Single-ensemble-based eigen-processing methods for color flow imaging--Part II. The matrix pencil estimator

Real time SVD-based clutter filtering using randomized singular value decomposition and spatial downsampling for micro-vessel imaging on a Verasonics ultrasound system

Singular value decomposition (SVD)-based clutter filters can robustly reject the tissue clutter as compared with the conventional high pass filter-based clutter filters. However, the computational burden of SVD makes real time SVD-based clutter filtering challenging (e.g. frame rate at least 10-15 Hz with region of interest of about 4 × 4 cm²). Recently, we proposed an acceleration method based on randomized SVD (rSVD) clutter filtering and randomized spatial downsampling, which can significantly reduce the computational complexity without compromising the clutter rejection capability. However, this method has not been implemented on an ultrasound scanner and tested for its performance. In this study, we implement this acceleration method on a Verasonics scanner using a multi-core CPU architecture, and evaluate the selections of the imaging and processing parameters to enable real time micro-vessel imaging. The Blood-to-Clutter Ratio (BCR) performance was evaluated on a Verasonics machine with different settings of parameters such as block size and ensemble size. The demonstration of real time process was implemented on a 12-core CPU (downsampling factor of 12, 12-threads in this study) host computer. The processing time of the rSVD-based clutter filter was less than 30 ms and BCRs were higher than 20 dB as the block size, ensemble size and the rank of tissue clutter subspace were set as 30 × 30, 45 and 26 respectively. We also demonstrate that the micro-vessel imaging frame rate of the proposed architecture can reach approximately 22 Hz when the block size, ensemble size and the rank of tissue clutter subspace were set as 20 × 20 pixels, 45 and 26 respectively (using both images and supplementary videos). The proposed method may be important for real time 2D scanning of tumor microvessels in 3D to select and store the most representative 2D view with most abnormal micro-vessels for better diagnosis.

High frame rate doppler ultrasound bandwidth imaging for flow instability mapping

Purpose

Flow instability has been shown to contribute to the risk of future cardiovascular and cerebrovascular events. Nonetheless, it is challenging to noninvasively detect and identify flow instability in blood vessels. Here, we present a new framework called Doppler ultrasound bandwidth imaging (DUBI) that uses high‐frame‐rate ultrasound and Doppler bandwidth analysis principles to assess flow instability within an image view.

Methods

Doppler ultrasound bandwidth imaging seeks to estimate the instantaneous Doppler bandwidth based on autoregressive modeling at every pixel position of data frames acquired from high‐frame‐rate plane wave pulsing. This new framework is founded upon the principle that flow instability naturally gives rise to a wide range of flow velocities over a sample volume, and such velocity range in turn yields a larger Doppler bandwidth estimate. The ability for DUBI to map unstable flow was first tested over a range of fluid flow conditions (ranging from laminar to turbulent) with a nozzle‐flow phantom. As a further demonstration, DUBI was applied to assess flow instability in healthy and stenosed carotid bifurcation phantoms.

Results

Nozzle‐flow phantom results showed that DUBI can effectively detect and visualize the difference in Doppler bandwidth magnitude (increased from 2.1 to 5.2 kHz) at stable and unstable flow regions in an image view. Receiver operating characteristic analysis also showed that DUBI can achieve optimal sensitivity and specificity of 0.72 and 0.83, respectively. In the carotid phantom experiments, differences were observed in the spatiotemporal dynamics of Doppler bandwidth over a cardiac cycle. Specifically, as the degree of stenosis increased (from 50% to 75%), DUBI showed an increase in Doppler bandwidth magnitude from 1.4 kHz in the healthy bifurcation to 7.7 kHz at the jet tail located downstream from a 75% stenosis site, thereby indicating flow perturbation in the stenosed bifurcations.

Conclusion

DUBI can detect unstable flow. This new technique can provide useful hemodynamic information that may aid clinical diagnosis of atherosclerosis.

Receiver-Operating Characteristic Analysis of Eigen-Based Clutter Filters for Ultrasound Color Flow Imaging

The eigen-based filter has theoretically established itself as a potent solution in ultrasound color flow imaging (CFI) for combating against clutter arising from moving tissues. Yet, it remains poorly understood on how much gain in flow detection sensitivity and specificity can be delivered by this adaptive clutter filter. Here, we investigated the receiver operating characteristic (ROC) of the eigen-based clutter filter to statistically evaluate its efficacy. Our investigation was conducted using a new vascular phantom testbed that incorporated both intrinsic tissue motion (vessel pulsation: 7.58 cm/s peak velocity) and extrinsic tissue motion (vibration: 5-Hz frequency, 2.98 cm/s peak velocity), as well as pulsatile flow (pulse rate: 60 beats/min; systolic flow rate: 6.5 mL/s). The eigen-filter (single-ensemble formulation) was applied to CFI raw data sets obtained from the phantom's short-axis view (slow-time ensemble size: 12; pulse repetition frequency: 2 kHz; and ultrasound frequency: 5 MHz), and post-filter Doppler power was compared between flow and tissue regions. Results show that, in the presence of vessel pulsation and tissue vibration, the eigen-filter yielded a high true positive rate in depicting flow pixels in CFI frames (0.945 and 0.917, respectively, during peak systole and end diastole at 60° beam-flow angle), while maintaining a low false alarm rate (0.10) in rendering tissue pixels. Also, the eigen-filter posed ROC curves whose area under curve was higher than those for the polynomial regression filter (statistically significant; t-test p values were less than 0.05). These findings serve well to substantiate the merit of using eigen-filters to enhance the vascular visualization capability of CFI.

Ultrasound Small Vessel Imaging With Block-Wise Adaptive Local Clutter Filtering

Robust clutter filtering is essential for ultrasound small vessel imaging. Eigen-based clutter filtering techniques have recently shown great improvement in clutter rejection over conventional clutter filters in small animals. However, for in vivo human imaging, eigen-based clutter filtering can be challenging due to the complex spatially-varying tissue and noise characteristics. To address this challenge, we present a novel block-wise adaptive singular value decomposition (SVD) based clutter filtering technique. The proposed method divides the global plane wave data into overlapped local spatial segments, within which tissue signals are assumed to be locally coherent and noise locally stationary. This, in turn, enables effective separation of tissue, blood and noise via SVD. For each block, the proposed method adaptively determines the singular value cutoff thresholds based on local data statistics. Processing results from each block are redundantly combined to improve both the signal-to-noise-ratio (SNR) and the contrast-to-noise-ratio (CNR) of the small vessel perfusion image. Experimental results show that the proposed method achieved more than two-fold increase in SNR and more than three-fold increase in CNR in dB scale over the conventional global SVD filtering technique for an in vivo human native kidney study. The proposed method also showed substantial improvement in suppression of the depth-dependent background noise and better rejection of near field tissue clutter. The effects of different processing block size and block overlap percentage were systematically investigated as well as the tradeoff between imaging quality and computational cost.

A GPU-Parallelized Eigen-Based Clutter Filter Framework for Ultrasound Color Flow Imaging

Eigen-filters with attenuation response adapted to clutter statistics in color flow imaging (CFI) have shown improved flow detection sensitivity in the presence of tissue motion. Nevertheless, its practical adoption in clinical use is not straightforward due to the high computational cost for solving eigendecompositions. Here, we provide a pedagogical description of how a real-time computing framework for eigen-based clutter filtering can be developed through a single-instruction, multiple data (SIMD) computing approach that can be implemented on a graphical processing unit (GPU). Emphasis is placed on the single-ensemble-based eigen-filtering approach (Hankel singular value decomposition), since it is algorithmically compatible with GPU-based SIMD computing. The key algebraic principles and the corresponding SIMD algorithm are explained, and annotations on how such algorithm can be rationally implemented on the GPU are presented. Real-time efficacy of our framework was experimentally investigated on a single GPU device (GTX Titan X), and the computing throughput for varying scan depths and slow-time ensemble lengths was studied. Using our eigen-processing framework, real-time video-range throughput (24 frames/s) can be attained for CFI frames with full view in azimuth direction (128 scanlines), up to a scan depth of 5 cm ( λ pixel axial spacing) for slow-time ensemble length of 16 samples. The corresponding CFI image frames, with respect to the ones derived from non-adaptive polynomial regression clutter filtering, yielded enhanced flow detection sensitivity in vivo, as demonstrated in a carotid imaging case example. These findings indicate that the GPU-enabled eigen-based clutter filtering can improve CFI flow detection performance in real time.

Efficiency of U.S. Tissue Perfusion Estimators

We measure the detection and discrimination efficiencies of conventional power-Doppler estimation of perfusion without contrast enhancement. The measurements are made in a phantom with known blood-mimicking fluid flow rates in the presence of clutter and noise. Efficiency is measured by comparing functions of the areas under the receiver operating characteristic curve for Doppler estimators with those of the ideal discriminator, for which we estimate the temporal covariance matrix from echo data. Principal-component analysis is examined as a technique for increasing the accuracy of covariance matrices estimated from echo data. We find that Doppler estimators are <50% efficient at directed perfusion detection between 0.1 and 2.0 mL/min per 2 cm(2) flow area. The efficiency was 20%-40% for the task of discriminating between two perfusion rates in the same range. We conclude that there are reasons to search for more efficient perfusion estimators, one that incorporates covariance matrix information that could significantly enhance the utility of Doppler ultrasound without contrast enhancement.

Clutter Mitigation in Echocardiography Using Sparse Signal Separation

In ultrasound imaging, clutter artifacts degrade images and may cause inaccurate diagnosis. In this paper, we apply a method called Morphological Component Analysis (MCA) for sparse signal separation with the objective of reducing such clutter artifacts. The MCA approach assumes that the two signals in the additive mix have each a sparse representation under some dictionary of atoms (a matrix), and separation is achieved by finding these sparse representations. In our work, an adaptive approach is used for learning the dictionary from the echo data. MCA is compared to Singular Value Filtering (SVF), a Principal Component Analysis- (PCA-) based filtering technique, and to a high-pass Finite Impulse Response (FIR) filter. Each filter is applied to a simulated hypoechoic lesion sequence, as well as experimental cardiac ultrasound data. MCA is demonstrated in both cases to outperform the FIR filter and obtain results comparable to the SVF method in terms of contrast-to-noise ratio (CNR). Furthermore, MCA shows a lower impact on tissue sections while removing the clutter artifacts. In experimental heart data, MCA obtains in our experiments clutter mitigation with an average CNR improvement of 1.33 dB.

Vector projectile imaging: time-resolved dynamic visualization of complex flow patterns

Achieving non-invasive, accurate and time-resolved imaging of vascular flow with spatiotemporal fluctuations is well acknowledged to be an ongoing challenge. In this article, we present a new ultrasound-based framework called vector projectile imaging (VPI) that can dynamically render complex flow patterns over an imaging view at millisecond time resolution. VPI is founded on three principles: (i) high-frame-rate broad-view data acquisition (based on steered plane wave firings); (ii) flow vector estimation derived from multi-angle Doppler analysis (coupled with data regularization and least-squares fitting); (iii) dynamic visualization of color-encoded vector projectiles (with flow speckles displayed as adjunct). Calibration results indicated that by using three transmit angles and three receive angles (-10°, 0°, +10° for both), VPI can consistently compute flow vectors in a multi-vessel phantom with three tubes positioned at different depths (1.5, 4, 6 cm), oriented at different angles (-10°, 0°, +10°) and of different sizes (dilated diameter: 2.2, 4.4 and 6.3 mm; steady flow rate: 2.5 mL/s). The practical merit of VPI was further illustrated through an anthropomorphic flow phantom investigation that considered both healthy and stenosed carotid bifurcation geometries. For the healthy bifurcation with 1.2-Hz carotid flow pulses, VPI was able to render multi-directional and spatiotemporally varying flow patterns (using a nominal frame rate of 416 fps or 2.4-ms time resolution). In the case of stenosed bifurcations (50% eccentric narrowing), VPI enabled dynamic visualization of flow jet and recirculation zones. These findings suggest that VPI holds promise as a new tool for complex flow analysis.

The singular value filter: a general filter design strategy for PCA-based signal separation in medical ultrasound imaging

A general filtering method, called the singular value filter (SVF), is presented as a framework for principal component analysis (PCA) based filter design in medical ultrasound imaging. The SVF approach operates by projecting the original data onto a new set of bases determined from PCA using singular value decomposition (SVD). The shape of the SVF weighting function, which relates the singular value spectrum of the input data to the filtering coefficients assigned to each basis function, is designed in accordance with a signal model and statistical assumptions regarding the underlying source signals. In this paper, we applied SVF for the specific application of clutter artifact rejection in diagnostic ultrasound imaging. SVF was compared to a conventional PCA-based filtering technique, which we refer to as the blind source separation (BSS) method, as well as a simple frequency-based finite impulse response (FIR) filter used as a baseline for comparison. The performance of each filter was quantified in simulated lesion images as well as experimental cardiac ultrasound data. SVF was demonstrated in both simulation and experimental results, over a wide range of imaging conditions, to outperform the BSS and FIR filtering methods in terms of contrast-to-noise ratio (CNR) and motion tracking performance. In experimental mouse heart data, SVF provided excellent artifact suppression with an average CNR improvement of 1.8 dB with over 40% reduction in displacement tracking error. It was further demonstrated from simulation and experimental results that SVF provided superior clutter rejection, as reflected in larger CNR values, when filtering was achieved using complex pulse-echo received data and non-binary filter coefficients.

Complex principal components for robust motion estimation

Bias and variance errors in motion estimation result from electronic noise, decorrelation, aliasing, and inherent algorithm limitations. Unlike most error sources, decorrelation is coherent over time and has the same power spectrum as the signal. Thus, reducing decorrelation is impossible through frequency domain filtering or simple averaging and must be achieved through other methods. In this paper, we present a novel motion estimator, termed the principal component displacement estimator (PCDE), which takes advantage of the signal separation capabilities of principal component analysis (PCA) to reject decorrelation and noise. Furthermore, PCDE only requires the computation of a single principal component, enabling computational speed that is on the same order of magnitude or faster than the commonly used Loupas algorithm. Unlike prior PCA strategies, PCDE uses complex data to generate motion estimates using only a single principal component. The use of complex echo data is critical because it allows for separation of signal components based on motion, which is revealed through phase changes of the complex principal components. PCDE operates on the assumption that the signal component of interest is also the most energetic component in an ensemble of echo data. This assumption holds in most clinical ultrasound environments. However, in environments where electronic noise SNR is less than 0 dB or in blood flow data for which the wall signal dominates the signal from blood flow, the calculation of more than one PC is required to obtain the signal of interest. We simulated synthetic ultrasound data to assess the performance of PCDE over a wide range of imaging conditions and in the presence of decorrelation and additive noise. Under typical ultrasonic elasticity imaging conditions (0.98 signal correlation, 25 dB SNR, 1 sample shift), PCDE decreased estimation bias by more than 10% and standard deviation by more than 30% compared with the Loupas method and normalized cross-correlation with cosine fitting (NC CF). More modest gains were observed relative to spline-based time delay estimation (sTDE). PCDE was also tested on experimental elastography data. Compressions of approximately 1.5% were applied to a CIRS elastography phantom with embedded 10.4-mm-diameter lesions that had moduli contrasts of -9.2, -5.9, and 12.0 dB. The standard deviation of displacement estimates was reduced by at least 67% in homogeneous regions at 35 to 40 mm in depth with respect to estimates produced by Loupas, NC CF, and sTDE. Greater improvements in CNR and displacement standard deviation were observed at larger depths where speckle decorrelation and other noise sources were more significant.

Reduction of echo decorrelation via complex principal component filtering

Ultrasound motion estimation is a fundamental component of clinical and research techniques that include color flow Doppler, spectral Doppler, radiation force imaging and ultrasound-based elasticity estimation. In each of these applications, motion estimates are corrupted by signal decorrelation that originates from nonuniform target motion across the acoustic beam. In this article, complex principal component filtering (PCF) is demonstrated as a filtering technique for dramatically reducing echo decorrelation in blood flow estimation and radiation force imaging. We present simulation results from a wide range of imaging conditions that illustrate a dramatic improvement over simple bandpass filtering in terms of overall echo decorrelation (< or =99.9% reduction), root mean square error (< or =97.3% reduction) and the standard deviation of displacement estimates (< or =97.4% reduction). A radiation force imaging technique, termed sonorheometry, was applied to fresh whole blood during coagulation, and complex PCF operated on the returning echoes. Sonorheometry was specifically chosen as an example radiation force imaging technique in which echo decorrelation corrupts motion estimation. At 2 min after initiation of blood coagulation, the average echo correlation for sonorheometry improved from 0.996 to 0.9999, which corresponded to a 41.0% reduction in motion estimation variance as predicted by the Cramer-Rao lower bound under reasonable imaging conditions. We also applied complex PCF to improve blood velocity estimates from the left carotid artery of a healthy 23-year-old male. At the location of peak blood velocity, complex PCF improved the correlation of consecutive echo signals from an average correlation of 0.94 to 0.998. The improved echo correlation for both sonorheometry and blood flow estimation yielded motion estimates that exhibited more consistent responses with less noise. Complex PCF reduces speckle decorrelation and improves the performance of ultrasonic motion estimation.