Directional Velocity Estimation Using Focusing Along the Flow ...

ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 50, no. 7, july 2003

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Directional Velocity Estimation Using Focusing Along the Flow Direction II: Experimental Investigation Jørgen Arendt Jensen, Senior Member, IEEE, and Rasmus Bjerngaard Abstract—A new method for directional velocity estimation is investigated through a number of flow rig measurements. The method uses beamformation along the flow direction to generate data, where the correct velocity magnitude can directly be estimated from the shift in position of the received consecutive signals. The shift is found by crosscorrelating the beamformed lines. The approach can find the velocity in any direction, including transverse to the traditionally emitted ultrasound beam. The method is investigated using a flow rig with a peak velocity of 0.15 m/s. A 7-MHz linear array transducer is used together with a dedicated sampling system to acquire signals from 64 transducer elements simultaneously. A technique for obtaining 128-element data using multiplexing is also presented. The data is beamformed off-line on a PC. A relative standard deviation of 1.4% can be obtained for a beam-to-flow angle of 45 and 4.3% at 90 . Color flow images are displayed showing that the correct velocity magnitude can be obtained with the method for beam-to-flow angles of 60 and 90 with an accuracy of 3 to 4%.

I. Introduction his paper is the second of two that describes a method for finding the correct velocity amplitude using directional beamforming. Here, a normally focused and apodized ultrasound field is emitted. The received signals are then focused along the direction of the flow, rather than along the emitted ultrasound direction. The motion between pulse emissions will then introduce a shift in the position of the directional signal, and this can be estimated by cross-correlating the directional signals. The velocity is found from the position of the peak value in the crosscorrelation functions, which gives the shift, and dividing by the time between pulse emissions gives the correct velocity magnitude provided the beam-to-flow angle is known. The first paper [1] gave a detailed introduction to the derivation of the approach and simulations of its performance. It showed that the velocity can be accurately estimated even for flow transverse to the ultrasound beam. The purpose of this paper is to investigate the performance of the approach on data from laminar and station-

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Manuscript received August 9, 2002; accepted January 28, 2003. This work was supported by grants 9700883 and 9700563 from the Danish Science Foundation, by B-K Medical A/S, Denmark. J. A. Jensen is with the Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark (e-mail: [email protected]). R. Bjerngaard is with Nokia Mobile Phones in the Digital Signal Processing Research and Development Department, Copenhagen, Denmark.

Fig. 1. Setup for the measurements using the flow rig. The transducer is mounted in a fixture with a predetermined angle between the flow vector and the ultrasound beam. The velocity is regulated by the valve, and the volume is determined by the mass flow meter (drawing by Svetoslav Nikolov).

ary flow in an experimental flow rig and show that the approach can be used for accurate velocity imaging. This is an extension of a preliminary investigation previously published in [2]. An experimental ultrasound system [3] was used for acquiring the data as described in Section II from the flow rig. The off-line processing is described in Section III, and examples of the obtained flow profiles are given in Section IV. Section IV also outlines how the 64 channels measurement system can use its 2-to-1 multiplexing to obtain 128 channel data useful for flow imaging. This idea is used to reduce the standard deviation on the transverse flow estimate from 10.6% to 4.3%. Finally, color flow images are shown in Section VI for beam-to-flow angles of 60 and 90◦ .

II. Measurement Set-up Measurements were performed on a circulating flow rig as shown in Fig. 1. A Smedegaard EcoWatt 1 pump circulates a blood mimicking fluid made by Danish Phantom Service consisting of water, glycerol, orgasol, Trition x-100, NaBenzoat, and K2 EDTA diluted 10 to 1 with demineralized water. A reduction valve was used to control the velocity, and the mass flow velocity was determined using a Danfoss MAG 1100 flow meter. The tubing consisted of a 1.2 m long, 20-mm-diameter steel tube before the flow entered an 18-mm-diameter heat shrink tubing. The thickness of the heat shrink tubing was 0.5 mm, giving an internal diameter of 17 mm. The flow was maintained with a

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ieee transactions on ultrasonics, ferroelectrics, and frequency control, vol. 50, no. 7, july 2003 TABLE I Standard Parameters for Transducer and Parabolic Flow Measurement. Transducer center frequency Assumed speed of sound Wavelength Pitch of transducer element Height of transducer element Kerf Number of active elements Elevation focus RF lines for estimation Pulse repetition frequency RF sampling frequency Distance between estimates Sampling interval for lines Correlation interval Radius of vessel Distance to vessel center Peak velocity in flow

Fig. 2. Photograph of the experimental ultrasound scanner RASMUS used for the experiments. The digital part of the system is shown with the 64 receivers in the top cabinet, the 128 transmitters in the middle, and the analog power supplies on the bottom. The analog front-end and transducer plug is at the other side of the 19-in racks.

peak velocity less than 0.15 m/s, giving a Reynolds number of Re =

2 · 0.0085 · 1000 2Rρ v¯ = · 0.15/2 = 638, µ 0.002

(1)

when the viscosity µ is assumed to be 2 cP. Here, R is the radius of the vessel, ρ is the fluid density, and v¯ is the spatial mean velocity over the vessel cross section. This ensures that there is no turbulence in the system. The steel tube ensures that a fully parabolic velocity profile has been developed, since the entrance length [4] given by Ze =

0.009 · 638 RRe = = 0.38 m 15 15

(2)

is much smaller than the length of the tube. The experimental ultrasound scanner shown in Fig. 2 is used for all the measurements. The system can acquire RF data from the individual transducer channels and store them. The data can then be transferred to a PC for

f0 c λ = c/f0 w he ke N Re

7 MHz 1480 m/s 0.22 mm 0.208 mm 4.5 mm 0.035 mm 128 25 mm

Ne fprf fs dz dx = λ/10 −10λ:10λ

10 5 kHz 40 MHz 0.5 mm 0.022 mm −2.2:2.2 mm

R Zves v0

8.5 mm 40 mm 0.15 m/s

off-line experimentation and processing. The experimental system RASMUS (Remotely Accessible Software configurable Multichannel Ultrasound Sampling-System) [3] is highly flexible and can be controlled over the network using Matlab (Mathworks, Inc., Natick, MA). The system contains two PCs running Linux for its control, and it consists of 128 transmitters, which can send arbitrary signals at 40 MHz and 12 bits for each individual channel and emission. The system can simultaneously sample 64 channels at 40 MHz and 12 bits, and it has 2-to-1 multiplexing to cover 128 individual receive channels in two emissions. The data can either be beamformed in the system, or they can be stored in the 16 GB of internal storage for later processing. A 7-MHz linear array transducer with 128 elements was used in all experiments. Its parameters are shown in Table I along with the standard processing parameters for the estimation. The transducer was mounted in the fixture shown in Fig. 3. The distance and angle to the tube and flow can here be set precisely. The transducer is submerged in demineralized water added with 10 mL of Rodalon per liter. The water was left standing for several days degassing before use.

III. Data Processing The data are stored on disk and processed off-line on PCs running Linux and Matlab 6.1. The approach described in the accompanying paper [1] is used with beamformation along the flow direction. The parameters for the processing are shown in Table I. The beam-to-flow angle is needed in the processing, and the actual angle set in the flow rig is used. Stationary echo canceling is done by subtracting the mean directional signal from all of the signals. The crosscorrelation is calculated on pairs of lines, and the result-

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Fig. 3. Photograph of the flow rig system. The transducer is mounted in the holder, where both angle and depth can be set. The black tube is made of heat shrink tubing and attached to the steel tubes. The Danfoss mass flow meter can be seen in the background on the right.

ing cross-correlation function is averaged for all pairs. The position of the peak in the cross-correlation is found, and interpolation is used to find a more precise estimate. A rejection scheme is employed to suppress estimates that are only based on noise after the echo canceling. The ratio is calculated as the peak value of the cross-correlation function divided by the power of the directional signals before echo canceling. For values below a certain threshold, the velocity is set to zero, as the estimate is only found from very noisy signals.

IV. Results The first set of measurements have been done in one direction for 800 emissions. The transmission was done using 64 elements with a Hamming weight on the elements. The received signal was recorded for all 64 receiving elements, and the data were processed as described in Section III. The vessel was placed 40 mm from the front face of the transducer and the transmit focus was placed at a depth of 40, 80, and 150 mm. The angle between the flow and the emitted ultrasound beam was 45, 60, 75, and 90◦ , where the latter corresponds to a purely lateral flow transverse to the ultrasound beam. For each of the setups, 800 pulseecho lines have been measured. The processing yields a set of profiles as shown in Fig. 4, in which the top graph shows the individual profiles, and the bottom graph shows the mean of all the profiles ±3 standard deviations of the estimates. A reference velocity profile has also been calculated from the volume flow rate measured by the mass flow meter. It is assumed that the profile is parabolic and that the volume flow rate Q is related to the peak velocity v0 at the center of the vessel as v0 =

2Q , πR2

(3)

Fig. 4. Typical estimated velocity profiles at a beam to flow angle of 45◦ , when using the new approach. Ten pulse-echo lines have been used with a transmit focus at 80 mm. The top graph shows the individual profiles, and the bottom graph shows the mean of the profiles ±3 standard deviations. The mean bias over the profile is 0.39% and the standard deviation is 3.7% relative to the true profile.

where R is the vessel radius. The parabolic profile is then given by r 2 v(r) = v0 1 − , (4) R where r is the radial distance from the center of the tube. This profile does not correspond to that estimated by the ultrasound. It was found that the center of the tube and the ultrasound beam was not properly aligned and that the tube was not perfectly round. Correcting for the 3mm misalignment gave the reference profile shown as the dashed-dotted line in Fig. 4. The bias averaged over the profile is 0.39% compared with v0 and the standard deviation of the estimates is 3.7% compared with v0 . The discrepancies are mainly due to estimates at the edges of the vessel, where the signals are dominated by the stationary signal from the vessel boundary. It is also influenced by the rejection threshold that will set velocities to zero for low velocities, and this is not really a property of the basic estimator. Finding the bias and standard deviation inside the vessel from 30 to 45 mm, which excludes the edges, gave a bias of −0.12% and a standard deviation of 1.4%. Velocity profiles measured for a purely transverse flow are shown in Fig. 5. The approach is less precise for a purely transverse flow, since the transverse beamprofile has a much less rapid variation than the axial pulse, and it is much wider. The correlation, therefore, has to be made over a longer interval and more lines have to be used to reduce the effect of noise. The shift in the peak of the cross-correlation compared to the width of the main lobe is also smaller, and this will decrease the precision of the estimation. A larger Tprf can be used to compensate for

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Fig. 5. Typical estimated velocity profiles at a beam to flow angle of 90◦ , when using the new approach. Twenty pulse-echo lines have been used with a transmit focus at 80 mm. The top graph shows the individual profiles, and the bottom graph shows the mean of the profiles ±3 standard deviations. The mean bias over the profile is 12.2% and the standard deviation is 10.6% relative to the true profile.

this, or the correlation can be done between line 1 and line 1 + Ns , where Ns is larger than one. It should also be mentioned that the reflection from the boundary of the vessel is much stronger, since the ultrasound encounters a smooth boundary perpendicular to the beam. This will reduce the signal-to-noise ratio of the data used for the estimation. The correlation interval has therefore been increased to ±20λ, and 20 directional signals are used in the estimation for the profiles shown in Fig. 5. The pulse repetition frequency has been lowered by a factor of 4 to 1250 Hz, and correlation is done with Ns = 4. The mean bias over the profile is 12.2% and the standard deviation is 10.6% relative to the true profile, which still are acceptable values for color flow mapping. The results can be further improved by using more pulse-echo lines and by using more receiving channels. The RASMUS experimental ultrasound scanner can only acquire data for 64 elements simultaneously, but by using the 2-to-1 multiplexing, data can be measured for 128 elements in two emissions. This is done in the next set of measurements. For the first emissions the odd-numbered elements are sampled, and for the second emission the evennumbered elements are measured. The directional signals are then beamformed for all the emissions, and the signal obtained from line 1 is added to line 2, and the signal from line 2 is added to line 3 and so on. Hereby, every resulting directional signal is beamformed using all 128 elements. The drawback is that the element signals are not fully aligned due to the movement between the two emis-

Fig. 6. Typical estimated velocity profiles at a beam to flow angle of 90◦ , when using 128 elements in received. Forty pulse-echo lines have been used with a transmit focus at 80 mm. The top graph shows the individual profiles, and the bottom graph shows the mean of the profiles ±3 standard deviations. The mean bias over the profile is 4.4%, and the standard deviation is 3.9% relative to the true profile.

sions, and one less directional signal than the number of emissions can be made. The pulse repetition frequency has been lowered by a factor of 4 to 1250 Hz, and correlation is done with Ns = 3. Using 40 pulse emissions and this scheme, the transverse velocity profiles shown in Fig. 6 are obtained. The bias is lowered to 4.4% and the relative standard deviation to 3.9%.

V. Parameter Variations For each angle and focusing depth, 800 to 3000 pulseecho emissions have been acquired. The processing of the data is then done on these data sets for variations in the various parameters for the estimation. A similar variation analysis has been done for simulated data in the accompanying paper [1]. Fig. 7 shows the performance as a function of number of lines used for the estimation for beam-to-flow angles of 45, 60, and 75◦ . It can be seen that both bias and standard deviation decrease for an increasing number of lines. The bias does not tend to zero, but this is probably due to measurement errors for the mass flow meter and misalignment of the ultrasound probe and the vessel. The standard deviation in general attains a low value after 10 lines, and this is independent of both angle and focusing depth. The results are generally in the same range as the simulated results in [1], and the general trends are the same. The parameter variation results in [1] can therefore be used for evaluating and optimizing the method. The variation


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Fig. 7. Variation in number of pulse-echo lines. The bias is shown on top and the standard deviation on the bottom as a function of number of directional signals used for the estimation.

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Fig. 8. Variation in number of pulse-echo lines for 90◦ beam-to-flow angle and 128 measurement elements. The bias is shown on top and the standard deviation on the bottom as a function of number of directional signals used for the estimation.

analysis will therefore be concentrated on the measured transverse velocity data. Fig. 8 shows the same variation for a transverse flow using 128 elements in receive using the multiplexing scheme described above. An increase in the number of lines both decrease the bias and standard deviation for all emit foci. The most significant reduction is seen from going between 10 to 20 lines, due to the influence from the stationary echo canceling and false peaks in the cross-correlation function. A significant reduction is also seen when going from 20 to 40 lines. The variation as a function of fprf is shown in Fig. 9 for a transverse flow and using 128 elements in reception. It can be seen that both bias and standard deviation decreases for a decreasing fprf above 1000 Hz. This is due to the slow-moving flow, where the peak in the crosscorrelation function is only slightly shifted compared to the width of the peak. An increase in bias and std is observed below fprf = 1000, which is due to the decorrelation of the data. False peaks are then often encountered, and this influences both bias and std. The graphs shown here give the same quantitative results as shown for the simulations in the first paper [1], and other variations in the different parameters can therefore be accurately predicted from the simulated data.

VI. Linear Array Flow Imaging A linear array color flow map (CFM) image has also been acquired from the system. A linear scan was performed by using 64 elements in transmit with a Hamming apodization. The transmit aperture was then translated one element between each imaging direction. All 128 ele-

Fig. 9. Variation in pulse repetition frequency for 90◦ beam-to-flow angle and 128 measurement elements. The bias is shown on top and the standard deviation on the bottom as a function of fprf .

ments were used in receive with the interleaving scheme described in Section IV. Otherwise the standard parameters show in Table I have been used for the measurement and processing. The first example shows a color flow image for a beamto-flow angle of 60◦ . This is at the limit in which current flow images are considered not to give reliable estimates. The CFM image is shown in Fig. 10, where the color scale indicates the magnitude of the velocity in direction of the flow. The peak velocity in the vessel is 0.142 m/s. No preprocessing or smoothing of the data has been done on the displayed data. It can be seen that the velocity profile is estimated accurately and that the flow is laminar as would be expected from the construction of the flow rig. The profile is slightly asymmetric around the tube center axis, and this is due to the vessel not being perfectly round. Velocity estimates can also be found outside the vessel. These are encountered, where there is only noise measured, and they could be suppressed by considering the signal-to-noise ratio in the received signal. A more quantitative mesh plot can be seen in Fig. 11, where the velocity magnitude in direction of the flow is shown. The accuracy of the estimates can be seen here, and from Fig. 7 the standard deviation can be determined to be on the order of 2.5%. For a transverse flow, it is beneficial to keep the pulse repetition frequency low, since the lateral beam profile is much wider than the axial length of the pulse. This will lower the frame rate, and interleaved sampling should therefore be employed. The data for the image shown in Fig. 12 has been acquired by interleaving for four directions. The emission sequence and channel acquisition is then for direction 1 (even), 2 (even), 3 (even), 4 (even), 1 (odd), 2 (odd), 3 (odd), 4 (odd), and so forth. The value for Ns is 3. The transverse velocity estimation is also more


Fig. 10. Color flow map image for a beam-to-flow angle of 60◦ . The velocity is superimposed on the B-mode image of the vessel. The color brightness indicates the velocity magnitude in direction of the flow.

Fig. 11. Mesh plot for a beam-to-flow angle of 60◦ showing the velocity magnitude in direction of the flow.

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Fig. 12. Transverse color flow map image, in which the velocity is superimposed on the B-mode image of the vessel. The color brightness indicates the velocity in the direction transverse to the ultrasound beam.

Fig. 13. Mesh plot for a beam-to-flow angle of 90◦ showing the velocity magnitude in direction of the flow.

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susceptible to noise and 40 lines has therefore been used for the flow estimation. The resulting color flow map image is shown in Fig. 12. The laminar flow in the tube is clearly visible, and it should be noted that no postprocessing or filtering has been done on the image. A quantitative mesh plot can be seen in Fig. 13, where the velocity magnitude in direction of the flow is shown. The accuracy of the estimates can be seen here, and the relative standard deviation can be determined to be on the order of 4%.

VII. Conclusion An experimental investigation of a new method for directional velocity estimation has been presented. The scheme can be used in a traditional delay-sum beamformer with a focused transmit field and gives a satisfactory performance with standard linear array transducers. Various graphs for the performance of the approach were given, and it was demonstrated that a linear array color flow map image can be obtained with a satisfactory precision for a purely transverse velocity.

[2] R. Bjerngaard and J. A. Jensen, “Experimental investigation of transverse velocity estimation using cross-correlation,” in Proc. IEEE Ultrason. Symp., 2001, pp. 1405–1408. [3] J. A. Jensen, O. Holm, L. J. Jensen, H. Bendsen, H. M. Pedersen, K. Salomonsen, J. Hansen, and S. Nikolov, “Experimental ultrasound system for real-time synthetic imaging,” in Proc. IEEE Ultrason. Symp., 1999, vol. 2, pp. 1595–1599. [4] W. W. Nichols and M. F. O’Rourke, McDonald’s Blood Flow in Arteries, Theoretical, Experimental and Clinical Principles. 3rd ed. Philadelphia: Lea & Febiger, 1990, p. 41.

Jørgen Arendt Jensen (M’93–S’02) earned his Master of Science degree in electrical engineering in 1985 and the Ph.D. degree in 1989, both from the Technical University of Denmark, Lyngby. He received the Dr.Techn. degree from the university in 1996. He has published a number of papers on signal processing and medical ultrasound and the book “Estimation of Blood Velocities Using Ultrasound,” Cambridge University Press in 1996. He has been a visiting scientist at Duke University, Stanford University, and the University of Illinois at Urbana-Champaign. He is currently full professor of Biomedical Signal Processing at the Technical University of Denmark at the Department of Information Technology and head of Center for Fast Ultrasound Imaging. He has given courses on blood velocity estimation at both Duke University and the University of Illinois and teaches biomedical signal processing and medical imaging at the Technical University of Denmark. He arranged an international summer school on advanced ultrasound imaging in 1999.

Acknowledgment Technician Kjeld Martinsen is thanked for having made the mechanical parts of the flow rig. This work was supported by grant 9700883, 9700563 and 26-01-0178 from the Danish Science Foundation and by B-K Medical A/S, Denmark.

References [1] J. A. Jensen, “Directional velocity estimation using focusing along the flow direction I: Theory and simulation,” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 50, no. 7, pp. 857–872, 2003.

Rasmus Bjerngaard earned his Master of Science degree in electrical engineering from the Technical University of Denmark, Lyngby, in 2001. His thesis work named “Transverse Blood Flow Estimation and Effective Coded Excitation using Ultrasound” was done at the Center for Fast Ultrasound Imaging. He has published papers and given conference presentations about blood velocity estimation and coded ultrasound imaging. He has been employed with BK Medical collaborating with the Center for Fast Ultrasound at the Technical University of Denmark and is currently employed with Nokia Mobile Phones in the Digital Signal Processing Research and Development department.