Removal or reduction of aliasing in ultrasound

Abstract

Disclosed is an ultrasound imaging approach employing a transmission scheme, termed "StaBle", to increase the Nyquist limit, through dealiasing, of conventional sequential angle, ultrafast (high-frame-rate) ultrasound imaging (e.g., plane-wave Doppler imaging or diverging wave imaging). The dealiased multi-angle Doppler estimates facilitate accurate least-squares estimates of flow magnitude and direction for vector Doppler imaging (VDI). "StaBle" combines the Nyquist velocity limit extension of staggered, multiple pulse repetition frequencies (PRFs) with a double transmission scheme. With 3 transmit angles and 2 PRFs, for example, the disclosed "StaBle" technique can achieve a 6-12 times higher velocity limit compared to sequential-angle VDI. The robustness of "StaBle" can be observed in derived measures from the VDI results, such as vorticity, kinetic energy, and energy loss obtained from the resolved vector field, which show consistent beat-to-beat variation.

Description

[0001]Atty. Dkt. No.: 093873-1476 REMOVAL OR REDUCTION OF ALIASING IN ULTRASOUND CROSS-REFERENCE TO RELATED PATENT APPLICATIONS This application claims priority to U.S. Provisional Patent Application 63 / 647,156 filed May 14, 2024, which is incorporated herein by reference in its entirety. STATEMENT REGARDING FEDERAL FUNDING This invention was made with government support under HL159869 awarded by the National Institutes of Health. The government has certain rights in the invention. FIELD This invention relates generally to enhanced ultrasound blood flow estimation techniques, such as for reducing or removing aliasing artifacts in ultrafast ultrasound imaging (e.g., plane-wave imaging or diverging wave imaging). In example implementations, the disclosed techniques for ultrasound imaging can enable earlier detection of, for example, heart failure by measuring blood flow speeds inside the heart. BACKGROUND Medical ultrasound imaging technology uses sound waves to produce images of organs, tissues, and other structures inside the human body. It provides health care professionals with a relatively lower cost, real-time, and non-invasive medical diagnostic tool. A medical ultrasound imaging system produces sound waves that echo off tissues and / or blood, which are detected for use in generating the images. When traditional ultrasound imaging methods are used for measuring high-velocity blood flows, however, they often exhibit aliasing. This aliasing occurs when the velocity of the blood flow exceeds the Nyquist limit determined by the pulse repetition frequency and transducer transmit frequency, leading to inaccurate velocity readings. -1- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 SUMMARY OF THE INVENTION Various embodiments of the disclosure combine double transmit and staggered pulse repetition frequency (PRF) techniques as applied to ultrafast (high-frame-rate) ultrasound imaging (e.g., plane wave ultrasound imaging or diverging wave ultrasound imaging) to reduce or remove aliasing errors. Example embodiments provide an ultrasound approach for obtaining alias-free, or reduced alias, vector flow (direction and magnitude) or color Doppler estimates using specific transmit sequences and post-processing techniques in ultrafast ultrasound. The disclosed approach can be applied, for example, to high-frequency ultrasound (e.g., > 20 MHz) imaging of small animals where aliasing is omnipresent in cardiac or aortic flow and in cardiovascular conditions that increase blood flow velocity, such as mitral regurgitation and aortic stenosis. This disclosure provides enhanced ultrasound imaging for detecting blood flow and related cardiac functions, providing significant improvements in ultrasound imaging accuracy for cardiac diagnostics. Various embodiments of the disclosure are capable of correcting for aliasing errors and enable accurate measurement of flow velocities over a wider range. Flow direction and velocity can be visualized using color maps and / or vector arrows. By addressing aliasing errors effectively, embodiments of the disclosed approach enhance the detection capability of high-velocity flows that are vital for early diagnosis and prognosis of heart-related ailments. In one aspect, various embodiments are directed to a method for ultrafast ultrasound imaging. The method may comprise generating a transmit sequence for transmission of ultrasound signals. Ultrasound data may be obtained based at least in part on ultrasound signals detected using an ultrasound transceiver (comprising, e.g., an ultrasound array such as a linear array, 2D array, row column array, etc.) following transmission of the ultrasound signals according to the transmit sequence. The transmit sequence may repeat a first angle at a first plurality of pulse repetition frequencies (PRFs) and repeat a second angle at a second plurality of PRFs. One or more images based at least in part on the ultrasound data may be rendered for presentation on a display device (which may be a display device of the ultrasound system and / or a display device of another system or device in communication with the ultrasound system). -2- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 In example embodiments, the second plurality of PRFs is different from the first plurality of PRFs. In example embodiments, aliasing is reduced by combining a staggered pulse repetition frequency (PRF) scheme with a double transmission scheme to effectively increase the Nyquist velocity limit and then to estimate the flow direction and magnitude to perform vector Doppler imaging (VDI). In example embodiments, the transmission scheme comprises at least three plane-wave transmit angles and, for each transmit angle, at least two staggered PRFs. In example embodiments, the method comprises beamforming all transmit-receive combinations based at least in part on filtered RF data. In example embodiments, the method comprises performing Doppler phase shift estimates with lag-one autocorrelation based at least in part on in-phase (I) and quadrature (Q) beamformed data. In example embodiments, the method comprises matching net steering angles during data processing to mitigate errors caused by rotation of the point spread function (PSF). In example embodiments, the method comprises generating vector-flow estimates from the Doppler phase shift estimates using a least-squares, multi-angle vector Doppler estimator. In example embodiments, the method comprises generating at least one of vorticity, energy loss, and / or kinetic energy based at least in part on an estimated vector field. In one aspect, various embodiments are directed to a system for ultrafast ultrasound imaging (e.g., plane-wave Doppler ultrasound imaging or diverging wave ultrasound imaging). The system may comprise an ultrasound transceiver configured to transmit ultrasound signals (e.g., plane-wave and / or diverging wave ultrasound signals) according to a transmit sequence. The system may comprise a controller comprising one or more processors. The system may be configured to generate the transmit sequence and obtain ultrasound data that is based at least in part on ultrasound signals detected using the ultrasound transceiver. The transmit sequence may repeat a first angle at a first plurality of pulse repetition frequencies (PRFs) and repeat a second angle at a second plurality of PRFs. The system may render one or more images based at least in part on the ultrasound data for presentation on a display device. -3- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 In example embodiments, the controller beamforms all transmit-receive combinations based at least in part on filtered RF data. In example embodiments, the controller performs lag-one autocorrelation based at least in part on IQ data. In example embodiments, the controller generates at least one of vorticity, energy loss, and / or kinetic energy based at least in part on an estimated vector field. In yet another aspect, various embodiments are directed to a method for ultrafast ultrasound imaging (e.g., plane-wave ultrasound imaging or diverging wave ultrasound imaging). The method may comprise receiving signals detected following transmission of a first plurality of waves at a first angle followed by a second plurality of waves at a second angle, the first plurality of waves at the first angle comprising a first wave having a first pulse repetition frequency (PRF) and a second wave having a second PRF. The method may comprise generating one or more ultrasound images based on the received signals. In example embodiments, the first and second pluralities of waves are transmitted at cardiac tissue for high-frequency cardiac imaging. In example embodiments, the method extends a Nyquist limit to enable measurement of higher cardiac blood flow velocities with reduced aliasing. BRIEF DESCRIPTION OF THE DRAWINGS The accompanying drawings are not intended to be drawn to scale. Like reference numbers and designations in the various drawings indicate like elements. For purposes of clarity, not every component may be labeled in every drawing. Figs. 1A – 1D depict sequential angle transmission (1A), sequential angle transmission with staggered PRF (1B), double transmission (1C), and embodiments of the disclosed “StaBle” (Staggered PRF with douBle Transmission) scheme (1D), according to various embodiments. Figs. 2A – 2E depict dealiasing performed on unmatched net angle (2A and 2B) and matched net angle (2A and 2C), according to various embodiments. Not all angle combinations are displayed. The velocity magnitude estimated from the unmatched net angle is erroneous (2D), whereas the estimate from the matched net angle is more accurate (2E). -4- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Fig.3 provides an example flowchart 300 for processing steps in implementing the “StaBle” approach, according to various embodiments. Fig. 4 provides an example of data processing steps of “StaBle”, according to various embodiments. The first row displays heavily aliased color Doppler images (saturated colormap) from individual double transmits at PRF 1 and 2 (see also block 340 in Fig.3). The second row presents the resolved color Doppler after performing the dealiasing process on each Tx-Rx pair with matching net steering angles (see also block 350 in Fig. 3). Not every pair is shown in the figure. The third row shows the vector field obtained from the resolved color Doppler using the least-squares estimate (see also block 360 in Fig. 3). Figs. 5A – 5C provide a comparison of a simulated vector field produced by “StaBle” with varying p / q ratios and the corresponding ideal vector field, according to various embodiments. Fig. 5A depicts global root mean square error (RMSE) in blue and normalized RMSE (NRMSE) in red. Fig.5B depicts velocity magnitude NRMSE as a function of distance from the center. Fig. 5C depicts the lateral and axial velocity for p / q = 2 / 3 and p / q = 5 / 6, with the disks spinning at 95% of their respective maximum extended velocity limit. Figs. 6A – 6D provide a simulation of a rotating disk with varying speeds, according to various embodiments. A comparison of the calculated velocity and the ideal velocity profile analyzed by “StaBle” using different average window lengths for (6A) lateral velocity in region of interest (ROI) 1 (magenta) and (6B) axial velocity in ROI 2 (yellow). An example of VDI calculated by “StaBle” during rapid acceleration at 38 milliseconds (ms), processed with window lengths of 32 (6C) and 64 (6D). Figs.7A – 7E provide examples of vector Doppler imaging (VDI) obtained from phantom experiments using various transmission sequences, according to various embodiments: sequential angle transmission sequence (7A), double transmission (7B), double transmission with 3x higher PRF (7C), and “StaBle” (7D). The magenta and yellow circles indicate the ROI for obtaining the velocity profile in the lateral (7E) and axial (7F) directions, respectively. -5- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Figs. 8A – 8I provide images depicting Doppler imaging of a mouse left ventricle (LV) using different transmission sequences, according to various embodiments. The top row shows images with aliasing artifact: VDI obtained with conventional (sequential angle) transmission sequence (8A), color Doppler with double transmission with PRF1 (8B) and PRF2 (8C). The second row displays unambiguous VDI obtained using “StaBle” on different cardiac phases: early diastole (8D), diastasis (8E), and systole (8F). The blue circles highlight the ROI used for vector field quantification. The final rows depict vorticity (8G), energy loss (8H), and kinetic energy (8I) calculated from the vector field generated by “StaBle”. The red dashed lines indicate the timing of the displayed vector field and the black dashed lines indicate discontinuities in the acquisition. Fig. 9 depicts conventional VDI at the top, and “StaBle” at the bottom, according to various embodiments. Figs. 10A – 10D depict low-resolution IQ images corresponding to various Tx- Rx pairs, according to various embodiments. Figs. 11A – 11D depict (aliased) estimated velocities corresponding to the Tx- Rx pairs of Figs. 10A – 10D, according to various embodiments. Figs. 12A – 12C depict dealiasing with staggered PRF, according to various embodiments. Fig. 12A corresponds to velocity below both PRFs Nyquist limit (no aliasing), Fig. 12B corresponds to velocity above Nyquist limit of PRF2 but below PRF1, and Fig. 12C corresponds to velocity above Nyquist limit of both PRF1 and PRF2. Fig. 13A corresponds to a sequential Tx scheme, Fig. 13B corresponds to a double transmission scheme, and Fig.13C corresponds to the “StaBle” approach, according to various embodiments. Fig. 14 depicts an example system capable of implementing the disclosed “StaBle” approach, according to various embodiments. Fig. 15 depicts an example process of implementing the disclosed “StaBle” approach, according to various embodiments. -6- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 DETAILED DESCRIPTION Vector Doppler imaging (VDI) addresses the limitations of traditional Doppler imaging by measuring blood flow in axial and lateral directions but VDI will produce incorrect results if aliasing is present. Aliasing becomes more likely when using high transmit frequencies, such as in small animal cardiac applications, and or with lower pulse repetition frequencies (PRFs). The use of multiple transmit angles, such as with plane-wave imaging, decreases the Nyquist limit, which further increases the likelihood of aliasing. In various embodiments of the disclosure, a new transmission scheme, termed “StaBle”, increases the Nyquist limit of conventional plane-wave, sequential angle VDI by multiple fold. “StaBle” combines the velocity limit extension of staggered multiple PRF with a double transmission scheme. With 3 transmit angles and 2 PRFs, for example, “StaBle” is able to achieve a 6-12 times higher velocity limit compared to sequential angle VDI. Simulation and phantom spinning disk experiments were conducted to evaluate the performance of “StaBle”. The simulation results showed a normalized root-mean-squared error (NRMSE) of less than 5% compared to an ideal vector field in both axial and lateral directions. Phantom results showed a 9-fold improvement in detecting peak axial velocity over sequential angle VDI. The performance of “StaBle” was also evaluated in an in vivo environment by imaging a mouse LV to demonstrate the ability to obtain an unaliased vector field, whereas the sequential angle VDI was corrupted by aliasing artifacts for the same center transmit frequency and PRF. Moreover, derived measures such as vorticity, kinetic energy, and energy loss obtained from the resolved vector field showed consistent beat-to-beat variation, confirming the robustness of “StaBle” under various conditions and its usefulness in investigative studies. Various embodiments of the disclosure comprise a transmission scheme that combines a staggered PRF and double transmission to substantially extend the velocity aliasing limit of VDI, such as for use with high-frequency ultrasound imaging. Matching net steering angle improves “StaBle” accuracy in extending the velocity limit by mitigating point spread function (PSF) rotation effects. The unaliased vector flow parameters obtained with “Stable” from a mouse LV model show consistent beat-to-beat variations, illustrating the disclosed approach’s capability in assessing cardiac blood flow. -7- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 I. Introduction SMALL animal models, such as murine, have been extensively used to study cardiovascular dynamics because they are relatively inexpensive, easy to manipulate genetically, and similar to humans. Doppler ultrasound is the most common imaging modality to study hemodynamics, but it is only sensitive to the velocity in the direction of the sound propagation. Ultrasound vector-flow imaging is an emerging technique that, unlike conventional Doppler, allows visualization of the axial and lateral flow components. Vector- flow imaging can be implemented using several methods including speckle tracking, transverse oscillation, and multi-angle vector Doppler imaging (VDI). Embodiments of the disclosed approach employ multi-angle plane-wave VDI, achieving fine temporal resolution, being robust to out-of-plane flow, and not requiring ultrasound contrast agent to achieve sufficient sensitivity. However, implementing VDI in mouse models is technically challenging because, relative to humans, mouse hearts are orders of magnitude smaller. High-frequency ultrasound (≥15 MHz) and high-frame-rate plane-wave imaging permit improvements in spatial and temporal resolution over conventional ultrasound imaging which facilitates cardiac imaging in small-animal models. However, while finer spatial resolution is achieved by increasing the ultrasound transmit center frequency, the higher frequency results in a lower Nyquist velocity limit, which increases the likelihood of aliasing artifacts when analyzing rapid blood flow such as in the mouse heart. The Nyquist velocity limit (VN) is defined by: where λ is the wavelength of the transmit center frequency, and PRF is the pulse repetition frequency. In multi-angle VDI, the velocity limit is reduced relative to conventional Doppler imaging by the number of transmit angles. In addition, when implementing beamforming with plane-wave transmissions, the round-trip distance extends from the edge of the transducer to the far corner of the image rather than just the axial image depth, which further lowers the maximum PRF compared to conventional line-by-line transmission. To provide context, the aliasing threshold is 12.3 cm / s for the multi-angle VDI technique with three transmit angles, a 31 MHz center frequency, and an imaging depth of 15 mm, and a PRF of 30 -8- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 KHz. The transmitral E-wave velocity in a baseline mouse model is around 54-81 cm / s, while in the aorta, the peak velocity may exceed 1 m / s. Aliasing is even more likely to occur in certain cardiovascular conditions, such as mitral regurgitation and aortic stenosis, where blood flow velocity can be multiple times higher than in healthy conditions. Therefore, to mitigate aliasing in VDI of murine cardiac blood flow, there is a practical need to extend the velocity limit to over five times the Nyquist limit. To extend the Nyquist velocity limit in ultrasound Doppler, one direct method is by unwrapping the phase of the aliased signal. Implementation in ultrasound imaging can be implemented on individual Doppler phase shifts or using phase shifts from multiple angles. Moreover, an unsupervised learning and deep learning approach can be adopted for phase unwrapping. However, these methods are limited to addressing 1 or 2 fold aliasing, and the robustness of the unsupervised learning approach in VDI for handling various angles has not been demonstrated. Another method is the extended least-squares vector Doppler method, where the least squares regression method and block matching are combined to extend the Nyquist limit by a factor of 5. This method is less effective in the presence of low signal-to- noise ratio and high spatial velocity gradients which are frequently encountered in cardiac imaging. Another plane-wave approach is to repeat transmits of each plane-wave angle (e.g. [1,1,2,2...] rather than using the common sequential angle transmission [ 1,2,1,2... ]). This strategy improves the velocity limit by the number of transmission angles relative to the sequential method. Typically, 2 to 5 transmit angles are utilized in VDI, which would lead to a 2- to 5-fold increase in the Nyquist limit when using double transmit. With the previous example of 31 MHz imaging with 3 transmission angles, the Nyquist velocity limit using the double transmit method becomes 36.6 cm / s, which is still below the required velocity range for murine cardiac blood flow. A dealiasing method that may be implemented in radar signal processing uses a staggered PRF and a post-processing dealiasing procedure which compares the phase wrapped velocities that occur with different PRFs to determine if any aliasing is present. This method can be translated to color Doppler ultrasound imaging. However, the implementation in VDI -9- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 using a conventional transmission sequence in cardiac imaging remains a challenge because it requires the true flow velocity to remain nearly constant during the transmit pattern, but flow varies rapidly over a cardiac cycle. In practice, the long, multi-angle transmission sequence of VDI, especially when using a triple PRF to achieve a 5-fold increase in the Nyquist limit, makes the translation of staggered PRF to cardiac application difficult. The dual-wavelength approach is an alternate VDI method but the velocity extension it provides is only effective up to 2 times the velocity limit. Various embodiments of this disclosure overcome the above challenges by implementing a new transmission scheme called “StaBle” (Staggered PRF with douBle Transmission), which extends the velocity aliasing limit of the commonly used multi-angle sequential angle ultrasound VDI transmission sequence (e.g., by more than 2-fold, such as 6- fold or greater). This extension can be achieved by combining a staggered PRF with a double angle transmission which results in a velocity extension of the double angle multiplied by the staggered PRF. An overview of the techniques that “StaBle” is built upon (e.g., staggered PRF, double transmission, and least-squares vector Doppler) is provided, and example approaches to implementing “StaBle” are described. The disclosed approach is validated with simulation and phantom experiments using a spinning disk phantom. The disclosed approach is also demonstrated in vivo with a mouse cardiac model. II. Theory A. Multi-Angle Vector Doppler Estimation with Least-Squares Regression The multi-angle vector Doppler estimation approach extends conventional Doppler (i.e., line-based Doppler ensembles) by using velocity estimates from multiple transmit angles to calculate axial and lateral velocity, and has the effect of mitigating the strong transmit angle dependency typical in conventional Doppler. The method can be implemented by transmitting, for example, M plane waves at transmit angles, Tx, (θ1, θ2, ..., θM ) and N virtual receive angles, Rx, (φ1, φ2, ..., φN) for each Tx. A 3-Tx, 3-Rx approach can be a good compromise between variability and temporal resolution. Various embodiments employ M = 3, as discussed herein. Velocity estimates, Umn, are obtained for each Tx-Rx pair (M × N) using the lag-one autocorrelation technique. -10- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 where PRFeff is the effective PRF between the transmission pulses with the same Tx angle (PRFabs / M for sequential angle transmit sequence, where PRFabs is the absolute PRF between any two consecutive transmissions), cois the speed of sound, f0is the transmit center frequency, Rmnis the autocorrelation value (l = 1 for lag-one), and xmnis the slow time signal of window length P. We can use a trigometric identity to define the relation of Umn to the axial,vz, and lateral, vx, velocity^^௭^cos ^^^ ^ cos ^^^^ ^ ^^௫^sin^^^ ^ sin^^^^ ൌ 2^^^^. (4)Matrix A is defined based on the Tx and Rx pairs and constructs a linear system to obtain vz and vx based on the Doppler velocity u: which is solved with least squares regression to find v: B. Staggered PRF The unambiguous estimated Doppler velocity is limited by the Nyquist velocity limit (VN), defined by Eq. 1. However, when aliasing occurs, the measured Doppler velocity(Umn) is not the true velocity but can be defined as where ^^^௨is the unambiguous (non-aliased) Doppler velocity, and nNis the Nyquist number or aliasing order (in the case of no aliasing, nN= 0). Because the aliasing order is always an integer, Eq.7 can be rearranged to -11- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 ^^ ൌ flo ^ವೠା^ಿே or ^ ଶ^ಿ ^. (8)The actual Doppler velocity can be inferred if the Nyquist number is known. However, in actual measurements, the aliasing order is unknown. A staggered PRF transmission can be utilized to estimate the aliasing order, thereby extending the Nyquist velocity limit and obtaining the actual velocity. This can be accomplished by transmitting another sequence of pulses, PRFi, with a PRF less than the PRF of the main pulse sequence, PRF1(i.e., PRFi< PRF1, i > 1). Because VNhas a linear relation to PRF, where pi and qi are positive integers, pi < qi, and their greatest common divisor is 1. If aliasing is present, the perceived velocity (Umn) will vary with different PRFs. By observing the different possible perceived aliased shifts at different PRFs, example embodiments can infer a common aliasing coefficient (ncoeff) and determine the true velocity. ^^^^^^^ ൌ round where round() means rounding to the nearest integer. Based on ncoeff, some example embodiments can obtain n1 and ni using a lookup table (an example can be found in the table below) to determine the unambiguous Doppler velocity using a weighted mean The Nyquist velocity limit increases based on the selected piof the PRF ratio. For instance, if PRF2 = 3 / 4PRF1, it will result in a three-fold increase in Nyquist velocity. -12- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 However, increasing the ratio also leads to higher errors. In practice, two staggered PRFs are reliable up to pi = 5. Therefore, achieving an improvement of more than five-fold requires the use of three staggered PRFs. However, implementing VDI with three or more staggered PRFs and a conventional transmission sequence is not ideal in cardiac blood flow applications. The dealiasing operation assumes the estimated velocity between the multiple PRFs ensemble to be the same, which is violated if there is high (de-)acceleration of blood flow velocity. The use of three Tx angles and two staggered PRFs (Fig.1B) is already at a disadvantage in estimating pulsating cardiac blood flow because it assumes the velocity remains constant for the moving average window length P ×12-pulse duration instead of 6 pulses in the conventional Tx sequence (Fig. 1A). When using three staggered PRFs, it is even more unlikely that the blood flow velocity is constant for the duration of P ×18 pulses. C. Double transmit sequence The conventional plane-wave transmission sequence involves transmitting the M angles sequentially (Fig. 1A) such that the beamformed Rx data can be coherently compounded to generate high-resolution images. This approach minimizes the compounding time interval to (M – 1) times the pulse repetition interval (PRI = 1 / PRFabs) but is not ideal for VDI because the time interval between the same Tx angle to perform the lag-one autocorrelation of each angle is also M*PRI. As a result, the Nyquist velocity limit relative to the PRI is reduced by the number of transmit angles, where PRFeff= PRFabs / M. To address this limitation, a double transmit sequence may be employed, where the same angle is transmitted repeatedly instead of sequentially (Fig.1C). Using this approach, the lag-one autocorrelation can be performed over a single PRI period, effectively increasing the Nyquist velocity limit by a factor of M compared to the conventional transmission scheme. However, the double-transmit sequence has two drawbacks. First, the Doppler ensemble length is halved over a fixed gate time because the lag-one autocorrelation can only be performed for the pair of transmissions with the minimum transmit times. Second, the resulting high- resolution image is not optimal due to the increased time span of the compounding (2M – 1) * PRI. For cardiac blood flow imaging, the benefits of increasing the velocity limit outweigh -13- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 these two drawbacks. Moreover, the use of the double transmit sequence enables the optimal use of the staggered PRF method, which will be described in the following section. D. Staggered PRF with douBle Transmission (“StaBle”) As noted, extending the Nyquist velocity limit with existing techniques such as extended least-squares and staggered PRF by more than 5 times is impractical. Here, various embodiments provide the “StaBle” transmission scheme that combines transmitting double transmission pulses with staggered PRF on different TX angles pairs (Fig.1D). This approach accumulates velocity extension from both methods and enables an increase in the velocity limit by more than 6-fold. For example, with M = 3, the double transmission extends the velocity limit by 3 times and, when multiplied by the p of the PRF ratio (2-4), results in 6-12 times velocity extension compared to the sequential angle VDI method (Fig.1D). Another advantage of this sequence is that it only requires half the number of pulses to perform the dealiasing process compared to the sequential angle with staggered PRF sequence (Fig.1B). This can be particularly important for pulsating blood flow, where a large number of pulses could lead to inaccuracies due to potentially measuring different velocities. The steps to implement the “StaBle” techniques are illustrated by example flowchart 300 in Fig. 3. After the data are collected (305), several processing steps are employed to achieve the velocity measurements beyond the traditional Nyquist limit. The initial step applies a spatiotemporal SVD clutter filter if necessary (315). It is performed on each transmission angle on the RF data. Subsequently, the filtered RF data (320) is used to generate low-resolution images (330) – see also, for example, Figs. 10A to 10D – through IQ beamforming of each Rx steering angle (325). Next, high-pass filtering may be applied to the slow-time signals followed by lag-one autocorrelation (335) for each Tx-Rx pair using Eq.12. Doppler velocity, (Umn), is estimated using Eq. 2. Because double transmission is utilized, the estimated velocity (340) – see also, for example, Fig. 4, top row, and 11A to 11D – has a velocity limit 3 (M) times higher than the conventional transmission scheme. The next step (345) is to unfold velocity aliasing (350) – see also, e.g., Fig. 4, middle row – by using the -14- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 staggered PRF method. The ncoeff is calculated by using Eq.10 for pairs of different PRFs, but now on the corresponding transmission PRFs and angles (i.e., Tx1 with Tx2 and Tx2 with Tx3). Care must be taken with the lag-one autocorrelation estimation because non- zero net steering angles (θ + for Tx and Rx, respectively, cause a rotation of the PSF and could lead to velocity estimate errors if the dealising calculations are performed between nonreciprocal transceiving angles. Because (θ1+ ϕ1) and (θ3+ ϕ3) do not have a reciprocal net steering angle on Tx2, additional Rx angles for Tx2need to be generated, i.e. (ϕ4= θ1+ ϕ1) and (ϕ5 = θ3 + ϕ3). For instance, when calculating the ncoeff for unmatched net angle, (θ1+ϕ1) (Fig. 2A) and (θ2+ϕ2) (Fig.2B), the resulting velocity estimate is erroneous (Fig.2D). To solve this problem, the ncoeffcalculations must be conducted on Tx-Rx pairs that have the same net steering angles to match the resulting rotation of the PSF. For example, using (θ1 + ϕ1) (Fig. 2A) and (θ2 + ϕ4) (Fig. 2C) results in accurate velocity estimates (Fig. 2E). An example of matching the net steering angle configuration is provided in Table I. After calculating ncoefffor all Tx-Rx angles, the Nyquist number nN can be obtained by using a lookup table derived from the selected PRF ratio. The non-aliased Doppler velocity (Umn) is obtained using Eq.7. Once all pixels at each time step have been dealiased, the final vector Doppler estimation (360) – see also, for example, Fig. 4, bottom row – is obtained using the least-squares regression method (355) as described in Section IIA. Process 300 includes generating derived flow parameters (365), such as vorticity, energy loss, and / or kinetic energy (370). III. Experimental Methods A. Spinning Disk The performance of “StaBle” was evaluated using a simulation and phantom with a rotating cylinder. The cylinder was rotated at a constant angular velocity and with an angular acceleration to test our algorithm in resolving accelerating and decelerating flow. 1) Ultrasound Plane Wave Sequences: High-frame-rate plane-wave data were acquired with a Verasonics Vantage 256 (Verasonics, Redmond, WA) and a 256 element, 30- 40 MHz linear array (MS550D, FUJIFILM VisualSonics, Inc, Toronto, ON, Canada). -15- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Beamforming was performed with MATLAB (MathWorks, Natick, MA) on a 0.5λ grid using GPU processing. TABLE I DEALIASING CONFIGURATION WITH 3 TRANSMIT ANGLES (-7.5°, 0°, AND 7.5°) AND 2 PRFS TABLE II TRANSMISSION SETTINGS FOR SIMULATION AND PHANTOM EXPERIMENTS Simulation and phantom Transmit Center Frequency 31.25 MHz Sampling Rate 62.5 MHz Transmit Cycles 2 f – number 2 Transmit Angles -7.5, 1, 7.5 degrees Receive Processing Angles (Tx1and Tx3) -7.5, 0, 7.5 degrees Receive Processing Angles “StaBle” (Tx2) -15, -7.5, 0, 7.5, 15 degrees Constant velocity simulation Transmit Voltage 10 V Window length (P) 32 frames Absolute PRF16 kHz Absolute PRF2 4 kHz, 4.5 kHz, 4.8 kHz, 5 kHz p / q ratio 2 / 3, 3 / 4, 4 / 5, 5 / 6Nyquist limit “StaBle” sequence 14.8 cm / s, 22 cm / s, 29.4 cm / s 61.36.7 cm / s Varying velocity simulation Transmit Voltage 10 V Window length (P) 16, 32, 64 frames p / q ratio 3 / 4 Absolute PRF1 18 kHz Absolute PRF213.5 kHz -16- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Nyquist limit “StaBle” sequence 66.5 cm / s Phantom Transmit Voltage 18 V Absolute PRF1 6 kHz Absolute PRF24.5 kHz p / q ratio 3 / 4 Nyquist limit Sequential Tx sequence 2.4 cm / s Nyquist limit Double Tx sequence 7.3 cm / s Nyquist limit “StaBle” sequence & Double Tx 22 cm / s (3xPRF) 2) Simulation: The simulation data of a 3.5-mm radius rotating disk were generated using the Verasonics simulation mode with the transmission settings in Table II. First, the disc was rotated with a constant angular velocity, with maximum velocity at the edge of disk being 95% of each (p / q) ratio extended velocity limit. Examples of “StaBle” data processing and the resulting unambiguous vector field are shown in Fig.4. The same disk was simulated but with rotated with a velocity profile with a peak acceleration of 6000 cm / s2(comparable to our in vivo LV data) and a peak velocity 5.5 times the minimum velocity. The maximum velocity at the edge of disk was limited to 95% of the extended velocity limit (p / q = 3 / 4). To evaluate the velocity estimates of “StaBle”, a reference ideal vector field was generated. The absolute error was calculated using the root mean square error (RMSE), definedas RMSE ൌ ^^^∑^^ୀ^ ^^^^ െ ^^^^^ଶ where y denotes the velocity of each pixel within the disk. Therelative error was determined using the normalized RMSE, which is defined as NRMSE ൌୖ^ୗ^^௬^ೌ^ି௬^^^^, with the range (max-min) referring to the ideal vector velocity. White Gaussiannoise was added to the RF data to achieve a signal-to-noise ratio of 40 dB. SVD clutter filtering was not applied because there was no additional tissue clutter signal in the simulated data. 3) Phantom: An ≈ 0.5-cm diameter cylindrical tissue-mimicking phantom (ATS, Bridgeport, CT) containing scattering particles was attached to a DC-servo motor. The phantom was rotated at ≈ 11.5 revs / s, which resulted in a velocity of 18.67 cm / s at the outer edge of the phantom. The probe was clamped to a holder and held in a fixed position relative -17- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 to the phantom. We acquired data using conventional sequence, double transmit sequence, double transmit sequence with 3 times higher PRF, and “StaBle” (p / q = 3 / 4). We also did not apply SVD clutter filtering because the SNR is good enough to get the velocity estimates. B. In vivo mouse model “StaBle” performance was evaluated in vivo in a mouse cardiac model by scanning the LV and obtaining vector velocity estimates. To quantify the unaliased vector field obtained from “StaBle”, vorticity, ω, energy loss, EL, and kinetic energy, KE, are commonly employed to quantify LV blood flow patterns: ^^ ൌ డ^^డ௫ െ డ^^డ௬ , (13) where µ is the blood viscosity (4 mPa · s) and ρ is the blood density (1060 kg / m3). To calculate KE, a slice thickness of 0.22 mm was used to obtain a volume measurement. All parameters were standardized based on the pixel count so that a value did not depend on the ROI size. The mouse acquisitions were performed on male adult mice that were 50 weeks old. The mice were given anesthesia using a low-flow digital anesthesia machine (SomnoSuite, Kent Scientific, Torrington, CT) with 2.5% isoflurane for induction and 1% isoflurane for maintenance, mixed with medical oxygen at a flow rate of 1 L / min. Chest hair was removed to improve acoustic coupling. Core temperature, respiration rate and ECG were monitored. TABLE III TRANSMISSION SETTINGS FOR IN VIVO EXPERIMENT In vivo Transmit Center Frequency 31.25 MHz Sampling Rate 125 MHz Transmit Voltage 25 V -18- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Transmit Cycles 3 Window length 32 frames f - number 2 Transmit Angles -10, 1, 10 degrees Receive Processing Angles (Tx1and Tx3) -10, 0, 10 degrees Receive Processing Angles “StaBle” (Tx2) -20, -10, 0, 10, 20 degrees p / q ratio 3 / 4 Absolute PRFI18 kHz Absolute PRFII13.5 kHz Nyquist limit conventional sequence 7.4 cm / s Nyquist limit Double transmit sequence 22.2 cm / s 66.5 cm / s A Vantage NXT 256 (Verasonics) and MS550D probe (Fujifilm Visualsonics) were used to acquire high-frame-rate plane-wave data using the transmission settings in Table III. The acquisition was not fully continuous because the acquisition rate exceeded the data transfer bandwidth. Consequently, there were intermittent pauses to transfer data in blocks to host controller. SVD clutter filtering was applied to the RF data for each transmission angle prior to the beamforming process. IV. Results A. Simulation The performance of “StaBle” for increasing p / q ratios in comparison to their respective ideal vector field is shown in Fig. 5. Axial velocity displayed a lower error than lateral velocity for every p / q ratio. This is expected because Doppler velocity estimates are most sensitive to axial motion. The RMSE and NRMSE values rose with increased velocity extension (p). For p ≤ 4, the NRMSE for axial and lateral measurements remained below 5%. However, the dealiasing performance deteriorated drastically at p = 5, with axial and lateral NRMSE increasing to 13 and 19%, respectively (Fig. 5a). The velocity magnitude obtained by “StaBle” at different p / q ratios, in comparison to their ideal vector field as a function of distance from the center, is shown in Fig. 5b. Given that the velocity near the center of the disk does not have aliasing, we can infer that the RMSE in this region (under 1.75 cm) represent the accuracy of velocity estimates in the unaliased area, which remained below 3% for all p / q ratios. For p < 4, the NRMSE across all -19- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 distances remained fairly constant (< 3%), whereas for p ≥ 4, the NRMSE increased with distance from the center, reaching 9% for p = 4 and 44% for p = 5 at the disk’s edge. The performance of “StaBle” in addressing acceleration and deceleration, evaluated with various average window lengths, is shown in Fig. 6. For all window lengths, the estimated axial velocity (evaluated using ROI 2, where the tangential velocity was mainly axial) showed a closer alignment with the ideal velocity than the estimated lateral velocity, which was assessed using ROI 1, where the tangential velocity was mainly lateral. Window lengths of 16 and 32 provided similar NRMSE values, with lateral measurements at 9% and 8.5%, and axial measurements at 1.4% and 1.8%. However, a window length of 64 was excessively long, resulting in poor NRMSE values for lateral and axial directions at 18.8% and 10.5%, respectively. Notably, around 38 ms, the axial velocity estimation (Fig.6 b) for the 64- length window was quite erratic. B. Phantom VDI of the spinning disk using different transmission sequences is depicted in Figs. 7A – 7F. The rotation was maintained at a constant rate for all transmission sequences (11.5 rev / s, maximum axial velocity of 18.67 cm / s). The sequential angle sequence failed to accurately represent the rotation due to the disk’s speed being nearly 9 times faster than its velocity limit (Fig.7A). The Double transmit sequence revealed some improvement compared to the conventional sequence, but still contained aliasing artifacts. This was due to the disk still spinning 3 times faster than its velocity limit (Fig.7B). The double transmission at 3 times higher PRF (Fig. 7C) and “StaBle” (Fig. 7D) successfully measured the velocity and direction of the rotation when the axial velocity on the outer edge is 85% of the velocity limit. The mean lateral velocity measured by Double Tx (3x PRF) and “StaBle” was 16.27 ± 1.5 cm / s and 16.51 ± 2 cm / s, respectively (Fig. 7E). Meanwhile, the mean axial velocity measured by Double Tx (3x PRF) and “StaBle” was 18.41 ± 0.46 cm / s and 18.48 ± 0.37 cm / s (Fig. 7F). C. Mouse Left Ventricle Figs.8A – 8F show the implementation of “StaBle” to address velocity aliasing in a mouse LV and the resulting intracardiac flow quantification. The VDI images with -20- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 significant aliasing, acquired with a conventional transmission scheme, are shown in Fig. 8a. Aliasing was also observed in the color Doppler of double transmit PRF 1 and PRF 2 (Fig. 8b and c), despite having a velocity limit 3 times higher than the conventional transmit sequence with the same respective PRF. The staggered PRF dealiasing approach was then applied to resolve the aliasing. Subsequently, all VDI images were generated using the least-squares regression method applied to the unambiguous color Doppler images. The resulting unambiguous VDI on different cardiac phases is shown on Fig.8 d-f. Vorticity, EL, and KE were calculated from the resulting resolved vector field to quantify the flow pattern in the LV. The vorticity and KE beat-to-beat trend were consistent, demonstrating the robust performance of “StaBle” in resolving velocity aliasing. However, due to rapid acceleration, there remained some estimation inaccuracies in the incoming jet flow during diastole (Fig. 8 d), which led to spikes in EL (Fig. 8h (1)). V. Discussion Various embodiments of the disclosure employ a novel transmission scheme (“StaBle”) that integrates the Double transmission and staggered PRF techniques to significantly increase the velocity limit of the commonly used sequential angle VDI. When using 3 transmission angles in example embodiments, the disclosed approach extends the sequential angle VDI Nyquist limit by over 6 times. The double transmission minimizes the autocorrelation time interval at a given PRF, while the staggered PRF extends the velocity range beyond its Nyquist limit. Additionally, various embodiments employ a technique of aligning the net steering angle to address errors when comparing staggered PRF with different transmit steering angles for dealiasing. In various embodiments, the multi-fold velocity limit extension is especially beneficial for high-frequency cardiac imaging with rapid blood flow. “StaBle’s” performance under controlled conditions was assessed by conducting simulation and phantom studies using a spinning disk setup. For the simulation study with a constant velocity, the vector field resolved by “StaBle” was compared to an ideal vector field. “StaBle” performed well with an NRMSE below 5% in the axial and lateral directions when using a parameter p ≤ 4. “StaBle” also performed consistently (p ≤ 4) across -21- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 the entire velocity range of the disk (Fig. 5). This indicates that, in various embodiments, “StaBle” can be implemented even in the absence of aliasing. The simulation of the spinning disk’s varying velocity demonstrates that “StaBle” is capable of estimating velocity during acceleration and deceleration. However, the length of the averaging window is an important parameter (Fig. 6); in example embodiments, a window length of 64 can be excessively long, leading to estimation inaccuracies in the axial direction. In the phantom experiment, the vector fields produced by sequential angle, double, and double with 3x higher PRF, alongside the “StaBle” transmission method (with p / q = 3 / 4), were evaluated while measuring a spinning disk moving at a velocity 9 times greater than the Nyquist limit of the sequential angle method. The results showed that “StaBle” provided mean and standard deviation velocity estimates comparable to those obtained with the double transmission method at 3x higher PRF. In vivo studies of LV blood flow in a mouse were performed. The selected transmission settings (Fc = 31 MHz and PRF 1 = 18 kHz) led to significant aliasing in the sequential angle transmission method. Although somewhat reduced, aliasing also occurred with the double transmission approach. With “StaBle”, aliasing was resolved and the flow better quantified. The parameters of vorticity, KE, and EL showed a consistent pattern from beat to beat, indicating the robustness of the method under realistic conditions. Phantom and in vivo experiments were conducted. The peak vorticity in the LV during diastole (approximately 300 – 350 rad / s) alignd with previously reported values of 300 rad / s that were obtained at a lower transmission center frequency of 16 MHz. Various embodiments of the disclosed methodology can establish ground truth at a high frequency transmission, and we demonstrated that the three derived vorticity-related parameters (vorticity, EL, and KE – block 365 in Fig.3) were repeatable with each heartbeat. The limited data transfer bandwidth caused interruption in our acquisition sequence and time gaps occurred between some cardiac cycles. -22- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Results show that SVD is effective, but not required, for in vivo applications, as depicted in Figs. 8A, 8D, and 8E, where the tissue signal was suppressed, and the blood flow signal was emphasized. Flow quantification can be obtained from the resulting vector field and a color Doppler image can be generated. To reduce computation time during matching of the net-steering angle (transmit and receive) through beamforming of images of the additional receive angles (ϕ4and ϕ5) more efficient parallelization (e.g., using GPU) can be employed to carry out calculations in real time. In discussion of various embodiments, the sequential angle Nyquist limit was used as the reference as is most commonly done. In example embodiments, 3 transmission angles were employed because they provide a major improvement compared to 2 transmission angles, whereas increasing to 4 or 5 transmission angles may only provide minor improvement. Thus, even though “StaBle” was implemented in example embodiments using three transmit angles and two PRFs, which was demonstrated to be sufficient for murine experiments, other embodiments may incorporate, for example, 3 PRFs for 3 or more transmit angles to accommodate lower PRF or higher transmit frequency. It is noted that, despite the use of low frequencies (2-5 MHz) in human cardiac imaging, aliasing remains a prevalent issue in Doppler imaging due to high peak flow velocities and a low PRF needed for deep penetration (up to 20 cm). In various embodiments, implementing “StaBle” in human cardiac applications may involve using a phased array probe with diverging wave transmissions, which tend to degrade signal quality, particularly near the image edges. The staggered PRF dealiasing method for color Doppler is effective in human cases with a phased array probe. High-frequency ultrasound VDI is advantageous for imaging due to its ability to provide high spatial resolution of blood flow. However, as the transmit frequency and number of transmit angles increase, aliasing becomes more likely as the Nyquist limit decreases. Various embodiments of the disclosed “StaBle” transmission scheme effectively increases the Nyquist limit by 6-12 times compared to the commonly used sequential angle vector Doppler transmission scheme when 3 transmission angles are used. Simulation, phantom, and in vivo experiments demonstrated that the technique performed well across all -23- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 scenarios. “StaBle” proved to be an effective tool to obtain unambiguous blood flow velocity, particularly in the challenging case of the mouse LV. Referring to Fig. 14, an example ultrasound system 1400 according to various embodiments is depicted. System 1400 may comprise a set of modules configured to perform ultrasound imaging, each module able to be interconnected with one or more other modules via physical wiring and / or via wireless communication protocols (e.g., “Bluetooth”, “Wi-Fi”, near-field communication (NFC), and / or other protocols). System 1400 includes a controller 1410, an ultrasound transceiver 1440, a display device 1450, a user interface 1460, and a network interface 1470. Although written in the singular, each module in Fig. 14 may have one or multiple components (e.g., multiple ultrasound transceivers, multiple controllers, multiple processors, multiple memory units, multiple display devices, multiple user interfaces, and / or multiple network interfaces). In various embodiments, components or modules of system 1400 may be communicatively coupled to facilitate a continuous workflow from signal acquisition to image display, enabling real-time diagnostic imaging. Controller 1410 may operatively couple to other components of system 1400 to manage system operations. Controller 1410 comprises one or more computing hardware processors and non-transitory computer-readable memory for storing computer instructions (e.g., firmware or other code) for operation of system 1400 and control of components thereof, and storing data generated by system 1400 or received from other devices or systems (e.g., via network interface 1470). Controller 1410 includes a pulse unit 1415 capable of generating sequences for ultrasound transmissions. The pulse unit 1415 may generate and control the timing and characteristics of transmitted ultrasound pulses. The sequences generated via pulse unit 1415 may be provided to ultrasound transceiver 1440 for emission toward a subject (e.g., a patient, an anatomical structure, an organ, a tissue, an object with moving and / or flowing components, etc.) being scanned. Ultrasound transceiver 1440 may transmit ultrasound pulses into a medium and receive echo signals reflected from structures within the medium. In various embodiments, the ultrasound transceiver 1440 may comprise a transducer or probe comprising piezoelectric crystals that emit ultrasound waves and receive echoes thereof. The transducer may include, or may be connected to, a pulser or transmitter that generates electrical signals to excite the crystals. -24- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Controller 1410 also includes a signal processor 1420 capable of receiving signals detected using ultrasound transceiver 1440 (e.g., raw signals reflected from the subject being scanned) and / or other data that is based on or derived from detected signals. Signal processor 1420 may perform pre-processing and / or post-processing operations on detected signals, and / or on data based on detected signals, such as filtering operations, statistical and / or other analyses, generation of derived metrics, machine learning operations such as training and / or application of machine learning models, etc. Signal processor 1420 may, for example, receive echo signals from the ultrasound transceiver 1440 and process them to extract relevant signal features, such as Doppler shifts or amplitude information. Image generator 1425 may receive data (e.g., from signal processor 1420, ultrasound transceiver 1440, and / or user interface 1460) and render images for visualization of the subject being scanned. The image generator 1425 may transmit image data (via wires or via wireless communications, such as via a network to a remote device) to display device 1450 for presentation to one or more users (e.g., one or more health care providers or patients). Additionally or alternatively, images, imaging data, and / or other data (e.g., metrics or other data detected or generated via system 1400) may be stored for subsequent access / retrieval (e.g., by system 1400 or by another system or device via network interface 1470) in one or more memories of system 1400 and / or in one or more remote devices (e.g., cloud storage systems, health information systems (HIS), medical information systems (MIS), etc.). Display device 1450 may display generated images to a user in real time. User interfaces 1460 may provide mechanisms for user interaction, including control of imaging parameters, initiation of imaging sequences, review of imaging or other data, providing instructions, control of system 1400 or components thereof, etc. User interfaces 1460 may comprise any suitable combination of input / output (I / O) devices, such as one or more keyboards (virtual and / or physical), touchscreens or other display screens, pointers (e.g., computer mouse or pointing stick, trackpoint), microphones, speakers, light sources (LEDs or otherwise), joysticks, tactile or haptic components, etc. Network interface 1470 may comprise any network adapters or communication devices for wired and / or wireless communication of data and / or instructions from system 1400 -25- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 to other devices and / or systems, or from other devices and / or systems to system 1400. Network interface 1470 may communicate with workstations, portable devices (e.g., smartphones, tablets, laptop computers, digital assistants, wearable devices, etc.), medical devices and / or systems (e.g., another imaging device or system), cloud computing systems, and / or HIS / MIS or other information systems. One or more components of system 1400 and / or external devices or systems may send and / or receive commands, instructions, or other input (e.g., via an application running on a smart device of a health care provider and / or patient), imaging data (e.g., for display using a portable device of a health care provider and / or patient), etc. Image generator 1425 may convert processed signal data into visual representations, such as grayscale or color Doppler images. Referring to Fig. 15, an example ultrasound process 1500 according to various embodiments is depicted. Method 1500 depicts a computer-implemented method for performing ultrasonic imaging (e.g., using system 1400). Process 1500 enables, for example, efficient and accurate acquisition and visualization of ultrasound data for diagnostic or monitoring purposes. Method 1500 may start at start block 1510, by for example receiving an initiation instruction (e.g., to begin imaging). For example, at block 1510, system 1400 may receive a command from a user (e.g., via user interface 1460) or automated process to begin an ultrasound imaging session. At block 1520, process 1500 comprises emitting ultrasound pulses (e.g., based on sequences generated by pulse unit 1415) into a target medium via the ultrasound transceiver 1440. At block 1530, ultrasound signals may be detected (e.g., using ultrasound transceiver 1440) and / or received (e.g., via network interface 1470). The ultrasound signals may be echo signals reflected from internal structures within the medium. At block 1540, process 1500 comprises processing of detected and / or received signals. Signal may be processed by, for example, signal processor 1420. Signals may be analyzed or otherwise processed for generation and / or extraction of, for example, derived metrics and / or imaging data. Process 1500 comprises rendering images at block 1550. Images may be constructed by, for example, image generator 1425. Visual images may be rendered based on processed data. At 1560, process 1500 comprises displaying images. Images may be displayed in real time, or at a later time, for user interpretation or other consumption. As images are being displayed, process 1500 may loop back to block 1520 to acquire additional data for -26- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 continued or subsequent visualization. Alternatively or additionally, process 1500 may proceed to block 1570, at which point imaging may cease. It is noted that process 1500 may proceed automatically to block 1570 at a predetermined occurrence (e.g., if no data is being detected or received), based on a user instruction to stop, based on power being turned off, based on insufficient quality in data being received, etc. Various non-limiting example embodiments include the following combinable embodiments / features: Embodiment A1: An ultrafast ultrasound imaging (e.g., plane-wave ultrasound imaging or diverging wave ultrasound imaging) method, the method comprising using a transmission scheme that combines a staggered pulse repetition frequency (PRF) technique with a double transmission technique. Embodiment A2: An ultrafast ultrasound imaging (e.g., plane-wave ultrasound imaging system or diverging wave ultrasound imaging), the system configured to use a transmission scheme that combines a staggered pulse repetition frequency (PRF) technique with a double transmission technique. Embodiment B1: A method for ultrafast imaging (e.g., plane-wave Doppler ultrasound imaging or diverging wave ultrasound imaging), the method comprising: generating a transmit sequence and transmitting first ultrasound signals according to the transmit sequence; obtaining second ultrasound data based at least in part on ultrasound signals detected using an ultrasound transceiver following transmission of the first ultrasound signals according to the transmit sequence; and rendering one or more images (e.g., beamformed IQ images) based at least in part on the ultrasound data for presentation on a display device; wherein the transmit sequence repeats a first angle at a first plurality of pulse repetition frequencies (PRFs) and repeats a second angle at a second plurality of PRFs. Embodiment B2: The method of any of Embodiments B1 or B3 – B15, wherein the second plurality of PRFs is different from the first plurality of PRFs. -27- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Embodiment B3: The method of any of Embodiments B1 – B2 or B4 – B15, wherein aliasing is reduced by combining a staggered pulse repetition frequency (PRF) scheme with a double transmission scheme to effectively increase the Nyquist velocity limit. Embodiment B4: The method of any of Embodiments B1 – B3 or B5 – B15, wherein the system is configured to use double transmission pulses with staggered PRF on different transmit angle pairs. Embodiment B5: The method of any of Embodiments B1 – B4 or B6 – B15, wherein the transmission scheme comprises at least three transmit angles and, for each transmit angle, at least two staggered PRFs, or wherein the transmission scheme comprises two staggered PRFs between all transmit angles. Embodiment B6: The method of any of Embodiments B1 – B5 or B7 – B15, comprising IQ beamforming all transmit-receive combinations based at least in part on filtered RF data. Embodiment B7: The method of any of Embodiments B1 – B6 or B8 – B15, comprising performing autocorrelation based at least in part on low-resolution IQ images to obtain Doppler phase shift estimates. Embodiment B8: The method of any of Embodiments B1 – B7 or B15, comprising generating at least one of vorticity, energy loss (EL), or kinetic energy (KE) based at least in part on an estimated vector field. Embodiment B9: The method of any of Embodiments B1 – B8 or B10 – B15, comprising matching net steering angles during data processing to mitigate errors caused by point spread function (PSF) rotation. Embodiment B10: The method of any of Embodiments B1 – B9 or B11 – B15, comprising using “StaBle” to effectively dealiase conventional Doppler images at multiple angle combinations, and performing VDI on the resulting corrected conventional Doppler. -28- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Embodiment B11: The method of any of Embodiments B1 – B10 or B12 – B15, comprising matching net transmit-receive steering angles to mitigate errors caused by point spread function (PSF) rotation in cardiac imaging. Embodiment B12: The method of any of Embodiments B1 – B11 or B13 – B15, comprising dealiasing with staggered PRF applied to extend the Nyquist limit. Embodiment B13: The method of any of Embodiments B1 – B12 or B14 – B15, comprising generating at least one of power Doppler or color Doppler. Embodiment B14: The method of any of Embodiments B1 – B13 or B15, comprising using a least-squares approach to estimate vector flow based at least in part on multi-angle phase estimates. Embodiment B15: The method of any of Embodiments B1 – B14, comprising generating at least one of a vector map at each times step, a map of velocity magnitude, or a map of flow direction. Embodiment C1: A system for ultrafast ultrasound imaging (e.g., plane-wave Doppler ultrasound imaging or diverging wave ultrasound imaging), the system comprising: an ultrasound transceiver configured to transmit plane-wave and / or diverging ultrasound signals according to a transmit sequence; and a controller comprising one or more processors to perform any of method of any of Embodiments A1, B1 – B15, or D1 – D3. Embodiment D1: A method for ultrafast ultrasound imaging (e.g., plane-wave ultrasound imaging or diverging wave ultrasound imaging), the method comprising: receiving signals detected following transmission of a first plurality of waves at a first angle followed by a second plurality of waves at a second angle, the first plurality of waves at the first angle comprising a first wave having a first PRF and a second wave having a second PRF; and generating one or more ultrasound images based on the received signals. Embodiment D2: The method of any of Embodiments A1, B1 – B15, D1, or D3, wherein the first and second pluralities of waves are transmitted at cardiac tissue for cardiac imaging. -29- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 Embodiment D3: The method of any of Embodiments A1, B1 – B15, or D1 – D2, wherein the method extends a Nyquist limit to enable measurement of higher cardiac blood flow velocities with reduced aliasing. Embodiment E1. A system for performing any method of any of Embodiments A1, B1 – B15, or D1 – D3. It should be noted that although method steps may be described in a specific order, it is understood that the order of these steps may differ from what is described. In a non- limiting example, two or more steps may be performed concurrently or with partial concurrence. Also, some method steps that are performed as discrete steps may be combined, steps being performed as a combined step may be separated into discrete steps, the sequence of certain processes may be reversed or otherwise varied, and the nature or number of discrete processes may be altered or varied. The order or sequence of any element or apparatus may be varied or substituted according to alternative embodiments. Accordingly, all such modifications are intended to be included within the scope of the present disclosure as defined in the appended claims. It is understood that all such variations are within the scope of the disclosure. While this specification contains many specific embodiment details, these should not be construed as limitations on the scope of any inventions or of what may be claimed, but rather as descriptions of features specific to particular embodiments of the systems and methods described herein. Certain features that are described in this specification in the context of separate embodiments may also be embodied in combination in a single embodiment. Conversely, various features that are described in the context of a single embodiment may also be embodied in multiple embodiments separately or in any suitable subcombination. Moreover, although features may be described above as acting in certain combinations and even initially claimed as such, one or more features from a claimed combination may in some cases be excised from the combination, and the claimed combination may be directed to a subcombination or variation of a subcombination. Having now described some illustrative embodiments and embodiments, it is apparent that the foregoing is illustrative and not limiting, having been presented by way of -30- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 example. In particular, although many of the examples presented herein involve specific combinations of method acts or system elements, those acts and those elements may be combined in other ways to accomplish the same objectives. Acts, elements, and features discussed only in connection with one embodiment are not intended to be excluded from a similar role in other embodiments. The phraseology and terminology used herein is for the purpose of description and should not be regarded as limiting. The use of “including,” “comprising,” “having,” “containing,” “involving,” “characterized by,” “characterized in that,” and variations thereof herein, is meant to encompass the items listed thereafter, equivalents thereof, and additional items, as well as alternate embodiments consisting of the items listed thereafter exclusively. In one embodiment, the systems and methods described herein consist of one, each combination of more than one, or all of the described elements, acts, or components. As utilized herein with respect to numerical ranges, the terms “approximately,” “about,” “substantially,” “essentially,” and similar terms generally mean + / - 10% of the disclosed values. When the terms “approximately,” “about,” “substantially,” “essentially,” and similar terms are applied to a structural feature (e.g., to describe its shape, size, orientation, direction, etc.), these terms are meant to cover minor variations in structure that may result from, for example, the manufacturing or assembly process and are intended to have a broad meaning in harmony with the common and accepted usage by those of ordinary skill in the art to which the subject matter of this disclosure pertains. Accordingly, these terms should be interpreted as indicating that insubstantial or inconsequential modifications or alterations of the subject matter described and claimed are considered to be within the scope of the disclosure as recited in the appended claims. Any references to embodiments or elements or acts of the systems and methods herein referred to in the singular may also embrace embodiments including a plurality of these elements, and any references in plural to any embodiment or element or act herein may also embrace embodiments including only a single element. References in the singular or plural form are not intended to limit the presently disclosed systems or methods, their components, acts, or elements to single or plural configurations. References to any act or element being -31- 4937-3703-1489.3 Atty. Dkt. No.: 093873-1476 based on any information, act, or element may include embodiments where the act or element is based at least in part on any information, act, or element. Any embodiment disclosed herein may be combined with any other embodiment, and references to “an embodiment,” “some embodiments,” “an alternate embodiment,” “various embodiments,” “one embodiment,” or the like are not necessarily mutually exclusive and are intended to indicate that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment. Such terms as used herein are not necessarily all referring to the same embodiment. Any embodiment may be combined with any other embodiment, inclusively or exclusively, in any manner consistent with the aspects and embodiment disclosed herein. References to “or” may be construed as inclusive so that any terms described using “or” may indicate any of a single, more than one, and all of the described terms. Where technical features in the drawings, detailed description or any claim are followed by reference signs, the reference signs have been included for the sole purpose of increasing the intelligibility of the drawings, detailed description, and claims. Accordingly, neither the reference signs nor their absence have any limiting effect on the scope of any claim elements. The foregoing description of embodiments has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the disclosure to the precise form disclosed, and modifications and variations are possible in light of the above teachings or may be acquired from this disclosure. The embodiments were chosen and described in order to explain the principals of the disclosure and its practical application to enable one skilled in the art to utilize the various embodiments and with various modifications as are suited to the particular use contemplated. Other substitutions, modifications, changes, and omissions may be made in the design, operating conditions and embodiment of the embodiments without departing from the scope of the present disclosure as expressed in the appended claims. -32- 4937-3703-1489.3

Claims

Atty. Dkt. No.: 093873-1476 WHAT IS CLAIMED IS:

1. A method for ultrafast ultrasound imaging, the method comprising: generating a transmit sequence and transmitting first ultrasound signals according to the transmit sequence; obtaining ultrasound data based at least in part on second ultrasound signals detected using an ultrasound transceiver following transmission of the first ultrasound signals according to the transmit sequence; and rendering one or more beamformed IQ images based at least in part on the ultrasound data for presentation on a display device; wherein the transmit sequence repeats a first angle at a first plurality of pulse repetition frequencies (PRFs) and repeats a second angle at a second plurality of PRFs.

2. The method of claim 1, wherein the second plurality of PRFs is different from the first plurality of PRFs.

3. The method of claim 1, wherein aliasing is reduced by combining a staggered pulse repetition frequency (PRF) scheme with a double transmission scheme to effectively increase a velocity limit of vector Doppler imaging (VDI).

4. The method of claim 1, wherein the transmission scheme comprises at least two staggered PRFs between all transmit angles.

5. The method of claim 1, comprising IQ beamforming all transmit-receive combinations based at least in part on filtered RF data.

6. The method of claim 1, comprising matching net transmit-receive steering angles to mitigate errors caused by point spread function (PSF) rotation in cardiac imaging.

7. The method of claim 1, comprising performing autocorrelation based at least in part on low-resolution IQ images to obtain Doppler phase shift estimates. -33- 4937-3703-1489.3Atty. Dkt. No.: 093873-1476 8. The method of claim 1, comprising dealiasing with staggered PRF applied to extend the Nyquist limit.

9. The method of claim 1, comprising generating at least one of power Doppler or color Doppler.

10. The method of claim 1, comprising using a least-squares approach to estimate vector flow based at least in part on multi-angle phase estimates.

11. The method of claim 1, comprising generating at least one of a vector map at each times step, a map of velocity magnitude, or a map of flow direction.

12. The method of claim 1, comprising generating at least one of vorticity, energy loss, or kinetic energy based at least in part on an estimated vector field.

13. A method for ultrafast ultrasound imaging, the method comprising: receiving signals detected following transmission of a first plurality of waves at a first angle followed by a second plurality of waves at a second angle, the first plurality of waves at the first angle comprising a first wave having a first pulse repetition frequency (PRF) and a second wave having a second PRF; and generating one or more ultrasound images based on the received signals.

14. The method of claim 13, wherein the first and second pluralities of waves are transmitted at cardiac tissue for cardiac imaging.

15. The method of claim 13, wherein the method extends a Nyquist limit to enable measurement of higher cardiac blood flow velocities with reduced aliasing. -34- 4937-3703-1489.3

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