Robust Tracking of Small Displacements With a Bayesian Estimator

In Vivo Longitudinal Monitoring of Cardiac Remodeling in Murine Ischemia Models With Adaptive Bayesian Regularized Cardiac Strain Imaging: Validation Against Histology

Adaptive Bayesian regularized cardiac strain imaging (ABR-CSI) uses raw radiofrequency signals to estimate myocardial wall contractility as a surrogate measure of relative tissue elasticity incorporating regularization in the Bayesian sense. We determined the feasibility of using ABR-CSI -derived strain for in vivo longitudinal monitoring of cardiac remodeling in a murine ischemic injury model (myocardial infarction [MI] and ischemia-reperfusion [IR]) and validated the findings against ground truth histology. We randomly stratified 30 BALB/CJ mice (17 females, 13 males, median age = 10 wk) into three surgical groups (MI = 10, IR = 12, sham = 8) and imaged pre-surgery (baseline) and 1, 2, 7 and 14 d post-surgery using a pre-clinical high-frequency ultrasound system (VisualSonics Vevo 2100). We then used ABR-CSI to estimate end-systolic and peak radial (er) and longitudinal (el) strain estimates. ABR-CSI was found to have the ability to serially monitor non-uniform cardiac remodeling associated with murine MI and IR non-invasively through temporal variation of strain estimates post-surgery. Furthermore, radial end-systole (ES) strain images and segmental strain curves exhibited improved discrimination among infarct, border and remote regions around the myocardium compared with longitudinal strain results. For example, the MI group had significantly lower (Friedman's with Bonferroni-Dunn test, p = 0.002) ES er values in the anterior middle (infarcted) region at day 14 (n = 9, 9.23 ± 7.39%) compared with the BL group (n = 9, 44.32 ± 5.49). In contrast, anterior basal (remote region) mean ES er values did not differ significantly (non-significant Friedman's test, χ2 = 8.93, p = 0.06) at day 14 (n = 6, 33.05 ± 6.99%) compared with baseline (n = 6, 34.02 ± 6.75%). Histology slides stained with Masson's trichrome (MT) together with a machine learning model (random forest classifier) were used to derive the ground truth cardiac fibrosis parameter termed histology percentage of myocardial fibrosis (PMF). Both radial and longitudinal strain were found to have strong statistically significant correlations with the PMF parameter. However, radial strain had a higher Spearman's correlation value (εresρ = -0.67, n = 172, p < 0.001) compared with longitudinal strain (εlesρ = -0.60, n = 172, p < 0.001). Overall, the results of this study indicate that ABR-CSI can reliably perform non-invasive detection of infarcted and remote myocardium in small animal studies.

The Revisited Frequency-Shift Method for Shear Wave Attenuation Computation and Imaging

Ultrasound (US) shear wave (SW) elastography has been widely studied and implemented on clinical systems to assess the elasticity of living organs. Imaging of SW attenuation reflecting viscous properties of tissues has received less attention. A revisited frequency shift (R-FS) method is proposed to improve the robustness of SW attenuation imaging. Performances are compared with the FS method that we originally proposed and with the two-point frequency shift (2P-FS) and attenuation measuring US SW elastography (AMUSE) methods. In the proposed R-FS method, the shape parameter of the gamma distribution fitting SW spectra is assumed to vary with distance, in contrast to FS. Second, an adaptive random sample consensus (A-RANSAC) line fitting method is used to prevent outlier attenuation values in the presence of noise. Validation was made on ten simulated phantoms with two viscosities (0.5 and 2 Pa [Formula: see text]) and different noise levels (15 to -5 dB), two experimental homogeneous gel phantoms, and six in vivo liver acquisitions on awake ducks (including three normal and three fatty duck livers). According to the conducted experiments, R-FS revealed mean reductions in coefficients of variation (CV) of 62.6% on simulations, 62.5% with phantoms, and 62.3% in vivo compared with FS. Corresponding reductions compared with 2P-FS were 45.4%, 77.1%, and 62.0%, respectively. Reductions in normalized root-mean-square errors for simulations were 63.9% and 48.7% with respect to FS and 2P-FS, respectively.

Spatiotemporal Bayesian Regularization for Cardiac Strain Imaging: Simulation and In Vivo Results

Cardiac strain imaging (CSI) plays a critical role in the detection of myocardial motion abnormalities. Displacement estimation is an important processing step to ensure the accuracy and precision of derived strain tensors. In this paper, we propose and implement Spatiotemporal Bayesian regularization (STBR) algorithms for two-dimensional (2-D) normalized cross-correlation (NCC) based multi-level block matching along with incorporation into a Lagrangian cardiac strain estimation framework. Assuming smooth temporal variation over a short span of time, the proposed STBR algorithm performs displacement estimation using at least four consecutive ultrasound radio-frequency (RF) frames by iteratively regularizing 2-D NCC matrices using information from a local spatiotemporal neighborhood in a Bayesian sense. Two STBR schemes are proposed to construct Bayesian likelihood functions termed as Spatial then Temporal Bayesian (STBR-1) and simultaneous Spatiotemporal Bayesian (STBR-2). Radial and longitudinal strain estimated from a finite-element-analysis (FEA) model of realistic canine myocardial deformation were utilized to quantify strain bias, normalized strain error and total temporal relative error (TTR). Statistical analysis with one-way analysis of variance (ANOVA) showed that all Bayesian regularization methods significantly outperform NCC with lower bias and errors (p < 0.001). However, there was no significant difference among Bayesian methods. For example, mean longitudinal TTR for NCC, SBR, STBR-1 and STBR-2 were 25.41%, 9.27%, 10.38% and 10.13% respectively An in vivo feasibility study using RF data from ten healthy mice hearts were used to compare the elastographic signal-to-noise ratio (SNR_e) calculated using stochastic analysis. STBR-2 had the highest expected SNR_e both for radial and longitudinal strain. The mean expected SNR_e values for accumulated radial strain for NCC, SBR, STBR-1 and STBR-2 were 5.03, 9.43, 9.42 and 10.58, respectively. Overall results suggest that STBR improves CSI in vivo.

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.

Accurate and Precise Time-Delay Estimation for Ultrasound Elastography With Prebeamformed Channel Data

Free-hand palpation ultrasound elastography is a noninvasive approach for detecting pathological alteration in tissue. In this method, the tissue is compressed by a handheld probe and displacement of each sample is estimated, a process which is also known as time-delay estimation (TDE). Even with the simplifying assumption that ignores out of plane motion, TDE is an ill-posed problem requiring estimation of axial and lateral displacements for each sample from its intensity. A well-known class of methods for making elastography a well-posed problem is regularized optimization-based methods, which imposes smoothness regularization in the associated cost function. In this article, we propose to utilize channel data that have been compensated for time gain and time delay (introduced by transmission) instead of postbeamformed radio frequency (RF) data in the optimization problem. We name our proposed method Channel data for GLobal Ultrasound Elastography (CGLUE). We analytically derive bias and variances of TDE as functions of data noise for CGLUE and Global Ultrasound Elastography (GLUE) and use the Cauchy-Schwarz inequality to prove that CGLUE provides a TDE with lower bias and variance error. To further illustrate the improved performance of CGLUE, the results of simulation, experimental phantom, and ex-vivo experiments are presented.

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.

On the Performance of Time Domain Displacement Estimators for Magnetomotive Ultrasound Imaging

In magnetomotive (MM) ultrasound (US) imaging, magnetic nanoparticles (NPs) are excited by an external magnetic field and the tracked motion of the surrounding tissue serves as a surrogate parameter for the NP concentration. MMUS procedures exhibit weak displacement contrasts due to small forces on the NPs. Consequently, precise US-based displacement estimation is crucial in terms of a sufficiently high contrast-to-noise ratio (CNR) in MMUS imaging. Conventional MMUS detection of the NPs is based on samplewise evaluation of the phase of the in-phase and quadrature (IQ) data, where a low signal-to-noise ratio (SNR) in the data leads to strong phase noise and, thus, to an increased variance of the displacement estimate. This paper examines the performance of two time-domain displacement estimators (DEs) for MMUS imaging, which differ from conventional MMUS techniques by incorporating data from an axial segment. The normalized cross correlation (NCC) estimator and a recursive Bayesian estimator, incorporating spatial information from neighboring segments, weighted by the local SNR, are adapted for the small MMUS displacement magnitudes. Numerical simulations of MM-induced, time-harmonic bulk and Gaussian-shaped displacement profiles show that the two time-domain estimators yield a reduced estimation error compared to the phase-shift-based estimator. Phantom experiments, using our recently proposed magnetic excitation setup, show a 1.9-fold and 3.4-fold increase of the CNR in the MMUS images for the NCC and Bayes estimator compared to the conventional method, while the amount of required data is reduced by a factor of 100.

Analytical Minimization-Based Regularized Subpixel Shear-Wave Tracking for Ultrasound Elastography

Ultrasound elastography is a convenient and affordable method for imaging mechanical properties of tissue, which are often correlated with pathologies. An emerging novel elastography technique applies an external acoustic radiation force to generate a shear wave in the tissue and uses ultrasound imaging to track the shear wave. Accurate tracking of the small tissue motion is a critical step in shear-wave elastography (SWE), but it is challenging due to various sources of noise in the ultrasound data. We formulate tissue displacement estimation as an optimization problem and propose two computationally efficient approaches to estimate the displacement field. The first algorithm is referred to as dynamic programming analytic minimization (DPAM), which utilizes first-order Taylor series expansion of the highly nonlinear cost function to allow for its efficient optimization, and was previously proposed for quasistatic elastography. The second algorithm is a novel technique that utilizes second-order derivatives of the nonlinear cost function. We call the new algorithm second-order analytic minimization elastography (SESAME). We compare DPAM and SESAME to the standard normalized cross correlation (NCC) approach in the context of displacement and speed estimation of wave propagation in SWE. The results of micrometer-order displacement estimation in a uniform simulation phantom illustrate that SESAME outperforms DPAM, which in turn outperforms NCC in terms of signal-to-noise ratio (SNR) and jitter. In addition, the relative difference between true and reconstructed shear modulus (averaged over excitations at different focal depths and several scatterer realizations at each depth) is approximately 3.41%, 1.12%, and 1.01%, respectively, for NCC, DPAM, and SESAME. The performance of the proposed methods is also assessed with real data acquired using a tissue-mimicking phantom, wherein, in comparison to NCC, DPAM and SESAME improve the SNR of displacement estimates by 7.6 and 9.5 dB, respectively. Experimental results on a tissue-mimicking phantom also show that shear modulus reconstruction substantially improved with the proposed DPAM technique over NCC and with some further improvement achieved by utilizing the second-order Taylor series approximation in SESAME instead of the first-order DPAM.

Improving Displacement Signal-to-Noise Ratio for Low-Signal Radiation Force Elasticity Imaging Using Bayesian Techniques

Radiation force-based elasticity imaging is currently being investigated as a possible diagnostic modality for a number of clinical tasks, including liver fibrosis staging and the characterization of cardiovascular tissue. In this study, we evaluate the relationship between peak displacement magnitude and image quality and propose using a Bayesian estimator to overcome the challenge of obtaining viable data in low displacement signal environments. Displacement data quality were quantified for two common radiation force-based applications, acoustic radiation force impulse imaging, which measures the displacement within the region of excitation, and shear wave elasticity imaging, which measures displacements outside the region of excitation. Performance as a function of peak displacement magnitude for acoustic radiation force impulse imaging was assessed in simulations and lesion phantoms by quantifying signal-to-noise ratio (SNR) and contrast-to-noise ratio for varying peak displacement magnitudes. Overall performance for shear wave elasticity imaging was assessed in ex vivo chicken breast samples by measuring the displacement SNR as a function of distance from the excitation source. The results show that for any given displacement magnitude level, the Bayesian estimator can increase the SNR by approximately 9 dB over normalized cross-correlation and the contrast-to-noise ratio by a factor of two. We conclude from the results that a Bayesian estimator may be useful for increasing data quality in SNR-limited imaging environments.