accuracy and reproducibility of a novel dual-beam vector doppler method

Ultrasound in Med. & Biol., Vol. 35, No. 5, pp. 829–838, 2009Copyright © 2009 World Federation for Ultrasound in Medicine & Biology

Printed in the USA. All rights reserved0301-5629/09/$–see front matter

doi:10.1016/j.ultrasmedbio.2008.10.012

● Original Contribution

ACCURACY AND REPRODUCIBILITY OF A NOVEL DUAL-BEAMVECTOR DOPPLER METHOD

STEFANO RICCI, STEFANO DICIOTTI, LORENZO FRANCALANCI, and PIERO TORTOLI

Department of Electronics and Telecommunications, Università degli Studi di Firenze, Firenze, Italy

(Received 18 July 2008; revised 13 October 2008; in final form 24 October 2008)

Abstract—Conventional Doppler ultrasound (US) investigations are limited to detect only the axial componentof the blood velocity vector. A novel dual-beam method has been recently proposed in which the Doppler angleis estimated through a reference US beam, and the velocity magnitude through a measuring US beam,respectively. In this study, the performance of such a method has been assessed quantitatively through in vitroand in vivo measurements made in different experimental conditions. In vitro, more than 300 acquisitions werecompleted using seven transducers to insonify a straight tube phantom at different Doppler angles. In steadylaminar flow conditions, the velocity magnitude was measured with mean error of –1.9% (95% confidenceinterval: –2.33% to –1.47%) and standard deviation of 3.4%, with respect to a reference velocity. In pulsatile flowconditions, reproducibility tests of the entire velocity waveforms provided an average coefficient of variation(CV) of 6.9%. For peak velocity measurements made at five Doppler angles and three flow rates, the intrasessionand intersession CVs were in the range 0.8–3.7% and 2.9–10.6%, respectively. The peak systolic velocities (PSVs)in the common carotid arteries of 21 volunteers were estimated with 95% limits of agreement of � 9.6 cm/s(intersession). This analysis shows that the proposed dual-beam method is capable of overcoming the Dopplerangle ambiguity by producing reliable velocity measurements over a large set of experimental conditions.(E-mail: [email protected]) © 2009 World Federation for Ultrasound in Medicine & Biology.

Key Words: Ultrasound, Vector Doppler, Dual-beam method, Angle-dependence, Blood velocity measurement,
Accuracy, Reproducibility, Carotid artery.
INTRODUCTION

The accuracy of Doppler ultrasound (US) velocity mea-surements is known to suffer for several possible sourcesof error, including translation and angle misregistrations,spectral broadening, tissue inhomogeneities and noise(Gill 1985; Jones 1993; Steinman et al. 2001; Thrush andEvans 1995; Willink and Evans 1995). Particularly rel-evant is the so-called Doppler angle ambiguity, whichconsists in the difficulty of estimating the orientation ofblood flow to the US beam, as requested to convert themeasured Doppler frequency to velocity.

The standard method to overcome this problem isstill represented by the manual alignment of the anglecursor with the vessel wall (Evans and McDicken 2000).However, this approach is devoted to fail when the flowis not aligned with the vessel axis or when the vessel istortuous (Landwehr et al. 2001). Moreover, it results

Address correspondence to: Piero Tortoli, Università degli Studi
di Firenze, Department of Electronics and Telecommunications, Via S.Marta N.3, 50139 Firenze, Italy. E-mail: [email protected]
829

operator- and machine-dependent even when tested byexperienced vascular technologists (Corriveau and John-stone 2004; Fillinger et al. 1996; Logason et al. 2001).

A possible alternative to solve the Doppler angleambiguity is represented by cross-beam techniques(Dunmire et al. 2000), which perform multiple Dopplerfrequency measurements of echo-data from a samplevolume (SV) insonified by US beams oriented alongdifferent directions. Through a trigonometric combina-tion of the Doppler equations related to each beam, thevelocity magnitude is estimated by correcting for thebeam-flow angle. It has been proven that dual-beamvector Doppler US can provide considerably reducedangle-dependence with respect to single-beam systems(Hoskins 1999). However, the main weakness of suchcross-beam methods is that the error sources that typi-cally affect single beam systems can be amplified, espe-cially at small interbeam angles, thus providing largererrors in the resulting velocity estimate (Steel and Fish2002). Steel et al. (2004) also showed that there is aresidual angle-dependence in dual-beam Doppler mea-
surements. Using a modified linear-array system with a
mailto:[email protected]

mailto:[email protected]

830 Ultrasound in Medicine and Biology Volume 35, Number 5, 2009

split receive aperture, they found that the peak systolicvelocity (PSV) estimated in the common carotid arteries(CCA) of nine volunteers was reduced by approximately7.9% as the angle between the transmit beam and thevessel axis was increased from 40–70°.

A novel dual-beam method has been introducedrecently (Tortoli et al. 2006a), characterized by the dif-ferent role played by each beam. One of the beams actsas “reference,” being devoted to estimate only the flowdirection. Such a goal is achieved by identifying thebeam-flow angle, which produces symmetrical spectrafrom the SV of interest, a unique signature of transverseDoppler angles (Newhouse et al. 1987). Once the flowdirection has been identified, the second beam can di-rectly estimate the velocity magnitude through a singleangle-corrected Doppler frequency measurement.

In this paper, the performance of the proposed dual-beam method is quantitatively assessed through in vitrovelocity measurements made in a variety of experimentalconditions. In vivo reproducibility is also estimated bymeasuring the velocity in the center streamlines of thecommon carotid arteries of 21 presumed healthy volun-teers.

MATERIALS AND METHODS

Dual-beam techniqueIn the novel technique, one beam is directed along

the reference line (RL), which should be ideally perpen-dicular (� � 90°) to the target flow, whereas the secondone is directed along the measuring line (ML), which isinclined by a known interbeam angle, � (see Fig. 1).

The orthogonal direction of the RL can be achievedby exploiting the unique features of transverse Dopplerspectrum. As demonstrated both in vitro and in vivo,transverse Doppler spectra are substantially symmetrical

MLRL

θ

δ

εFlow

Fig. 1. The velocity measurement method is based on twoDoppler lines playing different roles: the reference line (RL)should identify the transverse flow orientation (� � 90°), whilethe measuring line (ML) allows a classic Doppler measurement

to be made with known beam-flow angle, � � 90° – �.

around the zero mean frequency (Newhouse et al.1987;

Tortoli at al. 1993). Such a spectral feature is derivedfrom the transducer focusing properties, which involve aset of effective beam-flow angles equally distributedaround the nominal Doppler angle (Censor et al. 1988).

The degree of spectral symmetry can be quantita-tively evaluated through the use of a spectral symmetryindex (SSI) defined as:

SSI(%) � min�P�

P�

;P�

P�� 100 (1)

where P� and P– represent the spectral power estimatedover the positive and negative Doppler sub-bands, re-spectively. When � is closer to 90°, the SSI is expectedto be higher. This was experimentally confirmed in Tor-toli et al. (2006a), where the results of SSI measurementsmade at different flow velocities for a range of � 5°around a nominal 90° Doppler angle were reported. A �1° angle deviation was sufficient to move the SSI below85%, and when the angle error reached � 5° the SSIcollapsed below 10%. This high sensitivity to deviationsfrom the ideal 90° orientation is consistent with thedependency of mean Doppler frequency on the cosine ofthe beam-flow angle.

These unique characteristics of the transverseDoppler spectrum are exploited to solve the Dopplerangle ambiguity. Through a control of the SSI values, theRL can be oriented so that the beam-flow angle � can beassumed equal to 90°. In such a condition the ML-to-flow angle is given by:

� � 90 ° ��, (2)

and a standard Doppler frequency measurement can beused to directly estimate the velocity magnitude in theSV of interest.

Flow phantomThe dual-beam velocity measurement technique has

been tested in a flow phantom equipped with a gearpump controlled by a PC. Both steady and pulsatile flowscould be set through the software that manages the pump.The pump forced a blood-mimicking fluid (BMF) to flowin a rigid tube with nominal 8 mm internal diameter,immersed in a water tank (see Fig. 2). The tube was madeby Rilsan®, a plastic material characterized by a soundpropagation velocity of 2600 m/s and an attenuation ofabout 2 dB cm–1 MHz–1.

The BMF was prepared by dissolving 3.4g of Or-gasol® (Arkema Inc. Philadelphia, PA, USA) in 2 L ofdemineralized water (Ramnarine et al. 1998). To obtaina uniform particle distribution, 1.8g of surface-activeagent (Synperonic N, BDH, Dorset, UK) was added tothe fluid, and the solution was stirred for at least 12 hours
before the start of each experiment. A special probe

Accuracy and reproducibility of dual-beam vector Doppler ● S. RICCI et al. 831

holder capable of supporting two probes with knowninterbeam angle was positioned over the water tank sothat the US beams could intercept the flow in the centerof the Rilsan® tube. The measurement site was placedabout 80 cm far from the Rilsan® tube inlet, where theflow profile could be supposed fully developed (Nicholset al. 2005). A precision mechanism allowed the holderto rotate and translate in the scan plane containing thetube and the beam axes.

In all the experiments, we used cylindrical, single-element transducers whose main features are reported inTable 1. In particular, the transducer directed along theRL, called reference transducer (RT), worked at 9 MHz,whereas seven transducers operating between 5.3 MHzand 9.5 MHz were used to be directed along the ML.Because they were dedicated to measure the Dopplerfrequency, they will be hereinafter referred to as mea-suring transducers (MT1-MT7).

Ultrasound systemThe RT and MT were connected to the MultiGate–

MultiChannel (MCMG) Doppler system, which is capa-ble of simultaneously controlling two US transducers.The MCMG system is based on a home-made digitalboard specifically designed to work as flexible platformfor US research activities (Ricci et al. 2006). The boardis connected through the Universal Serial Bus (USB) 2.0to a personal computer (PC) in which a specific softwareruns under Windows® (Microsoft. Corp. Redmond, WA,USA).

Each transmit channel includes an arbitrary wave-form generator capable of producing complex excitationsequences between 1 MHz and 16 MHz. The receivedechoes, after being conditioned through a band-pass filterand a programmable amplifier, are sampled at radiofre-quency (RF) by two 14-bit analog-to-digital convertersoperating at 64 MHz. A state-of-the-art field program-mable gate array (FPGA) from Stratix Family (Altera,

MCMG

Water Tank

Rilsan® pipe

RT MT

Holder

Pump

Fig. 2. Experimental set-up: a PC-controlled pump pushes ablood-mimicking fluid (BMF) in the Rilsan® pipe immersed inthe water tank. The MCMG Doppler system performs thedual-beam analysis of echo-signals backscattered from the

moving BMF.

San Jose, CA, USA) demodulates the RF samples to

generate in-phase and quadrature (I/Q) base-band signalcomponents. A floating-point Digital Signal Processor(DSP) from the TMS320C67� family (Texas Instru-ments, Austin, TX, USA) can access RF and I/Q data toprocess them in real time according to the user-pro-grammed algorithm. The results of the elaboration arefinally sent to the PC through the USB connection, sothat the operator can check the real-time display to set upthe acquisition parameters. Several seconds of RF and/orI/Q samples stored in a large circular SDRAM buffer canbe downloaded in a PC file at any time.

During the dual-beam measurements, the US burstswere alternatively transmitted from each transducer. Thetransmitter connected to the RT was programmed toproduce 2-cycle bursts at 9 MHz, whereas the frequencyand the number of cycles were adapted to the selectedMT in each experiment. Each channel of the MCMGsystem could be programmed to work either in standardpulse-wave (PW) spectral Doppler or in multigate spec-tral Doppler (MSD) mode. In PW mode, the echo datareceived from the selected SV were processed in real-time by the DSP to produce the Doppler spectrum. Fordata received from the RL, the related SSI was alsocalculated. The MSD mode (Tortoli et al. 2006b) con-sists in the application of spectral analysis to 128 Dopp-ler signals received from different depths along the USbeam axis. The distribution of Doppler frequencies invessels is dynamically displayed in real-time in the formof spectral profiles. As explained below in more detail,the MSD mode was used in vitro to check the laminarityof the flow, and in vivo to facilitate coarse probe posi-tioning at the beginning of each measurement session.

Steady flow measurementsThe measurements in steady flow conditions were

aimed to assess the accuracy and robustness of themethod. The accuracy was assessed by comparing themeasured velocity with a reference velocity, whereas therobustness was evaluated by repeating the test in differ-ent measurement conditions.

Table 1. Main features of transducers used in steady flowconditions

Transducer

Centralfrequency

(MHz)

Bandwidth(–6 dB)(MHz)

Focallength(mm)

Focal width(–6 dB)(mm)

RT 9.0 3.1 20 0.9MT1 5.5 3.8 30 2.2MT2 6.3 3.7 20 1.5MT3 9.5 3.6 18 0.8MT4 5.3 2.7 15 1.2MT5 6.8 7.5 15 1.1MT6 5.6 4.2 20 1.3
MT7 9.0 3.1 20 0.9


A steady laminar flow running in a “long” andstraight circular pipe develops a typical parabolic profile(Caro et al. 1978), with maximum velocity equal to:

Vr �8Q

� · D2 (3)

where D is the diameter of the tube and Q the volumetricrate. The accuracy in Vr assessment depends on severalfactors. These include the uncertainty in the knowledgeof D and Q, and the extent at which the actual velocityprofile approximates the theoretical parabolic shape. Themean internal diameter was here estimated equal to 7.98� 0.01 mm by measuring the weight of the water held ina specimen tube of known length. For each experiment,Q was measured by weighing about 400 mL of accumu-lated fluid with � 1g accuracy, corresponding to a �0.25% error in the volumetric flow estimation. Becauseof the inaccuracies on D and Q, the reference velocity,Vr, was affected by an uncertainty 0.5%.

We used the MCMG system in MSD mode to verifythe flow conditions during the experiments. For eachpump setting, the actual flow profile was extrapolatedand compared to the ideal parabola. This analysisshowed that a satisfactory parabolic flow was establishedwhenever Vr was less than about 20 cm/s, correspondingto a 1200 Reynolds number.

Using the experimental set-up described above,more than 240 velocity measurements were made. Foreach measurement session one of the available transduc-ers was selected, and at least one of the parametersshown in Table 2 was changed. In particular, the TX toneburst length and the overall bandwidth of the TX-RXchain were set to produce SVs with axial lengths be-tween 0.3 mm and 1 mm. By locating such small SVs incorrespondence of the tube axis, we assumed that asingle velocity component (coincident with the maxi-mum velocity of the parabolic profile) contributed to theDoppler signal.

At the beginning of each acquisition, the probeholder was arbitrarily placed over the tube. A trainedoperator, while observing the RL spectrogram and the

Table 2. Experimental conditions used in steady flowmeasurements

Experimental conditions Values Unit

Measuring Transducer T1, T2, . . . , T6, T7 —Doppler angle 50, 60, 70, 80 °Max reference velocity (Vr) 8.8, 11.6, 15.4, 18.1 cm/sPRF 1, 2, 3 kHzN. of TX sinusoidal cycles 1, 2, 3 —Overall bandwidth 1, 2 MHz

SSI, rotated the holder and adjusted the SV position until

the transverse RT orientation was achieved (i.e., SSI�85%). After locking the holder, the operator tuned thedepth of the SV along the ML until the peak Dopplerfrequency in the corresponding spectrogram was maxi-mized.

Several seconds of raw I/Q data were collected foreach experimental condition. The saved data were thenprocessed in MATLAB through 128-point FFTs with50% overlap. For each spectrum, the instantaneous meanDoppler frequency shift, fd, was calculated according tothe Welch method (Stoica and Moses 2005) and con-verted to instantaneous velocity through the classicDoppler equation:

V �fd · c

2 · f0 · cos(�)(4)

where fo is the US frequency, c the sound velocity and �the Doppler angle estimated through the eqn (2).

By time averaging the measured instantaneous ve-locities, the velocity Vm was finally obtained and couldbe compared to the reference standard velocity, Vr. Thefollowing percent error was thus calculated:

Err(%) �Vm � Vr

Vr· 100 (5)

Pulsatile flow measurementsPulsatile flow measurements were aimed at evalu-

ating the reproducibility of the technique in experimentalconditions closer to those existing in main human arter-ies. In particular, three different time averaged volumet-ric flows, between 100 and 350 mL/min, were estab-lished, all with pulsation period of about 1 s. Two MTs(T6 and T7) were used. For each transducer-flow settingpair, five Doppler angles were set and raw data from twoconsecutive measurement sessions were saved, allowinga total of 60 measurements (see Table 3).

The experiments were carried out following thesame procedure employed in steady flow tests. Datasaved from each acquisition covered about 5 s. The timerequested to complete each group of 20 measurementsrelated to the same pump setting lasted about 1 h. Theflow configuration was assumed stable during this time.

For each pump setting, the measured velocities wereanalyzed through two tests. In the first test, the entire

Table 3. Experimental conditions used in pulsatile flowmeasurements

Values Unit

Measuring transducer MT6, MT7 —Mean volumetric flow 109, 236, 346 mL/min
Doppler angle 55, 60, 65, 70, 75 °


periodic peak velocity curves were compared with eachother. The acquisitions were collected in three groups(G1, G2, G3), each containing the data referring to thesame pump setting. Each group included 20 acquisitionsobtained through two MTs oriented at five differentDoppler angles, with two measurements (i.e., sessions)per angle. The acquisitions were first aligned in time sothat the sum of squared differences among them wasminimized. For example, Fig. 3 reports the 20 peakvelocity curves obtained at 236 mL/min mean volumeflow (top), and the associated standard deviation (SD)(bottom). For each group Gi, the coefficient of variability(CV) was also calculated by averaging the SD values anddividing the result by the mean velocity.

The second analysis was focused on the reproduc-ibility of the pulsatile peak velocity (PPV) measurement.For a given flow rate and angle, four acquisitions, eachincluding at least four pump cycles, were available.

The measurement reproducibility was quantitativelyevaluated through the intrasession CV (among the PPVsof the same acquisition) and the intersession CV (be-tween the four related acquisitions). For the intrasessionvariability, the SDs, i (i � 1, 2, 3, 4), of the velocitypeaks measured in each of the four acquisitions referringto the same flow conditions, were separately estimatedand subsequently averaged as:

t ��1 � 2 � 3 � 4

4· (6)

t was then normalized with the mean PPV obtainedfrom all measurements of the 4 sessions. The intersession

0 1 2 3 4 55

10

15

20

25

time (s)

velo

city

(cm

/s)

0 1 2 3 4 50

5

10

15

20

time (s)

SD

(mm

/s)

Fig. 3. Top: peak velocity curves obtained from acquisitionsof group G2, including two consecutive measurements madeat each Doppler angle (55°, 60°, 65°, 70°, 75°) with trans-ducer MT6 and MT7. Bottom: standard deviation (SD)

among all curves.

variability was estimated by calculating the CV of the

average PPVs measured for given pump and angle set-ting.

In vivo measurementsA group of 21 healthy volunteers (6 women, 15

men; age range 25 to 50 years) gave written informedconsent and were recruited to this study, which wasapproved by the local Institutional Review Board. A totalof 85 measurements were made on the left CCAs of thevolunteers, by using the MCMG system equipped withthe same dual-beam probe holder employed in in vitromeasurements. The transducer MT3 was coupled to theRT, with interbeam angle of 30°. Both transducers wereexcited with three cycles at 9 MHz. The pulse repetitionfrequency (PRF) was set at 7.8 kHz.

All measurements were made by the same operator.The volunteer was invited to seat on a comfortable chairwith his head leant on the headrest. A relax of someminutes was conceded to allow the heart to achieve astable rate. Because no B-mode imaging was used, theoperator started a coarse probe positioning by looking atthe spectral profiles produced by both transducers. Whenthe shape and extension of such profiles suggested thatthe vessel diameter was contained in the scan plane, theoperator rotated the probes in such a plane until the RTproduced Doppler spectra that appeared roughly sym-metrical during all phases of the cardiac cycle. TheMCMG system was finally switched to dual PW mode,and two spectrograms like those in Fig. 4 were obtainedin real time from the analysis of the SV located in theCCA centerline. When the SSI related to the RT wasstably larger than 75%, the raw Doppler data from bothtransducers were acquired and stored in a file.

The operator removed the probe from the neck ofthe volunteer and, after one minute, proceeded with thenext measurement, by repositioning the probe throughthe aforementioned procedure. For each subject, fouracquisitions were made, over a total time interval ofabout 10 min (up to 20 min for the most difficult cases).The CCA flow conditions were supposed stable duringthis time. The results from two volunteers, having deepcarotid arteries, were discarded because of the insuffi-cient S/N ratio achieved.

The 76 selected files were processed with the samealgorithm used for pulsatile in vitro experiments. As anexample, Fig. 5 shows the 4 peak velocity curves savedfor volunteer n.4.

RESULTS

Steady flowThe statistical distribution of the Err(%) parameter

over all measurements features a normal distribution (p
� 0.806 in Kolmogorov-Smirnov test) with mean of

nsduc


–1.9% (95%, confidence interval: –2.33% to –1.47%)and SD of 3.4%. The SDs of the instantaneous velocitiescalculated from each file, ranged between 2% and 3.5%of the mean velocity.

Pulsatile flowThe results of the first test are detailed in Table 4.

The CVs calculated over the entire peak velocity curvesranged between 6.2% and 7.4%.

The PPVs measurement results obtained from thesecond analysis are summarized in Fig. 6. Here, thePPVs estimated for each pump setting and angle are

Fig. 4. Typical spectrograms produced from a SV lospectrograms were simultaneously obtained by analyzing

(top) and the reference tra

0 1 2 3 410

20

30

40

50

60

70

80

90

time (s)

Velo

city

(cm

/s)

Fig. 5. Peak velocity curves obtained from four consecutive
measurements on volunteer number 4.
shown through error bars. The bars account for theminimum and maximum value among all measured val-ues. Detailed results are reported in Table 5, whichshows that the intrasession CVs ranged between 1.9%and 5.2% and the intersession CVs between 2.9% and10.6%.

In vivoEach acquisition contained 4 s of data, covering 3–5

heart cycles, which allowed the measurement of a cor-responding number of PSVs. The results are summarizedin Fig. 7, where the mean PSVs measured for eachvolunteer are aligned along a vertical line. The interses-sion variability (among the 4 consecutive acquisitions)was evaluated by calculating the CV of such values. Theresulting CV ranged between 0.3% and 10.2%.

The intrasession variability was evaluated accord-ing to the same procedure illustrated for PPV measure-ments. CVs ranging between 1.5% and 4.9% were thusobtained. Detailed results are given in Table 6.

The measurement error of PSV was finally esti-

in the center of a common carotid artery. The twooppler echo-data collected by the measuring transducerer (bottom), respectively.

Table 4. Results of velocity measurements obtained inpulsatile flow conditions

Mean flow(mL/min)

Mean velocity(cm/s)

Mean SD(mm/s) CV (%)

109 5.8 4.3 7.4236 13.2 8.2 6.2

catedthe D

346 19.3 14.0 7.2


mated. A Kendall Tau test was preliminarily made toestablish a possible correlation between mean and SD ofthe measurements. Because such a correlation was notrevealed (� � 0.18, p � 0.28), according to Bland andAltman (1986), the 95% limits of agreement and thecoefficient of repeatability (BSI 1979) could be assessedas � 1.96 · SDr, and 1.96�2 · SDr, respectively, whereSDr is the SD of repeated measurement of velocity. Theformer value represents the limits within which the truevelocity value (i.e., the average of all possible velocitymeasurements) can be found, whereas the latter repre-sents the maximum difference for two measurements atrandom (Bland and Altman 1986). The values obtainedin the present study are summarized in Table 7.

DISCUSSION

Steady flow measurementsSteady flow experiments highlighted a mean error

(measurement bias) of about –1.9%. Such evaluation wasbased on the reference velocity Vr, which is affected by

55 60 65 70 755

10

15

20

25

30

35

Doppler Angle (°)

PP

V (c

m/s

)

Fig. 6. Average pulsatile peak velocities (PPVs) measured atdifferent Doppler angles for the three pump settings. Each errorbar accounts for the minimum and the maximum values mea-sured during the four acquisitions referring to the same pump

setting and angle.

Table 5. Intrasession and intersession CVs obtained fromPPV measurements

CV (%)intrasession/intersession

Doppler angle (°)

55 60 65 70 75

Mean flow mL/min109 3.6/6.0 4.6/5.7 4.5/6.5 5.2/2.9 4.9/10.6236 2.8/3.9 2.8/5.3 2.8/4.1 2.3/4.3 3.0/5.1
346 2.3/5.9 1.9/3.4 2.3/5.4 2.2/4.9 2.1/4.1
an uncertainty of the order of 0.5%. The slight underes-timation suggested by this result can be explained byconsidering the noninfinitesimal dimensions of the SV,which intercepts scatterers moving at different velocitiesbelow the maximum value. As detailed in the Appendix,the dependence of steady flow velocity measurementerror on the effective SV length (SVLeff) can be theoret-ically predicted and compared with the measurementresults. This is graphically shown in Fig. 8, which reportsthe measured velocity errors (dots), together with theirbest fitting (continuous line) and the theoretical error(dashed line), as a function of SVLeff. Although thetheoretical behavior was calculated through a rough ap-proximation of the SV shape (see Appendix), the com-parison between measured and expected behavior, sug-gests that the measured underestimation can be partiallyrelated to the effective SV length.

In our experiments, this source of error was keptlow by using short SVs and narrow-beam transducers(see Table 1).

Pulsatile flow experimentsThe analysis of data carried out in pulsatile flow

conditions has shown good reproducibility over differentpeak velocity curves, as highlighted by the low SDvalues plotted in Fig. 3. The analysis of variability sug-gests that the CV, within the limits of our test, does notdepend on the flow rate, the used transducer or Dopplerangle.

These features have been confirmed by the PPVmeasurements. The estimated intrasession and interses-sion CVs are substantially in agreement with the valuesreported in literature (Steel et al. 2003) but, differently

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1950

60

70

80

90

100

110

120

130

Volunteer

PS

V (c

m/s

)

Fig. 7. The mean peak systolic velocities (PSVs) obtained fromfour consecutive measurements made on each volunteer are

represented by circles aligned along the same vertical line.

from other studies on dual-beam methods (Steel et al.

5.0


2004), we did not find significant performance depen-dence on the Doppler angle (Fig. 6, Table 5). This can beexplained through the following considerations. First ofall, the proposed method is characterized by high accu-racy in angle estimation. As demonstrated in Tortoli etal. (2006a) it is possible to determine the Doppler anglewith errors 1°. Moreover, because only one beam isused to make the Doppler measurement, there is not theamplification of Doppler error sources typical of otherdual-beam methods, especially at small interbeam angles(Steel and Fish 2002). Finally, by using single-elementtransducers, we could avoid the “virtual beam rotationeffect” associated to steering in linear arrays, which wasfound responsible of velocity measurement errors corre-lated to the Doppler angle (Steel et al. 2004).

In vivo experimentsThe in vivo reproducibility test was carried out

without the help of any B-mode display. The correctpositioning of probes was supported only by the multi-gate mode display. The CCA runs almost parallel to theskin, and this facilitated the transverse orientation of oneof the two beams. The operator could in fact find asatisfactory probe position for all volunteers except two.

The obtained CVs basically confirm the good inter-session and intrasession reproducibility highlighted bythe in vitro experiments. In particular, the small differ-ence between intrasession and intersession CVs denotesthat probe repositioning represents a limited source oferror. The 95% limits of agreement resulted � 9.6 cm/s.These results can be favorably compared with the � 40cm/s limits obtained in intraobserver experiments bySteel et al. (2004), who used a modified imaging systemto perform in vivo dual-beam studies. In that study,however, the measurement sessions were interrupted by

Table 6. Intrasession and intersession C

VolunteerCV (%)

intrasessionCV (%)

intersession VolunteerC

intr

1 3.3 0.3 82 3.6 4.3 93 3.3 4.7 104 2.8 4.3 115 4.2 7.6 126 2.2 6.2 137 3.2 4.5 14

Table 7. Measurement error for in vivo experiments

SDr95% limits

of agreementCoefficient ofrepeatability

4.9 cm/s � 9.6 cm/s 13.5 cm/s

a six-week interval, so that the patient variability prob-ably played a more important role (Corriveau andJohnston 2004).

Finally, the coefficient of repeatability obtained invivo is low enough (13.5 cm/s) to allow the physician tofollow-up patients distinguishing, e.g., PSV changes be-cause of stenosis progression from changes as a result ofmeasurement errors. This can help in the categorizationof the severity of carotid stenosis in the typical ranges(�50%, 50 to 70%, �70%), in particular when themeasured velocity is in the vicinity of a cutoff value.

Final considerationsClassic dual-beam techniques, based on the trigo-

nometric combination of two Doppler measurements, areknown to be sensitive to different potential sources oferror. For example, if the SVs considered by the twobeams are not perfectly overlapped, cover flow regionswith different velocity direction and/or magnitude sig-

0.5 1 1.5 2-10

-8

-6

-4

-2

0

2

4

6

8

10

SVLeff (mm)

Err

(%

)

Fig. 8. Effect of SV effective dimensions on the velocityunderestimation. Each point represents a measurement error(values over � 7% were considered outliers and excluded fromthis analysis); red-dashed and blue-continuous lines correspondto the theoretical trend (see Appendix) and measurement inter-

tained from in vivo PSV measurements

nCV (%)

intersession VolunteerCV (%)

intrasessionCV (%)

intersession

10.2 15 4.4 2.47.6 16 1.5 7.20.8 17 2.6 6.35.6 18 2.3 3.95.4 19 4.1 0.825.13.1

Vs ob

V (%)asessio

2.13.62.54.92.22.8

polation, respectively.


nificant translation misregistration errors may arise.Moreover, as mentioned previously, the difficulties typ-ical of single-beam measurements (e.g., spectral broad-ening, tissue inhomogeneity, SV shape, etc.), are empha-sized at the small interbeam angles that can be obtainedwith linear array transducers (Steel and Fish 2002).

The good performance obtained in this study can berelated to the overcoming of some of the above difficul-ties. The RT and MT are requested to investigate twoSVs, where the flow has the same direction, but notnecessarily the same magnitude. This significantly re-duces the possibility of having misregistration errors.Moreover, the RT data are not used to make a Dopplerfrequency measurement, but just to estimate the flowdirection by evaluating the spectral symmetry. Such anapproach has been shown able to align the beam-vesselangle to better than 1 degree, which makes the velocitymeasurement made through the MT virtually angle inde-pendent.

It should be noted that our method is significantlydifferent from other vector Doppler techniques that ex-ploit the transverse Doppler effect by making referenceto the linear relationship existing between the scatterervelocity and the bandwidth of the corresponding Dopplerspectrum (McArdle et al. 1995; Lee et al. 1999; Lee2006). Because such methods estimate the transversecomponent of the velocity vector through a Dopplerbandwidth measurement, they are made implicitly weakby the possibility that spectral broadening mechanismsdifferent from geometrical broadening are involved (Fish1991; Shen et al. 2007). This limitation does not affectthe performance of our method, which does not measurethe Doppler bandwidth, although it exploits the geomet-rical broadening to detect the spectral symmetry ex-pected at 90° beam-flow angle.

The proposed dual-beam method may be not appli-cable in vessels that do not allow achieving the neededtransverse beam orientation because of mechanical orsteering limitations. This restriction does not apply to theCCA, as confirmed by the positive results of the repro-ducibility test discussed previously nor to other impor-tant vessels like aorta, femoral or radial arteries.

CONCLUSION

The aim of this work was the investigation of theperformance attainable with a novel dual-beam method.More than 300 measurements were carried out overdifferent experimental and acquisition conditions. Invitro test showed a small (–1.9%) bias, mainly imputableto the used frequency estimator. The robustness testrevealed that velocity measurements are not appreciablyaffected by changes of measurement parameters or ex-
perimental conditions (SD of error distribution: 3.4%). In
vitro pulsatile flow test showed that the performance ofthe proposed method is reasonably independent from theabsolute flow velocity or Doppler angle. The intrasessionand intersession CVs were �4.9% and 10.2%, respec-tively. The feasibility of the method was also provenwith in vivo experiments, which substantially confirmedthe variability measured in vitro. In particular, the ob-tained CR of 13.5 cm/s suggests that the proposed tech-nique can represent a more sensitive diagnostic means tofollow the progression of severity of stenosis.

This method can potentially contribute to improvethe accuracy of blood velocity investigation, and canrepresent a step forward in the direction of better volu-metric flow assessment and wall shear rate extraction.

Acknowledgments—This work has been supported by the EU grant #QLG-CT-2002 to 01518 (UMEDS project) and by the Italian Ministryof Education, University and Research (PRIN 2005).

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APPENDIX

When a parabolic flow is interrogated, the intercepted range ofvelocities depends on the projection of the SV outline on the tubediameter (see Fig. 9). Although exhaustive models have been proposedto account for the related effects on the detected mean Doppler fre-quency (Evans and McDicken 2000), within the scope of this study anapproximate model can be used.

Let us suppose to have an ideal cylindrical SV of length l anddiameter d, overlapped to the tube centerline as in Fig. 9. The projec-tion of such a SV in the direction of the tube diameter, here called“effective SV length,” can be expressed by:

SVLef f � �d2 � l2 · cos�� arctanl

d� (7)

Assuming a uniform insonation within the SV, the detected meanDoppler frequency corresponds to the intercepted mean velocity. Theunderestimation error, for parabolic flow with apex velocity Vr in a tubeof diameter D, can thus be calculated as:

E � Vr ·SVLef f

2

2D2 (8)

Fig. 9. Velocity underestimation error, E, introduced when acylindrical SV of length l and diameter d is placed at angle � in

the middle of a vessel with diameter D.

accuracy and reproducibility of a novel dual-beam vector doppler method

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