Reprinted from

REGULAR PAPER

Accurate Estimation of Carotid Luminal Surface Roughness
Using Ultrasonic Radio-Frequency Echo
Kosuke Kitamura, Hideyuki Hasegawa, and Hiroshi Kanai

Jpn. J. Appl. Phys. 51 (2012) 07GF08# 2012 The Japan Society of Applied Physics

Person-to-person distribution (up to 10 persons) by the author only. Not permitted for publication for institutional repositories or on personal Web sites.

REGULAR PAPER

Japanese Journal of Applied Physics 51 (2012) 07GF08
DOI: 10.1143/JJAP.51.07GF08

Accurate Estimation of Carotid Luminal Surface Roughness
Using Ultrasonic Radio-Frequency Echo
Kosuke Kitamura1 , Hideyuki Hasegawa1;2 , and Hiroshi Kanai1;2 
12Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan

Received November 18, 2011; revised March 30, 2012; accepted April 12, 2012; published online July 20, 2012
It would be useful to measure the minute surface roughness of the carotid arterial wall to detect the early stage of atherosclerosis. In conventional
ultrasonography, the axial resolution of a B-mode image depends on the ultrasonic wavelength of 150 m at 10 MHz because a B-mode image isconstructed using the amplitude of the radio-frequency (RF) echo. Therefore, the surface roughness caused by atherosclerosis in an early stagecannot be measured using a conventional B-mode image obtained by ultrasonography because the roughness is 10–20 m. We have realized
accurate transcutaneous estimation of such a minute surface profile using the lateral motion of the carotid arterial wall, which is estimated by blockmatching of received ultrasonic signals. However, the width of the region where the surface profile is estimated depends on the magnitude of thelateral displacement of the carotid arterial wall (i.e., if the lateral displacement of the arterial wall is 1 mm, the surface profile is estimated in aregion of 1 mm in width). In this study, the width was increased by combining surface profiles estimated using several ultrasonic beams. In thepresent study, we first measured a fine wire, whose diameter was 13 m, using ultrasonic equipment to obtain an ultrasonic beam profile fordetermination of the optimal kernel size for block matching based on the correlation between RF echoes. Second, we estimated the lateraldisplacement and surface profile of a phantom, which had a saw tooth profile on its surface, and compared the surface profile measured byultrasound with that measured by a laser profilometer. Finally, we estimated the lateral displacement and surface roughness of the carotid arterial
wall of three healthy subjects (24-, 23-, and 23-year-old males) using the proposed method. # 2012 The Japan Society of Applied Physics

1. Introduction

Medical ultrasound is clinically used to make a diagnosis forvarious organs, and because it is noninvasive and relatively
stress free for patients, it can be repeatedly employed to
conﬁrm time-dependent changes. Ultrasound B-mode imaging is widely used for the morphological diagnosis of thearterial wall, particularly for measurement of the intima–
media thickness.1–3) In addition, methods for evaluating
the viscoelasticity of the arterial wall have recently beendeveloped4–9) because the mechanical properties of thearterial wall are related to atherosclerotic changes.
Diagnosis of atherosclerosis in an early stage is importantto prevent the occurrence of strokes and heart attacks. In
the early stage of atherosclerosis, the luminal surface of anarterial wall becomes rough as a result of endothelial
damage.10,11) It would be useful to measure such minutesurface roughness of the carotid arterial wall for early
diagnosis of atherosclerosis. For this purpose, sub-micron
resolution is required because endothelial cells are 10–20 m
thick.12) In conventional ultrasonography, the axial resolution of a B-mode image depends on the ultrasonicwavelength of 150 m at 10 MHz because a B-mode image
is constructed using the amplitude of the RF echo. Therefore, the surface roughness caused by atherosclerosis in an
early stage cannot be measured by conventional B-mode
imaging using ultrasonography.
Wilhjelm et al. and Kudo et al. evaluated micron-ordersurface roughness.13–15) They focused on the angle-dependent characteristics of echo energy or echo amplitude andfrequency characteristics.16) However, their methods cannot
measure the surface proﬁles of objects. Arihara et al.
measured the micron-order surface proﬁle of an object madeof silicone rubber using the phase shift of RF echoes during
the sweeping of an ultrasonic beam.17) However, a minutesurface proﬁle cannot be measured in vivo using this method
because the carotid arterial wall moves in the radialE-mail address: kanai@ecei.tohoku.ac.jp(= axial) direction but also in the longitudinal (= lateral)
direction.18) Thus, it is diﬃcult to distinguish the lateralmotion due to the probe sweeping and the arterial longitudinal motion.
Cinthio et al. suggested minute roughness measurementby combining phased-tracking and block matching.19–22)
They estimated the surface proﬁles of silicone phantoms,
which had ten saw tooth shapes on their surfaces, during
their lateral motion without sweeping an ultrasonic beam.
During a cardiac cycle, the carotid arterial wall moves not
only in the radial direction but also in the longitudinal
direction. This longitudinal movement induces the axial
displacement (change in height during longitudinal movement) of the surface at an ultrasonic beam when the surface
is rough. They could measure this axial displacement during
the lateral movement of the phantoms of 6 mm using thephased-tracking method,21–23) which can measure the axial
displacement with a sub-micron resolution and is used invarious applications, such as the measurement of hearts24–26)
and arteries.7,9) However, the longitudinal displacement of
the carotid artery is less than 1 mm, and this would limit thelength of the region of measurement. In this paper, we
propose a method to increase the measured region using
several ultrasonic beams.
2. Principles
2.1 Accurate estimation of surface roughness of arterial
wall

In this study, the axial (z-axis) displacement caused bysurface roughness is measured at an ultrasonic beam
position. During cardiac systole, the vascular diameter isdilated in the radial direction (z-axis) and the vascular wall isalso moved in the longitudinal direction (x-axis)18) owing to
the force caused by the arch of the aorta being pulled by thecontraction of the heart in cardiac systole.
Figure 1 illustrates displacements caused by a heart beat.
The lateral position of the m-th ultrasonic beam is denotedby xm (xm ¼ m  x, where x is the lateral spacing of thesampled points). Let us deﬁne the frame interval T . The

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K. Kitamura et al.

ultrasonic probe

xm

y

x
(m, n)

z(m, 0)

m−th ultrasonic beam
mediumd(m, n)d g (n)z m (m, n)= ds (m, n)anterior wallarteryposterior wall

zm 0 = 0

zm 0 = 0l (m, n)(m, n)(m, 0)

Fig. 1. Illustration of displacements between 0-th frame and n-th frame.

ð1Þ

Using the phase shift ðm; nÞ of RF signals between then-th frame and the (n þ 1)-th frame, which is caused byexpansion of the artery and surface roughness, the axial
displacement dðm; nÞ at the position xm of an ultrasonicbeam is estimated as follows:21,22)^ nÞ ¼
dðm;

c
^ nÞ;
ðm;
2!0

transverse position [mm]
0
5
0

5

10

15

lateral position [mm]
5
0

(b)
0

position of depth [mm]dðm; nÞ ¼ zðm; n þ 1Þ  zðm; nÞ:(a)position of depth [mm]axial (z-axis) displacement of the posterior wall surfacedðxm ; nÞ  dðm; nÞ between the n-th frame [t (s)] andthe (n þ 1)-th frame [(t þ T ) (s)] is obtained from thediﬀerence between the axial position zðxm ; nÞ  zðm; nÞ ofthe surface in the n-th frame and the axial positionzðxm ; n þ 1Þ  zðm; n þ 1Þ in the (n þ 1)-th frame as follows:

5

10

15

ð2Þ

where c is the sound speed in the medium (1540 m/s) and!0 ð¼ 2f0 Þ is the center angular frequency of ultrasound(center frequency f0 ¼ 10 MHz). The axial displacement^ nÞ between the 0-th frame and the n-th frame isdðm;calculated by accumulating instantaneous displacements^ nÞg estimated by the phased-tracking method21,22)fdðm;
as follows:
n
X
^ nÞ:
^ nÞ ¼
dðm;
ð3Þ
dðm;
n¼0

As shown in Fig. 2(a), which shows a B-mode image of the
carotid artery in the short-axis view, RF signals from theluminal surface of the carotid artery are obtained in a very
limited region of 0.8 mm in the transverse direction. Thus,
the position of the ultrasonic probe can be kept within
0:4 mm in the transverse direction by keeping the echoesfrom the luminal surface from being visualized. Also,
Fig. 2(b) is a B-mode image of a carotid artery in the longaxis view. If the lateral position of the ultrasonic probechanges by a few millimeters, the lateral displacement
caused by the lateral motion of the ultrasonic probe can be
estimated using block matching. However, the change in thelateral position of the ultrasonic probe may introduce achange in sound speed in the medium between the skin andthe artery. When the lateral velocity of the ultrasonic probe
is 0.5 mm/s, the change in the lateral position of the

0.8 mm20

Fig. 2. (Color online) B-mode image of carotid artery (24-year-old
healthy male). (a) Short axis view. Red lines show the region where RF
signals from the luminal surface of the carotid arterial wall could beobtained. (b) Long axis view.

ultrasonic probe between frames is 0.003 mm, when theframe rate is 160 Hz. The lateral displacement between
frames should be considered because the axial displacement
between frames is estimated in the phased-tracking method,
as shown in eq. (2). The transmitting region of ultrasoundshifts by about 0:003=3  100% ¼ 0:1% because theaperture size was 3 mm. The diﬀerence in sound speed is
5:8%  0:001 ¼ 0:0058% because the variation of soundspeed in vivo is about 5.8% (soft tissue: 1540 m/s–fat:1450 m/s27)). Therefore, the eﬀect of the change in soundspeed on the estimation of the distance of 15 mm from theskin surface to the artery is 0.87 m and it can be neglected
because it is much smaller than the surface roughness(10 m), which is desired to be measured.
^ nÞ isAs shown in Fig. 1, the estimated displacement dðm;composed of the global displacement of the arterial walldg ðnÞ due to the expansion of the artery and the displacementds ðm; nÞ caused by the surface proﬁle (roughness) as
follows:19)

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Jpn. J. Appl. Phys. 51 (2012) 07GF08^ nÞ ¼ dg ðnÞ þ ds ðm; nÞ:dðm;

K. Kitamura et al.

ð4Þ

In a region of a few millimeters in the x-direction, theinstantaneous axial displacements fdg ðm þ i; nÞg (i ¼0; 1; 2; . . . ; M  1) caused by global wall motion between
the n-th frame and the (n þ 1)-th frame at positions fxmþi g
are assumed to be the same because the wavelength ofthe pulse wave is a few meters and the pulse repetition
frequency is 13 kHz. Therefore, the instantaneous axial
displacement dg ðnÞ caused by global wall motion can be
estimated by averaging the axial instantaneous displacements fdðm; nÞg, as follows:nXd^g ðnÞ;ð5Þ
d^g ðnÞ ¼
n¼0
M
1
X

1
^ nÞ;
d^g ðnÞ ¼
dðm;
ð6Þ
M m¼0
where M is the number of ultrasonic beams, dðm; nÞ is theaxial displacement at the position xm of an ultrasonic beam,and d^g ðnÞ is the axial displacement caused by global wallmotion between the 0-th frame and the n-th frame.
Finally, the surface proﬁle zm ðx; zm0 Þ estimated at the m-th
ultrasonic beam is expressed as follows:19)^ nÞ; zm0 z^m ðx; zm0 Þ  z^m ½xm þ lðm;nX
d^s ðm; nÞ;¼ zm0 þ

ð7Þ
ð8Þ

n¼0

^ nÞ  d^g ðnÞ;d^s ðm; nÞ ¼ dðm;

ð9Þ

where zm0 is the initial height, which is determined as
described in x2.3.
Then, the arterial longitudinal displacement lðm; nÞ shouldbe estimated to obtain the surface proﬁle zm ðx; zm0 Þ as afunction of lateral position xm þ lðm; nÞ. Using the blockmatching,28,29) the estimated lateral displacement lðm; nÞ ofthe arterial wall at the m-th ultrasonic beam between the 0-th
frame and the n-th frame is given by19)^ nÞ ¼
lðm;

n
X

^ nÞ;
lðm;

ð10Þ

n¼0

^ nÞ is the estimated instantaneous lateral
where lðm;displacement of the arterial wall between frames. The
instantaneous lateral displacement lðm; nÞ is estimated as
described in x2.2. Using the estimated lateral displacement^ nÞ, the lateral position of a point on the arterial walllðm;
where the m-th ultrasonic beam crosses at the n-th frame is^ nÞ.
deﬁned as ðxm ; nÞ  ðm; nÞ ¼ ½xm þ lðm;2.2 Estimation of longitudinal displacement of arterial wall
based on block matching using correlation function

In the present study, the lateral displacement lðm; nÞ isestimated by block matching28,29) between RF echoes. To
apply block matching, the size of the correlation kernel,
which is deﬁned by the size of (2a þ 1) [lateral]  (2b þ 1)
[axial] (sampled points), was examined. An RF echo at
position ðx; zÞ in the n-th frame and the central position of
the correlation kernel are deﬁned as sn ðx; zÞ and ðxm ; zm0 Þ,
respectively. The initial lateral position xm is manuallyassigned in the ﬁrst frame and the initial axial position zm0 is
automatically assigned at a point shallower than the point at
the maximum value of the envelope of the RF signal by 
points (: constant value) and its position is tracked in the
successive frames by block matching. The normalized
correlation function Cn ½lðm; nÞ; dsp ðm; nÞ at the laterallag lðm; nÞ and axial lag dsp ðm; nÞ is calculated from RF
signals sn ðx; zÞ and snþ1 ðx; zÞ in the n-th frame and (n þ 1)-thframe as follows:dsp ðm; nÞlðm; nÞ;j þ
Sn ði; jÞSnþ1 i þxzi¼a j¼b
Cn ½lðm; nÞ; dsp ðm; nÞ ¼ vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃvﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ;
uX
uX


b
b
u a X
u a X
dsp ðm; nÞlðm; nÞ2t;jþSn2 ði; jÞt
Snþ1
iþ
x
z
i¼a j¼bi¼a j¼ba XbX

Sn ði; jÞ ¼ sn ðxm þ i  x; zm0 þ j  zÞ  sn ;where x and z are the lateral and axial spacings of sampled
RF echo, respectively, and sn is the spatial mean of RF
signals in a kernel in the n-th frame. The instantaneous
lateral and axial displacements lðm; nÞ and dsp ðm; nÞ of^ nÞ andthe arterial wall are determined from the lags lðm;^dsp ðm; nÞ, respectively, which maximize the normalized
correlation function Cn ½lðm; nÞ; dsp ðm; nÞ. In the estimation of the lateral displacement, the lateral spatial resolution
x depends on the ultrasonic beam interval (100 m). If
the frame rate is 160 Hz, the lateral displacement is 9 m
between frames when the average lateral moving speed of
the carotid arterial wall is 1.4 mm/s (measured in the carotid
artery of a healthy subject). Thus, the lateral spatial
resolution x, which depends on the interval of ultrasonicbeams (100 m), is not suﬃcient because the lateraldisplacement between frames is smaller than the lateral
spatial resolution x. To solve this problem, the normalized
correlation function Cn ½lðm; nÞ; dsp ðm; nÞ was interpo-

ð11Þ

ð12Þ

lated using reconstructive interpolation.30,31) Figure 3 shows^ nÞg after interpolathe estimated lateral displacements flðm;tion with various interpolation factors. As shown in Fig. 3,
100 point interpolation is suﬃcient to estimate the lateraldisplacement between frames of 9 m, which is a typicalarterial longitudinal displacement. Therefore, in this study,
the lateral spatial resolution after interpolation x0 was set atx=100. Similarly, the axial spatial resolution after interpolation z0 was set at z=100, where z is the original
spacing of the sampled points in the z-direction. The
estimated axial displacement dsp ðm; nÞ also corresponds
to global wall motion between the n-th frame and the(n þ 1)-th frame. However, the displacement caused by
global wall motion was already estimated as the axial
displacement d^g ðnÞ by the phased-tracking method. In thisstudy, the axial displacement d^g ðnÞ was adopted as thedisplacement caused by global wall motion because an
excellent accuracy in the estimation of the axial displace-

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lateral displacement [mm](a)

RMS error [mm](b)K. Kitamura et al.

100 points

16 points

5 points

25 points

13 points

actual

(a)

0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1.2

ultrasonic probeyx
x m−1 x mz

xm+1
0−th frame(at 0 [s])δx

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6time [s]0.3phantom

0.25
0.2

(b)

0.15

z (m−1)0

0.1
0.05
0

z (m+1)0z m0

εm (z m0)0

ε (m+1)(z (m+1)0)

5 10 15 20 25 30 35
interpolation factor [point]z (m−1)0
Fig. 3. (Color online) (a) Estimated lateral displacements flðm; nÞg, whichwere interpolated using various numbers of points, and actual displacementla ðm; nÞ (black line). (b) Distribution of RMS errors for diﬀerent
interpolation factors.

Fig. 4. (Color online) Illustration of expansion of region to estimate
surface proﬁle. (a) Data acquisition. (b) Estimated surface proﬁles before
expansion (green, blue, and pink lines) and after expansion (red line).

ment has already been achieved by the phased-tracking
method.

RF dataPhased−tracking method
Block matching
using a few ultrasonic beams
using an ultrasonic beamat each position
Lateraldisplacement
Axial displacement
as a function
at each beam
as a functionof timeof timeRemoval of global wall motion

2.3 Expansion of region of accurate estimation of surface
roughness

Thus far, we considered the estimation of the surface proﬁleusing an ultrasonic beam. However, the longitudinal
displacement of the carotid artery is less than 1 mm, andthis would limit the length of the region of measurement.
Therefore, we proposed a method to increase the length ofthe measured region using several ultrasonic beams. The
minute surface proﬁle zm ðx; zm0 Þ in eq. (8) is estimated withrespect to each beam (m-th beam). If the lateral displacementof the arterial wall is 1 mm and the beam intervals are
0.1 mm, regions of 0.9 mm overlap (i.e., 9 beams overlap).
Thus, we connect the surface proﬁles estimated using
adjacent ultrasonic beams by adjusting the initial heightzm0 to expand the region for the accurate estimation of
surface roughness. For this purpose, the RMS diﬀerencem ðzm0 Þ between surface proﬁles obtained at the (m  1)-th
and m-th beams in the overlapping region is evaluated asfollows [Figs. 4(a) and 4(b)]:vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
u N 1u1 X
m ð^zm0 Þ ¼ t½^zm ðx; z^m0 Þ  z^ðm1Þ ðx; z^ðm1Þ0 Þ2 ; ð13Þ
N n¼0
where z00 is assumed to be zero. The optimal initial heightz^m0 is determined by minimizing m ð^zm0 Þ. The surface proﬁlezðxÞ in the overlapping region is estimated as follows:z^ðxÞ ¼

1

M
total
X

Moverlap ðxÞ m¼0z^m ðx; z^m0 Þ;

ð14Þ

where Mtotal means the total number of ultrasonic beams andAxial displacement
caused by surface roughness
as a function
at each beamof time
Detection of the lateral position
Surface profile
as a function
at each beamof position
Expansion of region
Surface profile
as a function
in a wide regionof position

Fig. 5. (Color online) Accurate estimation of carotid lumial surface
roughness proposed in this study.

Moverlap ðxÞ is the number of surface proﬁles, which are
estimated at the lateral position x. If the surface proﬁles are
not estimated at x, the surface proﬁles f^zm ðx; z^m0 Þg are zero.
Figure 5 shows the above-mentioned procedure of themethod proposed in this study for the accurate estimationof the surface roughness of the carotid arterial wall.
3. Basic Experiments Using Silicone Phantom
3.1 Determination of the optimal size of a correlation
kernel^ nÞ and d^sp ðm; nÞ depend on
The estimated displacements lðm;the size of the correlation kernel. Therefore, determination

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Jpn. J. Appl. Phys. 51 (2012) 07GF08

position of depth [mm]K. Kitamura et al.

normalized amplitude

ultrasonic diagnostic equipmentprobe
13.6 mmwire (13 μ m)
water
fixed standFig. 6. (Color online) Illustration of system to measure ultrasonic beam

10

1

0.6

normalized amplitude

0.2 mm0.4
0.2
00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
position of depth [mm]

1

(c)

0.8
0.6
0.5 mm0.4
0.2
00 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
lateral position [mm]Fig. 7. (Color online) Measured ultrasonic beam proﬁle. (a) B-mode
image of a ﬁne wire (13 m in diameter). (b) Proﬁle in the axial direction.
(c) Proﬁle in the lateral direction.

ultrasonic diagnostic equipment

probe
phantomwater

0.5 mmcontroller

1.0 mmstatic standautomatic XYZ stage

Fig. 8. (Color online) Illustration of system for basic experiment using aphantom.

ð15Þ
ð16Þ

where Wl and Wd are the lateral and axial kernel sizes,
respectively, wl ¼ 5 points (0.5 mm), and wd ¼ 10
points (0.2 mm). In this experiment, the phantom, which
includes point scatterers, and the ultrasonic probe wereplaced using an automatic stage and a static stand,respectively, as shown in Fig. 8. RF echos were acquiredfor 1.4 s during the movement of the phantom of 1:0 and0:5 mm in the lateral and axial directions, respectively(lateral and axial velocities: 1.4 and 0.7 mm/s). The obtained
B-mode image is shown in Fig. 9. In this study, the sizes Wl

(b)

0.8

position of depth [mm]Wl ¼ 2  wl ðmmÞ ð¼ 2  5 þ 1 pointsÞ;Wd ¼ 2  wd ðmmÞ ð¼ 2  10 þ 1 pointsÞ;

(a)

15

proﬁle.

of the optimal correlation kernel size is important. When thesize of the correlation kernel is set to be small, there may be
several regions in the post frame, which have echo patterns
similar to those in the correlation kernel in the previous
frame. These multiple regions, which have similar echopatterns, introduce misestimation of displacement. On theother hand, when the size of the kernel is set to be large, theecho pattern in the correlation kernel is more unique and thedisplacement estimation is less susceptible to noise. However, the proﬁle around a peak of a normalized correlation
function C½lðm; nÞ; dsp ðm; nÞ becomes wider because it israre that the echo patterns in two frames exactly coincide,which degrades the accuracy and the spatial resolution of thedisplacement estimation. In this study, the ultrasonic beam
proﬁle was measured to deﬁne the optimal kernel size as anintegral multiple of the focal size. We used a 10 MHz lineartype probe of ultrasonic equipment (Aloka SSD-6500), witha sampling frequency of 40 MHz, a frame rate of 160 Hz,
lateral beam intervals of 100 m, and a pulse repetition
frequency of 13 kHz. Figure 6 shows the system used tomeasure the ultrasonic beam proﬁle. Figure 7(a) shows a Bmode image of a wire, which is 13 m in diameter and isconsidered as a point scatterer (wavelength of ultrasound:150 m). The lateral and axial amplitude distributions along
the red and green lines are shown in Figs. 7(b) and 7(c),respectively. The lateral and axial half-value widths, whichwere measured from Figs. 7(b) and 7(c), are 0.5 mm (lateral)and 0.2 mm (axial), respectively. Therefore, the lateral andaxial widths of the kernel are deﬁned as multiples of wl ¼
0:5 mm and wd ¼ 0:2 mm, respectively, as follows:

lateral position [mm]
5
10
15

0

lateral position [mm]
0
5
15

20

Fig. 9. (Color online) B-mode image of a phantom, which includes point
scatterers. The red square is the optimal size (5:0  2:0) mm2 of thecorrelation kernel and the red cross is the central position of the kernel.

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K. Kitamura et al.

RMS error ε (α l = 5, α d )[mm]

RMS error ε( α ) [mm]Jpn. J. Appl. Phys. 51 (2012) 07GF08

0.25
0.2
0.15
0.1
0.05
0

1

2

3

4
5
6
coefficient α

7

8

0.25
0.2
0.15
0.1
0.05
0

1

2

3
4
5
6
axial coefficient αd780.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2
axial kernel size W d [mm]1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
lateral kernel size W l [mm]Fig. 11. (Color online) Distribution of mean RMS errors fðl ¼ 5; d Þg
for diﬀerent sizes of kernels in seven measurements.

0.4 0.8 1.2 1.6 2.0 2.4 2.8 3.2
axial kernel size W d [mm]Fig. 10. (Color online) Distribution of mean RMS errors fðÞg fordiﬀerent sizes of kernels in seven measurements.

and Wd of the correlation kernel in the lateral and axial
directions, respectively, were deﬁned by 2. The optimal
size (Wl  Wd ) of the correlation kernel was determinedusing the value of  when the RMS error of the estimateddisplacement from the actual displacement was smallest.

To calculate the RMS error ðÞ, the lateral and axial
displacements were estimated using diﬀerent values of .
The RMS error ðÞ in the estimated lateral and axial
displacements, which was evaluated for each value of , wascalculated from the estimated lateral displacement lðm; nÞ,the estimated axial displacement dsp ðm; nÞ, the actual lateraldisplacement lac ðm; nÞ, and the actual axial displacementdac ðm; nÞ as follows:

vﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
u
1
u 1 N
X
½flðm; nÞ  lac ðm; nÞg2 þ fdsp ðm; nÞ  dac ðm; nÞg2 ;ðÞ ¼ t
2N n¼0where N is the number of frames. The central position of thekernel was initially placed at the surface of the phantom.
RMS errors fðÞg were calculated for seven measurements.
The mean RMS errors fðÞg are plotted in Fig. 10. In
Fig. 10, error bars show the maximum and minimum valuesof the calculated RMS errors fðÞg for seven measurements.
The mean RMS error  ðÞ was smallest (0.055 mm) when
the coeﬃcient  was 5. Therefore, the optimal kernel size
(Wl  Wd ) was determined as (5:0  2:0) mm2 . The determined optimal size is shown by the red square in Fig. 9. The
axial length of the kernel is much smaller than the lateral
length when the kernel size is determined by a single valueof , owing to uneven lateral and axial sizes of the ultrasonicpoint spread function. Therefore, separately deﬁned magniﬁcation factors l and d are also investigated to examine
smaller and larger axial lengths of the kernel. In Fig. 11, themean RMS errors fðl ¼ 5; d Þg are plotted as a function of
d and l of 5. This result shows that d of 5 and l of 5 are
optimal to estimate the lateral displacement of the arterial
wall. This is because echoes from the inside of the arterial
wall (i.e., tissues in the region deeper than the posterior wall)need to be included in the kernel because echoes from theluminal interface are similar among ultrasonic beams andthere is no distinct echo pattern to be tracked. For
comparison, lateral and axial displacements estimated atkernel sizes of fð0:8  0:8Þ mm2 g,32) fð2:0  1:5Þ mm2 g,33)
and fð3:2  2:5Þ mm2 g28) are shown in Figs. 12(a) and 12(c).
Figure 12(b) shows lateral displacements estimated at kernel
sizes of  ¼ 5, 6, 7, and 8. These results show that moreaccurate estimation of displacements of the phantom ispossible using the optimal kernel ( ¼ 5) size than with

ð17Þ

other kernel sizes. Also, the lateral displacements were
estimated at three diﬀerent depths of central position of thecorrelation kernel and were also estimated when the surfaceof the phantom is not parallel to the surface of the ultrasonicprobe. Figures 13(a)–13(e) show B-mode images of thesilicone phantom at a depth of 18.5 mm, a deeper depth of
25 mm, and a shallower depth of 12 mm, a B-mode image
obtained when the surface of the phantom is not parallel tothe surface of the ultrasonic probe, and the estimated lateraldisplacements, respectively. The RMS errors between theestimated lateral displacements and the actual values
were 0.067 mm (18.5 mm), 0.071 mm (25 mm), 0.068 mm(12 mm), and 0.072 mm (leaning). These results show thatthe determined optimal kernel size can be applied for various
depths and the case when the surface of the phantom is notparallel to the surface of an ultrasonic probe.
3.2 Estimation of surface roughness of the silicone
phantom

In a basic experiment, we used a silicone phantom, which
had ten saw tooth shapes on its surface. The phantom was
moved in the lateral (back and forth by 1 mm) and axial (upand down by 0.5 mm) directions using an automatic stage
to simulate arterial wall motion. To simulate the medium
between the skin and the arterial wall, a piece of pork cutlet
was put between the ultrasonic probe and the phantom. The
system of this experiment was similar to the previous system
shown in Fig. 8, except for the phantom and the pork cutlet.
The obtained B-mode images of the phantom are shown in
Figs. 14(a) and 14(b). Measurements were carried out threetimes. The estimated surface proﬁles z^ðxÞ from three

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2(2.0 x 1.5) mm

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0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6time [s]Fig. 12. (Color online) (a) Estimated lateral displacements flðm; nÞg andmeasurements and that measured using the laser proﬁlometerare shown in Figs. 15(a) and 15(b). These results show that
reproducible estimation of surface proﬁles z^ðxÞ for threemeasurements was possible. Also, the estimated periodicity
pitches of saw tooth shapes agreed well with those obtainedusing the laser proﬁlometer. These results show that thesurface roughnesses of phantoms could be estimated by the
proposed method. Moreover, in Figs. 15(a) and 15(b), redarrows show the magnitude of the lateral displacement of thephantom (1 mm). The results shown in Figs. 15(a) and 15(b)show that the regions of estimation of the surface proﬁlesz^ðxÞ could be expanded by more than the magnitude of thelateral displacement of the object. The black solid line in
Fig. 15(c) is the same as the result of the ﬁrst measurement

−0.2
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−1

0 0.2 0.4 0.6 0.8 1time [s]1.2 1.4 1.6

Fig. 13. (Color online) (a) B-mode image of the silicone phantom at a
depth of 18.5 mm. (b) B-mode image of the silicone phantom at a deeper
depth (25 mm). (c) B-mode image of the silicone phantom at a shallower
depth (12 mm). (d) B-mode image of the silicone phantom when the surfaceof the ultrasonic probe and the silicone phantom are not parallel.
(e) Estimated lateral displacements flðm; nÞg and actual displacement la ðm; nÞ(black line). For comparison, displacements estimated at various depths andangles of the ultrasonic probe are also shown.

(a)position of depth [mm]actual displacement la ðm; nÞ (black line). For comparison, displacements
estimated using various kernel sizes, (Wl  Wd ) of (5:0  2:0) mm2 ( ¼ 5,
red line), fð0:8  0:8Þ mm2 g32) (green line), fð2:0  1:5Þ mm2 g33) (blue line),and fð3:2  2:5Þ mm2 g28) (pink line), are also shown. (b) Estimated lateraldisplacements flðm; nÞg and actual displacement la ðm; nÞ (black line). For
comparison, displacements estimated using various kernel sizes,  ¼ 5(red line),  ¼ 6 (green line),  ¼ 7 (blue line), and  ¼ 8 (pink line), arealso shown. (c) Estimated axial displacements fdsp ðm; nÞg and actual
displacement dspa ðm; nÞ, (black line) which are shown in the same way
as (a).

0

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K. Kitamura et al.

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5

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Fig. 14. B-mode images of a phantom which has ten saw tooth shapes on
its surface. (a) Measurement with only water between ultrasonic probe andphantom. (b) Measurement with pork cutlet between ultrasonic probe andphantom.

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height [μ m]

(a)

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(d)
10
0

0

Fig. 15. (Color online) Estimated surface proﬁles fzðxÞg of the phantom for three measurements (red, green, and blue lines) and surface proﬁle measured
by the laser proﬁlometer (black line). The red arrow shows the magnitude of lateral displacement of the phantom. (a) Measurement with only water between
ultrasonic probe and phantom. (b) Measurement with pork cutlet between ultrasonic probe and phantom. (c) Estimated surface proﬁle with pork cutlet
between ultrasonic probe and phantom, which is the surface proﬁle in (b) (red line). Red dots are surface proﬁles f^zm ðx; z^m0 Þg estimated with respect toultrasonic beams used for estimation. (d) Standard deviation of measured surface proﬁles in (c).

β = 15 points
normalized amplitudein Fig. 15(b). Red dots and the black solid line show thesurface proﬁles f^zm ðx; z^m0 Þg estimated with respect to theultrasonic beams used for estimation and the averaged value,
which corresponds to the surface proﬁle zðxÞ, respectively.
Moreover, Fig. 15(d) shows the standard deviation of the red
dots in the z-direction. This result shows that a surface
proﬁle with a height smaller than 10 m could be measured
using the proposed method.
3.3 Discussion of estimation of surface roughness on thesilicone phantoms

The measured surface proﬁles f^zðxÞg depend on the assigned
initial axial position zm0 . Figure 16 shows an RF signal fromthe surface of the phantom. The initial tracking position zm0
was manually assigned at  ¼ 6 points (0.116 mm), 9 points(0.173 mm), 12 points (0.231 mm), 15 points (0.289 mm), 18
points (0.347 mm), and 21 points (0.404 mm) shallower thanthe point at the maximum value of the RF signal. The

1
0.5
0
−0.5
−1

14

14.2 14.4 14.6 14.8
time [ μ s]

15

Fig. 16. (Color online) Acquired RF signal from the surface of thephantom. The blue bracket shows the width of the correlation kernel inphase tracking.

estimated surface roughnesses are shown in Figs. 17(a)–17(c). When the distance  is too large (e.g., 18 points and
21 points), the estimated surface roughness is signiﬁcantly

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height [μ m](a)height [ μ m](b)height [μ m]

(c)

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β = 18laser

β = 211

2

3
4lateral position [mm]β = 12

5

6

5

6

5

6

laser

β = 1512

3
4
lateral position [mm]
β =6

laser

β =9

1

2

3
4
lateral position [mm]Fig. 17. (Color online) Estimated surface proﬁles of the phantom at various values of  (corresponding to the distance from the point at the maximum
amplitude of the echo). (a)  ¼ 21 points (brown line) and  ¼ 18 points (cyan line). (b)  ¼ 15 points (pink line) and  ¼ 12 points (blue line). (c)  ¼ 9
points (green line) and  ¼ 6 points (red line).

degraded [as shown in the red ellipse in Fig. 17(a)]. This isbecause there is no eﬀective RF echo from the surface of thephantom in the correlation kernel owing to the use of a
Hanning window. On the other hand, when the distance  is
too small (e.g., 6 points and 9 points), the estimated surface
roughness is smaller than that measured by the laser
proﬁlometer. This is because the RF signal during 14.4–
14.5 s in Fig. 18(a) varies signiﬁcantly owing to interference between RF signals from the top and bottom of thesaw tooth shapes at their turning point. Figure 18(a) shows
RF signals from various lateral positions of the saw tooth
shape (i.e., the turning point of the saw tooth shape andother points). The fourth positive peak (during 14.4–14.5 s)of these RF signals varied signiﬁcantly compared with theothers. Figure 18(b) shows RF signals from various lateralpositions of another saw tooth shape, whose height is doublethat of Fig. 18(a). Figure 18(c) shows an RF signal (pulse
signal) from a point scatterer. The RF signals in Figs. 18(a)and 18(b) were composed by two overlapping pulse signals,
which were reﬂected from the top and bottom of the saw
tooth shape because the full width at half maximum of theultrasonic beam proﬁle is 500 m in the lateral direction.
The variance of the amplitude of the fourth positive peakof these RF signals in Fig. 18(b) is larger than that inFig. 18(a). This is because the height of the saw tooth in
Fig. 18(b) is larger than that in Fig. 18(a). To analyze only
the echo from the peak of the saw tooth shape, the optimal

initial axial position zm0 in phase tracking and blockmatching should be determined to be as shallower as
possible. Therefore, the optimal initial axial position zm0 inphase tracking and block matching is determined to be ¼ 15 points because  larger than 18 points is not optimal,
as described previously.
As shown in Figs. 15(a) and 15(b), both sides of theestimated surface proﬁles fzðxÞg deviated from the estimatedsurface proﬁle measured by the laser proﬁlometer. This isbecause the surface proﬁle estimated by the proposed
method corresponds to the convolution of the surface proﬁlemeasured by the laser proﬁlometer (actual surface proﬁle)and the point spread function of ultrasound in the lateral
direction. Figure 19 shows the surface proﬁle obtained byconvolution of the Gaussian function, which was assumed as
the point spread function of ultrasound, to the surface proﬁlemeasured by the laser poﬁlometer. As shown in Fig. 19, theconvolved result deviated from the actual surface proﬁlemeasured by the laser proﬁlometer, as in Figs. 15(a) and15(b). Therefore, both sides of the estimated surface proﬁlesfzðxÞg deviated from the estimated surface proﬁle by thelaser proﬁlometer because of the point spread function ofultrasound in the lateral direction. Also, the estimated saw
tooth shapes became blurred.
The proposed method can be applied to the measurementof minute surface roughness in the case when the surface of
the ultrasonic probe and the carotid arterial wall are not

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height [μ m]

0.5
0
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42−th
43−th

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measured
Gaussianlaser

1 2 3 4 5 6 7lateral position [mm]8Fig. 19. (Color online) Estimated surface proﬁle zðxÞ by the proposed
method (red line), and the result (green line) obtained by convolving theGaussian function to the surface proﬁle measured using a laser proﬁlometer(black line).

1
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(a)

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4.2 4.4 4.6 4.8time [ μ s]205Fig. 18. (Color online) (a) Acquired RF signal from surface of phantom(11 m height) at each beam position. (b) Acquired RF signal from surfaceof phantom (22 m height) at each beam position. (c) Acquired RF signal
from a point scatterer.

Fig. 20. B-mode images of carotid arteries obtained from subject A (24year-old healthy male), subject B (23-year-old healthy male), and subject C(23-year-old healthy male). The direction of blood ﬂow corresponds the
direction from right to left. (a) Subject A. (b) Subject B. (c) Subject C.

distance  from the point at the maximum amplitude of the
RF echo from the lumen-intima boundary.
parallel. This is because the axial displacement dðm; n; Þestimated by the phased-tracking method is expressed by
dðm; n; Þ ¼ dðm; nÞ  cos , where  is the angle between theprobe and the arterial luminal surfaces. Also, the lateraldisplacement lðm; n; Þ estimated using block matching is
expressed as lðm; n; Þ ¼ lðm; nÞ  cos . The eﬀect of theangle can be ignored because cos  is 0.9848 at a typicalleaning angle of 10 . Moreover, as shown in Fig. 13(c), theoptimal size of the correlation kernel ðWl  Wd Þ ¼ ð5:0 
2:0Þ mm2 could also be applied for such a case.
4. In vivo Experimental Results
4.1 Acquisition of RF signals in vivo

The RF data of three subjects [subject A (24-year-old
healthy male), subject B (23-year-old healthy male), andsubject C (23-year-old healthy male)] were acquired during
two heart beats. Figures 20(a)–20(c) show B-mode imagesof the arterial walls obtained from the three healthy males.
The frame rates were set at 160 Hz. In this study, the RFdata were acquired using a 10 MHz linear-type probe ofultrasonic equipment, which was the same as that used in
the basic experiment. The optimal size of a correlation
kernel ðWl  Wd Þ ¼ ð5:0  2:0Þ mm2 determined by thebasic experiment was also used in the in vivo experiment.
Also, the initial axial position zm0 is determined using the

4.2 Results of estimation of surface roughness in vivo

^ nÞg of the arterial walls of
The lateral displacements flðm;the three subjects were measured during two heart beats.
Figures 21(a)–21(c) show estimated lateral displacements^ nÞg during one cardiac cycle obtained from subject A,flðm;subject B, and subject C (negative lateral displacement
corresponds to movement in the direction of blood ﬂow),
respectively. These results of estimated lateral displacements^ nÞg of the arterial wall were obtained using blockflðm;
matching and are reproducible. In addition, the estimatedminute surface proﬁles z^ðxÞ of the carotid arterial wall of
subject A, subject B, and subject C show the expanded
region of estimation using the proposed method, as shown in
Figs. 22(a)–22(c).
4.3 Discussion of estimation of surface roughness in vivo

The lateral displacements flðm; nÞg of the arterial wall in the
direction against the blood ﬂow existed between the S wave
and the T wave of the electrocardiogram and after the T
wave of the electrocardiogram. In addition, the estimatedsurface proﬁles f^zðxÞg were similar between two beats. These
results show that reproducible estimations of surface proﬁlesfzðxÞg are possible using the proposed method. Moreover, in
Figs. 22(a)–22(c), the red arrows show the magnitude of the

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ECG

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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1time [s](c)Fig. 21. (Color online) Estimated lateral displacements of carotid arterial walls during one cardiac cycle (red and green lines) and electrocardiograms(ECGs) (black line) obtained from subject A (24-year-old healthy male), subject B (23-year-old healthy male), and subject C (23-year-old healthy male).
Negative longitudinal displacement corresponds to movement in the direction of blood ﬂow. (a) Subject A. (b) Subject B. (c) Subject C.

lateral displacement

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Fig. 22. (Color online) Estimated surface proﬁles of the carotid arterial wall obtained from subject A (24-year-old healthy male), subject B (23-year-old
healthy male), and subject C (23-year-old healthy male). Red arrows show the magnitude of lateral displacement of arterial wall. (a) Subject A.
(b) Subject B. (c) Subject C.

lateral displacements of arterial walls. These results showthat regions of estimations of surface proﬁles fzðxÞg could be
expanded by more than the magnitude of lateral displacement of the arterial wall.
For estimation of the lateral displacement, in the present
study, the block matching technique based on correlation
between RF echoes was used, and the correlation kernel
size was optimized using a silicone phantom without any

deformation. However, under the in vivo condition, there
should be deformations of the arterial wall and external
tissue, such as shearing due to blood ﬂow and longitudinalmotion of the artery. The lateral displacement estimatedusing a correlation window including echoes from media,
adventitia, and external tissue in addition to that from theluminal interface would be inﬂuenced by the diﬀerencesamong displacements of intima, media, adventitia, and

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external tissue. Therefore, in a future work, it is necessary tofurther examine the optimum correlation kernel size using aphantom with deformation.
During one cardiac cycle, the anterior wall also moves
laterally, and the luminal surface of the anterior wall may berough. However, the eﬀect of the surface roughness of theanterior wall on the estimation of the minute surface proﬁleof the posterior wall is small. This is because the ultrasoundonly transmits though the anterior wall. If there is a surface
roughness of 10 m on the anterior wall, the eﬀect of thesurface roughness of the anterior wall owing to lateralmotion on the estimation results of the surface proﬁle ofthe posterior wall is 0.19 m (= 1570 mm/1540 m/s 
10 m  10 m), because sound speeds in the arterial walland in blood are 1540 and 1570 m/s, respectively.27)
Therefore, the eﬀect of surface roughness of the anteriorwall is negligible because it is smaller than the surface
roughness of 10 m on the posterior wall, which is desired tobe measured.

5) H. Kanai, H. Hasegawa, M. Ichiki, F. Tezuka, and Y. Koiwa: Circulation

107 (2003) 3018.
6) J. Maurice, J. Ohayon, Y. Frétigny, M. Bertrand, G. Soulez, and G.

Cloutier: IEEE Trans. Med. Imaging 23 (2004) 164.

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5. Conclusions

In this paper, we proposed a method for the accurate
estimation of the surface roughness zðxÞ of the carotid
arterial wall. To expand the measured region, surface
proﬁles f^zm ðx; z^m0 Þg estimated at several ultrasonic beams
were combined. In the basic experiment, the optimal kernel
size for block matching was determined as ðWl  Wd Þ ¼
ð5:0  2:0Þ mm2 . Then, the surface roughness of the carotid
arterial wall (for three healthy subjects) could be estimatedin vivo using the proposed method. The results of in vivo
measurements show that the proposed method is applicableto the accurate estimation of the carotid luminal surface
roughness. Further investigation will be conducted tomeasure the luminal surface roughness of the diseased
carotid artery.

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