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.

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.

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.

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.

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.

Quantitative Doppler Analysis Using Conventional Color Flow Imaging Acquisitions

Interleaved acquisitions used in conventional triplex mode result in a tradeoff between the frame rate and the quality of velocity estimates. On the other hand, workflow becomes inefficient when the user has to switch between different modes, and measurement variability is increased. This paper investigates the use of power spectral Capon estimator in quantitative Doppler analysis using data acquired with conventional color flow imaging (CFI) schemes. To preserve the number of samples used for velocity estimation, only spatial averaging was utilized, and clutter rejection was performed after spectral estimation. The resulting velocity spectra were evaluated in terms of spectral width using a recently proposed spectral envelope estimator. The spectral envelopes were also used for Doppler index calculations using in vivo and string phantom acquisitions. In vivo results demonstrated that the Capon estimator can provide spectral estimates with sufficient quality for quantitative analysis using packet-based CFI acquisitions. The calculated Doppler indices were similar to the values calculated using spectrograms estimated on a commercial ultrasound scanner.

Photochemical internalization in bladder cancer - development of an orthotopic in vivo model

The possibility of using photochemical internalization (PCI) to enhance the effects of the cytotoxic drug bleomycin is investigated, together with photophysical determination and outlines of a possible treatment for intravesical therapy of bladder cancer. In vitro experiments indicated that the employment of PCI technology using the novel photosensitizer TPCS_2a® can enhance the cytotoxic effect of bleomycin in bladder cancer cells. Furthermore, experiments in an orthotopic in vivo bladder cancer model show an effective reduction in both the necrotic area and the bladder weight after TPCS_2a based photodynamic therapy (PDT). The tumor selectivity and PDT effects may be sufficient to destroy tumors without damaging the detrusor muscle layer. Our results present a possible new treatment strategy for non-muscle invasive bladder cancer, with the intravesical instillation of the photosensitizer and bleomycin followed by illumination through an optic fiber by using a catheter.

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.

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.

Adaptive Spectral Envelope Estimation for Doppler Ultrasound

Estimation of accurate maximum velocities and spectral envelope in ultrasound Doppler blood flow spectrograms are both essential for clinical diagnostic purposes. However, obtaining accurate maximum velocity is not straightforward due to intrinsic spectral broadening and variance in the power spectrum estimate. The method proposed in this paper for maximum velocity point detection has been developed by modifying an existing method-signal noise slope intersection, incorporating in it steps from an altered version of another method called geometric method. Adaptive noise estimation from the spectrogram ensures that a smooth spectral envelope is obtained postdetection of these maximum velocity points. The method has been tested on simulated Doppler signal with scatterers possessing a parabolic flow velocity profile constant in time, steady and pulsatile string phantom recordings, as well as in vivo recordings from uterine, umbilical, carotid, and subclavian arteries. The results from simulation experiments indicate a bias of less than 2.5% in maximum velocities when estimated for a range of peak velocities, Doppler angles, and SNR levels. Standard deviation in the envelope is low-less than 2% in the case of experiments done by varying the peak velocity and Doppler angle for steady phantom and simulated flow, and also less than 2% in the case of experiments done by varying SNR but keeping constant flow conditions for in vivo and simulated flow. Low variability in the envelope makes the prospect of using the envelope for automated blood flow measurements possible and is illustrated for the case of pulsatility index estimation in uterine and umbilical arteries.

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.

Robust angle-independent blood velocity estimation based on dual-angle plane wave imaging

Two-dimensional blood velocity estimation has shown potential to solve the angle-dependency of conventional ultrasound flow imaging. Clutter filtering, however, remains a major challenge for large beam-to-flow angles, leading to signal drop-outs and corrupted velocity estimates. This work presents and evaluates a compounding speckle tracking (ST) algorithm to obtain robust angle-independent 2-D blood velocity estimates for all beam-to-flow angles. A dual-angle plane wave imaging setup with full parallel receive beamforming is utilized to achieve high-frame-rate speckle tracking estimates from two scan angles, which may be compounded to obtain velocity estimates of increased robustness. The acquisition also allows direct comparison with vector Doppler (VD) imaging. Absolute velocity bias and root-mean-square (RMS) error of the compounding ST estimations were investigated using simulations of a rotating flow phantom with low velocities ranging from 0 to 20 cm/s. In a challenging region where the estimates were influenced by clutter filtering, the bias and RMS error for the compounding ST estimates were 11% and 2 cm/s, a significant reduction compared with conventional single-angle ST (22% and 4 cm/s) and VD (36% and 6 cm/s). The method was also tested in vivo for vascular and neonatal cardiac imaging. In a carotid artery bifurcation, the obtained blood velocity estimates showed that the compounded ST method was less influenced by clutter filtering than conventional ST and VD methods. In the cardiac case, it was observed that ST velocity estimation is more affected by low signal-to-noise (SNR) than VD. However, with sufficient SNR the in vivo results indicated that a more robust angle-independent blood velocity estimator is obtained using compounded speckle tracking compared with conventional ST and VD methods.

Reconstruction of specular reflectors by iterative image source localization

A method is presented to reconstruct the geometry of specular reflectors with an ultrasonic array based on the image source principle. The ultrasonic beam is focused at a point in space emulating a point source within the medium. The transmitted wave interacts with the specular reflector and propagates back to the array as if it were generated by an image source. The reflected wave is analyzed with a sound source localization algorithm to estimate the image source location, and the reflector geometry is extracted using the mirror equation for spherical reflectors. The method is validated experimentally and its accuracy is studied. Under ideal conditions the method provides an accurate reconstruction of the position, orientation, and radius of curvature of specular reflectors, with errors Δr < 0.2 mm, Δα < 3°, and ΔR/R0 < 0.2, respectively. The method performs very well in the presence of high levels of thermal and speckle noise, with no degradation of the reconstruction as long as SNR(th) > -3 dB (signal-to-thermal-noise ratio) and SNR(sp) > 7 dB (signal-to-speckle-noise ratio). An iterative scheme based on the proposed method is presented to reconstruct the geometry of arbitrary reflectors by subdividing the reflector boundary into smaller segments. The iterative scheme is demonstrated both numerically and experimentally.

Combined vector velocity and spectral Doppler imaging for improved imaging of complex blood flow in the carotid arteries

Color flow imaging and pulsed wave (PW) Doppler are important diagnostic tools in the examination of patients with carotid artery disease. However, measurement of the true peak systolic velocity is dependent on sample volume placement and the operator's ability to provide an educated guess of the flow direction. Using plane wave transmissions and a duplex imaging scheme, we present an all-in-one modality that provides both vector velocity and spectral Doppler imaging from one acquisition, in addition to separate B-mode images of sufficient quality. The vector Doppler information was used to provide automatically calibrated (angle-corrected) PW Doppler spectra at every image point. It was demonstrated that the combined information can be used to generate spatial maps of the peak systolic velocity, highlighting regions of high velocity and the extent of the stenotic region, which could be used to automate work flow as well as improve the accuracy of measurement of true peak systolic velocity. The modality was tested in a small group (N = 12) of patients with carotid artery disease. PW Doppler, vector velocity and B-mode images could successfully be obtained from a single recording for all patients with a body mass index ranging from 21 to 31 and a carotid depth ranging from 16 to 28 mm.

Coherent plane wave compounding for very high frame rate ultrasonography of rapidly moving targets

Coherent plane wave compounding is a promising technique for achieving very high frame rate imaging without compromising image quality or penetration. However, this approach relies on the hypothesis that the imaged object is not moving during the compounded scan sequence, which is not the case in cardiovascular imaging. This work investigates the effect of tissue motion on retrospective transmit focusing in coherent compounded plane wave imaging (PWI). Two compound scan sequences were studied based on a linear and alternating sequence of tilted plane waves, with different timing characteristics. Simulation studies revealed potentially severe degradations in the retrospective focusing process, where both radial and lateral resolution was reduced, lateral shifts of the imaged medium were introduced, and losses in signal-to-noise ratio (SNR) were inferred. For myocardial imaging, physiological tissue displacements were on the order of half a wavelength, leading to SNR losses up to 35 dB, and reductions of contrast by 40 dB. No significant difference was observed between the different tilt sequences. A motion compensation technique based on cross-correlation was introduced, which significantly recovered the losses in SNR and contrast for physiological tissue velocities. Worst case losses in SNR and contrast were recovered by 35 dB and 27-35 dB, respectively. The effects of motion were demonstrated in vivo when imaging a rat heart. Using PWI, very high frame rates up to 463 fps were achieved at high image quality, but a motion correction scheme was then required.

Simultaneous quantification of flow and tissue velocities based on multi-angle plane wave imaging

A quantitative angle-independent 2-D modality for flow and tissue imaging based on multi-angle plane wave acquisition was evaluated. Simulations of realistic flow in a carotid artery bifurcation were used to assess the accuracy of the vector Doppler (VD) technique. Reduction in root mean square deviation from 27 cm/s to 6 cm/s and 7 cm/s to 2 cm/s was found for the lateral (vx) and axial (vz) velocity components, respectively, when the ensemble size was increased from 8 to 50. Simulations of a Couette flow phantom (vmax = 2.7 cm/s) gave promising results for imaging of slowly moving tissue, with root mean square deviation of 4.4 mm/s and 1.6 mm/s for the x- and z-components, respectively. A packet acquisition scheme providing both B-mode and vector Doppler RF data was implemented on a research scanner, and beamforming and further post-processing was done offline. In vivo results of healthy volunteers were in accordance with simulations and gave promising results for flow and tissue vector velocity imaging. The technique was also tested in patients with carotid artery disease. Using the high ensemble vector Doppler technique, blood flow through stenoses and secondary flow patterns were better visualized than in ordinary color Doppler. Additionally, the full velocity spectrum could be obtained retrospectively for arbitrary points in the image.