REGULAR PAPER

Japanese Journal of Applied Physics 53, 07KF19 (2014)
http://dx.doi.org/10.7567/JJAP.53.07KF19

Improvement of accuracy in ultrasonic measurement of luminal surface roughnessof carotid arterial wall by deconvolution ﬁltering
Yoshifumi Nagai1, Hideyuki Hasegawa1,2, and Hiroshi Kanai1,2*
1Graduate School of Biomedical Engineering, Tohoku University, Sendai 980-8579, Japan
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
E-mail: kanai@ecei.tohoku.ac.jp
2

Received November 29, 2013; accepted March 14, 2014; published online June 23, 2014
The diagnosis of early-stage atherosclerosis is important for preventing cardiovascular diseases such as a stroke or a heart attack. The maincause of such diseases is atherosclerosis. In early-stage atherosclerosis, the luminal surface of the arterial wall becomes rough because of thedetachment of endothelial cells and the degeneration of the internal elastic layer. Therefore, it would be useful if the minute luminal surface
roughness of the carotid arterial wall observed in the early stage of atherosclerosis can be measured noninvasively by ultrasonography. In
conventional ultrasonography, the axial resolution of a B-mode image depends on the ultrasonic pulse length of 150 µm (at 10 MHz) because a
B-mode image is constructed using the amplitude of the RF echo. However, the thickness of an endothelial cell covering the luminal surface is
10–20 µm. Therefore, a minute surface roughness cannot be measured from a conventional B-mode image. We have realized the transcutaneous
measurement of such a minute surface roughness of about 10 µm using the phased-tracking method. However, the lateral spatial resolution
degrades owing to the point spread function (PSF) because the diameter of an ultrasonic beam is ﬁnite. In the present study, we proposed amethod of improving the lateral spatial resolution in the estimation of surface roughness using a Wiener ﬁlter to suppress the effect of the PSF of
the ultrasound system employed. The proposed method was validated using a phantom and then applied to the in vivo measurement of carotid
arteries. © 2014 The Japan Society of Applied Physics

1.

Introduction

Circulatory diseases are considered to be mainly causedby atherosclerosis. Therefore, the early diagnosis andprevention of atherosclerosis are important. Medical ultrasonography is widely used for diagnosis and treatment inclinical situations. Diagnostic ultrasound is noninvasive
and, thus, can be repeatedly employed. Such properties ofdiagnostic ultrasound is suitable for the diagnosis of atherosclerosis because the progress of atherosclerosis requires
long-term monitoring.1–8)
In the early stage of atherosclerosis, the internal elastic
layer and endothelial cells are damaged, leading to thedetachment of endothelial cells and the degeneration of
the internal elastic layer.9,10) As a result, the luminal surfaceof the arterial wall becomes rough.11–13) Therefore, it isimportant for the diagnosis of atherosclerosis in its earlystage to measure such a minute luminal surface roughnessof the arterial wall. The luminal surface is covered withendothelial cells, and an endothelial cell is 10–20 µm thick.14)
Therefore, a high spatial resolution on the micron order isrequired, since such a minute roughness cannot be measured
by conventional ultrasonography whose spatial resolution isabout 0.1 mm at 10 MHz of ultrasonic center frequency.
Arihara et al. measured the micron-order surface proﬁle ofan object made of silicone rubber using the phase shift of
RF echoes during a sweep of an ultrasonic beam.15) However,in their method, the luminal surface cannot be measured
accurately in vivo because of the movement of the arterial
wall in the axial (arterial radial) direction due to pulsation.
In recent years, owing to signiﬁcant improvements in theperformance of ultrasonic diagnostic equipment, the movement of the arterial wall not only in the arterial radial
direction but also in the longitudinal direction have been
observed in a B-mode image.16) This longitudinal movement
is considered to be caused by the contraction of the heart.
Cinthio et al. suggested the measurement of a minuteroughness using this arterial wall movement in the arterial

longitudinal direction without sweeping an ultrasonicbeam.17,18) In this method, the phased-tracking and blockmatching methods are used to measure the displacements of
the luminal surface caused by surface roughness and theincrease in arterial diameter during a cardiac cycle. In Cinthio
et al.’s validation experiments, the surface proﬁle of silicone
phantoms, which had a roughness of 13–33 µm height, wasmeasured. It was shown that a minute surface roughness
could be measured by ultrasound. However, the movementof the arterial wall in the longitudinal direction is small (lessthan 1 mm) and, thus, the length of a region measured using
an ultrasonic beam is limited. Therefore, Kitamura et al.
expanded the measured region by combining multiple surface
proﬁles measured by multiple ultrasonic beams.19)
In Kitamura et al.’s measurement, the micron-order spatial
resolution was realized in the axial (arterial radial) direction
using the phases of ultrasonic echoes. However, theultrasonic ﬁeld does not oscillate in the lateral (arterial
longitudinal) direction and, thus, the spatial resolution isdegraded compared with that in the axial direction. Suchdegradation of the lateral spatial resolution depends on thelateral point spread function (PSF) of the employed ultrasound system. In the present study, a method using a Wiener
ﬁlter was proposed for the suppression of the effect of PSF,
and the effectiveness of the proposed method was validated
using a phantom. Then, the proposed method was applied tothe in vivo measurement of carotid arteries.
2.

Principles

2.1

Measurement of surface roughness of arterial wall
Figure 1 shows the displacement of the arterial wall during a
cardiac cycle. In a ﬁxed ultrasonic beam, the axial (z-axis)
displacement is detected when the luminal surface is roughand the arterial wall moves in the arterial longitudinal(lateral) direction.19) In addition, the arterial wall also moves
in the arterial radial (axial) direction owing to expansion of
the artery caused by an increase in blood pressure during a
cardiac cycle. As described above, the axial displacement

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Jpn. J. Appl. Phys. 53, 07KF19 (2014)

Y. Nagai et al.

ultrasonic probexmyxl (m, n)zm−th ultrasonic beam
mediumanterior wallarteryposterior wall

zm 0 =0

position of
0−th framez m0 =0d (m, n)zm(m, n)=ds (m, n)
position ofn−th framedg(n)Fig. 1. (Color online) Illustration of displacement of arterial wall between 0-th and n-th frames.

estimated by the ultrasonic phased-tracking method20–22) ina ﬁxed ultrasonic beam includes displacements caused bysurface roughness and arterial expansion.
In Fig. 1, the lateral position of the m-th ultrasonic beam
is denoted by xm (xm ¼ m  x, where ¤x is the spacing
between ultrasonic beams). The axial (z-axis) displacementof the posterior wall surface dðxm ; nÞ  dðm; nÞ between
the n-th frame [t (s)] and the (n + 1)-th frame [(t + ¦T) (s)](¦T: frame interval) obtained by the phased-tracking method
is expressed by the difference between the axial positionszðxm ; nÞ  zðm; nÞ and zðxm ; n þ 1Þ  zðx; n þ 1Þ in the n-thand (n + 1)-th frames asdðm; nÞ ¼ zðm; n þ 1Þ  zðm; nÞ:ð1Þ

The total displacement b
dðm; nÞ measured by the phased
tracking method contains both the global displacement of thearterial wall b
dg ðnÞ due to the expansion of the artery and thedisplacement b
ds ðm; nÞ due to the surface roughness asfollows:b
dðm; nÞ ¼ b
dg ðnÞ þ b
ds ðm; nÞ:ð2Þ

The width of the measured region is much smaller than thelength of the pulse wave. Therefore, the global wall motion
between the n-th and (n + 1)-th frames at positions fxmg
ðm ¼ 0; 1; 2; . . . ; M  1Þ are assumed to be the same. The
instantaneous axial displacement  b
dg ðnÞ caused by global
wall motion can be estimated by averaging the axial
instantaneous displacements fbdðm; nÞg as follows:nXbdg ðnÞ ¼
bdg ðlÞ;
ð3Þ
l¼0
1
X
1 M
b
dðm; nÞ;bdg ðnÞ ¼
M m¼0

ð4Þ

where M is the number of ultrasonic beams.
Finally, the surface proﬁle zm ðx; zm0 Þ measured at the m-th
ultrasonic beam is expressed as follows:bzm ðx; zm0 Þ  b
zm ðxm þblðm; nÞ; zm0 ÞnXbds ðm; nÞ;¼ zm0 þn¼0

ð5Þdðm; nÞ  b
dg ðnÞ;bds ðm; nÞ ¼ b

ð6Þwhere zm0 is the initial height.
The arterial longitudinal displacement lðm; nÞ should be
estimated by the block matching technique23–25) withreconstructive interpolation26–28) to obtain the surface proﬁlezm ðx; zm0 Þ as a function of the lateral position x ¼ xm þlðm; nÞ. Furthermore, several surface proﬁles fzm ðx; zm0 Þg
were measured in multiple ultrasonic beams fmg and combined to obtain a surface proﬁle in a wider region. The
proposed method using a Wiener ﬁlter, which will be
described in the subsequent section, was applied to the
combined surface proﬁle for the improvement in the lateral
spatial resolution.
2.2 Improvement in lateral spatial resolution using Wiener
ﬁlter

A measured surface proﬁle can be expressed by the
convolution of the true surface proﬁle and the lateral point
spread function of an ultrasound system. In diagnostic
ultrasound imaging, the Wiener ﬁlter is used for the
improvement in the spatial resolution of a B-mode ultrasonicimage.29–34) In the present study, the Wiener ﬁlter was used
for the improvement in the spatial resolution in themeasurement of a minute surface roughness. Figure 2 showsa block diagram illustrating how to estimate the true surface^
proﬁle fðxÞfrom the surface proﬁle gðxÞ measured by^ x Þ andultrasound using the Wiener ﬁlter Mð!x Þ, where Fð!
^Gð!x Þ are the spatial frequency spectra of fðxÞ and gðxÞ,respectively, where !x is the spatial angular frequency in thelateral direction. In Fig. 2, Hð!x Þ, Nð!x Þ, and Fð!x Þ are thespatial frequency spectra of the lateral PSF, noise, and true
surface proﬁle, respectively.
^ x Þ is determined so as to minimize
The Wiener ﬁlter Mð!
the mean squared difference between the spectrum of the true
^ x Þ. The estimate
surface proﬁle Fð!x Þ and its model Fð!
^
Fð!x Þ is given by^ x Þ ¼ Gð!x Þ  Mð!x ÞFð!
¼

Gð!x Þ  Hj ð!x Þ;ð7Þ
jHð!x Þj2 þ PN ð!x Þ=PF ð!x Þ
where PN ð!x Þ and PF ð!x Þ are the average power spectra of

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Jpn. J. Appl. Phys. 53, 07KF19 (2014)

Y. Nagai et al.
ultrasonic diagnostic
equipment

spatial domainnoise n(x ) surface profile
obtained byexperimentactualsurface profilef (x )g(x )h (x )F (ω x)m(x )^f (x )

filterpoint spread function
spatial frequency
domainestimate of thesurface profileprobe
13.6 mm

N (ω x)wire

G (ω x)H (ω x)M (ω x)

automaticstage^(ω x)
F^ x Þ using
Fig. 2. Block diagram of the procedure for obtaining estimate Fð!
Wiener ﬁlter Mð!x Þ.

(a) 20A i¼1^ xÞGi ð!x Þ ¼ Hð!

ð9Þ

A
1X
jNi ð!x Þj2 :
A i¼1

ð10Þ

A
1X
jFi ð!x Þj2 :
A i¼1

ð11Þ

In the present study, the weighting function PN ð!Þ=PF ð!Þ
determined in the basic experiment was also applied toin vivo measurement.
Determination of Wiener ﬁlter
To estimate the PSF in the lateral direction Hð!x Þ and theweighting function PN ð!x Þ=PF ð!x Þ in the Wiener ﬁlter
Mð!x Þ, a phantom consisting of a ﬁne wire (diameter:
15 µm), which can be considered as a point scatterer, placedon a ﬂat surface of a silicone rubber plate was measured.
Ultrasonic diagnostic equipment (Hitachi-Aloka SSD-6500)
with a 10 MHz linear array probe was used for the acquisitionof beamformed RF signals. Figure 3 shows the experimental
setup.
The surface proﬁle gðxÞ of the phantom was measured 10
times by the method presented in Ref. 19 by moving the
2.3

height [μm]

5
0
−5

(b)

Regarding PF ð!Þ, the same phantom was also measured A
times using laser. The power spectrum of the true surface
proﬁle PF ð!Þ was estimated by averaging the magnitudes ofthe spatial frequency spectra fFi ð!x Þg of the surface proﬁleffi ðxÞg measured using laser as follows:
PF ð!Þ ¼

10

2

3

4
lateral position [mm]

5

6

5
10
15
spatial frequency [mm−1]

20

0

ð8Þ

 xÞ
Ni ð!x Þ ¼ Gi ð!x Þ  Gð!
PN ð!x Þ ¼

laser f n (x)ultrasound gn (x )15

power spectra [dB]

 xÞ ¼
Gð!

static
stand

water

Fig. 3. (Color online) Illustration of experimental setup for measurementof PSF.

the noise Nð!x Þ and the true surface proﬁle Fð!x Þ,
respectively.35–39)
In the present study, the point spread function hðxÞ was
identiﬁed by measuring the surface proﬁle of a phantom, inwhich a ﬁne wire was placed on a ﬂat surface of a silicone
rubber plate as described in next section. Regarding PN ð!x Þ,
the phantom was measured A times, and the measured
proﬁles fgi ðxÞg ði ¼ 0; 1; 2; . . . ; A  1Þ were averaged. The
difference between the measured surface proﬁle fgi ðxÞg andthe average surface proﬁle g ðxÞ were deﬁned as the noisefni ðxÞg, and PN ð!x Þ was calculated by averaging themagnitudes of the spatial frequency spectra fNi ð!x Þg of thenoise fni ðxÞg as follows:A
1X

siliconerubber−20−40

laser Fn (ωx)
ultrasound Gn(ωx)−60
0Fig. 4. (Color online) Experimental results of measurement of ﬁne wirefor determination of PSF. (a) Surface proﬁles measured using ultrasound andlaser. (b) Spatial power spectra of measured surface proﬁles.

ultrasonic probe in the lateral direction using an automatic^ x Þ and PN ð!x Þ werestage. The frequency spectra Hð!
estimated by applying the Fourier transform to the meanand standard deviation of the surface proﬁles fgðxÞg for the 10
measurements. Also, PF ð!x Þ was obtained by applying theFourier transform to the surface proﬁle of the phantom
measured by a laser displacement meter (Keyence LT-9010
and LT-9000). In the laser measurement, the surface proﬁleof the phantom was also scanned using an automatic stage.
Measurements were also conducted 10 times for the laser
measurements. Figures 4(a) and 4(b) show the surface
proﬁles measured using ultrasound and laser and the power
spectra of the measured surface proﬁles, respectively. Using
the results shown in Fig. 4, the Wiener ﬁlter Mð!x Þ was

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Y. Nagai et al.

determined using the average power spectra of the surface
proﬁles measured using ultrasound as the estimated point^ x Þ.
spread function Hð!
Control parameter β used for weighting function
The relative magnitude of the weighting function
PN ð!x Þ=PF ð!x Þ to the PSF Hð!x Þ should be determined toappropriately control the effect of the proposed Wiener ﬁlter
Mð!x Þ. The Wiener ﬁlter Mð!x Þ behaves as an inverse ﬁlter
1=Hð!x Þ when the signal-to-noise ratio (SNR) is high. On
the other hand, if SNR is low, the effect of the Wiener
ﬁlter Mð!x Þ is suppressed. Conventionally, a real constant isused to control the contribution of the weighting function
PN ð!x Þ=PF ð!x Þ. This can be carried out by multiplying
PN ð!x Þ=PF ð!x Þ by a real constant ¢.40–42) A smaller control
parameter, ¢ (² 0), is preferred in order to improve the spatial
resolution at the expense of a noise increment. In theconventional Wiener ﬁlter, ¢ = 1.0. On the other hand, theﬁlter works as an inverse ﬁlter at every spatial frequency
when ¢ is low, corresponding to the assumption of a high
SNR at all spatial frequencies. In such a case, noise contained
at a high spatial frequency tends to be ampliﬁed, although ahigher spatial resolution is realized. To determine theoptimum value of the control parameter, the RMSE between^ measured by ultrasound and the true
the surface proﬁle fðxÞsurface proﬁle fðxÞ measured using laser was calculated forfg values of 0–1. The magnitude of the PSF jHð!x Þj wasnormalized to limit the range of the control parameter ¢ from0 to 1 as follows:1ﬃ  Hð!x Þ;Hð!x Þjnormalized ¼ sﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
ð12Þ
!n
X
2
jHð!x Þj

y
z

x

probe

where !n is a Nyquist angular frequency. Using this optimal
control parameter opt , the proposed Wiener ﬁlter is deﬁned
as follows:Mð!x Þ ¼

H  ð!x Þjnormalized
PN ð!x ÞjHð!x Þjnormalized j þ opt PF ð!x Þ:

ð13Þ

Determination of control parameter β

To determine the optimum control parameter ¢, anotherphantom made of silicone rubber, which has a minutesawtooth shape (the height of each teeth is 12 µm), wasmeasured using both ultrasound and laser. Figure 5 shows theexperimental setup for ultrasonic measurements. To simulate
the motion of the carotid arterial wall, the phantom was
moved in both axial and lateral directions by an automaticstage, and the probe was ﬁxed by a ﬁxed stand. RF echoes
were sampled at 40 MHz for 1.4 s during the movement of thephantom by «1.0 and «0.5 mm in the lateral and axial
directions, respectively. The frame rate and lateral intervals
between beams were 169 Hz and 100 µm, respectively.
Figure 6 shows a B-mode image of the phantom, and thesurface proﬁle measured by ultrasound before the applicationof the proposed Wiener ﬁltering is shown in Fig. 7 (greenline). The surface proﬁle was also measured using laser (redline in Fig. 7) by moving the laser displacement meter in thelateral direction using an automatic stage. In Fig. 7, thesurface proﬁle obtained by applying the proposed Wiener

1.0 mmstatic
stand

water

Fig. 5. (Color online) Illustration of experimental setup for ultrasonicmeasurement of surface roughness using a phantom.

depth [mm]

11
12
13
14
15
0

1

2

5
4
3
6
lateral position [mm]87Fig. 6. B-mode image of a silicone phantom with sawtooth shape.

0laser f (x)before filtering g(x)estimate f (x)

−10
−20
−30
−40
−50

2

2.5

phantom

automatic
stage

height [μm]!x ¼00.5 mm

2.4

0

1

2

3
4
5
lateral position [mm]

6

7

8

Fig. 7. (Color online) Results of measured surface proﬁle of a phantom(red line: true surface proﬁle measured by laser; green line: surface proﬁlebefore application of the ﬁltering; and blue line: estimated surface proﬁleafter application of the ﬁltering).

ﬁlter with the optimum control parameter opt is also shownby the blue line.
To determine the optimal control parameter opt , the root
mean square errors (RMSEs) between true surface proﬁlemeasured by laser fðxÞ and the estimated surface proﬁles^ffðxÞgwere evaluated at fg values of 0–1. In Fig. 8, RMSE
is plotted as a function of the control parameter ¢, and the
optimum control parameter opt was determined to be 0.036.
The power spectra of the measured surface proﬁle gðxÞ and^the estimate fðxÞare shown in Fig. 9(a). The Wiener ﬁlter
Mð!x Þ and the weighting function PN ð!x Þ=PF ð!x Þ are also
shown in Figs. 9(b) and 9(c), respectively. The signal-tonoise ratio (SNR) was higher in the spatial frequency range
of 0–5 mm¹1, and the proposed Wiener ﬁlter worked as aninverse ﬁlter mainly in this spatial frequency range.

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Y. Nagai et al.

7

11

RMSE [μm]depth [mm]

min
0.036

6.6

6.2

12
13
14
15

5.8

0
5.4

0

0.05

0.1
0.15
control parameter β

1

2

5
3
4
6
lateral position [mm]

7

8

0.2

Fig. 10. B-mode image of phantom in the presence of a porcine cutlet
between ultrasonic probe and phantom.

Fig. 8. (Color online) Root mean square errors between the measured andtrue surface proﬁles plotted as a function of control parameter ¢.

0

0

−30

−40

power spectrum [dB]power spectrum [dB]

(a)

−60

−90

−120

before filtering G (ω x)after filtering F (ω x)0

24
spatial frequency [mm−1]

6

−120

−160

8

0

5

10
15
spatial frequency [mm−1]

20

10
15
spatial frequency [mm−1]

20

(c)

(b)

0

0

−40

power spectrum [dB]power spectrum [dB]

−80

−80

−120

−160

0

5

10
15
spatial frequency [mm−1]

20

−20

−40

−60

0

5

Fig. 9. (Color online) (a) Power spectra of surface proﬁles pre- and post-ﬁltering (¢opt = 0.036). (b) Power spectrum of designed Wiener ﬁlter. (c) Power
spectrum of the weighting function.

3.
3.1

Experimental results

Basic experiments
Under the condition for in vivo measurements, there is amedium with a nonuniform sound velocity distribution
between the skin and the carotid anterior wall. Therefore,
the phantom was measured under the condition that a porcine
cutlet, which simulated soft tissue, was placed between theultrasonic probe and the phantom. The system for thisexperiment was the same as that shown in Fig. 5 except forthe porcine cutlet (the thickness of the cutlet was about
10 mm). A B-mode image of the phantom is shown in
Fig. 10. Figure 11 shows the measured surface proﬁles. As
shown in Fig. 11, the surface proﬁle became sharper and theheight of each sawtooth became closer to that obtained using
laser by our method with the proposed Wiener ﬁlter. Even in

the presence of an inhomogeneous propagating medium
between the ultrasonic probe and the target, the minutesurface proﬁle can be measured accurately. In this measurement, the weighting function PN ð!x Þ=PF ð!x Þ and the control
parameter ¢, which were determined in basic experiments
described in Sects. 2.3 and 2.5, respectively, were used.
In the present study, the control parameter ¢ and theweighting function PN ð!x Þ=PF ð!x Þ were determined by basic
experiments and, thus, RF echoes acquired in those experiments contain a smaller noise than that obtained in thein vivo measurement. Therefore, the proposed ﬁlter may notwork appropriately under a low-SNR condition and may leadto the appearance of false peaks in the estimated surface^
proﬁle fðxÞ.
To investigate the effect of SNR on the proposedﬁlter, the SNR of the acquired ultrasonic echo signal was
varied by adding white noise to the ultrasonic echo signal in

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Jpn. J. Appl. Phys. 53, 07KF19 (2014)

Y. Nagai et al.

(a) 0height [μm]

−10
−20
−30

laser f (x )before filtering g (x )after filtering f (x )

−40
−50

0

1

2

26.0 dB

25.0 dB

laser

−10
−20
−30
−50

3
4
5
lateral position [mm]

6

7

0

1

2

8

(b) 0

Fig. 11. (Color online) Measurement of surface proﬁle of phantom withporcine cutlet (red line: true surface proﬁle measured by laser; green line:
surface proﬁle before application of the ﬁltering; and blue line: estimatedsurface proﬁle after application of the ﬁltering).

ð14Þ
where fsm ðtÞg is the average of fsm;n ðtÞg for N frames, L is
the number of RF echo signals in the depth direction,corresponding to the length of the correlation window used in
the phased-tracking method, and Ts is the sampling interval.
Figure 12 shows the estimated surface proﬁles, whilechanging the SNR.
Figures 13(a) shows the RMS difference between thesurface proﬁle obtained at each SNR and that measured using
laser. Figure 13(b) shows the RMS difference between thesurface proﬁle obtained at each SNR and that obtained fromthe ultrasound echo signal without additional white noise(corresponding to an SNR of 27.1 dB). As shown in Fig. 12,
the RMS difference between the results obtained using
ultrasound and laser includes the differences in both thesawtooth shape and global shape of the surface proﬁle, and it
is difﬁcult to consider the effect of the SNR using the RMS
difference between the results obtained using ultrasound andlaser. Therefore, in the present study, the effect of the SNR
was discussed using the difference of the results obtainedwith and without the additional white noise shown in
Fig. 13(b).
As shown in Fig. 12, the height of the sawtooth decreases
signiﬁcantly when the SNR was lower than 20 dB. Therefore,
an SNR of more than 20 dB is required for the proposedﬁltering method. However, note that a peak in the lateralposition of 1–2 mm was separated at an SNR of 20 dB, as
shown in Fig. 12(c), even though the height of each sawtooth
does not change signiﬁcantly. Such deformation of thesurface proﬁle possibly occurs under an SNR of 20 dB.
Results of in vivo experiments

Ultrasonic RF data were obtained from carotid arteries ofthree healthy subjects [subject A (23-year-old healthy male),23.0 dB

22.0 dB

7

8

laser

−30
−40
0

1

2

height [μm]

(c) 0

3
4
5
lateral position [mm]21.0 dB

20.0 dB

6

7

19.0 dB

laser

6

7

8

−10
−20
−30
−40
−50

0

1

2

3
4
5
lateral position [mm]8Fig. 12. (Color online) Surface proﬁles of a phantom estimated under
different SNRs of ultrasonic echo signal. (a) SNRs from 25.0 and 27.1 dB.
(b) SNRs from 22.0 and 24.0 dB. (c) SNRs from 19.0 and 21.0 dB. The SNRof the ultrasonic echo signal without additional white noise is 27.1 dB.

(a)
7

RMS error [μm]

M
L
1 X
1X
½sm ðt þ lTs Þ
M m¼1 L l¼1
SNR ¼
;
M
L  X
1 X
1X
1 N
2
½sm;n ðt þ lTs Þ  sm ðt þ lTs Þ
M m¼1 L l¼1 N n¼1

24.0 dB

6

−20

6

5

4

3

(b)
RMS error [μm]

the data analysis. White noise was generated using MATLAB(MathWorks, U.S.A.), and its amplitude was controlled bymultiplying it by a variable constant. The SNR was evaluatedusing the envelope sm;n ðtÞ of the ultrasonic RF signal in them-th beam and n-th frame as follows:3
4
5
lateral position [mm]

−10

−50

3.2

27.1 dB−40

height [μm]height [μm]

0

18

20

22
SNR [dB]

24

26

20

22
SNR [dB]

24

26

4

3

2

1

0

18

Fig. 13. (Color online) (a) RMS difference between surface proﬁleestimated under each SNR and that measured by laser. (b) RMS difference
between surface proﬁle estimated with additional white noise and that
estimated without additional white noise.

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Jpn. J. Appl. Phys. 53, 07KF19 (2014)

Y. Nagai et al.

(a)height [μm]depth [mm]
14
13

4.

10
0
−10
−20
−30
−40

0

1

2

3

4

5

6

7

8

6

7

8

6

7

8

lateral position [mm]height [μm]14depth [mm]
13

(b)

20
10
0
−10
−20
−30
−40

0

1

2

3

4

5

lateral position [mm]height [μm]14depth [mm]
13

(c)

30
20
10
0
−10
−20

0

1

2

3

4

5

lateral position [mm]1st measurement

2nd measurement

3rd measurement

Fig. 14. (Color online) B-mode images of carotid arteries and estimatedluminal surface proﬁle after the application of the proposed ﬁltering obtained
from (a) subject A (23-year-old healthy male), (b) subject B (23-year-old
healthy male), and (c) subject C (24-year-old healthy male).

subject B (23-year-old healthy male), and subject C (24year-old healthy male)] for three cardiac cycles.
Figures 14(a)–14(c) show B-mode images of the carotid
arterial walls of the respective subjects. The frame rate wasset at 165 Hz. In the measurements, RF data were alsoacquired using a 10 MHz linear probe, which was the same asthat used in the basic experiment. Using our method with theproposed Wiener ﬁltering method, the proﬁles of luminal
surfaces were estimated for three cardiac cycles, as shown in
Fig. 14. The optimum control parameter opt of 0.036
was used. From Fig. 14, we conﬁrmed that minute luminal
surface proﬁles of carotid arteries could be estimatedreproducibly for each subject. The SNRs of the ultrasonicecho signals in in vivo measurements shown in Fig. 14 were22.2 dB (subject A), 20.2 dB (subject B), and 24.8 dB(subject C), which were over 20.0 dB. Figure 15 shows theluminal surface proﬁles before and after the application of
the proposed Wiener ﬁltering method obtained from the ﬁrst
measurement for all the subjects (a: subject A, b: subject B,
c: subject C).

Discussion

In the present study, the PSF of the employed ultrasoundsystem was identiﬁed by measuring a ﬁne wire placed on a
ﬂat surface of a silicone rubber plate. Figure 16 shows thepower spectra of the surface proﬁles of the ﬁne wiremeasured using laser (red line) and ultrasound (blue line),
the PSF estimated by averaging the power spectra obtained
from the ultrasound measurements (green line), and the
product of the power spectrum of the surface proﬁle of theﬁne wire measured using laser and the power spectrum ofPSF (pink line). By assuming the power spectrum measured
using laser as the true value, the product of the spectra of thetrue proﬁle and PSF corresponds to the power spectrum
obtained by the ultrasonic measurement. The power spectrumof the product of the spectra of the true proﬁle and PSF was
suppressed in the spatial frequency range over about 4 mm¹1.
The PSF was measured in water, and the noise could be
neglected. Therefore, the effect of the proposed Wiener ﬁlter
was suppressed in the spatial frequency range of over 4 mm¹1
because the difference between the power spectrum obtainedby the ultrasonic measurement and the product of spectraof the true proﬁle and PSF, which corresponds to noise
components, was signiﬁcant in that spatial frequency range.
In addition, the optimal control parameter was determinedby evaluating the RMSEs of the estimated surface proﬁlefrom the true surface proﬁle shown in Fig. 7. However, theRMSEs contained not only the error in each estimatedsawtooth shape but also that in the global shape of thephantom. Therefore, there is a possibility that the determined
optimum control parameter is not the best value to realize ahigh spatial resolution, which should minimize the error ineach estimated sawtooth shape. To determine the optimal
control parameter, it would be better to use a simple phantom,
which, for example, has a single minute rectangular shape on
its surface, to reduce the error caused by the global surface
shape of a phantom. In addition, in Figs. 7 and 11, false
peaks appeared around a lateral position of 1.3 mm in the^estimated surface proﬁle fðxÞobtained using the proposedﬁlter. Although no signiﬁcant false peak was found in thein vivo experimental results, the suppression of these false
peaks should be investigated in the future task. Also, itshould be conﬁrmed that the proposed ﬁlter works appropriately when other phantoms with different surface proﬁles
are used.
In in vivo measurements, the surface proﬁles of the threehealthy subjects were measured reproducibly. The standard
deviations (SDs) of the surface proﬁles measured three times
each for subjects A, B, and C were calculated as 1.1, 3.8, and1.0 µm, respectively. The SD in subject B was larger thanthose in subjects A and C. The reason for this could beconsidered that the amplitude of RF echoes from the luminal
surface of the carotid arterial wall of subject B was low andthe echoes could not be obtained stably during a cardiac
cycle. For example, in the regions of 0–1 and 6.5–8 mm inFig. 12(a) (subject A), the dispersion of the estimated surface
proﬁles became larger and the accuracy of the measurement
was degraded.
Furthermore, for the quantitative evaluation of the luminal
surface roughness, the root mean square roughness (Rq)would be useful. The calculated root mean square rough-07KF19-7© 2014 The Japan Society of Applied Physics

Jpn. J. Appl. Phys. 53, 07KF19 (2014)

Y. Nagai et al.

10

(a)

before filtering g ( x )after filtering f ( x )height [μm]

0
−10
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−30
−40

height [μm]

(b)

0

1

2

3
4
5
lateral position [mm]

8

10
−10

−50

height [μm]

7

30

−30

(c)

6

before filtering g ( x )after filtering f ( x)
0

1

2

3
4
5
lateral position [mm]

6

7

8

6

7

8

50
before filtering g ( x )after filtering f ( x )

40
30
20
10
0
−10
−20

0

1

2

3
4
5
lateral position [mm]Fig. 15. (Color online) Surface proﬁles before and after application of the proposed Wiener ﬁltering obtained from the ﬁrst measurement (blue line: surface
proﬁle after application of the ﬁltering; red line: surface proﬁle before application of the ﬁltering). (a) Subject A. (b) Subject B. (c) Subject C.

power spectrum [dB]

0

−30

−60

−90
laser F (ω x)
PSF H (ω x)

−120

0

5

ultrasound G (ω x)
product F (ω x) H (ωx)

10
spatial frequency [mm−1]

1520Fig. 16. (Color online) Power spectra of surface proﬁles measured bylaser (red line), ultrasound (blue line), PSF (green line), and product of power
spectra of true surface proﬁle and PSF (pink line).

nesses fRqg were 8.1, 10.6, and 8.1 µm for subjects A, B, andC, respectively. The Rq values were about 10 µm. However, it
is expected that, in the measurement of subjects sufferingfrom atherosclerosis, Rq is expected to become larger thanthose of the healthy subjects shown in the present study.
5.

Conclusions

In the present study, a method using a Wiener ﬁlter was
proposed to improve the spatial resolution in the measure-ment of the minute luminal surface proﬁle of the carotid
arterial wall. The point spread function of the employedultrasound system was determined by measuring a ﬁnewire for designing the Wiener ﬁlter. Also, to determine theoptimum parameter, which controls the effect of the Wiener
ﬁlter, the root mean square error between the surface proﬁleof a phantom measured by ultrasound and the true surface
proﬁle measured using laser was evaluated. By applying theidentiﬁed Wiener ﬁlter to the measured surface proﬁle of thephantom, we conﬁrmed that the spatial resolution of themeasurement of the surface proﬁle was improved. Furthermore, the proposed method was applied to in vivo ultrasounddata obtained from the carotid arteries of three healthy
subjects. We conﬁrmed that minute luminal surface proﬁlescould be estimated reproducibly. These results show that a
micron-order minute roughness can be estimated moreaccurately using the proposed ﬁltering method.
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