Japanese Journal of Applied
Physics

REGULAR PAPERS

Accuracy improvement in measurement of arterial wall elasticity by
applying pulse inversion to phased-tracking method
To cite this article: Yukiya Miyachi et al 2018 Jpn. J. Appl. Phys. 57 07LF08

View the article online for updates and enhancements.

This content was downloaded from IP address 219.167.133.202 on 05/06/2018 at 15:42

REGULAR PAPER

Japanese Journal of Applied Physics 57, 07LF08 (2018)https://doi.org/10.7567/JJAP.57.07LF08

Accuracy improvement in measurement of arterial wall elasticity
by applying pulse inversion to phased-tracking method
Yukiya Miyachi1,2*, Mototaka Arakawa2,3, and Hiroshi Kanai3,21
Medical Systems Research and Development Center R&D Management Headquarters, FUJIFILM Corporation,
Kaisei, Kanagawa 258-8538, Japan
2
Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
3
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan*E-mail: yukiya.miyachi@fujiﬁlm.com
Received November 5, 2017; revised February 2, 2018; accepted February 27, 2018; published online June 5, 2018
In our studies on ultrasonic elasticity assessment, minute change in the thickness of the arterial wall was measured by the phased-tracking
method. However, most images in carotid artery examinations contain multiple-reﬂection noise, making it diﬃcult to evaluate arterial wall elasticity
precisely. In the present study, a modiﬁed phased-tracking method using the pulse inversion method was examined to reduce the inﬂuence of themultiple-reﬂection noise. Moreover, aliasing in the harmonic components was corrected by the fundamental components. The conventional andproposed methods were applied to a pulsated tube phantom mimicking the arterial wall. For the conventional method, the elasticity was 298 kPa
without multiple-reﬂection noise and 353 kPa with multiple-reﬂection noise on the posterior wall. That of the proposed method was 302 kPa without
multiple-reﬂection noise and 297 kPa with multiple-reﬂection noise on the posterior wall. Therefore, the proposed method was very robust against
multiple-reﬂection noise. © 2018 The Japan Society of Applied Physics

1.

Introduction

Along with the recent changes in lifestyle in Japan, theincidence of coronary artery disease has increased steadily.1)
Atherosclerosis is considered to be the main cause ofcoronary artery disease. Since there are signiﬁcant diﬀerencesin elasticity between normal and atherosclerotic arterial
walls,2,3) it is eﬀective to evaluate the elasticity of the arterial
wall.4) Many studies have shown that some markers can be
noninvasively measured for the detection of atherosclerosis
such as the intima-media thickness (IMT) of the arterial wall,
pulse wave velocity (PWV), and the elasticity of the arterialwall.
IMT is measured accurately as the average distance
between the lumen–intima boundary and the media–
adventitia boundary from a B-mode ultrasonic image.5–11)
Carotid IMT is widely used as a surrogate marker ofatherosclerosis worldwide. However, a conventional B-mode
ultrasonic image provides only information on shape, andmechanical properties such as arterial wall elasticity cannot
be evaluated.
PWV is a measure of the arterial pulse propagating
through the circulatory system. PWV is used clinically asa noninvasive diagnostic tool for the measurement of theelasticity of the arterial wall.12–14) Although it is useful forthe evaluation of global elasticity such as from the heart
to the peripheral artery, regional elasticity has not been
evaluated.
In a series of studies,15–31) the elasticity of a local region
has been obtained by the ultrasonic phased-tracking method.
In these studies, the displacement and change in the thicknessof the arterial wall caused by the heartbeat have beenmeasured. The elasticity of the human carotid artery is
obtained from the measured change in thickness and theblood pressure. In these methods, to track the fast movementof the human carotid arterial wall, a high frame rate, of atleast 100 Hz, is necessary. These methods can be used toevaluate the elasticity precisely when images are clear.

However, unfortunately, most images in a clinical setting
contain various types of noise, such as multiple-reﬂection
noise, making it diﬃcult to measure the movement of the
carotid arterial wall and evaluate its elasticity precisely.
To suppress the multiple-reﬂection noise, tissue harmonic
imaging is widely used in carotid artery examinations.32,33)
The pulse inversion (PI) method is one of the tissue harmonic
imaging techniques and is preferred for obtaining more
broadband images.34–38) Although the multiple-reﬂection
noise is signiﬁcantly improved, the frame rate of the PI
method is reduced to half.
In the present study, we propose a modiﬁed phasedtracking method using the PI method for reducing theinﬂuence of multiple-reﬂection noise on the estimation ofelasticity. To avoid aliasing of the phase shift of harmonic
signals owing to the reduced frame rate, fundamental signals
are also used to correct the aliasing of the phase shift.
Improvement of accuracy by the proposed method wasvalidated using the silicone rubber tube phantom.
2.

Methods

2.1

Phased-tracking method
To obtain a small change in thickness of the arterial wall,
which is deﬁned as the diﬀerence between the displacement
Δh(t) of the intima–lumen boundary xin(t) and that of theadventitia–media boundary xad(t), the velocities vin(t) andvad(t) on the intima–lumen boundary and adventitia–media
boundary, respectively, are measured by the following
phased-tracking method.15,16)
Ultrasonic pulses are transmitted at the pulse repetitioninterval Tr from the transducer on the surface of the skin.
The pulse reﬂected from the object is received, ampliﬁed,
and converted to a digital signal. Quadrature demodulation isapplied to the digital signal. Using the quadrature demodulated signal zðt; dÞ reﬂected from depth d at a time t, the phaseshift ΔΨi(t) between echoes in two consecutive frames is
estimated from the following complex cross-correlation
function:

07LF08-1© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF08 (2018)

Y. Miyachi et al.
M
C =2
X

zðt þ Tr ; xi ðtÞ þ mDÞ  z ðt; xi ðtÞ þ mDÞ

m¼M =2C;expð j ^ i ðtÞÞ ¼  M =2
 X

C



zðt þ Tr ; xi ðtÞ þ mDÞ  z ðt; xi ðtÞ þ mDÞm¼M =2
ð1ÞCwhere D is the interval of sampled points in the depth
direction, i denotes the intima–lumen boundary or adventitia–
media boundary, xi(t) denotes the displacement of theseboundaries, and + represents the complex conjugate,
respectively. In Eq. (1), the number of sampled points,
MC + 1, is determined by considering the received pulse
length. The ^ above ΔΨi(t) denotes the estimate of thevariable (the phase shift). In the estimation of the phase shiftby Eq. (1), the object position is tracked by integration of
the average velocity, vi(t + Tr=2), during the pulse repetitioninterval Tr as follows:Tr^xi ðt þ Tr Þ ¼ x^i ðtÞ þ v^i t þ
 Tr
2
c0
¼ x^i ðtÞ þ ^ i ðtÞ  Tr ;
ð2Þ
2!0

2 mm

lumen

posterior wall(a) M-mode

πradian 0
-π

0

ð3Þ

From the ratio of the maximum decrease in thickness during
a cardiac cycle, Δhmax = maxt∣Δh(t)∣, to the maximum
thickness, h(0), the maximum strain is obtained by Δεmax =Δhmax=h(0). By assuming that the arterial wall is incompressible and that the blood pressure applied to the arterial wall isnormal, the elastic modulus Eθ is approximately given by 21)


3
2r0
p
1þ
E ¼
;
ð4Þ
8
hð0Þ "maxwhere r0 and Δp are respectively the inner radius at the
maximum thickness timing and the pulse pressure, which isthe diﬀerence of the systolic blood pressure from the diastolicblood pressure measured at the upper arm.
Experiments were conducted using ultrasonic diagnostic
equipment (Fujiﬁlm FC1) with a linear-type transducer, andthe quadrature demodulated signals were saved as raw data.
The transmitting and detection center frequencies were set to11.4 and 11 MHz, respectively. The frame rate and samplinginterval of the quadrature demodulated signal were 200 Hz
and 0.056 mm, respectively.
Figure 1(a) shows a magniﬁed M-mode image of thecommon carotid artery obtained from a healthy 44-year-old
male with the posterior wall boundary tracking results
overlaid. Figures 1(b), 1(c), and 1(d) show the phase shift
at the intima–lumen boundary, the phase shift at theadventitia–media boundary, and the change in the thicknessof the posterior wall, respectively. In Fig. 1(d), at the time
when the posterior wall was closest to the transducer, thechange in thickness is set to zero. Using these results, Eθwas estimated as 271 kPa using Eq. (4).

(b) phase shift at intima-lumen boundaryπradian 0-π
50μm

where ω0 and c0 are the center angular frequency of thequadrature phase detection and the speed of sound,respectively. From the displacement xi(t), the small change
in thickness, Δh(t), of the arterial wall is given byhðtÞ ¼ xin ðtÞ  xad ðtÞZt¼ ½vin ðtÞ  vad ðtÞ dt:

anterior wall

-35(c) phase shift at adventitia-media boundary(d) change in thickness

0

0.4
time [s]0.8

Fig. 1. (Color online) Carotid artery results without the multiplereﬂection noise on the posterior wall. (a) Magniﬁed M-mode with theposterior wall boundary tracking results overlaid. (b) Phase shift at the
intima–lumen boundary. (c) Phase shift at the adventitia–media boundary.
(d) Change in thickness of the posterior wall.

However, almost all ultrasonography images taken in aclinical setting of the carotid artery contain various types ofnoise, such as multiple-reﬂection noise, making it diﬃcult
to evaluate arterial wall elasticity precisely. For example,
Fig. 2(a) shows a magniﬁed M-mode image where themultiple-reﬂection noise from the anterior wall was overlaid
on the posterior wall. The subject is the same as that for theimage shown Fig. 1, but the transducer position was changed
to generate multiple-reﬂection noise from the anterior wall.
Figures 2(b)–2(d) show the phase shift at the intima–lumen
boundary, the phase shift at the adventitia–media boundary,and the change in thickness of the posterior wall, respectively. Figure 2(d) shows that the shape of change inthickness did not correspond to heartbeat, and the maximum
change in thickness was relatively smaller than that inFig. 1(d). Using these results, Eθ was estimated as 753 kPa
using Eq. (4). Comparison of the results in Fig. 1 with thosein Fig. 2 shows that the multiple-reﬂection noise could
decrease the accuracy of the measured elasticity.
2.2 Pulse inversion method
In B-mode imaging, tissue harmonic imaging has beenshown to reduce noise and improve image quality. Tissue
harmonic imaging utilizes the harmonic signals generated
during acoustic propagation through soft tissues. The
following two methods are commonly used to obtain the

07LF08-2© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF08 (2018)

2 mm

Y. Miyachi et al.
-50

anterior wall

power [dB]

-60

lumen

-70
-80
-90
-100

posterior wall

5
10
frequency [MHz]0(a)M-mode
M-mode
(a)

15

(a)

π
-50

radian 0-π(b) phase shift at intima-lumen boundary-60

radian 0-π15μm

power [dB]π(c) phase shift at adventitia-media boundary

-70
-80

0
-15

-90
(d) change in thickness

0.4
time [s]

0

0.8

-100
0

Fig. 2. (Color online) Carotid artery results with the multiple-reﬂection
noise on the posterior wall. (a) Magniﬁed M-mode image with the posteriorwall boundary tracking results overlaid. (b) Phase shift at the intima–lumen
boundary. (c) Phase shift at the adventitia–media boundary. (d) Change inthickness of the posterior wall.

lumen

posterior wall

15(b)Fig. 4. Power spectra. (a) RF echo reﬂected from the multiple-reﬂection
noise in the lumen. (b) RF echo reﬂected from the intima-media complex.

1.0

normalized amplitude

2 mm anterior wall

5
10
frequency [MHz]detected envelope
0.5

multiplereflectionnoise

intimamedia
complex0
RF echo-0.5-1.0

anterior wall

lumen
2.5

0

5
distance [mm]posterior wall
7.5
10

(b)

(a)

Fig. 3. (Color online) Magniﬁed B-mode image and RF echo from the carotid artery. (a) Magniﬁed B-mode image. (b) RF echo along the red vertical line
shown in (a).

harmonic signals. The ﬁrst is the ﬁltered method, where a
bandpass ﬁlter is used to select the harmonic components
from the received signals. The second is the PI method,where two pulses with opposite polarities are transmitted andthen are summed to cancel the fundamental components
while the harmonics double. Since the transducer bandwidthis limited, the PI method is widely used to obtain broadband
harmonic signals.
Figure 3(a) shows the B-mode image obtained by the PI
method for the common carotid artery and Fig. 3(b) shows
the received RF echo along the red vertical line in Fig. 3(a).
The dotted line is the detected envelope of the RF echo in
Fig. 3(b). The transmitting center frequency and the sampling
frequency of the received echo were set to 5.7 and 40 MHz,
respectively. Figures 4(a) and 4(b) show the power spectrumof the RF echo reﬂected from the multiple-reﬂection noise in

the lumen and that of the RF echo reﬂected from the intimamedia complex (IMC), which was extracted using a Hanningwindow at the position shown in Fig. 3(b). In Fig. 4(a), only
one peak appeared at approximately 5 MHz, which corresponds to the fundamental components of the transmitting
frequency of 5.7 MHz. In Fig. 4(b), not only the peak ataround 5 MHz but also a subpeak at around 11 MHz, whichcorresponds to the harmonic components of the transmitting
frequency of 5.7 MHz, were observed. The multiple reﬂection noise tends to be more attenuated than single-reﬂection
signals because it is reﬂected more than once. This could be
the reason that the harmonic component cannot be observedin the multiple-reﬂection noise in Fig. 4(a). This reason is
discussed in detail in Sect. 4. From these results, 11 MHz waschosen as the center detection frequency for the selection ofharmonic components and 5.5 MHz was chosen as a center

07LF08-3© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF08 (2018)

Y. Miyachi et al.

0.2 s
2 mm

2.3 Applying pulse inversion to phased-tracking
methodanterior wall

lumen
posterior wall

(a)
2 mm

(b)

0.2 s

anterior wall

lumen
posterior wall

(d)

(c)

Fig. 5. (Color online) B-mode and M-mode images of the fundamental
and the PI method at carotid artery. (a) B-mode image of the fundamental
method. (b) M-mode image of the fundamental method. (c) B-mode image of
the PI method. (d) M-mode image of the PI method.

Txintensitytransducer
bandwidth W ) n ¼ 1;2  W  fund <  þ W ) n ¼ 0 or 1;
22 þ W  fund <  W ) n ¼ 0;
22
 W  fund < þ W ) n ¼ 0 or 1;22þ W  fund <  ) n ¼ 1;
2
  fund < 

cutoff filterRxharmonic
intensity

Rx fundamental

ð5Þ

fundamental
quadrature
demodulated
signalfrequency

frequency

intensity

pair of pulse
invertedTx signals

intensity

detection frequency for the selection of fundamental
components in Sect. 3.
B-mode and M-mode carotid artery images obtained by thefundamental method, in which the transmitting center
frequency was set at 11.4 MHz and the center detection
frequency was set at 11 MHz, are shown in Figs. 5(a) and
5(b), respectively. On the other hand, B-mode and M-mode
images obtained by the PI method, in which transmitting
center frequency was set at 5.7 MHz and the center detection
frequency was set at 11 MHz, are shown in Figs. 5(c) and
5(d), respectively. The signal-to-noise ratios deﬁned by thesignal from IMC yellow circles in Figs. 5(b) and 5(d) and themultiple-reﬂection noise red circles in Figs. 5(b) and 5(d)were 9 dB for the fundamental method and 20 dB for the PI
method. Apparently, the PI method was superior to thefundamental method from the viewpoint of reduction of themultiple-reﬂection noise.

Although the PI method improves the signal-noise ratio, theframe rate was reduced by half because two pulses are needed
to be transmitted to create a single harmonic echo. Reduced
frame rate tends to result in aliasing of the phase shift andtracking error because of rapid arterial wall motion. In thepresent study, to avoid the aliasing of the phase shift ofharmonic components, the fundamental components, subtracted from the two pulses, were employed to correct thephase shift of the harmonic components. Figure 6 shows anoutline of the PI method used this study. As discussed in
the previous section, the transmitting center frequency ofthe pairs of inverted pulses was 5.7 MHz. To obtain harmonic quadrature demodulated signals, by summing pairs ofreceived echo, the fundamental components were canceledwhile the harmonic components were doubled. Summed RF
data were dominant at a center frequency of 11 MHz. On theother hand, to obtain the fundamental quadrature demodulated signals, by subtracting pairs of the received echo, theharmonic components were canceled while the fundamental
components became double. Subtracted RF data were
dominant at the center frequency of 5.5 MHz.
The phase shift of the harmonic quadrature demodulated
signal θharm was roughly equal to ( fharm=ffund ) × θfund, where
fharm, ffund, and θfund are the harmonic detection center
frequency, the fundamental detection center frequency, andthe phase shift of the fundamental quadrature demodulated
signal, respectively. θharm is roughly equal to 2θfund because
fharm is 11 MHz and ffund is 5.5 MHz in the present study.
Since the purpose of this correction is to compensate for the
reduction of the frame rate by half originating from the PI
method, only ﬁrst aliasing of θharm is corrected using θfund. To
correct aliasing of the phase shift of the harmonic signals,
ﬁrstly the aliasing number candidate n is evaluated byfrequency

harmonic
quadrature
demodulated
signalfrequency

Fig. 6. (Color online) Outline of the PI method in this study.

07LF08-4© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF08 (2018)
2π

π
0
-π

0

2π

phase shift [radian]phase shift [radian]phase shift [radian]

2π

-2π

Y. Miyachi et al.

π0-π

aliasing
-2π
0
2
3
1
time [s](a)2
1time [s]3anterior wall

4 mm
π
0

lumen

-π

-2π
0

(b)

2
1
time [s]3posterior wall(a) M-mode(c)πFig. 7. (Color online) Phase shifts of the (a) harmonic, (b) fundamentaland (c) corrected harmonic.

radian 0-ππradian 0
-π
10
0
μm

transducer
water
tank
pressure
sensortube
multiple reflection
noise

stepping
motor
pump

(a)

-70

(b)

Fig. 8. (Color online) Arterial-wall-mimicking phantom made of silicone
rubber tube pulsated by stepping motor pump. (a) Multiple-reﬂection noise
inside the lumen. (b) Multiple-reﬂection noise on the posterior wall.

where W is an empirical constant, which is suﬃciently
smaller than π=2. Secondly, in the case that n = 0 or 1, thealiasing number n is determined so that the following e(n)was minimized:eðnÞ ¼ jharm þ 2n  2fund j:

ð6Þ

The corrected θharm is expressed by θharm + 2πn. The phaseshift values of the harmonic, the fundamental, and thecorrected harmonic are shown in Figs. 7(a)–7(c), respectively. In Fig. 7(c), aliasing in Fig. 7(a) was corrected. The
corrected phase shift θharm + 2πn was applied to the phasedtracking method.15,16)
3.

(b) phase shift at intima-lumen boundary

Results

To evaluate the accuracy of the proposed method, we
prepared a phantom mimicking the arterial wall made of asilicone rubber tube, which was pulsated by a stepping motor
pump. The internal pressure was measured using a pressure
sensor (Keyence GP-M001). The wall thickness of thesilicone rubber tube was 1.1 mm and the inner diameter was
8 mm, which were similar to those of the common carotid
artery. The material of the silicone rubber tube included
graphite powder (weight ratio, 5%) to scatter ultrasound.
To evaluate the inﬂuence of the multiple-reﬂection noise
generated between the anterior wall and the transducer on theposterior wall, the distance from the transducer to the tube
was controlled, as shown in Fig. 8. Figure 8(a) shows the
position where the multiple-reﬂection noise generated
between the transducer and the anterior wall appeared inside
the lumen, and Fig. 8(b) shows the position where themultiple-reﬂection noise appeared only on the posterior wall.

(c) phase shift at adventitia-media boundary(d) change in thickness

0

0.65
time [s]1.3

Fig. 9. (Color online) Arterial-wall-mimicking phantom results of thefundamental method with the multiple-reﬂection noise inside lumen.
(a) Magniﬁed M-mode image with the posterior wall boundary tracking
results overlaid. (b) Phase shift at the intima–lumen boundary. (c) Phase shift
at the adventitia–media boundary. (d) Change in thickness of the posteriorwall.

In Fig. 8(b), the distance between the transducer and theposterior wall was controlled to be twice that between thetransducer and the anterior wall.
The change in thickness and elasticity were compared
between the fundamental and PI methods. The transmitting
center frequency of the PI method is chosen to be about halfof that of the fundamental method. The transmitting anddetection center frequencies for the fundamental method were11.5 and 11 MHz, respectively. Those for the PI method were
5.7 and 11 MHz for harmonic components and 5.5 MHz for
fundamental components, respectively. Since the motion of
the wall of the phantom was slower than that of the human
carotid artery, to validate how the proposed method prevents
aliasing noise, the frame rates in this experiment were set to66.7 Hz for the fundamental method and 33.4 Hz for the PI
method.
Figure 9 shows the results obtained by the fundamental
method, in which the multiple-reﬂection noise was inside
the lumen. Figure 9(a) shows a magniﬁed M-mode image
overlaid with the tracking results at the posterior wallboundary. We can see that the multiple-reﬂection noise
appeared inside the lumen clearly. Figures 9(b)–9(d) show
the phase shift at the intima–lumen boundary, the phase shift
at the adventitia–media boundary, and the change in thicknessof the posterior wall, respectively. In Fig. 9(d), when theposterior wall was closest to the transducer, the change inthickness was set to zero. The maximum change in thickness
was 62.0 µm and Eθ was estimated as 298 kPa by Eq. (4).
Figure 10 shows the results of the fundamental method, inwhich the multiple-reﬂection noise was only on the posteriorwall. Figure 10(a) shows a magniﬁed M-mode image over-

07LF08-5© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF08 (2018)

Y. Miyachi et al.

anterior wall

4 mm

anterior wall

4 mm

lumen

lumen

posterior wall

posterior wall(a) M-mode(a) M-modeπ

3π/2
radian 0-3π/2

radian 0-π(b) phase shift at intima-lumen boundaryπradian 0
-π
10
0
μm
-70

3π/2
radian 0
-3π/2
10
0
μm

(c) phase shift at adventitia-media boundary(d) change in thickness

0

0.65
time [s](b) phase shift at intima-lumen boundary

-70

1.3

(c) phase shift at adventitia-media boundary(d) change in thickness

0

0.65
time [s]1.3

Fig. 10. (Color online) Arterial-wall-mimicking phantom results of thefundamental method with the multiple-reﬂection noise on the posterior wall.
(a) Magniﬁed M-mode image with the posterior wall boundary tracking
results overlaid. (b) Phase shift at the intima–lumen boundary. (c) Phase shift
at the adventitia–media boundary. (d) Change in thickness of the posteriorwall.

Fig. 11. (Color online) Arterial-wall-mimicking phantom results of the PI
method with the multiple-reﬂection noise inside lumen. (a) Magniﬁed Mmode image with the posterior wall boundary tracking results overlaid.
(b) Corrected phase shift at the intima–lumen boundary. (c) Corrected phaseshift at the adventitia–media boundary. (d) Change in thickness of theposterior wall.

laid with the tracking results of the posterior wall boundary.
We can see the multiple-reﬂection noise appeared only on theposterior wall clearly. Figures 10(b)–10(d) show the phaseshift at the intima–lumen boundary, the phase shift at theadventitia–media boundary, and the change in thickness ofthe posterior wall, respectively. The maximum change inthickness was 52.3 µm and Eθ was estimated as 353 kPa
using Eq. (4).
Figure 11 shows the results obtained by the proposed
method, in which the multiple-reﬂection noise was inside thelumen, which corresponds to Fig. 9. Figure 11(a) shows amagniﬁed M-mode image overlaid with the tracking resultsof the posterior wall boundary. The multiple-reﬂection noise
was much more suppressed than that generated in thefundamental method. Figures 11(b)–11(d) show the corrected phase shift at the intima–lumen boundary, thecorrected phase shift at the adventitia–media boundary andthe resultant change in thickness of the posterior wall,
respectively. In Figs. 11(b) and 11(c), the scale of the phase
was expanded to 3π=2 since the phase of the harmoniccomponent was corrected in the range from −2π to 2π using
the proposed method. The maximum change in thickness was
61.1 µm and Eθ was estimated as 302 kPa using Eq. (4).
Figure 12 show the results obtained by the phase shiftcorrection method used in Figs. 11(b) and 11(c). The
harmonic component results are shown in Figs. 12(a),12(b), and 12(c); the fundamental component results areshown in Figs. 12(d), 12(e), and 12(f); and the corrected
harmonic results are shown in Figs. 12(g), 12(h), and 12(i).
Figures 12(a), 12(d), and 12(g) show magniﬁed M-mode
images overlaid with the tracking results of the posterior wallboundary. Figures 12(b), 12(e), and 12(h) show the phaseshift at the intima–lumen boundary. Figures 12(c), 12(f), and12(i) show the phase shift at the adventitia–media boundary.
Aliasing noise is shown in Fig. 12(b) and apparent tracking
error of the intima–lumen boundary is shown in Fig. 12(a).
It is shown that aliasing noise was corrected in Fig. 12(h)and the intima–lumen boundary was successfully traced inFig. 12(g).
Figure 13 shows the results of the proposed method, inwhich the multiple-reﬂection noise was only on the posteriorwall, which corresponds to Fig. 10. Figure 13(a) shows amagniﬁed M-mode image overlaid with the tracking results
at the posterior wall boundary. The multiple-reﬂection noise
is much more suppressed than that generated in thefundamental method. Figures 13(b), 13(c), and 13(d) show
the corrected phase shift at the intima–lumen boundary, thecorrected phase shift at the adventitia–media boundary, andthe change in thickness of the posterior wall, respectively. In
Figs. 13(b) and 13(c), the scale of the phase was expanded to
3π=2. The maximum change in thickness was 62.2 µm and Eθ
was estimated as 297 kPa using Eq. (4).
Figure 14 shows the phase shift correction method used in
Figs. 13(b) and 13(c). The harmonic component results areshown in Figs. 14(a), 14(b), and 14(c), the fundamental
component results are shown in Figs. 14(d), 14(e), and 14(f)and the corrected harmonic results are shown in Figs. 14(g),14(h), and 14(i). Figures 14(a), 14(d), and 14(g) show
magniﬁed M-mode images overlaid with the tracking results
at the posterior wall boundary. Figures 14(b), 14(e), and14(h) show the phase shifts at the intima–lumen boundary.
Figures 14(c), 14(f), and 14(i) show the phase shift at the07LF08-6© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF08 (2018)

4 mm

Y. Miyachi et al.

(a) anterior wall

(d)

(g)

(e)

(h)

(f)

(i)

lumen

posterior wall

3π/2 (b)radian 0-3π/2
3π/2 (c)radian 0
-3π/2
0

1.3 0

time [s]time [s]1.3 0time [s]1.3

Fig. 12. (Color online) Phase shift of the correction method with the multiple-reﬂection noise inside lumen. (a) Magniﬁed M-mode image of harmoniccomponent with the posterior wall boundary tracking results overlaid. (b) Phase shift of harmonic component at the intima–lumen boundary. (c) Phase shift ofharmonic component at the adventitia–media boundary. (d) Magniﬁed M-mode image of fundamental component with the posterior wall boundary tracking
results overlaid. (e) Phase shift of fundamental component at the intima–lumen boundary. (f) Phase shift of fundamental component at the adventitia–media
boundary. (g) Magniﬁed M-mode image of corrected harmonic component with the posterior wall boundary tracking results overlaid. (h) Phase shift ofcorrected harmonic component at the intima–lumen boundary. (i) Phase shift of corrected harmonic component at the adventitia–media boundary.

reﬂection noise on the posterior wall in the proposed method
shown in Fig. 13(d). Furthermore, these results are almost
the same as those of the fundamental method with themultiple-reﬂection noise inside the lumen as shown in
Fig. 9(d). Only the results of the fundamental method withthe multiple-reﬂection noise on the posterior wall show asmaller change in thickness and a larger elasticity, as shownin Fig. 10(d), which corresponds to a large error.

anterior wall

4 mm

lumen

4.

posterior wall(a) M-mode

3π/2
radian 0-3π/2(b) phase shift at intima-lumen boundary

3π/2
radian 0
-3π/2
10
0
μm
-70

(c) phase shift at adventitia-media boundary(d) change in thickness

0

0.65
time [s]1.3

Fig. 13. (Color online) Arterial-wall-mimicking phantom results of the PI
method with the multiple-reﬂection noise on the posterior wall. (a) Magniﬁed
M-mode image with the posterior wall boundary tracking results overlaid.
(b) Corrected phase shift at the intima–lumen boundary. (c) Corrected phaseshift at the adventitia–media boundary. (d) Change in thickness of theposterior wall.

adventitia–media boundary. Aliasing noise was shown in
Fig. 14(b) and the apparent tracking error of the intima–
lumen boundary was shown in Fig. 14(a). It is shown thataliasing noise was corrected in Fig. 14(h) and tracking of theintima–lumen boundary was obtained successfully in
Fig. 14(g).
The change in the thickness and elasticity were almost thesame in the case of the multiple-reﬂection noise inside thelumen shown in Fig. 11(d) and in the case of the multiple-

Discussion

The conventional phased-tracking method utilizes thefundamental method. Although this method leads to precise
elasticity measurement of the arterial wall if there is lessnoise on the posterior wall, it is not suﬃcient for elasticity
measurements in a clinical setting since they contains various
types of noises such as multiple-reﬂection noise. Only a few
studies have been carried out on the inﬂuence of noise on theelasticity measurement. In the present study, we investigated
the inﬂuence of the multiple-reﬂection noise on the accuracyof elasticity measurement.
To suppress multiple-reﬂection noise, the PI method wasintroduced. The suppression of multiple-reﬂection noise isdiscussed on the basis of the results of the experiment using
the phantom mimicking the arterial wall, in which multiplereﬂection noise in the lumen is as follows. Figures 15(a),15(b), and 15(c) shows B-mode images obtained by thefundamental method (a) in which the transmitting center
frequency was set at 11.4 MHz and the center detection
frequency was set at 11 MHz, by the PI method (b) in which
the transmitting center frequency was set at 5.7 MHz and thecenter detection frequency was set at 5 MHz, and by the PI
method (c) in which the transmitting center frequency was set
at 5.7 MHz and the center detection frequency was set at
11 MHz, respectively. Figure 16 shows the received RF
echoes and detected envelopes along the red vertical lines inFig. 15. The power of the detected envelope under transmission and detection frequency conditions is shown in
Fig. 17. The powers of the multiple-reﬂection noise at A22 inFig. 17 of methods (a), (b), and (c) were −39.3, −31.0, and07LF08-7© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF08 (2018)

4 mm

(a)

Y. Miyachi et al.

anterior wall

(d)

(g)

(e)

(h)

(f)

(i)

lumen

posterior wall

3π/2 (b)radian 0-3π/2
3π/2 (c)radian 0-3π/20time [s]1.3 0time [s]1.3 0time [s]1.3

Fig. 14. (Color online) Phase shift correction method with the multiple-reﬂection noise on the posterior wall. (a) Magniﬁed M-mode image of harmoniccomponent with the posterior wall boundary tracking results overlaid. (b) Phase shift of harmonic component at the intima–lumen boundary. (c) Phase shift ofharmonic component at the adventitia–media boundary. (d) Magniﬁed M-mode image of fundamental component with the posterior wall boundary tracking
results overlaid. (e) Phase shift of fundamental component at the intima–lumen boundary. (f) Phase shift of fundamental component at the adventitia–media
boundary. (g) Magniﬁed M-mode image of corrected harmonic component with the posterior wall boundary tracking results overlaid. (h) Phase shift ofcorrected harmonic component at the intima–lumen boundary. (i) Phase shift of corrected harmonic component at the adventitia–media boundary.

5 mm

5 mm

5 mm

anterior wall

anterior wall

anterior wall

lumen

lumen

lumen

posterior wall

posterior wall

posterior wall

(a)

(b)

(c)

Fig. 15. (Color online) B-mode image of the arterial-wall-mimicking phantom in which multiple-reﬂection noise in the lumen. (a) Fundamental method.
(b) PI method constructed from fundamental component. (c) PI method constructed from harmonic component.

−45.5 dB, respectively. It was shown that the multiplereﬂection noise was highly suppressed in the PI method usinga harmonic component. Possible reasons for the noise
suppression mechanism are as follows. The generation of
the harmonics component is in proportion to the square of thefundamental intensity based on nonlinear characteristics. The
multiple-reﬂection noise arises from reﬂection from theanterior wall and reﬂection from the transducer surface. Since
the depth of the anterior wall was small and defocused andthe depth of the posterior wall was near a focused pointof 1.5 cm, the generation of the harmonic component of theanterior wall was much less than that of the posterior wall.
This mechanism could lead to the suppression of themultiple-reﬂection noise.
In the proposed method, the phase shift of harmonic
quadrature demodulated signal θharm is corrected on theassumption that the phase shift of the harmonic quadrature
demodulated signal θharm is roughly equal to 2θfund. We
investigated whether the assumption is valid even at a setting
where the multiple-reﬂection noise is on the posterior wall.
Figure 18 shows the experimental results when the harmoniccomponent was not aliased. Figure 18(a) shows the phaseshift of the harmonic component and that of the doubled
fundamental component. The diﬀerence was small at eachtime and the maximum diﬀerence was 0.18 rad, which ismuch smaller than π=2, and the condition using Eq. (5) was
satisﬁed. This may be a reason why the signal from theposterior wall is much stronger than that from the multiplereﬂection noise. Although the phase diﬀerences were
suﬃciently small, the changes in position and thickness
may be aﬀected because they were obtained from the integralof the phase shift over one heartbeat. Figure 18(b) shows the07LF08-8© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF08 (2018)

Y. Miyachi et al.

power

0

detectedenvelop

0.5

-30
-60

0
RF echo-90(a) Fundamental method.

-1.0
1.0

-120
0

0.5

-30

0

-60

power [dB]

-0.5

-90

-0.5

(b) PI method constructed fromfundamental component.

-1.0
1.0

-120
0

0.5

-30

0

-60
-90

-0.5
-1.0

power [dB]

1.0

Multi
Multi
Multi
reflection reflection reflection Posterior Posteriornoise
Anoise A11
12 noise A22 wall P1 wall P2Anterior Anteriorwall A1 wall A2

power [dB]normalized amplitude

normalized amplitude

normalized amplitude

Transducer
surface S0(c) PI method constructed fromharmonic component.

-120
25

12.5
distance [mm]0Fig. 16. RF echo and detected envelope. (a) Fundamental method. (b) PI method constructed from fundamental component. (c) PI method constructed fromharmonic component.

power [dB]0

Transducer
surface S0

Multi
Multi
Multi
reflection reflection reflection PosteriorPosterior
noise A11 noise A12 noise A22 wall P1 wall P2Anterior Anteriorwall A1 wall A2

PI method
constructed fromfundamental component-30

Fundamental
method-60
PI method
constructed fromharmonic component

-90
-120

0

12.5
distance [mm]25Fig. 17. Powers of the detected envelopes.

changes in position evaluated from the harmonic component
and evaluated from the fundamental component. Figure 18(c)shows the diﬀerence between the changes in position andthe maximum diﬀerence was 12.9 µm. Although this 12.9 µm
diﬀerence was relatively smaller than the change in position,such as several hundred micrometers, it was not negligible incomparison with the change in thickness, such as several tensof micrometers. This reduction in the change in position
could lead to the reduction in the change in thickness andincrease in elasticity.
It was shown that the accuracy in the elasticity measurement was decreased in the fundamental method when themultiple-reﬂection noise was overlaid only on the posteriorwall. By introducing the PI method, the correction of thephase shift of the harmonic component using the fundamental
component prevented the tracking error of the arterial wallfrom aliasing owing to the reduced frame rate originatingfrom the PI method. The accuracy in the elasticity measurement did not decrease for the PI method when the multiple-πharmonic component

radian 0
doubled fundamental component

-π
-100
0
μm

evaluated fromfundamental component

-300

(a)
(b)

evaluated from harmonic component

0

(c)

μm
-15
0

0.65
time [s]1.3

Fig. 18. (a) Phase shifts, (b) changes in position, and (c) diﬀerence
between the changes in position at intima–lumen boundary with the multiplereﬂection noise on the posterior wall.

07LF08-9© 2018 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 57, 07LF08 (2018)

Y. Miyachi et al.

reﬂection noise was only on the posterior wall. It is shownthat it is important and eﬀective to introduce a method toprevent the multiple-reﬂection noise on the posterior wall inthe elasticity measurement of the arterial wall.
5.

Conclusions

We have proposed a modiﬁed phased-tracking method using
the PI method, in which aliasing of the phase shift of theharmonic component was corrected using that of thefundamental component. The PI method was applied toin vivo examination of carotid arteries and the detection
frequencies were selected to increase the signal-to-noise
ratios of the IMC of the posterior wall from the multiplereﬂection noise inside the lumen. The improvement of themeasurement of the arterial wall elasticity by the proposed
method was validated using a phantom mimicking the arterial
wall made of a silicone rubber tube pulsated by a stepping
motor pump. The elasticity diﬀerence of the multiplereﬂection noise on the posterior wall from that outside theposterior wall became much smaller when using the proposed
method than when using the conventional method. It was
shown that the proposed method is much more robust against
multiple-reﬂection noise than the conventional method. The
proposed method has potential use for measuring theelasticity of the arterial wall more accurately in the clinicalsetting than the conventional method.

1) H. Tanaka, M. Nishino, M. Ishida, R. Fukunaga, and K. J. Sueyoshi, Stroke
23, 946 (1992).
2) R. T. Lee, A. J. Grodzinsky, E. H. Frank, R. D. Kamm, and F. J. Schoen,
Circulation 83, 1764 (1991).
3) H. M. Loree, A. J. Grodzinsky, S. Y. Park, L. J. Gibson, and R. T. Lee,
J. Biomech. 27, 195 (1994).
4) P. C. G. Simons, A. Algra, M. L. Bots, D. E. Grobbee, and Y.
van der Graaf, Circulation 100, 951 (1999).
5) S. Kageyama, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 52, 07HF04(2013).
6) C. Arihara, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 45, 4727 (2006).
7) T. Kaneko, H. Hasegawa, and H. Kanaii, Jpn. J. Appl. Phys. 46, 4881
(2007).
8) K. Kitamura, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 51, 07GF08(2012).
9) Y. Nagai, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 53, 07KF19(2014).
10) J. Blacher, R. Asmar, S. Djane, G. M. London, and M. E. Safar,
Hypertension 33, 1111 (1999).
11) Y. Miyachi, H. Hasegawa, and H. Kanaii, Jpn. J. Appl. Phys. 54, 07HF18(2015).
12) P. Hallock, Arch. Int. Med. 54, 770 (1934).
13) M. Saito, Y. Yamamoto, Y. Shibayama, M. Matsukawa, Y. Watanabe, M.
Furuya, and T. Asada, Jpn. J. Appl. Phys. 50, 07HF10 (2011).
14) H. Hasegawa, M. Sato, and T. Irie, Jpn. J. Appl. Phys. 55, 07KF01 (2016).
15) H. Kanai, M. Sato, Y. Koiwa, and N. Chubachi, IEEE Trans. Ultrason.
Ferroelectr. Freq. Control 43, 791 (1996).
16) H. Kanai, H. Hasegawa, N. Chubachi, Y. Koiwa, and M. Tanaka, IEEE
Trans. Ultrason. Ferroelectr. Freq. Control 44, 752 (1997).
17) H. Hasegawa, H. Kanai, N. Hoshimiya, N. Chubachi, and Y. Koiwa, Jpn. J.
Appl. Phys. 37, 3101 (1998).
18) H. Hasegawa, H. Kanai, N. Hoshimiya, and Y. Koiwa, Jpn. J. Appl. Phys.
39, 3257 (2000).
19) H. Hasegawa, H. Kanai, and Y. Koiwa, Jpn. J. Appl. Phys. 41, 3563 (2002).
20) H. Hasegawa, H. Kanai, N. Chubachi, and Y. Koiwa, Electron. Lett. 33, 340(1997).
21) M. Cinthio, H. Hasegawa, and H. Kanai, IEEE Int. Ultrasonics Symp. Proc.,
2007, p. 997.
22) H. Hasegawa and H. Kanai, Jpn. J. Appl. Phys. 43, 3197 (2004).
23) J. Inagaki, H. Hasegawa, H. Kanai, M. Ichiki, and F. Tezuka, Jpn. J. Appl.
Phys. 44, 4593 (2005).
24) J. Tang, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 44, 4588 (2005).
25) K. Ikeshita, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 47, 4165
(2008).
26) K. Ikeshita, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 48, 07GJ10(2009).
27) K. Ikeshita, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 50, 07HF08(2011).
28) K. Ikeshita, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 51, 07GF14(2012).
29) M. Sato, H. Hasegawa, and H. Kanai, Jpn. J. Appl. Phys. 53, 07KF03(2014).
30) S. Miyashita, J. Murotsuki, J. Muromoto, K. Ozawa, N. Yaegashi, H.
Hasegawa, and H. Kanai, Ultrasound Med. Biol. 41, 1311 (2015).
31) Y. Sakai, H. Taki, and H. Kanai, Jpn. J. Appl. Phys. 55, 07KF11 (2016).
32) G. F. Pinton, G. E. Trahey, and J. J. Dahl, IEEE Trans. Ultrason.
Ferroelectr. Freq. Control 58, 1272 (2011).
33) T. Yamamura, M. Tanabe, K. Okubo, and N. Tagawa, Jpn. J. Appl. Phys.
51, 07GF01 (2012).
34) F. Tranquart, N. Grenier, V. Eder, and L. Pourcelot, Ultrasound Med. Biol.
25, 889 (1999).
35) Q. Ma, Y. Ma, X. Gong, and D. Zhang, Ultrasound Med. Biol. 31, 889(2005).
36) D. H. Simpson, C. T. Chin, and P. N. Burns, IEEE Trans. Ultrason.
Ferroelectr. Freq. Control 46, 372 (1999).
37) C. C. Shen, Y. H. Chou, and P. C. Li, J. Med. Ultrasound 13, 3 (2005).
38) J. R. Doherty, J. J. Dahl, and G. E. Trahey, IEEE Trans. Ultrason.
Ferroelectr. Freq. Control 60, 2347 (2013).

07LF08-10© 2018 The Japan Society of Applied Physics