HIGH FRAME RATE ULTRASONIC IMAGING OF ARTERIESFOR DETAILED ANALYSES OF DYNAMICS
HIDEYUKI HASEGAWA1)2) AND HIROSHI KANAI2)1)

1) Graduate School of Biomedical Engineering, Tohoku University,
6-6-05 Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8579, Japan
2) Graduate School of Engineering, Tohoku University,
6-6-05 Aramaki-aza-Aoba, Aoba-ku, Sendai 980-8579, Japan
Mechanical properties of the arterial walls are significantly altered by atherosclerosis, andvarious studies have been recently conducted to measure the regional elastic properties(radial strain) of the arterial wall. We have developed a phase-sensitive correlation-based
method, namely, the phased-tracking method, to measure the regional radial strain. On
the other hand, the measurement of blood flow is an important practical routine in thediagnosis of atherosclerosis. It would be useful if the regional strain of the arterial wall aswell as blood flow could be assessed simultaneously. Such measurement would require ahigh frame rate of several kilohertz. In this study, acquisition of ultrasonic RF echoes at ahigh frame rate (about 3500 Hz) was achieved using parallel beamforming, in whichplane waves were transmitted only three times and receive beamforming created 24
beams for each transmit beam. The accuracy in measurement of the minute radial strain
was evaluated by a basic experiment using a cylindrical phantom. The error of themeasured strain from the theoretical strain profile and its standard deviation were 4.8%
and 9.5%, respectively. Furthermore, the radial strain of a carotid arterial wall and bloodflow were simultaneously imaged in vivo.

1. Introduction
Mechanical properties of the arterial walls are significantly changed byatherosclerosis, and various studies have been recently conducted to measure theregional elastic properties (radial strain) of the arterial wall [1-3]. We havedeveloped a phase-sensitive correlation-based method, namely, the phasedtracking method, to measure the regional radial strain. On the other hand, themeasurement of blood flow is an important practical routine in the diagnosis ofatherosclerosis. It would be useful if the regional strain of the arterial wall andblood flow could be assessed simultaneously. Such measurement would requirea high frame rate of several kilohertz. In this study, a high frame rate acquisitionof ultrasonic RF echoes (about 3500 Hz) was achieved using parallel beamforming [4]. The accuracy in measurement of the minute radial strain was1

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evaluated by a basic experiment using a cylindrical phantom. Furthermore, theradial strain of a carotid arterial wall and blood flow were simultaneously
imaged in vivo.
2. Principles
2.1. Parallel Beamforming
In conventional linear scanning, both transmit and receive beamforming areperformed. Therefore, the frame rate, fFR, is determined by dividing the pulse
repetition frequency (PRF), fPRF, by the number of beams, Nbm. Typically, frame
rate fFR is about 140 Hz when fPRF = 10000 Hz and Nbm = 72.
On the other hand, only receive beamforming is performed in parallel
beamforming. Many beams are created by receive beamforming for eachtransmission of a wide beam. For example, a fFR of about 3300 Hz can beachieved when fPRF = 10000 Hz and the number of transmissions, Ntr, is 3.
Parallel beamforming achieves a high frame rate at the expense of the spatial
resolution because transmit beamforming is not performed.
In this study, a plane wave was transmitted using a commercial diagnosticsystem (α-10, Aloka, Tokyo, Japan) equipped with Nt = 96 elements of a linear
array probe, and RF echoes were received by the same 96 elements. Figure 1
shows an illustration of one transmit-receive procedure. One receiving beam
was formed using the RF signals received by Ne = 72 of the 96 elements.
Therefore, (Nt − Ne) = 24 receiving beams could be formed for eachtransmission.
The number of transmissions, Ntr, was set at 3, and the element number,{ni}, used for i-th transmission (i = 0, 1, ..., Ntr) is expressed as follows:( = 0, 1, 2, … , ).
(1)=( − )∙ +By performing receive beamforming for each of the three transmissions, (Nt −Ne)·Ntr = 72 receiving beams were created. In the receive beamforming, focusing
was performed with respect to each sampled point in the scanned region. ThefPRF was set at 10416 Hz (observable depth: 74 mm), and a fFR of 3472 Hz wasachieved. In the present study, the RF signal received by each of the 96 elements
was acquired at a sampling frequency of 40 MHz for off-line processing (receivebeamforming, calculations of strain and blood flow).
In this study, the imaging plane and the surface of the linear array probe
were parallel to the arterial longitudinal direction. Under such condition, thereceiving beam at an angle, φ (in Fig. 1), of 90 degrees coincided with thearterial radial direction. Therefore, receiving beams at φ = 90 degrees were3

formed to estimate the radial strain of the arterial wall. For imaging of bloodflow, receiving beams at φ = 85 and 95 degrees were formed. As shown in Fig. 2,
these beamformed RF signals were combined for simultaneous imaging of theradial strain and blood flow. Images of the radial strain of the arterial wall andblood flow in the shadowed region in the right-hand side of Fig. 2 were obtained.

Figure 1.Illustration of one transmit-receive procedure in parallel beamforming.

The beamformed RF signals at φ = 90 degrees were processed as describedin [6] to estimate the radial strain. For imaging of blood flow, a standard double
delay line canceler was used for high-pass filtering of the beamformed RFsignals at φ = 85 and 95 degrees. The power of the high-pass filtered RF signals
was estimated and displayed based on the conventional power Dopplertechnique.
2.2. Estimation of Two-dimensional Motion of the Arterial Wall
To obtain complex signals h(x, z; n) (x and z: lateral and axial positions, n:frame number) whose phase relates to the lateral fluctuation of received echoes,
the Hilbert transform was applied to envelope signals {s(x, z; n)} of RF echoeswith respect to the lateral position x as follows:ℎ( , ; ) = HT ( , ; ) ,(2)where HTx [·] shows the Hilbert transform with respect to x.
Using the complex signal h(x, z; n), the correlation function R(x,z),n(τ) isevaluated at two different lags, τ = τx1 and τx2, as follows:∗(3)( , ), ( ) = ∑( , )∈ ℎ ( , ; ) ∙ ℎ( + , ; + 1),
where lags τx1 and τx2 were set at 0 and Δx (lateral spacing of scan lines),
respectively, and ∗ represents complex conjugate.

4Figure 2. (a) Original elasticity distribution of the tissue. (b) Ascending sequence of the elasticmodulus in an elasticity distribution. (c) Normal distribution whose number of boxes depends on thenumber of data points of (a).

The difference in phases arg[R(x,z),n(τx1)] and arg[R(x,z),n(τx2)] shows that themagnitude of the phase shift caused by the lateral displacement corresponds toΔx (in this case, the lateral displacement is artificially induced by setting the lag
in eq. (3) to be τx1 and τx2). Therefore, the lateral displacement ux(x, z; n) can be
estimated as follows:( , ; )=∠∙∠ ( , ), ( )∗( , ), ( )∙ ( , ), ().

(4)

2.3. Directional Flow Estimation Using Gradient-Based Optical Flow
Let us define the brightness of a point P(x, z) (x and z: lateral and axialpositions) by I(x, z; t) at time t (corresponding to frame n), and point P(x, z)
moves to P’(x + ux, z + uz) during a short period δt. By assuming that the echopattern {I(x, z; t)} does not change (there is only translation) during a shortperiod δt, the following relationship will be maintained.
( , ; ) = ( + , + ; + ).
(5)
By applying the Taylor expansion to eq. (5) and neglecting higher-order terms,eq. (6) is obtained as follows:++ = 0,(6)
where vx and vz are the lateral and axial velocities, respectively.
By setting a region of interest Rp around point P(x, z), mean squared error α
expressed by eq. (7) is evaluated as follows:= ∑( , )∈,++,(7)5where wx,z is the weight which is defined as the mean of envelope-detectedsignals in Rp.
By minimizing α in eq. (7) based on the least squares procedure, twodimensional velocities vx and vz at point P(x, z) at t (= frame n) are estimated.

Figure 3. B-mode images of fine wires embedded in agar. (a) Conventional linear scanning. (b)Parallel beamforming. (c) Amplitude profiles along the cyan lines in (a) and (b), which arenormalized by the maximum amplitudes of the respective profiles.

3. Basic Experimental Results
3.1. Comparison of Spatial Resolutions of Conventional Linear
Scanning and Parallel Beamforming
Nylon wires (0.1 mm in diameter) embedded in agar (403GS, Gammex, Inc.,
Middleton, WI, USA) were imaged to investigate the spatial resolution inparallel beamforming.
Figures 3(a) and 3(b) show B-mode images obtained by conventional linear
scanning and parallel beamforming, respectively. Clear images of the four wires
were obtained. In the measurement by conventional linear scanning, RF signals
focused in real time were acquired at a sampling frequency of 40 MHz.
As shown by these results, the spatial resolution was slightly degraded, butparallel beamforming achieved a much higher frame rate (3472 Hz).
3.2. Measurements of the Cylindrical Phantom for Evaluation ofAccuracy in Strain Estimation
In basic experiments for evaluation of the accuracy of strain estimation, acylindrical phantom made of silicone rubber was measured by ultrasound. The
outer and inner diameters were 10 and 8 mm, respectively. The phantom

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contained 5% carbon powder (by weight) to obtain sufficient scattering frominside the wall.

Figure 4. (a) B-mode image of the phantom in the longitudinal plane. (b) Radial strains plotted as afunction of the distance from the luminal boundary of the posterior wall. Plots and vertical bars aremeans and standard deviations for 72 ultrasonic beams.

Change in pressure inside the phantom was induced by circulating a fluidusing a flow pump. The change in internal pressure was measured by a pressure
sensor (NEC, Tokyo, 9E02-P16). The applied pulse pressure was 48 mmHg.
To measure the elastic moduli of silicone rubber for the calculation of thetheoretical strain profile, pressure-diameter testing was conducted. In that testing,the change in external diameter of the phantom was measured with a laser line
gauge (KEYENCE, Osaka, VG-035).
Figure 4(a) shows a longitudinal B-mode image of the phantom obtained byparallel beamforming. In Fig. 4(a), angles φ of the receiving beams were 90
degrees. The radial strain distribution in the posterior wall was then estimated by
the method described in [6] using the phases of RF echoes. In Fig. 4(b), theestimated radial strains are plotted as a function of the distance from the luminalboundary of the posterior wall (in the directions of the ultrasonic beams). Plotsand vertical bars show the mean and standard deviation, respectively, at eachradial position r, which were obtained by the individual strain distributions
along 72 ultrasonic beams. The solid curve in Fig. 4(b) shows the theoreticalradial strain εr,r of a homogeneous tube at each radial position r, which wasobtained using the elastic modulus E measured by different pressure-diameter
testing and the measured internal pressure. The estimated strain distributionagrees well with the theoretical strain profile. Mean error emean and standard
deviation SDmean were 4.8% and 9.5%, respectively.

74. In Vivo Experimental Results
4.1. Simultaneous Imaging of Artery-Wall Radial Strain and Blood FlowThe right common carotid artery of a 33-year-old male was measured invivo. The beamformed RF signals were envelope-detected and converted intobrightness. The envelope-detected signals (instantaneous amplitude) werenormalized by their maximum value among all frames. Let us define thenormalized envelope by Gp(j, l; k), where j, l, and k define depth, beam number,and frame number, respectively. The radial strain of the posterior wall wasestimated by applying the same procedure as in [6] to the beamformed RFsignals at φ = 90 degrees.

Figure 5. Ultrasonic images of the carotid artery of a 33-year-old male obtained at (a) the time of Rwave and (b) 0.15 s after R-wave.

Blood flow was imaged using ultrasonic beams formed with angles φ of 85
and 95 degrees. Obliquely beamformed RF signals were high-pass filtered using
a standard double delay line canceler. The powers of the high-pass filtered RF
signals were estimated by the conventional power Doppler technique. The
number of frames used for calculation of the average power was 64. The roots ofthe estimated average power were normalized by their maximum among allframes. Let us define the normalized roots of power by G85(j, l; k) and G95(j, l; k)for beam angles φ of 85 and 95 degrees, respectively. The regions scanned bybeams at these angles overlap. The normalized root of power, Go(j, l; k), for
obliquely formed beams is defined as follows:( , ; )=(, ; )( ,; )(, ; )( ,; )(),().

(8)

8Echo amplitude G(j, l; k) at each point (j, l) in the k-th frame was obtained
as follows:( , ; ) + (1 − ) ( , ; )(0 ≤ ≤ 1).
( , ; )=(9)In this study, α was set at 0.9.
Figure 5(a) and 5(b) show images of G(j, l; k) at the R-wave of theelectrocardiogram and 0.15 s after the R-wave. As shown in Fig. 5(b), echoesfrom blood particles are enhanced when the blood flow velocity is high (at 0.15s). This result shows that the proposed method successfully imaged blood flow.
4.2. Estimation of 2D Motion of Arterial Wall
Complex deformation of atherosclerotic plaque would relate to itsvulnerbility. We tried to estimate such complex motion of a carotid
atherosclerotic plaque. The red points in Fig. 4 show points of interest set in theposterior wall of the carotid artery. As shown in Fig. 6(b), in cardiac systole,
there are stretch and shearing along the arterial longitudinal direction in addition
to radial strain. Assessment of such complex motion and deformation would be
useful for evaluation of plaque vulnerability.

Figure 6. Two-dimensional tracking of points of interest (shown by the red points) in the posteriorwall of the carotid artery. At (a) 0 s and (b) 0.21 s after the time of R-wave of electrocardiogram.

4.3. Directional Flow Velocity Estimation
Figures 7(a) and 7(b) show blood flow images at two different moments.
The time difference is 6.6 ms, and there are 30 other images between them. InFig. 7(c), estimated velocities are shown by the red lines. As is well known, themagnitude of the estimated velocity decreases near the arterial wall. Althoughfurther improvements and quantitative validation are required, this result shows
the possiblity of the proposed method for quantitative measurement of bloodflow.

9Figure 7. (a) Blood flow image and (b) that 6.6 ms after (a). (c) Flow velocity estimated by gradientbased optical flow.

4.4. Measurement of Pulse Wave Velocity
One strategy for assessment of artery-wall elasticity is the measurement ofpulse wave velocity. Figure 8 shows the velocities of the carotid arterial wallmeasured at intervals of 0.2 mm along the arterial longitudinal direction. The
velocity waveforms were sampled at 3472 Hz. It was difficult to identify theleading edges of the pulsive velocities. Therefore, transients of the central timeof velocity peaks were observed. There was a difference of about 2 ms in thecentral times during the propagation along a distance of 14.4 mm. The
propagation velocity was roughly estimated to be 7 m/s. The proposed highframe rate imaging would be useful for the measurement of regional pulse wave
velocity. However, it was difficult to differentiate the change in velocity
waveform and the time shift due to propagation in time domain. Frequency
domain analysis of velocity waveforms would be useful for the evaluation of thelinearity between waveforms and the precise estimation of time delay.
5. Conclusions
In this study, a high frame rate acquisition of RF echoes (3472 Hz) wasachieved using parallel beamforming which realizes the simultaneous imaging
of artery-wall strain and blood flow. Using the proposed method, the arterial
wall strain and blood flow of a carotid artery were successfully imaged in vivo.
The proposed method would provide useful information on the dynamics of theartery for diagnosis of atherosclerosis.

10Figure 8. Velocity waveforms of posterior wall measured at intervals of 0.2 mm along the arterial
longitudinal direction.

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