博士学位論文要約（平成 23 年 9 月）

Imaging of Transverse Cross Section of Carotid Artery Using Diverging Transmit
Beams from Linear Array Ultrasonic Transducer with Multiple Steered Receive
Beamforming
Akinlolu PONNLE
Supervisor: Hiroshi KANAI, Research Advisor: Hideyuki HASEGAWA
Transverse cross sectional ultrasound imaging of the intima-media complex of the carotid arterial wall is very
difficult using conventional linear scanning. The extent of the arterial wall that is clearly imaged is very limited. The
use of multi-element diverging beam from a linear array transducer with parallel steered receive beamforming andscanning in a linear sequential fashion is proposed. The B-mode image is reconstructed from combinations of many
steered receiving beams from multiple transmissions per frame. In order to further suppress receive grating lobe
artifacts in re-constructed B-mode images, a technique is proposed, which involves modulating the receiving beams bya factor that is governed by the envelope of a corresponding signal, formed by filtering the receiving beam by abidirectional zero phase low-pass filter with a cut-off frequency that is determined by the receive-steering angle.
Using these methods, offline reconstructed B-mode images from simulations, silicone-rubber tube phantom and invivo imaging of the carotid artery showed that the extent of the clearly imaged region is wider than that of conventional
linear scanning. Also, receive-grating lobe artifacts were suppressed without significant loss in spatial resolution.

1. Introduction
In Fig. 1, fd is the distance from the virtual acoustic point
source to the array surface, and L is the transmit
sub-aperture length.
Since the transmitted beams are wide, strong reception
is possible from the directions of the receive-main lobe
and receive-grating lobes leading to grating lobe artifacts.
Therefore, a method of modulating the receiving beams
was proposed to further suppress grating lobe artifacts.

Ultrasound imaging of the intima-media complex of
the carotid arterial wall in the transverse cross-sectional
plane is very difficult using conventional linear scanningas the extent of the arterial wall that are clearly imaged
is very limited. The intima-media region of the artery isa useful place to probe in the diagnosis of atherosclerosis[1].The angular width of the limited imaged region is ameasure of the extent of the anterior and posterior wallsof the arterial cross-section that are clearly imaged, if thetransverse cross-section of the arterial lumen is assumed
to be circular.
The use of multi-element diverging beam from a
linear array transducer with parallel steered receive
beamforming and scanning in a linear sequential fashionis proposed in order to obtain a wider angular width ofimaged region without steering of transmit beams and at
the same frame rate as in conventional linear scanning.
This type of beam has previously been investigated bysome researchers for diverse purposes [2,3]. B-mode
image was reconstructed from combinations of many
steered receiving beams from multiple transmissions perframe. The transmission and reception scheme of the
proposed method is illustrated in Fig. 1.
Beam-spreadangle Φ2.

Principle
The principle of the proposed imaging method using
multi element diverging transmit beams is summarized
in Fig. 2. In this method, within a transmit-receive event,diverging beams are transmitted from a linear arraytransducer and echoes are received. From the echoes
received, steered receiving beams y(t,θ) are createdoffline at regular angular intervals (θ is the receive
steering angle). The created, steered receiving beams arethen modulated by modulating weights W(t,θ) before
being spatially combined for image formation.
Transmissionof Diverging
Beams

L
Divergingtransmit
beam

Modulation of
Receiving Beams
by W(t,θ)Combination ofMultiple
Receiving Beams

V Virtual acoustic
point source

fd

Creation ofSteered Receiving
Beams, y(t,θ)

p

y1(p)

x

W1(p)

p

y2(p) xW2(p)Linear transducer
array probe

Σ

Image
formation
at pSteeredreceiving beams
Diverging
wavefrontspyNT(p) x WNT(p)Figure 2 Overview of the principle of the proposed
imaging method.

Figure 1 Illustration of the transmission-reception
scheme of the proposed method.

1

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pulses

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Lateral[mm]
At depthof 20 mm[mm](b)Lateraldistance
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(1)
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Trailing pulses
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1010

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Main pulses-100

kPa100200 1000
0
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At (x,z) = (0,15) mm

Pressure [kPa]Time [s]Time [s]
[s]
[s]
Time
Time
[s]
Time
Time [s]
[s]
Time

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0

0

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1384
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100 -100

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Pressure [kPa]-5[kPa] [kPa]Pressure [kPa]
Pressure [kPa]Pressure
Pressure

-10

kPa

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1515

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0
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(b)

11

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(2)

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Time [s]

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14
15

Figure 4(1) (a) Simulated emitted waves and (b)AcousticLateralpressure
as measured with the hydrophone, atdistance [mm]axial depth of 20 mm. 4(2) The emitted pressure
waveform as it passes a point below the center of theaperture at an axial depth of 20 mm. (a) Simulation (b)Measurement (waveform along the white lines in (1-a)
and (1-b)).
-15

-10

-5

0

5

10

15

Acoustic field characteristics of the transmit beamfrom linear array transducer was investigated bysimulation using Field II program [6], for beams ofvarious beam-spread angles, Φ ranging from 0o to 180o.
The simulated emitted acoustic waveform was found to
be a composite of two components which in thisresearch are referred to as ‘main pulses’ and the ‘trailing
pulses’ (Figs. 4(2-a) and 4(2-b)).
The main pulses are effective for imaging, but thetrailing pulses affect the image contrast and cause depth
sidelobe and range ambiguity artifacts in B-mode images.
The trailing pulses depend on the beam parameters suchas the aperture length, inter-element pitch and thebeam-spread angle. As the beam-spread angle increases,
the absolute amplitude of the main pulses reduces while
those of the trailing pulses increases. The spatial andtemporal length, as well as the amplitude of the main
and trailing pulses, vary for different locations within thebeam, but is prominent within the region defined by theboundaries of the two edges of the transmit sub aperture(Fig. 5).

Figure 3 The modulating technique.
The cut-off frequency fc of the ZP-LPF is expressed as
c
,
(1)
fc 
p1  sin  where c is the speed of ultrasound in the medium, p is
the inter-element pitch, and θ is the receive steering
angle.
The modulating signal RF(n,θ) is obtained by operation
A1 defined by(2)otherwise

where yenv(n,θ) is the envelope of the original receiving
beam signal y(n,θ), and yf(env)(n,θ) is the envelope of the
ZP-LP filtered signal yf(n,θ). The output signal ym(n,θ) is
the modulated receiving beam signal given by(3)ym (n, )  RF (n, )  y(n, ) ,

Φ = 870

Φ = 1800
0

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dB

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dB

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(b)
TP-MP Ratio

(c)

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10

dB

-10

10

(b)

3. Computer Simulations
3.1 Acoustic Field
The acoustic field of the diverging beam in waterfrom a linear array transducer was simulated using Field
II program [6]. Also, the acoustic field in water wasmeasured using a hydrophone (Toray, H025-002), andα-10 ALOKA diagnostic ultrasound equipment with a 10

0

5

(a)
Trailing Pulses field

where θ is the receive beam steering angle and (⊗)
connotes multiplication.

Main Pulses field

dB

-10

Depth [mm]Depth [mm]Main Pulses field
5

Depth [mm]y f (env) (n, )  yenv (n, ) ,At (x,z) = (0,10) mm

84

yenv(n,θ)RF(n,θ)env.
(modulating signal)
A1
det.
yf(n,θ) yf(env)(n,θ)
ZP-LPFenv.
det.
(fc ∝ θ)

if

6

-15

ym(n,θ)(modulated signal)

 y f (env) (n, )RF (n, )   yenv (n, )

1


4

2.5
2

15

1.5

20

1

25

0.5

30
-50

-40

(1)

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10

TP-MP Ratio

3

5
10

20

30

Lateral distance [mm]

40

50

0

Depth [mm]y(n,θ)(original signal)

MHz, 192-element linear array transducer (UST-5545,
Aloka Co., Ltd., Tokyo, Japan). Figure 4(1-a) shows thesimulated Atultrasonictime-pressure waves and Fig. 4(1-b)
depth of 10 mmshows the acoustic pressure as measured by thehydrophone, at a depth of 20 mm below the transducer
surface (active
transmit sub-aperture of 96 elements and
AtAtdepth
depthof of1015mmmm
beam-spreadΦ of 87o). The time axis is referenced
At depthangleof 10 mmto the time of the last element(s) to be fired, which are
the two extreme elements in the transmit sub aperture.
Time [s]In multi-element diverging beam production, theexcitation of each of the elements that make up thetransmit sub-aperture is time-delayed so that sphericalresultant wavefronts are produced in front of thetransducer array over a limited angle. During scanning,coincident active transmit/receive sub-apertures are
stepped across the array at a pitch of one element.
For one transmit beam from a transmit sub-aperture,
several steered receiving beams in parallel are formed.
The maximum steering angle of receiving beams in eachtransmit beam is limited to ±65 degrees. Angularseparation of steered receiving beams is 0.5o. B-mode
image was reconstructed from combinations of many
steered receiving beams at each image point of interest
from multiple transmissions per frame.
Grating lobe artifacts was further suppressed by atechnique of modulating the receiving beams by a factor
that is governed by the envelope of a corresponding
signal, formed by filtering the receiving beam by abidirectional zero phase Butterworth low-pass IIR filter(ZP-LPF) [4,5], with a cut-off frequency that isdetermined by the receive-steering angle. The technique
is described in Fig. 3.

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Lateral distance [mm]Figure 5 Simulated acoustic fields (from transmit sub
aperture of 96 elements), separated into fields due to (a)the main pulses, (b) the trailing pulses and (c) ratio of2

the maximum amplitude of the main pulses to the
maximum amplitude of the trailing pulses at every pointfor (1) Φ of 87o, and (2) Φ of 180o. Similar figuresobtain for sub aperture sizes of 56 and 36 elements.

Maximum observable angular width of 85o withbeam-spread angle of 87o and transmit sub aperture sizeof 36 elements was obtained from simulations (Fig.
7(2)).

Simulation also shows that within this region, thespatial average ratio of the maximum amplitude of thetrailing pulses to the maximum amplitude of the main
pulses is less than one (1) for beam-spread angles up to
120o (Fig.6).
Average TP-MP Ratio between 10 mm and 20 mm of Region R

4. Phantom Experiments
A silicone-rubber tube phantom in water was scannedin transverse cross sectional plane using conventional
linear scanning and the proposed method for beams withbeam-spread angles ranging from 87o to 150o; and sub
apertures sizes of 36, 56 and 96 elements. The scanningwas performed using α-10 ALOKA ultrasoundequipment and a 10 MHz, 192-element linear arraytransducer probe (UST-5545, Aloka Co., Ltd., Tokyo,
Japan). Received ultrasonic RF echoes were sampled ata frequency of 40 MHz. Number of transmissions foreach sub-aperture size is given by equation (4).
Figure 8(1) shows the reconstructed B-mode imagesof the silicone-rubber tube phantom. The plot in Fig.
8(2) shows the variation of the angular width (AW) of
the clearly imaged region with different beam-spreadangles, Φ, for the silicon-rubber tube phantom incomparison with the angular width obtained withconventional scanning. Maximum angular width of 60owith beam-spread angle of 87 o and transmit sub aperturesize of 36 elements was obtained from diverging beamscanning as opposed to 24o obtained from conventional
linear scanning. This is an increase of about 2.5.

Valuepulsesto Submain
pulses of the acoustic beam between
0.8
aperture size: 36 elements
Submm
apertureelements
depth
andsize:
2056mmbelow the transducer surface
0.6 of 10
Sub aperture size: 96 elementsfor0.4sub aperture sizes of 36, 56 and 96 elements.
0.2

3.2 0Virtual Scanning
20
40
60
80
100
140
160
A 0 2-interfacecylindricaltube120composedof180point
 [deg]scatterers of inter-scatterer distance of 20 μm (outer wall
diameter of 10 mm and inner wall diameter of 8 mm)
was simulated, and virtual scanning in the transverse
plane, using conventional linear scanning and the
proposed scheme with a 192-element linear arraytransducer, were performed for various beam-spreadangles and sub apertures sizes of 36, 56 and 96 elements
using Field II program [5]. The center of the tube’s crosssection is positioned at a depth of 14.1 mm.
Number of transmissions, NT, for each sub-aperturesize is given byNT  N ea  N es  1 ,
(4)

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Lateral distance [mm] Lateral distance [mm](1) (a)

(1)
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Depth [mm]

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64

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Sub aperture size: 36 elements
Sub aperture size: 56 elements
Sub aperture size: 96 elements
Conventional (96 elements)
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distance[mm][mm]
Lateraldistance[mm][mm]Lateral
Lateraldistance
distance[mm][mm]Lateral
Lateraldistance
Lateraldistance

(a)

(b2)

(b1)

2

(b3)

Sub aperture size: 36 elements
Sub aperture size: 56 elements
Sub aperture size: 96 elements
Conventional (96 elements)

40
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(2)
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In vivo Imaging
A beam-spread angle of 90o with transmit sub
aperture size of 36 elements were selected for in vivo
imaging. In vivo imaging of the transverse cross sectionof the carotid artery of three human subjects (adultmales) were taken using the α-10 ALOKA ultrasoundequipment and the 192-element linear transducer arrayprobe used in the phantom experiments. Two scans
were performed in each experiment; conventional

180

Beam-spread angle [deg](2)Figure 7(1) B-mode images of the simulated cylindricaltube. (a) Conventional scanning, (b) Diverging beamscanning, beam-spread angle Φ of 87o and sub aperturesize of (b1) 96, (b2) 56, and (b3) 36 elements. 7(2)Variation of angular width (AW) of the imaged region
for different Φ and sub aperture sizes of 36, 56 and 96
elements.

3

160

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6

Lateral distanceAngular Width (phantom)

50

0.5
80

20

12

14

14

1

60

0

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14

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phantom. (a) Conventional scanning. (b) Diverging
beam scanning (b1) Φ of 87o and sub aperture of 96
elements, (b2) Φ of 90o and sub aperture of 56 elements,(b3) Φ of 90o and sub aperture of 36 elements. 8(2)Variation of angular width (AW) of the clearly imaged
regionBeam-spreadfor different
and coincident
transmit/receive
angleΦ,[deg]
Beam-spreadangle [deg]sub-aperture sizes of 36, 56 and 96 elements.

(b3)

(b2)

80

40

10

12

Beam-spread angle [deg]CR B-mode(phantom) images of theCR [same
receive sub aperture
Figure 8(1)silicone-rubber
tube (96)]Lateral distance [mm]

(b1)

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14

60

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Lateral distance [mm]

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Angular width vs beam-spread angle from simulation

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CR

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AW

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CR

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Angular Width [deg]10
Depth [mm]8Angular Width [deg]Depth [mm]

8

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20

Conventional

10
10

12

where Nea is the number of elements in the array and Nes
is the number of elements in the sub aperture.
8

8

8
10

Depth [mm]Sub aperture size: 36 elements
Sub aperture size: 56 elements
Sub aperture size: 96 elements
0
0
20
40
60
80
100
120
140
160
180
 [deg]Average
TP-MP Ratio
between
10 mmamplitude
and 20 mm ofof
RegionFigure6 Average
ratio
of thetheRRtrailing1
0.2

Depth [mm]0.4

Depth [mm]

Value

0.6

Depth [mm]10.8

focused linear scanning and the proposed method(diverging beam scanning). Received RF signals were
sampled at a frequency of 40 MHz and the elements’received RF data for each transmission were acquired foroffline processing.
Figures 9(a) and 9(b) shows the re-constructed
B-mode images obtained from the carotid arteryscanning of the first subject. Figure 9(b) was
re-constructed from 141 sequential transmissions(symmetrical about center of lumen) per frame. Widerregions of the posterior intima and adventitia can be seenin the diverging beam image than in the conventional
focused beam image. The average result obtained (fromthe three subjects) for the angular width from diverging
beam scanning is about 45o and 24o from conventional
linear scanning; yielding a ratio of about 1.9.

16 16

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Lateraldistance[mm]

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Depth [mm]10Depth [mm]

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Magnitude [dB]

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(a)

rcv beams
ZP-LPF beams
mod-rcv beams

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1

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Depth [mm]Positions of the scatterers

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Lateral distance [mm]

(1)

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Depth [mm]

(c)

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Depth [mm]1020Lateral distance [mm]

(1)

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Lateral distance [mm]
ZP-LPF Receiving Beams

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(b) 0

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Mod-Receiving

30

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0

(c)

(2)

References
1) H. Hasegawa and H. Kanai, IEEE Trans. UFFC, 55(2008) 1921-1934.
2) M. Karaman, P. Li, and M. O’Donnell, IEEE Trans.
UFFC, 42 (1995) 429-442.
3) G. R. Lockwood, J. R. Talman, and S. S. Brunke,
IEEE Trans. UFFC, 45 (1998) 980-988.
4) F. Gustafsson, IEEE Trans. Signal Process, 44 (1996)
988-992.
5) I. W. Selesnick and C. S. Burrus, Proc IEEE Inter
Conf Acoust Speech Signal Proces, 3 (1996)
1688-1694.
6) J. A. Jensen, Med. Biol. Eng. Comp., 34, (1996)
351-353.

15

(c)

20

0

Conclusion
This research has demonstrated through simulations,phantom and in vivo imaging that by employing
multi-element diverging beams from a linear arraytransducer, improved image of the carotid artery in thetransverse cross-sectional plane can be obtained than ispossible with conventional linear scanning. In thismethod, there is no need for steering of transmit beams.
Also, the proposed method of modulation ofreceiving beams further suppresses receive-grating lobe
artifacts. It is effective for keeping the phases of thesteered receiving beams unaffected as well forpreserving the spatial resolution of the reconstructed
image.

rcv beams
ZP-LPF beams
mod-rcv beams

30
Magnitude [dB]

Depth [mm]

15

15

20

7.

rcv beams
ZP-LPF beams
mod-rcv beams

5

30

15

Figure 11 Reconstructed B-mode images of (1)silicone-rubber tube phantom in the transverse
cross-sectional plane, and (2) carotid artery of the firstsubject in the transverse cross sectional plane (a) fromreceiving beams, (b) from ZP-LPF signals and (c) frommodulated receiving beams. All images are in 60 dB
range.

Suppression of Grating Lobe Artifacts
The proposed method of suppression of grating lobe
artifacts by modulation of receiving beams was applied
to reconstructed B-mode image
obtained from virtual1
scanning of simulated columns of point scatterers in
0.5
water (Fig. 10(1)), and a grating
lobe artifact suppressionof about 40 dB was realized (Fig.
10(2)).
0
0

6

10
20
Lateral distanceBeams[mm]
Mod-Receiving

10

Lateral distance [mm]

6.

10

0

0
0

(a)
(b)
Figure 9 B-mode images of the carotid artery of the firstsubject in the transverse cross sectional plane. (a)Conventional scanning, (b) Diverging beam scanning, Φof 90o and transmit/receive sub-aperture size of 36/96
elements. Images are in 50 dB range.

0

20

10

(a)
Depth [mm]Depth [mm]Depth [mm]

17

10
20
30
Lateral distance [mm]
ZP-LPF Receiving Beams

15

(b)

22

0 0

Lateral distance [mm]

0

10

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22 22
0

Diverge

16

45o

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18 18

20

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(a)

14

17 17

18

10

Depth [mm]

15 15

16

Receiving Beams

Receiving Beams

Depth [mm]15Depth [mm]Depth [mm]Depth [mm]Conv
Diverge

14 14

Depth [mm]

Conv

14

The proposed method of modulation of receiving
beams was also applied to the phantom B-mode image,and the in vivo images. It suppresses grating lobe
artifacts without loss in spatial resolution (Figs. 11(1)and 11(2)).

20

(3)

Figure 10(1) Reconstructed B-mode image of virtualscanning of simulated columns of point scatterers using
diverging beam scanning, (a) from receiving beams, (b)from ZP-LPF signals and (c) from modulated receiving
beams. 10(2) Lateral profile at a depth of 14 mm.
10(3-a) Depth profile along the scatterers of the central
column, 10(3-b) Positions of the point scatterers of10(3-a).

4