J Med Ultrasonics
DOI 10.1007/s10396-011-0304-0

ORIGINAL ARTICLE

High-frame-rate echocardiography using diverging transmit
beams and parallel receive beamforming
Hideyuki Hasegawa • Hiroshi Kanai

Received: 23 February 2011 / Accepted: 20 March 2011 The Japan Society of Ultrasonics in Medicine 2011

Abstract
Purpose Echocardiography is a widely used modality for
diagnosis of the heart. It enables observation of the shape ofthe heart and estimation of global heart function based on
B-mode and M-mode imaging. Subsequently, methods for
estimating myocardial strain and strain rate have beendeveloped to evaluate regional heart function. Furthermore,
it has recently been shown that measurements of transmuraltransition of myocardial contraction/relaxation and propagation of vibration caused by closure of a heart valve would
be useful for evaluation of myocardial function and viscoelasticity. However, such measurements require a frame rate
much higher than that achieved by conventional ultrasonicdiagnostic equipment. In the present study, a method basedon parallel receive beamforming was developed to achieve
high-frame-rate (over 300 Hz) echocardiography.
Methods To increase the frame rate, the number oftransmits was reduced to 15 with angular intervals of 6,and 16 receiving beams were created for each transmission
to obtain the same number and density of scan lines asrealized by conventional sector scanning. In addition,
several transmits were compounded to obtain each scanline to reduce the differences in transmit–receive sensitivities among scan lines. The number of transmits forcompounding was determined by considering the width of
the transmit beam. For transmission, plane waves anddiverging waves were investigated. Diverging waves

showed better performance than plane waves because thewidths of plane waves did not increase with the range
distance from the ultrasonic probe, whereas lateral intervalsof scan lines increased with range distance.
Results The spatial resolution of the proposed method
was validated using fine nylon wires. Although the widths
at half-maxima of the point spread functions obtained bydiverging waves were slightly larger than those obtained byconventional beamforming and parallel beamforming withplane waves, point spread functions very similar to thoseobtained by conventional beamforming could be realizedby parallel beamforming with diverging beams and compounding. However, there was an increase in the lateralsidelobe level in the case of parallel beamforming withplane and diverging waves. Furthermore, the heart of a23-year-old healthy male was measured.
Conclusion Although the contrast of the B-mode image
obtained by the proposed method was degraded due to theincreased sidelobe level, a frame rate of 316 Hz, muchhigher than that realized by conventional sector scanning ofseveral tens of Hertz, was realized with a full lateral field ofview of 90.
Keywords Diverging beam  Parallel beam forming High-frame-rate imaging  Echocardiography

Introduction
H. Hasegawa (&)  H. Kanai
Graduate School of Biomedical Engineering, Tohoku University,
Aramaki-aza-Aoba 6-6-05, Aoba-ku, Sendai 980-8579, Japane-mail: hasegawa@ecei.tohoku.ac.jp
H. Hasegawa  H. Kanai
Graduate School of Engineering, Tohoku University,
Aramaki-aza-Aoba 6-6-05, Aoba-ku, Sendai 980-8579, Japan

Echocardiography is one of the predominant modalities fordiagnosis of the heart because it provides a cross-sectional
image of the heart noninvasively in real time. Owing to thehigh temporal resolution of ultrasonic diagnostic equipment, global heart function, such as ejection fraction (EF),can be estimated based on B-mode and M-mode imaging

123

J Med Ultrasonics

much more easily compared with other diagnostic modalities, such as magnetic resonance imaging (MRI) or computed tomography (CT). To evaluate regional myocardial
function quantitatively, methods for measurements of
myocardial strain and strain rate have been developed[1–3]. These methods enable estimation of regional
deformation of the heart wall based on measurements ofmovement. Although measured strain and strain ratethemselves are useful for evaluation of regional myocardial
function, it has recently been shown that measurements oftransmural transition of myocardial contraction/relaxationand propagation of vibration caused by closure of a heart
valve would be useful for evaluation of myocardial function and viscoelasticity [4–6]. However, such measurements require a frame rate much higher than that achievedby conventional ultrasonic diagnostic equipment; forexample, electrical excitation propagates in Purkinje fibers
and ventricular muscle at typical velocities of 0.3–4 m/s[7], and corresponding propagation velocities of myocardial contraction of 0.5–7 m/s were measured by ultrasound[5, 8]. A high frame rate, typically higher than 200 Hz,
which is much higher than that realized by conventional
ultrasonic diagnostic equipment of several tens of Hertz, isrequired to measure the propagation of this electromechanical wave and the resulting transient small motion of
the heart wall.
Konofagou et al. [9] and D’hooge et al. [10] increased
the frame rate to above 200 Hz by reducing the size of the
field of view and the total number of scan lines in an
ultrasonic image. Furthermore, Konofagou et al. introduced an electrocardiogram (ECG)-gating technique inultrasound imaging to combine individual small sectors
into a large field of view [11]. In this method, the lateralsize of a sector (corresponding to the number of scan lines)
obtained in one acquisition is narrowed to achieve a higher
frame rate of about 500 Hz. By measuring a number ofsmall sectors during the corresponding number of cardiac
cycles, the measured small sectors are combined into alarge sector format based on ECG gating. Although thismethod achieves a frame rate of about 500 Hz, which ismuch higher than the conventional frame rate of several
tens of Hertz, measurements for a number of cardiac cycles
are required.
To achieve a high frame rate of about 500 Hz without
ECG gating, we used sparse sector scanning, in which thenumber of scan lines was decreased to about 10 [12]. In thismethod, the angle intervals between scan lines are
increased to obtain a large lateral field of view with a small
number of scan lines. Therefore, the lateral image resolution is significantly degraded.
The above-mentioned methods are based on conventional beamforming. Therefore, they need to sacrifice the123

density of scan lines or field of view to achieve a highframe rate. To overcome this problem, parallel receive
beamforming with a wide transmit beam has been developed [13] to illuminate a wider region by one transmission
to reduce the number of transmissions. This could be donein the cited study by conventional transmit beamforming(focusing at a certain range distance) because such beams
are wide in the region shallower than the focal distance(between the transducer surface and the focal point). Using
this method, real-time three-dimensional (3D) imaging of
the heart was realized at a frame rate of a few tens of Hertz.
However, the width of the transmit beam is narrower than
the size of the aperture, and this would limit the number ofreceiving beams created by one transmission.
Lu et al. [14–17] proposed an alternative imaging
method using an unfocused but nondiverging transmit
beam, namely, a limited diffraction beam. Unfocused
beams achieved a wider beam width, and nondiverging
beams used in these cited studies prevent insonified energy
from being spread to assure the required penetration depth.
However, the width of a nondiverging beam is still limitedby the size of the aperture.
On the other hand, diverging beams have potential toenlarge the region illuminated by one transmission. In
synthetic-aperture ultrasound imaging, a single element ora small number of elements are used to produce sphericalwaves [21, 22]. Although a spherical wave can illuminate awide area by one transmission, acoustic pressure significantly decreases with propagation distance, and the signalto-noise ratio (SNR) of the received signal would be significantly reduced.
In the present study, the feasibility of using a diverging
transmit beam in ultrasonic imaging with parallel beamforming [18–20] was investigated to achieve a frame rate
above 200 Hz with adequate lateral spatial resolution,
wider field of view, and no ECG gating. Diverging waves
can be produced by using all transducer elements in an
ultrasonic array probe to obtain ultrasonic echoes with
better SNR [23]. The width of the diverging angle waslimited to suppress the decay of acoustic pressure due tothe propagation distance. Furthermore, the diverging beam
was steered to obtain an ultrasonic image of a heart with afull angle of 90 with a limited beam width. To increase theframe rate, the number of transmits was reduced to 15 witha transmit angular interval of 6, and 16 receiving beams
were created in each transmit to obtain the same number
and density of scan lines as realized by conventional sector
scanning. The spatial resolution of the proposed imaging
method was evaluated by basic experiments using finenylon wires. Furthermore, B-mode images of the heart of a23-year-old healthy male measured by the proposed
method were obtained.

J Med Ultrasonics

Materials and methods
Mathematical description of ultrasound waves emitted
from transducer elements
Let us describe ultrasound waves emitted from transducer
elements of a phased-array ultrasonic probe. To achieve aframe rate over 200 Hz under a typical pulse repetition
frequency of 5 kHz (realized by the ultrasound system usedin the present study with an observation range setting of
130 mm), the number of transmits should be \25. Therefore, in the present study, plane waves or diverging
waves were transmitted in 15 directions fmHgðm ¼ 7;
6; . . .; 0; 1; . . .; 7Þ with angular intervals of H ¼ 6 . The
ultrasonic wave gi;m ðp; tÞ at time t from the time of transmission, which is emitted from the ith transducer element(i = 0, 1, …, L - 1) in the mth transmission and insonifies to a spatial point p ¼ ðr; hÞ, as shown in Fig. 1, isexpressed as follows:
gi;m ðp; tÞ ¼ si ðt  st;i;m ðpÞÞ;ð1Þ

where si(t) is the impulse response of the ith transducer
element, and st;i;m ðpÞ is the time delay due to propagationof an ultrasonic wave from the ith element to the spatial
point p. The time delay st;i;m ðpÞ of gi;m ðp; tÞ is given by
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
 2
r 2 cos2 h þ r sin h  i  L1
2 Dxst;i;m ðpÞ ¼
c0
þ TTBF;i;m ;ð2Þwhere Dx and c0 are the lateral pitch of transducer elements
and speed of sound, respectively, and TTBF,i,m is the timeΔx..
.......
0 i
L−1

i . Δx . sin(m Θ)mΘθrr cos(m Θ − θ )pFig. 1 Illustrations of a plane wave insonifying to spatial point p ¼
ðr; hÞ and propagation distance r cosðmH  hÞ required to illuminate
spatial point p; which is located at distance r from the center of thearray, using a plane wave

delay applied to the ith element in the mth transmission by
the transmit beamformer.
To emit a plane wave at steering angle of mH; TTBF;i;mshould be given by( iDxsinðmHÞ
if m  0;c0
TTBF;i;m ¼ ðiLþ1ÞDxsinðmHÞ
ð3Þ
if m\0:c0

ði ¼ 0; 1; . . .; L  1ÞThe time delay TTBF,i,m applied by the transmit beamformer
is greater than or equal to zero.
For a circular planar transducer, the Fresnel zone (rangeof near field) is defined by the diameter of the aperture D
and the ultrasonic wavelength k as D2/(4k). The aperture
width D of the sector probe and the ultrasonic wavelength kused in the present study were about 20 mm and about
0.4 mm (center frequency 3.75 MHz), respectively.
Although the phased-array probe used in the present study
was not circular, the range of near field can be approximately obtained based on this equation. The range of theFresnel zone of the probe used was 250 mm, and thus arange of about 130 mm, which was imaged in the present
study, was included in the near field. In the near field, thewidth of a plane wave is constant. On the other hand, inultrasonic imaging in sector format, the lateral width of asmall sector imaged by one transmission increases withrange distance, and thus the performance of a plane wave
would be limited because the lateral width of a plane wave
does not increase with range distance in the near field.
To solve this problem, in the present study a diverging
wave, illustrated in Fig. 2a, was used for transmission in
addition to a plane wave. In synthetic-aperture imaging,each element is individually used to emit a spherical wave.
Such diverging waves would be useful for ultrasonicimaging in sector format. However, the intensity of theemitted wave would significantly decrease because a single
element is used. Alternatively, spherically diverging waves[22] can be produced using all the transducer elements inevery transmission. In the present study, such a diverging
wave was realized by applying a time delay TTBF,i,m to the
ith transducer element in the mth transmission, given by
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
82
2>
fðiL1>
2 ÞDxg þrf rf>< iDxsinðmHÞ þ
if m0;c0c0TTBF;i;m ¼
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
>
2
>
2
>
fðiL1
2 ÞDxg þrf rf: ðiLþ1ÞDxsinðmHÞ
þ
if m\0;c0c0
ði ¼ 0;1;...;L1Þ

ð4Þ

where rf is the distance from a virtual point source Ov
behind the array to the surface of the transducer array.
The first term in the right-hand side of Eq. 4 is required
to steer the direction of the transmit beam to mH: The
second term, which is required to realize a diverging

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J Med Ultrasonics
Fig. 2 Illustration of adiverging wave. a Propagation
distance r1 required toilluminate spatial point p; which
is located at distance r from thecenter of the array, using adiverging wave. b Geometry forconsideration of time delays
applied to transducer elements
for diverging wave transmission

(a)

(b)

z
x

1 ( L −1) Δx
2(L −1)Δx
Ov (0, 0)Ov
rf
0.. i ....... L−1( x0 , z 0 )

rf
r’

θ
r mΘ
r1

Δx

p(x , z )wave, was obtained in the present study by considering
the geometry illustrated in Fig. 2b. The second term
depends on the distance from the virtual point source Ov
to the ith element in Fig. 2b.

sRBF;i;m ðpÞ ¼ TTW;m ðpÞ
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
2
r 2 cos2 h þ r sin h  Dx i  L1
2
:
þ
c0
ð6Þ

Parallel receive beamforming
In this study, ultrasonic beams (plane or diverging waves)emitted in 15 directions at angle intervals of H ¼ 6 and 16
receiving beams with angle intervals of 0.375 were created for each transmit to realize a similar number anddensity of scan lines as obtained by conventional sectorb m ðpÞ; of the beamformed radio
scanning. The value, O
frequency (RF) signal at a spatial point p is generated fromultrasonic echo signals {yi,m(t)} received by the elementsði ¼ 0; 1; . . .; L  1Þ; which contain echoes scattered at all
points illuminated by the mth transmission, as follows:b m ðpÞ ¼
O

L1
X

wr;i  yi;m ðt  sRBF;i;m ðpÞÞ;

ð5Þ

i¼0

where wr;i ði ¼ 0; 1; . . .; L  1Þ corresponds to the receive
apodization, and sRBF;i;m ðpÞ is the time delay which should
be applied by a receive beamformer to compensate thepropagation delay of the emitted wave from the probe to p
and that of the scattered wave from p to the ith element.
The time delay sRBF;i;m ðpÞ, which was applied by thereceive beamformer to echo signal yi,m(t) received by theith element, is given by123

The second term of Eq. 6 corresponds to the propagation
delay of a scattered echo from the spatial point p to the ithelement. The first term, TTW;m ðpÞ; of Eq. 6 corresponds tothe propagation delay of the emitted ultrasonic wave tospatial point p, which depends on the receiving beam angle
h. In the present study, as illustrated in Fig. 1, for a planewave, TTW;m ðpÞ was assigned as follows:
TTW;m ðpÞ ¼

r cosðh  mHÞ
:
c0

ð7Þ

For diverging waves, as illustrated in Fig. 2b, TTW;m ðpÞ
was assigned as follows:
pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
x2 þ z2  rf þ r 0
TTW;m ðpÞ ¼;
ð8Þ
c0
x ¼ rf sinðmHÞ  r 0 sinðmHÞ þ r sin h;ð9Þ

z ¼ rf cosðmHÞ þ r 0 cosðmHÞ  r cos h;

ð10Þ

r0 ¼

1
 ðL  1Þ  Dx  sinðmHÞ;2

ð11Þ

where (x, z) is the position of p in Cartesian coordinates.
By changing hððm  0:5Þ  H  h\ðm þ 0:5Þ  HÞ atintervals of 0.375 at each range position r in each of the m

J Med Ultrasonics

b m ðpÞg at alltransmissions, beamformed RF signals f O
spatial points fp ¼ ðr; hÞg in the field of view are obtained.
Problem in parallel beamforming with phased array
To obtain an ultrasonic image in sector format, ultrasonicbeams need to be steered. Therefore, the directivity of theultrasound beam changes depending on the steering angle.
In receive beamforming, the difference between the
directivities of neighboring receiving beams is not so significant because the angle intervals of receiving beams are
small (0.375). However, such difference is significant intransmission because of the relatively large angle intervalof neighboring transmit beams of 6 (used in the present
study). This significant change in directivity in transmission produces discontinuities in a resultant ultrasonicimage at a pitch of 6, which corresponds to angularintervals of transmit beams, because the transmit–receive
directivity is defined by the product of the transmit andreceive directivities [24]. Figure 3 shows a B-mode imageof the heart of a 23-year-old healthy male, which was
obtained using parallel beam forming expressed by Eq. 5
with plane wave transmission. As can be seen in Fig. 3,
there are significant discontinuities at the edges of eachregion imaged by one transmission.
Spatial compounding of multiple transmits in receive
beamforming
As described in the previous section, there are discontinuities in the ultrasound image when each scan line iscreated by a single transmission, because the lateralintensity profiles of transmit beams significantly differ
between transmissions due to the large angular interval oftransmit beams (in general, the intensity is decreased by

Fig. 3 Longitudinal B-mode image of the heart of a 23-year-old maleobtained by parallel beamforming without spatial compounding

steering due to the directivities of the transducer elements).
Such discontinuities consist of high spatial (angular) frequency components, which degrade the image quality. A
simple way to reduce such discontinuities (high spatial
frequency components) in an ultrasound image obtained byparallel beamforming is to use spatial moving average, i.e.,
low-pass filtering. The spatially averaged beamformed RFb s ðr; hÞ at a spatial point p ¼ ðr; hÞ is expressed as
signal O
follows:b s ðr;hÞ ¼
O

Ms
X

b m0 ðr;hþHjÞ
wj  Oj¼Ms



b m0 ðr;hþHjÞexpfj2pfh ðHjÞg
wj  O
¼

j¼M
Ms
X

s

;
fh ¼0

ð12Þ
where the number of averaged signals is expressed by(2Ms ? 1), wj is a weighting function, and m0 is thetransmission number that gives the minimum difference
between the direction of transmission mH and the direction h of point p ¼ ðr; hÞ: As can be seen in Eq. 12, themoving average operation corresponds to a Fouriertransform with respect to angular frequency fh of zero.
The spatial frequency spectrum obtained by Eq. 12 isexpressed by the convolution of the spatial frequency
b m ðr; hÞ, and thus the spatial
characteristics of wj and O
frequency characteristics of the low-pass filtering appliedby the moving average operation is determined by that of
the weighting function wj. It is well known that a rectangular weighting function exhibits a higher sidelobe
level in the frequency domain, which corresponds tohigher leakage of high spatial frequency components.
Therefore, a tapered function, such as a Hanning window,
which exhibits lower sidelobe level, is preferable for theweighting function wj.
Although the high spatial frequency components can be
reduced by spatial averaging, the image would be blurred,b m ðpÞg at different
because the beamformed RF signals f O
spatial positions fpg are averaged in Eq. 12. To avoid suchb m ðpÞg
blurring effect, in the present study, RF signals f O
beamformed with respect to the same spatial position p indifferent transmissions {m} are compounded. This procedure has a similar effect as Eq. 12, because the lateralintensity profiles of unfocused beams, such as plane wave
and diverging wave, are almost homogeneous at every
angle h within the beams. Therefore, we assumed thatb m0 ðr; h þ H  jÞ  O
b m0 þj ðr; hÞ:O
By replacing the summation with respect to angle in
Eq. 12 by that with respect to transmission, the comb c ðpÞ at p is expressed
pounded beamformed RF signal O
as follows:123

J Med Ultrasonics
McX

b c ðpÞ ¼
O

b m0 þj ðpÞ;wc;m0 þj ðpÞ  O

ð13Þ

hw ¼ 2 arctanj¼Mc

where the number of compounded signals is expressed as(2Mc ? 1). In the present study, Hanning weighting wasused in spatial compounded signals, expressed as follows:()ðh  mHÞ
2 p

wc;m ðpÞ ¼ cos;
ð14Þ
2 12  ð2Mc þ 1ÞH
where the number of compounded signals is expressed as(2Mc ? 1). In the present study, Mc was determined fromthe angular width of the emitted wave by considering thetransducer geometry, as illustrated in Fig. 4. For planewaves, the angular width hw at range distance r is given byL  Dxhw ¼ 2 arctan
:
ð15Þ
2r
For diverging waves, the diverging angle / is obtained asfollows:
L  Dx/ ¼ arctan
:
ð16Þ
2rf
In the present study, using the diverging angle /, the lateralbeam width lw at range distance r is approximately given bylw ¼ ðrf þ rÞ tan /:ð17Þ

The angular width hw for a diverging wave is obtained asfollows:

Fig. 4 Illustration of angularwidth hw of emitted wave.
a Plane wave. b Diverging wave

(a)


lw
:
r

ð18Þ

The number of compounded signals (2Mc ? 1) isdetermined so that the contribution of the emissions
whose directions are different from the direction ofinterest h by larger than half the angular beam width hw
is gradually decreased. In the present study, this was givenby ð2Mc þ 1ÞH=2\hw : To satisfy this condition, thenumber of compounded signals was determined as follows:
hw
:
ð19Þ
H
In the present study, the angular beam width hw was
introduced to consider the relationship between the beamwidth and the interval of transmit beams, because sparser
transmissions require a larger beam width to illuminate alarger region between the directions of successive transmissions. The angular beam width is more convenient thanthe beam width in distance, because the angular interval oftransmit beams does not change with the range distance,
whereas the interval in distance changes. In Fig. 5, angularwidths {hw} calculated for plane and diverging waves using
Eqs. 15 and 18 are plotted as functions of range distance r(the aperture size L  Dx ¼ 19:2 mm was the same as that of
the ultrasonic probe used). The angular width hw of adiverging wave at distance rf from a virtual point source
larger than 100 mm does not change so much compared withthat of a plane wave. At the longest range distance of interestin the present study (130 mm), the angular width hw doubles
Mc ¼

(b)

L Δx

L Δx

φ
0.. i ....... L−1

0.. i ....... L−1

Δx θ

Δx

r0

w

lw
123

lw

θw

rf

r0

J Med Ultrasonics

angular width [degrees]

100
plane
diverge ( rf = 50 mm)
diverge ( rf = 100 mm)
diverge ( rf = 150 mm)
diverge ( rf = 200 mm)
diverge ( rf = 300 mm)

80
60
40
20
0

0

20

40

60

80

100

120

140

range distance [mm]Fig. 5 Angular widths {hw} calculated for plane and diverging waves

at rf = 100 mm and triples at rf = 50 mm. The angularwidth hw would further increase at smaller rf. However, theintensity of the emitted wave would decrease further.
Therefore, in the present study, diverging waves at rf = 100
and 50 mm are investigated in the subsequent sections.

Evaluation of spatial resolution using a wire phantom
In the present study, a commercial ultrasonic diagnostic
system (a-10; Aloka, Tokyo, Japan) was used with a 3.75MHz phased-array probe. This system was modified so that
RF echoes received by L = 96 individual elements could beacquired at sampling frequency of 30 MHz for offline processing (receive beamforming, spatial compounding, etc.).
In the basic experiment, fine nylon wires (diameter*100 lm) placed in water were used for evaluation of thespatial resolution. Figure 6a–d shows B-mode images of thewires obtained by conventional sector scanning and parallel
beamforming with spatial compounding using planewaves and diverging waves at rf = 100 and 50 mm,
respectively. In Fig. 6(1) and (2), rectangular apodization
ðwr;i ¼ 1; i ¼ 0; 1; 2; . . .; L  1Þ and Hamming apodization
ðwr;i ¼ 0:54  0:46 cosð2pi=LÞ; i ¼ 0; 1; 2; . . .; L  1Þ wereused, respectively. As can be seen in Fig. 6, the sidelobe
levels significantly increased when rectangular apodization
was used. Therefore, Hamming apodization was used insubsequent experiments.
In the B-mode image obtained by parallel beamformingwith plane waves, the point spread function at larger steering
angle (surrounded by white dashed lines in Fig. 6, 2b) was
distorted (split in the lateral direction) because the widths ofplane waves were narrow compared with diverging waves
and the widths decreased when the steering angle wasincreased. Therefore, use of plane waves is limited toimaging at smaller steering angles. On the other hand, such
distortion was not found in the B-mode images obtained byparallel beamforming with diverging waves.

Figure 7a, b shows axial and lateral profiles of theimages (corresponding to point spread functions) at angular
position h of 0 and range distance r of 41 mm, respectively. The widths at half-maxima of the point spreadfunctions shown in Fig. 7 are presented in Table 1. As
shown in Fig. 7, plane wave transmission achieved the best
lateral spatial resolution. Although the widths at halfmaxima of the point spread functions obtained by diverging waves were slightly larger than those obtained byconventional beamforming and parallel beamforming withplane waves, point spread functions very similar to thoseobtained by conventional beamforming could be realizedby parallel beamforming with diverging beams and compounding. Figure 8a, b illustrates point spread functions
created by compounding plane and diverging waves,respectively. The wavefronts and point spread functions
shown by the dashed and solid lines illustrate thoseobtained by transmission at the lowest and the maximum
steering angle in beamforming with respect to spatial point
p: The overlapping area of two point spread functions in
Fig. 8 is enhanced in the resultant point spread function
obtained by compounding. As can be seen in Fig. 8, theoverlapping area obtained by plane waves is smaller thanthat obtained by diverging beams, even when the maximum
steering angles are the same. Therefore, it was consideredthat plane wave transmission achieved the best lateral
spatial resolution. However, there was an increase of thelateral sidelobe level with use of parallel beamforming withboth plane and diverging waves. Although this increase of
the sidelobe level would degrade image contrast, lateral
spatial resolution comparable to that of conventional sector
scanning was achieved by the proposed method.
In Fig. 7, the number of compounded signals (2Mc ? 1)
was determined by Eq. 19. In Fig. 9(1) and (2), Mc wasalso determined by Eq. 19; however, the maximum Mc waslimited to 4 and 2, respectively. For diverging waves,
B-mode images obtained by limiting the maximum numberof compounded signals were better than those obtainedwith unlimited Mc, as shown in Fig. 6. In the present study,
the propagation delay of the emitted wave was calculated
based on Eq. 8 without considering wavefront distortiondue to beam steering. Therefore, it can be considered that a
number of compounded signals Mc larger than 2 (corresponding to larger differences among the steering angles inemissions used for compounding) degraded the resultant
images, because it would be difficult to estimate propagation delays at larger steering angles using Eq. 8 and thelarge number of transmissions (meaning a large difference
among the angles of transmissions) used for compounding
degrades coherent compounding. As in Fig. 7, Fig. 10shows lateral profiles of envelopes of compounded beamformed RF echoes at range distance of 41 mm obtained bya diverging beam at rf = 50 mm with and without the123J Med Ultrasonics
Fig. 6 B-mode images of finewires obtained bya conventional sector scanningand parallel beamforming usingb plane waves, c diverging
waves at rf = 100 mm, andd diverging waves at
rf = 50 mm. 1 Rectangular and2 Hamming apodizations wereusedlimitation Mc B 2. In Fig. 10, only profiles obtained with adiverging beam at rf = 50 mm are shown, because thenumber of compounded signals is largest among thetransmit beams used in the present study. As shown in
Fig. 10, degradation of coherent compounding reduces thedifference between the main lobe and sidelobe levels anddoes not improve the spatial resolution. Consequently, inthe present study, the number of compounded signals(2Mc ? 1) was determined by Eq. 19; however, its maximum was restricted to be 5 for diverging waves.

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In general, the insonified energy of a diverging wave
spreads and acoustic intensity decreases with propagation
distance. To reduce this decay, in the present study, thewidth of the diverging beam was limited. Figure 11 shows
the axial profiles of the ultrasound images of the wire
phantom (shown in Fig. 6) at lateral angle of 0. As
expected, the intensity at the deepest wire was strongest
when focusing was done in both transmit and receive, as
shown in Fig. 11. Although the intensity was lower thanthat obtained by focusing in both transmit and receive, theJ Med Ultrasonics(a)normalized amplitude [dB]0conventionalplane
diverging ( rf = 100 mm)
diverging ( rf = 50 mm)

−20

−40

−60

−80

40

35

50

45

55

range distance [mm]

p

p

(b)
normalized amplitude [dB]

0

−20

−40

−60

−80
0

20

60

40

80

lateral angular position [degrees]Fig. 7 Axial and lateral profiles of envelopes of beamformed RF
echoes obtained by respective methods. a Axial profile at lateralangular position of 0. b Lateral profile at range distance of 41 mm

Table 1 Widths at half-maxima of point spread functions shown in
Fig. 7
Conventional Plane Diverging wave Diverging wave
beamforming wave (rf = 100 mm) (rf = 50 mm)
Axial (mm)

0.73

0.71

0.88

0.84

Lateral (mm) 0.68

0.52

0.81

0.86

diverging waves used in the present study achieved decays
of intensities (Fig. 11c, d) similar to those realized by planewaves (Fig. 11b).

In vivo imaging of a human heart
Figure 12a–d shows B-mode images of the heart of a23-year-old healthy male obtained by conventional sector
scan and parallel beamforming with plane waves anddiverging waves at rf = 50 and 100 mm, respectively. The
maximum of the number of compounded signals Mc waslimited to 2 for diverging waves. Although a B-mode
image of the heart could be obtained by plane wave
transmission, the point spread function produced by

(a)

(b)

Fig. 8 Wavefronts and point spread functions produced by a planewaves and b diverging waves

parallel beamforming with plane waves was split in thelateral direction, as shown in Fig. 6. Therefore, it might bebetter to use plane wave transmission with a smaller
maximum steering angle. By using diverging waves, as
shown in Fig. 12c, d, B-mode images of the heart could beobtained at a high frame rate of 316 Hz with a full lateralfield of view of 90, and the diverging waves at rf = 50
and 100 mm showed similar performance. Although image
contrast was degraded due to the higher lateral sidelobe
levels, a B-mode image with image quality comparable tothat obtained by conventional sector scanning could beobtained at a frame rate (316 Hz) significantly higher thanthat (39 Hz) obtained by conventional sector scan, and afull field of view of 90 was achieved without requiring
ECG gating [11].

Discussion
In the present study, a method based on parallel beamforming
was investigated for high-frame-rate echocardiography. To

123

J Med Ultrasonics
Fig. 9 B-mode images of finewires obtained by parallel
beamforming with a planewaves, b diverging waves at
rf = 100 mm, and c diverging
waves at rf = 50 mm. The
maximum number ofcompounded signals wasconstrained to be 1 4 and 2 2

normalized amplitude [dB]0

Mc < 2
non−limited

−20

−40

−60

−80
0

20

40

60

80

lateral angular position [degrees]Fig. 10 Lateral profiles of envelopes of beamformed RF echoes at
range distance of 41 mm obtained by a diverging beam at
rf = 50 mm with and without the limitation Mc B 2

realize B-mode imaging in sector format based on parallel
beamforming, spherically diverging waves were used intransmission.

123

In the present study, in receive beamforming, the propagation delay of the emitted diverging wave was calculated
by considering the geometry of the transducer array and thevirtual point source. However, increase of the number ofcompounded signals Mc, corresponding to increase of thetransmission steering angle from the direction of interesth, degraded the resultant B-mode images. This would becaused by wavefront distortion of the emitted wave due tosteering. In future work, methods for accurate realization of
the desired wavefront or accurate calculation of the resultant wavefront will be necessary to increase the number ofcompounded signals for further improvements of image
resolution, because the difference in angles of wavefronts indifferent transmissions would increase when using a greaternumber of transmissions for compounding, as illustrated inFig. 8. In addition, phase aberration correction [26, 27]
would be useful for receive beamforming.
Although diverging waves should be used to achieve afull lateral field of view of 90, plane waves could be used

J Med Ultrasonics
0

(a)

−20
−40
−60
−80
−100
0

(b)

normalized amplitude [dB]

−20
−40
−60
−80
−100
0

(c)

−20
−40
−60
−80
−100
0

(d)

−20
−40
−60
−80
−100

0

20

40

60

80

100

120

140

axial distance [mm]Fig. 11 Axial profiles of the images of wires (shown in Fig. 6) atlateral angle of 0. a Conventional beamforming (focusing in bothtransmit and receive). b Parallel beamforming with plane waves.
c and d Parallel beamforming with diverging beams at rf = 100 and
50 mm, respectively

for imaging of a narrower region. Plane waves are moreeasily implemented in ultrasonic diagnostic equipment andmake it easier to calculate the propagation delay of the
wavefront. This was shown by the results in Fig. 9, where
increase of the maximum number of compounded signals
did not degrade the resultant B-mode image in the case ofplane wave transmission. The error in the calculated
propagation delay at larger steering angles was considered
to be smaller for plane waves than for diverging waves.
Figure 13 shows a longitudinal B-mode image of the heartof the same subject as in Fig. 12 obtained with plane wave
transmission and smaller steering angles. As can be seen in
Fig. 13, a B-mode image of good quality can be obtained at
a very high frame rate (1010 Hz) that is much higher thanthat (200 Hz) achieved by conventional sector scanningwith a narrow field of view [10].
The limitation of the hardware used in the present
study is that it takes about 1 min to prepare for transmission of diverging waves. During this preparation, an
operator needs to fix the position of the ultrasonic probe
without viewing B-mode images. This limitation significantly increases the difficulties of in vivo measurements,

Fig. 12 B-mode images of the heart of a 23-year-old healthy maleobtained by a conventional sector scanning, and parallel beamforming
using b plane waves, c diverging waves at rf = 100 mm, andd diverging waves at rf = 50 mm. The maximum number ofcompounded signals was limited to be 2 for diverging waves

particularly scanning of the same section several times.
In future work, we need to develop a real-time system
realizing the method proposed in the present study.

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J Med Ultrasonics

Fig. 13 B-mode image of the heart of the same subject as in Fig. 12
obtained by parallel beamforming with plane waves and a smaller
maximum steering angle (frame rate 1010 Hz)

Conclusions
In this study, a method based on parallel beamforming andspatial compounding was proposed for high-frame-rateechocardiography. Although there was no significant degradation of axial or lateral spatial resolution, the lateralsidelobe levels increased. This increased sidelobe level
degraded the contrast of the resultant B-mode image.
However, a B-mode image of a heart could be obtained at ahigh frame rate of 316 Hz with a full lateral field of view of90 and with image quality comparable to that obtained byconventional sector scanning. The image resolution
achieved by the proposed method was much better thanthat obtained by sparse scanning [12], and the proposed
method achieved a full lateral field of view without
requiring ECG gating [11].

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