signal-to-noise and contrast-to-noise ratios obtained using 1D, 2D, and 3D motion tracking algorithms, are compared to evaluate the performance with the 3D strain imaging system. The effect of the aperture size for 2D arrays and other factors that affect signal decorrelation are also discussed.

A model-based time-reversal of left ventricular motion improves cardiac motion analysis using tagged MRI data

BACKGROUND

Myocardial motion is an important observable for the assessment of heart condition. Accurate estimates of ventricular (LV) wall motion are required for quantifying myocardial deformation and assessing local tissue function and viability. Harmonic Phase (HARP) analysis was developed for measuring regional LV motion using tagged magnetic resonance imaging (tMRI) data. With current computer-aided postprocessing tools including HARP analysis, large motions experienced by myocardial tissue are, however, often intractable to measure. This paper addresses this issue and provides a solution to make such measurements possible.

METHODS

To improve the estimation performance of large cardiac motions while analyzing tMRI data sets, we propose a two-step solution. The first step involves constructing a model to describe average systolic motion of the LV wall within a subject group. The second step involves time-reversal of the model applied as a spatial coordinate transformation to digitally relax the contracted LV wall in the experimental data of a single subject to the beginning of systole. Cardiac tMRI scans were performed on four healthy rats and used for developing the forward LV model. Algorithms were implemented for preprocessing the tMRI data, optimizing the model parameters and performing the HARP analysis. Slices from the midventricular level were then analyzed for all systolic phases.

RESULTS

The time-reversal operation derived from the LV model accounted for the bulk portion of the myocardial motion, which was the average motion experienced within the overall subject population. In analyzing the individual tMRI data sets, removing this average with the time-reversal operation left small magnitude residual motion unique to the case. This remaining residual portion of the motion was estimated robustly using the HARP analysis.

CONCLUSION

Utilizing a combination of the forward LV model and its time reversal improves the performance of motion estimation in evaluating the cardiac function.

Normal and shear strain estimation using beam steering on linear-array transducers

In current 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 following a uniaxial compression. Previous work evaluated the technique using both simulations and a mechanically translated phased array transducer. In this paper, we present initial results using beam steering on a linear array transducer attached to a commercial scanner to acquire echo signals for estimating 2-D displacement vectors. Single-inclusion and anthropomorphic breast phantoms with different boundary properties between the inclusion and background material are imaged by acquiring echo data along beam lines ranging from -15 degrees to 15 degrees relative to the compression direction. 1-D cross-correlation is used to calculate "angular displacements" in each acquisition direction, yielding axial and lateral components of the displacement vector. Strain tensor components are estimated from these displacements. Features on shear strain images generated for the inclusion phantom agree with those predicted using FEA analysis. Experimental results demonstrate the utility of this technique on clinical scanners. Shear strain tensors obtained using this method may provide useful information for the differentiation of benign from malignant tumors. For the linear array transducer used in this study, the optimum angular increment is around 3 degrees. However, more work is required for the selection of an appropriate value for the maximum beam angle for optimal performance of this technique.

A novel performance descriptor for ultrasonic strain imaging: a preliminary study

Ultrasonic strain imaging that uses signals from conventional diagnostic ultrasound systems is capable of showing the contrast of tissue elasticity, which provides new diagnostically valuable information. To assess and improve the diagnostic performance of ultrasonic strain imaging, it is essential to have a quantitative measure of image quality. Moreover, it is useful if the image quality measure is simple to interpret and can be used for visual feedback while scanning and as a training tool for operator performance evaluation. This report describes the development of a novel quantitative method for systematic performance assessment that is based on the combination of measures of the accuracy of motion tracking and consistency among consecutive strain fields. The accuracy of motion tracking assesses the reliability of strain images. The consistency among consecutive strain images assesses the signal quality in strain images. The clinical implications of the proposed method to differentiate good or poor strain images are discussed. Results of experiments with tissue-mimicking phantoms and in vivo breast-tissue data demonstrate that the performance measure is a useful method for automatically rating elasticity image quality.

Correlation analysis of the beam angle dependence for elastography

Signal decorrelation is a major source of error in the displacements estimated using correlation techniques for elastographic imaging. Previous papers have addressed the variation in the correlation coefficient as a function of the applied compression for a finite window size and an insonification angle of zero degrees. The recent use of angular beam-steered radio-frequency echo signals for spatial angular compounding and shear strain estimation have demonstrated the need for understanding signal decorrelation artifacts for data acquired at different beam angles. In this paper, we provide both numerical and closed form theoretical solutions of the correlation between pre- and post-compression radio-frequency echo signals acquired at a specified beam angle. The expression for the correlation coefficient obtained is a function of the beam angle and the applied compression for a finite duration window. Accuracy of the theoretical results is verified using tissue-mimicking phantom experiments on a uniformly elastic phantom using beam-steered data acquisitions on a linear array transducer. The theory predicts a faster decorrelation with changes in the beam or insonification angle for longer radio-frequency echo signal segments and at deeper locations in the medium. Theoretical results provide useful information for improving angular compounding and shear strain estimation techniques for elastography.

Elastography imaging of small animal oncology models: a feasibility study

To test the feasibility of applying ultrasonic elastography on small animal oncology models, experiments were performed in vitro and in situ on murine mammary lesions induced exogenously by tumor cell line 66.3. In vitro studies involved three 1-week-old excised tumors embedded in a phantom block with ultrasonic properties similar to those of soft biologic tissues. In situ studies involved five mice whose bodies were embedded in pure gelatin blocks. The data were acquired from the blocks with a clinical scanner modified to have an automated compressor assembly and processed to construct the elastograms at various imaging planes within each block. The results were analyzed both qualitatively and quantitatively to assess the merits of the elastographic imaging and its limitations for in vivo serial studies of tumors in small animal oncology models.