Jpn. J. Appl. Phys. Vol. 40 (2001) pp. 4753–4762
Part 1, No. 7, July 2001c
2001
The Japan Society of Applied Physics

Cross-Sectional Elastic Imaging of Arterial Wall Using Intravascular Ultrasonography
Hitoshi M ITA, Hiroshi K ANAI, Yoshiro KOIWA1 , Masataka I CHIKI2 and Fumiaki T EZUKA3
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan
1 Graduate School of Medicine, Tohoku University, Sendai 980-8574, Japan
2 JR Sendai Hospital, Itsutsubashi 1-1-5, Sendai 980-8508, Japan
3 Sendai National Hospital, Miyagino 2-8-8, Sendai 983-8520, Japan(Received November 23, 2000; accepted for publication April 16, 2001)

There have been several studies on the imaging of the distribution of the elasticity of the arterial wall using intravascularultrasonography (IVUS). In those studies, the elasticity is estimated only during ventricular diastole. However, the viscouscharacteristics of the smooth muscle in the media of the arterial wall are also included in the strain measured during diastole.
Alternatively, during systole, the smooth muscle has an almost purely elastic characteristic. However, the IVUS probe moves
greatly due to the arrival of the pulsatile wave at the beginning of the ejection period. Therefore, in this paper, we propose amethod to compensate for the movement of the IVUS probe in order to precisely measure the regional change in thickness of
the arterial wall during one cardiac cycle. Basic experiments using a silicone rubber tube, in which pulsatile flow is generated
by an artificial heart, determined the two-dimensional (2-D) distribution of the regional change in thickness and the elasticity.
The obtained incremental elastic modulus coincides with that determined by the static pressure-strain test. Furthermore, in an
in vitro experiment performed on an extracted human iliac artery, the 2-D distribution of elasticity is obtained and comparedwith pathological results.
KEYWORDS: cross-sectional elastic image, intravascular ultrasonography (IVUS), atherosclerosis

1. Introduction
The number of serious circulatory diseases such as myocardial infarction and cerebral infarction has recently increased.
These diseases are mainly caused by the rupture of an unstable atherosclerotic plaque. Since the elasticity of the arterial wall, on which the atherosclerotic plaque is formed, ishighly dependent on its tissue properties,1) evaluation of theregional elasticity of the arterial wall has the potential for supplying useful information for diagnosis of the vulnerability ofatherosclerotic plaque.
In conventional intravascular ultrasonography (IVUS), thecross-sectional B-mode image of the artery is obtained by inserting the IVUS probe into the artery and rotating the probe
in order to scan the ultrasonic beam. From the B-mode image,the size and shape of the atherosclerotic plaque on the arterial
wall can be observed. For calcified tissue, the intensity of thereflective wave generally increases and is highly apparent on
the B-mode image.2) For lipid-rich plaque or fibrous plaque,however, it is difficult to discriminate them from normal tissue
based on the B-mode image obtained by conventional IVUS.
Several studies have been conducted where cross-sectional
images of the elasticity of the arterial wall have been obtainedusing IVUS.3–6) In those studies, elasticity is estimated only
during ventricular diastole. However, both elastic and viscous characteristics of the smooth muscle in the media, which
is dominant in the arterial wall, are included in the strain
measured during ventricular diastole.7) Therefore, the strain
measurement should be conducted during ventricular systole
when the smooth muscle has an almost purely elastic characteristic. However, the IVUS probe moves greatly due tothe pulsatile flow during the ejection period. Therefore, eachpoint along the arterial wall should be tracked before measuring the change in thickness or the strain.
In addition, when the IVUS probe is inserted into the artery,the inner pressure around the IVUS probe is reduced due tothe occlusion of the arterial lumen caused by blood flow. It

is, therefore, necessary to compensate for the inner pressure
measured near the IVUS probe.
In this experiment, a new method is proposed for accurately measuring the change in thickness of the arterial wallby tracking the wall position. Moreover, a method for compensating for the inner pressure is proposed. The elasticityof the arterial wall is obtained from the measured change inthickness. The proposed method is validated by basic experiments using a water tank to estimate the change in thickness,and the cross-sectional image of the elasticity is obtained in
an in vitro experiment performed on an extracted human iliac
artery.
2. Principle
2.1 Tracking the instantaneous position of the arterial wall
At the beginning of the ejection period, the IVUS probemoves greatly due to the arrival of the pulsatile wave since
the IVUS probe cannot be fixed in place in the artery. The
motion of the IVUS probe causes displacement and rotationin the 2-D cross-sectional image of the IVUS.
In the IVUS system employed in this experiment, the period of one rotation of the IVUS probe, T , is 33 ms, whichis called the frame interval. The maximum displacement of
the IVUS probe in the actual artery is about 10 µm during theframe interval T . Thus, we assume that the cross-sectional
shape of the artery and its center position O(t) do not change
during each short frame interval T .
The initial inner radius R(t0 ; θ0 ) and the wall thickness
h(t0 ; θ0 ) for each angle θ0 (0 ≤ θ0 < 2π ) were set attime t0 , as shown in Fig. 1(a). Multiple measurement points{P(r0 , θ0 )} were set with a constant interval r from the inner surface of the artery along the ultrasonic beam with anangle θ0 at time t0 , where r0 denotes the distance of the point
P(r0 , θ0 ) from the center position O(t0 ) of the IVUS probe,
as shown in Fig. 1(b). Since 360◦ is divided into 512 angles
in the employed IVUS, the resolution θ for detecting the

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H. M ITA et al.

x

P(r0 , 0)

at t= t 0

small region

(r 0,
(t;P
Rin

x
0

P( r 0 , 0)r

r0

) h(t 0 ; 0)y0; 0O(t 0) R(t

R

out

))

0

)
0)
(r 0,
(t;P

y
O(t)

lumen

(a) at t=t

P(r0 , 0)arterial wall

small region
(a)
0,
;P(r
+ T

x
+
at t=t 0

small region

(t)

Rin

)

P(r0 , 0 -

y
r

/2

(t

(r 0 ,
T;P
+
t
(
out

))

0

O(t)

P(r0 , 0)

/2

x

R

))

0

(b) at t=t+ T
/2

r0

0

/2

P(r0 , 0 +y)Fig. 2. Change in the distances of the inner and outer surfaces of the small
region around point P(r0 , θ0 ) from the center position O(t) of the IVUS
probe (a) at t = t and (b) t = T + T .

(b)

O(t 0 )

Fig. 1. Multiple measurement points and small regions. (a) The set of multiple measurement points {P(r0 , θ0 )}. P(r0 , θ0 ) was set at constant interval
r at time t0 . (b) The small regions were set for the change in thicknessh(t; P(r0 , θ0 )) around each point P(r0 , θ0 ) with a thickness of ±r/2
and an angle of ±θ/2.

rotation  during T is 0.7◦ . A small region was set withthickness of ±r/2 and angle of ±θ/2 around each point
P(r0 , θ0 ), as shown in Fig. 1(b). We tracked the movementof each point P(r0 , θ0 ) during T and obtained the change
in thickness of the small region around P(r0 , θ0 ) as follows.
We assumed that during the frame interval T from timet, the IVUS probe rotated by  (t), and that the distancesfrom the center position O(t) of the IVUS probe to the innerand outer surfaces of the small region around point P(r0 , θ0 )changed from Rin (t; P(r0 , θ0 )) to Rin (t + T ; P(r0 , θ0 )) andfrom Rout (t; P(r0 , θ0 )) to Rout (t + T ; P(r0 , θ0 )), respectively, as shown in Fig. 2. The changes in Rin (t; P(r0 , θ0 ))and Rout (t; P(r0 , θ0 )) during T are respectively given by

Rin (t; P(r0 , θ0 )) = Rin (t + T ; P(r0 , θ0 )) − Rin (t; P(r0 , θ0 )),(2.1)

Rout (t; P(r0 , θ0 )) = Rout (t + T ; P(r0 , θ0 )) − Rout (t; P(r0 , θ0 )).

(2.2)

Using the complex cross-correlation function, α(t;  ), between the echo signals reflected by the entire arterial wall at timet and those of the succeeding frame at time t +T , rotation  (t) of the IVUS probe and the displacement, Rin (t; P(r0 , θ0 ))and Rout (t; P(r0 , θ0 )), of point P(r0 , θ0 ) during T are determined as follows.
Let us denote the quadrature-demodulated echo signal reflected by the object at a distance r from the center O(t) of the
IVUS probe and an angle θ at time t by y(t; r, θ ). Rotation  (t) of the IVUS probe during the frame interval T fromt to t + T is determined from that which maximizes the following magnitude of the complex cross-correlation function,α(t;  ), between y(t; r, θ ) received at time t and y(t + T ; r, θ ) received at time t + T :α(t;  ) = 













∗


y
r,
θ
y
+
T
;
r,
θ
+

(t;
)
(t
)


 R(t;θ0 )−L≤r≤R(t;θ0 )+L0≤θ <2π,|y (t; r, θ )|2 |y (t + T ; r, θ +  )|2

R(t;θ0 )−L≤r≤R(t;θ0 )+L0≤θ <2πR(t;θ0 )−L≤r≤R(t;θ0 )+L0≤θ <2π(2.3)

Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7x

H. M ITA et al.

where 0 is equal to 7◦ and L is equal to 225 µm in the following experiments.
The change in thickness, h(t; P(r0 , θ0 )), in the small region around point P(r0 , θ0 ) set at time t0 , is estimated fromthe difference between the displacement Rin (t; P(r0 , θ0 )) at
the inner surface and the displacement Rout (t; P(r0 , θ0 )) at
the outer surface of the small region as

(t)
0

0

4755

h(t; P(r0 , θ0 )) = R out (t; P(r0 , θ0 )) − R in (t; P(r0 , θ0 )).
(2.5)

2L
0

R(t;

0

)

y

o

lumen

arterial wallFig. 3. Estimation of rotation  (t) of the IVUS probe during frame interval T by maximizing the cross-correlational function, α(t;  ), of
the quadrature-demodulated echo signals.

where ±L is the window length in the radial direction aroundthe initial inner surface R(t; θ0 ), as shown in Fig. 3. For various values { } of − 0 ≤  ≤ + 0 , {α(t;  )} are
calculated and rotation  (t) of the IVUS probe during T
is estimated from their maximum values as follows.

α t;  (t) =maxα(t;  ),(2.4)

For this purpose, the instantaneous positions of
Rin (t; P(r0 , θ0 )) and Rout (t; P(r0 , θ0 )) are tracked as follows. From the complex cross-correlation function between
the quadrature-demodulated echo signals, y(t; r, θ ) and y(t +T ; r, θ ), the phase shift, ϕin (t; P(r0 , θ0 )), at the inner surface Rin (t; P(r0 , θ0 )) and the phase shift, ϕout (t; P(r0 , θ0 )),at the outer surface Rin (t; P(r0 , θ0 )) of the small region
around point P(r0 , θ0 ) are estimated byϕ in (t; P(r0 , θ0 )) =  C in (t; P(r0 , θ0 )),(2.6)

ϕ out (t; P(r0 , θ0 )) =  C out (t; P(r0 , θ0 )),(2.7)

where  C in (t; P(r0 , θ0 )) and  C out (t; P(r0 , θ0 )) are thephases of the complex cross-correlation functions,
C in (t; P(r0 , θ0 )) and C out (t; P(r0 , θ0 )), respectively, between
the signal y(t; r, θ ) reflected at point P(r0 , θ0 ) at time t andthe signal y(t + T ; r, θ ) reflected at time t + T , and therotation angle is corrected by  (t) estimated in eq. (2.4).
The complex cross-correlation functions C in (t; P(r0 , θ0 )) andC out (t; P(r0 , θ0 )) are respectively averaged around the surfaces Rin (t; P(r0 , θ0 )) and Rout (t; P(r0 , θ0 )) and they are
given by− 0 ≤ ≤+ 0

C in (t; P(r0 , θ0 )) =1
Din (t; P(r0 , θ0 )) ∗
in (t; P(r0 , θ0 )) + r, θ0 + θ
y t; R×(2.8)− 2δ ≤r≤+ 2δ
− ω2 ≤θ≤+ ω2in (t; P(r0 , θ0 )) + r, θ0 + θ +  (t)×y t + T ; R
C out (t; P(r0 , θ0 )) =,1
Dout (t; P(r0 , θ0 )) ∗
out (t; P(r0 , θ0 )) + r, θ0 + θ
y t; R×(2.9)− 2δ ≤r≤+ 2δ
− ω2 ≤θ≤+ ω2out (t; P(r0 , θ0 )) + r, θ0 + θ +  (t)×y t + T ; R
where

,

 

 

 y t; R
in (t; P(r0 , θ0 )) + r, θ0 + θ 2
Din (t; P(r0 , θ0 )) =  − δ ≤r≤+ δ2

2− ω2 ≤θ≤+ ω2

 

 

 y t + T ; R
in (t; P(r0 , θ0 )) + r, θ0 + θ +  (t) 2 ,× − δ ≤r≤+ δ2

2− ω2 ≤θ≤+ ω2(2.10)

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H. M ITA et al.

 

 

 y t; R
out (t; P(r0 , θ0 )) + r, θ0 + θ 2
Dout (t; P(r0 , θ0 )) =  − δ ≤r≤+ δ2

2− ω2 ≤θ≤+ ω2

 

 

 y t + T ; R
out (t; P(r0 , θ0 )) + r, θ0 + θ +  (t) 2 ,× − δ ≤r≤+ δ
2(2.11)

2− ω2 ≤θ≤+ ω2

and δ and ω respectively denote the window widths for the radial direction and the circumferential direction of the small region around surfaces Rin (t; P(r0 , θ0 )) and Rout (t; P(r0 , θ0 )),as shown in Fig. 4.
Therefore,
theinstantaneous
displacement
Rin (t; P(r0 , θ0 )) at the inner surface and Rout (t; P(r0 , θ0 ))at the outer surface of the small region around P(r0 , θ0 ) during the frame interval T are respectively estimated bycϕ in (t; P(r0 , θ0 )),(2.12)
R in (t; P(r0 , θ0 )) =4π f 0c
ϕ out (t; P(r0 , θ0 )),(2.13)
R out (t; P(r0 , θ0 )) =4π f 0where c denotes the sound velocity in tissue and is assumed tobe 1,540 m/s and f 0 is the center frequency of the employedultrasound (10 MHz).
By repeating these operations from eq. (2.3) to eq.
(2.13) for each frame and by accumulating the resultant instantaneous displacements Rin (t; P(r0 , θ0 )) andRout (t; P(r0 , θ0 )), the distance Rin (t; P(r0 , θ0 )) of the inner surface and Rout (t; P(r0 , θ0 )) of the outer surface of thesmall region from the center position O(t) of the IVUS probe
are respectively tracked as tin (t; P(r0 , θ0 )) = r0 − r +R
R in (t; P(r0 , θ0 )),2
t=tout (t; P(r0 , θ0 )) = r0 + r
R
2


+

t


R out (t; P(r0 , θ0 )).

t=t0(2.15)
From the difference between the estimated instantaneous displacements R in (t; P(r0 , θ0 )) and R out (t; P(r0 , θ0 )), thechange in thickness, h(t; P(r0 , θ0 )), of the small region
around point P(r0 , θ0 ) is given by eq. (2.5).
2.2 Calculation of elasticity of the arterial wall
As shown in the hysteresis loop of Fig. 5, during ventricular
diastole, the arterial wall has both elastic and viscous properties. During ventricular systole, however, the strain causedby the increase in blood pressure has an almost purely elastic
property. In this experiment, therefore, the elastic propertyof the arterial wall is estimated during ventricular systole asfollows.
The instantaneous strain in the radial direction,εr (t; P(r0 , θ0 )), in the small region around point P(r0 , θ0 ) set
at time t0 is obtained byεr (t; P(r0 , θ0 )) =h(t; P(r0 , θ0 )),h d (r0 , θ0 )(2.16)

ECG

0(2.14)
blood pressuret0
Rin

P(r 0, 0)

B

Rout

A

r

Aà

small region

time

t

in

t+ T

(t; P(r 0, 0))

R in (t+ T; P(r 0, 0))

R out (t; P(r 0, 0))(t)(t; P(r 0, 0))out

Rout (t+ T; P(r 0, 0))blood pressure

R in (t; P(r 0, 0))Bsystolediastole
Eà
A

Fig. 4. Estimation of the phase shift, ϕin (t; P(r0 , θ0 )), at the innersurface Rin (t; P(r0 , θ0 )) and ϕout (t; P(r0 , θ0 )) at the outer surface
Rout (t; P(r0 , θ0 )) of the small region around point P(r0 , θ0 ).

E

AàstrainFig. 5. Smooth muscle during one cardiac cycle.

Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7

H. M ITA et al.

where h(t; P(r0 , θ0 )) is estimated using eq. (2.5) andh d (r0 , θ0 ) is the initial thickness of Rout (t0 ; P(r0 , θ0 )) −Rin (t0 ; P(r0 , θ0 )) = r in the small region around point
P(r0 , θ0 ) at end-diastole, when the blood pressure reaches its
minimum. From the ratio of the difference (pulse pressure)p in Pa between the maximum blood pressure and the minimum blood pressure during one cardiac cycle to the maxεr (t; P(r0 , θ0 )) durimum εrm (r0 , θ0 ) of the resultant strain 
ing one cardiac cycle, the elastic modulus E θ (r0 , θ0 ) in Pa in
the circumferential direction of the small region around point
P(r0 , θ0 ) is given by8)

p
1 r
+1
,
(2.17)E θ (r0 , θ0 ) =2 r
εrm (r0 , θ0 )where distribution of the regional stress is not taken in consideration and it is assumed that the stress in the radial direction
is homogeneously applied to the arterial wall.
2.3 Compensating for the measured inner pressure underpulsatile flow
Due to the insertion of the IVUS probe and/or theatherosclerotic plaque at point B in Fig. 6, the cross-sectionalarea, S A , of the lumen at point A is reduced to S B at point
B. Based on the continuity of fluid flow Q along the artery,which is the product of the cross-sectional area Si and theflow velocity vi at point i (i = A, B), the following equation
is given.
S A · v A = S B · v B = Q,

(2.18)

where the flow velocity is assumed to remain constant for the
short duration at the beginning of the ejection period10) andS A > S B . Based on the Bernoulli theorem, on the other hand,
1 2
1
ρv + p A = ρv 2B + p B ,(2.19)
2 A
2where ρ denotes the density of the fluid. From eq. (2.18),
v A < v B . Thus, the pressure p A at point A is higher than theactual pressure p B at the IVUS probe.
From eqs. (2.18) and (2.19), the pressure p B at point B
is obtained from the pressure p A and the flow velocity v A atpoint A as follows.


1 2
SA 2
(2.20)
p B = p A + ρv A 1 −2
SB
Thus, the actual pressure p B at point B is corrected usingpressure p A and velocity v A , both measured at point A.
Figure 7 shows the actual geometry of the measurement

A

l

B
pB

pA
vA

vB

SB

IVUS probeSA
plaquearterial wallFig. 6. Decreased cross-sectional area caused by the occlusion resulting
from the insertion of the IVUS probe and/or the atherosclerotic plaque.

7 cm

A
pA

4757

vA
15mm

C
pC
SC

vC

B
pB

IVUS probe

vB
8mm

SB

SA
pressure sensor
SA=56.3 mm2
S B =14.2 mm2
SC =16.0 mm2= 1000 kg/m3 (density of water)
p A =75 mmHg (max)v C =1.5 m/s(mean of the maximal inner pressure)Fig. 7. Geometry of the IVUS probe at point B and the pressure sensor atpoint A in the silicone rubber tube of Fig. 12.

points in the experimental setup employed in the following
experiments using a water tank for estimating the regionalchange in thickness of a silicone rubber tube. The pressure
sensor and the IVUS probe are placed at point A and point
B, respectively, as shown in Fig. 7. However, the flow velocity at points A and B cannot be measured in the actual
system. Thus, the flow velocity vC at point C is measured using the conventional ultrasonic FFT-Doppler method. In thisexperimental setup, the pressure p B at point B is estimated asfollows. From the continuity of fluid flow Q along the artery,
S A · v A = S B · v B = SC · vC = Q,

(2.21)

where SC is the cross-sectional area at point C. Thus, the flow
velocity v A at point A is given by
vA =

SC
vC .
SA

(2.22)

By substituting this equation into eq. (2.20), the pressure p B
at point B is obtained from the pressure p A measured at point
A corrected by the flow velocity vC measured at point C as
follows.



SC 2
ρ
SC 2 2−(2.23)
pB = p A +
vC
2
SA
SB
2.4 Experimental system
Figure 8 shows the experimental system for measuring thechange in thickness of the arterial wall. The detailed specifications of the IVUS probe of the intravascular ultrasonic diagnostic equipment (Aloka, SSD-550) are shown in Table I.
In the following experiments, the IVUS probe is rotated witha speed of 30 rotations/s and 2π radian is divided into 512
angles.
2.5 Pulse width of the employed ultrasonic beam
The pulse width of the employed ultrasound is measured
using a hydrophone. As shown in Fig. 9(a), the hydrophone
is set at a distance of 3 mm from the center of the IVUS transducer. The hydrophone moved along the x-axis as shown in4758

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H. M ITA et al.

probe
1.3 mmultrasonicdiagnostic equipment

RF signal

quadrature
demodulation

10 MHz CLK.

IVUS probe
1.6 mmpower
dividermixer

function
generator

gate

0.22 mmtransducer

mixer
42 degreefunction cos
generator sin

A/D CLK(ch3,ch4)

A/D convertor
10 MS/s, 12bitlogic input
beam address(8bit)

3 mm

Re

ch1
Im
ch2
VAD drive pulse
ch3pressurech4

GPIB

workstation

Fig. 8. Block diagram of the employed experimental system.

Table I. Specifications of the square transducer of the employed IVUS
probe.
Center frequency f 0
Material
Size
Thickness
Diameter of the IVUS probehydrophone(a)sound pressure [dB]

TRG.

amplifier

100

0

m

-4
-8
-12
(b)

-14
-2

-1

10 MHzPZT
1.6 mm × 1.6 mm
0.22 mm
8 F (2.7 mm)

10x [mm]

2

0.35 s2
10-1

Fig. 9(a) and the sound pressure of the employed ultrasoundis measured at each point as shown in Fig. 9(b). Based onthese results, the aperture of the IVUS transducer is about
42◦ . Moreover, in order to measure the pulse width of theemployed ultrasound, the output voltage of the hydrophone
at x = 0 is measured and shown in Fig. 9(c). Based on thisresult, the pulse width of the ultrasound is 0.35 µs, which corresponds to 270 µm when the velocity of the object is approximately 1,540 m/s. From this pulse width, the window width δemployed in the calculation of the complex cross-correlation
functions C in (t; P(r0 , θ0 )) in eq. (2.8) and C out (t; P(r0 , θ0 ))in eq. (2.9) is determined to be 300 µm in the following experiments. Since the width r along the ultrasonic beam ofthe small region around P(r0 , θ0 ) should be equal to or larger
than the window width δ, the thickness r is determined to
be 300 µm in this experiment.

(c)

-2
0

0.2

0.4
0.6
time [ s]

0.8

1.0

Fig. 9. Beam profile of the employed ultrasound. (a) Relationship between
the positions of the IVUS transducer and the hydrophone. (b) Sound pressure of the employed ultrasound measured by moving the hydrophone at
an interval of 100 µm for each point along the x-axis. (c) Waveform measured by the hydrophone at x = 0.

manually moved

30 rotation/s

IVUS probe
fixed silicone
rubber tube

water

3. Basic Experiments using Silicone Rubber Tubes
3.1 Validation of the tracking operation
To validate the tracking operation described above, theIVUS probe is put into a silicone rubber tube as shown in
Fig. 10 and the IVUS probe is moved manually by about
1 mm in the x–y plane. For the employed silicone rubber
tube, the inner diameter and the outer diameter are 12 mm
and 14 mm, respectively. A stainless steel needle is attachedto the outer surface of the silicone rubber tube.
Figure 11 roughly shows the tracking results. The window
width L in the radial direction in eq. (2.3) is 225 µm. The

yneedlexzFig. 10. Experimental setup for validating the tracking operation of the silicone rubber tube using a needle in a water tank.

Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7

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4759

Fig. 11. Experimental results of the tracking operation, which is manually moved along the tube wall. From (a) to (f), the tracked results
are displayed on the B-mode image at an interval of every 4th frame. The actual position of the needle along the wall is indicated bya blackend area and the estimated position of the needle is marked by a yellow dot.

tracking operation is applied continuously between successively obtained frames. The frame interval T in eq. (2.3)
is 33 ms. Typical frames are selected at an interval of 132 ms(every 4th rotation) and their B-mode images are shown in
Figs. 11(a) to Fig. 11(f). The position of the needle is manually set at the first frame (t = t0 ) and the estimates of theneedle position (black point) are marked by a yellow dot ineach of Figs. 11(a) to 11(f). The position of the needle issuccessfully tracked as shown in these figures.
3.2 Compensating for the inner pressure
In the following basic experiments, the regional change inthickness of a different silicone rubber tube, in which pulsatile

flow is generated by an artificial heart, is measured using thesame IVUS probe as that used in the experiments describedabove. Figure 12 shows the experimental setup. The silicone
rubber tube has already been shown in Fig. 7. From eq. (2.23),
the inner pressure p B at point B is obtained from the pressure
measurement p A at point A and the velocity measurement vC
at point C.
3.3 Measuring the change in thickness and the elasticity
Using the experimental setup shown in Fig. 12, the instantaneous regional change in thickness, h(t; P(r0 , θ0 )), of thesilicone rubber tube caused by the pulsatile flow generated by
the artificial heart is measured by the proposed method de-4760

Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7

drive
unit

safetyreliefcontrol valve
circuitair

artifical
heart

water

H. M ITA et al.

scribed above. The inner pressure p A of the tube is simultaneously measured by the pressure sensor at point A in Figs. 7

air
pump
compliancechamber

inner surface
1cm

silicone tube

22cm
7cm

IVUS
probe

specimenBAsilicone rubber tube
or
extracted arterypressure
detector

controlpulse

outer surface

intravascular ultrasonicdiagnostic equipment

measurement
system1cm

Fig. 12. Experimental setup using a silicone rubber tube or an extracted
human iliac artery for an artificial circulatory system.

IVUS probe

Fig. 13. Cross-sectional image of the silicone rubber tube (B-mode image)displayed by the intravascular ultrasonic equipment.

[V]beam address=41

5V(t) 0(a) signal driving the artificial heart-5[mmHg]
75

p(t) 0(b) inner pressure

-75

[ m]
20

^ in(t;P(r , )) 0R
0 0(c) displacement of inner surface

-20

[ m]
20

^
R out (t;P(r0, 0)) 0(d) displacement of outer surface

-20

[ m]
10

^h(t;P(r , ))00 0(e) change in thickness

-10
0

2

1
time [s]Fig. 14. The change in thickness of the silicone rubber tube in the artificial circulatory system of Fig. 12. (a) The signal driving theartificial heart. (b) The inner pressure of the silicone rubber tube. (c) The displacement of the inner surface of the tube wall. (d)The displacement of the outer surface of the tube wall. (e) The regional change in thickness of the tube obtained using the proposed
method.

Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7

4761

pressure [kPa]

10
8

EIVUS

6

Elinear14.7 mmHg(2.0 kPa)

4
2
0
(a)
-0.00100.001 0.002 0.003
strain00.001 0.002 0.003
strain10
pressure [kPa]and 12. The employed silicone rubber tube is homogeneousand isotropic in elasticity, and the inner diameter and outer
diameter are 8 mm and 11 mm, respectively. Figure 13 shows
the cross-sectional image (B-mode image) of the employedsilicone rubber tube displayed by the intravascular ultrasoundequipment.
Figure 14(a) shows the driving signal of the artificial heart,by which pulsatile flow is generated in the silicone rubber
tube. The inner pressure p A of the tube measured by the pressure sensor is shown in Fig. 14(b). The inner pressure p A
increases due to the arrival of the pulsatile flow. Figures 14(c)and 14(d) show the instantaneous displacement of the innersurface of the tube and that of the outer surface of the tube,
respectively. The instantaneous regional change in thickness, h(t; P(r0 , θ0 )), of the tube estimated using eq. (2.3)
is shown in Fig. 14(e) for θ0 = 2.8◦ and r0 = 5.0 mm. In thisexperiment, the window widths δ in the radial direction andω in the circumferential direction obtained by calculating thecomplex cross-correlation functions, C in (t; P(r0 , θ0 )) in eq.
(2.8) and C out (t; P(r0 , θ0 )) in eq. (2.9), are 300 µm and 21.7◦ ,respectively, as described above. Thickness r of the small
region is 1.5 mm. Although the change in thickness is very
minute, there is reproducibility in the estimation of the change
in thickness during three beats. The waveform of the estimation of the regional change in thickness, h(t; P(r0 , θ0 )), in
Fig. 14(e) is similar to that of the inner pressure p A in the tube
in Fig. 14(b) although they have mutually inverse polarity.
The instantaneous strain εr (t; P(r0 , θ0 )) is obtained fromthe resultant change in thickness, h(t; P(r0 , θ0 )), of the
tube for each direction θ . Figure 15(a) shows the relationshipbetween the inner pressure p A and the estimation of the instantaneous strain, εr (t; P(r0 , θ0 )), of the tube for θ0 = 2.8◦ .
To validate the results estimated by the proposed method
using IVUS, we used a linear-type probe (7.5 MHz) in theconventional ultrasonic system (Toshiba, SSH-140A), andmeasured the change in thickness of the wall from the direction of θ = 0◦ (anterior wall) in a separate experiment basedon the method developed by our group.8) In this experiment,
the IVUS probe maintains the same position in the silicone
tube. The static pressure-strain relationship is shown in Fig.
15(b). The maximum of the inner pressure p A at point A during the ejection period is corrected using eq. (2.23), as shownin Fig. 15(a).
From the average gradient, p/εrm (r0 , θ0 ), which is denoted by the dotted lines in Fig. 15(a), the elastic modulusE θ (r0 , θ0 ) in the circumferential direction obtained using eq.
(2.17) is 2.7 MPa using the IVUS probe, and 2.4 MPa using the linear-type probe. From the separate static pressurestrain test shown in Fig. 15(b), the elastic modulus is 2.4 MPa.
These values are almost the same.
In the same manner, the elastic modulus E(r0 , θ ) is obtained for each direction θ (0 ≤ θ < 2π ). Figure 16 shows
the 2-D distribution of the elastic moduli {E θ (r0 , θ )} in thecircumferential direction of the tube overlaid in the crosssectional image. The measured elastic moduli are almost homogeneous in the circumferential direction θ . Their averagevalue and the standard deviation are 2.7 MPa and 0.4 MPa,
respectively.
According to reported values11) of tissue elasticity, fibrous
tissue is 4.1±5.1 MPa and normal tissue is 0.6±0.7 MPa. The

H. M ITA et al.

8
6
4
2
0
(b)
-0.001

Fig. 15. Relationship between strain εr (t; P(r0 , θ0 )) and pressure p A . (a)The result obtained with the proposed method using the IVUS probe(θ0 = 2.8◦ ) and a linear-type probe (θ0 = 0◦ ). (b) The result obtaiendwith the static pressure-strain test.

Fig. 16. 2-D distribution of the elastic moduli {E θ (r0 , θ)} of the silicone
rubber tube.

difference in elasticity of fibrous tissue from that of normal
tissue is much larger than the standard deviation (0.4 MPa)mentioned above using the proposed method. Thus, the 2-D
distribution of the elastic modulus obtained by the proposed
method has the potential to discriminate the different tissue
properties.

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Jpn. J. Appl. Phys. Vol. 40 (2001) Pt. 1, No. 7

4. In vitro Experiment using an Extracted Human Iliac
ArteryUsing the same experimental setup as the above basic experiment in Fig. 12, the elastic modulus of an extracted humaniliac artery is measured by the proposed method. The thickness of the layer, r, is 300 µm and is equal to the window
width δ of the complex cross-correlational function for estimating the phase shift. Figures 17(a) and 17(b) respectively
show the 2-D distribution of the elastic moduli {E θ (r, θ )}measured by the proposed method and its pathological image, which is visualized by elastica-masson (EM) stain. The
extracted artery is preserved in formalin immediatedly after
the in vitro experiment and is visualized by EM stain. The
EM stain dyes the collagen blue and the smooth muscle pink.
The region with the lipid plaque (A in Fig. 17) has an elas-

H. M ITA et al.

ticity of 0.1–0.3 MPa and is elastically soft compared to theother regions in Fig. 17(a). On the other hand, the soft region(B in Fig. 17) corresponds to a blood clot and the stiff region(C in Fig. 17) corresponds to fibrous tissue. The measured
elastic moduli {E θ (r, θ )} around the fibrous tissue is approximately 5.0–7.0 MPa, which corresponds to the reported valueof the elasticity for the fibrous tissue of 4.1 ± 5.1 MPa.11)
5. Conclusions
In this experiment, we proposed a method for tracking thearterial wall in order to measure the regional change in thickness using IVUS. The proposed method was validated by
the two basic experiments using two different silicone rubber tubes, and a cross-sectional image of the elasticity of theextracted human iliac artery was obtained in the in vitro experiment. The 2-D distribution of the elastic modulus had thepotential for suppling useful information for the diagnosis of
the vulnerability of atherosclerotic plaque.
It is well known that the elastic modulus of the arterial wall
depends on blood pressure. In this experiment, it was assumed that the pressure dependence is negligible. For patientswith hypertension, however, the pressure dependence should
be compensated for. Further investigation of the proposed
method, including this compensation and its clinical application to the local diagnosis of arterial disease and atherosclerosis, is being conducted.
Acknowledgments
We express appreciation to Mr. Keiji Kato and Mr.
Kazuhiro Shiro of Aloka Co., Ltd., Japan for providing the
IVUS equipment. Part of this work is supported by the
Terumo Life Science Foundation.

Fig. 17. Results of in vitro experiments using the extracted iliac artery. (a)The 2-D distribution of the elastic modulus. (b) The pathological image
with EM staining.

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