Improved blood velocity estimation using the maximum Doppler frequency

Automatic Measurement of the Carotid Blood Flow for Wearable Sensors: A Pilot Study

The assessment of the velocity of blood flowing in the carotid, in modern clinical practice, represents an important exam performed both in emergency situations and as part of scheduled screenings. It is typically performed by an expert sonographer who operates a complex and costly clinical echograph. Unfortunately, in developing countries, in rural areas, and even in crowded modern cities, the access to this exam can be limited by the lack of suitable personnel and ultrasound equipment. The recent availability of low-cost, handheld devices has contributed to solving part of the problem, but a wide access to the exam is still hampered by the lack of expert sonographers. In this work, an automated procedure is presented with the hope that, in the near future, it can be integrated into a low-cost, handheld instrument that is also suitable for self-measurement, for example, as can be done today with the finger oximeter. The operator should only place the probe on the neck, transversally with respect to the common tract of the carotid. The system, in real-time, automatically locates the vessel lumen, places the sample volume, and performs an angle-corrected velocity measurement of the common carotid artery peak velocity. In this study, the method was implemented for testing on the ULA-OP 256 scanner. Experiments on flow phantoms and volunteers show a performance in sample volume placement similar to that achieved by expert operators, and an accuracy and repeatability of 3.2% and 4.5%, respectively.

Specification and Evaluation of Plasticizer Migration Simulants for Human Blood Products: A Delphi Study

Potentially toxic plasticizers are commonly added to polyvinyl chloride medical devices for transfusion in order to improve their flexibility and workability. As the plasticizers are not chemically bonded to the PVC, they can be released into labile blood products (LBPs) during storage. Ideally, LBPs would be used in laboratory studies of plasticizer migration from the medical device. However, short supply (i.e., limited stocks of human blood in collection centres) has prompted the development of specific simulants for each type of LBP in the evaluation of new transfusion devices. We performed a Delphi study with a multidisciplinary panel of 24 experts. In the first (qualitative) phase, the panel developed consensus definitions of the specification criteria to be met by each migration simulant. Next, we reviewed the literature on techniques for simulating the migration of plasticizers into LBPs. A questionnaire was elaborated and sent out to the experts, and the replies were synthesized in order to obtain a consensus. The qualitative study established specifications for each biological matrix (whole blood, red blood cell concentrate, plasma, and platelet concentrate) and defined the criteria required for a suitable LBP simulant. Ten criteria were suggested: physical and chemical characteristics, opacity, form, stability, composition, ability to mimic a particular clinical situation, ease and safety of use, a simulant–plastic interaction correlated with blood, and compatibility with analytical methods. The questionnaire data revealed a consensus on the use of natural products (such as pig’s blood) to mimic the four LBPs. Opinions diverged with regard to synthetic products. However, an isotonic solution and a rheological property modifier were considered to be of value in the design of synthetic simulants. Consensus reached by the Delphi group could be used as a database for the development of simulants used to assess the migration of plasticizers from PVC bags into LBPs.

Spectral Doppler Measurements With 2-D Sparse Arrays

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

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.

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.

Clinical Applicability of Assessment of Jugular Flow over the Individual Cardiac Cycle Compared with Current Ultrasound Methodology

There is growing interest in measuring cerebral venous outflow with ultrasound (US). However, results obtained with the current US Doppler methodology, which uses just a single value of cross-sectional area (CSA) of the vessel, are highly variable and inconclusive. The product of CSA and time-averaged velocity in the case of pulsatile vessels may be a possible source of error, particularly for a pulsatile vein like the internal jugular vein (IJV), where the cardiac pump transmits a sequence of well-established waves along the conduit. We herein propose a novel technique for US IJV flow assessment that accurately accounts for IJV CSA variations during the cardiac cycle. Five subjects were investigated with a high-resolution real-time B-mode video, synchronized with an electrocardiography trace. In this approach, CSA variations representing the pulsatility of the IJV are overlapped with the velocity curve obtained by the usual spectral Doppler trace. The overlap is then phased point by point using the electrocardiography pacemaker. This allows us to experimentally measure the velocity variation in relation to the change in CSA precisely, ultimately enabling calculation of IJV flow. (i) The sequence of CSA variation with respect to the electrocardiography waves corresponds exactly to the jugular venous pulse as measured in physiology. (ii) The methodology permits us to phase the velocity and CSA, which is ultimately what is currently lacking to precisely calculate the flow in the IJV with US. (iii) The time-averaged flow, calculated with the described technique, is very close to that calculated assuming a constant IJV CSA, whereas the time-dependent flow shows differs as much as 40%. (iv) Finally, we tested the accuracy of the technique with a methodology that may allow for universal assessment of the accuracy of each personal US-based evaluation of flow rate.

Pitfalls of Doppler Measurements for Arterial Blood Flow Quantification in Small Animal Research: A Study Based on Virtual Ultrasound Imaging

High-resolution Doppler is a popular tool for evaluating cardiovascular physiology in mutant mice, though its 1-D nature and spectral broadening processes complicate interpretation of the measurement. Hence, it is crucial for pre-clinical researchers to know how error sources in Doppler assessments reveal themselves in the murine arterial system. Therefore, we performed virtual Doppler experiments in a computer model of an aneurysmatic murine aorta with full control of the imaging and insonified fluid dynamics. We observed significant variability in Doppler performance and derived vascular indices depending on the interrogated flow, operator settings and signal processing. In particular, we found that (i) Doppler spectra in the upper aortic branches and celiac artery exhibited more broadening because of complex out-of-beam flow paths; (ii) mean frequency tracking outperforms tracking of the outer envelope, but is sensitive to errors in angle correction; and (iii) imaging depths deviating much from the elevation focus suffer from decreased spectral quality.

An ultrasonographic technique to assess the jugular venous pulse: a proof of concept

The purpose of the work described here was to investigate the feasibility of assessing the jugular venous pulse (JVP) using ultrasound (US) equipment. Three young healthy subjects underwent a B-mode US scan of the internal jugular vein (IJV) to acquire a sonogram sequence in the transverse plane. On each acquired sonogram, the IJV contour was manually traced, and both the cross-sectional area (CSA) and the perimeter were measured. The CSA data set represents the US jugular diagram (USJD). The arterial distension waveform of the subjects was compared with its USJD. The correlation between the CSA and the perimeter was assessed during the cardiac cycle to verify IJV distension. For each subject, a short sonogram sequence of a few seconds was recorded, and the USJD obtained exhibited periodic behavior. Furthermore, for all subjects, the CSA was found to be correlated with the perimeter (Pearson coefficient, R > 0.9), indicating that the IJV in supine position is distended. We compared 390 manually traced contours of the IJV cross-sectional area with corresponding values semi-automatically calculated by an algorithm developed in-house. For all subjects, the sensitivity, specificity and accuracy were around 95%, 85% and 90% respectively. We found that a diagram reflecting the JVP can be obtained by analyzing a B-mode sonogram sequence of the IJV; such a diagram can result in a new methodology to assess the IJV functionality.

Comparison of carotid artery blood velocity measurements by vector and standard Doppler approaches

Although severely affected by the angle dependency, carotid artery peak systolic velocity measurements are widely used for assessment of stenosis. In this study, blood peak systolic velocities in the common and internal carotid arteries of both healthy volunteers and patients with internal carotid artery stenosis were measured by two vector Doppler (VD) methods and compared with measurements obtained with the conventional spectral Doppler approach. Although the two VD techniques were completely different (using the transmission of focused beams and plane waves, respectively), the measurement results indicate that these techniques are nearly equivalent. The peak systolic velocities measured in 22 healthy common carotid arteries by the two VD techniques were very close (according to Bland-Altman analysis, the average difference was 3.2%, with limits of agreement of ± 8.6%). Application of Bland-Altman analysis to comparison of either VD technique with the spectral Doppler method provided a 21%-25% average difference with ± 13%-15% limits of agreement. Analysis of the results obtained from 15 internal carotid arteries led to similar conclusions, indicating significant overestimation of peak systolic velocity with the spectral Doppler method. Inter- and intra-operator repeatability measurements performed in a group of 8 healthy volunteers provided equivalent results for all of the methods (coefficients of variability in the range 2.7%-6.9%), even though the sonographers were not familiar with the VD methods. The results of this study suggest that the introduction of vector Doppler methods in commercial machines may finally be considered mature and capable of overcoming the angle-dependent overestimation typical of the standard spectral Doppler approach.

Accurate blood peak velocity estimation using spectral models and vector doppler

Ultrasound blood peak velocity estimates are routinely used for diagnostics, such as the grading of a stenosis. The peak velocity is typically assessed from the Doppler spectrum by locating the highest frequency detectable from noise. The selected frequency is then converted to velocity by the Doppler equation. This procedure contains several potential sources of error: the frequency selection is noise dependent and sensitive to the spectral broadening, which, in turn, is affected by the Doppler angle uncertainty. The result is, often, an inaccurate estimate. In this work we propose a new method that removes the aforementioned errors. The frequency is selected by exploiting a mathematical model of the Doppler spectrum that has recently been introduced. When a very large sample volume is used, which includes all the vessel section, the model is capable of predicting the exact threshold to be used without the need of broadening compensation. The angle ambiguity is solved by applying the threshold to the Doppler spectra measured from two different directions, according to the vector Doppler technique. The proposed approach has here been validated through Field II simulations, phantom experiments, and tests on volunteers by using defocused waves to insonify a large region from a linear array probe. A mean error lower than 1% and a mean coefficient of variability lower than 5% were measured in a variety of experimental conditions.

An improved Doppler model for obtaining accurate maximum blood velocities

Maximum blood velocity estimates are frequently required in diagnostic applications, including carotid stenosis evaluation, arteriovenous fistula inspection, and maternal-fetal examinations. However, the currently used methods for ultrasound measurements are inaccurate and often rely on applying heuristic thresholds to a Doppler power spectrum. A new method that uses a mathematical model to predict the correct threshold that should be used for maximum velocity measurements has recently been introduced. Although it is a valuable and deterministic tool, this method is limited to parabolic flows insonated by uniform pressure fields. In this work, a more generalized technique that overcomes such limitations is presented. The new approach, which uses an extended Doppler spectrum model, has been implemented in an experimental set-up based on a linear array probe that transmits defocused steered waves. The improved model has been validated by Field II simulations and phantom experiments on tubes with diameters between 2mm and 8mm. Using the spectral threshold suggested by the new model significantly higher accuracy estimates of the peak velocity can be achieved than are now clinically attained, including for narrow beams and non-parabolic velocity profiles. In particular, an accuracy of +1.2±2.5 cm/s has been obtained in phantom measurements for velocities ranging from 20 to 80 cm/s. This result represents an improvement that can significantly affect the way maximum blood velocity is investigated today.

Finding the peak velocity in a flow from its Doppler spectrum

The signal backscattered by blood cells crossing a sample volume produces a Doppler power spectrum determined by the scatterers¿ velocity distribution. Because of intrinsic spectral broadening, the peak Doppler frequency observed does not correspond to the peak velocity in the flow. Several methods have been proposed for estimating the maximum velocity component--an important clinical parameter--but these methods are approximate, based on heuristic thresholds that can be inaccurate and strongly affected by noise. Reported here is a method of modeling the Doppler power spectrum of a flow, and from that model, determining what Doppler frequency on the descending slope of the power spectrum corresponds to the peak velocity in the insonated flow. It is shown that, for a fully insonated flow with a parabolic velocity distribution, the peak velocity corresponds to the Doppler frequency at the half-power point on that slope. The method is demonstrated to be robust with regard to the effects of noise and valid for a wide range of acquisition parameters. Experimental maximum velocity measurements on steady flows with rates between 100 and 300 mL/min (peak velocity range 6.6 cm/s to 19.9 cm/s) show a mean bias error that is smaller than 1%.

Simultaneous ultrasound assessment of brachial artery shear stimulus and flow-mediated dilation during reactive hyperemia

In flow-mediated dilation (FMD) studies, brachial artery diameter changes due to reactive hyperaemia are typically measured through manual or automatic analysis of high resolution B-mode images while the stimulus of diameter change, i.e., the flow change, is qualitatively estimated by measuring the mean velocity in the vessel and assuming a parabolic velocity profile. This article describes an experimental approach to simultaneously measure the wall shear rate (WSR) and the diameter variations, through multigate spectral Doppler and B-mode image processing, respectively. By using an ultrasound advanced open platform (ULA-OP), experimental results from the brachial arteries of 15 presumed healthy volunteers have been obtained. The mean increments during reflow against baseline were 105% ± 22% for the peak WSR and 8% ± 3% for the FMD. The mean time interval between the WSR peak and the beginning of plateau of diameter waveform was 38 ± 8 s. The results confirm that in young healthy subjects the postischemic vasodilation of brachial artery is largely correlated to the WSR increase.

Comparison of blood velocity measurements between ultrasound Doppler and accelerated phase-contrast MR angiography in small arteries with disturbed flow

Ultrasound Doppler (UD) velocity measurements are commonly used to quantify blood flow velocities in vivo. The aim of our work was to investigate the accuracy of in vivo spectral Doppler measurements of velocity waveforms. Waveforms were derived from spectral Doppler signals and corrected for intrinsic spectral broadening errors by applying a previously published algorithm. The method was tested in a canine aneurysm model by determining velocities in small arteries (3-4 mm diameter) near the aneurysm where there was moderately disturbed flow. Doppler results were compared to velocity measurements in the same arteries acquired with a rapid volumetric phase contrast MR angiography technique named phase contrast vastly undersampled isotropic projection reconstruction magnetic resonance angiography (PC-VIPR MRA). After correcting for intrinsic spectral broadening, there was a high degree of correlation between velocities obtained by the real-time UD and the accelerated PC-MRA technique. The peak systolic velocity yielded a linear correlation coefficient of r = 0.83, end diastolic velocity resulted in r = 0.81, and temporally averaged mean velocity resulted in r = 0.76. The overall velocity waveforms obtained by the two techniques were also highly correlated (r = 0.89 ± 0.06). There were, however, only weak correlations for the pulsatility index (PI: 0.25) and resistive index (RI: 0.14) derived from the two techniques. Results demonstrate that to avoid overestimations of peak systolic velocities, the results for UD must be carefully corrected to compensate for errors caused by intrinsic spectral broadening.

Improved transverse flow estimation using differential maximum Doppler frequency

Conventional Doppler technique can only provide the axial component of the blood flow vector, which is actually a three dimensional (3-D) quantity. To acquire the complete flow vector, estimations of the other two velocity components are essential. For the two dimensional (2-D) Doppler-bandwidth-based transverse estimation, however, accuracy is generally limited because of the complex dependence of the Doppler spectral shape on the flow variation within the sample volume. Two factors that may lead to the Doppler spectral change were considered in this study. One is the position offset of the sample volume and the other is the length of the sample volume. Simulations were performed and experimental data were also collected. Results indicate that the position offset may result in severe underestimation of Doppler shift frequency. Consequently, Doppler bandwidth is overestimated when it is determined by the difference between Doppler shift frequency and maximum Doppler frequency. Compared with the position offset, influence of the length of sample volume on the Doppler bandwidth is minor. To overcome this problem, a novel method, which is based on the differential maximum Doppler frequency, is proposed. Specifically, two beams with different beam widths are simultaneously generated to observe the blood flow and the difference between the corresponding maximum Doppler frequencies is used to estimate the transverse velocity. It is demonstrated that the accuracy and stability of transverse estimation are significantly improved by the proposed method even when the position offset is present.

Noninvasive simultaneous assessment of wall shear rate and wall distension in carotid arteries

A novel technique has been developed for the noninvasive real-time simultaneous assessment of both blood velocity profile and wall displacements in human arteries. The novel technique is based on the use of two ultrasound beams, one set at optimal angle for wall motion measurements and the other for blood velocity profile measurements. The technique was implemented on a linear array probe divided into two subapertures. A modified commercial ultrasound machine and a custom PC board based on a high-speed digital signal processor was used to process the quadrature demodulated echo signals and display results in realtime. Flow phantom experiments demonstrated the validity of the technique, providing wall shear rate (WSR) estimates within 10% of the theoretical values. The system was also tested in the common carotid arteries of 16 healthy volunteers (age 30 to 53 y). Results of simultaneous diameter distension and WSR measurements were in agreement with published data.

An improved spectral width Doppler method for estimating Doppler angles in flows with existence of velocity gradients

Doppler angle (i.e., beam-to-flow angle) is an important parameter for quantitative flow measurements. With known Doppler angles, volumetric flows can be obtained by the mean flow velocity times the cross-section area of the vessel. The differences or changes between prestenotic and poststenotic volumetric flows have been quantified as an indicator for assessing the clinical severity of the stenosis. Therefore, several research groups have dedicated themselves to developing user-independent methods to determine automatically the Doppler angle. Nevertheless, most of these methods were developed for narrow ultrasound beam measurements. For small vessels, where the beam width is a significant fraction of the diameter of the vessel, the effect of velocity gradients plays an important role and should not be ignored in the Doppler angle estimations. Accordingly, this paper is concerned with a method for improving the estimation of Doppler angles from spectral width Doppler (SWD) method, but correcting for velocity-gradient broadening that may arise when the beam has a nonzero width. In our method, Doppler angles were firstly calculated by SWD and then were corrected by an artificial neural network (ANN) method to neutralize the contribution of velocity gradient broadening (VGB). This SWD and ANN conjoint method has been successfully applied to estimate Doppler angles from 50 degrees to 80 degrees for constant flows in 10 mm, 4 mm and 1 mm diameter tubes, whose mean flow velocities were 15.3, 19.9 and 25.5 cm/s, respectively, and the achieved mean absolute errors of the estimated Doppler angles were 1.46 degrees , 1.01 degrees and 1.3 degrees.

Vector-velocity estimation in swept-scan using a K-space approach

The swept-scan technique (i.e., continuously moving a single-crystal transducer during pulse-echo data acquisition) is used in high-frequency, ultrasonic flow imaging. Relative to the conventional step-scan technique, swept scanning improves the rate of data acquisition and enables near-real-time, high-frequency color flow mapping. However, the continuous transducer movement may have non-negligible effects on accuracy of velocity estimation. This paper introduces a spatial frequency domain (i.e., k-space) approach that quantifies the effects of both lateral and axial motions in a swept scan. It is shown that the k-space representation is equivalent to a Doppler-radio frequency (RF) frequency domain representation, and that transducer movement in the swept-scan technique results in a change in Doppler bandwidth. In addition, a vector velocity estimator is developed based on the proposed k-space approach. Both simulations and flow-phantom experiments were performed to evaluate the performance of the proposed vector velocity estimator. A 45-MHz transducer was scanned at 20 mm/s. The Doppler angle ranged from 29 degrees to 90 degrees, and the flow velocities ranged from 15 to 30 mm/s. The results show that the proposed k-space vector velocity estimator exhibited a mean error of 2.6 degrees for flow-direction estimation, with the standard deviation ranging from 2.2 degrees to 8.2 degrees. In comparison, for the conventional spectral-broadening-based vector velocity estimator ignoring the swept-scan effect, the mean error became 15 degrees and the standard deviations were from 2.7 degrees to 6.6 degrees.

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

In Doppler ultrasound, transit-time broadening arises from the finite scatterer transit time through the sample volume. As a unifying description of this broadening mechanism, a generalized amplitude modulation signal model was developed to collectively account for the transit-time effects of the ultrasound beam geometry and the range gate characteristics. Simulations based on a pulsed linear-array system also were performed to study the broadening extent for different scatterer flow lines. With our signal model and simulation results, some generalized insights were obtained on the characteristics of transit-time broadening. First, as consistent with previous findings, we found that, for scatterers passing though the center of the sample volume, the broadening extent mainly depends on beam-forming characteristics at higher beam-flow angles, but it is more dependent on range gate parameters at smaller angles. Second, for the central flow line, a transition angle exists in which a significant change occurs in the governing parameters of transit-time broadening. Third, for the general case in which scatterers undertake an off-central path through the sample volume, the broadening extent depends on both the beam geometry and the range gate. Bandwidth skewing and further spectral broadening also can be seen for these off-central flow lines.

Sample volume shape for pulsed-flow velocity estimation using a linear array

Various definitions of the sample volume (SV) shape have been proposed, but they are mostly based on transducers with axisymmetrical geometry. We have defined the SV as that spatial region in which scatterers contribute a component to the total gated received-signal energy above a defined threshold. This definition is consistent with modern pulsed transducer arrays and accounts for the need to impose a signal/noise threshold. Based on this definition, SVs for a typical linear phased-array transducer were simulated using custom-designed software. The effects of different transmit pulses, receive gates, apertures, SV depths and lateral foci were studied using a one-dimensional (1-D) beam-forming array, with a fixed lens in the elevation direction. Based on a simplified method of analysis, the features of the beam-steered SV are qualitatively similar to those of the nonsteered SV, when compared at the same beam-flow angle. These studies have helped provide a clearer understanding of the manner in which the SV energy distribution is affected by various parameters. The results can have potentially significant implications in the use of ultrasound (US) for blood velocity estimation, specifically with respect to locating the SV within the blood vessel and the origin of the velocity spectrum.

A new method of ultrasound color flow mapping

Conventional ultrasound color flow mapping systems estimate and visualize only the axial velocity component. To obtain the transverse velocity component a modification of a multiple-beam method is proposed. The new two-dimensional color flow mapping system has a small size and consists of three transducers. The central transducer is an appodized and focused phased array. The other transducers are unfocused probes. Three transducers act as receivers and the central transducer operates as a transmitter. All receivers acquire rf scan lines that are then processed to estimate three axial velocity components using an autocorrelation method. These estimates are then combined to estimate the transverse velocity component, taking into account the geometric relationships among three transducers. Two algorithms for transverse velocity estimation are proposed. The first uses the Doppler angle estimate for calculation of the transverse velocity component. The other algorithm calculates the transverse velocity component directly from the axial components. The accuracy of the flow velocity estimators is estimated by simulations. Analysis of accuracy allows choosing the more effective algorithm for two-dimensional velocity estimation, which is insensitive to variations of the Doppler angle.

Spectral power density calculations for pulsed Doppler

Range-gated pulsed Doppler can be used to make localized velocity measurements within a blood vessel. A spectral flow profile can be created by stepping a sufficiently small sample volume across the lumen, but no set of spectra will correspond directly to the true velocity profile. Spectral flow profiles are affected by a complex interplay between different sources of spectral broadening. In this study we developed a systematic theoretical method which allows spectral power density functions to be calculated under a very wide range of conditions, and used it to obtain simulated flow spectra. The model was formulated analytically. It is based on the weighted-volume approach and incorporates, through the concept of a spread function, the intrinsic spectral broadening associated with a focused transducer. It can be applied for arbitrary values of the spread parameter; for non-uniform beam profiles; with maximal (continuous wave-type) or minimal (pulse wave-type) range-gated sample volumes; and for beams that intersect the flow tube axis, or are off centre. Results are presented for a Gaussian beam and parabolic flow. Simulated spectral flow profiles are given which illustrate how a profile's appearance can be altered by the different sources of spectral broadening.

Doppler angle estimation using AR modeling

The transit time spectrum broadening effect has long been explored for Doppler angle estimation. Given acoustic beam geometry, the Doppler angle can be derived based on the mean Doppler frequency and the Doppler bandwidth. Spectral estimators based on the fast Fourier transform (FFT) are typically used. One problem with this approach is that a long data acquisition time is required to achieve adequate spectral resolution, with typically 32-128 flow samples being needed. This makes the method unsuitable for real-time two-dimensional Doppler imaging. This paper proposes using an autoregressive (AR) model to obtain the Doppler spectrum using a small number (e.g., eight) of flow samples. The flow samples are properly selected, then extrapolated to ensure adequate spectral resolution. Because only a small number of samples are used, the data acquisition time is significantly reduced and real-time, two-dimensional Doppler angle estimation becomes feasible. The approach was evaluated using both simulated and experimental data. Flows with various degrees of velocity gradient were simulated, with the Doppler angle ranging from 20 degrees to 75 degrees. The results indicate that the AR method generally provided accurate Doppler bandwidth estimates. In addition, the AR method outperformed the FFT method at smaller Doppler angles. The experimental data for Doppler angles, ranging from 33 degrees to 72 degrees, showed that the AR method using only eight flow samples had an average estimation error of 3.6 degrees, which compares favorably to the average error of 4.7 degrees for the FFT method using 64 flow samples. Because accurate estimates can be obtained using a small number of flow samples, it is concluded that real-time, two-dimensional estimation of the Doppler angle over a wide range of angles is possible using the AR method.

Doppler angle estimation of pulsatile flows using AR modeling

In quantitative ultrasonic flow measurements, the beam-to-flow angle (i.e., Doppler angle) is an important parameter. An autoregressive (AR) spectral analysis technique in combination with the Doppler spectrum broadening effect was previously proposed to estimate the Doppler angle. Since only a limited number of flow samples are used, real-time two-dimensional Doppler angle estimation is possible. The method was validated for laminar flows with constant velocities. In clinical applications, the flow pulsation needs to be considered. For pulsatile flows, the flow velocity is time-varying and the accuracy of Doppler angle estimation may be affected. In this paper, the AR method using only a limited number of flow samples was applied to Doppler angle estimation of pulsatile flows. The flow samples were properly selected to derive the AR coefficients and then more samples were extrapolated based on the AR model. The proposed method was verified by both simulations and in vitro experiments. A wide range of Doppler angles (from 3o degrees to 78 degrees) and different flow rates were considered. The experimental data for the Doppler angle showed that the AR method using eight flow samples had an average estimation error of 3.50 degrees compared to an average error of 7.08 degrees for the Fast Fourier Transform (FFT) method using 64 flow samples. Results indicated that the AR method not only provided accurate Doppler angle estimates, but also outperformed the conventional FFT method in pulsatile flows. This is because the short data acquisition time is less affected by the temporal velocity changes. It is concluded that real-time two-dimensional estimation of the Doppler angle is possible using the AR method in the presence of pulsatile flows. In addition, Doppler angle estimation with turbulent flows is also discussed. Results show that both the AR and FFT methods are not adequate due to the spectral broadening effects from the turbulence.

The impact of theoretical errors on velocity estimation and accuracy of duplex grading of carotid stenosis

Two potential errors in velocity estimation, Doppler angle misalignment and intrinsic spectral broadening (ISB), were determined and used to correct recorded blood velocities obtained from 20 patients (38 bifurcations). The recorded and corrected velocities were used to grade stenoses of greater than 70% using two duplex classification schemes. The first scheme used a peak systolic velocity (PSV) of > 250 cm/s in the internal carotid artery (ICA), and the second a PSV ratio of > 3.4 (ICA PSV/common carotid artery PSV). The "gold standard" was digital subtraction angiography (DSA). The maximum error in velocity estimation due to Doppler angle misalignment was 33 cm/s, but this did not alter sensitivity of stenosis detection. ISB correction caused a reduction in PSV that decreased the sensitivity of the PSV scheme from 65% to 45%. The PSV ratio classification was not affected by ISB errors. Centres using a PSV criterion for grading stenosis should use a fixed Doppler angle and should establish velocity thresholds in-house.

Sources of error in maximum velocity estimation using linear phased-array Doppler systems with steady flow

Using linear-array Doppler ultrasound (US) transducers, the measured maximum velocity may be in error and lead to incorrect clinical diagnosis. This study investigates the existence and cause of maximum velocity estimation errors for steady flow of a blood-mimicking fluid in a tissue-mimicking phantom. A specially designed system was used that enabled fine control of flow rate, transducer positioning and transducer angle relative to the flow phantom. Doppler machine settings (transducer aperture size, focal depth, beam-steering, gain) were varied to investigate a wide range of clinical applications. To estimate the maximum velocity, a new signal-to-noise ratio (SNR) independent method was developed to calculate the maximum frequency from an ensemble averaged Doppler power spectrum. This enabled the impact of each factor on the total Doppler error to be determined. When using the new maximum frequency estimator, it was found that the effect of transducer focal depth, intratransducer, intramachine, intermachine (that was tested) and beam-steering did not significantly contribute to maximum velocity estimation errors. Instead, it was the dependence of the maximum velocity on the Doppler angle that made, by far, the greatest contribution to the estimation error. Because our maximum frequency estimator took into account the effect of intrinsic spectral broadening, the degree of overestimation error was not as great as that previously published. Thus, the effects of Doppler angle and intrinsic spectral broadening are the chief sources of Doppler US error and should be the focus of future efforts to improve the accuracy.

Intrinsic spectral broadening (ISB) in ultrasound Doppler as a combination of transit time and local geometrical broadening

Doppler signals collected with a focused transducer are known to be affected by the so-called intrinsic spectral broadening (ISB). This article aims to point out how ISB is, in general, related to both the limited lateral extent of a focused beam (leading to a finite transit time), and the presence of several local insonation angles around the beam axis, due to focusing and diffraction effects (local geometrical broadening). The influence of these two elementary spectral contributions on the whole ISB is shown by considering the Doppler signal as simultaneously modulated in amplitude and frequency, and applying well-known relationships employed in the communication field. Such an analysis reveals that transit time and local geometrical broadening are two different phenomena, whose simultaneous knowledge is necessary for correctly evaluating the overall ISB. Finally, thanks to a novel technique for separately measuring transit time and local geometrical broadening effects on transducers with markedly different focusing properties, more than 1000 experimental acquisitions show how a proper combination of such measured contributions gives an accurate ISB estimation, confirming the theoretical expectations.

Application of autoregressive methods to multigate spectral analysis

Multigate analysis is known to be capable of detecting accurate blood velocity profiles from human vessels. Experimental systems so far presented in the literature use time-domain frequency estimations and, more recently, the fast Fourier transform (FFT) for real-time analysis of Doppler signals from multiple range cells. This experimental study is aimed at evaluating the application of an autoregressive (AR) method (Burg algorithm) to multigate Doppler analysis. Both in vitro and in vivo results were collected with a commercial Duplex scanner coupled with a prototype multigate unit developed in our laboratory. The same multigate signals are, thus, processed according to both the FFT and the Burg algorithms. The related spectral and maximum frequency profiles are reported and statistically compared. AR, implemented with the Burg algorithm, is demonstrated to be a way to perform multigate spectral analysis with reduced spectral variance, suitable for maximum velocity profile extraction through a simple threshold.

Implementation of spectral width Doppler in pulsatile flow measurements

In this paper, we present an automatic beam-vector (Doppler) angle and flow velocity measurement method and implement it in pulsatile flow measurements using a clinical Doppler ultrasound system. In current clinical Doppler ultrasound flow velocity measurements, the axis of the blood vessel needs to be set manually on the B-scan image to enable the estimation of the beam-vector angle and the beam-vector angle corrected flow velocity (the actual flow velocity). In this study, an annular array transducer was used to generate a conical-shaped and symmetrically focused ultrasound beam to measure the flow velocity vectors parallel and perpendicular to the ultrasound beam axis. The beam-vector angle and flow velocity is calculated from the mode frequency (f(d)) and the maximum Doppler frequency (f(max)) of the Doppler spectrum. We develop a spectrum normalization algorithm to enable the Doppler spectrum averaging using the spectra obtained within a single cardiac cycle. The Doppler spectrum averaging process reduces the noise level in the Doppler spectrum and also enables the calculation of the beam-vector angle and flow velocity for pulsatile flows to be measured. We have verified the measurement method in vivo over a wide range of angles, from 52 degrees to 80 degrees, and the standard deviations of the measured beam-vector angles and flow velocities in the carotid artery are lower than 2.2 degrees and 12 cm/s (about 13.3%), respectively.

Detection of vascular haemodynamics through a high-speed velocity profiler

OBJECTIVE

This paper aims at demonstrating that ultrasound Doppler multigate spectral analysis performed with advanced equipment may provide detailed and significant haemodynamic information.

METHODS

A novel multigate system was recently introduced and shown capable of performing real-time spectral analysis of Doppler data from 64 resolution cells located at different depths from the transducer. The system extends the typical capabilities of conventional Pulsed Wave (PW) equipment by displaying the full spectral content of Doppler signals over an ultrasound scan line rather than in a single resolution cell. In cases where it is appropriate to display the available information in a simpler form, parameters such as the maximum frequency can be extracted from each spectrum, by using conventional or advanced image processing methods.

RESULTS

In-vitro experiments show that the multigate system can perform velocity measurements with good accuracy and precision. Examples of in vivo profiles detected from carotid, femoral and radial arteries are presented. In particular, the first results obtained from the aorta are shown.

CONCLUSIONS

Blood flow behavior can be accurately investigated using a real-time multigate system which extends Doppler spectral analysis to a whole scan line.

Effect of catheter placement on 3-D velocity profiles in curved tubes resembling the human coronary system

Novel measurement techniques based on intravenous ultrasound (IVUS) technology ('IVUS-Flowmetry') require the location of a catheter inside the coronary bed. The present study quantifies disturbances in the 3-D velocity profile induced by catheter placement inside a tube, applying computational fluid dynamics. Two curved, circular meshes (radius K = 0.025 m and K = 0.035 m) with and without a catheter inside the lumen were applied. The catheter was located at the inner curve, the outer curve and at the top position. Boundary conditions were: no slip on the wall, zero stress at the outlet, uniform inflow with entrance velocities of 0.1, 0.2 and 0.4 m/s. Curvature-associated centrifugal forces shifted the maximal velocity to the outer curve and introduced two symmetrical vortices. Additional catheter placement redistributed the 3-D axial velocity field away from the catheter, which was accompanied by the appearance of multiple low-strength vortices. In addition, peak axial velocity increased, peak secondary velocities decreased, axial pressure drop increased and shear stress increased. Flow calculations simulated to resemble IVUS-based flowmetry changed by only 1% after considering secondary velocity. In conclusion, placement of a catheter inside a curved tube resembling the human coronary system changes the velocity field and reduces secondary patterns. The present study supports the usefulness of catheter-based flowmetry during resting flow conditions. During hyperemic flow conditions, flow measurements might be accompanied by large axial pressure drops because the catheter, itself, might act as a significant stenosis.

A comparison of single- and dual-beam methods for maximum velocity estimation

The purpose of this study was to compare the precision and accuracy of maximum velocity estimation when the target direction is known (a string phantom), and when the target direction is unknown (a flow model of arterial stenosis with stenoses of 0-80% by area). Maximum velocity was estimated using single- and dual-beam methods. A linear-array system was used to acquire Doppler spectra from a single-beam direction. The same array was used for sequential acquisition of Doppler spectra from 2 beam directions; the velocity estimates from these were then compounded in a vector manner. The variation of estimated maximum velocity with beam-string angle over the range 40-80 degrees was 27% for conventional Doppler, 2.6% for angle correction from the edge of the array and 1.6% for the vector Doppler. In the stenosis model, for the single-beam methods, the highest frequency shift was obtained just prior to the point of minimum lumen. At this location, the variation with beam-vessel angle over the range 40-80 degrees was 35% for conventional Doppler, 7.4% for the correction factor method and 6.9% for correction from the edge of the array. For the vector method, the maximum velocity is obtained from within the poststenotic jet, the variation was 2% over the range 40-80 degrees. It is recommended that existing Doppler systems use the correction-factor method to reduce variation in measured maximum velocity. The use of the vector technique by future generations of Doppler systems may lead to angle-independent velocity estimation.

Doppler angle and flow velocity estimations using the classic and transverse Doppler effects

Current clinical Doppler ultrasound systems could only measure the flow vector parallel to the ultrasound beam axis, and the knowledge of the Doppler angle (beam-to-flow angle) is needed to calculate the real flow velocity. Currently, the Doppler angle is determined visually by manually aligning a vessel axis marker along the blood vessel on the duplex scan image of the ultrasound. The application of this procedure is often limited by practical constraints; therefore, measurements are not reliable. In order to overcome this problem, the authors developed a simple Doppler angle and flow velocity estimation method using a combination of the classic and transverse Doppler effects. This method uses only a single focused annular array transducer to estimate the Doppler angle and the flow velocity. The authors have verified experimentally that this method is successful for measuring constant flow in a flow phantom between 45 degrees and 80 degrees Doppler angle. The standard deviation of the estimated Doppler angles is less than 4.5 degrees . This method could be implemented easily in medical Doppler ultrasound systems to automatically estimate the Doppler angle and the flow velocity.

Estimation of axial blood velocity using the Doppler equation corrected for broadening

To estimate axial velocity for vessels that are so narrow that their width is comparable to the minimum length of the range cell, it has been customary to substitute the maximum Doppler frequency fmax into the classical Doppler equation [eqn (1)]. It was shown here that this ignores transit time broadening, which can lead to significant errors at large beam-to-flow angles. We use a relation [eqn (2)], which does take this broadening into account, and give in vivo experimental proof of this allows accurate estimation of the axial velocity even when the range cell extends across the whole vessel lumen. It may be concluded, therefore, that, by using the above procedure for taking transit time spectral broadening into account, more accurate velocity estimates can be obtained for laminar flow than is possible with the current method using the classical Doppler equation uncorrected for broadening.

Correction of intrinsic spectral broadening errors in Doppler peak velocity measurements made with phased sector and linear array transducers

Commercial duplex ultrasound systems primarily measure peak velocity of blood flow to provide important information in diagnosing vascular disease. However, due to errors caused by intrinsic spectral broadening (ISB), the accuracy decreases as the Doppler angle increases. In general, vascular technologists and surgeons keep the Doppler angle under 60 degrees. Even at 60 degrees, ISB can produce an overestimation of peak velocity as high as 40%. This would indicate the necessity of reducing the Doppler angle even lower than 60 degrees. Since most vessels in the body run parallel with the skin surface any criteria requiring a Doppler angle of say 45 degrees or less would be difficult to achieve. Using the transverse Doppler equation as a correction for ISB, in conjunction with the classical Doppler equation, accurate peak velocity measurements were obtained at Doppler angles as high as 80 degrees. Corrections were made using both phased sector and linear array transducers for steered and unsteered beams. However, for beams steered at large angles, 20 degrees or more, corresponding to Doppler angles of < 70 degrees, the transverse Doppler equation failed to correct ISB errors in measurements made. This may be due to the experimental setup and not due to limitations in the transverse Doppler equation.