Jpn. J. Appl. Phys. Vol. 42 (2003) pp. 3255–3261
Part 1, No. 5B, May 2003
#2003 The Japan Society of Applied Physics

Measurement of Change in Wall Thickness of Cylindrical Shell Due to Cyclic Remote Actuation
for Assessment of Viscoelasticity of Arterial Wall
Hideyuki H ASEGAWA, Hiroshi K ANAI, Yoshiro K OIWA1 and James P. B UTLER2
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan1
Graduate School of Medicine, Tohoku University, Sendai 980-8575, Japan
2
Faculty of Public Health, Harvard University, Boston, MA 02115, USA(Received November 18, 2002; accepted for publication March 5, 2003)

To characterize tissues in atherosclerotic plaques, we have developed a method, the phased tracking method, for measuring
the strain (change in wall thickness) and elasticity of the arterial wall. However, some types of tissue, such as lipids and bloodclots, cannot be discriminated from each other based only on elasticity because of the small diﬀerence in their elasticity. For
more precise tissue characterization, we are attempting to measure the regional viscoelasticity. To determine viscoelastic
properties, elastic moduli at multiple frequencies were obtained by generating the change in internal pressure due to remote
cyclic actuation. From basic experiments using a silicone rubber tube, it was found that the change in internal pressure at theultrasonic beam position (for measurement of the elastic modulus) can be generated by remotely applied actuation.
Furthermore, from the resultant minute changes in wall thickness of less than 10 mm measured by the phased tracking method,elastic moduli were obtained at multiple actuation frequencies. [DOI: 10.1143/JJAP.42.3255]
KEYWORDS: remote actuation, change in internal pressure, small change in wall thickness, frequency characteristics,
viscoelasticity, atherosclerosis

1.

Introduction

The steady increase in the number of patients withmyocardial infarction or cerebral infarction, both of which
are considered to be mainly caused by atherosclerosis, isbecoming a serious problem. Therefore, it is important todiagnose atherosclerosis in the early stage. Computed
tomography (CT) and magnetic resonance imaging (MRI)
are employed for the diagnosis of atherosclerosis. Althoughthese methods entail subjecting the patients to physical andmental hardship, they provide information only on the shapeof the artery, such as the diameter of the lumen. However,the diameter of the lumen does not change by early-stage
atherosclerosis.1)
Since there are signiﬁcant diﬀerences between the elastic
moduli of the normal arterial wall and that aﬀected byatherosclerosis,2,3) evaluation of the elasticity of the arterial
wall is useful in the diagnosis of early-stage atherosclerosis.4) In addition to the diagnosis of early-stage atherosclerosis, it is also important to diagnose the vulnerability of
the atherosclerotic plaque because its rupture may cause
acute myocardial infarction and cerebral infarction.5–7) The
evaluation of mechanical properties, such as atherosclerotic
plaque elasticity, is useful for these purposes.
To obtain the circumferential distensibility of the arterial
wall in the plane perpendicular to the axial direction of theartery, measurement methods for the change in arterydiameter have been proposed.8–12) By assuming the arteryto be a cylindrical shell, the average elasticity of the entire
circumference in the plane has been evaluated.13–15) However, the regional elasticity of the atherosclerotic plaquecannot be obtained by these methods because an artery withan atherosclerotic plaque cannot be assumed to be acylindrical shell with uniform wall thickness.
To characterize tissues in the atherosclerotic plaque, ameasurement method for the regional elastic modulus of thearterial wall in patients with or without an atheroscleroticE-mail address: hasegawa@us.ecei.tohoku.ac.jp

plaque is needed. Such a measurement technique for the
spatial distribution of the regional elasticity would be usefulin the diagnosis of the vulnerability of an atherosclerotic
plaque as well as for the diagnosis of early-stage atherosclerosis. For this purpose, we have developed a method, thephased tracking method, for measurement of the smallchange in arterial wall thickness (less than 100 mm) due tothe heartbeat.16–24) From basic experiments, the accuracy inmeasurement of the change in thickness has been found to beless than 1 mm using the phased tracking method.17,20,21)
From the change in thickness measured by our method, theregional strain and the elasticity of the arterial wall can be
noninvasively evaluated.23)
From the measured elastic property, it should be possible
to discriminate tissues in the atherosclerotic plaque, such as
ﬁbrous tissue, lipids, and calciﬁed tissue, from each otherdue to large diﬀerences in their elasticity. However, it isdiﬃcult to discriminate some tissues such as lipids and bloodclots because of the small diﬀerence in their elasticity.25)
Another mechanical property of tissue which has thepotential of providing useful information on discriminationof tissues is viscosity.
In the above-mentioned methods, including our method,the elastic modulus at about 1 Hz due to the heartbeat is
obtained. However, it is diﬃcult to determine viscoelastic
property by measurement of the elastic modulus at only one
frequency. To do so, elastic moduli at multiple frequencies
should be obtained from the changes in wall thickness at
multiple frequencies, which are generated by the change ininternal pressure due to remote cyclic actuation.
In this study, basic experiments using a silicone rubber
tube were conducted to investigate the change in internalpressure at the position where the change in wall thickness ismeasured using ultrasound. Such a change in internalpressure can be generated by remotely applied actuation.
The resultant minute change in wall thickness was measured
by the phased tracking method. Moreover, by sweeping theactuation frequency, the elastic moduli of the tube were
measured at several actuation frequencies. Such frequency

3255

3256

Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5B

H. HASEGAWA et al.

characteristics of the elastic modulus have potential for theassessment of viscoelastic properties.
2.

Principles

2.1

Measurement of change in wall thickness by phased
tracking method
As illustrated in Fig. 1, for measurement of the smallchange in wall thickness, the phase shift of the echo, whichis caused by displacement of an object, is estimated fromtwo consecutive echoes.16) For this purpose, quadrature
M=2
X^

demodulation is applied to the received ultrasonic waves
reﬂected by the object, and then the in-phase and thequadrature signals are A/D-converted. From the demodulated signal, zðt; d þ xðtÞÞ, reﬂected at a depth d þ xðtÞ attime t, where d and xðtÞ are the initial depth set at t ¼ 0 andthe displacement of the object in the depth direction, thephase shift, ðtÞ, between two consecutive echoes isobtained from the complex cross correlation function
calculated for M þ 1 samples in the depth direction aszðt þ T; d þ xðtÞ þ mDÞ  z ðt; d þ xðtÞ þ mDÞm¼M=2;ejðtÞ ¼  M=2

 X



zðt þ T; d þ xðtÞ þ mDÞ  z ðt; d þ xðtÞ þ mDÞm¼M=2
where D and T are the spacing of sample points in the depth
direction and the pulse repetition interval, respectively, and represents the complex conjugate. In the measurement of
the change in thickness, M þ 1 in eq. (2:1) is set at 5(=0.4 ms) in consideration of the pulse length of 0.46 ms.
From the estimated phase shift, ^ðtÞ, the velocity, vðtÞ, ofthe object is obtained asc0 ^ðtÞð2:2Þ
v^ðtÞ ¼ ;
2!0 T
where !0 and c0 are the center angular frequency of theultrasonic pulse and the speed of sound, respectively.
In the estimation of the phase shift using eq. (2:1), theobject position is tracked by the integration of the averagevelocity, vðtÞ, during the pulse repetition interval, T, asx^ðt þ TÞ ¼ x^ðtÞ þ v^ðtÞ  T
c0¼ x^ðtÞ ^ðtÞ:2!0

ð2:3Þ

From the displacements, xA ðtÞ and xB ðtÞ, of two points,
which are set in the arterial wall along an ultrasonic beam,
the small change in thickness, hðtÞ, between these twopoints is obtained aspulse repetitioninterval T
triggerskinsurfacearterial wallv(t)received
signalultrasonictransducer
original
sinusoidal
signaltime (depth)0low–pass filter
Zr(t)

T

Zi(t)
2T

A/D convertor
3T

workstation

4T

time

received signal for eachtransmitted RF pulsev(t)Fig. 1. Schematic diagram of the phased tracking method.

h^ðtÞ ¼ x^A ðtÞ  x^B ðtÞZt¼ fv^A ðtÞ  v^B ðtÞgdt:

ð2:1Þ

ð2:4Þ

0

2.2

Elastic modulus obtained by measured change in wall
thickness
From the measured change in wall thickness, thecircumferential elastic modulus is obtained as follows:23)
Under in vivo conditions, the artery is strongly restricted in
the axial direction. Therefore, a two-dimensional stressstrain relationship can be assumed.
Under such conditions, the radial incremental strain,"r ðtÞ, which is deﬁned by dividing the change in thickness,hðtÞ, by the thickness of the wall, h0 , at the end diastole, isexpressed by the radial and circumferential incremental
stresses, r ðtÞ and  ðtÞ, ashðtÞ"r ðtÞ ¼
h0
ð2:5Þ
r ðtÞ ðtÞ
¼

;
Er
E
where Er , E , and  are the radial and circumferential elastic
moduli and Poisson’s ratio, respectively.
From the change in internal pressure, pðtÞ, the circumferential and the radial incremental stresses, r ðtÞ and ðtÞ, are expressed asr0 ðtÞ ¼ pðtÞ;
ð2:6Þ
h0
1
ð2:7Þ
r ðtÞ ¼  pðtÞ:2
By substituting eqs. (2:6) and (2:7) into eq. (2:5), eq. (2:5)
is rewritten as
1 pðtÞ
r0 pðtÞ
ð2:8Þ
"r ðtÞ ¼ 

:
2 Er
h0 E 
By assuming that the arterial wall is incompressible( 0:5) and elastically isotropic (Er E ), the elastic
modulus, Eh , obtained from the change in wall thickness isdeﬁned as

Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5B

Eh ¼


r 0 1 ErpðtÞ þ
h0 2 E "r ðtÞ


1 r0
pðtÞ
þ1
;
hðtÞ
2 h0

h0

H. HASEGAWA et al.



ð2:9Þ

where r0 is the inner radius at the end diastole.
When we describe the changes in wall thickness, hðtÞ,and internal pressure, pðtÞ, as complex sinusoidal functions, h0  ejð2 fac tÞ and p0  ej2 fac t , at an actuation
frequency, fac , eq. (2:9) can be rewritten as the complex
elastic modulus as
1 r0
p0 j
h
þ1
e ;
E ¼
ð2:10Þ
h0
2 h0h0
where h0 and p0 are the amplitude of the change in wall
thickness and that of the change in internal pressure,respectively, and  is the phase diﬀerence between changes
in internal pressure, pðtÞ, and wall thickness, hðtÞ.
In this paper, the absolute value, jEh j, of the complex
elastic modulus deﬁned by eq. (2:10) is obtained from h0
and p0 , which are measured at each actuation frequency,
fac .
3.

Experimental Setup

3.1 Experimental system for basic experiments
The experimental system for basic experiments using asilicone rubber tube is illustrated in Fig. 2. In this system,
the change in pressure inside the silicone rubber tube is
generated by compressing a rubber balloon, which is placed

safetyrelease

valve

air

pump
air

compliancechamber3257

40 cm away from the ultrasonic probe, with an actuator. Thissystem simulates measurement of the change in wall
thickness of the carotid artery due to the remote actuation
applied at the brachial artery. The change in wall thickness
due to the resulting change in internal pressure is measured
using ultrasound, and the internal pressure is also measured
using a pressure transducer (NEC 9E02-P16) placed inside
the tube. From the measured changes in wall thickness andinternal pressure, elastic modulus can be obtained using eq.
(2:10).
3.2 Measurement system
An ultrasonic pulse (center frequency: 7.5 MHz) wastransmitted and received by the ultrasonic probe of standard
ultrasonic diagnostic equipment (TOSHIBA SSH-140A).
The received signal was ampliﬁed and demodulated. The
resultant in-phase and quadrature signals were simultaneously A/D-converted with a 12-bit A/D converter at a sampling
frequency of 10 MHz. The measured digital signals were
inputted into a computer, and the change in wall thickness
was obtained by applying the phased tracking method,
described in §2.1, to these digital signals.
3.3 Experimental system for pressure diameter test
In order to validate the elastic modulus, jEh j, measured by
the phased tracking method, the elastic modulus of the tube
was also evaluated by testing the relationship between
internal pressure and external diameter. The measurement
system is illustrated in Fig. 3. In this experiment, therelationship between internal pressure and external diameter
was tested by generating the change in the internal pressure
by compressing a rubber balloon using an actuator. Theinternal pressure and the external diameter were measured
using a pressure transducer (NEC 9E02-P16) and a laser line
gauge (KEYENCE VG-035). From the obtained relationship, the elastic modulus in the circumferential direction was
evaluated based on the incremental elastic modulus, Einc ,deﬁned as13,26)

water

Einc ¼

3 r02 re pðtÞ;2 re2  r02 re ðtÞð3:1Þ

ultrasonicprobe
specimenpressure
detector

air
pump
air

measurement
systemspecimenpressuretransducer(9E02–P16)

actuatorpressure
sensor(9E02–P16)

ultrasonicprobe
rubberballoonlaser line
gauge (VG–035)

rubberballoonmeasurement system

specimen

actuator
40 cm

Fig. 2. Experimental system for basic experiments.

Fig. 3. Experimental system employed for testing the relationshipbetween internal pressure, pðtÞ, and external diameter, 2re ðtÞ.

3258

Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5B

H. HASEGAWA et al.

where re and r0 are the external and inner radii at the end
diastole, respectively, and re ðtÞ is the change in external
radius from re .
As in eq. (2:10), eq. (3:1) is rewritten by describing
re ðtÞ ¼ re0  ejð2 fac tÞ and pðtÞ ¼ p0  ej2 fac t as
Einc ¼

3 r02 re p0 je ;2 re2  r02 re0

ð3:2Þ

where re0 is the amplitude of the change in external
diameter.
4.

Basic Experiments Using a Silicone Rubber Tube

Figure 4 shows the B-mode image of a silicone rubber
tube. By setting the ultrasonic beam position as shown in
Fig. 4, the M-mode image was obtained as shown in Fig.
5(a). Figure 5(b) shows the measured internal pressure. From
Fig. 5(b), it is found that the change in internal pressure at
the measurement position can be generated by remotely
applied actuation. By setting two points, A and B, along theultrasonic beam at t ¼ 0 in the M-mode image, thevelocities, vA ðtÞ and vB ðtÞ, of these points were obtainedby the phased tracking method, as shown in Figs. 5(c) and
5(d), respectively. The change in thickness, hðtÞ, of theanterior wall was obtained by integrating the diﬀerence
between these two velocities. In Fig. 5(e), a minute change
in thickness of less than 10 mm was measured at an actuation
frequency of 7.5 Hz. Furthermore, the change in internalpressure, pðtÞ, at other frequencies can be generated bychanging the actuation frequency, fac . In this study, changes
in wall thickness, hðtÞ, and internal pressure, pðtÞ, were
measured at multiple frequencies from 7.5 Hz to 20 Hz as
shown in Fig. 6. To obtain the amplitude of the change inwall thickness, h0 , and that of the change in internalpressure, p0 , at the actuation frequency, fac , the Fouriertransform was applied to those waveforms. Figures 7(a) and7(b) show the amplitude of the change in internal pressure,p0 , and that of the change in wall thickness, h0 ,respectively. The relationship between h0 and p0 are
shown in Fig. 7(c). If the wall is purely elastic, therelationship between p0 and h0 always falls on the same
linear line which passes through the original point. However,in Fig. 7(c), not all of the measured relationships between
p0 and h0 fall on the same linear line. Therefore, it isfound that the wall is not purely elastic.
The frequency characteristic measured using ultrasoundshown in Fig. 7(c) was validated by measurement using thelaser line gauge as described in §3.3. Figure 8 showschanges in internal pressure, pðtÞ, and external diameter,

Fig. 4. B-mode image of the silicone rubber tube.

Fig. 5. (a) M-mode image of the silicone rubber tube. (b) Internalpressure. (c) Velocity, vA ðtÞ, of point A. (d) Velocity, vB ðtÞ, of point B. (e)Change in thickness, hðtÞ, of the anterior wall (actuation frequency of
7.5 Hz).

Fig. 6. Measured changes in internal pressure, pðtÞ, and wall thickness,hðtÞ, at multiple frequencies from 7.5 Hz to 20 Hz. (a) Change ininternal pressure, pðtÞ. (b) Change in wall thickness, hðtÞ.

Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5B

H. HASEGAWA et al.

3259

change in internalpressure ∆ p0 [mmHg]

30
(a)
20
10
0

0

10

actuation frequency f ac [Hz]20change in wall
thickness ∆ h0 [µm]

5
(b)

4
3
2
1
0

10

0

20
actuation frequency f ac [Hz]change in internalpressure ∆ p0 [mmHg]

30
(c)

20

10

2

4
5
3
change in wall thickness ∆ h 0 [µ m]Fig. 7. (a) Amplitude of change in internal pressure, p0 . (b) Amplitudeof change in wall thickness, h0 . (c) Relationship between h0 and p0 .

2re ðtÞ, at each actuation frequency, fac , from 7.5 Hz to
20 Hz. As in Fig. 7, Figs. 9(a) and 9(b) show the amplitudeof the change in internal pressure, p0 , and that of thechange in external diameter, 2re0 , respectively. In Fig.
9(c), not all of the measured relationships between p0 and2re0 fall on the same linear line, as in the ultrasonicmeasurement.
From the amplitude of the change in internal pressure,p0 , and that of the change in wall thickness, h0 , as shownin Fig. 7, the elastic modulus, jEh j, was obtained using eq.
(2:10) at each actuation frequency, fac . The incremental
elastic modulus, jEinc j, was also obtained from the amplitudeof the change in internal pressure, p0 , and that of thechange in external diameter, 2re0 shown in Fig. 9.
In Fig. 10, the elastic moduli, jEh j, measured by theultrasonic phased tracking method are shown by diamonds,
which are plotted as a function of actuation frequency, fac .
The elastic modulus, jEh j, was measured three times at eachactuation frequency with high reproducibility. In Fig. 10, it
can be seen that the elastic modulus, jEh j, increases withactuation frequency, fac . In Fig. 10, the elastic moduli,jEinc j, measured using the laser line gauge are shown bysquares, which are superimposed on results of the ultrasonicmeasurement shown by diamonds. As in the ultrasonicmeasurement, the elastic modulus, jEinc j, is measured threetimes at each actuation frequency, fac . In Fig. 10, the elastic
moduli measured using the laser line gauge have a tendency
similar to those measured by ultrasound. From these results,
it is found that the change in elastic modulus due to theincrease in actuation frequency, fac , can be measured
accurately using the ultrasonic phased tracking method.

Fig. 8. Measured changes in internal pressure, pðtÞ, and external
diameter, 2re ðtÞ, at multiple frequencies from 7.5 Hz to 20 Hz. (a)Change in internal pressure, pðtÞ. (b) Change in external diameter,2re ðtÞ.

30
change in internalpressure ∆ p0 [mmHg]

1

(a)
20
10
0

0

10

60
change in external
diameter 2∆ re0 [µm]0actuation frequency f ac [Hz]

20

(b)

50
40
30
20
10
0

10

0

20
actuation frequency f ac [Hz]30change in internalpressure ∆ p0 [mmHg]

0

(c)

20

10

0

0

10

20

30
50
60
40
change in external diameter 2∆ re0 [µ m]Fig. 9. (a) Amplitude of change in internal pressure, p0 . (b) Amplitudeof change in external diameter, 2re0 . (c) Relationship between 2re0and p0 .

elastic modulus [MPa]3260

Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5B

H. HASEGAWA et al.

4¼ Es þ j2 fac
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ¼ Es2 þ ð2 fac Þ2  ej ;
1 2 fac
 ¼ tan
:
Es

US
3
laser
2

1

0

0

10

20
actuation frequency f ac [Hz]Fig. 10. Elastic moduli, jEh j and jEinc j, at each actuation frequency, fac .
Diamonds and squares show results obtained using ultrasound and thoseobtained using the laser line gauge, respectively.

∆σ(t)

Es

η

∆ε(t)

η: coefficient ofviscosity
Es: elastic modulus
Fig. 11. Voigt model.

5.

Discussion

In Fig. 10, the elastic modulus, jEh j, is observed toincrease with actuation frequency, fac . The reason for this is
as follows: When we assume the Voigt model, which isillustrated in Fig. 11, as a viscoelastic model of the silicone
rubber, the relationship between stress, ðtÞ, and strain,"ðtÞ, is expressed asdð5:1ÞðtÞ ¼ Es  "ðtÞ þ  "ðtÞ;dt
where Es andare the static elastic modulus and theviscosity constant, respectively, and Es and are assumed
not to be dependent on the actuation frequency, fac . In eq.
(5:1), "ðtÞ and ðtÞ correspond to "r ðtÞ ¼ hðtÞ=h0
and ðr0 =h0 þ 1ÞpðtÞ=2 in eq. (2:9), respectively.
By deﬁning ðtÞ ¼ 0  ej2 fac t and "ðtÞ ¼
"0  ejð2 fac tÞ , eq. (5:1) can be rewritten asðtÞ ¼ Es  "ðtÞ þ j2 fac  "ðtÞ;ð5:2Þ

where 0 and "0 are the amplitude of the stress and thatof the strain, respectively.
From eq. (5:2), the complex elastic modulus,
EVoigt ¼ ðtÞ="ðtÞ, is expressed asðtÞ
EVoigt ¼
"ðtÞ

ð5:3Þ
ð5:4Þ

In eq. (5:3), it is found that the absolute value of thecomplex elastic modulus of the Voigt model increases withthe frequency of the applied stress, and such frequency
characteristics can be observed in the elastic modulus
measured using ultrasound, as shown by diamonds in
Fig. 10.
From these results, it is found that the measurement ofelastic moduli, jEh j, at multiple frequencies is useful in theassessment of viscoelastic property. To determine thefrequency characteristic of elastic modulus, jEh j, it isnecessary to induce changes in internal pressure at multiple
frequencies. This study yielded signiﬁcant results demonstrating that changes in internal pressure at multiple
frequencies can be induced by remotely applied actuationand that the resultant minute change in wall thickness can bemeasured by our phased tracking method.
Let us consider the application of the proposed method toactual in vivo measurements. Under in vivo conditions, thedeformation of the arterial wall caused by remote actuation
will be inﬂuenced by tissues surrounding the artery. Whenthe proposed method is applied to the artery deep inside thebody, the inﬂuence of the surrounding tissues will besigniﬁcant. Therefore, we intend to apply the proposed
method to a superﬁcial artery, i.e. the carotid artery. Since
the carotid artery is mainly surrounded by a thin subcutaneous layer of fats and muscles, the inﬂuence of thesurrounding tissues is supposed to be not signiﬁcant because
the artery is covered and restricted by the adventitia (mainlycomposed of collagen ﬁber) which is harder than thesurrounding tissues. Furthermore, using the method previously proposed by our group,23,25) the elastic modulus of afemoral artery was measured in an in vivo experiment before
surgery and an in vitro experiment using a water tank and an
artiﬁcial heart after the surgical extraction. The diﬀerence
between the average elastic modulus before and that after
extraction was about 8% (0:96 0:48 MPa: before extraction, 0:89 0:31 MPa: after extraction). Thus, the inﬂuenceof the surrounding tissues can be neglected in the cases ofsuperﬁcial arteries.
In actual in vivo measurement at the carotid artery, one
way of generating a cyclic change in blood pressure is to
apply actuation on the skin surface above the brachial arteryand measure the change in wall thickness due to remote
actuation at the carotid artery.
To realize the proposed method in the in vivo measurement, a method of measuring the change in blood pressurecaused by remote actuation must be established. It isreported that the waveform of the change in artery diameter
almost corresponds to that of the change in blood pressure
due to the heartbeat.27) Therefore, the change in bloodpressure is supposed to be estimated using the waveform of
the change in artery diameter with blood pressure bycalibration using the systolic and diastolic pressures. However, if the same changes in blood pressure are caused by

Jpn. J. Appl. Phys. Vol. 42 (2003) Pt. 1, No. 5B

remote actuation at diﬀerent frequencies, changes in arterydiameter will be diﬀerent due to the viscoelasticity of thearterial wall. Thus, it is diﬃcult to calibrate the change indiameter. An alternative way of measuring blood pressure is
to use applanation tonometry,28) which measures thecontinuous waveform of blood pressure by applanation of
the radial artery using a pressure detector for measuring thestress caused by the change in blood pressure.
Since the stress-strain relationship of the arterial wall isnonlinear, the elastic property of the arterial wall changes
during one cardiac cycle due to the change in blood pressurecaused by the heartbeat. Therefore, in in vivo measurement,
the amplitude of the change in wall thickness and that of thechange in blood pressure must be estimated during each
short period by applying short-time Fourier transform.
However, it is diﬃcult to measure elastic modulus at
diﬀerent frequencies during one cardiac cycle because theactuation frequency cannot be changed during such a shortperiod. This problem can be overcome by changing actuation frequency per heartbeat. By referring to the electrocardiogram, elastic modulus at diﬀerent frequencies can bemeasured at the same time (= similar blood pressure) during
the cardiac cycle.
As mentioned above, although there are many things to
consider in order to realize the proposed method in an actualin vivo measurement, the most important problem toovercome is the measurement of the change in bloodpressure due to remote actuation. Further investigation isnecessary to measure blood pressure under in vivo conditions.
6.

Conclusions

In this study, basic experiments were performed to assess
the viscoelastic properties of the arterial wall. If the wall isviscoelastic, elastic modulus changes with the frequency of
the applied stress. To investigate the frequency characteristicof elastic modulus, it is necessary to generate changes ininternal pressure at multiple frequencies. In this study, theresults of basic experiments using a silicone rubber tube
demonstrated that changes in internal pressure at multiple
frequencies can be generated by remotely applied actuation.
By measuring the resultant minute change in wall thickness
by our phased tracking method, the frequency characteristicof elastic modulus is obtained. These results suggest that
remote actuation has potential for application to theassessment of viscoelastic properties due to its ability tochange the frequency of the stress.

H. HASEGAWA et al.

3261

1) S. Glagov, E. Weisenberg, C. K. Zarins, R. Stankunavicius and G. J.
Kolettis: New Engl. J. Med. 316 (1987) 1371.
2) R. T. Lee, A. J. Grodzinsky, E. H. Frank, Roger D. Kamm and F. J.
Schoen: Circulation 83 (1991) 1764.
3) H. M. Loree, A. J. Grodzinsky, S. Y. Park, L. J. Gibson and R. T. Lee:
J. Biomech. 27 (1994) 195.
4) P. C. G. Simons, A. Algra, M. L. Bots, D. E. Grobbee and Y. van derGraaf: Circulation 100 (1999) 951.
5) E. Falk, P. K. Shah and V. Fuster: Circulation 92 (1995) 657.
6) M. J. Davies: Circulation 94 (1996) 2013.
7) J. Golledge, R. M. Greenhalgh and A. H. Davies: Stroke 31 (2000)
774.
8) A. P. G. Hoeks, C. J. Ruissen, P. Hick and R. S. Reneman: UltrasoundMed. Biol. 11 (1985) 51.
9) T. Länne, H. Stale, H. Bengtsson, D. Gustafsson, D. Bergqvist, B.
Sonesson, H. Lecerof and P. Dahl: Ultrasound Med. Biol. 18 (1992)
451.
10) A. P. G. Hoeks, X. Di, P. J. Brands and R. S. Reneman: UltrasoundMed. Biol. 19 (1993) 727.
11) P. J. Brands, A. P. Hoeks, M. C. Rutten and R. S. Reneman:
Ultrasound Med. Biol. 22 (1996) 895.
12) J. M. Meinders, P. J. Brands, J. M. Willigers, L. Kornet and A. P. G.
Hoeks: Ultrasound Med. Biol. 27 (2001) 785.
13) D. H. Bergel: J. Physiol. 156 (1961) 445.
14) L. H. Peterson, R. E. Jensen and J. Parnell: Circ. Res. 8 (1960) 622.
15) K. Hayashi, H. Handa, S. Nagasawa, A. Okumura and K. Moritake: J.
Biomech. 13 (1980) 175.
16) H. Kanai, M. Sato, Y. Koiwa and N. Chubachi: IEEE Trans. Ultrason.,Ferroelect., Freq. Control 43 (1996) 791.
17) H. Kanai, H. Hasegawa, N. Chubachi, Y. Koiwa and M. Tanaka: IEEE
Trans. Ultrason., Ferroelect., Freq. Control 44 (1997) 752.
18) H. Hasegawa, H. Kanai, N. Chubachi and Y. Koiwa: Electron. Lett. 33(1997) 340.
19) H. Hasegawa, H. Kanai, N. Chubachi and Y. Koiwa: Jpn. J. Med.
Ultrason. 24 (1997) 851.
20) H. Hasegawa, H. Kanai, N. Hoshimiya, N. Chubachi and Y. Koiwa:
Jpn. J. Appl. Phys. 37 (1998) 3101.
21) H. Kanai, K. Sugimura, Y. Koiwa and Y. Tsukahara: Electron. Lett. 35(1999) 949.
22) H. Hasegawa, H. Kanai, N. Hoshimiya and Y. Koiwa: Jpn. J. Appl.
Phys. 39 (2000) 3257.
23) H. Hasegawa, H. Kanai, N. Hoshimiya and Y. Koiwa: Jpn. J. Med.
Ultrason. 28 (2001) 3.
24) H. Hasegawa, H. Kanai and Y. Koiwa: Jpn. J. Appl. Phys. 41 (2002)
3563.
25) H. Hasegawa, H. Kanai, Y. Koiwa, M. Ichiki and F. Tezuka: to be
published in IEEE 2002 Int. Ultrason. Symp. Proc. (2002).
26) A. G. Hudetz: J. Biomech. 12 (1979) 651.
27) M. Sugawara, H. Furuhata, S. Kikkawa, S. Suzuki, S. Ohnishi, W.
Takabayashi, N. Suzuki, T. Kurokawa, S. Yoshimura and C. G. Caro:
Jpn. J. Med. Electron. Biol. Eng. 21 (1983) Suppl. 429.
28) J. D. Cameron, B. P. Mcgrath and A. M. Dart: J. Am. Coll. Cardiol. 32(1998) 1214.