Japanese Journal of Applied Physics 49 (2010) 07HF10REGULAR PAPER

Line-Focus Array Transducers for Effective Actuation of Tissue
Tomotaka Sawada1 , Hideyuki Hasegawa1;2 , and Hiroshi Kanai2;1 
1
2Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan

Received November 24, 2009; accepted March 16, 2010; published online July 20, 2010
Acoustic radiation forces induced by ultrasound can be used to apply external forces to an object, and the viscoelastic property of the object canbe evaluated by measuring the resultant regional displacement of the object using a different ultrasonic probe for measurement. However,according to safety guidelines for the use of ultrasound, the recommended intensity is below 1 W/cm2 for continuous waves. Therefore, togenerate a measurable displacement or strain by acoustic actuation, a method of effectively applying acoustic radiation forces needs to bedevised. A potential way to improve the efficiency of acoustic actuation is to use line-focus transducers. However, there are undesired fluctuationsin the emitted sound field due to the finite aperture size with uniform apodization when a single-element line-focus transducer (SELFT) is used toemit plane waves, which are focused only in the elevational direction. To suppress such undesired fluctuations, in the present study, a pair of linefocus array transducers (LFATs) was constructed to realize spatially smoother radiation forces by applying an appropriate apodization. As aresult, the three dominant undesired peaks in the sound field emitted from a SELFT were suppressed using the LFATs with the examined
appropriate apodization, and the displacement distribution induced in a phantom, which was measured by the phased tracking method using thedifferent ultrasonic probe, became spatially smooth. # 2010 The Japan Society of Applied Physics
DOI: 10.1143/JJAP.49.07HF10

1.

Introduction

The evaluation of muscle elasticity is important for
examining the health of muscle. In this study, acoustic
radiation forces resulting from focused continuous ultrasound are simultaneously applied to an object from two
opposite horizontal directions and the resultant displacement
is measured using another ultrasound transducer.
In recent years, some remote actuation methods based on
acoustic radiation forces have been reported. Fatemi andGreenleaf proposed an imaging modality that uses theacoustic responses of an object, which are closely related
to the mechanical frequency response of the medium. By
measuring the acoustic emission with a hydrophone, hardinclusions such as calciﬁed tissues in soft material weredetected experimentally.1,2) However, the spatial resolution
in the depth direction corresponds to the size of theintersectional area of ultrasound beams at two slightly
diﬀerent frequencies and is not particularly high.
Nightingale and coworkers proposed an alternative imaging method in which focused ultrasound is employed toapply a radiation force to soft tissue for a short duration (lessthan 1 ms). The viscoelastic properties of the tissue were
investigated from the magnitude of the transient response,
which was measured as the displacement dðtÞ of thetissue.3–5) In order to generate a measurable displacementdðtÞ by several ultrasonic pulses, high-intensity pulsed
ultrasound (1,000 W/cm2 ) was employed. However, according to safety guidelines for the use of ultrasound, theintensity is recommended to be below 240 mW/cm2 forpulsed waves and 1 W/cm2 for continuous waves.6) Therefore, the intensity of the pulsed ultrasound employed by
Nightingale and coworkers is far greater than that indicatedin the safety guidelines.
The maximum intensity of 1 W/cm2 for continuous waves
given by the safety guidelines corresponds to an acoustic
radiation force of 6.67 Pa, which is very small. Therefore, togenerate a measurable displacement by acoustic actuation,a method of eﬀectively applying acoustic radiation forcesneeds to be devised. In our previous study, we proposed amethod in which two cyclical radiation forces were
simultaneously applied to a phantom from two opposite
horizontal directions so that the object was cyclicallycompressed in the horizontal direction.7) A potential way
to further improve the eﬃciency of acoustic actuation is touse line-focus array transducers (LFATs). In the present
study, LFATs were newly constructed, and the voltages
applied to the transducer elements were set so that the soundpressure at the focal area became as constant as possible in
the lateral direction, whereas the sound ﬁeld was focused
only in the elevational direction. In basic experiments usinga phantom, it was conﬁrmed that a more homogeneous
distribution of displacements was successfully generatedusing the dual LFAT compared with that generated by a dual
single-element point-focus transducer (SEPFT) or a dual
single-element line-focus transducer (SELFT).
2.

Principles

2.1 Actuation method using acoustic radiation force

When ultrasound propagates in a medium (density: 1 ,sound speed: c1 ), a constant force is generated in the
direction of propagation. This force is called the acoustic
radiation force.8) When an object is assumed to be aperfectly absorbing material, the acoustic radiation pressure,PR ðtÞ, is deﬁned as the acoustic radiation force per unit area
as follows:PR ðtÞ ¼ ð1 þ R2 ÞeðtÞ;ð2:1Þ

where R and eðtÞ are the pressure reﬂection coeﬃcient andthe energy density at the interface between the medium andthe object, respectively. In eq. (2.1), the transmitted wave isassumed to be perfectly absorbed by the object behind the
medium. Using the density 2 and sound speed c2 of theobject, the reﬂection coeﬃcient R and the energy density eðtÞare deﬁned byE-mail address: kanai@ecei.tohoku.ac.jp

07HF10-1

Z2  Z1
Z2 þ Z1
2 c2  1 c1¼;
2 c2 þ 1 c1
1eðtÞ ¼fpðtÞg2 :1 c21
R¼

ð2:2Þ
ð2:3Þ

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T. Sawada et al.

For example, the speeds of sound in muscle and fat are
1,568 and 1,465 m/s, respectively. By assuming the densityof both tissues to be 1:0  103 kg/m3 , the reﬂection
coeﬃcient R is 0.034. Thus, R2 in eq. (2.1) is assumed to
be zero.
As shown in eq. (2.3), the energy density eðtÞ is proportional to the square of the sound pressure pðtÞ of the incident
ultrasonic wave. When two ultrasound waves with the same
sound pressure p0 and slightly diﬀerent frequencies, f andf þ  f , are crossed with each other, an acoustic radiationpressure PR ðtÞ, which ﬂuctuates at the frequency diﬀerence f , is generated in the intersectional area. The soundpressure psum ðtÞ generated in the intersectional area is givenbypsum ðtÞ ¼ p0 cos 2 f t þ p0 cos 2ð f þ  f Þt;

synchronized
acoustic radiation
force
y

x

0
z

time
transducer

probe

acoustic radiationforce

for measurement

for actuation

time

0transducer

for actuation
water
object25°

25°
focal point

focal point

Fig. 1. Illustration of the experimental setup for actuation and themeasurement of resultant displacements.

ð2:4Þ
(a)

and the resultant energy density eðtÞ is given by
1½psum ðtÞ2
1 c211¼½p0 cos 2 f t þ p0 cos 2ð f þ  f Þt2
1 c21
p2¼ 0 2 1 þ cos 2 f t þ cos 2ð2 f þ  f Þt
1 c1

1
1
þ cos 4 f t þ cos 4ð f þ  f Þt :22eðtÞ ¼

(b)
y

x

z

ð2:5Þ

From the second term on the right-hand side of eq. (2.5), it isfound that the energy density eðtÞ has a component at thefrequency diﬀerence  f . With respect to the low-frequency
component, the acoustic radiation pressure PR ðtÞ of eq. (2.1)
actually acting on the interface is given byp2
PR ðtÞ ’ ð1 þ R2 Þ 0 2 ð1 þ cos 2 f tÞ
1 c1
p20
ð1 þ cos 2 f tÞ:
ð2:6Þ
1 c21
To improve the spatial resolution in the measurement of the
response of an object to the acoustic radiation force, anultrasound correlation-based method, the phased tracking
method,9,10) was used to measure the distribution of theminute displacements, fdðtÞg. The accuracy of the displacement measurement by the phased tracking method has
already been evaluated to be 0.2 mm by performing basic
experiments using a rubber plate.11)’

2.2 Possibility of effective actuation by line-focus
transducers

The experimental setup used for actuation and the measurement of resultant displacements is illustrated in Fig. 1.
When the elastic modulus of an object is much greater thanthat of the surrounding medium, a single acoustic radiation
force may generate only a change in the position of theobject. For the eﬀective generation of strain in the object,
we applied two acoustic radiation forces, which were
induced by two synchronized ultrasounds both containing
frequency components at f and f þ  f , to two diﬀerent
positions in the object from two opposite directions, as
shown in Fig. 1.7) Therefore, the region compressed by thetwo acoustic radiation forces was compressed along thehorizontal axis.

Fig. 2. Illustration of strains generated by (a) the dual point-focus
transducer and (b) the dual line-focus transducer.

The directions of the strains generated by a dual pointfocus transducer and a dual line-focus transducer are
illustrated in Figs. 2(a) and 2(b), respectively. When aregion is compressed in the y-direction by two synchronizedradiation forces generated by the dual point-focus ultrasonictransducer, as shown in Fig. 2(a), the region expands in boththe x- and z-directions owing to its incompressibility. Whenthe dual line-focus ultrasonic transducer is employed, as
shown in Fig. 2(b), the region will expand further in thevertical (z) direction than in the case shown in Fig. 2(a) topreserve its volume because the region is diﬃcult to
expand in the x direction, as shown in Fig. 2(b), which istheoretically explained as follows:12)
The strains "pz and "lz in the vertical (z) direction
generated by the dual point-focus and dual line-focus
transducers are respectively given byy"pz ¼ ;ð2:7ÞE
y"lz ¼   ð1 þ Þ;
ð2:8Þ
E
where y , E, and  are the stress in the y-direction, theYoung’s modulus, and the Poisson’s ratio of an object,
respectively. By assuming that the object is an incompressible material ( ¼ 0:5) such as biological tissue, the strain
generated by the dual line-focus transducer illustrated inFig. 2(b) is 1 þ  ¼ 1:5 times larger than that generated by
the dual point-focus transducer illustrated in Fig. 2(a).

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Jpn. J. Appl. Phys. 49 (2010) 07HF10

T. Sawada et al.
synchronization

focal
length
40 mm

75 mm

signal generator
f+ f
f

adder

adder

divider

divider

power AMP

power AMP

mixer
y

35 mm
Fig. 3.

signal generator
f
f+ f

x
z

workstation

ultrasonicprobe

Illustration of the SELFT.

ultrasonictransducer θ=25°

34 ch

θ=25°

ultrasonictransducer

diagnostic
ultrasoundsystemobjectfocal
distance
80 mm
75 mm

LPF

mixer

water

block

Fig. 5.

yblock

Illustration of the experimental setup.

x
70 mm
Fig. 4.

z

Illustration of the LFAT.

In our previous study, a dual SEPFT, whose aperture sizeand focal distance were both 50 mm, was used for acoustic
actuation. In the present study, aiming for eﬀective
actuation, a new dual SELFT was constructed as illustrated
in Fig. 3. The focal distance was 40 mm. Moreover, a new
dual LFAT was also constructed to realize more ﬂexibility indesigning the sound ﬁelds. The structure of the LFAT is
illustrated in Fig. 4. This transducer is composed of 34
elements and, thus, the voltage applied to each element canbe controlled. Its aperture in the x-direction is 70 mm wide,
which is twice as wide as the SELFT of 35 mm width
illustrated in Fig. 3. The element pitch of the LFAT in Fig. 4
is 2.0 mm.
In the present study, the array was divided into threegroups: 9 or 3 elements on both sides and 16 or 28 central
elements, and the voltages applied to these groups were
weighted as (w1 : w2 : w3 ), which was deﬁned as the voltage
ratio. The voltages applied to the groups on both sides wereset at 20 –100% of that applied to the central elements(w1 ; w3 ¼ 0:2 {1:0, w2 ¼ 1:0).
3.

Experimental Setup

Basic experiments using a phantom were conducted to
conﬁrm whether it was homogeneously actuated along
the focal region of each transducer by measuring the
spatial distribution of the displacements fdz ðx; zÞg in thevertical (z) direction at multiple points fx; zg in thephantom.
The experimental setup is illustrated in Fig. 5. In order
to measure the displacement distribution fdz ðx; zÞg at ahigh spatial resolution, we employed ultrasonic diagnostic
equipment (Dynamic Imaging DIASUS) with a linear-typeprobe (center frequency: 16 MHz). The equipment was
modiﬁed to detect the minute displacement of an object
by the ultrasonic phased tracking method.9,10) The soundpressure of the ultrasonic pulse used for measurement is

56 kPa, which corresponds to an acoustic radiation force
of one-quarter that produced by the ultrasound used for
actuation. In addition, the ultrasonic pulses used for measurement are transmitted at a pulse repetition frequency of
15 kHz, which is much larger than the frequency (5 Hz) of
cyclic ﬂuctuation of the radiation force produced by theultrasound used for actuation. Therefore, the radiation
forces produced by the ultrasonic pulses used for measurement hardly aﬀect that produced by the ultrasound used for
actuation.
A homogeneous object made of gel (60  60  25 mm3 ,containing 5% carbon powder by weight to provide
suﬃcient scattering) was placed in a water tank as shownin Fig. 5. To apply the radiation pressures PR1 ðtÞ and PR2 ðtÞ,a dual ultrasonic transducer was employed. Each ultrasonictransducer (center frequency: 1 MHz) was driven by the sumof continuous waves at two slightly diﬀerent frequencies of
1 MHz and 1 MHz þ 5 Hz. Each focal point was set at thesurface of the object at a beam angle of 25 degrees from thehorizontal direction.
The ultrasound signals used for actuation (approximately
1 MHz) unintentionally received by the linear-array probe(16 MHz) used for measurement were removed by ﬁltering
to make it possible to estimate the displacement distribution
fdz ðx; zÞg.
4.

Results

4.1 Measurement of displacement at the boundary
between oil and water

As illustrated in Fig. 6, the displacement distribution
fdz ðx; zÞg along the interface between oil and water wasmeasured with ultrasound since the interface between liquids
is easily actuated at a large amplitude and the actuated region
can be easily identiﬁed. In this experiment, both beam anglesof the dual ultrasound wave used for actuation were set at 25 .
Figures 7(a) and 7(b) show the spatial distributions
fdz ðx; zÞg of displacements during one cycle of acoustic
radiation forces generated by the dual SEPFT and the dual
SELFT, respectively. Blue and red correspond to the upwardand downward displacements, respectively. Using the dual

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yT. Sawada et al.
xxytransducerzz

ultrasonicprobe

ultrasonictransducer

ultrasonictransducer

oil
θ=25°
water

probe

transducer

θ=25°
25°
oil
water

normalized sound pressure

Jpn. J. Appl. Phys. 49 (2010) 07HF10

SEPFT

1.0
0.8

SELFT
0.6
0.4
0.2
0
–40 –30 –20 –10 0 10 20
distance x [mm]Fig. 6. Illustration of the displacement measurement at the boundary ofoil and water.

30

40

depth
2 mm

Fig. 8. (Color online) Spatial distributions of the sound pressure along
the x -axis at the focal distances measured for the SEPFT and the SELFT.

(a) 25 mm

(b)

25 mm

acoustic
radiation
force
0 1.5
[Pa]

P’( x )

z

time

80 mm

y

x

-10
0
10 [μm]upward downward

x

0
P(ξ)

200
[ms]

0.1 mmaperture, 70 mm

ztransducer

Fig. 7. (Color online) Spatial distributions of the displacements
fdz ðx ; zÞg of the interface between oil and water generated by (a) the
dual SEPFT and (b) the dual SELFT.

SEPFT, the generated displacements fdz ðx; zÞg were large
only at the focal point of the dual transducer [the center inthe lateral (x) direction]. The purpose of using the dual
SELFT was to actuate a wider region in an object almost
uniformly in the horizontal (x) direction. However, inFig. 7(b), there were three regions where the amplitudes ofthe displacements, fdz ðx; zÞg, were large, as shown by the
downward arrows in Fig. 7(b).
Figure 8 shows the spatial distributions of the soundpressure in the x-direction at the focal distances of the
SEPFT (z ¼ 50 mm) and the SELFT (z ¼ 40 mm). As shownby the red line in Fig. 8, there were three peaks in the soundpressure distribution generated by the SELFT owing to theﬁnite size of the aperture.13)
4.2 Revised sound field using the LFAT

To obtain a ﬂat distribution of sound pressure, the array was
divided into three groups, fig (i ¼ 1; 2; 3), and the voltages
applied to these groups were weighted as (w1 : w2 : w3 ). The
number of elements in each group and the weight of thevoltage applied to each group were determined by simulation of the sound ﬁeld at the focal distance of the LFAT.
In this simulation, as shown in Fig. 9, the aperture of thetransducer was assumed to be an assembly of point soundsources. The wavelength , the aperture size L of thetransducer, and the pitch x between the point soundsources were set at 1.5, 70, and 0.1 mm, respectively. The ydirection (elevational direction) is not considered in thissimulation because it mainly changes the amplitude of thesound ﬁeld produced at the focal distance. The number of
elements ni of each group i was varied between (n1 ¼ n3 ¼
16 ch, n2 ¼ 2 ch) and (n1 ¼ n3 ¼ 1 ch, n2 ¼ 32 ch). Two
examples are shown below.

Fig. 9. Illustration of simulation method for calculating the spatial
distributions of the sound pressure along the x-axis at the focal distances.

Figures 10(a-1) and 10(a-2) show the ﬁrst example(pattern A) of the simulated and measured spatial distributions of sound pressures in the x-direction at a focal distanceof 80 mm under various voltage ratios (w1 : w2 : w3 ) for thethree groups (9 ch : 16 ch : 9 ch) of the LFAT. When thevoltages applied to the 9 elements (groups 1 and 3) on bothsides were equal to the voltage applied to the 16 central
elements (w1 ¼ w2 ¼ w3 ¼ 1:0), the sound pressures onboth sides were signiﬁcantly larger than that at the center.
The peaks in the sound pressure decreased as the voltage
applied to the groups on both sides decreased and, at w1 ¼
w3 ¼ 0:85 (w2 ¼ 1:0), the sound pressures on both sides
became similar to that at the center.
Similarly, Figs. 10(b-1) and 10(b-2) show the calculated
and measured spatial distributions of sound pressures in thex-direction under various voltage ratios (w1 : w2 : w3 ) for
the three groups (3 ch : 28 ch : 3 ch), deﬁned as pattern B. In
this case, at w1 ¼ w3 ¼ 0:3 (w2 ¼ 1:0), the sound pressures
on both sides became similar to that at the center.
Figure 11 shows the spatial distributions of the soundpressures generated by the SELPT, the SELFT, and the
LFAT with a voltage ratio of w1 ¼ w3 ¼ 0:85 (9 elements
on each side) and w2 ¼ 1:0 (16 central elements) in the caseof pattern A and with a voltage ratio of w1 ¼ w3 ¼ 0:3 (3elements on each side) and w2 ¼ 1:0 (28 central elements)
in the case of pattern B. A wider and smoother spatial
distribution of the sound pressure was successfully realized
by the LFAT. Additionally, pattern B realized a ﬂatter
distribution than pattern A. As shown in Fig. 10, when thevoltages applied to the groups on both sides decreased, in thecase of pattern A, sound pressures in broader regions on
both sides were decreased compared with pattern B. As aresult, for pattern A, large dips were generated slightly

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T. Sawada et al.

0.6

z

0.4
x

0.2

y

0

(a –2) measured

16 ch

0.6
0.4

0.8
0.6
0.4

x

0.2

x

y

0

–40 –30 –20 –10 0 10 20 30
distance x [mm]

16 ch

40
3 ch

3 ch

28 ch
w1 : w2 : w3
1
:1:1
0.9 : 1 : 0.9
0.8 : 1 : 0.8
0.7 : 1 : 0.7
0.6 : 1 : 0.6
0.5 : 1 : 0.5
0.4 : 1 : 0.4
0.3 : 1 : 0.3
0.2 : 1 : 0.2

1.0
0.8
0.6
0.4

z

0.2
x

0
–40 –30 –20 –10 0 10 20 30
distance x [mm]

40
9 ch

y

0

(b–2) measured

z

z

0.2

9 ch

w1 : w2 : w31
:1:1
0.95 : 1 : 0.95
0.9 : 1 : 0.9
0.85 : 1 : 0.85
0.8 : 1 : 0.8
0.75 : 1 : 0.75
0.7 : 1 : 0.7

1.0–40 –30 –20 –10 0 10 20 30
distance x [mm]

0.8

40
9 ch

w1 : w2 : w3
1
:1:1
0.9 : 1 : 0.9
0.8 : 1 : 0.8
0.7 : 1 : 0.7
0.6 : 1 : 0.6
0.5 : 1 : 0.5
0.4 : 1 : 0.4
0.3 : 1 : 0.3
0.2 : 1 : 0.2

1.0

normalized sound pressure

0.8–40 –30 –20 –10 0 10 20 30
distance x [mm]normalized sound pressure(b –1) simulated

w1 : w2 : w31
:1:1
0.95 : 1 : 0.95
0.9 : 1 : 0.9
0.85 : 1 : 0.85
0.8 : 1 : 0.8
0.75 : 1 : 0.75
0.7 : 1 : 0.7

1.0

normalized sound pressure

normalized sound pressure(a–1) simulated

9 ch

y

40
3 ch

3 ch

28 ch

1.0

SEPFT

0.8

SELFT

(a)

(b)
0

0.6

12.5 mm-12.5 mm
depth
5 mm

-12.5 mm
depth
5 mm

normalized sound pressure

Fig. 10. (Color online) Calculated and measured spatial distributions of the sound pressure along the x -axis at the focal distance of the LFAT. The
voltages applied to the three groups [(a) 9 ch : 16 ch : 9 ch, (b) 3 ch : 28 ch : 3 ch] of the transducer elements were weighted.

0

acoustic
radiationforce
12.5 mm
0 3.5[Pa]

LFAT (9 ch:16 ch:9 ch)
w1 : w2 : w3
0.85 : 1 : 0.85

0.4
0.2
0
–40 –30 –20 –10 0 10 20
distance x [mm]3040

LFAT (3 ch:28 ch:3 ch)
w1 : w2 : w3
0.3 : 1 : 0.3

time

Fig. 11. (Color online) Spatial distributions of sound pressure along thex -axis at the focal distance measured for the SEPFT, the SELFT, and the
LFAT with voltage weighting.
yinside of the peaks on both sides as shown by the arrows in
Fig. 10. On the other hand, for pattern B, a decrease in theapplied voltage had little eﬀect on these regions. From thesesimulations, it was determined that pattern B was moresuitable for realizing a ﬂat distribution of sound pressure.
4.3 Measurement of displacements in a phantom

Figures 12(a) and 12(b) show the spatial distributions ofdisplacements fdz ðx; zÞg during one cycle of the acoustic
radiation forces generated by the dual SELFT and the dual
LFAT at w1 ¼ w3 ¼ 0:3 (w2 ¼ 1:0) for the three groups(3 ch : 28 ch : 3 ch), respectively. Blue and red correspond to
the upward and downward displacements at amplitudes of up
to 1 mm, respectively. Overall downward displacements weregenerated by the downward component of acoustic radiation
forces during the period when the acoustic radiation forces
increased as shown in Fig. 1. As shown in Fig. 12(a), thespatial distribution of displacements, fdz ðx; zÞg, generated by
the dual SELFT was nonuniform since the displacements inthe black boxes were signiﬁcantly larger than those elsewhere. On the other hand, as shown in Fig. 12(b), the spatial

x

z

-1
0
1 [μm]
upward downward

200
[ms]

Fig. 12. (Color online) Spatial distributions of displacements fdz ðx ; zÞgin a phantom generated by (a) the dual SELFT and (b) the dual LFAT.

distribution of displacements, fdz ðx; zÞg, generated by thedual LFAT is more uniform during a cycle of the acoustic
radiation forces.
5.

Discussion

In this study, in basic experiments using a phantom, it was
conﬁrmed that a more homogeneous distribution of displacements was generated using the dual LFAT than using
the dual SEPFT or the dual SELFT. To show the improvement in the eﬀectiveness of actuation using the dual LFAT,
it is necessary to measure the strain generated by theultrasonic actuation. However, in the present study, it wasdiﬃcult to generate a measurable strain owing to thelimitations of the hardware employed for the ultrasoundtransmission. The maximum sound pressure that could be
generated in the present study by the dual LFAT was

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T. Sawada et al.

100 kPa, which corresponds to 0.225 W/cm2 . In a future
work, we plan to increase the acoustic output to close to
1 W/cm2 by improving the hardware to generate a measurable strain and to show that the eﬀectiveness of theactuation is improved using the LFAT.
6.

Conclusions

In this study, for eﬀective ultrasonic actuation, we improved
ultrasonic ﬁelds using a dual LFAT. A more desirable ﬂat
distribution of the sound pressure compared with thatgenerated by a dual SELFT was obtained, and the displacements in a phantom generated by the dual LFAT at
amplitudes of 1 mm were almost uniform.

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