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Robust analysis method for acoustic properties of
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Japanese Journal of Applied Physics 57, 07LB07 (2018)https://doi.org/10.7567/JJAP.57.07LB07

Robust analysis method for acoustic properties of biological specimens
measured by acoustic microscopy
Mototaka Arakawa1,2*, Shohei Mori2, Hiroshi Kanai2,1, Ryo Nagaoka1, Miki Horie1,
Kazuto Kobayashi3, and Yoshifumi Saijo1
1

Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan3
Department of Research and Development, Honda Electronics Co., Ltd., Toyohashi, Aichi 441-3193, Japan2*E-mail: arakawa@ecei.tohoku.ac.jp
Received November 6, 2017; revised December 30, 2017; accepted January 2, 2018; published online April 20, 2018
We proposed a robust analysis method for the acoustic properties of biological specimens measured by acoustic microscopy. Reﬂected pulse
signals from the substrate and specimen were converted into frequency domains to obtain sound speed and thickness. To obtain the average
acoustic properties of the specimen, parabolic approximation was performed to determine the frequency at which the amplitude of the normalized
spectrum became maximum or minimum, considering the sound speed and thickness of the specimens and the operating frequency of theultrasonic device used. The proposed method was demonstrated for a specimen of malignant melanoma of the skin by using acoustic microscopy
attaching a concave transducer with a center frequency of 80 MHz. The variations in sound speed and thickness analyzed by the proposed method
were markedly smaller than those analyzed by the method based on an autoregressive model. The proposed method is useful for the analysis of
the acoustic properties of bilogical tissues or cells. © 2018 The Japan Society of Applied Physics

1.

Introduction

Acoustic microscopy1–3) is one of the useful modalities fortissue characterization, because it can obtain acoustic
properties, viz., sound speed and attenuation, in a microscopic region. Usually, thin-sliced specimens with a thickness of about 10 µm are used for measurements. It is
impossible to separate the reﬂected signals from the front
and back surfaces of a specimen if rf tone burst signals areused as input signals. To obtain the thickness and soundspeed of the specimen, it is necessary to measure thefrequency characteristics of the superposed signal as theinterference output. However, it is time-consuming. Thus,
pulse signals are widely used as input signals.4)
Acoustic property measurement methods for biological
specimens using pulse signals by acoustic microscopy werebroadly divided into time and frequency domain analyses. In
time domain analysis, the arrival times of reﬂected pulses
from the substrate surface without a specimen and the front
and back surfaces of the specimen are measured to obtainthe sound speed and thickness. The pulse spectrum method isthe analysis method in the frequency domain.5) It is possible
to obtain the thickness and sound speed of the specimen
simultaneously from the amplitude and phase of the frequency spectrum of the reﬂected signals. In addition, amethod using an autoregressive (AR) model was proposed6,7)
and the software was installed into a commercial acoustic
microscopy system.8)
Acoustic microscopy has been applied to the characterization of biological tissues and cells.9–31) Water or physiological saline solution is used for the coupler in the measurements of biological specimens. Then, the reﬂected signal
from the specimen surface, SS, shown in Fig. 1 becomes
small, because the acoustic impedance diﬀerence between thespecimen and the coupler is small. The backscattered waves
produced by the inhomogeneity inside biological specimens
might be larger than the signal SS. Thus, sound speed andthickness errors would be fairly large. In this paper, a robust
analysis method for the acoustic properties of biological
specimens measured by acoustic microscopy is discussed.

Fig. 1. (Color online) Measurement signals for acoustic property
measurement by acoustic microscopy.

2.

Analysis method

Figure 1 shows the measurement signals for the acoustic
property measurements of biological specimens. Each specimen is placed on a substrate such as a slide glass or a petri
dish. The ultrasonic waves emitted from the ultrasonictransducer were irradiated to the specimen through a coupler
such as water or physiological saline solution. SW, SS, andSB are the reﬂected signals from the substrate surface, thespecimen surface, and the boundary between the specimen
and the substrate, respectively. On the basis of the acoustic
transmission line model, these signals are represented as
SW ¼ A  R13  expð21 dÞ;

ð1Þ

SS ¼ A  R12 ;ð2Þ

SB ¼ A  T12  R23  T21  expð22 dÞ;ð3Þi ¼ i þ jki ;ð4Þwhere A is the amplitude coeﬃcient, Rij and Tij are thereﬂection and transmission coeﬃcients from medium i to
medium j, respectively, γi is the propagation constant, αi isthe attenuation coeﬃcient, ki is the wave number, and d isthe thickness of the specimen. The coupler, specimen, andsubstrate are media 1, 2, and 3, respectively. If the signals
SS and SB cannot be separated in the time domain, thesuperposed signal of SS and SB normalized by the signal SW isexpressed as

07LB07-1© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LB07 (2018)
1.05

1.05

V2 [m/s]

1.00

1485

0.95

1530
1580

0.90

1630
1680

0.85

10 W

0.90

20 W
50 W

0.85
0.80

1.0

0.20

30 40 50 60 70 80 90 100 110
FREQUENCY [MHz]

(b)

(b)
PHASE [rad]PHASE [rad]

W

2 W

0.95

0.80
30 40 50 60 70 80 90 100 110
FREQUENCY [MHz]

0.8

2

(a)
1.00
AMPLITUDE(a)
AMPLITUDE

M. Arakawa et al.

0.6
0.4
0.2
0.0
-0.2

0.15
0.10
0.05
0.00
30 40 50 60 70 80 90 100 110
FREQUENCY [MHz]30 40 50 60 70 80 90 100 110
FREQUENCY [MHz]Fig. 2. (Color online) Frequency spectra of (a) amplitude and (b) phasecalculated by changing V2.

Fig. 3. (Color online) Frequency spectra of (a) amplitude and (b) phasecalculated by changing α2.

SS þ SB R12¼
 expð21 dÞ
SW
R13


T12  R23  T21
 1þ
 expð22 dÞ :R12

specimen and water increased. Moreover, the rate of phasechange increased with V2. Next, the amplitude and phaseof the frequency spectra were calculated by changing theattenuation coeﬃcient of the specimen, α2, when water wasused as the coupler. The results are shown in Fig. 3. The
sound speed, density, and thickness of the specimen wereassumed to be 1530 m=s, 1000 kg=m3, and 7 µm, respectively. The amplitude of the interference of the amplitude
spectrum decreased with increasing α2. In particular, monotonic decreases in the amplitude spectrum were observed
when α2 was more than 20 times larger than αW. Phasechanges were almost the same regardless of α2.
Relationships among ϕm, V2, and fm for each n can beobtained using Eqs. (8) and (9), if d is known. The
relationship for n = 1, that is, the ﬁrst minimum in thefrequency spectrum, is shown in Fig. 4. fm exists in thefrequency range of 40–105 MHz if d is 4–8 µm and V2 is
1,400–1,700 m=s. In the case of n = 2, fm exists in the same
frequency range if d is 8–16 µm from Eq. (9). Therefore, it ispossible to predict the frequency range of the maxima andminima of the amplitude spectrum, if the thickness andsound speed of the specimen and the operating frequency
range of the ultrasonic device used in the measurement are
known. The frequency fm might shift if there exist ripples
on the amplitude spectrum produced by the scattered wave
and multiple reﬂections. To reduce the eﬀects and robustly
obtain the average properties, fm can be determined asfollows.
(1) The frequency fm at which the amplitude spectrum
becomes maximum or minimum is calculated by theparabolic approximation of the amplitude spectrum
considering the sound speed and thickness of thespecimen and the operating frequency range of theultrasonic device.
(2) d and V2 are calculated using Eqs. (6) and (7) using fm
and ϕm.

ð5Þ

By performing Fourier transform for the signal, the frequency
spectrum can be obtained. From the frequency fm at which
the amplitude spectrum becomes maximum or minimum andthe phase ϕm of the phase spectrum at fm, the thickness d andsound speed V2 of the specimen were obtained from5)
V1
ðm þ nÞ;
ð6Þ
4fm


1
m 1
V2 ¼

;
ð7Þ
V1 4fm dwhere n is the natural number.
The following equation can be obtained by transforming
Eq. (6):d¼

m ¼

4fm d
 n:
V1

ð8Þ

Equation (9) was obtained by substituting V1 in Eq. (7) into
Eq. (8).
V2 ¼

4fm d
:
n

ð9Þ

The amplitude and phase of the frequency spectra
calculated using Eq. (5) by changing the sound speed of
the specimen, V2, are shown in Fig. 2. Here, water (V1 =1485 m=s, ρ1 = 998 kg=m3, α1 = αW = 2.23 × 10−14 s2=m)
was used as the coupler. The density and thickness of thespecimen were assumed to be 1000 kg=m3 and 7 µm,
respectively. The attenuation coeﬃcient of the specimen,
α2, was assumed to be equal to αW. The amplitude of theinterference of the amplitude spectrum increased with V2,
because the acoustic impedance diﬀerence between the

07LB07-2© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LB07 (2018)

M. Arakawa et al.

1.5
4

Analyzed results
α2=αW

5
0.5

6

0
-0.5

55

6.955

2

55

6.955

1530.1

9

10

61

6.281

1532.5

RELATIVE OUTPUT [arb. unit]

SOUND SPEED [m/s]1530.1

1

(b)

1800
1700
1600
1500
1400
30 40 50 60 70 80 90 100 110 120
fm [MHz]

Fig. 4. (Color online) Relationships among phase of the phase spectrum,
ϕm, sound speed of specimen, V2, and frequency at which the amplitude
spectrum becomes minimum, fm. (a) ϕm vs fm and (b) V2 vs fm.

Sound speed
(m=s)

1485

53

7.005

1485.0

1530

55

6.955

1530.1

1580

56

7.052

1579.7

1630
1680

58
60

7.025
7.000

1629.71680.0

0
-200
-400
-600
0

0.02

0.04 0.06
TIME [µ s]

0.08

0.1

(b)

0.8
0.6
0.4
0.2
0
0

20

40 60 80 100 120 140
FREQUENCY [MHz]1

The average acoustic properties of the specimen will beobtained even if ripples exist on the amplitude spectrum,
because the proposed method can obtain a single maximum
or minimum point from the entire frequency range of theamplitude spectrum.
Sound speed and thickness were obtained by the proposed
method for the frequency spectra in Figs. 2 and 3. Theirresults are shown in Tables I and II, respectively. The
analyzed sound speed error was within 0.3 m=s for α2 = αW.
On the other hand, the sound speed error increased up to
2.5 m=s for α2 = 10αW, because the frequency at which theamplitude spectrum becomes minimum increased. Such error
was within 0.2%, which is fairly small compared with thesound speed distributions for tissues.
Results and discussion

A specimen of malignant melanoma of the skin was taken.
An unstained pathological tissue was ﬁxed with formalin.
The specimen was embedded in paraﬃn, sliced to a thicknessof 5–7 µm, and ﬁxed on a slide glass. The specimen was
deparaﬃnized with xylene and ethanol before the ultrasonicmeasurement.

RELATIVE OUTPUT

Thickness
(µm)

(a)

200

RELATIVE OUTPUT

Analyzed results
fm
(MHz)

400

1

Table I. Results analyzed by the proposed method for the amplitude andphase spectra in Fig. 2.

3.

Sound speed
(m=s)

8

2000

V2
(m=s)

Thickness(µm)

730 40 50 60 70 80 90 100 110 120
fm [MHz]

1900

fm
(MHz)

1

(c)

0.8

0.9

0.6
0.4

0.8

PHASE [rad]1
φm [rad]Table II. Results analyzed by the proposed method for the amplitude andphase spectra in Fig. 3.

d [µ m]

(a)

0.2
0.7

0
20

40
60
80
FREQUENCY [MHz]100

Fig. 5. (a) Reﬂected signals from a substrate (solid line) and a specimen of
malignant melanoma (dotted line) in time domain, (b) frequency spectra of(a) (solid line: substrate, dotted line: specimen), and (c) normalized frequency
spectrum (solid line: amplitude, dotted line: phase).

Commercial acoustic microscopy (Honda Electronics
AMS-50SI)8) was used for the measurement using a concave
transducer with an ultrasonic transducer of poly(vinylidene
ﬂuoride) (PVDF) ﬁlm, a operating center frequency of
80 MHz, and a focal length of 1.5 mm. Two-dimensionalscanning of 2.4 × 2.4 mm2 was conducted in 8 µm steps.
Eight rf signals were measured at each point and averaged.
Distilled water was used as the coupler.
The reﬂected signals from the substrate and specimen are
shown in Fig. 5(a). The frequency spectra obtained by fast
Fourier transform are shown in Fig. 5(b). The 6 dB
bandwidth of the amplitude spectrum reﬂected from thesubstrate was 30–100 MHz, and the frequency range was

07LB07-3© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LB07 (2018)

M. Arakawa et al.

used for the analysis. The amplitude and phase of thenormalized frequency spectrum are shown in Fig. 5(c). The
minimum of the amplitude spectrum was observed at87.2 MHz in Fig. 5(c). The sound speed and thickness ofthe specimen were obtained as n = 1 in Eqs. (6) and (7) from
Figs. 4 and 5(c).
The C-mode image of the specimen is shown in Fig. 6.
The two-dimensional thickness and sound speed distributions
analyzed by the method based on the AR model are shownin Figs. 7(a) and 7(b), respectively. Those along the x-axis
direction at y = 1.5 mm are shown in Figs. 7(c) and 7(d),respectively. Sound speeds higher than 2,500 m=s andthicknesses larger than 20 µm were observed.
Next, by considering Ref. 5, thicknesses and sound speeds
were analyzed using the frequency fMin at which theamplitude spectrum became minimum in the frequency rangeof 30–100 MHz. The results are shown in Fig. 8. The
thicknesses and sound speeds analyzed by the proposed
method are shown in Fig. 9. The average, maximum, andminimum values at y = 1.5 mm obtained by the proposed
method, the method using fMin, and the method based on the
AR model are shown in Table III. Variations in sound speeds
and thicknesses obtained by the method using fMin and the
proposed method were markedly smaller than those obtainedby the method based on the AR model.
By comparing the sound speed distribution with the Cmode image, sound speed was observed to increase withdecreasing intensity in Fig. 6. This is caused by the increasein acoustic impedance and the decrease in T12 · T21 in Eq. (3)with higher sound speed.
In the analysis method based on the AR model,6,7) soundspeed and thickness were obtained by estimating the phasesof the reﬂected signals from the normalized frequency
spectrum as shown in Fig. 5(c). As one of the factors oflarge sound speed and thickness errors obtained by themethod based on the AR model, it is thought that amplitudeFig. 6. C-mode image of a specimen of malignant melanoma of skin.

Table III. Thicknesses and sound speeds analyzed by the proposed methodin Figs. 9(c) and 9(d), those analyzed by the frequency fMin at which theamplitude spectrum became minimum in Figs. 8(c) and 8(d), and thoseanalyzed by the method based on the AR model in Figs. 7(c) and 7(d).

Proposed method

fMin

AR modelThickness(µm)

Sound speed
(m=s)

Ave

5.04

1669

Max

5.75

1822

Min

3.86

1505

Ave

5.16

1671

Max

6.07

1813

Min

3.76

1507

Ave

5.99

1681

Max

29.3

4069

Min

−0.01

1473

of the scattered wave reﬂected inside the specimen became
larger than that of the reﬂected wave from the specimen
surface.
By comparing the results in Figs. 8 and 9, the variation in
analyzed thickness obtained by the proposed method was

(a)

(b)

(c)

(d)

Fig. 7. (Color online) Results analyzed by the method based on the AR model. (a) Thickness distribution, (b) sound speed distribution, (c) thicknesses alongy = 1.5 mm in (a), and (d) sound speeds along y = 1.5 mm in (a).

07LB07-4© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LB07 (2018)

M. Arakawa et al.

(a)

(b)

(c)

(d)

Fig. 8. (Color online) Results analyzed using the frequency fMin at which the amplitude spectrum became minimum in 30–100 MHz range. (a) Thickness
distribution, (b) sound speed distribution, (c) thicknesses along y = 1.5 mm in (a), and (d) sound speeds along y = 1.5 mm in (a).

(a)

(b)

(c)

(d)

Fig. 9. (Color online) Results analyzed by the proposed method. (a) Thickness distribution, (b) sound speed distribution, (c) thicknesses along y = 1.5 mm
in (a), and (d) sound speeds along y = 1.5 mm in (a).

07LB07-5

1
RELATIVE OUTPUT

observed to be smaller than that obtained from fMin, although
the analyzed velocities were almost the same. At the pointof ðx; yÞ ¼ ð1:1 mm; 1:5 mmÞ, d and V2 were analyzed as
3.94 µm and 1,573 m=s in Fig. 8, and 4.71 µm and 1,578 m=s
in Fig. 9, respectively. d obtained from fMin was fairly small.
The amplitude spectrum at this point is shown in Fig. 10. fm
was determined to be 99.9 and 83.7 MHz by fMin and the
proposed method, respectively. The following equations canbe obtained from Eqs. (6) and (7):


nV1
m
d¼
1þ
;
ð10Þ
4fm
n

0.9

0.8

0.7
20

Fig. 10.

40
60
80
FREQUENCY [MHz]100

Amplitude spectrum at ðx; yÞ ¼ ð1:1 mm; 1:5 mmÞ.

© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LB07 (2018)
7

1900

(a)

6

1700

4

1600

3
7

1500
1900

(b)

(b)

1800
SOUND SPEED [m/s]

5
4
3
7

(c)

6

(a)

1800

5

6
THICKNESS [µ m]M. Arakawa et al.

5
4

1700
1600
1500
1900

(c)

1800
1700
1600

3
7

1500
1900

(d)

6

(d)

1800

5

1700

4

1600

3

1500
0

0.4 0.8 1.2 1.6 2
x POSITION [mm]

2.4

0

(A)

0.4 0.8 1.2 1.6 2
x POSITION [mm]

2.4

4.

(B)

Fig. 11. Thickness (A) and sound speed (B) analyzed by the proposed
method at y = 1.5 mm by changing the frequency range. (a) 30–120,(b) 30–100, (c) 40–90, and (d) 50–80 MHz.

V2 ¼ V1


m
1þ
:
n

analyzing the frequency spectrum in the frequency range
with good SNR including the minimum or maximum of theamplitude spectrum using the proposed method.
In this experiment, the specimen thickness was controlled
to 5–7 µm during specimen preparation. In the present
method, the roughly estimated sound speeds and thicknesses
are required to investigate the relationship between V2 and fm
shown in Fig. 4(b). The average sound speeds and thicknesses analyzed by the method based on the AR model were
almost the same as those analyzed by the proposed method asshown in Table III. Therefore, those analyzed by the method
based on the AR model could be used as rough values todetermine the analysis region in the proposed method.
As shown in Fig. 3, the local minimum was not observedin the amplitude spectrum when α2 was larger than 20αW,
although intereferences of the amplitude spectrum wereobserved. If a frequency spectrum is measured more thana cycle, the low-frequency component of the amplitude
spectrum can be obtained by the linear approximation, andonly the interference component can be extracted bysubtracting it from the amplitude spectrum. Thereafter, theanalysis using the proposed method would be conducted.

ð11Þ

The accuracies of fm and ϕm directly aﬀect that of d from
Eq. (10). On the other hand, fm does not directly aﬀect theaccuracy of V2, but ϕm does, as determined from Eq. (11).
In Fig. 2, ϕm changes from 0.254 to 0.282 rad when thefrequency changes from 80 to 88 MHz in the case of
V2 = 1,580 m=s. With these frequency and phase changes,
d and V2 change by −8.3 and +0.9%, respectively, if n = 1
in Eqs. (10) and (11). Therefore, the variation in thickness
was reduced by accurately obtaining fm by the parabolic
approximation in the proposed method.
Next, the eﬀect of the frequency range on the analysis in
the proposed method was investigated. The frequency rangesof (a) 30–120 MHz, (b) 30–100 MHz, (c) 40–90 MHz, and(d) 50–80 MHz were investigated. The results for y = 1.5 mm
are shown in Fig. 11. The variations in thickness and soundspeed in Fig. 11(a) were slightly larger than those in
Figs. 11(b) and 11(c). This is due to the worse signal-tonoise-ratio (SNR) regions in the amplitude spectrum being
included in the analysis region, and the decrease in theaccuracy of fm. The minimum thicknesses in Fig. 11(d) were
obviously larger than those in Figs. 11(b) and 11(c). This iscaused by the limitation of the analysis region. The upper
frequency of the analysis was 80 MHz, and the minimum
thickness was limited to a value larger than about 5 µm from
Fig. 4. From these results, the robustness of the analyzed
sound speeds can be improved by selecting an appropriate
frequency range for analysis, and that of thicknesses can be
improved by accurately obtaining fm using the parabolic
approximation of the amplitude spectrum. Therefore, it ispossible to robustly obtain the thickness and sound speed byConclusions

In this paper, a robust analysis method for the acoustic
properties of biological specimens measured by acoustic
microscopy is proposed. Average acoustic properties can beobtained by the proposed method considering the operating
frequency range of the ultrasonic device, even if there areunwanted ripples on the amplitude spectrum because of the
low SNR or existence of scattered waves. The proposed
method is useful for the analysis of the acoustic properties of
biological tissues or cells.

1)
2)
3)
4)
5)

6)

7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)

07LB07-6

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