Japanese Journal of Applied Physics
Vol. 43, No. 5B, 2004, pp. 3220–3226#2004 The Japan Society of Applied Physics

Cross-Sectional Elasticity Imaging of Carotid Arterial Wallin Short-Axis Plane by Transcutaneous UltrasoundNozomi N AKAGAWA, Hideyuki HASEGAWA and Hiroshi K ANAI
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan(Received November 20, 2003; accepted January 30, 2004; published May 28, 2004)

We have developed the phased tracking method [H. Kanai, M. Sato, Y. Koiwa and N. Chubachi: IEEE Trans. UFFC 43 (1996)
791.] for measuring the minute change in thickness during one heartbeat and the elasticity of the arterial wall withtranscutaneous ultrasound. When this method is applied to a plane perpendicular to the axis of the artery (short-axis plane)using a linear-type probe, only an ultrasonic beam which passes through the center of the artery coincides with the direction of
the change in thickness. At other beam positions, the wall motion cannot be accurately tracked because the direction of wall
expansion slips oﬀ the beam. To obtain the cross-sectional image of elasticity in the short-axis plane using transcutaneous
ultrasound, in this paper, the directions of ultrasonic beams are designed so that each beam always passes through the center of
the artery; thus, they always coincide with the direction of the wall expansion. In basic experiments, the accuracy in elasticity
measurement was evaluated using a silicone rubber tube. In in vivo experiments, the minute change in wall thickness wasmeasured along each ultrasonic beam, and the cross-sectional image of elasticity was obtained in the short-axis plane withtranscutaneous ultrasound. [DOI: 10.1143/JJAP.43.3220]
KEYWORDS: elasticity of arterial wall, short-axis plane, small change in wall thickness

1.

Introduction

Recently, the increase in the number of patients suﬀeringfrom myocardial infraction or cerebral infraction has
become a serious social problem. Therefore, it is important
to diagnose atherosclerosis in an early stage because suchcirculatory diseases are mainly caused by atherosclerosis.
Because the elasticity of the arterial wall changes asatherosclerosis develops,1) the evaluation of the regionalelasticity of the arterial wall using ultrasound is useful forthe diagnosis of atherosclerosis.
Ultrasound B-mode imaging is widely used for therepetitive diagnosis of atherosclerosis because it is noninvasive and patients have few diﬃculties. Using theultrasound B-mode image, the shape and the size ofatherosclerotic plaque on the arterial wall can be observedin real time, but it is diﬃcult to evaluate the stability of theplaque quantitatively. To evaluate the vulnerability ofatherosclerotic plaque, we have developed a method, thephased tracking method, for measuring the minute change inwall thickness during one heartbeat and the regionalelasticity of the arterial wall with transcutaneous ultrasound.2–5)
In this method, when the ultrasonic beam is not coincident
with the direction of the change in thickness, the wall motion
cannot be accurately tracked because the direction of wall
expansion slips oﬀ the beam. Therefore, this method iseﬃcient if applied to a plane parallel to the axis of the artery(the long-axis plane as shown in Fig. 1) using a linear-typeprobe because the region where the ultrasonic beam isperpendicular to the arterial wall is wider than thatperpendicular to the axial direction of the artery (the shortaxis plane as shown in Fig. 1). However, it is diﬃcult todiagnose the entire portion of the plaque with only themeasurement in the long-axis plane. Therefore, it isnecessary to measure the elasticity of the plaque in the
short-axis plane in addition to the measurement in the longaxis plane.
E-mail address: hasegawa@us.ecei.tohoku.ac.jp

Fig. 1. Schematic of probe positioning.

A method for measuring the cross-sectional image of theelasticity of the arterial wall in the short-axis plane using
intravascular ultrasonography (IVUS) has been reported. De
Korte and coworkers measured the strain of the arterial wallcaused by the change in inner pressure and calculated theelasticity during cardiac diastole when the motion of the
IVUS probe caused by the pulsatile ﬂow is negligible.6,7)
However, the elasticity can be estimated only during cardiac
diastole with this method. Mita and coworkers developed amethod for measuring the strain during an entire heart cycleby compensating the change in the position of the IVUS
probe caused by pulsatile ﬂow.8) Although these methods areuseful for evaluating the vulnerability of the plaque, they are
not suitable for repetitive diagnosis due to invasion during
catheterization.
When the artery is measured transcutaneously in the
short-axis plane by conventional linear scanning, only anultrasonic beam which passes through the center of theartery coincides with the direction of wall motion (change in

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N. NAKAGAWA et al.

wall thickness). At other beam positions, wall motion cannot
be accurately tracked because the direction of wall expansion slips oﬀ the beam. Watanabe and coworkers showedthat the change in the thickness of the arterial wall can bemeasured accurately in the region of 0:45 mm around theultrasonic beam which passes through the center of theartery by setting the focal depth deeper than the outer surfaceof the posterior wall.9) However, to measure the change inwall thickness accurately within a wider region in the shortaxis plane, each ultrasonic beam should be scanned so as tobe perpendicular to the wall.
In this paper, for the assessment of the cross-sectionalelasticity image in the short-axis plane, the directions of theultrasonic beams are designed so that each beam always
passes through the center of the artery and the direction ofeach beam becomes always perpendicular to the arterial
wall.
2.

Principles

2.1 Beam steering
Figure 2 shows the schematic of beam scanning. In thisstudy, the ultrasonic beams are transmitted in the (N þ 1)
directions and designed so that each beam passes through thecenter, O, of the artery. Under such a setting, the ultrasonicbeams are always perpendicular to the arterial wall if thecross-section of the artery lumen can be assumed to be acircle. The beam scanning system is designed as follows:
The distance, dk , from the center, ck , of the transmit apertureof the k-th beam (k ¼ N=2;    ; 0;    ; N=2) to the centerof the probe is expressed as
dk ¼ 0:4  k

½mm:

ð2:1Þ

The beam angle, k , of the k-th beam is expressed asdkk ¼ arctan
Li½rad;

with a pitch of 1 mm (i ¼ 1; 2;    ; 14). The focal distance,
fk , of the k-th beam is deﬁned by
fk ¼

Li
þ9
cos k

½mm:

ð2:3Þ

In eq. (2.3), 9 mm is added to the distance from ck to O sothat the focal depth becomes deeper than the posterior wall.
The beam width at the posterior wall is increased by thissetting, and a wider beam is more robust against wall motion
which slips oﬀ the beam.10) By changing the distance, Li ,each ultrasonic beam can be perpendicular to the arterial
wall even in the case of a subject with a diﬀerent distancefrom the skin surface to the artery.
2.2 Calculation of change in wall thickness
Using the phased tracking method,2) the velocities of innerand outer surfaces were obtained from the phase shift, ^ðtÞ,
between ultrasonic pulses transmitted and received with arepetition interval T as
c0 ^ðtÞv^ðtÞ ¼ 
;
ð2:4Þ
2!0 T
where !0 and c0 are the center angular frequency of theultrasonic pulse and the speed of sound, respectively.
From the displacements, xA ðtÞ and xB ðtÞ, of two points,
which are set in the arterial wall along an ultrasonic beam,
the change in thickness, hðtÞ, between these two points is
obtained ash^ðtÞ ¼ x^A ðtÞ  x^B ðtÞð2:5Þ
Zt¼ fv^A ðtÞ  v^B ðtÞgdt:
ð2:6Þ
0

3.
ð2:2Þ

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Basic Experiments

where Li is the distance from the surface of the probe to thepoint O. In this paper, Li is variable from 8.5 mm to 21.5 mm

Figure 3 shows the schematic of the basic experimental
system. The change in the wall thickness of a silicone rubber
tube (static elastic modulus: 5.7 MPa, sound speed: 992 m/s,
inner diameter: 10 mm, outer diameter: 13 mm) caused by

Fig. 2. Schematic of beam scanning.

Fig. 3. Schematic of basic experimental setup.

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N. NAKAGAWA et al.

pulsatile ﬂow generated by an artiﬁcial heart is measured in
the short-axis plane with a linear-type probe (center
frequency: 10 MHz). Figures 4(a) and 4(b) show the Bmode images measured by a conventional linear scanning
method and the proposed method (Li ¼ 11:5 mm, the largest
beam angle max ¼ 24:3 ), respectively. In Fig. 4, beams at
positions l1 and l2 measured the same regions of theposterior wall, as measured by beams at positions l01 and l02 .
M-mode images, signals driving the artiﬁcial heart, innerpressures, velocities of inner and outer surfaces and changes
in wall thickness measured at beam positions l1 , l2 , l01 and l02
in Fig. 4 are shown in Figs. 5(a), 5(b), 6(a) and 6(b),respectively.
By linear scanning, as shown in Fig. 5(a-6), the change inthickness measured at the beam position l1 is measured withhigh reproducibility, and its waveform correlates well withthat of the change in inner pressure. At the beam position l2 ,where the ultrasonic beam was not perpendicular to thearterial wall, the amplitude of the change in thickness,shown in Fig. 5(b-6), was diﬀerent from that measured at l1
because the direction of wall expansion due to the pulsatile
ﬂow slipped oﬀ the beam.
On the other hand, using the proposed method, thechanges in the thickness of the silicone rubber tube, at bothbeam positions l01 and l02 were measured with the similar
amplitude, waveform and high reproducibility as shown in
Figs. 6(a-6) and (b-6). At the position l02 , a beam cannot bescanned so as to be perpendicular to the wall by linear
scanning.
Figure 7(a-1) shows the mean value and the standard
deviation of the maximum change in thickness for 5 heartbeats measured in the region of 2:2 mm (the number ofbeams: 27) around the beam which passes through the centerof the silicone rubber tube.
Figure 7(a-2) shows the mean value and the standard
deviation of the elasticity, which is obtained from the
maximum change in thickness and the maximum change in
inner pressure measured by the pressure sensor (NEC 9E02Fig. 5. Basic experimental results obtained by the conventional linear
scanning method: (a) beam position l1 in Fig. 4(a) and (b) beam position
l2 in Fig. 4(a). (1) M-mode image. (2) Signal driving the artiﬁcial heart.
(3) Inner pressure. (4) Small vibration velocity of inner surface. (5) Small
vibration velocity of outer surface. (6) Change in thickness.

Fig. 4. B-mode images of a silicone rubber tube obtained by theconventional linear scanning method (a) and the proposed method (b).

P16). The beam number of 26 corresponds to the beam
position l2 shown in Fig. 4(a).
Using linear scanning, the change in thickness wasmeasured with suﬃcient reproducibility in the region whichcorresponds to 8 beams around the beam which passes
through the center of the tube. As shown in Fig. 7(a-2), withrespect to these 8 beams, mean values of the elastic modulus
agreed well with those of the elastic modulus measured by adiﬀerent static experiment (5.8 MPa), and the standard
deviations were found to be small ((the standard deviation)/(mean value) ranged from 5.1 to 5.8% at these 8 beam
positions).
In other beam positions, mean values of elastic modulus
did not agree well with that obtained by the static experiment, and the standard deviations increased due to adecrease in the signal-to-noise ratio of the reﬂected ultra-Jpn. J. Appl. Phys., Vol. 43, No. 5B (2004)

N. NAKAGAWA et al.

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were calculated as shown in Figure 7(b-2).
In Fig. 7(b-2), the mean value of the elastic modulus
measured at each beam was close to 5.8 MPa which wasmeasured by a diﬀerent static experiment ((the standard
deviation)/(mean value) ranged from 0.7 to 7.2%, andA(l02 )/A(l01 ) is 0.97). The mean values of elastic moduli
measured at all beams for 5 beats was 5.6 MPa.
These results indicate that the elastic modulus of the tube
can be accurately measured in the short-axis plane by the
proposed method.
4.

Fig. 6. Basic experimental results obtained by the proposed method: (a)beam position l01 in Fig. 4(b) and (b) beam position l02 in Fig. 4(b). (1) Mmode image. (2) Signal driving the artiﬁcial heart. (3) Inner pressure. (4)Small vibration velocity of inner surface. (5) Small vibration velocity ofouter surface. (6) Change in thickness.

sonic waves. The ratio, A(l2 )/A(l1 ), of amplitudes, A(l1 ) andA(l2 ), of echoes at the beam positions l1 and l2 in Fig. 4, was
0.33.
Figure 7(b-1) shows the mean value and the standard
deviation of the change in thickness for 5 beats measured
within the entire region of the B-mode image shown in Fig.
7(b-3) (number of beams: 53) using the proposed method,
and the beam number of 27 corresponds to the beam positionl02 shown in Fig. 4(b).
In Fig. 7(b-1), changes in thickness were measured with
suﬃcient reproducibility at all beam positions ((the standard
deviation)/(mean value) ranged from 0.28 to 5.3% at all
beam positions). As well as the case of linear scanning, themean value and the standard deviation of the elastic modulus

In vivo Experiments

The change in the thickness of a human common carotid
artery of a 29-year-old male was measured in the short-axis
plane. The B-mode image measured by the 10 MHz lineartype probe is shown in Fig. 8. The B-mode images weredrawn at the time of the R-wave of the electrocardiogram.
Figures 8(a) and 8(b) show B-mode images measured by theconventional linear scanning method and the proposed
method, respectively. In this experiment, Li ¼ 15:5 mm
and the largest beam angle, max , was 21.2 . In Fig. 8,
beams at positions l1 and l2 measured the same regions ofposterior wall, as measured by beams of the positions l01 andl02 .
As shown in Fig. 8(a), using the conventional linear
scanning method, an echo reﬂected from the lumen-intima
interface was recognized only in the region of about 0.9 mm
around the ultrasonic beam, l1 , which passes through thecenter of the artery. At other beam positions such as l2 ,surrounded by a circle in Fig. 8(a), an echo from the lumenintima interfaces was barely recognized because the ultrasonic beam was not perpendicular to the wall. On the other
hand, as shown in Fig. 8(b), echoes from the lumen-intima
interface were clearly recognized at all ultrasonic beam
positions by controlling each beam so as to be perpendicular
to the wall. As a result, echo from the lumen-intima interface
could be recognized in a wider region of 2.0 mm.
M-mode images, electrocardiograms, velocities at the
intimal side and the adventitial side of the posterior wall, andchanges in wall thickness measured at beam positions l1 , l2 ,l01 and l02 in Figs. 8(a) and 8(b) are shown in Figs. 9(a), 9(b),10(a) and 10(b), respectively. By linear scanning, as shownin Fig. 9(a-5), the change in thickness was measured withhigh reproducibility at the beam position l1 , where theultrasonic beam was perpendicular to the arterial wall.
However, at the beam position l2 , where the ultrasonic beam
was not perpendicular to the arterial wall, the amplitude of
the change in thickness was diﬀerent from that measured at
l1 because the direction of wall expansion due to theheartbeat slipped oﬀ the beam. Moreover, the reproducibility
during heartbeats was made worse by the decrease in thesignal-to-noise ratio of the reﬂected ultrasonic waves. The
ratio, A(l2 )/A(l1 ), of amplitudes A(l1 ) and A(l2 ) of echoes atthe beam positions l1 and l2 in Fig. 8 was 0.059.
As shown in Figs. 10(a-5) and (b-5), using the proposed
method, the changes in the thickness of the arterial wallcaused by the heartbeat were measured with a similar
amplitude, waveform, and high reproducibility at both beam
positions l01 and l02 . (The ratio A(l02 )/A(l01 ) was 0.92.) At thebeam position l02 , a beam cannot be scanned so as to beperpendicular to the wall by linear scanning.

N. NAKAGAWA et al.

µJpn. J. Appl. Phys., Vol. 43, No. 5B (2004)

µ

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Fig. 7. Basic experimental results obtained by (a) the conventional linear scanning method and (b) the proposed method. (1) Meanvalue and standard deviation of the maximum change in wall thickness. (2) Mean value and standard deviation of the elastic modulus.
(3) B-mode image of the corresponding region.

Fig. 8. B-mode images measured by the conventional linear scanning
method (a) and the proposed method (b).

Figure 11(a-1) shows the mean value and the standard
deviation of the change in thickness measured by theconventional linear scanning for 6 heartbeats in the region of1:0 mm (shown in Fig. 11(a-2), number of beams: 15)
around a beam which passes through the center of the artery.
Figure 11(b-1) shows the mean value and the standard

deviation of the change in thickness measured by the
proposed method for 6 heartbeats at all beam positions(number of beams: 30). Figures 11(a-2) and 11(b-2) show
the B-mode images around the regions where changes inthickness were estimated by the conventional linear scanning method and the proposed method, respectively. As
shown in Figs. 11(a) and 11(b), the beam numbers 7 and 15
correspond to the beam positions l01 and l02 shown in Fig. 8,
respectively. In Fig. 11(a-1), the standard deviation of thechange in thickness measured by the linear scanning was
small in the region which corresponds to only 6 beams
around the beam which passes through the center of theartery ((the standard deviation)/(mean value) ranged from
2.6 to 6.4% at the 6 beam positions). At other beam
positions, the standard deviations were large, i.e., reproducibility worse.
Figure 11(b-1) shows the mean value and the standard
deviation of the change in thickness measured by the
proposed method for 6 heartbeats. Changes in wall thickness
were measured with high reproducibility at all beam
positions (width: 2.0 mm) ((the standard deviation)/(meanvalue) ranged from 1.5 to 12.1% at all beam positions). In
Fig. 11(b-1), there are diﬀerences in mean values between
beam positions. It is supposed that changes in wall thickness
are actually inhomogeneous in the circumferential directionJpn. J. Appl. Phys., Vol. 43, No. 5B (2004)

Fig. 9. In vivo experimental results obtained by the conventional linear
scanning method: (a) beam position l1 in Fig. 8(a) and (b) beam position
l2 in Fig. 8(a). (1) M-mode image. (2) Electrocardiogram. (3) Small
vibration velocity on intima. (4) Small vibration velocity on adventitia.
(5) Change in the thickness of the posterior wall.

because of the facts that the accuracy of the proposed
method was validated by basic experiments and themeasured changes in thickness in Fig. 11(b-1) have highreproducibility for 6 heartbeats at all beam positions.
Figures 12(a) and 12(b) show the B-mode images of the
carotid artery obtained by conventional linear scanning at
two diﬀerent angles. The regions shown by the yellow
dotted lines and red dotted lines in Fig. 12(a) correspond to
those shown in Fig. 12(b). Figures 12(c) and 12(d) show thecross-sectional images of elastic modulus measured in two
diﬀerent regions shown by yellow dotted lines and red
dotted lines in Figs. 12(a) and 12(b), respectively. Figures12(c) and 12(d) were measured at the same angles as Fig.
12(a) and 12(b), respectively. The elastic modulus isobtained by the maximum change in thickness and the pulsepressure measured at the upper arm. The resolution of thecross-sectional image of elastic modulus was 80 mm in thedepth direction and 1:43  0:5 in the circumferential
direction.
The region of the carotid artery between two red dotted

N. NAKAGAWA et al.

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Fig. 10. In vivo experimental results obtained by the proposed method: (a)beam position l01 in Fig. 8(b) and (b) beam position l02 in Fig. 8(b). (1) Mmode image. (2) Electrocardiogram. (3) Small vibration velocity on
intima. (4) Small vibration velocity on adventitia. (5) Change in the
thickness of the posterior wall.

lines in Fig. 12(b) was measured. Then, the probe wasrotated about 20 deg along the neck, and the region between
two yellow dotted lines in Fig. 12(a) was measured. It is
recognized that the elasticity images of the regions between
two green dotted lines shown in Figs. 12(c) and 12(d), which
are measured by both measurements, correspond to eachother. The mean value and the standard deviation of themeasured elastic modulus shown in Figs. 12(c) and 12(d)were 0:18  0:14 MPa and 0:2  0:15 MPa, respectively.
From these results, using the proposed method, theelasticity distribution of the arterial wall can be measured
transcutaneously within the wide region in the short-axis
plane.
5.

Conclusion

In this study, the ultrasonic beams are designed so thateach beam is always perpendicular to the arterial wall in the
short-axis plane. In basic experiments using a silicone rubber

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N. NAKAGAWA et al.

Fig. 12. (a) and (b) are B-mode images of the carotid artery in the shortaxis plane obtained by the conventional linear scanning method. (c)Cross-sectional elasticity image measured from the direction shown withyellow lines in (a). (d) Cross-sectional elasticity image measured from thedirection shown with red lines in (b).

tional image of elasticity was obtained in the short-axis
plane by the proposed method.
Fig. 11. (a) Measurement by the conventional linear scanning method. (b)Measurement by the proposed method. (1) Mean value and standard
deviation of the maximum change in wall thickness. (2) B-mode image ofthe corresponding region.

tube, changes in wall thickness were accurately measured
along all scan lines by the proposed method, and themeasured elastic modulus agreed well with that obtained by
the static experiment. In in vivo experiments, the change inthickness could not be accurately measured in the region
where echo from the lumen-intima interface was notrecognized by the conventional linear scanning method.
Using the proposed method, however, the echo from thelumen-intima interface was clearly recognized and thechange in thickness was measured with high reproducibility
along each scan line. From the minute change in wall
thickness measured at each beam position, the cross-sec-

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