Transit-time broadening in pulsed Doppler ultrasound: a generalized amplitude modulation model

Pulsed Wave Doppler Measurements of Maximum Velocity: Dependence on Sample Volume Size

Pulsed wave (PW) Doppler ultrasound is routinely used in the clinic to assess blood flow. Our annual Doppler quality assurance tests revealed unexpectedly large errors in measurement of maximum velocity, exceeding our tolerance (error >20%), when using certain scanners with small Doppler sample volume dimensions. The aim of this study was to assess the dependence of maximum velocity estimates on PW Doppler sample volume size. A flow phantom with known steady flow was used to acquire maximum velocity estimates (maximum velocities of 24, 39 and 85 cm/s and sample volume range of 0.3-20 mm) with a variety of transducers and scanners in clinical use (51 probes from 4 manufacturers). Selected acoustic outputs were characterized using free-field hydrophone measurements. All maximum velocity estimates were within our tolerance for sample volume sizes ≥1.5 mm, although maximum velocity estimates typically increased with decreasing sample volume size. Errors exceeding our tolerance were commonly found for one manufacturer when using smaller sample volumes, resulting in up to 75% overestimation. Although intrinsic spectral broadening based on transit time considerations may help explain our findings, the sample volume dependence raises potential clinical concerns that users should be aware of and which manufacturers should consider addressing.

Hydrophone Spatial Averaging Correction for Acoustic Exposure Measurements From Arrays-Part I: Theory and Impact on Diagnostic Safety Indexes

This article reports underestimation of mechanical index (MI) and nonscanned thermal index for bone near focus (TIB) due to hydrophone spatial averaging effects that occur during acoustic output measurements for clinical linear and phased arrays. TIB is the appropriate version of thermal index (TI) for fetal imaging after ten weeks from the last menstrual period according to the American Institute of Ultrasound in Medicine (AIUM). Spatial averaging is particularly troublesome for highly focused beams and nonlinear, nonscanned modes such as acoustic radiation force impulse (ARFI) and pulsed Doppler. MI and variants of TI (e.g., TIB), which are displayed in real-time during imaging, are often not corrected for hydrophone spatial averaging because a standardized method for doing so does not exist for linear and phased arrays. A novel analytic inverse-filter method to correct for spatial averaging for pressure waves from linear and phased arrays is derived in this article (Part I) and experimentally validated in a companion article (Part II). A simulation was developed to estimate potential spatial-averaging errors for typical clinical ultrasound imaging systems based on the theoretical inverse filter and specifications for 124 scanner/transducer combinations from the U.S. Food and Drug Administration (FDA) 510(k) database from 2015 to 2019. Specifications included center frequency, aperture size, acoustic output parameters, hydrophone geometrical sensitive element diameter, etc. Correction for hydrophone spatial averaging using the inverse filter suggests that maximally achievable values for MI, TIB, thermal dose ( t ₄₃ ), and spatial-peak-temporal-average intensity ( [Formula: see text]) for typical clinical systems are potentially higher than uncorrected values by (means ± standard deviations) 9% ± 4% (ARFI MI), 19% ± 15% (ARFI TIB), 50% ± 41% (ARFI t ₄₃ ), 43% ± 39% (ARFI [Formula: see text]), 7% ± 5% (pulsed Doppler MI), 15% ± 11% (pulsed Doppler TIB), 42% ± 31% (pulsed Doppler t ₄₃ ), and 33% ± 27% (pulsed Doppler [Formula: see text]). These values correspond to frequencies of 3.2 ± 1.3 (ARFI) and 4.1 ± 1.4 MHz (pulsed Doppler), and the model predicts that they would increase with frequency. Inverse filtering for hydrophone spatial averaging significantly improves the accuracy of estimates of MI, TIB, t ₄₃ , and [Formula: see text] for ARFI and pulsed Doppler signals.

Spectral Doppler Measurements With 2-D Sparse Arrays

The 2-D sparse arrays, in which a few hundreds of elements are distributed on the probe surface according to an optimization procedure, represent an alternative to full 2-D arrays, including thousands of elements usually organized in a grid. Sparse arrays have already been used in B-mode imaging tests, but their application to Doppler investigations has not been reported yet. Since the sparsity of the elements influences the acoustic field, a corresponding influence on the mean frequency (Fm), bandwidth (BW), and signal-to-noise ratio (SNR) of the Doppler spectra is expected. This article aims to assess, by simulations and experiments, to what extent the use of a sparse rather than a full gridded 2-D array has an impact on spectral Doppler measurements. Parabolic flows were investigated by a 3 MHz, 1024-element gridded array and by a sparse array; the latter was obtained by properly selecting a subgroup of 256 elements from the full array. Simulations show that the mean Doppler frequency does not change between the sparse and the full array while there are significant differences on the BW (average reduction of 17.2% for the sparse array, due to different apertures of the two probes) and on the signal power (Ps) (22 dB, due to the different number of active elements). These results are confirmed by flow phantom experiments, which also highlight that the most critical difference between sparse and full gridded array in Doppler measurements is in terms of SNR (-16.8 dB).

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.

The variation in frequency locations in Doppler ultrasound spectra for maximum blood flow velocities in narrowed vessels

This study assessed the variation in the frequency locations in the Doppler ultrasound spectra for the maximum blood flow velocities of in vessels with different degrees of bilaterally axisymmetric stenosis. This was done by comparing the relationship between the velocity distributions and corresponding Doppler power spectra. First, a geometric vessel model with axisymmetric stenosis was established. This made it possible to obtain the blood flow velocity distributions for different degrees of stenosis from the solutions of the Navier-Stokes equations. Then, the Doppler spectra were calculated for the entire segment of the vessel that was covered by the sound field. Finally, the maximum frequency locations for the spectra were determined based on the intersections of the maximum values chosen from the calculated blood flow velocity distributions and their corresponding spectra. The computational analysis showed that the maximum frequencies, which corresponded to the maximum blood flow velocities for different degrees of stenosis, were located at different positions along the spectral falling edges. The location for a normal (stenosis free) vessel was in the middle of the falling edge. For vessels with increasing degrees of stenosis, this location shifted approximately linearly downward along the falling edge. For 40% stenosis, the location reached a position at the falling edge of 0.32. Results obtained using the Field II simulation tool demonstrated the validity of the theoretical analysis and calculations, and may help to improve the maximum velocity estimation accuracy for Doppler blood flow spectra in stenosed vessels.

Least-Squares Multi-Angle Doppler Estimators for Plane-Wave Vector Flow Imaging

Designing robust Doppler vector estimation strategies for use in plane-wave imaging schemes based on unfocused transmissions is a topic that has yet to be studied in depth. One potential solution is to use a multi-angle Doppler estimation approach that computes flow vectors via least-squares fitting, but its performance has not been established. Here, we investigated the efficacy of multi-angle Doppler vector estimators by: 1) comparing its performance with respect to the classical dual-angle (cross-beam) Doppler vector estimator and 2) examining the working effects of multi-angle Doppler vector estimators on flow visualization quality in the context of dynamic flow path rendering. Implementing Doppler vector estimators that use different combinations of transmit (Tx) and receive (Rx) steering angles, our analysis has compared the classical dual-angle Doppler method, a 5-Tx version of dual-angle Doppler, and various multi-angle Doppler configurations based on 3 Tx and 5 Tx. Two angle spans (10°, 20°) were examined in forming the steering angles. In imaging scenarios with known flow profiles (rotating disk and straight-tube parabolic flow), the 3-Tx, 3-Rx and 5-Tx, 5-Rx multi-angle configurations produced vector estimates with smaller variability compared with the dual-angle method, and the estimation results were more consistent with the use of a 20° angle span. Flow vectors derived from multi-angle Doppler estimators were also found to be effective in rendering the expected flow paths in both rotating disk and straight-tube imaging scenarios, while the ones derived from the dual-angle estimator yielded flow paths that deviated from the expected course. These results serve to attest that using multi-angle least-squares Doppler vector estimators, flow visualization can be consistently achieved.

Spread-Spectrum Beamforming and Clutter Filtering for Plane-Wave Color Doppler Imaging

Plane-wave imaging is desirable for its ability to achieve high frame rates, allowing the capture of fast dynamic events and continuous Doppler data. In most implementations of plane-wave imaging, multiple low-resolution images from different plane wave tilt angles are compounded to form a single high-resolution image, thereby reducing the frame rate. Compounding improves the lateral beam profile in the high-resolution image, but it also acts as a low-pass filter in slow time that causes attenuation and aliasing of signals with high Doppler shifts. This paper introduces a spread-spectrum color Doppler imaging method that produces high-resolution images without the use of compounding, thereby eliminating the tradeoff between beam quality, maximum unaliased Doppler frequency, and frame rate. The method uses a long, random sequence of transmit angles rather than a linear sweep of plane wave directions. The random angle sequence randomizes the phase of off-focus (clutter) signals, thereby spreading the clutter power in the Doppler spectrum, while keeping the spectrum of the in-focus signal intact. The ensemble of randomly tilted low-resolution frames also acts as the Doppler ensemble, so it can be much longer than a conventional linear sweep, thereby improving beam formation while also making the slow-time Doppler sampling frequency equal to the pulse repetition frequency. Experiments performed using a carotid artery phantom with constant flow demonstrate that the spread-spectrum method more accurately measures the parabolic flow profile of the vessel and outperforms conventional plane-wave Doppler in both contrast resolution and estimation of high flow velocities. The spread-spectrum method is expected to be valuable for Doppler applications that require measurement of high velocities at high frame rates.

Optimization of beam-flow angles for Doppler ultrasound flow velocity measurements using slanted gel pads

The aim of this study was to assess whether slanted gel pads can be used to optimize beam-flow angles and flow velocity measurements for Doppler ultrasound. The right carotid artery of a single healthy female volunteer was measured alternatively five times without and with an 18° angled slanted gel pad between the ultrasound transducer and skin by 13 radiologists. Beam-flow angles and peak systolic flow velocities (PSV) were measured along with assessment of spectral broadening. Beam-flow angles (P = 0.001) and PSV (P = 0.001) measurements showed a significant decrease when using slanted gel pads. The mean (±SD) beam-flow angles without and with the use of slanted gel pads were 66.7 (±4.2) and 56.1 (±5.8) degrees, respectively. The mean (±SD) PSVs without and with the use of slanted gel pads were 92.0 (±17.4) and 76.9 (±10.9) cm/s, respectively. There was a noticeable decrease in spectral broadening when using slanted gel pads. There was a significant linear correlation between beam-flow angle and peak systolic velocity. Coefficients of variation for peak systolic velocity without and with the use of gel pads were 18.9 and 14.2 %, respectively. These results demonstrate that slanted gel pads decrease beam-flow angles and overestimation of Doppler flow velocity measurements while potentially increasing the reliability of measurements.

In vitro verification of multiple-receiver Doppler ultrasound for velocity estimation improvement

The coherent scattering effect, which introduces noise in Doppler-derived velocity estimates, is caused by constructive and destructive interference of sound waves scattered from multiple particles. Because the phase relationship between signals scattered from different particles depends on the orientation of the receiver, the error in a given velocity estimate depends on the receiver location. To examine this dependence, the velocity of a steady uniform flow was measured simultaneously with a transceiver and three receivers, and the cross-correlation coefficients between velocity estimates for pairs of crystals were calculated. The velocity estimates were nearly independent, with cross-correlation coefficients of approximately 0.2. This result agrees with our previously published numerical simulation studies which demonstrated that the coherent scattering noise in receivers separated by 5 degrees or more was nearly uncorrelated. Consequently, the contribution of coherent scattering noise can be reduced by averaging out noise in signals obtained from multiple receivers.

Single-ensemble-based eigen-processing methods for color flow imaging--Part I. The Hankel-SVD filter

Because of their adaptability to the slow-time signal contents, eigen-based filters have shown potential in improving the flow detection performance of color flow images. This paper proposes a new eigen-based filter called the Hankel-SVD filter that is intended to process each slowtime ensemble individually. The new filter is derived using the notion of principal Hankel component analysis, and it achieves clutter suppression by retaining only the principal components whose order is greater than the clutter eigen-space dimension estimated from a frequency based analysis algorithm. To assess its efficacy, the Hankel-SVD filter was first applied to synthetic slow-time data (ensemble size: 10) simulated from two different sets of flow parameters that model: 1) arterial imaging (blood velocity: 0 to 38.5 cm/s, tissue motion: up to 2 mm/s, transmit frequency: 5 MHz, pulse repetition period: 0.4 ms) and 2) deep vessel imaging (blood velocity: 0 to 19.2 cm/s, tissue motion: up to 2 cm/s, transmit frequency: 2 MHz, pulse repetition period: 2.0 ms). In the simulation analysis, the post-filter clutter-to- blood signal ratio (CBR) was computed as a function of blood velocity. Results show that for the same effective stopband size (50 Hz), the Hankel-SVD filter has a narrower transition region in the post-filter CBR curve than that of another type of adaptive filter called the clutter-downmixing filter. The practical efficacy of the proposed filter was tested by application to in vivo color flow data obtained from the human carotid arteries (transmit frequency: 4 MHz, pulse repetition period: 0.333 ms, ensemble size: 10). The resulting power images show that the Hankel-SVD filter can better distinguish between blood and moving-tissue regions (about 9 dB separation in power) than the clutter-downmixing filter and a fixed-rank multi ensemble-based eigen-filter (which showed a 2 to 3 dB separation).