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Japanese Journal of Applied Physics 55, 07KF13 (2016)
http://doi.org/10.7567/JJAP.55.07KF13

Three-dimensional visualization of shear wave propagation
generated by dual acoustic radiation pressure
Yuta Mochizuki1, Hirofumi Taki1,2, and Hiroshi Kanai2,1*
1

Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan2*E-mail: kanai@ecei.tohoku.ac.jp
Received November 14, 2015; revised March 2, 2016; accepted March 27, 2016; published online June 16, 2016An elastic property of biological soft tissue is an important indicator of the tissue status. Therefore, quantitative and noninvasive methods forelasticity evaluation have been proposed. Our group previously proposed a method using acoustic radiation pressure irradiated from two directions
for elastic property evaluation, in which by measuring the propagation velocity of the shear wave generated by the acoustic radiation pressure
inside the object, the elastic properties of the object were successfully evaluated. In the present study, we visualized the propagation of the shear
wave in a three-dimensional space by the synchronization of signals received at various probe positions. The proposed method succeeded invisualizing the shear wave propagation clearly in the three-dimensional space of 35 ' 41 ' 4 mm3. These results show the high potential of theproposed method to estimate the elastic properties of the object in the three-dimensional space. © 2016 The Japan Society of Applied Physics

1.

Introduction

It is well known that the progression of a lesion isaccompanied by changes in the hardness of biological tissue.
For example, owing to pyramidal tract disorders or peripheral
neuropathy, the elastic modulus of muscle decreases. In
amyloidosis, atrophy and the elevation of muscle hardness
occur. Also, polymyositis and myoglobinuria lead to muscle
weakness or a decrease in muscle elasticity.1,2) Therefore, itwould be valuable to measure the elasticity of muscle forthe early detection and quantitative diagnosis of muscle
disorder.
Ultrasound imaging is a noninvasive test with highperformance in depicting soft tissue. Several methods havebeen reported for the improvement in image quality,3–5) tissue
characterization,6–8) and the estimation of tissue displacement.9–11) Many methods that can be used to noninvasively
measure the hardness of soft biological tissue have been
proposed; in these method, external pressure is applied tobiological tissue and the resulting deformation and movementof the tissue are observed to obtain the parameters regarding
the hardness of the tissue. Recently, some methods have beendeveloped for the noninvasive evaluation of the elasticity ofsoft tissue.12,13) Other research groups have reported several
methods based on the hysteresis property between force anddisplacement,14) and based on the dispersion of shear wave
propagation velocity.15)
Ultrasound-based measurement methods can be classiﬁed
into two categories according to the methods used to applypressure. One is the application of static pressure and theother is the application of dynamic pressure. In the former
method, by measuring the deformation of the tissue withultrasound before and after the application of static pressure,the elasticity of the biological tissue is estimated. However,
the elasticity of the tissue cannot be evaluated quantitatively.16) Therefore, our group has applied dynamic pressure
produced by acoustic radiation to quantitatively evaluate theelastic properties of the tissue by the ultrasound measurementof the propagation of the generated shear wave.
Over the past decade, remote actuation methods based on
acoustic radiation pressure have been reported. Fatemi andcoworkers proposed an imaging modality that uses theacoustic response of an object, which is closely related to its
mechanical properties. By measuring the acoustic emission
with a hydrophone, hard inclusions, such as calciﬁed tissuesin soft materials, were detected experimentally.17,18) However, the amplitude of the radiated acoustic emission signal
was very small for soft tissue and the spatial resolution waslimited by the size of the intersectional area of ultrasoundbeams at two slightly diﬀerent frequencies.
Nightingale and coworkers proposed an alternative imaging method (acoustic radiation pressure impulse: ARFI), in
which focused ultrasound is employed to apply radiationpressure to soft tissue for a short duration (less than 1 ms).
The elastic properties of the tissue were investigated on thebasis of the magnitude of the transient response, which wasmeasured as the displacement of tissue with ultrasound.19–21)
However, in order to generate a measurable displacement
by several successive ultrasound pulses, high-intensity pulsed
ultrasound at 1,000 W=cm2 was required. According to safety
guidelines for the use of diagnostic ultrasound, it isrecommended that the intensity be below 240 mW=cm2(ISPTA) for pulsed waves and 1 W=cm2 for continuous
waves.22) The intensity of the pulsed ultrasound employed by
Nightingale et al. was, therefore, far greater than thatrecommended in the safety guidelines.19)
Subsequently, many groups studied methods for actuation
using high-intensity pulsed ultrasound to measure elastic
properties of biological tissue.23,24) To decrease the ultrasound intensity for the actuation of soft tissue, our groupchose continuous-wave ultrasound, as did Fatemi et al.,17) inwhich the maximum intensity of 1 W=cm2 for continuous
waves given by safety guidelines generates an acoustic
radiation pressure of 6.67 Pa, which is very small. Therefore,
to generate a measurable displacement by acoustic actuation,an eﬀective method of applying acoustic radiation pressure
should be developed.
A single acoustic radiation pressure does not generate
deformation eﬀectively because it primarily changes theposition of the object. Thus, our group has developed amethod in which two cyclical radiation pressures are simultaneously applied to a phantom from two opposite horizontal
directions to cyclically compress the object along the horizontal direction. Furthermore, the resultant regional displace-07KF13-1© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 07KF13 (2016)

Y. Mochizuki et al.

ment and strain in the phantom simulating soft biologicaltissue or any type of tissue were measured using a diﬀerent
ultrasound probe. This method enables the eﬀective generation of deformation by acoustic actuation.25,26)
In another study using two sources of shear waves,27) themechanical properties of an object were evaluated bygenerating two shear waves that interfered with each other.
However, this method requires that two shear wave sources
be perfectly opposite, and that shear waves be insoniﬁed fromthe skin surface by an external vibrator.
Our group has proposed a method to actuate phantoms
using dual acoustic radiation pressure and to measure thepropagation velocity of the generated shear wave, fromwhich the elastic properties of an object can be estimated.28)
However, the study reported the measurement of the shear
wave propagation only in the vertical plane. In the present
study, therefore, we propose a novel method that visualizes
the propagation of the generated shear wave in a threedimensional (3D) space in a medium. This method wasapplied to a phantom that simulates uniform soft tissue.
2.

(a)

(b)

Experimental methods

2.1 Generation principle of the displacement inside thephantom due to acoustic radiation pressure

We apply an acoustic radiation pressure that consists of two
continuous sinusoidal waves, whose center frequencies are f0and ( f0 + Δf ), to an object in a water tank. The acousticpressure in the object is given bypsum ðd; tÞ ¼ e$!d fp0 cosðkd $ 2"f0 tÞþ p0 cos½kd $ 2"ð f0 þ !f Þt'g;

ð1Þ

where d, α, k, and p0 are the distance from the object surface,
the attenuation coeﬃcient, the wave number, and the soundpressure in the object, respectively. The acoustic radiationpressure PR ðd; tÞ is given byPR ðd; tÞ (!p20 $2!deð1 þ cos 2"! ftÞ;#2 c22ð2Þ

where ρ2 and c2 are the density and sound speed of the object,respectively. When the acoustic radiation pressure in Eq. (2)is generated in the phantom, a locally vibrated displacement
is induced, and a shear wave propagates from the focal
point.28)
In the present study, we employed two focused transducers
to generate a shear wave, where each transducer was appliedby the overlaid component of the two continuous sinusoidal
waves of f0 and ( f0 + Δf ). To generate the shear wave
eﬀectively, both foci of the transducers were located at thesame excitation position and both radiation directions werelocated in the same plane as shown in Fig. 1(a). The radiation
direction of each transducer adopted an angle of 25° to thehorizontal plane. Since the focal length of each transducer
was 50 mm, the distance between the excitation position andeach transducer surface was 91 mm.
As shown in Eq. (2), the acoustic radiation pressurePR ðd; tÞ vibrates from 0 to ð2!p20 =#2 c22 Þ expð$2!dÞ at thefrequency of Δf. Therefore, the region around the focal point
vibrates in the depth direction at the frequency of Δf, and theshear wave propagates to the surrounding region as shown in
Fig. 1(b). We measured the propagation of the shear wave
by an ultrasound diagnostic equipment (Hitachi-Aloka ProFig. 1. (Color online) Schematic diagram showing the mechanism of theshear wave generation by irradiation dual acoustic pressure at the(a) minimum ½PR ðd; tÞ ¼ 0' and (b) maximum acoustic radiation pressures.

Sound F75) with a 7.5 MHz linear probe (Hitachi-Aloka
UST-5415).
2.2

Measurement of the shear wave in 3D space
We prepared a phantom that consisted of 98% massconcentration silicone (Sin-Etsu Silicone KE114L) and 2%graphite powder. The dimensions of the phantom were 110,
150, and 34 mm in the x-, y-, and z-directions, respectively.
Its density was 1,208 kg=m3. The phantom was set in thewater tank, whose dimensions were 450, 300, and 300 mm inthe x-, y-, and z-directions, respectively.
For ultrasound measurement, the ultrasound diagnostic
equipment with the linear probe of 7.5 MHz was employed.
The frame rate was 521 Hz and the scan line interval was3.3 mm. The number of beams used in the measurement was
11, and the beams were numbered from 0 to 10. As shown in
Fig. 2, the foci of two focused transducers were set about
20 mm away from beam 0 for generating vibration with Δf =100 Hz. The acoustic radiation pressure was applied from thetwo focused transducers 1 min before the measurement.
The shear wave propagation was measured by shifting
the ultrasound probe by 1 mm along the x-axis direction in
the range from −20 to +20 mm. To detect the irradiation
time of the acoustic radiation pressure at each measurement
x-position, the input signal for the acoustic radiation pressure
was input into the vital information acquisition port of theultrasound diagnostic equipment, as shown in Fig. 2, where
the sampling frequency of the acquisition system was 1 kHz.
RF data at a measurement x-position along each of the 11
beams on the y–z plane had a synchronization signal.
Consequently, all the signals received at various probe
x-positions were synchronized.

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Y. Mochizuki et al.

Fig. 3. (Color online) Displacements of the shear waves at the depth ofz = 1 mm in the vertical direction in the plane of x = −5 mm.

Fig. 2. (Color online) Measurement image for visualization in 3D space.

In each y–z plane, there is a small delay of 174 µs =1=(11 × 521) in acquisition time of RF data between thesucceeding beams. However, it cannot be neglected to show
the propagation of the shear wave generated by the acoustic
radiation pressure (Δf = 100 Hz). Thus, in the present study,
this delay time between the beams was deleted in thecalculation process to show the phase of the shear wavecomponent. Therefore, the propagation of the shear wave canbe visualized in a 3D space.
The instantaneous velocity v(t + Δt=2) was calculated
from the phase shift from the received signal b(t) to b(t + Δt)
after quadrature detection, where the phase shift wasdetermined by an ultrasound correlation-based method, thephased-tracking method.29,30) A FIR band-pass ﬁlter H( f )was applied to the instantaneous velocity v(t) to extract thefrequency component of Δf. Then, the instantaneous velocityv(t) was integrated to estimate the displacement waveform.
3.

Results

Figure 3 shows the displacements of the shear waves at thedepth of z = 1 mm in the vertical direction on the plane ofx = −5 mm. In all of the three beams, the vibration frequencyof the displacement was about 100 Hz, the diﬀerence frequency Δf. The phase shift of the displacement in beam 10
from the phase in beam 0 was larger than that in beam 5.
Since beam 0 was located near the focal point as shown inFig. 2, this result shows the propagation of the shear wave inthe direction away from the focal point.
Figure 4 shows the amplitude and phase of the instantaneous velocity of the shear wave, Av ðx; y; z; tÞ and$v ðx; y; z; tÞ, in four horizontal z-planes. Each horizontal
z-plane was constructed by the synchronization of signals
received at various probe positions using the input signal forthe acoustic radiation pressure. As shown in Figs. 4(a) and4(b), in the planes of z = 0 mm, z = 3.0 mm in depth, theshear wave clearly propagated in the direction away from thefocal point. The cycle of the instantaneous velocity was about
10 ms, which corresponded to the diﬀerence frequency
Δf = 100 Hz. This result shows the capability of the proposed
method based on the synchronization process in the 3D
visualization of the shear wave propagation.
Figure 5 shows the amplitude and phase of the instantaneous velocity of the shear wave, Av ðx0 ; y; z; t0 Þ and$v ðx0 ; y; z; t0 Þ, in a vertical plane of ðx0 ; t0 Þ ¼ ð$5 mm; 4 msÞ.
We succeeded in visualizing the propagation of the shear
wave clearly in the direction away from the focal point within
the depths from z = 0 to 4 mm.
Figure 6 shows the phase shift of the instantaneous
velocity at a measurement point ðx0 ; y; zÞ from the phase ata reference point ðx0 ; y0 ; z0 Þ given by$d ðx0 ; y; zÞ ¼ Et ½$v ðx0 ; y; z; tÞ $ $v ðx0 ; y0 ; z0 ; tÞ';ð3Þ

where each value was averaged among 2,080 frames in0 ≤ t ≤ 1 s. We set the reference point at ðx0 ; y0 ; z0 Þ ¼
ð$5; 0; 0 mmÞ. We determined the propagation velocity ofthe shear wave using the least-mean-squares method. Thevelocity was estimated to be 4.5, 4.5, 4.7, and 4.7 m=s at thedepths of z = 0, 1.0, 2.0, and 3.0 mm, respectively. In ourprevious study, it was reported that the propagation velocity
of a 100 Hz shear wave was 3.5 m=s in a diﬀerent phantom,28)
which is similar to the above result.
4.

Discussion

The proposed method succeeded in visualizing the shear
wave propagation clearly in the 3D space, as shown inFigs. 4 and 5, which show a high potential of the proposed
method with a synchronization process. In the region of x > 0in Figs. 4(a) and 4(b), the wavefront of the shear wave
was not clearly visualized. On the other hand, at depths ofz = 6.0 and 9.0 mm in Figs. 4(c) and 4(d), the shear wave
propagation was diﬃcult to observe. This asymmetry in thex-direction might be caused by the misalignment between thefoci of the ultrasound transducers for actuation in the settingof the experiment.
The phase shift $d ðx0 ; y ¼ 0; z ¼ 3:0 mmÞ at the leftmost
side of Fig. 6(b) was almost zero, which coincides with

07KF13-3© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 07KF13 (2016)

Y. Mochizuki et al.

Fig. 4. (Color online) Amplitude and phase of the instantaneous velocity of the shear wave, Av ðx; y; z; tÞ and $v ðx; y; z; tÞ, at the depths of (a) z = 0 mm,(b) z = 3.0 mm, (c) z = 6.0 mm, and (d) z = 9.0 mm.

(a)

(b)

Fig. 5. (Color online) (a) Amplitude and (b) phase of the instantaneous velocity of the shear wave, Av ðx0 ; y; z; t0 Þ and $v ðx0 ; y; z; t0 Þ, in a vertical plane ofðx0 ; t0 Þ ¼ ð$5 mm; 4 msÞ.

07KF13-4© 2016 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 55, 07KF13 (2016)

Y. Mochizuki et al.

(a)estimated to be 4.5, 4.5, 4.7, and 4.7 m=s at the depths ofz = 0, 1.0, 2.0, and 3.0 mm, respectively. These results showa high potential of the proposed method with a synchronization process in the 3D visualization of the shear wave
propagation.

(b)

Fig. 6. (Color online) Phase shift of the instantaneous velocity at ameasurement point ðx0 ; y; zÞ from the phase at a reference point ðx0 ; y0 ; z0 Þ atthe depths of (a) z = 0.0 mm and (b) z = 3.0 mm.

$d ðx0 ; y ¼ 0; z ¼ 0Þ at the leftmost side of Fig. 6(a), showingthat the phase shift in the z-direction did not appear. This
result indicates that the shear wave propagated toward thehorizontal direction.
As shown in Figs. 4(a), 4(b), and 5(b), the shear wave
propagated more than 30 mm along the y-axis on the x–yhorizontal plane. However, as shown in Figs. 5(b), 4(c), and4(d), it was diﬃcult to visualize the propagation of the shear
wave at the depth of z = 5 mm or more. This diﬃculty in 3D
visualization would be caused by the large attenuation in the7.5 MHz ultrasound for measurement in the phantom. Future
work should include an experimental study using a phantom
that satisﬁes the following conditions: suitability for thepropagation of a 100 Hz shear wave and a low attenuation in
the 7.5 MHz ultrasound for measurement.
5.

Conclusions

In the present study, shear wave propagation was measured ina uniform phantom to visualize its state in a 3D space for theelastic characterization of biological soft tissue. The shear
wave propagation was measured in a 3D space by scanning
an ultrasound probe along the x-axis direction in the rangeof 41 mm. Each horizontal plane was constructed by thesynchronization of signals received at various probe positions
using the input signal for the acoustic radiation pressure.
The proposed method succeeded in visualizing the shear
wave propagation clearly in the 3D space of 35 × 41 × 4 mm3in the x-, y-, and z-directions. The propagation velocity was

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07KF13-5© 2016 The Japan Society of Applied Physics