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REGULAR PAPER

Ultrasonic measurement of carotid luminal surface
roughness with removal of axial displacement
caused by blood pulsation
To cite this article: Ryota Yamane et al 2023 Jpn. J. Appl. Phys. 62 SJ1042

View the article online for updates and enhancements.

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REGULAR PAPER

Japanese Journal of Applied Physics 62, SJ1042 (2023)
https://doi.org/10.35848/1347-4065/acc07a

Ultrasonic measurement of carotid luminal surface roughness with removal of
axial displacement caused by blood pulsation
Ryota Yamane1, Shohei Mori2*, Mototaka Arakawa1,2, Jens E. Wilhjelm3, and Hiroshi Kanai1,2
1Graduate School of Biomedical Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai, Miyagi 980-8579, Japan3
Department of Health Technology, Technical University of Denmark, Kgs. Lyngby, Denmark2*E-mail: mori@tohoku.ac.jp

Received November 15, 2022; revised February 3, 2023; accepted March 1, 2023; published online April 3, 2023
For early diagnosis of atherosclerosis, we have developed a method to measure the initial minute surface roughness utilizing the natural
longitudinal displacement of the intima-media-complex (IMC) on the carotid artery caused by pulsation. However, the IMC displaces not only in thelongitudinal direction but also in the axial direction due to the pulsation. In the present paper, we proposed a novel method to remove the pulsation
component by spatially convolving a high-pass filter with the measured depths of IMC in the longitudinal direction. The proposed method wasvalidated by a phantom experiment, and the surface roughness with ten saw teeth was correctly measured. Next, the surface roughness of the
carotid artery wall was measured for two healthy volunteers. The proposed method reduced the variation of measured surface roughness among
beams compared to the previous method. © 2023 The Japan Society of Applied Physics

1. Introduction

Cardiovascular diseases such as strokes and myocardial
infarctions are the leading causes of death worldwide.1)
These diseases are primarily caused by atherosclerosis.2)
Thus, diagnosis of atherosclerosis in the early stage would
be very beneﬁcial.
Several techniques for this end have been applied. Pulse
wave velocity (PWV), an indicator of arterial wall stiffness,has been used to diagnose atherosclerosis.3–5) An intimamedia complex (IMC) thickness (IMT) of the carotid artery
wall, measured by ultrasound, has also been used for the
diagnosis of atherosclerosis6) because the hypertrophy of thearterial wall is associated with future atherosclerosis.7)
In experiments on the blood vessels of rabbits exposed tohigh blood pressure for seven days, it was considered that theluminal surface on the arterial wall became rough at
approximately 10 micrometers.8) The appearance of surface
roughness is considered the ﬁrst step in arterial hypertrophycaused by ﬂow and shear stress,8–10) and its noninvasive
evaluation contributes to the early detection of atherosclerosis. Thus, methods to ultrasonically measure surface
roughness have been studied.11–22) It has been reported that
this roughness is caused by an increase in endothelial cells
and damage to the internal elastic lamina.8) Since there is no
signiﬁcant difference in cell size between humans andrabbits,23,24) the height of the surface roughness in human
may be the same order with that of rabbits.
An ultrasound B-mode image is normally constructedusing a constant assumed sound speed; however, there areregions of non-uniform sound-speed between the probe andthe anterior wall of the carotid artery. If the thickness of theregion of non-uniform sound-speed is 8 mm and the assumed
sound speed is 1540 m s−1, then a difference of 1% in thesound speed causes a measured depth error of approximately
80 μm. Since the measured depth error varies with the beam
position due to inhomogeneities in sound speed, it is difﬁcult
to measure the minute surface roughness only from theconventional B-mode image.
In previous studies, we proposed a method to measure theminute surface roughness using a single ultrasound beam byutilizing the naturally occurring longitudinal displacement of
IMC caused by pulsation. The method can measure thesurface roughness without being affected by the region of
non-uniform sound-speed by combining the naturally occurring longitudinal displacement caused by pulsation and theaxial displacement caused by the difference in the surface
roughness in the longitudinal direction, described in detail inthe methods section. However, the IMC displaces not only inthe longitudinal direction but also in the axial direction by thepulsation, and the measured axial displacement includes not
only the surface roughness component but also the axial
displacement of the IMC due to pulsation (pulsation component). Therefore, the pulsation component should be removed. Previously, this pulsation component was removed
by assuming that it is the same in all longitudinal
positions.19–21) However, the pulsation component slightly
differs by the longitudinal position25–28), and its effect on theestimate of the surface roughness is not negligible. The
inﬂuence on inclination angle change between IMC and theprobe surface by pulsation during the surface roughness
measurement is discussed in result section. This study aims todiagnose atherosclerosis at a very early stage where theplaque has not yet formed; therefore, it is assumed that there
is no sound-speed difference in the longitudinal direction of
the arterial wall itself.
Thus, in the present study, we propose a novel method to
remove the axial displacement due to pulsation by introducing a spatial high-pass ﬁlter (HPF) along the longitudinal
direction. The proposed method is validated by the phantom
experiment.29) Finally, the luminal surface roughness of the
carotid artery wall for two healthy young volunteers wasmeasured as well.
2. Methods
2.1. Surface roughness estimation using natural
longitudinal movement of carotid arterial wall

Consider the measurement situation in Fig. 1(a). The global
coordinate system is deﬁned by (x, z) with the origin (0, 0) at
the interface between the transducer composed of an array of
piezoelectric elements and skin, and at the center lateralposition of beam 0. The transducer creates M beams

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enveloped RF signal. As shown by the purple arrow in
Fig. 1(a), zˆ (xm ; 0) is divided into the following threecomponents as shown by the blue arrows:(a)zˆ (xm ; 0) = D 0 + DDm - r (x = xm) ,(1 )where ΔDm is the height shift caused by the region of nonuniform sound-speed between the probe surface and anteriorwall. The negative sign for r(ξ = xm) is due to the differenceof the direction of z in the global coordinate system and thatof h in the coordinate system set on the luminal surface of
IMC. Here, the surface roughness r(ξ = 0) at ξ = 0 is deﬁned
as 0 as shown in Fig. 1(a); thereforezˆ (0; 0) = D 0 + DD 0.

(b)

(2 )

From frame (n−1) to frame n, the surface proﬁle r(ξ)
displaces by the 2D vector (Dx p (n ), Dd p (n ; x )), where thedisplacement is naturally caused by the pulsation of the wall,that is, the movements in the longitudinal and axial directions. The total longitudinal displacement xp(n) and the total
axial displacement d p (n; x ) of the wall from the initial frame
0 to frame n are given by the following accumulationsnx p (n) = å Dx p (k ) ,

(3 )

k= 0
n

d p (n ; x ) = å Dd p (k ; x ).

(4 )

k= 0

Fig. 1. (Color online) Schematic of the surface roughness measurement (a)at initial frame and (b) at frame n.

[0; M − 1] and N image frames [0; N − 1]. The lateralposition of the center of the beam m is deﬁned by xm.
The interface between blood and intima of the posteriorwall is described by the surface proﬁle r(ξ) (black dottedline), which we would like to estimate, in the coordinate
system (ξ, h) set on the luminal surface of the IMC. At frame
0, the origin of the ξ axis is located at x = 0 in the global
coordinate system, i.e. the lateral position of the center ofbeam 0. The depth from the probe surface to the surface
proﬁle r(ξ = 0) at beam 0 at frame 0 is deﬁned by a baselineof the surface proﬁle, D0. At this time, the position of thesurface proﬁle at beam 0 at frame 0 in the global coordinate
system (x, z) is (x = 0, z = D0) as shown in Fig. 1(a).
Since the surface proﬁle r(ξ) moves in the global coordinate system (x, z) by pulsation, a single scan line can measurea part of the posterior wall surface that moves across thebeam. Since the region of non-uniform sound-speed does not
move and the single beam passes through the same region
during the measurement, surface roughness measured by thesingle beam is not affected by the region of non-uniform
sound-speed, as clariﬁed in our previous methods.19–22)
At the initial frame 0, the depth of IMC, zˆ (xm ; 0) at xm[purple arrow in Fig. 1(a)], is determined by thresholding the

As with previous studies,19–22) the longitudinal displacement xp(n) due to pulsation is assumed to be the same in themeasurement region (its width was 9.15 mm in this study)
and is estimated using the block-matching method30,31) byapplying the reconstructive interpolation32) to the correlation
values between the envelope of RF signals of consecutive
frames.
Let zˆ (xm ; n ) denotes the measured depth of the surface
proﬁle by beam m at frame n. This is the red arrow in
Fig. 1(b) and is given bynzˆ (xm ; n) = zˆ (xm ; 0) + å D
d (k ; x m ) ,

(5 )

k= 0

 (n ; xm ) is the axial displacement from frames n−1
where Ddto n measured by applying the phased-tracking method to theRF signals.33–35) As shown by the orange arrows in Fig. 1(b),the total axial displacement dˆ (n ; xm ) of the wall from frames
0 to n is divided asndˆ (n; x m ) = å D
d ( k ; x m ).
k=0

= d p (n; x = x m - x p (n))- {r (x = x m - x p (n)) - r (x = x m ) + DDm }+ DDm= d p (n; x = x m - x p (n))- {r (x = x m - x p (n)) - r (x = x m )}.

(6 )The ﬁrst term d p (n ; x = xm - x p (n)) of the last equationshows the axial displacement of the wall at the positionx = xm - x p (n ) caused by the pulsation from frames 0 to n.
The second term shows the difference in roughness betweenr (x = xm - x p (n )) measured by beam m at frame n and

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r (x = xm ) measured by beam m at frame 0, whose differenceis caused by the longitudinal displacement x p (n ) of IMC.
By substituting Eqs. (1) and (6) into Eq. (5), the measured
depth of IMC at frame n, zˆ (xm ; n ), is divided into four
components aszˆ (xm ; n) = D 0 - r (x = xm - x p (n))+ d p (n ; x = xm - x p (n)) + DDm.

(7 )Thus, it is found that the measured depth of the surface of
IMC, zˆ (xm ; n ), is composed of the base depth D0 from theprobe to the surface of IMC at the initial frame at x = 0, thetrue surface proﬁle r (x = xm - x p (n )) at the longitudinal
position of x = xm - x p (n ), the axial displacement of thewall, d p (n ; x = xm - x p (n )), caused by pulsation, and theheight shift DDm due to the regions of non-uniform soundspeed. It is necessary to remove the three components
d p (n; x ), DDm , and D0 from zˆ (xm ; n ) to estimate the surface
roughness r (x ), as will be described below.
2.2. Removal of total axial displacement dp (n; x )caused by pulsation
The axial displacement caused by pulsation, d p (n; x ), isremoved as follows. Since the typical PWVs in humans areapproximately 5–10 m s−1 36) and the dominant frequency ofthe pulse wave is less than 20 Hz, the wavelength at 20 Hz isapproximately 25–50 cm. Therefore, the spatial frequency
along the longitudinal direction of the axial displacement
caused by pulsation can be assumed to be much lower thanthat of surface roughness. Thus, the axial displacement
caused by pulsation, d p (n; x ), is removed by applying the
spatial convolution of the HPF g (x ) to the measured depth of
the IMC, zˆ (xm ; n ), obtained by Eq. (5), along the longitudinal direction. The resultant zˆHPF (xm ; n ) is given byzˆHPF (xm ; n)Fig. 2. (Color online) HPF for removing axial displacements caused bypulsation. By applying HPF, components of pulsation d p (n; x ) and baselineof surface proﬁle, D0 , are removed, while components of the surface
roughness r HPF (x ) and height shift due to region non-uniform sound-speed,
DD HPF , pass through the HPF.

the HPF. The resultant components, denoted by rHPF, m (x ) andDD HPF, m , are given by Eqs. (9) and (10), respectively.

W= å g (dx · i) · zˆ (xm - i; n)i =-W

r HPF, m (x = xm - x p (n))

W= å g (dx · i)
i =-W

W

= å g (dx · i) · r (x = xm - i - x p (n)) ,{D0 - r (x = xm - i - x p (n)) + d p (n ; x = xm - i - x p (n)) + DDm - i}

i =-W

W

= å g (dx · i){D0 + d p (n ; x = xm - i - x p (n))}
i =-WW+ å g (dx · i){DDm - i - r (x = xm - i - x p (n))} ,

(9 )

(8 )

DD HPF, m =i =-Wwhere 2W + 1 denotes the window width of the HPF and dx
is the beam spacing.
Figure 2 shows the measured depth zˆ (xm ; n ) and the four
components included in the measured depth zˆ (xm ; n ) together with the results of the convolutions with the HPF. As
shown in Fig. 2, the depth D0 from the probe to the base of
the surface proﬁle is a constant, and the axial displacement
caused by pulsation, d p (n; x ), is assumed to include spatiallylower frequency components. Thus, these components can beremoved by the HPF g (x ). That is, the ﬁrst term in the lastequation of Eq. (8) becomes zero by properly setting thecutoff frequency. The second term, which is composed of thesurface roughness r (x ) and the height shift DDm due to theregions of non-uniform sound-speed, remains after applyingWå g (dx · i) DDm - i.

(10)

i =-W

Thus, by applying the HPF, the remaining displacementzˆHPF (xm ; n ) has the following two components aszˆHPF (xm ; n) » - r HPF, m (x = xm - x p (n)) + DD HPF, m. (11)2.3. Removal of height shift DDHPF, m caused byregion of non-uniform sound-speed

Though the axial displacement of IMC due to pulsation,d p (n; x ), is removed by a HPF, the resultant zˆHPF (xm ; n ) stillcontains the height-shift component DD HPF, m caused by theregion of non-uniform sound-speed. The height-shift component DD HPF, m is removed by the following procedure.
The resultant measured depth zˆHPF (xm ; n ), deﬁned in the
global coordinate system (x, z ), is converted into the surface

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proﬁle hˆm (x ) measured with the beam m in the coordinate
system (x , h) deﬁned on the artery wall as follows:hˆm (x = xm - x p (n)) = zˆHPF (xm ; n)
» - r HPF, m (x = xm - x p (n)) + DD HPF, m.

(12)

Figure 3 shows the surface proﬁle hˆm - 1 (x ) and hˆm (x )measured with the beams m - 1 and m in the coordinate
system (x , h ). As shown in Eq. (12) and in Fig. 3, hˆm (x )contains the height-shift component, DD HPF, m , in addition to
the roughness rHPF, m (x ).
The height shift DDm obtained before applying the HPF isdetermined by the sound speed distribution in the region of
non-uniform sound-speed. Therefore, both DDm of Eq. (1)and DD HPF, m of Eq. (10) do not change by frame n. Thus,
for the surface proﬁle measured by beam m,hˆm (x = xm - x p (n )), the component DD HPF, m is constantregardless of x = xm - x p (n ), as shown in Fig. 3.
The longitudinal measurement ranges of hˆm - 1 (x ) andˆh m (x ) partly overlap because the typical longitudinal displacement of the IMC during one heartbeat is approximately
1 mm19) and much larger than the beam spacing dx (150 m inthis study). In the overlapped measurement range, only theheight-shift components DD HPF, m - 1 and DD HPF, m are different between beams, as shown in Fig. 3.

em =
=

1
∣ x m - 1 - (x m - x p (N - 1)) ∣1∣ x m - 1 - (x m - x p (N - 1)) ∣

xm- 1

å

Therefore, the height shift DD HPF, m can be estimated byminimizing the root mean squared difference (RMSD)
between hˆm - 1 (x ) and hˆm (x ) in the overlapped measurement
range by the following procedure.
The spatial sampling position x of the surface proﬁlehˆm (x = xm - x p (n )) measured by beam m is determined by
the initial beam position xm and the longitudinal displacement
caused by pulsation, x p (n ). Because the longitudinal instantaneous displacement of IMC, x p (n ) - x p (n - 1), differs byframe n, the spatial sampling position x = xm - x p (n ) is notevenly spaced. In addition, the initial sampling positionx = xm of the surface proﬁle hˆm (x = xm ) at frame 0 differs
by beam m. Thus, the RMSD between hˆm (x ) and hˆm - 1 (x )cannot be evaluated at the same longitudinal position.
Therefore, the surface proﬁle hˆm (x = xm - x p (n )) is interpolated to obtain the surface proﬁle hˆ in, m (x ) at the constantsampling intervals of 1 μm for the evaluation of the RMSD atthe same longitudinal position, as shown in Fig. 3.
For the roughness measurement, only the relative differ
D HPF, m - D
D HPF, m - 1 should be estimated, whereence D
DD HPF,0 at initial beam 0 is set to 0. Thereafter, the heightshift DD HPF, m is estimated by minimizing the following
RMSD em for the spatially interpolated surface proﬁlehˆ in, m (x ) in the overlapped measurement range as
0,
m=0
⎧

D
D HPF, m = arg min em , m > 0,
⎨ DD HPF, m
⎩

(13)


{hˆ in, m (x ) - hˆ in, m - 1(x ) + D
D HPF, m - 1}2x = x m - x p (N - 1)
xm- 1

å




{D
D HPF, m - D
D HPF, m - 1 + D
D HPF, m - 1}2 ,(14)x = x m - x p (N - 1)

where N is the total number of frames used for the surface
roughness measurement.
Thus, the surface roughness rˆHPF, m (x ) measured by beamm is obtained by removing the estimated height shift HPF, m from hˆ in, m (x ) as
DD

(a)

(b)

Fig. 3. (Color online) Measured surface proﬁle hˆm (x ) after removing theaxial displacement d p (n; x ) due to pulsation using the HPF, which still HPF, m , caused by the non-uniform
contains the height shift component, DD
sound speed in addition to the surface roughness r HPF (x ).

Fig. 4. (Color online) (a) Interpolated surface proﬁle hˆ in, m (x ) and (b) HPF, m
Surface roughness rˆHPF, m (x ) obtained by removing the height shift DD
from the interpolated surface proﬁle hˆ in, m (x ).

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R. Yamane et al.

rˆHPF, m (x ) = hˆ in, m (x ) - D
D HPF, m.

(15)

Figures 4(a) and 4(b) show the interpolated surface proﬁleshˆ in, m (x ) and the surface roughnesses rˆHPF, m (x ) measured bybeam m. Finally, the surface roughness rˆHPF (x ) is obtained byaveraging rˆHPF, m (x ) for multiple beams that measure thesurface roughness for the same longitudinal position x, as
shown in Fig. 4(b) as follows:rˆHPF (x ) = m

1max (x ) - m min (x ) + 1

m max (x )årˆHPF, m (x ) ,(16)⎡ arg {xm - x p (n) < x}⎤ ,
⎥
⎦

(17)

⎡ arg {xm > x}⎤.
⎥
⎦

(18)

m = m min (x )wherem max (x ) =

max

⎢ m
0£m£M-1 ⎣m min (x ) =

min

⎢ m
0£m£M-1 ⎣2.4. Basic experiments using silicone phantom

Figure 5 shows the conﬁguration of the basic experiment. We
used a silicone phantom that had ten saw teeth with 10 μm
height and 500 μm interval on the surface, that is, the spatial
frequency of the surface roughness is 2 mm−1. This phantom
had the same saw teeth surface in the y direction as in Fig. 5.
The reference surface proﬁle of the phantom was measured
using a laser displacement meter (LT9010; Keyence, Osaka,
Japan). For simulating the blood vessel pulsation, thephantom was translated 1.0 mm at a speed of 1.4 mm s−1 inthe longitudinal direction concurrently with a translation of
0.5 mm at a speed of 0.7 mm s−1 in the axial direction by anautomated stage (ALD-906-E1P and ALZ-906-E1P; Chuo
Precision Industrial, Tokyo, Japan). An ultrasound diagnostic
apparatus (ProSound F75; Hitachi Aloka, Tokyo, Japan) witha linear array probe (UST-5415; Hitachi Aloka, Tokyo,
Japan) was used for the ultrasonic measurements. The
transmitted ultrasound frequency and sampling frequencyof the received echoes were 7.5 and 40 MHz, respectively.
The longitudinal cross-section of the phantom was measured
with M = 61 ultrasonic beams. The beam spacing δx was 150

Fig. 5. (Color online) Schematic of the basic experiment using a silicone
phantom.

μm, and the frame rate was 187 Hz. As discussed in the
results section, a rectangular window with a width of
0.48 mm (−6 dB cutoff spatial frequency: 1.22 mm−1) wasused for the HPF.
2.5. In vivo experiments
Ultrasonic RF data were obtained for two heartbeats from theright common carotid arteries of two young and healthy
volunteers, A (22 year old male, non-smoker) and B (23 year
old male, non-smoker). The in vivo measurement in thisstudy was approved by the Ethics Committee of the Graduate
School of Engineering at Tohoku University (No. 19A-5).
Both participants agreed to participate in the study. The
ultrasound measurement conditions were the same as for thephantom experiment. The cutoff spatial frequency of the HPF
is determined in the results section.
Based on the degree of coincidence among beams forroughness rˆHPF, m (x ) measured by each beam m using
Eq. (15), the proposed method was compared with theprevious method19) which assumes that the axial displacement caused by pulsation is the same in all longitudinal
positions. The root mean squared deviation (RMSD) of theroughness rˆHPF, m (x ) measured for each beam m [Eq. (15)]from the ﬁnally estimated roughness rˆHPF (x ) [Eq. (16)] was
obtained, and the averaged value SDr for all beams wasevaluated by the previous and proposed methods for eachheartbeat and subject:SDr =M- 1- W1´ å
M - 2Wm=W

x - max x (n )mp1åmax x p (n) + 1 x = xm

∣ rˆHPF, m (x ) - rˆHPF (x )∣2 .

(19)
3. Results
3.1. Basic experiments using silicone phantom

Figure 6 shows the spatial frequency spectrum of the axial (n ; xm ) measured by the phased-tracking
displacement Dd
33–35)
method(blue line), which was averaged for all frames,
the phantom surface roughness measured by the laser (redline), and the HPF (black line). The surface roughness

Fig. 6. (Color online) Spatial frequency spectra of the phantom surface
proﬁle measured by laser displacement meter (red line, right vertical axis)
and ultrasound using the proposed method (blue line, right vertical axis), andspatial frequency characteristic of the HPF g (x ) (black line, left vertical axis)
whose window width is 2W + 1 = 0.48 mm (−6 dB cutoff frequency:
1.22 mm-1).

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0.71 μm (average ± standard deviation for ten saw teeth), andthe interval between adjacent bottoms was 481 ± 35 μm.
From the results, the proposed method measured the surface
proﬁle with ten saw teeth, although the average height was
2.37 μm lower and the measured top edges of teeth wererounded compared with those measured by the laser.
3.2. In vivo experiments
Figures 8(a) and 8(b) show B-mode images of the rightcommon carotid artery for the two healthy young volunteers,
A and B, respectively. The red line on the IMC represents the
tracking depth zˆ (xm ; 0) of the IMC determined by thethresholding.
Figure 9 shows the measured axial displacement dˆ (n ; xm )for each beam m; these differ by up to 100 μm in the same
frame [different colors in Fig. 9]. If IMC is inclined by theangle q , the measured surface roughness, r (x ) relates to thetrue surface roughness rt (x ) as shown in Eq. (20)

(a)

(b)

(c)

r (x ) = rt (x ) cos q.
Fig. 7. Results of the phantom experiment. (a) B-mode image of thephantom surface, (b) estimated surface roughness rˆHPF (x ) by the proposed
method, and (c) surface roughness measured by the laser displacement meter.

measured by laser had approximately 7 μm height components at a spatial frequency of 2 mm−1. The measured axial (n ; xm ) components were also observed
displacement Dd−1around 2 mm spatial frequency. Based on these spectra, acutoff frequency for the HPF was set to 1.22 mm−1 such thatthe surface roughness components with the spatial frequency
band of 2 mm−1 pass through, as shown by the black line in
Fig. 6.
Figures 7(a)–7(c) show the B-mode image of the phantom
surface, the estimated surface roughness rˆHPF(x ) by the
proposed method, and the surface roughness measured
from the laser displacement meter, respectively. The longitudinal position of the measurement result from the laser
displacement meter was adjusted to be that the top of the saw
teeth aligned with that measured by the proposed method.
The difference of the height between the top and bottom of
the saw teeth estimated by the proposed method was 4.91 ±

(a)

(b)

Fig. 8. (Color online) B-mode images of the right common carotid artery.
(a) Subject A and (b) subject B. Red lines show the initially measured depthszˆ (xm ; 0).

(20)

In this study, the measurement range was 9.15 mm, and thevalue of cosq is 0.9999. Therefore, the measured surface
roughness and the true surface roughness are almost identical.
Figure 10 shows the spatial frequency spectra of the measured (n ; xm ), averaged for all frames. It hasaxial displacements Ddbeen reported that this roughness is caused by an increase inendothelial cells and damage to the internal elastic lamina.8)
Since there is no signiﬁcant difference in cell size between
humans and rabbits,23,24) the height of the surface roughness inhumans may be of the same order of ten micrometers as inrabbits. Thus, we set the −6 dB cutoff frequency of the HPF to
0.12 mm−1 (2 W + 1 = 1.5 mm) as shown by the black line in
Fig. 10, to pass through the higher frequency components thathave approximately a height of 10 μm.
Figure 11(a) shows examples of the measured depths of
IMC at different frames n, zˆ (xm ; n = 84) (red line) andzˆ (xm ; n = 112) (blue line). Although the lateral positions ofzˆ (xm ; n ) were adjusted to the longitudinal positions x on the
IMC by x = xm - x p (n ), the measured depths do notcorrespond to each other even at the same longitudinal
position x. The axial displacement caused the differenced p (n; x ) due to pulsation and/or height shift DDm due to theregions of non-uniform sound-speed.
Figure 11(b) shows the surface proﬁle hˆm (x ) for each beam
m obtained by removing the axial displacement d p (n; x ) due
to pulsation and the base depth D0 from zˆ (xm ; n ) using the
HPF by Eq. (8).
In Fig. 11(b), similar surface proﬁles were measured foreach beam by applying the HPF [different colors in
Fig. 11(b)], although there are offset-differences among
surface proﬁles measured by different beams, that are caused
 HPF, m due to the region of non-uniformby the height shift DD
sound-speed, as shown in Fig. 3.
Figure 11(c) shows the surface roughness rˆHPF, m (x ) ob HPF, m from hˆ in, m (x ) bytained by removing the height shift DD
 HPF, m caused by
Eq. (15). By removing the height shift DD
the regions of non-uniform sound-speed, similar surface
roughnesses were measured by each beam [different colors in
Fig. 11(c)].
Figures 12(a) and 12(b) show the ﬁnally estimated surface
roughnesses rˆHPF (x ) by Eq. (16) for subjects A and B,

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Jpn. J. Appl. Phys. 62, SJ1042 (2023)

R. Yamane et al.

Fig. 9. (Color online) Measured axial displacement dˆ (n; xm ) for each beam m.

(a)

(b)

Fig. 10. (Color online) Averaged spectra of measured axial displacementsdˆ (n; xm ) for all frames (blue line: subject A, red line: subject B, right verticalaxis), and spatial frequency characteristics of HPF (black line, left verticalaxis) whose window width is 2W + 1 = 1.5 mm (−6 dB cutoff frequency:
0.12 mm-1).

Table I. Root mean squared deviation SDr of estimated roughness values.
Speciﬁcally, the deviation between the estimated roughness rˆHPF, m (x )obtained from each individual beam and the average roughness rˆHPF (x )overall beams are shown below.

Subject A (ﬁrst beat)Subject A (second beat)Subject B (ﬁrst beat)Subject B (second beat)Previous method

Proposed method

0.63 μm0.51 μm0.45 μm0.53 μm0.44 μm0.27 μm
0.36 μm
0.29 μm

respectively. The results for two consecutive heartbeats areoverlaid. The surface roughness of approximately 10 μm
height was estimated for both subjects, and the results foreach heartbeat matched well.
Table I shows the averaged RMSD for all beams, SDr ,obtained by Eq. (19). The proposed method reduced the
RMSD, that is, reduced the deviation of the measured surface
roughness rˆHPF, m (x ) among beams, compared with the previous method19) which assumes that the axial displacement
caused by pulsation was the same in all longitudinal positions.
4. Discussion

In this paper, we propose a method to measure the minutesurface roughness on the IMC of the carotid artery by
removing the axial displacement caused by pulsation. The(C)

Fig. 11. (Color online) (a) Measured depths of the IMC at different framesn, zˆ (xm ; 84) (red line) and zˆ (xm ; 112) (blue line). (b) Surface proﬁle hˆ in, m (x )measured for each beam m. (c) Surface roughnesses rˆHPF, m (x ) obtained by
 HPF, m from hˆ in, m (x ).
removing the height shift DD

(a)

(b)

Fig. 12. (Color online) Finally estimated surface roughnesses rˆHPF (x ) by
the proposed method. (a) Subject A, (b) subject B (purple: 1st heartbeat,green: 2nd heartbeat).

proposed method was validated by phantom and in vivo
measurements.
The proposed method correctly measured the surface
proﬁle with ten saw teeth in the phantom experiment.

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Jpn. J. Appl. Phys. 62, SJ1042 (2023)

R. Yamane et al.

However, the height of the saw teeth measured by the
proposed method was approximately 2.37 μm lower, andthe measured top edges of the saw teeth were rounded
compared with those measured by the laser. These results
may be caused by the ultrasonic beam’s lower spatial
resolution in the lateral direction than the laser. Thus, there
is a limitation caused by the ultrasound spatial resolution forthe measurable spatial frequency of the surface roughness, aswith the other ultrasonic measurement techniques.
In in vivo measurements, the cutoff frequency of the HPF
to remove the axial displacement caused by pulsation wasdetermined from the spatial frequency spectrum of themeasured axial displacement based on the assumption thatthe height of surface roughness is approximately 10 μm
because the actual spatial frequency characteristics of thesurface roughness were unknown in in vivo. However, thecutoff frequency should be determined considering the actual
spatial frequency characteristics of the surface roughness in
our future study, which requires animal experiments, whose
real surface roughness is measurable.
As shown in Table I, it was conﬁrmed that the proposed
method was superior to the previous method19) whichassumed that the axial displacement caused by pulsation
was the same in all longitudinal positions.
5. Conclusion

In this paper, we propose an ultrasonic measurement
method for the luminal surface roughness on the carotid
artery wall by removing the axial displacement due topulsation using the spatial HPF. The proposed methodmeasured the surface roughness in tens of micrometers inthe basic experiment using the phantom. In in vivo
measurements involving two healthy subjects, the variation in measured surface roughness among beams was
reduced by the proposed method, and reproducible results
were obtained for consecutive heartbeats.
Acknowledgments

The part of this work was supported in part by JSPS
KAKENHI 19KK0100 and 21H03835.

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