System and method for estimating cardiac dynamics and flow instability using ultrasound

Abstract

The present disclosure relates to ultrasound-based strategies and techniques that are specially designed for time-resolved simultaneous cardiac tissue visualization and intracardiac flow instability mapping. First, to achieve high-resolution tissues images while also acquiring flow data, we devised an acquisition scheme which consists of two batches. The first batch is dedicated to tissue imaging, where we transmit a series of diverging waves emitted from different virtual source locations. These pulses have a single pulse-cycle to optimize axial resolution and are coherently compounded for improving lateral resolution. This paradigm generates tissue images with an improved resolution, allowing for real-time guidance at frame rates up to 50 fps. The second batch is dedicated for flow imaging where all diverging waves are transmitted from the same virtual source location. These flow pulses have a 5-cycle pulse length for improved flow signal. The length of this batch can be adjusted, but our experiments use a length of 64. The final transmission scheme alternates between the tissue batch and flow batch.

Description

SYSTEM AND METHOD FOR ESTIMATI NG CARDIAC DYNAMICS ANDFLOW I NSTABI LITY USI NG U LTRASOU N DCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] The present application claims the benefit of U.S. Provisional Application No. 63 / 697,488 filed on September 21, 2024, entitled SYSTEM AND METHOD FOR ESTIMATING CARDIAC DYNAMICS AND FLOW INSTABILITY USINGULTRASOUND, which is hereby incorporated by reference in their entirety.FIELD

[0002] This disclosure relates to the field of ultrasound.BACKGROUND OF THE INVENTION

[0003] Echocardiographic examinations provide critical diagnostic information since they allow quantitative and qualitative analysis of cardiac tissues and blood flow dynamics [1], Conventional color flow mapping, however, often fails to detect underlying flow disturbances which are indicators associated with valvular dysfunction. Recent developments of high-frame rate ultrasound have made it possible to visualize both cardiac tissues [2] and blood flow patterns [3] with higher temporal resolutions (100s of Hz). These improved acquisition tools allow for improved tracking of myocardial tissue motion [4] and the quantification of diastolic flow patterns related to the heart [5], However, subtle flow disturbances and / or sharp flow gradients associated to valvular dysfunction can be masked by the spatial resolution of the color flow imaging modality used for flow quantification [6],

[0004] High-frame rate cardiac imaging typically employs diverging wave transmissions, insonifying the entire heart with a single firing [7], While improving temporal resolution, these unfocused firings have lower spatial resolution [7], which degrades tissue image quality and can mask flow disturbances. Two techniques have been developed to address these issues: (1) coherent compounding, which improves tissue image quality [7], and (2) Doppler bandwidth mapping, which maps regions of increased flow complexity [8], Unfortunately, these techniques have conflicting transmission requirements - coherent compounding requires different virtual source locations for compounding and benefits from shorter pulse lengths for improving axialresolution [9], Doppler processing, such as DBM, uses static virtual sources with longer pulse cycles to increase Doppler signal SNR

[0010]

[0005] Batch processing provides a solution to this conflict, where alternating transmission batches can be used to form high quality tissue images and obtain flow information. To maintain temporal resolution for both the flow estimation and tissue visualization, the ensemble length available for Doppler processing, becomes a constraint. This constraint of shorter ensembles affects current Doppler processing techniques such as lag-one autocorrelation

[0011] , since lag- one autocorrelation has worse statistical accuracy with shorter ensembles

[0012] , leading to less accurate bandwidth estimations. Autoregressive techniques for Doppler bandwidth (DBW) estimation, as proposed by Yiu et al. [8], can be effectively used with shorter ensembles

[0013] , However, these autoregressive models benefit from data-dependent parameter tuning

[0013] , which requires longer ensembles and become unreliable when short data frames (<64 samples) are used

[0014] ,

[0006] In the following, we provide a review of the bandwidth estimation literature by direct ultrasound imaging and highlight their limitations:

[0007] C. Kasai et al., "Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique, "IEEE Transactions on Sonics and Ultrasonics, vol. 32, no. 3, pp. 458- 464, 1985. doi:10.1109 / T-SU.1985.31615. This is one of the first demonstrations of a method for estimating the Doppler bandwidth via time-domain methods. The method is demonstrated using focused transmission allowing for shorter ensembles. Unfocused transmissions require longer ensembles for robust estimation using the auto-correlation approach, making their approach not feasible for high-temporal resolution.

[0008] B. Osmanski et al., "Cancellation of Doppler intrinsic spectral broadening using ultrafast Doppler imaging," IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 61, no. 8, pp. 1396-1408, 2014. doi:10.1109 / TUFFC.2014.3049. This paper uses plane waves to insonify a region of interest, calculates the power spectrum at various locations, estimate the intrinsic broadening effects, then improves the Doppler spectrum to remove the broadening effects. This paper does not estimate Doppler bandwidth for the purposes of flow stability measurement, making it unrelated to our framework.

[0009] S. Hovda, H°avard Rue, and Bjprn Olstad, "Bandwidth of the Ultrasound Doppler Signal with Applications in Blood / Tissue Segmentation in the Left Ventricle," Medical Imaging and Informatics, vol. 4987, 2015. This paper uses multi-line transmissions and an auto-correlationapproach to estimate the Doppler bandwidth for the purposes of segmenting the ventricle. This paper does not perform any mapping of the Doppler bandwidth or relate it to flow stability and is therefore unrelated to our framework.

[0010] What is therefore needed is an improved system and method which addresses at least some of the limitations of the prior art.SUMMARY OF THE INVENTION

[0011] Our technology is the first solution that can solve all of the above problems. We have achieved so by devising a series of ultrasound-based strategies and techniques that are specially designed for time-resolved simultaneous cardiac tissue visualization and intracardiac flow instability mapping. First, to achieve high-resolution tissues images while also acquiring flow data, we devised an acquisition scheme which consists of two batches. The first batch is dedicated to tissue imaging, where we transmit a series of diverging waves emitted from different virtual source locations. These pulses have a single pulse-cycle to optimize axial resolution and are coherently compounded for improving lateral resolution. This paradigm generates tissue images with an improved resolution, allowing for real-time guidance at frame rates up to 50 fps. The second batch is dedicated for flow imaging where all diverging waves are transmitted from the same virtual source location. These flow pulses have a 5-cycle pulse length for improved flow signal. The length of this batch can be adjusted, but our experiments use a length of 64. The final transmission scheme alternates between the tissue batch and flow batch.

[0012] Using the data acquired with the flow batch, we then beamform and pass the resulting signal through a projection initialized infinite impulse response (HR) clutter filter. This filter removes unwanted tissue signals, addressing problem 5 listed above.

[0013] Once clutter filtered, a minimum variance power spectrum is calculated for each pixel using a short ensemble length (16 for our experiments, but this value can be adjusted). The minimum variance approach allows for short ensembles to be used, meaning no sliding- ensembles are needed to achieve high temporal resolutions of 200 fps.

[0014] To robustly estimate Doppler bandwidth, a cumulative power integral is used to smoothen the effects of noise and incoherent frequency summations present in the Doppler signal. Using the cumulative power integral and specific thresholding chosen based on the relationship between a gaussian distribution and its cumulative density function, the bandwidth associated to the first standard deviation of the signal is extracted. This approach is lesssusceptible to noise and incoherent frequency summations compared to a full width at half max approach as used by Yiu et al.

[0015] Our invention has five major features that are unique and offer us competitive advantage:1. A new tissue and flow batch transmission strategy for concurrent high- resolution tissue imaging and flow instability measurement2. Clutter filtering to suppose unwanted tissue echoes from the moving myocardium, so as to enable robust, accurate Doppler bandwidth estimation at every identified flow pixel in the image frame for flow instability mapping3. Low ensemble length estimation of Doppler power spectrum for flow instability measurement at every flow pixel position4. Minimum-variance power spectrum estimation for robust Doppler power spectrum estimation within the signal processing pipeline for flow instability quantification5. Cumulative integration of each Doppler power spectrum to facilitate robust Doppler bandwidth estimation as needed for robust flow instability assessment

[0016] BRIEF DESCRIPTION OF DRAWINGS

[0017] FIG. 1 shows an illustrative example of operation of the present system and method for measurement of cardiac flow instability in accordance with an illustrative embodiment.

[0018] FIG. 2 summarizes a transmission scheme and processing pipeline in accordance with an illustrative embodiment.

[0019] FIG. 3 shows procedures for robust bandwidth estimation in accordance with an illustrative embodiment.

[0020] FIG. 4 shows a Doppler spectrogram and illustrative examples of a stable flow and an unstable flow.

[0021] FIG. 5 illustrates a high-frame rate pipeline in accordance with an illustrative embodiment.

[0022] FIG. 6 shows an image formatting and clutter filtering process in accordance with an illustrative embodiment.

[0023] FIG. 7 shows a minimum variance (MV) power spectrum optimization and bandwidth estimation process in accordance with an illustrative embodiment.

[0024] FIG. 8 shows an acquisition scheme and bandwidth processing pipeline in accordance with an illustrative embodiment.

[0025] FIG. 9 shows a physiological scenario featuring flow instability such as mitral regurgitation jets.

[0026] FIG. 10 shows an illustrative results scenario in accordance with an embodiment.

[0027] FIG. 11 shows another illustrative results scenario in accordance with another embodiment.

[0028] FIG. 12 shows an in-vivo demonstration of Doppler bandwidth visualization during left ventricular dynamics.

[0029] FIG. 13 shows an example of bandwidth decomposition and an illustrative clinical application potential.

[0030] FIG. 14 shows that EMFI is able to quantify changes in flow stability in-vitro.

[0031] FIG. 15 shows a generic computing device which may provide a platform for various embodiments.

[0032] FIG. 16 shows a CAD model for a negative mold in accordance with an embodiment.

[0033] FIG. 17 Figure 17 summarizes the orifice phantom fabrication process.

[0034] FIG. 18 shows various views of the phantom in accordance with an embodiment.

[0035] FIG. 19 shows a single frame from which flow rate was extracted, in accordance with an embodiment.

[0036] FIG. 20 shows a log-scaled power spectrum from a point of interest.

[0037] FIG. 21 shows three time-points of interest from each regurgitant volume were extracted.

[0038] FIG. 22 shows a frame from the ventricular filling and ejection phases, for better analysis of the flow maps.DETAILED DESCRIPTION OF TH E INVENTION

[0039] There are a variety of challenges when visualizing and quantifying flow stability in the heart at fine temporal resolution using ultrasound.

[0040] The first problem originates from the depth of the heart in the body. In general, an imaging depth of around 15cm is needed for imaging the heart in the 4-chamber view. Due to the two-way propagation time required for pulse-echo sensing, this limits the maximum pulse repetition frequency (PRF) of the ultrasound pulses to no higher than 5000 Hz. This affects thetemporal resolution of ensemble defined quantities, as the time required to acquire a full ensemble is equal to the ensemble divided by the PRF. Due to the limit on the maximum possible PRF, this means that to improve temporal resolution, a shorter ensemble is desired. One technique which can potentially fix this problem is sliding ensembles, but this requires a continuous pulse train to be effective.

[0041] The next problem originates from the width of the heart. High-frame rate ultrasound relies on two types of unfocused transmissions: plane wave and diverging waves. Plane waves can only be as wide as the transducer used to transmit them, but cardiac probes have narrow footprints ranging between 1 to 2cm. For the 4-chamber view of the heart however, 8cm or more are needed to fully visualize the entire heart. As such, diverging waves are required, as these waves grow radially, allowing for the entire heart to be imaged. However, the consequence of these diverging wave fronts is decreased signal strength with depth, and the increased effect of incoherent frequency summations due to the wide wave front.

[0042] Another problem are the resolution limitations from the diverging waves and the cardiac probe. The resolution of an ultrasound image depends on the F-number, a quantity defined by the ratio of the imaging depth to the aperture width. The consequence of this ratio is that the ultrasound image has less resolution with depth, making it more difficult to visualize tissues. Image compounding can be used to improve this, but this requires a different transmission scheme which does not work with flow imaging. While feasible, this prevents the sliding-ensemble approach from being used, which is often used for flow processing to improve temporal resolution.

[0043] Finally, another problem with cardiac imaging is the clutter filtering requirements to extract flow information. Clutter filtering is a process of removing tissue signal from a slow-time ensemble to emphasize the blood flow information. These filters are designed as high pass filters which have a fixed cut-off frequency based on stationary tissues.

[0044] To summarize, cardiac flow instability imaging has a list of requirements which need to be fulfilled:1. There is a limit to the maximum PRF available for cardiac imaging due to depth requirements2. Diverging waves are necessary to achieve high temporal resolution while also capturing the entire width of the heart3. Resolution improvement is necessary since diverging waves lead to worse resolutions since they are unfocused4. When using image compounding for resolution improvement, sliding ensembles cannot be used to improve temporal resolution. So, short ensembles, non-overlapping ensembles are necessary.5. Clutter filtering is necessary to filter out tissue motion.6. Diverging waves lead to increased incoherent frequency summations, making the Doppler spectrum more complex and requiring more advanced bandwidth estimation.

[0045] Our invention is a new way to simultaneously achieve 1) high-frame-rate, high- resolution cardiac tissue visualization and 2) intracardiac flow instability quantification and mapping using ultrasonic means. Our invention involves the use of a novel pulse-echo ultrasound imaging paradigm that involves innovation in both transmission and reception. On the transmit end, a new pulse-echo transmission strategy has been devised to alternate between tissue and flow data acquisition using diverging waves sent from an ultrasound array transducer. On the receive end, ultrasound echoes collected from each array transducer channel were coherently compounded to achieve cardiac tissue visualization; also, projection initialized HR clutter filtering and robust, short-ensemble bandwidth estimations are performed to quantify and map intracardiac flow instability. Our framework can generate flow instability maps (rendered in the form of Doppler bandwidth maps) with a frame rate of 250 fps, a figure of merit for providing insights into local flow stability during a single cardiac cycle at a fine temporal resolution of 4 ms that is not currently capable on clinical ultrasound scanners.

[0046] The invention would be integrated into an ultrasound scanner to perform the new, unique ultrasound transmit-receive sequence and the new signal processing pipeline required to measure Doppler bandwidth, a quantity which is related to flow stability. During operation, the ultrasound probe would be aligned with the desired cross-section of the heart (see Figure 1 for an example examining the 4-chamber view of the heart). Ultrasound pulses would be transmitted into tissues beneath the transducer and the received echoes would be recorded and processed to extract high-resolution images and local flow stability information.

[0047] FIG. 2 summarizes the transmission scheme (2A) and processing pipeline (2B) involved with the recorded echoes. For acquisition, two batches are required. The first batch consists of multi-source transmissions which are used to generate high resolution images for real-time visualization of cardiac tissue. The second consists of pulses fired at the same angle, allowing forthe estimation of Doppler bandwidth. The processing pipeline contains two main branches; one for tissue processing and one for flow processing; which converge for visualization. All the acquired tissue frames and flow frames are beamformed then passed to their respective branch. For the tissue branch, the tissue frames are compounded to generate a high-resolution image to allow for a clear visualization of the heart.

[0048] For the flow branch, first the beamformed flow images are passed through a clutter filter to remove clutter (tissue signal) and extract flow information. Next, each pixel's slow-time signal is extracted and used to calculate a power spectrum. A cumulative integral for each power spectrum is taken and normalized to the maximum, smoothening the profile to mitigate the effects of noise and incoherent frequency summations (IFS). Using the normalized, cumulative integral, a maximum and minimum threshold is determined based on 68.2% of the cumulative power, and the cross-over frequencies at these thresholds are used to estimate the bandwidth of the signal by subtracting the maximum frequency from the minimum frequency (see Figure 3). These bandwidth estimation steps are repeated for each pixel, generating a Doppler bandwidth image. Finally, the bandwidth image is superimposed onto the tissue image.

[0049] The invention has been implemented on an ultrasound research scanner. A complete proof of concept trial has been completed on a phantom designed to mimic mitral valve regurgitation, and the framework has been tested in vivo to demonstrate feasibility.

[0050] To our knowledge, no investigation has been dedicated to estimating and mapping the Doppler bandwidth in the heart using diverging waves. There is one published paper which performs automatic Doppler bandwidth mapping for ultrafast transmissions.

[0051] The above framework is designed for arterial imaging and makes use of plane-wave imaging at pulse repetition frequencies of 10 kHz, both of which are not compatible due to limitations outlined above.

[0052] Due to the arterial imaging target, resolution issues do not need to be solved using image compounding as they are not targeting deep tissues and they are using a wider aperture linear probe, giving them lower f-numbers and thus better resolution. This allows them to use long ensemble lengths (~50) for their spectrum estimation approach and use a sliding-ensemble to further improve temporal resolutions. Again, these are not feasible for cardiac imaging as outlined above.

[0053] Their full width at half maximum approach to bandwidth estimation is heavily susceptible to incoherent frequency summations, limiting the efficacy of their bandwidth results.

[0054] Our invention opens several market opportunities, particularly in the healthcare and medical technology sectors. Flow variability is a potential biomarker for cardiac regurgitation and stenosis phenomena.

[0055] One specific opportunity is the grading and monitoring of mitral valve regurgitation. Our preliminary phantom study indicates that the amount of flow instability present in the atrium increases as the amount of backward flow increases. The severity of mitral regurgitation is linked to the amount of backward flow into the atrium, and as such Doppler bandwidth estimates can be a biomarker for mitral regurgitation severity.

[0056] The market for non-invasive cardiac diagnostics is expanding due to the increasing prevalence of cardiac diseases, aging populations, and a growing emphasis on preventive healthcare. Advances in technology and the broader adoption of telemedicine and wearable health devices are also driving this expansion, making innovative solutions like ultrasound-based flow stability measurement techniques highly relevant and valuable in these diverse markets. Target markets are as follows:

[0057] Clinical Healthcare in Hospitals and Medical Centers: Targeting established healthcare facilities for routine cardiac assessments and diagnosis of cardiac diseases.

[0058] Primary Care such as General Practitioners' offices and senior care facilities: Integrating flow instability measurements into primary care settings for regular health check-ups, particularly for patients and retirement communities with risk factors like cardiac regurgitation and stenosis.

[0059] Research and Development: Supporting the development of interventions (e.g. pharmaceutical) and clinical trials by providing a non-invasive tool to assess the impact of medications on cardiac health.

[0060] Our invention overcomes critical defects of currently available technology. In comparison to magnetic resonance imaging, our invention will have significantly lower cost, and it does not require the use of multi-cardiac cycle information to synchronously reconstruct flow patterns, which tend to be unreliable in cases with unstable flow due to inter-cardiac-cycle variations.

[0061] In comparison to Doppler ultrasound, our invention provides image-based information instead of single-gate information at fine temporal resolution. The extra spatial dimension made available by our invention allows us to visualize how unstable flow may vary spatially due to its dissipative nature.

[0062] In comparison to intravascular catheter, our invention is non-invasive, so it is much more suitable for clinical use in humans and involves less training cost.

[0063] From the perspective of medical facilities, ultrasound scanners are ubiquitous in their daily operations. In fact, this technology's integration could potentially lead to cost savings by streamlining cardiovascular assessments and reducing the need for more time-consuming MRI based studies. When considering the potential economic benefits of early detection of cardiac issues using flow instability measurements, identifying and managing cardiac risks earlier can lead to cost savings in the long run by preventing more severe cardiac conditions.

[0064] Now referring to FIG. 4, shown is a Doppler spectrogram and illustrative examples of a stable flow and an unstable flow. Cardiac pathologies can be characterized by flow instabilities with the heart. One way to view this instability is to use a Doppler spectrogram. What is seen in the Doppler spectrogram is the power spectrum at a given point in time, at a specific location. From the power spectrum, the Doppler bandwidth can be extracted, which is related to the stability of flow at that region. When the flow is stable, the Doppler spectrogram is narrow.When the flow is unstable, the Doppler spectrogram is broader. However, the problem with this approach is that it is not possible to visualize regions of higher and lower flow stability.

[0065] A potential solution is to quantify bandwidth for all pixels in the field of view in order to visualize where there is higher or lower flow stability.

[0066] Therefore, the objective of the present system and method is to use high frame rate diverging waves and Doppler spectrum analysis to map Doppler bandwidth.

[0067] FIG. 5 illustrates a high-frame rate pipeline in accordance with an illustrative embodiment which can achieve this objective, and automatically calculate Doppler bandwidth for all pixels. Starting from left, as shown, there is a high-frame rate scanner with a phased array, an image formation and clutter filtering step, and a power spectral density (PSD) estimation step.

[0068] Instead of a conventional approach which requires a large ensemble size (~100) for sufficient PSD, what is proposed is to use a minimum variance PSD to obtain sufficient PSD fromshorter ensemble sizes (~16). This has the advantage of a much higher frame rate to ~150 fps, which is significantly higher than the conventional approach at ~40 fps.

[0069] A bandwidth estimation step then looks at the power spectrum, assuming that the power spectrum is a gaussian distribution, and then extracting the first standard deviation of this gaussian for the bandwidth BW.

[0070] FIG. 6 shows an image formatting and clutter filtering process in accordance with an illustrative embodiment. Shown from the left, an image stack is created to extract specific signals of interest from a particular location. Using the signal of interest, a covariance matrix is calculated, with D: # depth averaging and K: # slow-time averaging to make the covariance matrix more robust.

[0071] FIG. 7 shows a minimum variance (MV) power spectrum optimization and bandwidth estimation process in accordance with an illustrative embodiment. The covariance matrix of FIG. 6 is used to estimate the power spectrum using a minimum variance approach, which optimizes filter weights (w(f)) to minimize output power for specific frequences. As this is done for each of the frequencies of interest, a power spectrum can be estimated as shown here.

[0072] Next would be bandwidth estimation, but this can be difficult due to the noise and incoherence frequency summations (IFS) which are present in this spectrum. To compensate, a cumulative power integral can be used to smooth the profile, and use this profile to estimate a maximum and minimum threshold to extract an fmax and fmin which crosses over at that location. Then the bandwidth is estimated as BW = (fmax - fmin). A key point is that the Doppler bandwidth is calculated based on 1-standard deviation of the power spectrum.

[0073] Now referring to FIG. 8, shown is an acquisition scheme and bandwidth processing pipeline in accordance with an illustrative embodiment. In this example, and SA4-2 cardiac probe is used to generate divergent waves at a central frequency fO of 2.5 MHz and a pulse repetition frequency (PRF) of 4 kHz. In this examples, 16 frames are generated for the tissue batch, and 64 frames are generated for the flow batch.

[0074] The acquired data is passed to a delay and sum beamformer where the high resolution image can be extracted from the 16 tissue frames.

[0075] The flow frames data is passed to a projection initialized HR clutter filter to estimate the polynomial order. From this clutter filtered signal, a covariance matrix can be created which has a 16-frmae ensemble, and a 3x3 slow time x depth averaging.

[0076] A power spectrum estimation can be performed using a minimum variance power spectrum, where BW estimation is calculated, and flow detection can be performed using power thresholding, with a lower and upper threshold, so that we are looking at the fight flow regions.

[0077] Finally, visualization is performed by combining everything together, allowing visualization of the bandwidth maps.

[0078] Advantageously, the present pipeline and system and method allows visualization of BW and tissues at 200 fps and 50 fps, respectively.

[0079] FIG. 9 shows a physiological testing scenario featuring flow instability such as mitral regurgitation jets.

[0080] Scenario A illustrates an unconstrained jet flow, with an area of 0.23 cmA2 modeling a grade 1 mitral regurgitation case. A fluctuating Reynolds number changes the flow rate, and an increasing Reynolds number increases instability.

[0081] Scenario B illustrates a more complex testing scenario in which a ventricle and atrium are modeled, with an area of 0.23 cmA2. In this case, the inlet flow profile is fluctuated to adjust the amount of regurgitation volume in the atrium. The expectation is that higher Reynolds number flows should depict increased Doppler bandwidth.

[0082] FIG. 10 shows illustrative results for scenario A from FIG. 9. As the Reynolds number increases, the jet flows increase in width, and have higher flow instability near the orifice. A mean bandwidth (MBW) can be estimated by averaging the bandwidth inside the jet area after power thresholding. A key point is that Doppler bandwidth increases as Reynolds number increases, indicating changes in flow stability.

[0083] FIG. 11 shows illustrative results for scenario B from FIG. 9. In this illustrative example, EMFI allows a high-frame-rate visualization of a one second pulse at different flow regions. The mean Doppler bandwidth with respect to time graphed on the right shows that the Doppler bandwidth is much higher for the 30mL case in comparison to the 20mL and 14mL cases. A Minimum detectable BW can also be measured. A key point is that increasing backward flow into the atrium leads to increasing Doppler bandwidths.

[0084] FIG. 12 shows an in-vivo demonstration of Doppler bandwidth visualization during left ventricular dynamics of a heathy 29 year-old male. This test confirms the feasibility of utilizing the bandwidth BW mapping pipeline in-vivo.

[0085] As the Doppler bandwidth is imaged with respect to time, very predictable regions of higher flow instability can be seen. Regions of lower instability and higher instability can bedistinguished using different colors, and the boundaries between these regions of two directional flows can be shown in yet another color, as a region of high shear and high flow instability at the boundary.

[0086] A key point is that the present framework is compatible for in-vivo visualization of Doppler bandwidth during a cardiac cycle at high frame rates.

[0087] FIG. 13 shows an example of bandwidth decomposition and an illustrative clinical application potential. Given a minimum measurable bandwidth, there is an intrinsic bandwidth of the system. If this intrinsic bandwidth is removed, the Doppler bandwidth consistency may be improved.

[0088] Furthermore, given that increasing volumes of MV regurgitation result in higher Doppler bandwidths, Doppler bandwidth may be used to grade the severity of MR of different patients.

[0089] In summary, FIG. 14 shows that EMFI is able to quantify changes in flow stability in-vitro. EMFI was able to quantify changes in flow stability in-vitro as predicted by Reynolds number changes, and was compatible with in-vivo at high frame rates. Using the spectrum and bandwidth estimation processes of the present system and method, experimentation on a phantom confirmed that increasing backward flow volume results in higher Doppler bandwidths. Furthermore, experimentation demonstrated that the present system and method is feasible for use on a patient in-vivo, to provide a clear visualization of flow instability.

[0090] A suitably configured computer device, and associated communications networks, devices, software, and firmware may provide a platform for enabling one or more embodiments as described above. By way of example, FIG. 15 shows a generic computer device 1500 that may include a central processing unit ("CPU") 1502 connected to a storage unit 1504 and to a random-access memory 1506. The CPU 1502 may process an operating system 1501, application program 1503, and data 1523. The operating system 1501, application program 1503, and data 1523 may be stored in storage unit 1504 and loaded into memory 1506, as may be required. Computer device 1500 may further include a graphics processing unit (GPU) 1522 which is operatively connected to CPU 1502 and to memory 1506 to offload intensive image processing calculations from CPU 1502 and run these calculations in parallel with CPU 1502. An operator 1510 may interact with the computer device 1500 using a video display 1508 connected by a video interface 1505, and various input / output devices such as a keyboard 1510, pointer 1512, and storage 1514 connected by an I / O interface 1509. In known manner, the pointer 1512 may be configured to control movement of a cursor or pointer icon in the video display 1508, and tooperate various graphical user interface (GUI) controls appearing in the video display 1508. The computer device 1500 may form part of a network via a network interface 1511, allowing the computer device 1500 to communicate with other suitably configured data processing systems or circuits. A non-transitory medium 1516 may be used to store executable code embodying one or more embodiments of the present method on the generic computing device 1500.Additional Embodiments

[0091] In another embodiment, in order to address the limitations of the prior art outlined in the background section above, batch processing can provide a solution, where alternating transmission batches can be used to form high quality tissue images and obtain flow information. To maintain temporal resolution for both the flow estimation and tissue visualization, the ensemble length available for Doppler processing, becomes a constraint. This constraint of shorter ensembles affects current Doppler processing techniques such as lag-one autocorrelation

[0011] , since lag-one autocorrelation has worse statistical accuracy with shorter ensembles

[0012] , leading to less accurate bandwidth estimations. Autoregressive techniques for Doppler bandwidth (DBW) estimation, as proposed by Yiu et al. [8], can be effectively used with shorter ensembles

[0013] , However, these autoregressive models benefit from data-dependent parameter tuning

[0013] , which requires longer ensembles and become unreliable when short data frames (<64 samples) are used

[0014] ,

[0092] Here, we propose EMFI, Echocardiographic Mapping of Flow Instability, a batched acquisition and processing scheme that can acquire coherently compounded cardiac tissue images at 50 fps and high frame rate DBW images at 250 fps for a 4kHz pulse repetition frequency (PRF) acquisition. Our pipeline leverages the blood power Capon

[0015] , a spectrum estimation technique capable of estimating accurate Doppler spectra with short ensembles (<16)

[0016] , To compensate for partial aliasing spectra, we propose a spectral correction technique using bandwidth estimates. To demonstrate feasibility, we tested our pipeline in three different experiments. The first experiment is a phantom experiment with constant flow, where we demonstrate how the bandwidth mapping approach can detect regions of increased flow gradients. For the second experiment, we demonstrate feasibility of the batched acquisition format and investigate a pulsatile flow condition within a mitral regurgitation phantom, analysing changes in DBW for different regurgitant flow volumes. Finally, we demonstrate our framework's in vivo capabilities on a healthy volunteer.Theoretical Framework

[0093] Our proposed framework aims to address the fundamental strategies associated with acquiring high-quality cardiac tissue and flow images using a batched acquisition scheme and optimized processing techniques. This section provides the theoretical foundation for the key concepts we leveraged: batched transmissions, coherent compounding, short ensemble clutter filtering, and data dependent DBW estimation.Batched Acquisitions and Ensemble Constraints

[0094] To enable both high quality tissue and Doppler processing, a batched transmission sequence is used. Batched transmissions allow for different pulse lengths and virtual source locations for different batches but introduce limitations on the ensemble lengths available for Doppler processing and coherent compounding. The total length of a batch Nbatch is defined based on the ensemble lengths desired for flow processing Nflow and tissue image formation Ntlssue

[0095] To maintain frame rates for tissue (Ftlssue) and flow (Fflow), processing steps need to meet the following temporal constraints:

[0096] From these equations, it is evident that higher frame rates can be achieved by lowering the ensemble length required for tissue and flow frame formations.Coherent Compounding and Clutter Filtering

[0097] Coherent compounding is a technique which exploits the phase coherence across multiple virtual source transmissions to enhance image quality

[0017] , For Ntlssue different virtual source locations, the coherently compounded image is defined as I(x,z) is:

[0098] here, In(x,z) is the delay and sum beamformed image before envelope detection. While additional virtual sources can enhance the signal to noise ratio (SNR), SNR improvement increases with the square root of Ntissue

[0017] , leading to diminishing returns.

[0099] For Doppler processing, tissue clutter must be separated from blood flow signals

[0018] , High-pass filtering can isolate flow signals, as blood flow contains higher frequency content compared to tissue motion

[0018] , Infinite impulse response (HR) filters are well-suited for short ensemble processing, as projection initialization effectively mitigates startup transient effects

[0019] allowing all filtered samples ready for processing. While HR filters introduce a non-linear phase response

[0020] , this is not a concern for our Doppler spectrum estimation since we only utilize the power spectrum magnitude from the Capon estimator, not the spectral phase information.DBW Estimation

[0100] Our DBW (DBW) estimation process consists of three components: (1) Spectrum Estimation, (2) Bandwidth Estimation, and (3) Aliasing Compensation. First, the Doppler spectrum was estimated using the Capon spectral estimator 3

[0101]

[0015] ; a more detailed explanation of the steps can be found in

[0021] , For a brief overview, the procedure starts with a vector of N beamformed and clutter-filtered slow-time samples:where (-)T’ is the transpose of (•). The covariance of the slow-time signal is then calculated using:

[0102] where (-)H is the complex conjugate of (•). Here, K and L, respectively, represent the number of slow-time and depth samples used for averaging, respectively. The Capon spectralestimate for a specific, normalized frequency component, ip, can be calculated using the following

[0021] :6

[0103] where e(ip) represents the Fourier vector defined by:

[0104] and c represents a scaling factor, typically determined by the matched filter's bandwidth. Since only the shape of the spectrum is of interest for bandwidth estimation, c is set to 1. Equation (6) relies on the covariance matrix being non-singular. To ensure the matrix is non-singular, the covariance matrix was diagonally loaded using the trace of the covariance matrix

[0022] :

[0105] Adding the trace to the covariance matrix ensures singularity but effectively adds broadband noise to the power spectrum. By assuming that the bandwidth of the Doppler signal does not span the entire Doppler spectrum, this added noise can be removed by subtracting the minimum power of the resulting spectrum:DBW Estimation

[0106] DBW (DBW) was estimated by analyzing the cumulative Doppler power spectrum. The DBW is estimated as being the Doppler frequency range which contains 68.2% of the total power, defined using an upper / lower threshold. This threshold range is associated as the standard deviation of a Gaussian distribution (Montgomery et al 2018). The cumulative spectrum C(k) is calculated using:P(l / >) 90.5 T

[0107] The upper and lower thresholds, ipupper and iplower respectively, are then calculated such that:0. 682 10

[0108] In Equation (6), C(0.5) represents the maximum of the cumulative density function. The DBW is then defined as being the difference between the upper and lower thresholds, multiplied by the pulse repetition frequency to convert back to the denormalized frequency domain:DBW = PRF * (llfupper~ Slower) 11Aliasing Adjustments

[0109] The above formulation assumes that there is no aliasing in the Doppler signal, but is sufficient in the presence of aliasing when the spectrum does not partially wrap around from positive to negative frequencies. In scenarios where the Doppler signal spectrum is partially aliased, the above formulation will overestimate DBW. To compensate for these scenarios, the maximum of the power spectrum in Equation (8) is estimated, and the power spectrum is shifted so the maximum is in the center of the spectrum. After shifting, the cumulative spectrum is calculated, and the DBW is calculated using the new upper and lower threshold locations.Experimental Implementation

[0110] To demonstrate feasibility of our batched processing pipeline, two flow phantom experiments and an in vivo demonstration were performed. The first phantom experiment was performed to test that our bandwidth estimation framework could detect changes in flow variance based on expected changes in flow velocity gradients. For this experiment, a simple, flow-only acquisition sequence was used. The second phantom experiment used a physiologically relevant flow scenario involving a wall-less left heart phantom. For this cardiacphantom experiment, our entire batched acquisition sequence was tested to see if changes in regurgitant flow volume could be detected. Finally, our framework was tested in-vivo on a healthy volunteer, visualizing the left ventricular flow profile.Implementation of EMFI on Research Scanner

[0111] Radiofrequency (RF) data acquisition was performed using an SA4-2 phased array (SA4- 2; Sonosray; Shenzhen, China) connected to a programmable research scanner (US4R; US4US; Warsaw, Poland). Before applying our DBW estimation framework, the RF data was beamformed using a DAS beamformer

[0023] , Due to the nature of the different phantom experiments, the two different transmission techniques used in our experiments can be found outlined in detail below.

[0112] HR clutter-filtering was performed with different cut-off frequencies based on the different experiments. For the constant flow scenario, where no tissue motion was present, a normalized cut-off frequency of 0.05 used to primarily filter stationary reflections inside the imaging reservoir. For the pulsatile phantom experiment, a slightly higher cut-off frequency of 0.1 was used, as slight wall motion was present. Finally, in vivo, a cut-off frequency of 0.25 was used due the excessive tissue motion. Post clutter-filtering, the resulting signal was passed through the DBW algorithm introduced above, where the input sample yk was the clutter- filtered signal. The correlation matrix in equation (5) was formed using a slow-time and depth averaging of 3 (K=L=3). The power spectrum in equation (8) is calculated with a series of Fourier vectors with p ranging from -0.5 to 0.5, with a spectral resolution of 0.002. Flow detection was performed using a combination of Doppler power and B-mode thresholding. For Doppler power thresholding, a low power threshold was chosen empirically used to remove locations of no flow. To ensure consistency, Doppler power was maintained constant when comparisons were being performed. When clutter-filtering and Doppler power were not sufficient, an empirical B- mode threshold was chosen to assist in tissue motion removal.Unimpeded, Constant Jet Flow Scenario

[0113] The goal of our first phantom experiment was to investigate our DBW estimation performance in a simplified regurgitant jet flow scenarios. The expectation with this experiment was that higher regurgitant jet flow speeds would lead to increased DBW near the orifice due to increased flow gradients between the jet and surrounding fluid. Mitral regurgitation jets are apotential clinical application for flow variance estimation

[0024] , so the flow phantom's orifice was designed to have an effective regurgitant orifice area (EROA) of 0.15 cm2, a value associated to grade 1 mitral regurgitation

[0025] ,Orifice Jet Phantom Fabrication

[0114] The orifice phantom was fabricated using lost core moulding procedures. First, a casting box was designed using CAD software (SolidWorks; Dassault Systems, Waltham, MA, USA) to be a negative mold for the final phantom. The casting box was designed to be a 75 mm x 85 mm rectangular box, with a central, cylindrical pillar which starts with a 4.4 mm diameter and transitions to a 6 mm diameter. The 4.4 mm corresponds to the orifice diameter, with the 6 mm being chosen to fit the 6-mm hose barb connector used to attach the phantom to the flow circuit. The CAD model for the negative mold can be seen in figure 16. The 4.4 mm orifice was located at the base of the casing box to ensure that the orifice would maintain a smooth surface after thermocycling. The 3D negative mold was exported in stererolithography (STL) format, and sliced using CHITUBOX (CHITUBOX; CBD-Tech, Shenzhen, China) for resin printing using the Saturn 3 Ultra (Saturn 3 Ultra; Elegoo, Shenzhen, China). Standard, clear resin (Anycubic, Hong Kong, China) was used for printing. The resin print was post-processed using isopropyl alcohol to remove residual resin and additional ultraviolet exposure was used to ensure the resin was fully cured. A 10% polyvinyl alcohol (PVA) solution was prepared

[0026] and cast into the negative mold. The solution was then thermocycled with three 24-h freeze-thaw cycles to solidify the hydrogel. Once solid, the PVA block was removed from the mold. Figure 17(a-d) summarizes the orifice phantom fabrication process.

[0115] To finalize the flow phantom, a reservoir was 3D printed using polylactic acid (PLA) filament to contain the employed blood mimicking fluid (BMF)

[0025] , The purpose of this reservoir is to hold the orifice phantom in place and connect the phantom to a programmable gear pump

[0026] to generate flow. A wall-mounted 6-mm nylon hose-barb connector was placed at the base of the reservoir, and a custom acoustic absorption pad was placed to mitigate reverberations caused by the reservoir base. A small boundary was extruded from the base of the reservoir to assist in holding the orifice phantom in position. Since the flow connection was made at the base of the reservoir, an additional platform was printed to raise the reservoir off the table. To ensure that the reservoir was watertight, a thin layer of epoxy resin (part # of epoxy resin) was used to coat the interior of the reservoir. Figure 17 (e) shows the reservoirafter fabrication, and figure 17 (f) shows the orifice phantom mounted inside the reservoir. With the orifice phantom fixed in place, the reservoir was connected to the programmable flow pump, where an inlet to the pump was hung inside the reservoir, and the outlet was connected to the opposite side of the hose-barb at the base of the reservoir. The reservoir was then filled with BMF, finalizing the flow phantom setup.Orifice Flow Phantom Experimental Procedure

[0116] Three constant flow scenarios were investigated to demonstrate the capability of our bandwidth mapping framework to correctly identify changes in spatial flow variance. The different flow rates were investigated: 3.5 mL / s, 6 mL / s, and 10 mL / s. As the flow rate increased, the spatial flow variance near the orifice of the jet was expected to increase due to the higher velocity gradient between the main jet and the stationary surrounding fluid (BMF). This increasing flow variance should result in an increased DBW near the jet orifice

[0027] ,

[0028] ,

[0117] To acquire DBW data, the phased array was aligned to the central axis of the jet under real-time color flow guidance. The phased array was placed approximately 10 cm away from the jet. Once aligned, data was acquired for the three different flow rates without moving the transducer. For this experiment, the scanner was programmed to transmit diverging waves (77.3° opening angle, 2.5 MHz, 3-cycle, 4 kHz PRF) with a constant virtual source position. One second of data was acquired and saved for offline processing. Comparisons of DBW near the orifice were performed using a 5 mm x 10 mm region of interest (ROI) mask centered on the orifice. The mean DBW and standard deviation within the ROI were calculated. Spearman's rank correlation coefficient

[0029] was used to determine whether the DBW increase with flow rate was statistically significant.Wall-less Left Heart Phantom Experiments

[0118] While the constant flow experiment provided a fundamental comparison of flow gradients with our algorithm, real cardiac flow is characterized by pulsatile flow patterns and complex geometries

[0030] , Additionally, in cases such as mitral regurgitation, the regurgitant jet dynamics depend on the shape of the atrium

[0031] , To better evaluate the performance of our algorithm in more realistic conditions, a wall-less cardiac phantom incorporating both left ventricular and atrial geometries was employed.Wall-less Cardiac Phantom Fabrication

[0119] The wall-less cardiac phantom consisted of three main components: (1) left ventricle, (2) circular orifice, (3) left atrium. The phantom was designed specifically to mimic mitral regurgitation events. The ventricle and atrium phantom components were fabricated separately using lost-core fabrication procedures, using the same 10% PVA formulation mentioned above.

[0120] First, the cores for the desired ventricular and atrial geometries were 3D printed using PLA filament. The generic ventricle shape was provided by Edwards Lifesciences, which was an engineered model of an enlarged ventricle with smooth walls. To mimic regurgitation, a positive pressure gradient between the ventricle and atrium was required

[0032] , For our flow experiment, this pressure gradient was generated using a cardiac flow pump (55-3305; Harvard Apparatus, Holliston, MA, USA) to increase the pressure in the ventricle directly. For this, an inlet to the ventricle is required. For simplicity, this inlet was added to the base of the ventricle core. Two outlets were added to the core, the first being in the aortic valve location, the second being a circular orifice in the center of the mitral valve location. The outlet by the aortic valve was made by extruding a 6mm diameter cylinder in the center of the aortic valve position. For the mitral orifice, an EROA of 0.25 cm2 was used, mimicking a moderate severity of mitral regurgitation

[0025] , The mitral orifice was designed to have an approximate thickness of 3mm by extruding the cylinder 3mm. This configuration mimics the ventricular outflow of blood during regurgitation, where part of the blood goes to the aorta and part goes back into the atrium. The ventricular core of the phantom can be seen in figure 18a). The atrium was designed based off previous research, where the atrium was approximated using an ellipsoid model

[0033] , Our phantom was designed with a PLAX of 2.75cm, SI of 4.75 cm, and LAT of 3.99cm to align with the ventricular core model and falling within clinically relevant dimensions

[0033] , The atrium core can be seen in figure 18e).

[0121] To cast the atrium and ventricle phantoms, two casting boxes were fabricated, one for the ventricle and one for the atrium. Since the atrium and ventricle are cast as separate phantoms, these casting boxes included holes to accommodate 6-mm alignment rods. After 3D printing the cores and the casting boxes, the ventricular and atrial cores were mounted inside their respective casting boxes using the appropriate hardware, as shown in figure 18b and 18f respectively. An additional alignment rod fixture was 3D printed to ensure the rods would stay upright during casting. The same PVA hydrogel, as outlined above, was used for casting. Three freeze-thaw cycles were used to solidify the hydrogels. The congealed phantoms can be seen in figure 18c and 18g for the ventricle and atrium respectively. After thermocycling, the core of thewall-less ventricle was dissolved using Dichloromethane (DCM), the resulting wall-less ventricle phantom can be seen in figure 18d). The core from wall-less atrium could be removed from the casting box without dissolving. A visual summary of the phantom fabrication process can be found in figure 18a-f).Establishing Fluid Flow Within Wall-Less Flow Phantom

[0122] The flow phantom was finalized by 3D printing a flow reservoir, similar to the reservoir mentioned above. The inlet to this reservoir was placed on the side of the reservoir, with a nylon hose-barb connector used to connect the wall-less ventricle to the reservoir. The wall-less atrium was then placed on top of the ventricle, and the same 6-mm metal rods used during the fabrication process were used to ensure correct alignment between the atrium and the ventricle. Once the phantom components were aligned inside the reservoir, the reservoir was attached to a cardiac flow pump using 3 / 8" ID PVC tubing. The outlet of the flow pump was attached to the opposite side of the hose-barb connector, and the inlet was hung inside the reservoir. BMF was used to fill the reservoir, completing the flow phantom circuit. An example reservoir with acrylic walls can be seen in figure 18h, along with the mounted wall-less ventricle and atrium stacked.

[0123] For experimentation, three different volumetric displacements were investigated using the cardiac flow pump: 14 mL, 20 mL, and 30 mL. The expectation was that as the volumetric flow into the base of the ventricle increased, the amount of backflow into the atrium would increase as well. With increasing backflow, more flow variability is expected, leading to increased DBW. The cardiac flow pump was set to a repetition rate of 60 beats per minute, and a flow ratio of 75 / 25 diastolic / systolic.Batched Acquisition and Processing Parameters for Cardiac Phantom

[0124] For this experiment, we implemented the batched acquisition pipeline with 16- ensemble coherent compounding and 16-ensemble DBW processing. The same research scanner configuration as described above was used. To increase Doppler temporal resolution, we used two different batch sizes: 16 pulses for tissue imaging and 64 pulses for Doppler imaging. This configuration gave us a total of 5 Doppler images (4 true estimates and 1 interpolated) and 1 tissue image every 80 frames. With a 4 kHz PRF, this yielded frame rates of 50 Hz for tissue images and 250 Hz for Doppler images.

[0125] Both imaging batches used diverging waves at 2.5 MHz central frequency and 4 kHz PRF, with virtual sources positioned 5mm axially behind the transducer surface. For tissue images, the 16 virtual sources were equally spaced laterally from -8mm to 8mm. For flow images, all 64 waves originated from a central virtual source. Diverging waves had a 1-cylce and 3-cycle pulse length for tissue and flow frames respectively. Two seconds of data were acquired for each volume displacement tested. The SA4-2 was placed in a transesophageal echocardiography (TEE) orientation typically used for mitral valve regurgitation scans

[0034] , with the transducer aligned approximately 6 cm from the mitral orifice.

[0126] To compare the resulting bandwidth maps quantitatively, the mean DBW and variance within the jet were measured at three phase-matched time-points of jet development. These time-points were determined by analyzing the temporal evolution of jet area throughout the cardiac cycle: (1) peak jet area (maximum jet development), (2) 50% amplitude on upstroke (50% between baseline and peak during jet acceleration), and (3) 50% amplitude on downstroke (50% of the amplitude between baseline and peak during jet deceleration. The phase matching approach was chosen to ensure jets were compared at equivalent development stages, rather than fixed temporal intervals, accounting for differences in jet duration between regurgitation severities. The mean DBW indicates global trends in spatial flow variances during the jet cycle, and the standard deviation indicates the degree of organization of the jet structure.Additionally, the difference in mean DBW was compared between the two cycles for each of the time-points to compare cycle-to-cycle consistency.

[0127] Jet area was quantified by applying power Doppler thresholding to identify jet pixels, which were then counted and converted to area using the pixel dimensions (0.1mm x 0.1mm). For each regurgitant volume, peaks were determined using MATLAB's findpeaks function, and 50% crossover points were calculated relative to each cycle's baseline. Comparisons were performed over both cardiac cycles, with time-points averaged between cycles to improve measurement stability.In-vivo Demonstration of Cardiac DBW Mapping

[0128] In vivo feasibility was tested on a healthy volunteer (29M), using the same acquisition parameters described above. The volunteer was asked to lie in the left lateral decubitus position, the clinical standard orientation for obtaining the 2-chamber left heart view

[0035] , and a two-chamber left heart view was captured using real-time guidance with the high-quality tissueimages. Three seconds of data were acquired and saved for offline processing. To obtain a complete picture of the flow phenomena within the ventricle, lag-one autocorrelation

[0011] (post clutter-filtering, ensemble of 64), was used to estimate the mean flow speeds along with the DBW mapping technique (ensemble of 16).Cineloop Rendering Strategies

[0129] Cineloops were rendered differently for the constant flow and pulsatile flow scenarios due to the different acquisition schemes used. For the constant flow phantom experiment described above, a continuous stream of DBW frames was available for visualization. Power Doppler thresholding was used to identify the extents of the different flow jets. Regurgitant jets were superimposed onto a background brightness mode image. To remove outliers, a [3,3,5] sliding median filter was used, and a persistence of 0.2 was used to smoothen the flow visualization

[0036] ,

[0130] For the pulsatile phantom flow scenarios described above, MATLAB's interp function was used to interpolate the DBW maps for time-points where the tissue images were being acquired. Low power Doppler thresholds were used to ignore regions of low flow, and high B- mode amplitude thresholding was used to remove residual tissue clutter. The same persistence and median filtering were used as in the constant flow scenarios to help mitigate SNR related artifacts. Background tissue images were updated after every tissue image acquisition.ResultsDetection of Increased DBW with Increasing Velocity Gradients

[0131] Our DBW estimation approach successfully captured changes in spatial flow gradients. Movie SI shows three DBW mapping cineloops of the unenclosed, circular orifice jet phantom for the three constant flow rates tested: 3 mL / s (Left), 6.5 mL / s (Middle), 10 mL / s (Right). DBW frames were acquired at an effective frame rate of 250 fps and are played back in slow motion at 25 fps.

[0132] For further analysis, a single frame from which flow rate was extracted and is presented in figure 19. The ROI box used to estimate the mean DBW near the orifice are shown for the three flow frames. Over the three second acquisition, the mean BW within the ROI for the 3.0,6.5, and 10.0 mL / s flow rates were 563.3 ± 35.9 Hz, 1379.0 ± 33.4 Hz, and 2232.3 ± 60.2 Hz,respectively. Figure 19d depicts a box and whisker plot demonstrating the statistical difference (p<0.05) of DWB near the orifice with increasing flow rates.Successful Unwrapping of Partially Aliased Flow Regions

[0133] Figure 19 a-b) shows temporally averaged DBW maps for the 10 mL / s flow scenario, with and without the partial aliasing unwrap procedure explained above, respectively. A log- scaled power spectrum from a point of interest, depicted with a white star in Figure 20 (a-b), with and without spectrum centering can be seen in Figure 20 (c) and (e), where (e) shows the spectrum wrapping around from the Nyquist frequency. Figure 20 (d) and (f) demonstrate the resulting cumulative spectra with and without the unwrap correction, respectively, along with the DBW estimated as 1560 Hz after correction and 2940 Hz before correction. These results demonstrate the importance of the spectrum centering approach, as these partially aliased locations can result in overestimated DBWs with almost twice the magnitude of the expected result.DBW Increases with Increasing Backward Flow

[0134] Movie S2 depicts the DBW cineloops obtained from the wall-less cardiac phantom investigation. In the movie, the left, middle, and right columns show the 14, 20, and 30mL pulse volumes, respectively. From the movie, a qualitative increase in DBW can be seen as the pulse volume increases.

[0135] For a more quantitative comparison, three time-points of interest from each regurgitant volume were extracted and can be seen in Figure 21. A complete summary of the mean DBW, standard deviation, and cycle-to-cycle difference for the different pulse volumes tested can be seen tabulated in Table 1. Figure 21 a-c) show the 14 ml volumetric displacement volume experiment at 50% upstroke, peak, and 50% downstroke, respectively. Figure 21 d-f) and g-i) show the same three time-points but for the 20 mL displacement volume and 30 mL displacement volume, respectively. Two preliminary trends can be seen from the data: (1) DBW is highest during the jet acceleration phase, and (2) DBW in the jet acceleration phase increases with regurgitant volume, ranging from 983.3 Hz for the 14 mL test case, 1183.3 Hz for the 20 mL case, and 1352.1 Hz for the 30 mL case.Flow Instabilities Tracked In-vivo at High Frame Rates

[0136] A three second cardiac acquisition from a healthy volunteer (M29) can be seen in Movie S3, depicting the DBW mapping visualization (left) and the associated Color Doppler (right). Both flow mapping visualizations are overlaid onto a background B-mode of the left heart (40 dB dynamic range) as acquired using the batched acquisition sequence. For better analysis of the flow maps, a frame from the ventricular filling and ejection phases is presented in Figure 22.TABLE IMITTAL REGURGITANT FLOW PHANTOM SUMMARYPulse Jet Phase C ycle Mean BW Std. Deviation Global Mean C ycle to C ycle MeanVolume (Hz) (Hz) BW (Hz) Difference (°o)

[0137] Figure 22a-b) shows the ventricular filling stage, where (a) presents the DBW map obtained using our pipeline and (b) shows the corresponding color flow map processed using 64- ensemble lag-one autocorrelation. The crossflow region, a high shear location between the mitral inflow and recirculation within the ventricle, is highlighted by the yellow arrows. The crossflow region has a higher DBW of 1674.4 Hz compared to the inward jet which has an average of 511.9 Hz. This result is expected, as the high shear between the two flow directions results in increase flow variance

[0037] which should, in turn, result in a broader DBW. Figure 22c- d) shows the ventricular voiding stage, with c) and d) representing the DBW and color flow maps, respectively. In this frame, some artifacts can be seen from inadequate clutter suppression. After removing these artifacts by zeroing out DBWs above 2000 Hz, an average bandwidth of 476.7 Hz ± 387.6 Hz was measured, indicating the flow during ventricular voiding is uniform.DiscussionSummary of Contributions

[0138] Capturing cardiac flow variations with high temporal resolution while maintaining tissue image quality is necessary for accurately evaluating cardiac flow function. To address this requirement, we have presented a high frame rate, diverging wave ultrasound data acquisition and processing pipeline that could visualize DBW and tissue structures at 250 Hz and 50 Hz, respectively, for a 4 kHz PRF acquisition (Figure 22). Our pipeline leverages a DBW mapping framework which combined Capon spectral estimation with cumulative spectrum estimation to estimate DBW maps using short ensembles of length 16 (Figures 19, 21, and 22).

[0139] As demonstrated using various flow phantoms (Figures 16, 17, and 18) our framework could successfully detected changes in spatial flow variances in constant flow scenarios (Figure 4) while compensating for partial aliasing scenarios (Figure 20). Furthermore, our framework could capture changes in pulsatile flow conditions (Figure 21), where increasing regurgitant volumes led to increasing DBW estimates. Additionally, our framework was capable of visualizing cardiac flow profiles in vivo (Figure 22), where DBW could detect regions of increased spatial variations in high shear regions during ventricular filling.

[0140] Our cardiac bandwidth mapping pipeline offers distinct advantages over conventional bandwidth mapping approaches such as lag-one autocorrelation

[0011] and DUBI [8], Unlike lag- one, which suffers from poor statistical accuracy with short ensembles

[0012] , our Capon-based estimator maintained expected Doppler spectrum estimates with 16 frame ensemble processing

[0016] , enabling higher temporal resolutions without requiring overlapping processing windows. This short ensemble processing is crucial for cardiac applications where higher temporal resolution is required to capture short-lived cardiac events

[0038] , An advantage our framework has over DUBI's autoregressive spectrum estimation is that the Capon method adapts itself to the signal characteristics through its covariance-based formulation

[0039] , whereas an autoregressive modeling approach with parameter tuning would become unreliable with such short ensembles

[0014] , These advantages allow for increased DBW frequency and temporal resolution which are important for detecting subtle flow disturbances as present in cardiac applications.Potential for DBW as a Regurgitation Biomarker

[0141] An interesting observation shown in the regurgitant flow phantom experiments is the preliminary trend of increasing DBW with increasing regurgitant volume. This trend is in-line with magnetic resonance imaging studies, which have also investigated clinical trends in spatial flow variance for regurgitant events

[0024] , From our experiments, the jet acceleration phase has the most prominent DBW increase, with higher bandwidths being detected for higher regurgitant volume cases. This is a theoretically expected result, as DBW is expected to broaden with increasing levels of acceleration

[0040] ,

[0142] Interestingly, while DBW increased with regurgitant volume across the three time-points examined, the magnitude of this increase varied based on the time-point investigated. The most pronounced difference occurred during the jet acceleration phase (50% upstroke), showing a 37.5% increased from the 14 mLtest case to the 30 mL case. At the peak jet area, the trend persists but was less pronounced, showing only a 22.9% increase, likely because DBW was averaged over the entire jet area. Since larger jets include more peripheral regions with lower flow gradients, the higher DBW near the orifice affected to overall mean DBW measurement less. Other orifice sizes, geometries, and jet propagation directions may lead to different DBW trends. Nonetheless, our results indicate clinical potential in mapping DBW during echocardiographic examinations, encouraging further investigation.

[0143] From a clinical perspective, current echocardiographic assessment of mitral regurgitation relies on multiple parameters, such as vena contracta width, effective regurgitant orifice area, and regurgitant volume

[0041] , Although preliminary, our data shows DBW values increasing from 983.3 to 1352.1 Hz for increasing amounts of backflow volumes, indicating a potential trend for gauging mitral regurgitation severity based on DBW. Clinical thresholds, however, will require larger scale studies to compare and analyze these trends more robustly. One additional consideration here is that these trends may differ when regurgitant orifice geometries change. For example, if the regurgitant orifice is > 0.4 cm2, as in severe mitral regurgitation

[0042] , the regurgitant volume is expected to increase, but the spatial flow variance near the orifice may be lower as there could be a lower flow velocity. A combination of mean flow and Doppler variance could be beneficial here, as combining these two quantities could enhance clinical observations through turbulence intensity quantifications like those investigated using Magnetic Resonance Imaging (MRI)

[0024] ,Future Work

[0144] While our framework can visualize DBW profiles with high temporal resolution, the bandwidth estimation algorithm needs to be accelerated to allow for real-time processing. Since the Capon method is pixel independent, our DBW estimation can be parallelized; real-time viability of our algorithm has yet to be demonstrated. To assist in achieving real-time processing speeds, a potential parameter that could be adjusted is the normalized spectrum resolution. For our experiments, we processed results using a normalized spectral resolution of 0.002, but increasing this parameter would allow for faster processing speed at the cost of some bandwidth resolution.

[0145] Another avenue for investigation would be testing different spectrum estimation algorithms. While our Capon-based estimator can estimate Doppler spectra accurately with ensembles of length 16, other spectrum estimators, such as the blood amplitude and phase spectrum estimation (BAPES) and modified amplitude spectrum capon (MASC), have shown superior performance for estimating Doppler spectra with even shorter ensembles

[0043]

[0016] , Although BAPES and MASC have enhanced performance, they come at the cost of increased computational overhead as they require additional computations from estimating the noise / interference covariance matrix

[0016] and eigenspace decompositions, respectively

[0043] , These additional computations could make real-time implementations difficult, as additional computational resources would be required to achieve real time visualizations. Nonetheless, it would be interesting to compare the performance of these different spectrum estimation approaches in the context of DBW estimation and quantify if the enhancements would justify this increased computational overhead.

[0146] From a validation standpoint, it would be useful to experimentally validate the performance of this framework. While in vivo validation could potentially be performed using MRI; an in vitro validation could more readily be performed to determine the accuracy and limitations of the flow variance estimation. Recent work towards simultaneous dual-modality validation using optical PIV shows promise

[0044] , as optical PIV can achieve much higher spatial resolutions compared to ultrasound

[0044] , By measuring flow profiles at higher spatial resolutions as those achievable with ultrasound, the underlying flow profiles within the ultrasound resolution cell can be quantified, allowing for better relationships between spatial flow variance, turbulence, and DBW to be established. With this additional information, turbulence intensity could be directly compared to bandwidth measurements to quantify the relationships more distinctly.

[0147] Finally, while the in vivo test case demonstrates that the processing pipeline can depict regions of increased flow variance, adaptive clutter-filtering techniques could be introduced to allow for better tissue motion and blood flow separation. A potential candidate for this would be an adaptive polynomial clutter-filter which is capable of adaptively filtering with a 16-frame ensemble

[0045] , As for tissue-images, motion compensation [2], and dehazing

[0046] would allow for even further enhanced B-mode quality. These additional processing steps may require additional tissue image acquisitions which would lower the temporal resolution of the flow imaging.Conclusion

[0148] As high-frame rate echocardiographic imaging continues to advance, a fundamental challenge remains between balancing the conflicting requirements of high-quality tissue visualizations and high temporal resolution flow processing. Our batched acquisition and DBW mapping framework presented in this paper addresses this challenge by simultaneously acquiring coherently compounded tissue and DBW frames at 50 and 250 Hz respectively for a 4 kHz PRF. Such an acquisition and processing framework represents a significant step towards more sensitive detection of valvular dysfunction indicator, potentially improving the diagnostic value of routine echocardiographic examinations.

[0149] While the above example has described the use of the present system and method for cardiac ultrasound applications, it will be appreciated that the present system and method could be extend to other medical ultrasound applications such as urology and other medical fields in which measurement and analysis of flows are required.

[0150] Thus, in an aspect, there is provided a computer-implemented method for mapping and estimating blood flow dynamics and instability in a heart using ultrasound, the method comprising: transmitting a first batch of diverging ultrasound waves from multiple virtual source locations using a first pulse sequence; coherently compounding echoes of the first batch to generate brightness-mode cardiac tissue images; transmitting a second batch of diverging ultrasound waves from at least one fixed virtual source location using a second pulse sequence; beamforming echoes of the second batch to generate raw data for flow estimation;applying a clutter filter to suppress tissue motion artifacts and isolate flow signals; estimating a Doppler power spectrum for each pixel from the flow data using a minimum variance estimator with short ensembles; performing a cumulative integration of the Doppler power spectrum to extract Doppler bandwidth values; and mapping the Doppler bandwidth values across the imaged cardiac region to visualize flow stability and instability.

[0151] In an embodiment, the tissue images are generated at a frame rate of at least 10 frames per second.

[0152] In another embodiment, the flow instability maps are generated at a frame rate of at least 50 frames per second.

[0153] In another embodiment, the clutter filter is configured to suppress myocardial motion.

[0154] In another embodiment, the Doppler bandwidth estimation comprises selecting frequency thresholds corresponding to the cumulative power spectrum.

[0155] In another embodiment, the method further comprises superimposing the Doppler bandwidth map onto the tissue image to provide simultaneous anatomical and hemodynamic visualization.

[0156] In another embodiment, the Doppler bandwidth is used as a biomarker for assessing severity of cardiac pathologies.

[0157] In another embodiment, the cardiac pathologies include valvular regurgitation or other valvular dysfunctions, ventricular hypertrophy, and heart failure.

[0158] In another embodiment, the method further comprises correcting aliased Doppler spectra by re-centering spectral power prior to bandwidth estimation.

[0159] In another embodiment, the method further comprises computing both mean Doppler velocity and Doppler bandwidth and combining the parameters as a composite biomarker for cardiac pathology severity.

[0160] In another embodiment, the Doppler bandwidth estimation is accelerated using parallel processing to enable real-time visualization.

[0161] In another embodiment, the mapping of flow instability is applied to non-cardiac biological flows selected from urological or cardiovascular systems.

[0162] In another embodiment, the method further comprises fabricating and using a tissuemimicking phantom with simulated regurgitant flow for calibration and validation of the Doppler bandwidth mapping.

[0163] In another aspect, there is provided a system for mapping and estimating blood flow dynamics and instability in the heart using ultrasound, the system comprising:

[0164] an ultrasound transducer configured to transmit diverging wave pulses in alternating batches comprising: a tissue batch of single-cycle diverging waves from multiple virtual source locations; a flow batch of multi-cycle diverging waves from a fixed virtual source location; a beamformer configured to process echoes of the transmitted pulses; a tissue imaging processor configured to coherently compound the tissue batch echoes to generate high-resolution tissue images; a flow processing unit configured to apply an adaptive clutter filter to the flow batch echoes, estimate Doppler power spectra using a minimum variance estimator, and determine Doppler bandwidth values; a mapping module configured to generate Doppler bandwidth maps representing flow stability and instability; and a display configured to present the tissue images with superimposed Doppler bandwidth maps.

[0165] In an embodiment, the system generates tissue images at a frame rate of at least 50 frames per second.

[0166] In another embodiment, the system generates flow instability maps at a frame rate of at least 200 frames per second.

[0167] In another embodiment, the adaptive clutter filter is a polynomial-based filter configured to adapt to myocardial motion.

[0168] In another embodiment, the mapping module determines Doppler bandwidth by cumulative integration of the power spectrum and extraction of frequency thresholds corresponding to one standard deviation of a Gaussian distribution.

[0169] In another embodiment, the Doppler bandwidth map is configured to indicate regions of increased instability associated with mitral regurgitation or stenosis.

[0170] In another embodiment, the system further comprises a computing device configured to parallelize Doppler bandwidth estimation across pixels to achieve real-time visualization.

[0171] In another embodiment, the flow processing unit is further configured to perform aliasing correction by re-centering Doppler spectra prior to bandwidth estimation.

[0172] In another embodiment, the adaptive clutter filter comprises an autoregressive HR filter with projection initialization.

[0173] In another embodiment, the system is configured to compute and display both mean Doppler velocity and Doppler bandwidth as a composite diagnostic index.

[0174] In another embodiment, the system is configured to perform Doppler bandwidth estimation using GPU-based or multi-core processors for parallelized real-time visualization.

[0175] In another embodiment, the system is configured to map instability in non-cardiac biological flows selected from urological, vascular, or respiratory systems.

[0176] In another embodiment, the system further comprises a phantom calibration module configured to utilize a hydrogel-based phantom with simulated regurgitant flow for validation of Doppler bandwidth mapping.

[0001] While various embodiments of the invention have been described above with reference to the drawings, it will be appreciated that the scope of the invention is defined by the following claims.REFERENCES[1] N. S. Anavekar and J. K. Oh, "Doppler echocardiography: A contemporary review," J. Cardiol., vol. 54, no. 3, pp. 347-358, Dec. 2009, doi: 10.1016 / j.jjcc.2009.10.001.[2] J. Poree, D. Posada, A. Hodzic, F. Tournoux, G. Cloutier, and D. Garcia, "High-Frame-Rate Echocardiography Using Coherent Compounding With Doppler-Based Motion-Compensation," IEEE Trans. Med. Imaging, vol. 35, no. 7, pp. 1647-1657, July 2016, doi: 10.1109 / TMI.2016.2523346.[3] A. Ramalli, A. Rodriguez-Molares, J. Avdal, J. D'hooge, and L. Lovstakken, "High-Frame-Rate Color Doppler Echocardiography: A Quantitative Comparison of Different Approaches," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 67, no. 5, pp. 923-933, May 2020, doi: 10.1109 / TUFFC.2019.2958031.[4] P. Joos et al., "High-Frame-Rate Speckle-Tracking Echocardiography," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 65, no. 5, pp. 720-728, May 2018, doi: 10.1109 / TUFFC.2018.2809553.[5] J. Voorneveld et al., "High-Frame-Rate Echo-Particle Image Velocimetry Can Measure the High- Velocity Diastolic Flow Patterns," Circ. Cardiovasc. Imaging, vol. 12, no. 4, p. e008856, Apr. 2019, doi: 10.1161 / CIRCIMAGING.119.008856.[6] D. J. Sahn, "Instrumentation and physical factors related to visualization of stenotic and regurgitant jets by Doppler color flow mapping," J. Am. Coll. Cardiol., vol. 12, no. 5, pp. 1354-1365, Nov. 1988, doi: 10.1016 / 0735-1097(88)92621-6.[7] C. Papadacci, M. Pernot, M. Couade, M. Fink, and M. Tanter, "High-contrast ultrafast imaging of the heart," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 61, no. 2, pp. 288-301, Feb. 2014, doi:10.1109 / TUFFC.2014.6722614.[8] B. Y. S. Yiu, A. J. Y. Chee, G. Tang, W. Luo, and A. C. H. Yu, "High frame rate Doppler ultrasound bandwidth imaging for flow instability mapping," Med. Phys., vol. 46, no. 4, pp. 1620-1633, 2019, doi: 10.1002 / mp.13437.[9] A. Ng and J. Swanevelder, "Resolution in ultrasound imaging," Contin. Educ. Anaesth. Crit. Care Pain, vol. 11, no. 5, pp. 186-192, Oct. 2011, doi: 10.1093 / bjaceaccp / mkr030.

[0010] I. Amir and V. L. Newhouse, "On the signal-to-noise ratio enhancement of the Doppler process," Ultrasonics, vol. 22, no. 5, pp. 231-239, Sept. 1984, doi: 10.1016 / 0041-624X(84)90018-0.

[0011] C. Kasai, K. Namekawa, A. Koyano, and R. Omoto, "Real-Time Two-Dimensional Blood Flow Imaging Using an Autocorrelation Technique".

[0012] K. Kristoffersen, "Time-domain estimation of the center frequency and spread of Doppler spectra in diagnostic ultrasound," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 35, no. 4, pp. 484-497, July 1988, doi: 10.1109 / 58.4186.

[0013] A. Herment and J. F. Giovannelli, "An Adaptive Approach to Computing the Spectrum and Mean Frequency of Doppler Signals," Ultrason. Imaging, vol. 17, no. 1, pp. 1-26, Jan. 1995, doi:10.1006 / uimg.1995.1001.

[0014] F. S. Schlindwein and D. H. Evans, "Selection of the order of autoregressive models for spectral analysis of Doppler ultrasound signals," Ultrasound Med. Biol., vol. 16, no. 1, pp. 81-91, Jan. 1990, doi: 10.1016 / 0301-5629(90)90089-U.

[0015] J. Capon, "Maximum-likelihood spectral estimation," in Nonlinear Methods of Spectral Analysis, S. Haykin, Ed., Berlin, Heidelberg: Springer, 1983, pp. 155-179. doi: 10.1007 / 3-540-12386-5_12.

[0016] F. Gran, A. Jakobsson, and J. A. Jensen, "Adaptive spectral Doppler estimation," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 56, no. 4, pp. 700-714, Apr. 2009, doi: 10.1109 / TUFFC.2009.1093.

[0017] G. Montaldo, M. Tanter, J. Bercoff, N. Benech, and M. Fink, "Coherent plane-wave compounding for very high frame rate ultrasonography and transient elastography," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 56, no. 3, pp. 489-506, Mar. 2009, doi: 10.1109 / TUFFC.2009.1067.

[0018] A. C. H. Yu and L. Lovstakken, "Eigen-based clutter filter design for ultrasound color flow imaging: a review," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 57, no. 5, pp. 1096-1111, May 2010, doi: 10.1109 / TUFFC.2010.1521.

[0019] S. Bjaerum, H. Torp, and K. Kristoffersen, "Clutter filter design for ultrasound color flow imaging," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 49, no. 2, pp. 204-216, Feb. 2002, doi: 10.1109 / 58.985705.

[0020] A. . Oppenheim and R. W. Schafer, Discrete-time signal processing, 3rd ed. Upper Saddle River: Pearson, 2010.

[0021] J. Benesty, J. Chen, and Y. Huang, "Recursive and Fast Recursive Capon Spectral Estimators," EURASIP J. Adv. Signal Process., vol. 2007, no. 1, Art. no. 1, Dec. 2007, doi: 10.1155 / 2007 / 45194.

[0022] F. Makouei and B. Mohammadzadeh Asl, "Subspace-Based Blood Power Spectral Capon Combined with Wiener Postfilter to Provide a High-Quality Velocity Waveform with Low Mathematical Complexity," Ultrasound Med. Biol., vol. 46, no. 7, pp. 1783-1801, July 2020, doi:10.1016 / j.ultrasmedbio.2020.03.015.

[0023] B. Y. S. Yiu, I. K. H. Tsang, and A. C. H. Yu, "GPU-based beamformer: Fast realization of plane wave compounding and synthetic aperture imaging," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 58, no. 8, pp. 1698-1705, Aug. 2011, doi: 10.1109 / TUFFC.2011.1999.

[0024] P. Dyverfeldt et al., "Hemodynamic aspects of mitral regurgitation assessed by generalized phasecontrast MRI," J. Magn. Reson. Imaging JMRI, vol. 33, no. 3, pp. 582-588, Mar. 2011, doi:10.1002 / jmri.22407.

[0025] T. Irvine, X. K. Li, D. J. Sahn, and A. Kenny, "Assessment of mitral regurgitation," Heart, vol. 88, no. suppl 4, pp. ivll-ivl9, Nov. 2002, doi: 10.1136 / heart.88.suppl_4.ivll.

[0026] C. K. Ho, A. J. Y. Chee, B. Y. S. Yiu, A. C. O. Tsang, K. W. Chow, and A. C. H. Yu, "Wall-Less Flow Phantoms With Tortuous Vascular Geometries: Design Principles and a Patient-Specific Model Fabrication Example," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 64, no. 1, pp. 25-38, Jan. 2017, doi: 10.1109 / TUFFC.2016.2636129.

[0027] J. L. Garbini, F. K. Forster, and J. E. Jorgensen, "Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 1. Analysis," J. Fluid Meeh., vol. 118, pp. 445-470, May 1982, doi: 10.1017 / S0022112082001153.

[0028] J. L. Garbini, F. K. Forster, and J. E. Jorgensen, "Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 2. Experimental investigation," J. Fluid Meeh., vol. 118, pp. 471-505, May 1982, doi: 10.1017 / S0022112082001165.

[0029] C. Spearman, "The proof and measurement of association between two things," Am. J. Psychol., vol.15, no. 1, pp. 72-101, 1904, doi: 10.2307 / 1412159.

[0030] P. J. Kilner, G.-Z. Yang, A. J. Wilkes, R. H. Mohiaddin, D. N. Firmin, and M. H. Yacoub, "Asymmetric redirection of flow through the heart," Nature, vol. 404, no. 6779, pp. 759-761, Apr. 2000, doi: 10.1038 / 35008075.

[0031] L. Feng, H. Gao, B. Griffith, S. Niederer, and X. Luo, "Analysis of a coupled fluid-structure interaction model of the left atrium and mitral valve," Int. J. Numer. Methods Biomed. Eng., vol. 35, no. 11, p. e3254, 2019, doi: 10.1002 / cnm.3254.

[0032] W. H. Gaasch and T. E. Meyer, "Left Ventricular Response to Mitral Regurgitation," Circulation, vol. 118, no. 22, pp. 2298-2303, Nov. 2008, doi: 10.1161 / CIRCULATIONAHA.107.755942.

[0033] G. P. Aurigemma, J. S. Gottdiener, A. M. Arnold, M. Chinali, J. C. Hill, and D. Kitzman, "Left Atrial Volume and Geometry in Healthy Aging," Circ. Cardiovasc. Imaging, vol. 2, no. 4, pp. 282-289, July 2009, doi: 10.1161 / CIRCIMAGING.108.826602.

[0034] R. T. Hahn et al., "Guidelines for Performing a Comprehensive Transesophageal Echocardiographic Examination: Recommendations from the American Society of Echocardiography and the Society of Cardiovascular Anesthesiologists," J. Am. Soc. Echocardiogr., vol. 26, no. 9, pp. 921-964, Sept. 2013, doi: 10.1016 / j. echo.2013.07.009.

[0035] R. M. Lang et al., "Recommendations for Chamber Quantification: A Report from the American Society of Echocardiography's Guidelines and Standards Committee and the Chamber Quantification Writing Group, Developed in Conjunction with the European Association of Echocardiography, a Branch of the European Society of Cardiology," J. Am. Soc. Echocardiogr., vol. 18, no. 12, pp. 1440-1463, Dec. 2005, doi: 10.1016 / j.echo.2005.10.005.

[0036] H. F. Routh, "Doppler ultrasound," IEEE Eng. Med. Biol. Mag., vol. 15, no. 6, pp. 31-40, Nov. 1996, doi: 10.1109 / 51.544510.

[0037] S. Fortini, G. Querzoli, S. Espa, and A. Cenedese, "Three-dimensional structure of the flow inside the left ventricle of the human heart," Exp. Fluids, vol. 54, no. 11, p. 1609, Oct. 2013, doi: 10.1007 / s00348- 013-1609-0.

[0038] M. Cikes, L. Tong, G. R. Sutherland, and J. D'hooge, "Ultrafast Cardiac Ultrasound Imaging: Technical Principles, Applications, and Clinical Benefits," JACC Cardiovasc. Imaging, vol. 7, no. 8, pp. 812-823, Aug. 2014, doi: 10.1016 / j.jcmg.2014.06.004.

[0039] C. D. Richmond, "Capon-Bartlett cross-spectrum and a perspective on robust adaptive filtering," Signal Process., vol. 171, p. 107473, June 2020, doi: 10.1016 / j.sigpro.2020.107473.

[0040] G. Guidi, C. Licciardello, and S. Falteri, "Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening," Ultrasound Med. Biol., vol. 26, no. 5, pp. 853-862, June 2000, doi: 10.1016 / 50301-5629(00)00218-0.

[0041] N. Kagiyama and S. Shrestha, "Echocardiographic assessment of mitral regurgitation," J. Med. Ultrason., vol. 47, no. 1, pp. 59-70, Jan. 2020, doi: 10.1007 / sl0396-019-00971-l.

[0042] K. C. El-Tallawi, D. Messika-Zeitoun, and W. A. Zoghbi, "Assessment of the severity of native mitral valve regurgitation," Prog. Cardiovasc. Dis., vol. 60, no. 3, pp. 322-333, Nov. 2017, doi: 10.1016 / j.pcad.2017.11.005.

[0043] S. M. M. Tabatabaei Majd and B. Mohammadzadeh Asl, "Adaptive Spectral Doppler Estimation Based on the Modified Amplitude Spectrum Capon," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol.68, no. 5, pp. 1664-1675, May 2021, doi: 10.1109 / TUFFC.2020.3044774.

[0044] C. M. Kallweit, A. J. Y. Chee, B. Y. S. Yiu, S. D. Peterson, and A. C. H. Yu, "Dual-modality flow phantom for ultrasound and optical flow measurements," Phys. Med. Biol., vol. 70, no. 3, Jan. 2025, doi: 10.1088 / 1361-6560 / ada5a3.

[0045] D. Posada et al., "Staggered Multiple-PRF Ultrafast Color Doppler," IEEE Trans. Med. Imaging, vol.35, no. 6, pp. 1510-1521, June 2016, doi: 10.1109 / TMI.2016.2518638.

[0046] T. S. W. Stevens, F. C. Meral, J. Yu, I. Z. Apostolakis, J.-L. Robert, and R. J. G. van Sloun, "Dehazing Ultrasound Using Diffusion Models," IEEE Trans. Med. Imaging, vol. 43, no. 10, pp. 3546-3558, Oct. 2024, doi: 10.1109 / TMI.2024.3363460.

Claims

Claims1. A computer-implemented method for mapping and estimating blood flow dynamics and instability in a heart using ultrasound, the method comprising: transmitting a first batch of diverging ultrasound waves from multiple virtual source locations using a first pulse sequence; coherently compounding echoes of the first batch to generate brightness-mode cardiac tissue images; transmitting a second batch of diverging ultrasound waves from at least one fixed virtual source location using a second pulse sequence; beamforming echoes of the second batch to generate raw data for flow estimation; applying a clutter filter to suppress tissue motion artifacts and isolate flow signals; estimating a Doppler power spectrum for each pixel from the flow data using a minimum variance estimator with short ensembles; performing a cumulative integration of the Doppler power spectrum to extract Doppler bandwidth values; mapping the Doppler bandwidth values across the imaged cardiac region to visualize flow stability and instability.

2. The method of claim 1, wherein the tissue images are generated at a frame rate of at least 10 frames per second.

3. The method of claim 1, wherein the flow instability maps are generated at a frame rate of at least 50 frames per second.

4. The method of claim 1, wherein the clutter filter is configured to suppress myocardial motion.

5. The method of claim 1, wherein the Doppler bandwidth estimation comprises selecting frequency thresholds corresponding to the cumulative power spectrum.

6. The method of claim 1, further comprising superimposing the Doppler bandwidth map onto the tissue image to provide simultaneous anatomical and hemodynamic visualization.

7. The method of claim 1, wherein the Doppler bandwidth is used as a biomarker for assessing severity of cardiac pathologies.

8. The method of claim 7, wherein the cardiac pathologies include valvular regurgitation or other valvular dysfunctions, ventricular hypertrophy, and heart failure.

9. The method of claim 1, further comprising correcting aliased Doppler spectra by re-centering spectral power prior to bandwidth estimation.

10. The method of claim 1, further comprising computing both mean Doppler velocity and Doppler bandwidth and combining the parameters as a composite biomarker for cardiac pathology severity.

11. The method of claim 1, wherein the Doppler bandwidth estimation is accelerated using parallel processing to enable real-time visualization.

12. The method of claim 1, wherein the mapping of flow instability is applied to non-cardiac biological flows selected from urological or cardiovascular systems.

13. The method of claim 1, further comprising fabricating and using a tissue-mimicking phantom with simulated regurgitant flow for calibration and validation of the Doppler bandwidth mapping.

14. A system for mapping and estimating blood flow dynamics and instability in the heart using ultrasound, the system comprising: an ultrasound transducer configured to transmit diverging wave pulses in alternating batches comprising: a tissue batch of single-cycle diverging waves from multiple virtual source locations; a flow batch of multi-cycle diverging waves from a fixed virtual source location; a beamformer configured to process echoes of the transmitted pulses; a tissue imaging processor configured to coherently compound the tissue batch echoes to generate high-resolution tissue images; a flow processing unit configured to apply an adaptive clutter filter to the flow batch echoes, estimate Doppler power spectra using a minimum variance estimator, and determine Doppler bandwidth values; a mapping module configured to generate Doppler bandwidth maps representing flowstability and instability; and a display configured to present the tissue images with superimposed Doppler bandwidth maps.

15. The system of claim 14, wherein the system generates tissue images at a frame rate of at least 50 frames per second.

16. The system of claim 14, wherein the system generates flow instability maps at a frame rate of at least 200 frames per second.

17. The system of claim 14, wherein the adaptive clutter filter is a polynomial-based filter configured to adapt to myocardial motion.

18. The system of claim 14, wherein the mapping module determines Doppler bandwidth by cumulative integration of the power spectrum and extraction of frequency thresholds corresponding to one standard deviation of a Gaussian distribution.

19. The system of claim 14, wherein the Doppler bandwidth map is configured to indicate regions of increased instability associated with mitral regurgitation or stenosis.

20. The system of claim 14, further comprising a computing device configured to parallelize Doppler bandwidth estimation across pixels to achieve real-time visualization.

21. The system of claim 14, wherein the flow processing unit is further configured to perform aliasing correction by re-centering Doppler spectra prior to bandwidth estimation.

22. The system of claim 14, wherein the adaptive clutter filter comprises an autoregressive HR filter with projection initialization.

23. The system of claim 14, wherein the system is configured to compute and display both mean Doppler velocity and Doppler bandwidth as a composite diagnostic index.

24. The system of claim 14, wherein the system is configured to perform Doppler bandwidth estimation using GPU-based or multi-core processors for parallelized real-time visualization.

25. The system of claim 14, wherein the system is configured to map instability in non-cardiac biological flows selected from urological, vascular, or respiratory systems.

26. The system of claim 14, further comprising a phantom calibration module configured to utilize a hydrogel-based phantom with simulated regurgitant flow for validation of Doppler bandwidth mapping.

Images