J Med Ultrasonics (2012) 39:279–281
DOI 10.1007/s10396-012-0372-9

ULTRASOUND IMAGE OF THE MONTH

Measurement of displacement and strain in biological tissue
generated by ultrasonic dual acoustic radiation force
Jun Yamaguchi • Hideyuki Hasegawa •Hiroshi Kanai

Received: 4 February 2011 / Accepted: 12 April 2012 / Published online: 25 May 2012Ó The Japan Society of Ultrasonics in Medicine 2012

Keywords Acoustic radiation force Phased tracking method  Strain

Introduction
The tenderness of muscle tissue is decreased by aging andexcessive exercise, potentially leading to disorders such as
injuries and decreased supply of nutrients due to poor
blood circulation. It is therefore important to diagnose
muscle condition, but quantitative and noninvasive diagnostic methods have not yet been established.
In recent years, some remote actuation methods basedon acoustic radiation forces have been reported. Fatemi andGreenleaf proposed an imaging modality that uses theacoustic responses of an object, which are closely related tothe 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 the ultrasound beams at slightly different frequencies and is not particularly high.
Nightingale et al. proposed an alternative imaging
method in which focused ultrasound is employed to apply aradiation force to soft tissue for short durations (less thanJ. Yamaguchi  H. Hasegawa  H. Kanai (&)
Graduate School of Engineering, Tohoku University,Aramaki-aza-Aoba 6-6-05, Aoba-ku, Sendai 980-8579, Japane-mail: kanai@ecei.tohoku.ac.jp
H. Hasegawa  H. Kanai
Graduate School of Biomedical Engineering, Tohoku University,
Aramaki-aza-Aoba 6-6-05, Aoba-ku, Sendai 980-8579, Japan

1 ms). The viscoelastic properties of the tissue wereinvestigated from the magnitude of the transient response,
which was measured as the displacement, d(t), of the tissue[3–5]. In order to generate measurable displacement byseveral ultrasonic pulses, high-intensity pulsed ultrasound(1,000 W/cm2) was employed. However, according tosafety guidelines for the use of ultrasound, it is recommended that the intensity be below 240 mW/cm2 (ISPTA)
for pulsed waves and 1 W/cm2 for continuous waves [6].
The intensity of the pulsed ultrasound employed by
Nightingale et al. is therefore far greater than that indicatedin the safety guidelines.
The aim of our study was to evaluate muscle condition
by noninvasively measuring its viscoelasticity. To evaluate
muscle viscoelasticity, muscle needs to be deformed. In
this study, two ultrasonic acoustic radiation forces fromdifferent directions were shown to be able to deformmuscle tissue effectively. Furthermore, the resultant
regional displacement and strain in the muscle tissue weremeasured using a different ultrasonic probe.

MethodWhen a single acoustic radiation force is applied to biological tissues, strain (deformation) is not generated
effectively, because one acoustic radiation force generates
not only strain but also a change in the position of thetissue that has zero spatial gradient in displacement (nostrain). In this study, for effective generation of strain in anobject, two acoustic radiation forces, which were inducedby two continuous ultrasound beams at frequencies of f0and (f0 ? Df), were synchronously applied to two different
positions in the object from two different directions, as
shown in Fig. 1 [7]. The region pinched by two acoustic

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J Med Ultrasonics (2012) 39:279–281

Fig. 1 Schematic ofdeformation generation in an
object using two ultrasonicacoustic radiation forces andultrasonic measurement of theresultant displacement andstrainradiation forces oscillating at a frequency of Df wastherefore compressed along the horizontal axis. In the caseof biological tissues, such as muscle and tendons, verticalexpansion occurred due to their incompressibility.
With respect to the low-frequency component, theacoustic radiation pressure, PR(t), acting on the interface
between the medium and the tissue is given by [7]p20ð1 þ cos 2pDftÞ
qc2
p2
ﬃ 02 ð1 þ cos 2pDftÞ;qc

In-vitro experimental results

PR ðtÞ ¼ ð1 þ R2 Þð1Þ

where R, p0, q, and c are the pressure reflection coefficientat the interface between the medium and the object, thesound pressure of the transmitted ultrasound, the density ofthe medium, and the sound speed in the medium, respectively. The pressure reflection coefficient is defined by thespeed of sound and the densities of the medium and theobject. For example, the speed of sound in muscle and fat is
1,568 m/s and 1,465 m/s, respectively. By assuming thedensity of soft tissue to be 1.0 9 103 kg/m3, the reflection
coefficient R is 0.034. Thus, the squared reflection coefficient R2 in Eq. (1) is assumed to be zero. The resultant
displacement in the vertical direction was measured by ourultrasonic phased tracking method [8, 9]. In the present
study, the center frequency, f0, of ultrasound for actuation
generated by the two transducers and the actuation frequency, Df, were set at 1 MHz and 5 Hz, respectively. The
two transducers used for generating acoustic radiation
forces were single-element focused transducers. The soundpressure of the continuous ultrasonic wave used for actuation was 180 kPa, which corresponds to 1.08 W/cm2123(ISPTA) in ultrasonic intensity (safe level of continuous
wave is 1 W/cm2 [6]) and 7.4 Pa in acoustic radiation
force. The intensity of the ultrasonic pulse for measurement
was 11.2 mW/cm2 (ISPTA), which was smaller than the safe
level (240 mW/cm2).

In this study, an in-vitro experiment using chicken breast
muscle was conducted to investigate whether the proposed
method could generate the presumed deformation in biological tissue. Figures 2a and b show the instantaneous
displacement and the strain, respectively, in the verticaldirection inside the object during one cycle of acoustic
radiation forces. Figure 2c shows waveforms of theacoustic radiation forces (black line), the instantaneous
displacement (green line), and the strain (blue line) at(x, z) = (1.4 mm, 1.0 mm) during one cycle of the acoustic
radiation force. As shown in Fig. 2, the region between thetwo focal points of the ultrasound beams for actuation
expanded in the vertical direction when the region moved
downward due to the increase in acoustic radiation forces.
The horizontal components of the applied acoustic radiation forces should have increased when the region moved
downward, because this downward motion occurred due tothe vertical components of the acoustic radiation forces.
Consequently, this result suggests that the proposed
method successfully generated the deformation in biological tissue that was expected, as illustrated in Fig. 1,i.e., the targeted region expanded vertically, due to thehorizontal compression by two acoustic radiation forces.

J Med Ultrasonics (2012) 39:279–281

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Fig. 2 Distributions of a instantaneous displacement and b strain in
the vertical direction in each frame during a cycle of radiation force.
c Waveform of instantaneous displacement and strain at (x,z) = (1.4 mm, 1.0 mm) during one cycle of acoustic radiation force.

The black line, the green line, and the blue line show the acoustic
radiation force, the instantaneous displacement, and the strain,
respectively

Discussion and conclusion

2. Fatemi M, Greenleaf JF. Vibro-acoustography: an imaging
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Acoustic radiation force impulse imaging of the abdomen:
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6. Japan society of ultrasonics in medicine: Cho-onpa Igaku 1. 1984:
41 [in Japanese].
7. Hasegawa H, Takahashi M, Nishio Y, Kanai H. Generation ofstrain inside objects using dual acoustic radiation force. Jpn J ApplPhys. 2006;45:4706–11.
8. Kanai H, Sato M, Koiwa Y, Chubachi N. Transcutaneous
measurement and spectrum analysis of heart wall vibrations. IEEETrans Ultrason Ferroelect Freq Contr. 1996;43:791–810.
9. Kanai H, Hasegawa H, Chubachi N, Koiwa Y, Tanaka M.
Noninvasive evaluation of local myocardial thickening and its
color-coded imaging. IEEE Trans Ultrason Ferroelect Freq Contr.
1997;44:752–68.

In this study, it was confirmed that strain was successfully
generated in muscle tissue using two synchronous acoustic
radiation forces, and that the strain generated could bemeasured by our ultrasonic phased tracking method.
Skeletal muscle is composed of muscle fibers that show
significant elastic anisotropy. However, such elastic
anisotropy was not considered in the present study. The
elastic anisotropy of muscle tissue will be investigated in a
future work by applying acoustic radiation forces fromdifferent directions.
In addition, there were phase delays in the displacement
and strain from the applied acoustic radiation forces, asshown in Fig. 2c. These phase delays depend on the viscoelasticity (not only on elasticity) of the tissue. By analyzing such phase delays, it would be possible to assess theviscosity, which would be a useful marker for diagnosis of
the physiological status of muscle tissue.
Conflict of interest

None.

References
1. Fatemi M, Wold LE, Alizad A, Greenleaf JF. Vibro-acoustic tissue
mammography. IEEE Trans Med Imag. 2002;21:1–8.

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