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REGULAR PAPER

Ultrasonic measurement of thickness of carotid
arterial wall using its natural longitudinal
displacement
To cite this article: Yoshifumi Nagai et al 2023 Jpn. J. Appl. Phys. 62 SJ1039

View the article online for updates and enhancements.

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Grigorios M Karageorgos, Iason Z
Apostolakis, Pierre Nauleau et al.

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Japanese Journal of Applied Physics 62, SJ1039 (2023)
https://doi.org/10.35848/1347-4065/acba26

Ultrasonic measurement of thickness of carotid arterial wall using its natural
longitudinal displacement
Yoshifumi Nagai1, Shohei Mori2*, Mototaka Arakawa1,2, and Hiroshi Kanai1,2
1Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan2*

E-mail: mori@tohoku.ac.jp

Received November 15, 2022; revised January 30, 2023; accepted February 7, 2023; published online March 21, 2023
The thickness of the carotid arterial wall obtained from B-mode imaging using ultrasonic diagnostic devices is widely used for the diagnosis ofatherosclerosis. However, the measurement interval in the lateral direction of the B-mode image depended on the beam interval (>100 μm).
Therefore, the B-mode image is discrete in the lateral direction and cannot reflect changes in local and minute thicknesses. A method formeasuring the roughness of the luminal surface of the wall was proposed using the displacement of the carotid arterial wall in the lateral direction
during one heartbeat. In this method, the lateral measurement interval is much shorter than the beam interval, enabling a smooth measurement of
the luminal surface. By simultaneously applying the method to the lumen-intima and medial-adventitia boundaries of the wall, we propose a novel
method to measure the local and minute thicknesses of the carotid arterial wall. © 2023 The Japan Society of Applied Physics

1. Introduction

Circulatory diseases, such as stroke and myocardial infarction, are cited as major causes of death worldwide,1) and theincidence of such diseases is increasing in Japan.2)
Atherosclerosis is considered the main cause of circulatory
diseases; therefore, the early diagnosis and prevention ofatherosclerosis are important. Atherosclerosis is known toprogress gradually with age;3) therefore, long-term observation is required. There are several methods for diagnosing
atherosclerosis, including computed tomography (CT), magnetic resonance imaging (MRI), arteriography, angioscopy,
intravascular ultrasound, and the measurement of arterial
walls using ultrasound. Ultrasound is effective because it isnon-invasive for the diagnosis of lifestyle diseases.4–6) Many
studies have assessed ultrasound application to variousorgans such as the blood vessels,7) heart,8,9) liver,10)
blood,11) skin,12) and bones.13) Many research have been
conducted on high-intensity focused ultrasound therapy14)
and its safety.15)
Many ultrasonic studies involving measuring the properties of the intima-media complex (IMC) have been conducted to evaluate the degree and state of progression ofatherosclerosis.16–21) At present, the IMC thickness (IMT)of the carotid arterial wall measured using B-mode imaging
is regarded as an indicator for diagnosis with a high levelof evidence,22–24) demonstrating its importance in the
diagnosis of atherosclerosis.25–28) Regarding IMT measurement on a B-mode image,29,30) an echo from the
carotid artery in the longitudinal cross-sectional view was
acquired using a linear probe and the boundary was
detected for each beam position, as illustrated in Fig. 1.
Therefore, the measurement interval in the lateral (longitudinal) direction depended on the beam interval (greaterthan or equal to 100 μm in conventional ultrasonic diagnostic devices). Because the beam interval is generally
larger than the sampling interval (approximately 20 μm) in
the axial (beam or depth) direction at a sampling frequencyof 40 MHz, the results in the lateral direction are more
discrete than those in the axial direction, and a change inthickness smaller than the beam interval cannot be measured with high accuracy.

As a simple method for measuring luminal surface roughness of the posterior wall of the artery using ultrasound, along-axis image of the blood vessel was visualized, as shownin Fig. 1. The depth proﬁle was obtained by mechanicallymoving the ultrasound probe along the artery or scanning theultrasonic beam.20) The sound wave speed in soft tissues
between the skin directly under the probe and the anteriorwall of the artery is heterogeneous by approximately 10%.
Consequently, measurement errors up to several hundred
microns could occur when measuring the distance from theprobe to the lumen surface. Thus, measuring surface roughness of several microns on the luminal surface is not possible.
It has been reported that the carotid arterial wall could be
displaced not only in the axial direction but also in the lateral
direction toward the heart during the cardiac cycle.31–33)
Using the natural lateral displacement of the carotid arterial
wall, our group proposed a method34,35) to measure theminute roughness of the wall that occurs in the early stages ofatherosclerosis as follows. The blood vessels are pulled in the
direction of the heart by cardiac contraction as shown in
Fig. 1. However, at this time, soft tissues between the skinand the anterior wall of the blood vessel remain in place: only
the blood vessels slide. Using this motion, we aimed to
improve the accuracy of surface roughness measurement
while keeping each beam of the ultrasonic probe ﬁxed.
Figure 2 shows the schematic diagram of the measurement
method used. When the blood vessel moves by Δx in thelateral direction during time ΔT, measurement position at theluminal surface also moves by Δx, where the lateraldisplacement Δx can be estimated by block matching of
ultrasonic radiofrequency (RF) signals.36,37)
Simultaneously, a change of Δd in the distance to theblood vessel wall occurring during time (ΔT) for one
ultrasonic beam can also be measured with high accuracy
using the phased tracking method.38,39) Combining temporalchanges in these quantities (Δx, Δd), surface roughness canbe measured, as shown in Fig. 2. Using this method, theheterogeneity of the sound wave velocity in soft tissues
between the skin and anterior wall of the artery is notaffected. Therefore, the luminal surface roughness of theposterior wall of the artery can be measured from the skinsurface on a range of several microns. This method was

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Fig. 1. (Color online) Using the ultrasonic probe for measurement, the related structure of the carotid artery is shown. During one heartbeat, contraction of
the heart pulls the carotid artery toward the heart: only the arterial wall slides toward the heart side. The present study employs the phenomena to measure theminute luminal surface and thickness of the intima-media complex (IMC), which is essential for the diagnosis of early stage atherosclerosis.

Fig. 2. (Color online) A schematic diagram of the measurement method proposed by our group to measure the luminal surface roughness using ultrasound.
The blood vessels are pulled in the direction of the heart by cardiac contraction. However, at this time soft tissues between the skin and the anterior wall of theblood vessel remain in place: only the blood vessel slides. Using this motion, we improve the accuracy of surface roughness measurement while keeping eachbeam of the ultrasonic probe ﬁxed.

experimentally validated by measuring the surface proﬁle ofa silicone tissue-mimicking phantom with a roughness of 13–
33 μm height.40–42)
However, in human individuals, the longitudinal displacement of the arterial wall caused by pulling toward the heart as
the heart contracts is small (less than 1 mm), which limits thelength of the region that can be measured with a single beam.
Kitamura et al. expanded the measurement region by
combining multiple surface roughness values measured using
multiple beams as shown at the bottom of Fig. 2.41) In thismethod, echoes from the arterial wall can be acquired atintervals shorter than the beam interval using the natural
displacement of the carotid arterial wall in the lateral
direction. Thus, the boundary can be measured smoothly inthe lateral direction compared to the method based on Bmode imaging.
In a recent study,42) we simultaneously applied this method
to the lumen-intima boundary (LIB) and media-adventitialboundary (MAB), and the thickness was estimated from theRF signal of all frames of a cardiac cycle. In conventional Bmode images, the measurement interval of the thickness in
the lateral direction depends on the ultrasonic beam interval

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(approximately 100 μm), resulting in discrete and discontinuous results. In contrast, in the proposed method, the carotid
arterial wall is effectively scanned using the natural lateraldisplacement of the carotid artery by ﬁxing the probe
position. As the lateral displacements between the frames
are much smaller than the beam interval, echoes can beacquired from the wall at short intervals in the lateral
direction. Therefore, the estimated thickness becomessmoother in the lateral direction. In the present study, after
veriﬁcation using a tissue-mimicking phantom, the proposed
method was applied to in vivo measurements of the carotid
artery. Moreover, the thickness estimated using the proposed
method was compared with that estimated using conventional
B-mode imaging.

which there is a minute displacement of several tens of
micrometers. Figure 4(c) shows the global axial displacement dg(n) of the wall during the cardiac cycle, whichcorresponds to the expansion of the arterial wall due to theincrease in the inner pressure.
As shown on the right-hand side of Fig. 3, considering
the coordinates at the wall, the lateral position of the mth(m = 1, 2, …, M = 62) beam is displaced by Δxm (n) fromthe nth frame to the (n + 1)th frame. The depth of the wallat lateral position x m (n) is denoted by z(xm (n); m). The
lateral instantaneous displacement Δxm (n) of the wallfrom the nth frame to the (n + 1)th frame is given as
follows:

2. Principles

At the position of the mth beam, the axial instantaneous
displacement Δd(n; m) from the nth frame to the (n + 1)th
frame is denoted as follows:

2.1. Measurement of surface roughness using natural
displacement of arterial wall

Figure 3 illustrates the displacement of the carotid arterial
wall (posterior wall) during measurement. As shown on theleft-hand side of the ﬁgure, the coordinates of the probe are
the z′ and x′ axes in the axial and lateral directions,
respectively. At a ﬁxed position of the mth beam on thecoordinate system x′ on the probe, the wall was longitudinally displaced toward the heart during the systole of the
cardiac cycle.
As shown in the ﬁgure on the right-hand side, thecoordinates of the arterial wall are z and x in the axial andlateral directions, respectively. In coordinate system x on thewall, the lateral position of the mth beam moves from xm(n) at
the nth frame to xm(n +1) at (n +1)th frame along the arterial
wall. In the proposed method, echoes are acquired over time,
and the probe position is ﬁxed using this natural displacement.
Figure 4 shows the actual in vivo data of a healthy
subject. Figure 4(a) shows the lateral (longitudinal) displacement xm(n) of the carotid arterial wall toward theheart during systole. Figure 4(b) depicts the lateral
instantaneous displacement Δxm(n) between frames, fromDxm (n) = xm (n + 1) - xm (n).

Dd (n ; m) = z (xm (n + 1) ; m) - z (xm (n) ; m).

(1 )

(2 )


The estimated D
d (n ; m ) of Δd(n; m) was measured
using the phased tracking method. 33) The axial displacement d(n; m) from the 0th frame to the nth frame is givenby the accumulation of displacements {Δd(n; m)} as
follows:n-1

dˆ (n ; m) = å Dd (n¢ ; m).

(3 )n ¢= 0Let us divide dˆ (n ; m ) into the global axial displacement
owing to the expansion of the wall, dg(n; m), and the axial
displacement due to the surface roughness of the wall, ds(n;m), as follows:dˆ (n ; m) = dg (n ; m) + ds (n ; m).

(4 )To obtain ds(n; m), it was necessary to estimate dg(n; m).
Because the measurement region in the lateral direction is as
small as approximately 9 mm, compared with the wavelength(approximately 102 mm) of the pulse wave, we can assume

Fig. 3. (Color online) Displacement Δxm(n) of the carotid arterial wall for mth beam during the measurement. Left-hand side: along the coordinate system (x′, y′, z′) on the ultrasonic probe. Right-hand side: along the coordinate system (x, y, z) on the arterial wall.

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Y. Nagai et al.

(a)

(b)

(c)

Fig. 4. (Color online) Upper: Electrocardiogram (ECG). (a) Lateral displacement xm(n) of the carotid arterial wall (LIB) during a cardiac cycle. (b)Instantaneous lateral displacement Δxm(n) between frames of the carotid arterial wall (LIB) during a cardiac cycle. (c) Global axial displacement dg(n) of the
carotid arterial wall (LIB) during a cardiac cycle.

that dg(n; m) is constant regardless of the beam position, andcan be expressed by dg(n), which is obtained by theaccumulation of the spatial average of the axial instantaneous
displacements Dd (n ; m ) as

where
M-1

1


D
d g (n ) =d (n ; m ) ,
åD
M m=0

(6 )

n-1


dg (n) = å D
dg (n¢) ,n ¢= 0(5 )where M is the number of ultrasonic beams used formeasurement. The estimated dg (n ) value in Eq. (5) isremoved from dˆ (n ; m ) in Eq. (4) to obtain the surface
roughness ds (n ; m ) of the wall as follows:

Fig. 5. (Color online) Surface roughness zˆ (x; m ) along the coordinate system (x, y, z) on the arterial wall measured by a single beam (mth beam).

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Fig. 6. (Color online) Overlapped measurement region Rm between the surface roughnesses zˆ (x; m - 1) and zˆ (x; m ) measured by (m−1)th beam and mth
beam.

Fig. 7. (Color online) RF echo acquired from the carotid artery and its
envelope signal around the posterior wall, by which the LIB and the MAB
were determined.

ds (n ; m) = dˆ (n ; m) - dg (n).

(7 )To obtain ds (n ; m ) from Eq. (7), dˆ (n ; m ) of Eq. (4) and axial
instantaneous displacement Δd(n; m) of Eq. (2) is required.
To obtain z(xm(n); m) of Eq. (2), the lateral direction
displacement xm(n) at the nth frame is determined from theaccumulation of the instantaneous displacements {Δxm(n)}of Eq. (1) as follows:

Fig. 8. (Color online) B-mode image of the carotid artery and detectedboundaries of LIB and MAB based on the amplitude of echoes.

depth are denoted as xm(0) and zˆ (xm (0); m ), respectively. Using
the axial displacement d(n; m) and the lateral displacement xm(n)obtained from Eqs. (3) and (8), the surface roughness zˆ (x; m )for the mth beam at x along the wall can be determined using:zˆ (x ; m) º zˆ (x
m (n ) ; m )n-1


= zˆ ⎛⎜⎜⎛xm (0) + å D
xm (n¢) ⎟⎞ ; m⎞⎟n ¢= 0⎠ ⎠⎝⎝n-1

xm (n) = å Dxm (n¢) ,(8 )n ¢= 0n-1

where Δxm(n) can be estimated by block matching.36,37)
To estimate the surface roughness z(x; m) at the mth beam, therelationship between the instantaneous lateral displacement
D
xm (n ) and instantaneous axial displacement D^ds (n ; m ) for
each frame n was considered as a parameter, as shown in Fig. 5.
The lateral position of the mth beam at the 0th frame and its= zˆ (xm (0) ; m) + å D
ds (n¢ ; m).

(9 )n ¢= 0As shown in Eq. (9), the measurement interval in the lateraldirection is D
xm (n ) for zˆ (x; m ), which is much smaller thanthe beam interval δx = 0.15 mm of the conventional
ultrasonic probe, as shown in Fig. 4(b). Therefore, theSJ1039-5© 2023 The Japan Society of Applied Physics

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Fig. 9. (Color online) (a) B-mode image of the tissue-mimicking phantom. (b) Axial displacements dˆ (n; m ) for the two boundaries of the two-layer phantom.
(c) Lateral displacements xm (n ) for the two boundaries of the phantom.

(a)

(b)

(c)

Fig. 10. (Color online) (a) Estimated surface roughnesses z(x) for the two boundaries of the two-layer tissue-mimicking phantom estimated by the proposed (x ) obtained by the proposed method. (c) For the same phantom, the reproducibility in the three measurements of the thickness th (x )
method. (b) Thickness th
was conﬁrmed. The deviation among the three thickness values measured at each lateral position was obtained and their maximum was 0.8 μm.

measurement results obtained using the proposed method
were smoother in the lateral direction.
2.2. Combining surface roughness measured bymultiple ultrasound beams
The principle for measuring the surface roughness zˆ (x; m )using a single beam is described above. Multiple ultrasonicbeams were used in the proposed measurement, and thesurface roughness was obtained for a wider lateral region, as
described below.
Because we assume that the longitudinal displacementof the carotid arterial wall is larger than the beam interval
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(a)

(b)

^ (x )[ detected from the B-mode
Fig. 11. (Color online) (a) Detected boundary zˆ (xm (0); m ) from the conventional B-mode image. (b) Thickness thBmodeimage.

(a)(b)^ (x ) obtained by the B-mode image for sampling intervals δz in the axial direction of 3.2–12.9 μm. (b) Thickness
Fig. 12. (Color online) (a) Thickness thBmode^ (x ) for varying δz of 0.4–1.6 μm.
thBmodeoverlap for region Rm along the lateral x-axis, as shown in
Fig. 6. As the depths of zˆ (x; m - 1) and zˆ (x; m ) do notalways coincide because the depth zˆ (xm - 1 (0); m - 1) of
the arterial surface along the (m−1)th beam set at the 0thframe does not match the depth zˆ (xm (0); m ) along m thbeam set at the 0th frame, the measured roughnesszˆ (x; m - 1) and zˆ (x; m ) should be adjusted in the axial
direction for the overlapped region Rm as follows:
By rearranging the principle described in the previous
study,41) let us minimize the difference of zˆ (x; m ) fromzˆ (x; m - 1) in the axial direction for the overlapped region
Rm to adjust the depth αm of zˆ (x; m ). To decide theadjustment depth αm, the following root mean squared error
εm(αm) is minimized in the region Rm with respect to αm as
follows:em (am )=1
am - 1)∣2 ,å ∣(zˆ (x; m) + am ) - (zˆ (x; m - 1) + 
Nm - 1, m x Î Rm

for m = 1, 2, ¼, M

(10)am - 1 for (m−1)th beam has already been
where a0  0, 
determined, and Nm−1,m denotes the number of the same
lateral positions of zˆ (x; m ) and zˆ (x; m - 1) included in Rm.
After the depth adjustment, the surface roughness zˆ (x; m )of Eq. (9) can be corrected using zˆ (x; m )¢ º zˆ (x; m ) + am.
Because multiple results {zˆ (x; m )¢} at position of x aremeasured by multiple beams, the ﬁnal surface roughness
estimate zˆ (x ) along the wall surface is obtained by averaging
the corrected results {zˆ (x; m )¢} at x as follows:zˆ (x ) = E Mm, x [zˆ (x ; m)¢]= E Mm, x [zˆ (x ; m) + a^m ] ,(11)where E Mm, x [] represents the averaging operation of thecorrected surface roughnesses {zˆ (x; m )¢} measured for theultrasonic beams at the lateral position x.
2.3. Application of surface roughness measurement
to thickness measurement of IMT
From the B-mode image, it is known that there is alongitudinal displacement xm(n) of the carotid arterial wall
not only at the depth of the LIB, but also at the depth of theMAB.33) However, as in previous studies,40,42) although the

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(a)

(b)

Fig. 13. (Color online) Upper: Electrocardiogram (ECG). (a) Axial displacements {dˆ (n; m )} for LIB and MAB of the carotid arterial wall. (b) Lateraldisplacements {xm(n)} for LIB and MAB.

method described in Sects. 2.1 and 2.2 was applied tomeasure the surface roughness zLIB(x) of the LIB of the
carotid arterial wall, the surface roughness zLIB(x) of MAB
was not measured. In the methods described in Sects. 2.1 and
2.2, the lateral displacement xm(n) of the object must belarger than the ultrasonic beam interval δx. MAB is also
applicable because this condition is satisﬁed.
To estimate the thickness th(x) of the posterior wall of the
carotid artery, we simultaneously applied the method described above to measure the surface roughness zLIB(x) of
LIB and that zMAB(x) of MAB.
For the axial displacement, it is necessary to detect theinitial depth zLIB(xm(0); m) for the LIB and depth zMAB(xm(0);m) for the MAB from the amplitude of the echoes. Figure 7
shows the RF signal (blue) and its envelope signal (dashedline), acquired near the posterior wall of the carotid artery.
The amplitude of the echo increased near the LIB and a local
maximum was observed between the media and adventitia. In
the present study, the initial depth zLIB(xm(0); m) of the LIB
was determined by detecting the ﬁrst local maximum byscanning the envelope signal from the lumen to a deeper
region. Since the amplitude of the echoes increased again in
deeper MAB regions, the initial depth zMAB(xm(0); m) of the
MAB could be determined by detecting this increase in theenvelope signal as follows. When increase in the envelope
amplitude is determined by the depth at which the differential
waveform reaches the maximum, a deeper portion with alarge gradient of the envelope amplitude would be adopted.
However, the point, where the amplitude ﬁrst becomes thelowest at a point deeper than that determined LIB, issusceptible to noise. Therefore, the MAB was determined
as a depth deeper than that determined LIB (maximum pointof the envelope curve), where the amplitude decreased once,

then increased again, and reached the same amplitude as thedetermined LIB, as shown in Figs. 7 and 8.
Furthermore, the magnitude and speed of the lateraldisplacements xm(n) of the LIB and MAB differed.31)
Therefore, it is necessary to independently measure theselateral displacements. In this study, the lateral displacementsof the LIB and MAB are estimated by block matching at thedepths of the LIB and MAB for each beam position using awindow of the same size (lateral direction: 16
points = 2.4 mm, axial direction: 20 points = 372.5 μm).
From the measurements of the surface roughness of LIB
 (x ) of the carotidzˆLIB (x ) and MAB zˆMAB (x ), the IMT tharterial wall is given by (x ) = zˆMAB (x ) - zˆLIB (x ).
th

(12)

2.4. Experimental method

Regarding the basic experiment described in Sect. 3, a twolayer tissue-mimicking phantom comprising silicone rubber
and a silicone rubber sheet was used to simulate the structureof the carotid arterial wall. A thin sheet (0.5 mm) was used tosimulate the IMC, and the surface was roughened using
sandpaper (roughness #60) to simulate surface properties at
an early stage of atherosclerosis.
Considering the method of making the two-layer phantom,
a silicone rubber sheet (IMC simulated phantom) with athickness of 0.5 mm was spread in a container. Thereafter,
liquid silicone (base part) mixed with a hardening agent waspoured over the 0.5-mm thick rubber sheet and hardened.
Thus, the two layers did not peel in water during theexperiment. The surface of the phantom at the base wassticky, which was used to adhere to the metal plate ﬁxed tothe motorized stage. Furthermore, the not-measured parts ofthe phantom and the metal plate were ﬁxed with a rubber

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Fig. 14. (Color online) (a) B-mode images of carotid arteries with the detected boundaries of LIB and MAB based on the amplitude of echoes. (b) Estimated^ (x )
 (x ) and thBmodesurface roughness z(x) by the proposed method. (c) Detected boundary zˆ (xm (0); m ) from the conventional B-mode image. (d) Thicknesses th
obtained by the proposed method and from the B-mode image, respectively.

band. The sound velocity of the silicone rubber sheet was
assumed to be 1030 m s−1. The overall size of the phantom
was 65 mm long, 45 mm wide, and 10 mm thick. The waterin the tank was degassed by allowing it to stand for one day.
The displacements of the carotid arterial wall in the lateraland axial directions during one cardiac cycle were simulatedusing a two-axis automatic stage. The two-layer phantom wasdisplaced ±1.0 mm in the lateral direction and ±0.5 mm in theaxial direction in a water tank (lateral velocity: 1.4 mm s−1
and axial velocity: 0.7 mm s−1). These lateral and axial
motions were provided by motorized stages (ALD-906-E1P
and ALZ-906-E1P, Chuo-Precision-Industrial Corp. Ltd.,
Japan). Although xm(n) on the LIB side is larger than thaton the MAB side for in vivo data, as described above, bothboundaries were displaced by the same amount in thephantom experiment.
The RF data during this period were acquired with anultrasonic diagnostic device (Prosound F75, Aloka, Japan)
using a linear array probe at 10 MHz (UST-5415, Hitachi
Aloka, Japan). The number of beams M was set to 62, beaminterval δx was 150 μm, frame rate fr was 187 Hz, andsampling frequency fs was 40 MHz. For the in vivo measurements described in Sect. 4, the measurement conditions were
the same.
3. Phantom experiment3.1. Results of phantom experiment

Figure 9(a) presents a B-mode image of the two-layer tissuemimicking phantom. A two-layer structure simulating the
LIB and MAB was visually conﬁrmed. Figures 9(b) and 9(c)show the axial displacements dˆ (n ; m ) and lateral displacements xm (n ) at the depths of the LIB and MAB, respectively,
measured using the method described in Sect. 2.1.
The surface roughnesses zˆLIB (x ) and zˆMAB (x ) at bothboundaries were then estimated, as shown in Fig. 10(a).
 (x ) obtained from these results using Eq. (12)The thickness th

is presented in Fig. 10(b), which is approximately 0.5 mm,
which is almost the same as the set thickness of the silicone
sheet of the tissue-mimicking phantom.
To assess reproducibility of the measurement of the (x ) for the same phantom, the same lateral andthickness thaxial motions were applied three times by motorized stages,
and the results are shown in Fig. 10(c). The experiments in
Fig. 10(c) were on a different day from those in Figs. 10(a)and 10(b). The deviation among the three thickness values
measured at each lateral position was obtained and theirmaximum was 0.8 μm, which was sufﬁciently less than thesize (several micrometers) of the disabled cell around theluminal surface of the arterial wall.
3.2. Discussion regarding phantom experiment^ (x ) of the tissueFigure 11 shows the thickness thBmode
mimicking phantom detected from the conventional Bmode image. Figure 11(a) shows the boundary depths^ (xm (0); m ) of the LIB and MAB, which were deterzBmodemined using the same procedure based on the amplitude ofthe envelope signal, as described in Sect. 2.3 using Fig. 7.
^ (x ) obtained from
Figure 11(b) shows the thickness thBmodethe difference between the results z
Bmode (xm (0) ; m ) in
Fig. 11(a). By comparing the thickness estimate in
Fig. 10(b) obtained using the proposed method with thatobtained using the conventional B-mode image in Fig. 11(b),the estimate in Fig. 10(b) was smoother because its measurement interval in the lateral direction was shorter, as describedabove.
Meanwhile, for the axial direction shown in Fig. 11(b), thesampling interval in the axial direction of the acquired RF
signal was set to dz  13 mm when the sampling frequency fs
was 40 MHz. The spatial resolution of the RF signal envelope
was increased in the axial direction to consider the effect of
the sampling interval on the estimated thickness, as follows:
By interpolating the envelope signal using the reconstruction
interpolation method,43) the sampling interval δz was

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Y. Nagai et al.

equivalently reduced, and then the thickness th
Bmode (x ) was
updated, as shown in Fig. 12. Although thBmode (x ) becamesmoother when dz was interpolated up to 1/4 times [green in
Fig. 12(a)], the results did not improve when the samplinginterval δz was further reduced, as shown in Fig. 12(b).
Compared with the conventional B-mode images in
Figs. 11(b) and 12, better results were achieved, as shown in
Fig. 10(b), that is, close to the true value (500 μm) of the
thickness, using the method proposed in Sect. 2.3, for thefollowing reasons:From the conventional B-mode image, the thickness
estimates th
Bmode (x ) in Figs. 11(b) and 12 are independently
determined for each beam position based on the envelope
signal, and the continuity of the measurement results withadjacent beams was not considered. In contrast, in the
proposed method, the depth of zˆ (x; m ) estimated for eachbeam was adjusted by calculating em (am ) using Eq. (10). By
adjusting the axial direction, the continuity of the measurement results between the beams is maintained at theestimated roughness zˆ (x ).
In regard to the 0.5-mm thick rubber sheet used in thephantom experiment, it was difﬁcult to measure the minutechange in thickness with the laser displacement sensor. The
surface roughness on one side was measured using a laser
displacement sensor (LT9010; Keyence Corp. Ltd., Japan) at
different ﬁve positions, and the standard deviation sL was
3.3  0.7 mm (average  standard deviation at ﬁve different
positions). Thus, the standard deviation of the thickness canbe given by 2 sL = 4.7  0.9 mm. On the other hand, for (x )} obtained by theeach of the three estimated thickness {thproposed method in Fig. 10(c), the standard deviation along
the lateral direction was 4.3 mm. Thus, the estimate obtainedby the proposed method was close to the actual target value.
Because the ultrasonic beam has a spatial width of several
hundred micrometers in the lateral direction, the measurement accuracy in the lateral direction may be degraded. To
address this problem, our previous study42) attempted tosuppress the point spread function using a Wiener ﬁlter toincrease the spatial resolution of the measured surface
roughness zˆ (x ). However, the spatial frequency range inwhich the improvement was observed was limited to
0–5 mm−1, and further consideration is necessary.
The results of the phantom experiments conﬁrm that theresults obtained using the proposed method are closer to thetrue thickness than those obtained using the conventional
method. To further improve the accuracy of the thickness
measurement, a method that increases the spatial resolution,
which is restricted by the beam width, is required.
4. Results and discussion for in vivo measurement

Ultrasonic RF data were obtained from the carotid artery of ahealthy 33 year-old male. The measurement was approved by
the Ethics Committee of the Graduate School of Engineeringat Tohoku University (No. 19A-5). The participant agreed toparticipate in this study. The B-mode image is shown in
Fig. 8. Figures 13(a) and 13(b) show the axial displacements
xm (n ) of the LIB anddˆ (n ; m ) and lateral displacements 
MAB, respectively, during a cardiac cycle. From Fig. 13(b),it can be conﬁrmed that the lateral displacement 
xm (n ) of the
MAB is larger than the beam interval dx = 150 mm.

Figure 14(a) shows a B-mode image near the posteriorwall of the carotid artery. Figure 14(b) shows the surface
roughness of LIB zˆLIB (x ) and MAB zˆMAB (x ). For comparison, Fig. 14(c) shows the result zˆ (xm (0); m ) of the boundary
detection of the LIB and MAB from the conventional B (x ) andmode image. The arterial wall thicknesses ththBmode (x ) obtained from these results [Figs. 14(b) and14(c)] are shown in Fig. 14(d).
From the thickness estimates of the proposed method,
shown in Fig. 14(d), the thickness was smoother than thatobtained using the conventional method.
5. Conclusions

In this study, a method for estimating the thickness of the
carotid arterial wall was proposed. Using the longitudinal
displacement of the carotid arterial wall, the surface roughness of the LIB and MAB was simultaneously estimatedusing the phased tracking method and block matching.
Subsequently, the thickness of the carotid arterial wall was
estimated using estimated surface roughness values. Basedon the measurement results of the two-layer tissue-mimicking
phantom that simulated the structure of the IMC of the
carotid arterial wall, the thickness obtained by the proposed
method was conﬁrmed to be smoother in the lateral direction
and closer to the true thickness compared with the result
obtained from the conventional B-mode image. Moreover,the proposed method was applied to in vivo data obtained
from the carotid artery of a healthy subject. From the results,
we conﬁrmed that the local arterial wall thickness can bemeasured smoothly using the proposed method compared tothe conventional method.
Acknowledgments

This work was supported in part by JSPS KAKENHI
20H02156 and 21H03835.

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