BRIEF NOTEJapanese Journal of Applied Physics 53, 07KF05 (2014)
http://dx.doi.org/10.7567/JJAP.53.07KF05

Measurement of elastic wave propagation velocity near tissue surface
by optical coherence tomography and laser Doppler velocimetry
Yukako Kato1, Yuji Wada2, Yosuke Mizuno1, and Kentaro Nakamura1
1

Precision and Intelligence Laboratory, Tokyo Institute of Technology, Yokohama 226-8503, Japan
Faculty of Science and Technology, Seikei University, Musashino, Tokyo 180-8633, Japan2

Received November 29, 2013; accepted March 24, 2014; published online June 6, 2014
We demonstrate a new technique for measuring the velocity of elastic waves propagating near a tissue surface by swept-source optical coherence
tomography (OCT). We establish a theory for estimating the elastic wave velocity from the OCT images taken with a slow mechanical scanning,which is experimentally veriﬁed using agar and tissue samples. The elastic wave velocity measured by this technique agrees well with previous
results and that measured with a laser Doppler velocimeter. We also carry out some trial measurements of the elastic wave velocities of several
tissue samples by this method. © 2014 The Japan Society of Applied Physics

Although the endoscope is a powerful tool for detecting
incipient tumors, it is still difﬁcult to detect small tumors
efﬁciently from optical images of the surface. Tumors are
known to be generally harder than that of normal tissues.
According to previous studies, it is expected that small
tumors can be detected on the basis of their elastic
properties.1,2) However, endoscopic elastography requires
deformation measurement with a high spatial resolution. A
principle for estimating the elastic properties of tissues bydisplacement measurement is also essential.
Ultrasonic elastography has been intensively studied andpartly used in practice for nonendoscopic ﬁelds.3–10) Opticalcoherence tomography (OCT) has a higher spatial resolution11) than ultrasound-based techniques, and has alreadybeen put to practical use in eye clinics. The spatial resolutionof standard OCT systems in the B-mode image is fromseveral to 10 µm for the depth and from several to 20 µm
for the lateral direction.12) The penetration depth reaches
approximately 3 mm. Elastography based on OCT hasincreasingly become attractive,13–15) as it takes advantage ofthe high spatial resolution of the OCT. In the meantime, thedisplacements with compression provided by applying an
external static force or using an acoustic radiation force havebeen measured. However, the absolute value of an elastic
constant cannot be estimated, since it is difﬁcult to determine
the absolute value of stress. To date, the elastic properties oftissues have been estimated from various viewpoints.16,17) If
the elastic wave velocity is measured, the elastic constant canbe estimated quantitatively, since the velocity is determinedby the elastic nature and the density of the media.
In this work, we carry out a trial to detect the velocity ofthe elastic wave propagation using a swept-source (SS-)
OCT. The depth scanning in SS-OCT is sufﬁciently fast withthe use of a high-speed frequency-swept light source, thescanning rate of which is as fast as 20 to 100 kHz. However,the lateral scanning is performed using a mechanical moving
mirror and is relatively slow (less than 1 m/s). Shear waves
and surface acoustic waves travel in tissues at the velocity
ranging from 1 to 20 m/s, which is much slower than thatof longitudinal waves. A method for estimating the velocityof such slower waves using a low-speed imaging system isdiscussed.
One point on the surface of a tissue sample is continuously
vibrated with a small stick (a pick) connected to the corn ofa small loudspeaker, and the sample is observed by SS-OCT(OCT optics: Santec IV-2000; swept light source: SantecFig. 1. (Color online) Setup for wave generation and detection.

Fig. 2. Example of OCT image for agar surface.

HSL-2000) as illustrated in Fig. 1. We put the samples into acontainer of 36 mm width, 65 mm length, and 11.5 mm depth.
The measurements were carried out from 500 to 1000 Hz at
50 Hz intervals. The lowest frequency is determined by thescanning width (5 mm in this experiment), since the wavelength of the elastic wave should be much shorter than thescanning width. The highest frequency is limited by thedisplacement resolution of the OCT, because the vibration
displacement decreases with increasing frequency. Figure 2
shows an example of the OCT image of the sample. A
periodical waveform is clearly observed on the surface, theperiod of which is deﬁned as ª. In the OCT image, ª is not
the real wavelength of the elastic wave, because of thedifference between the scanning velocity v of the OCT and
the elastic wave velocity c. There is a mathematical relation
among ª, v, and c.
Here, let us explain how to calculate the elastic wave
velocity v from the OCT images. Using the lateral scanningvelocity v in the OCT, the observed position x can be
expressed as07KF05-1© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF05 (2014)

Y. Kato et al.

Fig. 3. (Color online) Sample surface observed by OCT.

Fig. 5. (Color online) Elastic wave velocity for 1, 2, and 3% agar
measured by OCT and LDV.

experiment, the scanning velocity of the OCT was calculated
to be 0.193 m/s using
v ¼ f:Fig. 4. (Color online) Observed pitch vs inverse of frequency. A 2% agar
sample was used. Four trends indicate measured points and their linear
approximation in each scanning direction (to and fro): parallel andperpendicular to the elastic wave propagation.

x ¼ vt;ð1Þ

where t is time. The vertical displacement of the elastic wave
is then expressed asy ¼ A cosðkx  2ftÞ;

ð2Þ

where f is the frequency and k is the wave number of thewave. In our experiment, the elastic wave velocity c isapproximately 10 times higher than the lateral scanningvelocity v of the OCT. In such a case, a waveform with apitch ª is observed as shown in Fig. 3. Note that theobserved pitch ª is different from the wavelength of thewave as explained above. By eliminating the time fromEq. (2) using Eq. (1), we obtain
1 1y ¼ A cos 2f

x:
ð3Þ
c v
Here, considering that ª is the pitch,f

1 1
 ¼1c v

ð4Þ

is satisﬁed. Thus, from Eq. (4), we can calculate the elastic
wave velocity c using the experimentally obtained ª asfollows. The pitch ª is measured at many different
frequencies and plotted as a function of the inverse of thefrequency, as shown in Fig. 4; the elastic wave velocity isthen obtained from its slope. To derive the scanning velocityv, the same procedure is performed by scanning perpendicularly to the propagating direction of the elastic waves, inwhich the elastic wave velocity can be regarded as ¨. In thisð5ÞWe measured three agar samples with different concentrations of 1, 2, and 3%. Measurements were performed threetimes for each sample. Figure 5 shows the results, in which aline represents the average value. The averages of the elastic
wave velocity were 3.7, 5.2, and 6.5 m/s for the 1, 2, and 3%
samples, respectively. The elastic wave velocity was linearly
increased with increasing agar concentration. The results
almost agree with those shown in Ref. 19, where the elastic
wave velocity was about 3.5 m/s in 1% agar and proportional
to the agar concentration.18,19)
We also measured the elastic wave velocity in the 2% agar
sample using a scanning laser Doppler velocimeter (LDV)
to verify the results. We scanned 10 points along the wave
propagation path with a half-wavelength pitch, and the phaseof the vibration velocity was recorded at every point. The
elastic wave velocity was calculated from the phase difference between the two adjacent points. The measurements
were carried out at 2 kHz. As plotted in the ﬁgure, theaverage of the LDV results was 5.6 m/s, which is close to theresults obtained by the above-mentioned method with OCT.
As observed in the results for the agar samples (Fig. 5),with the increase in the elastic wave velocity, the deviation of
the estimated elastic wave velocity was increased. If theelastic wave velocity exceeded 6 m/s (30 times larger than
the scanning velocity), the error reached 50%.
Finally, we measured the elastic wave velocities of tissue
samples such as chicken liver and white chicken meat. For
the white chicken meat, measurements were performed inboth directions: perpendicular and parallel to the ﬁber.
Figure 6 shows the OCT images of the chicken liver andthe white chicken meat when the waves were propagated.
Attenuation in the chicken liver [Fig. 6(a)] was so high thatthe wave was observed only for half of the image. In the caseof the white chicken meat with the propagation direction
perpendicular to the ﬁber [Fig. 6(c)], it was difﬁcult toobserve the displacement, resulting in the failure in
estimating the elastic wave velocity. The elastic wave
velocity of the liver was 1.2 m/s, while that of the whitechicken meat was 8.7 m/s.

07KF05-2© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF05 (2014)

Y. Kato et al.

for estimating the elastic wave velocity (1–20 m/s) usingthe slow imaging system (less than 1 m/s). As a result, therelationship between the agar concentration and the elastic
wave velocity agreed qualitatively with a previous study and with the elastic wave velocity measured with an LDV.
By the same method, we also estimated the elastic wave
velocity of several tissue samples. Estimating the elastic
constants using the elastic wave properties is left for a future
study.20)

(a)

(b)

(c)
Fig. 6. (a) OCT image of chicken liver. (b) OCT image of white chicken
meat observed with parallel scan to the ﬁber. (c) OCT image of white chicken
meat observed with perpendicular scan to the ﬁber.

In conclusion, we tried to measure the elastic wave
velocity propagating near the surface of tissue samples byvertical displacement measurement using an SS-OCT with aslow horizontal scanning system. We developed the method

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07KF05-3© 2014 The Japan Society of Applied Physics