Jensen, Jørgen Arendt

Nikolov, Svetoslav

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Velocity estimation using synthetic aperture imaging [blood flow]

Presented an approach for synthetic aperture blood flow ultrasound imaging. Estimates with a low bias and standard deviation can be obtained with as few as eight emissions. The performance of the new estimator is verified using both simulations and measurements. The results demonstrate that a fully functioning synthetic aperture scanner can be mad

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Downloaded from orbit.dtu.dk on: Dec 17, 2017Velocity estimation using synthetic aperture imaging [blood flow]Nikolov, Svetoslav; Jensen, Jørgen ArendtPublished in:Proceedings of IEEE Ultrasonics SymposiumLink to article, DOI:10.1109/ULTSYM.2001.991985Publication date:2001Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Nikolov, S., & Jensen, J. A. (2001). Velocity estimation using synthetic aperture imaging [blood flow]. InProceedings of IEEE Ultrasonics Symposium (Vol. 2, pp. 1409-1412). IEEE. DOI:10.1109/ULTSYM.2001.991985Velocity estimation using synthetic aperture imagingSvetoslav Ivanov Nikolov∗and Jørgen Arendt JensenCenter for Fast Ultrasound Imaging, Ørsted•DTU, Build. 348,Technical University of Denmark, DK-2800 Lyngby, DenmarkAbstractIn a previous paper we have demonstrated that the velocitycan be estimated for a plug flow using recursive ultrasoundimaging [1]. The approach involved the estimation of the ve-locity at every emission and using the estimates for motioncompensation. An error in the estimates, however, would leadto an error in the compensation further increasing the error inthe estimates.In this paper the approach is further developed such that nomotion compensation is necessary. In recursive ultrasoundimaging a new high resolution image is created after everyemission. The velocity was estimated by cross correlating RFlines from two successive emissions n and n+1, and then av-erage over a number of lines. In the new approach images nand n+N, n+1 and n+N+1 are cross correlated, where N isthe number of emissions for one image. These images expe-rience the same phase distortion due to motion and thereforehave a high correlation without motion compensation. Theadvantage of the approach is that a color flow map can becreated for all directions in the image simultaneously at ev-ery emission, which makes it possible to average over a largenumber of lines. This makes stationary echo canceling easierand significantly improves the velocity estimates. The ap-proach is verified using simulations with the program Field IIand measurements on a blood-mimicking phantom. The esti-mates from the simulations have a bias of -3.5 % and a meanstandard deviation less than 2.0 % for a parabolic velocityprofile. The estimates from the measurements for the samesetup exhibit a larger bias - 11 %, but the standard deviationis comparable to the simulations (σ∼ 2.5 %).1 IntroductionSynthetic aperture ultrasound imaging (SAUI) is appealingwith its capability to produce high-quality images, which aredynamically focused both in transmit, and in receive. Theuse of a synthetic transmit aperture imaging STAU has theadditional advantage of low number of emissions and highframe rates. The SAUI in general, and the (STAU) in particu-∗E-mail: sn@oersted.dtu.dklar, have therefore been investigated for many years, but havenever left the area of research, and are not used in the medicalscanners yet. One of the major hold-backs to the clinical useis that till present day there have not been any reports of es-timation and visualization of blood flow. Without this featurea modern scanner cannot be considered full featured. Thispaper shows a way how to solve this problem by designing anew velocity estimator based on STAU.The previous attempts for velocity estimation have beenconfined to the estimation of the gross tissue motion and usedfor motion compensation [2, 3]. The approach suggested byNock and Trahey [2] uses cross-correlation between the re-ceived raw RF signals. The algorithm, however, relies on thefact that the transmission is focused, and that the receivedsignals come from the same direction. It is therefore not suit-able for STAU. The method suggested by Bilge et al. [3] re-lies on the cross-correlation between low-resolution images,which are formed using the same transmit/receive pairs oftransducer elements. The beam is, however, broad and theblood cells within its limits have a wide spread of velocities.This results in an increased bias and standard deviation of theestimates.Both types of motion compensation schemes show im-proved performance, when the images are obtained using thesame transmit/receive element pairs, or in other words havethe same spatial frequencies. The high-resolution images(HRI) have the highest overlap of spatial frequencies, andtherefore they should give the best estimates. The correla-tion of the signals received from the blood cells decreasesrapidly due to migration of scatterers, beam-width modula-tion, and flow gradients (change in the relative positions be-tween the scatterers) [4]. The HRIs must be generated af-ter every emission, which is possible using recursive ultra-sound imaging. These images suffer from motion artifacts,which change from frame to frame. In a previous article [1]we have shown that it is possible to compensate for the mo-tion artifacts and to estimate the velocity from the motion-compensated HRIs. The success of the velocity estimation re-lies on the success of the motion compensation, which makesthe whole approach unstable. In the next section it is shownhow to modify a velocity estimator in such a way, that no mo-tion compensation is needed prior to the velocity estimation.1Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on April 12,2010 at 13:47:34 UTC from IEEE Xplore.  Restrictions apply. Emission     (n−3)L(n−3)Emission     (n−2)L(n−2)Emission     (n−1)L(n−1)Emission     (n)L(n)2∆zLow−resolution imagesH(n−3) H(n−2) H(n−1) H(n)2∆z 2∆zHigh−resolution imagesFigure 1: Creating several successive high-resolution images.2 TheoryFig. 1 shows the creation of several successive high-resolution images, when a single scatterer moves towards thetransducer. The top row illustrates the emission sequence.Only the outermost two elements are used in transmit (N = 2),and the active one is drawn with a dark gray color. They emitsequentially - first element number 1 then element numberNxdc, then again element number 1 and so on. Nxdc is the totalnumber of transducer elements. The emissions have a globalindex n, and are counted from the start of the process. Therelation between the index of the transmit element and theemission number is given by:i = ((n−1) mod N)Nstep +1, (1)where Nstep is the increment of the index of the transmittingelements. If every of the Nxdc transducer elements was used,then Nstep would be 1. All of the transducer elements are usedupon reception, and after every emission n a low-resolutionimage (LRI) L(n)(t) is formed. The point spread functionsfor these LRIs are tilted at different angles to the transducersurface. The angles depend on the position of the transmittingelement. The middle row of Fig. 1 illustrates the low resolu-tion images of a single point. The point moves from emissionto emission towards the transducer at a distance ∆z. It can beshown that L(n)(t) and L(n−N) are translated versions of eachother, when ∆z is on the order of a millimeter [5].At every emission a high-resolution image can be formed1 2 N 2NN+2N+1t54321SegmentnumberEmission number* * *= = =R(τ)R(τ)R(τ)τ τ τAverageCross−correlateFigure 2: Estimation of the cross-correlation function of sev-eral consecutive high-resolution lines formed in the same di-rection.by summing the last N low-resolution images [6]:H(n)(t) =n∑i=n−N+1L(i)(t), (2)where t is the time from the start of the emission. If thetissue is motionless, then L(i)(t) ≡ L(i−N)(t) and H(n)(t) ≡H(n−N)(t). In the presence of motion, however, L(n)(t) =L(n−N)(t− 2(N∆z)/c), where c is the speed of sound. It canbe shown that if the velocity is constant, then:H(n)(t) = H(n−N)(t−2NvzTpr fc), (3)where Tpr f = 1/ fpr f is the pulse repetition period, and vz isthe component of the velocity towards the transducer. Thissituation is depicted in the bottom row of Fig. 1. It can be seenthat two successive high-resolution images differ due to thedifferent transmit sequences with which they were obtained,but the high resolution images, that are N transmissions apart,are shifted versions of one another. This shift can be es-timated using cross-correlation of the high-resolution linesHn(t) and H(n−N)(t), which are formed in the same directionof the image (see Fig. 2).The cross-correlation becomes [5]:Rn−N,n(τ) =12T TH(n−N)(t)H(n)(t + τ) dt=12T TH(n−N)(t)H(n−N)(t− ts + τ) dt= Rn−N,n−N(τ− ts),(4)Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on April 12,2010 at 13:47:34 UTC from IEEE Xplore.  Restrictions apply. Nikolov and Jensen 3where ts = 2NvzTpr fcis the time shift due to motion. The peakof the cross-correlation function is located at τ = ts. The ve-locity can be found from the time shift:vz =c2tsNTpr f. (5)The lines at emissions n− i and n−N− i are subject to thesame time shift and the peak of their cross-correlation func-tion is also located at a lag τ = ts, as shown in Fig. 2. Thedifferent cross-correlation functions can, thus, be averaged.In the case of a flow profile, such as the parabolic flowprofile, the velocity of the blood flow changes as a functionof space and time. To estimate the velocity at the differentspatial positions, each of the RF lines is divided into a numberof segments as shown in Fig. 2. A cross-correlation functionis estimated for each of the segments. Normally the signalsare digital, and the discrete version of the cross-correlation is:ˆRn−N,n[η, iseg] =1NsisegNs−1∑k=(iseg−1)NsH(n−N)[k]H(n)[k+η], (6)where Ns is the number of samples in a segment and iseg is thenumber of the segment. If the the velocity does not changesignificantly for several sequential acquisitions Nc, then theestimate can be improved by averaging the estimated cross-correlation functions:ˆR(n)av [η, iseg] =1Nc0∑l=−Nc+1ˆRn−l−N,n−l [η, iseg]. (7)Fig. 2 shows the case for which Nc = N. If the images werecreated after every N emissions, then the total number ofemissions needed for the velocity estimate would be NcN. ForN = 8 and Nc = 16, the total number of emissions would beNcN = 128. The correlation between the high-resolution lineswould decrease due to acceleration, velocity gradients andmigration of scatterers. In the new approach only N+Nc = 24emissions are necessary, thus preserving the high-correlationbetween the images and giving the possibility of estimatingthe flow with a low bias and variance.Let the lag at which the maximum occurs be ηm. The esti-mated velocity is:vˆz =c2ηm fpr fN fs (8)The estimate can be improved by fitting a second ordercurve to the estimate, and interpolating the time shift [4]:ηs = ηm−ˆR(n)av [ηm +1]− ˆR(n)av [ηm−1]2(ˆR(n)av [ηm +1]−2 ˆR(n)av [ηm]+ ˆR(n)av [ηm−1]) .(9)Parameter Value UnitTransducer center frequency 7.5 MHzRelative transducer bandwidth 66 %Number of elements 64Transducer pitch 205 µmTransducer height 4 mmExcitation type chirpExcitation start frequency 0 HzExcitation end frequency 17 MHzExcitation duration 20 µsSampling frequency 100 MHzPulse repetition frequency 7000 HzPropagation velocity 1540 m/sMaximum velocity 0.18 m/sTable 1: Relevant parameters for the simulation of theparabolic flow.The stationary echo canceling is done only on the imagesthat were obtained at every Nth emission, i.e. between imagesn and n− kN, where k ∈ Z.One of the major problems of synthetic aperture imaging isthe low signal-to-noise ratio. A linear frequency modulatedpulse can be used in transmit in order to increase the trans-mitted energy, and hence, the signal-to-noise ratio.3 ResultsThe method is verified through simulations and measure-ments. The simulation is done using the program Field II[7]. Some of the relevant simulation parameters are given inTable 1.The simulated vessel has a diameter of 1 cm, and length of5 cm. The center of the vessel is positioned 50 mm away fromthe transducer surface. The angle between the vessel wallsand the transducer surface is 45◦. The number of scatterersinside the vessel is 78,549. The positions of the scatterers arerandomly selected with an uniform (white) distribution. Theiramplitudes have a random Gaussian distribution with a zeromean.Fig. 3 shows the result of the new estimator applied on thesimulated data. The dash-and-dotted line corresponds to thetrue velocity. The thick line gives the mean of 200 estimates,and the dashed lines outline the mean of the estimates± threestandard deviations (±3σ). The maximum bias of the esti-mated profile for θ = 45◦ and Nc = 24 is −3.05 % and themaximum standard deviation is 2.7 %. From Fig. 3 it can beseen that the performance for the case of Nc = 4 is compa-rable: the maximum bias of the estimated profile is −2.5 %.The standard deviation varies between 1.2 % at 50th mm and5 % at 42nd mm.Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on April 12,2010 at 13:47:34 UTC from IEEE Xplore.  Restrictions apply. 40 50 6000.050.10.15Axial distance [mm]Velocity [m/s]Nc= 24, θ = 45°40 50 60Axial distance [mm]Nc= 4, θ = 45°Figure 3: Velocity profiles obtained with the new cross-correlation approach.35 40 45 50 55 6000.050.10.15Axial distance [mm]Velocity [m/s]Nc= 24, θ = 45°Figure 4: Velocity profile measured on a flow phantom.Fig. 4 shows a velocity obtained by measuring the flow ona blood-flow mimicking phantom “EU-DFS-BMF-ver.1” byDanish Phantom Design (http://www.fantom.suite.dk). Thefluid is driven by a Smedegaard Type EcoWatt 1 pump. Themean flow is measured by a Danfoss MAG 1100 flow me-ter. The length and diameter of the tube are 1 m and 17 mm,respectively. Except for the propagation velocity of soundc ≈ 1485 m/s, and the sampling frequency fs = 40 MHz, theparameters of the experiment are the same as in Table 1. Thesolid line in Fig. 4 is the mean estimated velocity, the dashedlines are± three standard deviations (3σ), and the dashed anddotted line is the true velocity profile. The standard deviationvaries between 1.7 and 6 %. The bias at the peak (at depth of47.5 mm) is -11 %.4 ConclusionIn this paper we have presented an approach for syntheticaperture blood flow ultrasound imaging. Estimates with a lowbias and standard deviation can be obtained with as few as 8emissions (Nc = 4). The performance of the new estimatoris verified using both simulations and measurements. The re-sults demonstrate that a fully functioning synthetic aperturescanner can be made.AcknowledgmentThis work was supported by grant 9700883 and 9700563from the Danish Science Foundation and by B-K MedicalA/S, Gentofte, Denmark.References[1] S. I. Nikolov, K. Gammelmark, and J. A. Jensen. Ve-locity estimation using recursive ultrasound imaging andspatially encoded signals. In Proc. IEEE Ultrason. Symp.,volume 2, pages 1473–1477, 2000.[2] L. F. Nock and G. E. Trahey. Synthetic receive apertureimaging with phase correction for motion and for tissueinhomogenities - part II: effects of and correction for mo-tion. IEEE Trans. Ultrason., Ferroelec., Freq. Contr.,39:496–501, 1992.[3] H. S¸. Bilge, M. Karaman, and M. O’Donnell. Motionestimation using common spatial frequencies in syntheticaperture imaging. In Proc. IEEE Ultrason. Symp., pages1551–1554, 1996.[4] S. G. Foster, P. M. Embree, and W. D. O’Brien. Flow ve-locity profile via time-domain correlation: Error analysisand computer simulation. IEEE Trans. Ultrason., Ferro-elec., Freq. Contr., 37:164–175, 1990.[5] S. I. Nikolov. Synthetic aperture tissue and flow ultra-sound imaging. PhD thesis, Ørsted•DTU, Technical Uni-versity of Denmark, 2800, Lyngby, Denmark, 2001.[6] S. I. Nikolov, K. Gammelmark, and J. A. Jensen. Recur-sive ultrasound imaging. In Proc. IEEE Ultrason. Symp.,volume 2, pages 1621–1625, 1999.[7] J. A. Jensen. Field: A program for simulating ultrasoundsystems. Med. Biol. Eng. Comp., 10th Nordic-BalticConference on Biomedical Imaging, Vol. 4, Supplement1, Part 1:351–353, 1996b.Authorized licensed use limited to: Danmarks Tekniske Informationscenter. Downloaded on April 12,2010 at 13:47:34 UTC from IEEE Xplore.  Restrictions apply. 

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Velocity estimation using synthetic aperture imaging [blood flow]

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