FLUST: A fast, open source framework for ultrasound blood flow simulations.

BACKGROUND AND OBJECTIVE: Ultrasound based blood velocity estimation is a continuously developing frontier, where the vast number of possible acquisition setups and velocity estimators makes it challenging to assess which combination is better suited for a given imaging application. FLUST, the Flow-Line based Ultrasound Simulation Tool, may be used to address this challenge, providing a common platform for evaluation of velocity estimation schemes on in silico data. However, the FLUST approach had some limitations in its original form, including reduced robustness for phase sensitive setups and the need for manual selection of integrity parameters. In addition, implementation of the technique and therefore also documentation of signal integrity was left to potential users of the approach. METHODS: In this work, several improvements to the FLUST technique are proposed and investigated, and a robust, open source simulation framework developed. The software supports several transducer types and acquisition setups, in addition to a range of different flow phantoms. The main goal of this work is to offer a robust, computationally cheap and user-friendly framework to simulate ultrasound data from stationary blood velocity fields and thereby facilitate design and evaluation of estimation schemes, including acquisition design, velocity estimation and other post-processing steps. RESULTS: The technical improvements proposed in this work resulted in reduced interpolation errors, reduced variability in signal power, and also automatic selection of spatial and temporal discretization parameters. Results are presented illustrating the challenges and the effectiveness of the solutions. The integrity of the improved simulation framework is validated in an extensive study, with results indicating that speckle statistics, spatial and temporal correlation and frequency content all correspond well with theoretical predictions. Finally, an illustrative example shows how FLUST may be used throughout the design and optimization process of a velocity estimator. CONCLUSIONS: The FLUST framework is available as a part of the UltraSound ToolBox (USTB), and the results in this paper demonstrate that it can be used as an efficient and reliable tool for the development and validation of ultrasound-based velocity estimation schemes.

Effect of bubble size on ultrasound backscatter from bubble clouds in the context of gas kick detection in boreholes.

Early detection of gas influx in boreholes while drilling is of significant interest to drilling operators. Several studies suggest a good correlation between ultrasound backscatter/attenuation and gas volume fraction (GVF) in drilling muds, and thereby propose methods for quantification of GVF in boreholes. However, the aforementioned studies neglect the influence of bubble size, which can vary significantly over time. This paper proposes a model to combine existing theories for ultrasound backscatter from bubbles depending on their size, viz. Rayleigh scattering for smaller bubbles, and specular reflection for larger bubbles. The proposed model is demonstrated using simulations and experiments, where the ultrasound backscatter is evaluated from bubble clouds of varying bubbles sizes. It is shown that the size and number of bubbles strongly influence ultrasound backscatter intensity, and it is correlated to GVF only when the bubble size distribution is known. The information on bubble size is difficult to obtain in field conditions causing this correlation to break down. Consequently, it is difficult to reliably apply methods based on ultrasound backscatter, and by extension its attenuation, for the quantification of GVF during influx events in a borehole. These methods can however be applied as highly sensitive detectors of gas bubbles for GVF [Formula: see text]1 vol[Formula: see text].

Quantifying Valve Regurgitation Using 3-D Doppler Ultrasound Images and Deep Learning.

Accurate quantification of cardiac valve regurgitation jets is fundamental for guiding treatment. Cardiac ultrasound is the preferred diagnostic tool, but current methods for measuring the regurgitant volume (RVol) are limited by low accuracy and high interobserver variability. Following recent research, quantitative estimators of orifice size and RVol based on high frame rate 3-D ultrasound have been proposed, but measurement accuracy is limited by the wide point spread function (PSF) relative to the orifice size. The aim of this article was to investigate the use of deep learning to estimate both the orifice size and the RVol. A simulation model was developed to simulate the power-Doppler images of blood flow through orifices with different geometries. A convolutional neural network (CNN) was trained on 30 000 image pairs. The network was used to reconstruct orifices from power-Doppler data, which facilitated estimators for regurgitant orifice areas and flow volumes. We demonstrate that the network improves orifice shape reconstruction, as well as the accuracy of orifice area and flow volume estimation, compared with a previous approach based on thresholding of the power-Doppler signal (THD), and compared with spatially invariant deconvolution (DC). Our approach reduces the area estimation error on simulations: (THD: 13.2 ± 9.9 mm2, DC: 12.8 ± 15.8 mm2, and ours: 3.5 ± 3.2 mm2). In a phantom experiment, our approach reduces both area estimation error (THD: 10.4 ± 8.4 mm2, DC: 10.98 ± 8.17, and ours: 9.9 ± 6.0 mm2) and flow rate estimation error (THD: 20.3 ± 9.9 ml/s, DC: 18.14 ± 13.01 ml/s, and ours: 7.1 ± 10.6 ml/s). We also demonstrate in vivo feasibility for six patients with aortic insufficiency, compared with standard echocardiography and magnetic resonance references.

Tapered Vector Doppler for Improved Quantification of Low Velocity Blood Flow.

A new vector velocity estimation scheme is developed, termed tapered vector Doppler (TVD), aiming to improve the accuracy of low velocity flow estimation. This is done by assessing the effects of singular value decomposition (SVD) and finite impulse response (FIR) filters and designing an estimator which accounts for signal loss due to filtering. Synthetic data created using a combination of in vivo recordings and flow simulations were used to investigate scenarios with low blood flow, in combination with true clutter motion. Using this approach, the accuracy and precision of TVD was investigated for a range of clutter-to-blood and signal-to-noise ratios. The results indicated that for the investigated carotid application and setup, the SVD filter performed as a frequency-based filter. For both SVD and FIR filters, suppression of the clutter signal resulted in large bias and variance in the estimated blood velocity magnitude and direction close to the vessel walls. Application of the proposed tapering technique yielded significant improvement in the accuracy and precision of near-wall vector velocity measurements, compared to non-TVD and weighted least squares approaches. In synthetic data, for a blood SNR of 5 dB, and in a near-wall region where the average blood velocity was 9 cm/s, the use of tapering reduced the average velocity magnitude bias from 26.3 to 1.4 cm/s. Complex flow in a carotid bifurcation was used to demonstrate the in vivo performance of TVD, and it was shown that tapering enables vector velocity estimation less affected by clutter and clutter filtering than what could be obtained by adaptive filter design only.

Retrospective Transmit Beamforming and Coherent Plane-Wave Compounding for Microvascular Doppler Imaging: A Comparison Study.

Imaging blood flow in small vessels is of great clinical value for evaluating increased vascularization, potentially related to angiogenesis in cancer or inflammation processes in musculoskeletal disease. Using a traditional duplex imaging approach, a major challenge in color Doppler imaging is the limited amount of samples available for clutter filtering. Coherent plane-wave compounding (CPWC) enables a continuous high frame rate acquisition and improved image quality due to dynamic transmit focusing. However, the presence of moving scatterers in the image can lead to a loss in signal-to-noise ratio (SNR) and contrast. In this study, typical CPWC sequences for low-flow imaging were compared with retrospective transmit beamforming (RTB) sequences with similar frame rates and transmit power. The comparison was based on resolution, contrast, and SNR, using a stationary phantom, a flow phantom, a thread phantom, and in vivo recordings of blood vessels in the thyroid and kidney. A model was developed to estimate the difference in SNR between RTB and CPWC in the presence of static and moving scatterers while varying the transmit sequence parameters. The model predicted that RTB may yield an increased SNR compared with CPWC, especially for flow imaging, where the SNR difference reached 6 dB for a maximum velocity of 15 cm/s. The measured SNR values were in agreement with the predicted values, both in the case of stationary scatterers and for the flow phantom. We further demonstrated that reducing beam density to increase frame rate is associated with spatial undersampling (stripe) artifacts for RTB and grating lobes for CPWC. Both phantom and in vivo results indicate that transmit focusing may be beneficial in a low-flow imaging setup that, combined with adaptive clutter filtering, can yield superior microvascular imaging.

Validation of a novel ultrasound Doppler monitoring device (earlybird) for measurements of volume flow rate in arteriovenous fistulas for hemodialysis.

BACKGROUND: Controversy exists regarding surveillance of arteriovenous fistulas for hemodialysis to increase patency. A significant reduction in volume flow rate (VFR) should lead to diagnostic evaluation and eventually intervention. Several methods are available for VFR measurements, but all of them are associated with low reproducibility. VFR trend analysis is suggested as an improved solution. It is therefore a need to find user-friendly, cost and time-effective modalities. We present a novel Doppler ultrasound device (earlybird) which could bridge this gap. It includes an easy-to-use and light-weight single element transducer. METHODS: In an experimental and clinical setting, we compared earlybird to duplex ultrasound to assess VFR. In a closed circuit of blood-mimicking fluid, 36 paired calculations of calibrated, duplex ultrasound and earlybird VFR was measured. In addition, 23 paired recordings of duplex ultrasound and earlybird VFR was measured in 16 patients with underarm arteriovenous fistulas. Pearson correlation, intraclass correlation coefficient, root-mean-square and Bland-Altman plots were analyzed. RESULTS: Strong correlation (r = 0.991, p < 0.001), and excellent level of agreement (ICC = 0.970 (95% CI 0.932 - 0.985), p < 0.001) between earlybird and the calibrated VFR was found in the experimental setup. This was confirmed in the clinical setting, with a strong correlation (r = 0.781, p < 0.001) and moderate to good level of agreement (ICC = 0.750 (95% CI 0.502-0.885), p < 0.001) between earlybird and duplex ultrasound VFR measured at the arteriovenous fistulas outflow veins. In the Bland-Altman plot-analysis for the experimental setup, we found smaller limits of agreement, a smaller consistent and proportional bias, as well as greater accuracy of earlybird than DUS when compared to the calibrated VFR. CONCLUSION: Earlybird is a feasible tool for VFR measurements and could be a future promising device for easy assessment and surveillance of AVF for hemodialysis.

Translation of Simultaneous Vessel Wall Motion and Vectorial Blood Flow Imaging in Healthy and Diseased Carotids to the Clinic: A Pilot Study.

This study aims to investigate the clinical feasibility of simultaneous extraction of vessel wall motion and vectorial blood flow at high frame rates for both extraction of clinical markers and visual inspection. If available in the clinic, such a technique would allow a better estimation of plaque vulnerability and improved evaluation of the overall arterial health of patients. In this study, both healthy volunteers and patients were recruited and scanned using a planewave acquisition scheme that provided a data set of 43 carotid recordings in total. The vessel wall motion was extracted based on the complex autocorrelation of the signals received, while the vector flow was extracted using the transverse oscillation technique. Wall motion and vector flow were extracted at high frame rates, which allowed for a visual appreciation of tissue movement and blood flow simultaneously. Several clinical markers were extracted, and visual inspections of the wall motion and flow were conducted. From all the potential markers, young healthy volunteers had smaller artery diameter (7.72 mm) compared with diseased patients (9.56 mm) ( p -value ≤ 0.001), 66% of diseased patients had backflow compared with less than 10% for the other patients ( p -value ≤ 0.05), a carotid with a pulse wave velocity extracted from the wall velocity greater than 7 m/s was always a diseased vessel, and the peak wall shear rate decreased as the risk increases. Based on both the pathological markers and the visual inspection of tissue motion and vector flow, we conclude that the clinical feasibility of this approach is demonstrated. Larger and more disease-specific studies using such an approach will lead to better understanding and evaluation of vessels, which can translate to future use in the clinic.

Data-Adaptive 2-D Tracking Doppler for High-Resolution Spectral Estimation.

Spectral broadening in pulsed-wave Doppler caused by the transit-time effect deteriorates the frequency resolution and may cause overestimation of maximum velocities in high-velocity blood flow regions and for large beam-to-flow angles. Data-adaptive spectral estimators have been shown to provide improved frequency resolution, especially for small ensemble lengths, but offer little or no improvement when the transit-time effect dominates. In this work, a method is presented that combines a data-adaptive spectral estimation method, the power spectral Capon, and 2-D tracking Doppler to enable improved frequency resolution for both high and low velocities. For each velocity, a time signal is extracted by tracking scatterers over time and space to decrease the transit-time effect, and power spectral Capon is used for spectral estimation. The method is evaluated using simulations, flow phantom recordings, and recordings from healthy and stenotic carotid arteries. Simulation results showed that the spectral width was decreased by 60% compared to 2-D tracking Doppler for velocities around 2.3 m/s using 12 time samples. The reduction was estimated to be 66% using the flow phantom results for 0.85-m/s mean velocity. A 5-dB SNR gain was observed from the in vivo results compared with Welch's method. Computer simulations confirm that in the presence of velocity gradients or out-of-plane motion, the proposed method can be used to reduce spectral broadening by requiring shorter observation windows.

High-Frame-Rate Color Doppler Echocardiography: A Quantitative Comparison of Different Approaches.

Ultrasound color Doppler imaging (CDI) provides a map of the axial blood flow velocities in a 2-D/3-D region of interest. While CDI is clinically effective for a qualitative analysis of abnormal blood flows, e.g., for valvular disease in cardiology, it is in limited use for quantitative measures, mainly hampered by low frame rate and measurement bias. These limitations can be reduced by different approaches toward high-frame-rate (HFR) imaging at the expense of reduced image quality and penetration depth. The aim of this study was to compare the impact of different HFR sequences on CDI quantitatively. Different cardiac scan sequences, including diverging waves and multiline transmission, were designed, implemented on a research system, and compared in terms of patient safety parameters, image quality, and penetration depth. Furthermore, in vivo images were acquired and compared for healthy volunteers. Results showed that the HFR techniques spread artifacts on larger areas than the standard single-line scans (> +50%). In addition, due to patient safety limitations, they reduce the penetration depth up to -5 cm. On the other hand, the HFR techniques provide comparable velocity estimates (relative difference <6%) and enhance the time resolution of the color Doppler images, achieving frame rates up to 625 Hz in continuous acquisition.

Validation of a novel ultrasound Doppler monitoring device (earlybird) for detection of microvascular circulatory changes.

OBJECTIVE: In this proof-of-concept study we aim to validate a novel ultrasound Doppler monitoring device for evaluating microcirculation (earlybird) against LDF and pulsed Doppler. METHODS: In ten healthy subjects, we measured microcirculatory function at rest and during different autonomic tests (forced respiration, isometric exercise, Valsalva maneuver and cold pressor). Earlybird, LDF and pulsed Doppler were recorded simultaneously. We performed a ZNCC to determine correlation. RESULTS: The curves for earlybird and LDF or pulsed Doppler correlates visually well. Overall median ZNCC 0.87 (interquartile range 0.77 -0.91) between the LDF and earlybird measurements, and 0.90 (0.82 - 0.95) for pulsed Doppler and earlybird. Median ZNCC for baseline and each provocation test for earlybird against LDF and pulsed Doppler were calculated; baseline: LDF 0.87 (0.73 - 0.97) pulsed Doppler 0.91 (0.81 - 0.94), forced respiration: LDF 0.87 (0.28 - 0.90) pulsed Doppler 0.90 (0.85 - 0.96), isometric exercise: LDF 0.82 (0.59 - 0.90) pulsed Doppler 0.87 (0.68 - 0.94), Valsalva maneuver: LDF 0.88 (0.82 - 0.91) pulsed Doppler 0.94 (0.92 - 0.97) and cold pressor: LDF 0.90 (0.85 - 0.95) pulsed Doppler 0.89 (0.65 - 0.94). CONCLUSION: Earlybird records vasoconstrictions in healthy subjects as well as LDF and pulsed Doppler.

Fast Flow-Line-Based Analysis of Ultrasound Spectral and Vector Velocity Estimators.

A new technique, termed FLUST (FlowLine Ultrasound Simulation Tool), is proposed as a computationally cheap alternative to simulations based on randomly positioned scatterers for the simulation of stationary blood velocity fields. In FLUST, the flow field is represented as a collection of flow lines. Point spread functions are first calculated at regularly spaced positions along the flow lines before realizations of single scatterers traversing the flow lines are generated using temporal interpolation. Several flow-line realizations are then generated by convolution with temporal noise filters, and finally, flow-field realizations are obtained by the summation of the individual flow-line realizations. Flow-field realizations produced by FLUST are shown to correspond well with conventional Field II simulations both quantitatively and qualitatively. The added value of FLUST is demonstrated by using the proposed simulation technique to obtain multiple realizations of realistic 3-D flow fields at a significantly reduced computational cost. This information is utilized for a performance assessment of different spectral and vector velocity estimators for carotid and coronary imaging applications. The computational load of FLUST does not increase substantially with the number of realizations or simulated frames, and for the examples shown, it is the fastest alternative when the total number of simulated frames exceeds 48. In the examples, the standard deviation and bias of the velocity estimators are calculated using 100 FLUST realizations, in which case the proposed method is two orders of magnitude faster than simulations based on random scatterer positions.

Combining Automatic Angle Correction and 3-D Tracking Doppler for the Assessment of Aortic Stenosis Severity.

Aortic valve stenosis (AS) is a narrowing of the aortic valve opening, which causes increased load on the left ventricle. Untreated, this condition can eventually lead to heart failure and death. According to current recommendations, an accurate diagnosis of AS mandates the use of multiple acoustic windows to determine the highest velocity. Furthermore, the optimal positioning of both patient and transducer to reduce the beam-to-flow angle is emphasized. Being operator dependent, the beam alignment is a potential source of uncertainty. In this work, we perform noncompounded 3-D plane wave imaging for retrospective estimation of maximum velocities in aortic jets with automatic angle correction. This is achieved by combining a hybrid 3-D speckle tracking method to estimate the jet direction and 3-D tracking Doppler to generate angle-corrected sonograms, using the direction from speckle tracking as input. Results from simulations of flow through an orifice show that 3-D speckle tracking can estimate the jet orientation with acceptable accuracy for signal-to-noise ratios above 10 dB. Results from 12 subjects show that sonograms recorded from a standard apical view using the proposed method yield a maximum velocity that matches continuous wave (CW) Doppler sonograms recorded from the acoustic window with the lowest angle within a ±10% margin, provided that a high enough pulse repetition frequency could be achieved. These results motivate further validation and optimization studies.

Maximum velocity estimation in coronary arteries using 3D tracking Doppler.

Several challenges currently prevent the use of Doppler echocardiography to assess blood flow in the coronary arteries. Due to the anatomy of the coronary tree, out-of-plane flow and high beam-to-flow angles easily occur. Transit time broadening in regions with high velocities leads to overestimation of the maximum velocity envelope, which is a standard clinical parameter for flow quantification. In this work, a commercial ultrasound system was locally modified to perform trans-thoracic, 3D high frame-rate imaging of the coronary arteries. The imaging sequence was then combined with 3D tracking Doppler for retrospective estimation of maximum velocities. Results from simulations showed that 3D tracking Doppler delivers sonograms with better velocity resolution and spectral SNR compared to conventional PW Doppler. Results were confirmed using in vitro recordings. Further simulations based on realistic coronary flow data showed that 3D tracking Doppler can provide improved performance compared to PW Doppler, suggesting a potential benefit on patients. In vivo feasibility of the method was also shown in a healthy volunteer.

Maximum Velocity Estimation in Coronary Arteries Using 3-D Tracking Doppler.

Several challenges currently prevent the use of Doppler echocardiography to assess blood flow in the coronary arteries. Due to the anatomy of the coronary tree, out-of-plane flow and high beam-to-flow angles easily occur. Transit-time broadening in regions with high velocities leads to overestimation of the maximum velocity envelope, which is a standard clinical parameter for flow quantification. In this paper, a commercial ultrasound system was locally modified to perform trans-thoracic, 3-D high frame-rate imaging of the coronary arteries. The imaging sequence was then combined with 3-D tracking Doppler for retrospective estimation of maximum velocities. Results from simulations showed that 3-D tracking Doppler delivers sonograms with better velocity resolution and spectral SNR compared to conventional pulsed wave (PW) Doppler. Results were confirmed using in vitro recordings. Further simulations based on realistic coronary flow data showed that 3-D tracking Doppler can provide improved performance compared to PW Doppler, suggesting a potential benefit to patients. In vivo feasibility of the method was also shown in a healthy volunteer.

Combined 2-D Vector Velocity Imaging and Tracking Doppler for Improved Vascular Blood Velocity Quantification.

Measurement of the maximum blood flow velocity is the primary means for determining the degree of carotid stenosis using ultrasound. The current standard for estimating the maximum velocity is pulsed-wave Doppler with manual angle correction, which is prone to error and interobserver variability. In addition, spectral broadening in the velocity spectra leads to overestimation of maximal velocities. In this paper, we propose to combine two velocity estimation methods to reduce the bias and variability in maximum velocity measurements. First, the direction of the blood flow is estimated using an aliasing-resistant least squares vector Doppler technique. Then, tracking Doppler is performed on the same data, using the direction of the vector Doppler estimate as the tracking direction. Simulations show that the method can estimate a maximum velocity of 2 m/s with accuracy 5% for beam-to-flow angles between 20° and 75°, and that the primary source of error is inaccuracy in the flow direction estimate from vector Doppler. Simulations of complex flow in a carotid bifurcation demonstrated that the combined technique provided spectral velocity profiles corresponding well with the true maximum velocity trace, and that the bias originating from the directional estimate was within 5% for all spatial points. A healthy volunteer and a volunteer with carotid artery stenosis were imaged, showing in vivo feasibility of the method, for high velocities and with beam-to-flow angles varying throughout the cardiac cycle.

An Extended Least Squares Method for Aliasing-Resistant Vector Velocity Estimation.

An extended least squares method for robust, angle-independent 2-D vector velocity estimation using plane-wave ultrasound imaging is presented. The method utilizes a combination of least squares regression of Doppler autocorrelation estimates and block matching to obtain aliasing-resistant vector velocity estimates. It is shown that the aliasing resistance of the technique may be predicted using a single parameter, which is dependent on the selected transmit and receive steering angles. This parameter can therefore be used to design the aliasing-resistant transmit-receive setups. Furthermore, it is demonstrated that careful design of the transmit-receive steering pattern is more effective than increasing the number of Doppler measurements to obtain robust vector velocity estimates, especially in the presence of higher order aliasing. The accuracy and robustness of the method are investigated using the realistic simulations of blood flow in the carotid artery bifurcation, with velocities up to five times the Nyquist limit. Normalized root-mean-square (rms) errors are used to assess the performance of the technique. At -5 dB channel data blood SNR, rms errors in the vertical and horizontal velocity components were approximately 5% and 15% of the maximum absolute velocity, respectively. Finally, the in vivo feasibility of the technique is shown by imaging the carotid arteries of healthy volunteers.

Adaptive Spectral Estimation Methods in Color Flow Imaging.

Clutter rejection for color flow imaging (CFI) remains a challenge due to either a limited amount of temporal samples available or nonstationary tissue clutter. This is particularly the case for interleaved CFI and B-mode acquisitions. Low velocity blood signal is attenuated along with the clutter due to the long transition band of the available clutter filters, causing regions of biased mean velocity estimates or signal dropouts. This paper investigates how adaptive spectral estimation methods, Capon and blood iterative adaptive approach (BIAA), can be used to estimate the mean velocity in CFI without prior clutter filtering. The approach is based on confining the clutter signal in a narrow spectral region around the zero Doppler frequency while keeping the spectral side lobes below the blood signal level, allowing for the clutter signal to be removed by thresholding in the frequency domain. The proposed methods are evaluated using computer simulations, flow phantom experiments, and in vivo recordings from the common carotid and jugular vein of healthy volunteers. Capon and BIAA methods could estimate low blood velocities, which are normally attenuated by polynomial regression filters, and may potentially give better estimation of mean velocities for CFI at a higher computational cost. The Capon method decreased the bias by 81% in the transition band of the used polynomial regression filter for small packet size ( N=8 ) and low SNR (5 dB). Flow phantom and in vivo results demonstrate that the Capon method can provide color flow images and flow profiles with lower variance and bias especially in the regions close to the artery walls.

Effects of reverberations and clutter filtering in pulsed Doppler using sparse sequences.

Duplex ultrasound is a modality in which an ultrasound system is used for simultaneous acquisition of both B-mode images and velocity (Doppler) data. Conventional duplex sequences interleave packets of B-mode and Doppler transmissions, producing undesirable gaps during B-mode interruptions. In recent years, several techniques have been proposed for avoiding such gaps by using sparse sequences, in which velocity spectra are generated from nonuniformly sampled Doppler data containing frequent B-mode interruptions. In this work, two negative effects are discussed that may influence velocity estimation when using nonuniformly sampled sequences. First, it is shown that long reverberation times lead to discontinuities in the signal from stationary clutter after each B-mode interruption. Second, using frequency analysis, it is shown that clutter filtering of nonuniformly sampled data may introduce artifacts in the velocity spectrum, and also lead to significant bias in mean velocity estimates. Methods are presented for quantification of these effects, and utilized to analyze three types of sparse duplex sequences for blood velocity estimation. In particular, it is argued that the use of such sequences in cardiac applications is not recommended because of long reverberation time. Additionally, it is found that the use of regression filters to filter nonuniformly sampled data may produce significant artifacts in pulsed wave Doppler spectra, but is less significant for color Doppler imaging applications. In vitro and in vivo examples are included showing the presence and magnitude of these problems in clinically relevant applications.

Investigations of spectral resolution and angle dependency in a 2-D tracking Doppler method.

An important source of error in velocity measurements from conventional pulsed wave (PW) Doppler is the angle used for velocity calibration. Because there are great uncertainties and interobserver variability in the methods used for Doppler angle correction in the clinic today, it is desirable to develop new and more robust methods. In this work, we have investigated how a previously presented method, 2-D tracking Doppler, depends on the tracking angle. A signal model was further developed to include tracking along any angle, providing velocity spectra which showed good agreement with both experimental data and simulations. The full-width at half-maximum (FWHM) bandwidth and the peak value of predicted power spectra were calculated for varying tracking angles. It was shown that the spectra have lowest bandwidth and maximum power when the tracking angle is equal to the beam-to-flow angle. This may facilitate new techniques for velocity calibration, e.g., by manually adjusting the tracking angle, while observing the effect on the spectral display. An in vitro study was performed in which the Doppler angles were predicted by the minimum FWHM and the maximum power of the 2-D tracking Doppler spectra for 3 different flow angles. The estimated Doppler angles had an overall error of 0.24° ± 0.75° when using the minimum FWHM. With an in vivo example, it was demonstrated that the 2-D tracking Doppler method is suited for measurements in a patient with carotid stenosis.