Japanese Journal of Applied Physics
Vol. 43, No. 5B, 2004, pp. 3197–3203#2004 The Japan Society of Applied Physics

Measurement of Elastic Moduli of the Arterial Wall at Multiple Frequencies
by Remote Actuation for Assessment of Viscoelasticity
Hideyuki H ASEGAWA and Hiroshi K ANAI
Graduate School of Engineering, Tohoku University, Sendai 980-8579, Japan(Received November 7, 2003; accepted February 5, 2004; published May 28, 2004)

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 due to the small diﬀerence in their elasticity. For more
precise tissue characterization, we have measured the regional viscoelasticity. To obtain the viscoelasticity, in this study,
elastic moduli at multiple frequencies were measured with ultrasound by generating the change in internal pressure due toremote cyclic actuation. Furthermore, the viscoelasticity of the arterial wall was estimated from the measured elastic moduli at
multiple actuation frequencies. [DOI: 10.1143/JJAP.43.3197]
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 caused primarily 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. They
subject patients to physical and mental hardships, and they
provide information only on the shape of the artery, such as
the diameter of the lumen. However, the diameter of thelumen is not changed by early-stage atherosclerosis.1)
Because signiﬁcant diﬀerences exist between the elastic
moduli of normal arterial walls and those aﬀected byatherosclerosis,2,3) the evaluation of the elasticity of thearterial wall is useful for the diagnosis of early-stage
atherosclerosis.4) In addition, it is also important to assess
the vulnerability of the atherosclerotic plaque, because therupture of the plaque may cause acute myocardial infarction
and cerebral infarction.5–7) The evaluation of mechanicalproperties, such as the elasticity of the atherosclerotic
plaque, is useful for these purposes.
To obtain the circumferential distensibility of the arterial
wall in the plane perpendicular to the axial direction of theartery, methods for the measurement of the change in arterydiameter have been proposed.8–12) By assuming the artery to
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 withatherosclerotic plaques cannot be assumed to be a cylindricalshell with uniform wall thickness.
To characterize the tissue in the atherosclerotic plaque, amethod for the measurement of the regional elastic modulusof the arterial wall in patients with or without atherosclerotic
plaques is needed. Such a technique for the measurement of
the spatial distribution of the regional elasticity would be
useful for the assessment of the vulnerability of theatherosclerotic plaque as well as for the diagnosis of earlystage atherosclerosis. For this purpose, we have developed amethod, the phased tracking method, for the measurement ofsmall changes in the thickness of the arterial wall (less than
100 mm) due to the heartbeat.16–24) From basic experiments,
the accuracy in the measurement of the change in thickness
has been less than 1 mm using the phased tracking
method.17,20,21) From the change in thickness measured byour method, the regional strain and the elasticity of thearterial wall can be evaluated noninvasively.23,25)
From the measured elastic property, it should be possible
to discriminate tissues in the atherosclerotic plaque, such as
ﬁbrous tissue, lipids, and calciﬁed tissue, due to large
diﬀerences in their respective elasticities. However, it isdiﬃcult to discriminate some tissues such as lipids and bloodclots because of small diﬀerences in their elasticities. An
additional mechanical property of tissue with the potential toprovide useful information for the discrimination of tissues
is viscosity.
In the methods mentioned, including our method, theelastic modulus at about 1 Hz due to heartbeat is obtained.
However, it is diﬃcult to determine the viscoelasticity fromthe measurement of the elastic modulus at only one
frequency. To obtain the viscoelasticity, we measured theelastic moduli from changes in wall thickness at multiple
frequencies generated by the change in internal pressure duepulse repetitioninterval T
triggerskinsurfacearterial wallv(t)received
signalultrasonictransducer
original
sinusoidal
signaltime (depth)0lowpass 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.

E-mail address: hasegawa@us.ecei.tohoku.ac.jp
3197

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

H. HASEGAWA and H. KANAI

to remote cyclic actuation.26) The elastic modulus increased
with actuation frequency.
In this study, by assuming the Voigt model as a
viscoelastic model of the wall, the static elastic modulus
and the viscosity constant of a silicone rubber tube are
estimated from the elastic moduli measured at multiple
actuation frequencies. The estimated static elastic modulus
and viscosity constant are validated by comparison withthose measured by a laser line gauge. Furthermore, theviscoelasticity of a human carotid artery is measured byapplying remote actuation at the brachial artery.
2.

Principles

change in wall thickness, the phase shift of the echo causedby displacement of an object is estimated from twoconsecutive echoes.16) For this purpose, quadrature demodulation is applied to the received ultrasonic waves reﬂectedby the object and the analog-to-digital (A/D) conversion isapplied to the in-phase and the quadrature signals. From thedemodulated signal, zðt; d þ xðtÞÞ, reﬂected at a depth d þxðtÞ at a time t, where d and xðtÞ are the initial depth set at
t ¼ 0 and the displacement of the object in the direction of
the depth, the phase shift, ðtÞ, between two consecutive
echoes is obtained from the complex cross-correlation
function calculated for M þ 1 samples in the direction of
the depth as follows:

2.1

Measurement of the change in wall thickness by thephased tracking method
As illustrated in Fig. 1, for the measurement of the small
M=2X^zðt þ T; d þ xðtÞ þ mDÞ  z ðt; d þ xðtÞ þ mDÞm¼M=2;e jðtÞ ¼  M=2

 X



zðt þ T; d þ xðtÞ þ mDÞ  z ðt; d þ xðtÞ þ mDÞm¼M=2

ð2:1Þ

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.
bðtÞ, the velocity, vðtÞ,From the estimated phase shift, of the object is obtained as follows:bðtÞ
c 0 b;ð2:2ÞvðtÞ ¼ 
2!0 T

Under such conditions, the radial incremental strain,"r ðtÞ, which is deﬁned by dividing the change in thickness,hðtÞ, by the thickness of wall, h0 , at the end of diastole, isexpressed by the radial and circumferential incremental
stresses, r ðtÞ and  ðtÞ, as follows:hðtÞ"r ðtÞ ¼
h0
r ðtÞ ðtÞ
¼

;
ð2:5Þ
Er
E

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 from eq. (2.1), theposition of the object is tracked by the integration of theaverage velocity, vðtÞ, during the pulse repetition interval, T,
as follows:

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 radial incremental stresses, r ðtÞ and  ðtÞ,are expressed as follows:r0 ðtÞ ¼ pðtÞ;
ð2:6Þ
h0
1
ð2:7Þ
r ðtÞ ¼  pðtÞ;2bxðt þ TÞ ¼ bxðtÞ þ bvðtÞ  Tc0 b¼bxðtÞ 
ðtÞ:
2!0

ð2:3Þ

From the displacements, xA ðtÞ and xB ðtÞ, of two points set
in the arterial wall along an ultrasonic beam, the smallchange in thickness, hðtÞ, between these two points is
obtained as follows:bhðtÞ ¼ b
xA ðtÞ  b
xB ðtÞ
Zt¼ fb
vA ðtÞ  bvB ðtÞgdt:
ð2:4Þ
0

2.2

Elastic modulus obtained by measuring the change inwall thickness
From the measured change in wall thickness, the circumferential elastic modulus is obtained as follows:23) Under invivo conditions, the artery is strongly restricted in the axial
direction. Therefore, a two-dimensional stress-strain relationship can be assumed.

where r0 is the inner radius at the end of diastole.
By substituting eqs. (2.6) and (2.7) into eq. (2.5), eq. (2.5)
is rewritten as follows:"r ðtÞ ¼ 

1 pðtÞ
r0 pðtÞ

:2 Er
h0 E 

ð2:8Þ

By assuming that the arterial wall is incompressible(  0:5), eq. (2.8) can be rewritten as follows:
1 r 0 Er
pðtÞ
E ¼
þ
:
ð2:9Þ
2 h0 E "r ðtÞ
Furthermore, by assuming isotropy (Er  E ), the elastic
modulus, Eh , obtained from the change in wall thickness isdeﬁned as follows:Jpn. J. Appl. Phys., Vol. 43, No. 5B (2004)

Eh ¼

H. HASEGAWA and H. KANAI



1 r0
pðtÞ
þ1
:
hðtÞ
2 h0

h0

ðtÞ ¼ Es  "ðtÞ þ j2fac   "ðtÞ;ð2:10Þ

In the literature,27) the Er =E of the arterial wall isreported to be 0.8. By substituting r0 =h0 ¼ 4:7 andpðtÞ="r ðtÞ ¼ 200 kPa as typical values into eqs. (2.9)
and (2.10), the error in Eh from E at Er =E ¼ 0:8 is about
3%.23) This error is negligible.
When we describe the change in wall thickness, hðtÞ,and the change in internal pressure, pðtÞ, as complex
sinusoidal functions, h0  ejð2fac t Þ and p0  ej2fac t , at an
actuation frequency, fac , eq. (2.10) can be rewritten as thecomplex elastic modulus as follows:


1 r0
p0 j
h
þ1
e ;
ð2:11Þ
E ð fac Þ ¼
h0
2 h0
h0
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, jEh ð fac Þj, of the complex
elastic modulus deﬁned by eq. (2.11) is obtained from h0
and p0 , which are measured at each actuation frequency,
fac .
2.3 Estimation of viscoelasticity using the Voigt modelIn our previous study,26) it was found that the elastic
modulus, jEh ð fac Þj, increased with actuation frequency, fac .
The reason for this can be thought of as follows: When we
assume the Voigt model, which is illustrated in Fig. 2, as a
viscoelastic model of the wall, the relationship between the
stress, ðtÞ, and the strain, "ðtÞ, is expressed as follows:In eq. (2.14), the absolute value of the complex elastic
modulus of the Voigt model increases with the frequency of
the applied stress, and such frequency characteristics can beobserved in the elastic modulus measured by ultrasound.26)
In this study, the static elastic modulus, Es , and the viscosity
constant, , are estimated by ﬁtting jEVoigt ð fac Þj to jEh ð fac Þj
measured at multiple actuation frequencies, 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. 3. In this system, thechange in pressure inside the silicone rubber tube is
generated by compressing a rubber balloon, which is placed
at a position 40 cm away from an ultrasonic probe, with anactuator. This system simulates the measurement of thechange in the wall thickness of the carotid artery due toremote actuation applied at the brachial artery. The change
in wall thickness due to the resulting change in internalpressure is measured using ultrasound, and the internalpressure is also measured by a pressure transducer (NECsafetyrelief

valve

air

pump
air

compliancechamberwaterultrasonicprobe
specimenpressure
detector

measurement
system

Es

η

∆ε(t)

η: coefficient ofviscosity
Es : elastic modulus
Fig. 2. Voigt model.

ð2:13Þ

where 0 and "0 are the amplitude of the stress and thatof the strain, respectively.
From eq. (2.13), the complex elastic modulus,
EVoigt ð fac Þ ¼ jEVoigt ð fac Þjej ¼ ðtÞ="ðtÞ, is given by
qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
jEVoigt ð fac Þj ¼ Es2 þ ð2fac Þ2 ;ð2:14Þ

2fac 
¼ tan1:
ð2:15Þ
EsdðtÞ ¼ Es  "ðtÞ þ   "ðtÞ;ð2:12Þ
dt
where Es and  are the static elastic modulus and theviscosity constant, respectively, and Es and  are assumed to
be unchanged by the actuation frequency, fac . In eq. (2.12),
"ðtÞ and ðtÞ correspond to "r ðtÞ ¼ hðtÞ=h0 andðr0 =h0 þ 1ÞpðtÞ=2 in eq. (2.10), respectively.
By deﬁning ðtÞ ¼ 0  ej2fac t and "ðtÞ ¼ "0 
jð2fac t Þe, eq. (2.12) can be rewritten as follows:

∆σ(t)

3199

actuatorpressure
sensor(9E02 − P16)

ultrasonicprobe
rubberballoonspecimen

40 cm

Fig. 3. Experimental system for basic experiments.

3200

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

H. HASEGAWA and H. KANAI

9E02-P16) placed inside the tube. From the measuredchanges in wall thickness and internal pressure, the elastic
modulus can be obtained by eq. (2.11).
3.2 Measurement system
An ultrasonic pulse (center frequency: 7.5 MHz) wastransmitted and received by an ultrasonic probe in standard
ultrasonic diagnostic equipment (TOSHIBA SSH-140A).
The signal received was ampliﬁed and demodulated. The
resultant in-phase and quadrature signals were simultaneously A/D converted with a 12-bit A/D converter at asampling frequency of 10 MHz. The measured digital signals
were transfered to a computer, and the change in wall
thickness was obtained by applying the phased tracking
method to these digital signals.
3.3 Experimental system for pressure diameter test
To validate the elastic modulus, jEh ð fac Þj, measured by thephased tracking method, the elastic modulus of the tube wasalso evaluated by testing the relationship between internalpressure and external diameter. The measurement system is
illustrated in Fig. 4. In this experiment, the relationshipbetween internal pressure and external diameter was tested
by generating the change in internal pressure by compressing a rubber balloon using an actuator. Internal pressure andexternal diameter were measured by a pressure transducer(NEC 9E02-P16) and a laser line gauge (KEYENCE VG035), respectively. From the relationship obtained, theelastic modulus in the circumferential direction was evaluated by the incremental elastic modulus, Einc , deﬁned asfollows:28)
Einc ¼

3 r02 re pðtÞ;2 re2  r02 re ðtÞð3:1Þ

Einc ð fac Þ ¼

4.

Basic Experiments Using a Silicone Rubber Tube

4.1 Estimation of viscoelasticity with ultrasoundFigure 5 shows the B-mode image of a silicone rubber
tube. By setting the ultrasonic beam at the position shown in
Fig. 5, the M-mode image was obtained as shown in Fig.
6(a). Figure 6(b) shows the measured internal pressure. From
Fig. 6(b), it was 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 a time t ¼ 0 in the M-mode image, thevelocities, vA ðtÞ and vB ðtÞ, of these points were obtained by
the phased tracking method as shown in Figs. 6(c) and 6(d).
The change in the thickness, hðtÞ, of the anterior wall was
obtained by integrating the diﬀerence between these twovelocities. In Fig. 6(e), a minute change in the thickness of

1 cm
beam position
point A(outside)

specimenpressuretransducer(9E02 − P16)

laser line
gauge (VG − 035)

rubberballoonlumen

Fig. 5. B-mode image of a silicone rubber tube.

AB(a) M − mode

65
mmHg 5035
1mm/s 0–1
1mm/s 0
–1
5
µm 0
–5

(b) internal pressure(c) velocity at A(d) velocity at B

0measurement system
actuator
Fig. 4. Experimental system employed for testing the relationshipbetween the internal pressure, pðtÞ, and the external diameter, 2re ðtÞ.

anterior
wall

point B(inside)

1 cm

3.75 mm

air

ð3:2Þ

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

where re and r0 are the external radius and the inner radius at
the end of diastole, respectively, and re ðtÞ is the change inexternal radius from re .
As with eq. (2.11), eq. (3.1) is rewritten by describing
re ðtÞ ¼ re0  ejð2fac t Þ and pðtÞ ¼ p0  ej2fac t as follows:

air
pump

3 r02 re p0 j
e ;2 re2  r02 re00.5(e) change in thickness
1
1.5
time [s]Fig. 6. (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).

70
60
50
40
30

(a)

4
measured3

estimated2
Es =1.3 MPaη =24 kPa·s

1mean internal pressure [mmHg]

H. HASEGAWA and H. KANAI

elastic modulus [MPa]elastic modulus [MPa]mean internal pressure [mmHg]

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

70
60
50
40
30

(a)

4
measuredestimated32
Es =1.5 MPa

1

η =25 kPa·s

(b)
0

0

5

10

3201

(b)
0

15
20
actuation frequency [Hz]

0

5

10

15
20
actuation frequency [Hz]Fig. 7. (a) Mean internal pressure. (b) Elastic moduli, jEh ð fac Þj, measured
at each actuation frequency, fac , using ultrasound (plot), and the estimatedVoigt model (solid curve).

Fig. 8. (a) Mean internal pressure. (b) Elastic moduli, jEinc ð fac Þj,
measured at each actuation frequency, fac , using the laser line gauge(plot), and the estimated Voigt model (solid curve).

less than 10 mm was measured at an actuation frequency of
7.5 Hz. Furthermore, the change in internal pressure, pðtÞ,at other frequencies can be generated by changing theactuation 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. To obtain
the amplitude of the change in wall thickness, h0 , and thatof the change in internal pressure, p0 , at the actuation
frequency, fac , the Fourier transform was applied to those
waveforms. The elastic modulus, jEh ð fac Þj, at each actuation
frequency, which is shown by diamonds in Fig. 7, wasobtained from the estimated h0 and p0 . The static elastic
modulus, Es , and the viscosity constant, , were estimated asEs ¼ 1:3 MPa and  ¼ 25 kPas, respectively, by minimizing
the mean squared diﬀerence between eq. (2.14) and jEh ð fac Þj
measured by ultrasound. In Fig. 7, the estimated Voigt
model is shown by a solid curve.

The static elastic modulus, Es , and the viscosity constant,, measured by ultrasound (Es ¼ 1:3 MPa,  ¼ 25 kPas)were in good agreement with those obtained by the laser line
gauge (Es ¼ 1:5 MPa,  ¼ 25 kPas). From these results, it isfound that the viscoelasticity of the silicone rubber tube canbe estimated using the ultrasonic phased tracking method
combined with remote actuation.
Comparison with the static elastic modulus measured
by the static experiment
The measured static elastic modulus, Es , by ultrasoundwas also validated by comparing it with Es obtained by thediﬀerent static experiment.
In this experiment, the change in internal pressure wasincreased using an air pump. Figure 9 shows the relationshipbetween the change in wall thickness measured by ultra100

4.2

internal pressure [mmHg]

Comparison with results obtained using a laser line
gauge
The static elastic modulus and the viscosity constantmeasured by ultrasound as shown in Fig. 7 were validated bymeasurements using the laser line gauge.
In Fig. 8, the elastic modulus, jEinc ð fac Þj, which was
obtained by measuring the change in internal pressure,pðtÞ, and the change in external diameter, 2re ðtÞ, using apressure transducer and a laser line gauge, respectively, isshown by diamonds. The static elastic modulus, Es , and theviscosity constant, , were estimated to be Es ¼ 1:5 MPa and ¼ 25 kPas, respectively, by minimizing the mean squared
diﬀerence between eq. (2.14) and jEinc ð fac Þj measured usinga laser line gauge.

4.3

80

60

40

20

0

0

5

10

15
20
change in thickness [ µm]25

Fig. 9. Relationship between the change in wall thickness, hðtÞ, and thechange in internal pressure, pðtÞ.

3202

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

H. HASEGAWA and H. KANAI

3.75 mm

1 cm
anterior wall(a) M−mode

A
B

lumen
(b) electrocardiogram

5.

In vivo Measurement at a Human Carotid Artery(e) velocity at B

00.5

time [s]Fig. 11. (a) M-mode image of a human carotid artery. (b) Electrocardiogram. (c) Blood pressure measured at the radial artery using anapplanation tonometer. (d) Velocity of the intimal side. (e) Velocity of
the adventitial side.

102
(1−a)
100
98

0.2
(1−b)
0
−0.2

0.6 mm/s
outside

96
−0.4
94
−0.6

92
1.7 mmHg

0.72 mm/s

−0.8

90

inside
88
0.6

0.7

−1
0.6

0.8
0.9
time from R−wave [s]

86

0.8
0.9
time from R−wave [s]

0.7

0.4
(2−a)

84
82
1.5 mmHg

80

(2−b)
0.2
0

0.93 mm/s

−0.2
−0.4

78

−0.6

76

In in vivo experiments, remote actuation was applied fromthe skin surface at the brachial artery using an actuator, andthe change in wall thickness due to the remote actuation wasmeasured at the carotid artery.
Figure 10 shows the B-mode image of the carotid artery ofa 29-year-old male. By setting the ultrasonic beam at theposition shown in Fig. 10, the M-mode image was obtained
as shown in Fig. 11(a). Figure 11(c) shows the bloodpressure measured at the radial artery with an applanation
tonometer (COLIN JENTOW7700). By setting two points,
A (intimal side) and B (adventitial side), along the ultrasonicbeam at the R-wave of the electrocardiogram shown in Fig.
11(b), the velocities, vA ðtÞ and vB ðtÞ, of these points wereobtained by the phased tracking method as shown in Figs.
11(d) and 11(e), respectively. In Figs. 11(d) and 11(e), there
are velocity components caused by remote actuation (10 Hz).
Furthermore, changes in internal pressure, pðtÞ, at otherfrequencies were generated by changing the actuation
frequency, fac . In this in vivo measurement, changes in wall
thickness, hðtÞ, and internal pressure, pðtÞ, were measured at frequencies of 7.5 Hz, 10 Hz, and 12.5 Hz.
In cardiac systole, there are velocity components causedby the heartbeat, and it is diﬃcult to discriminate those fromthe velocity component caused by remote actuation. Therefore, in this study, the amplitude of velocity components
caused by remote actuation was measured in cardiac
diastole. Figures 12(1), 12(2), and 12(3) show internalpressures and velocities at the intimal and adventitial sides
approximately 0.6 s after the R-wave of the electrocardiogram at actuation frequencies of 7.5 Hz, 10 Hz and 12.5 Hz,

1velocity [mm/s]

sound and the change in internal pressure measured by thepressure transducer. Because of the nonlinearity in the
stress-strain relationship shown in Fig. 9, the static elastic
modulus, Es , changes with the pressure level (1.2 MPa at
30 mmHg, 1.5 MPa at 50 mmHg, 1.6 MPa at 70 mmHg). In§4.1 and §4.2, jEh ð fac Þj and jEinc ð fac Þj were measured at amean internal pressure of 50 mmHg. At a pressure of
50 mmHg, the static elastic modulus, Es , was determined tobe 1.5 MPa by this static experiment, and the value agreed
well with that obtained by ultrasound (1.3 MPa).

(d) velocity at A

velocity [mm/s]

Fig. 10. B-mode image of a human carotid artery (29-year-old male).

(c) blood pressure74
0.6

0.82 mm/s

−0.8
−1
0.64

0.68

0.72
time from R−wave [s]

100

(3−a)

98
96

velocity [mm/s]

beam position

blood pressure [mmHg]

1 cm

blood pressure [mmHg]

posterior wall

125mmHg 85455mm/s 0–55mm/s 0
–5

0.6

0.64

0.68

0.72
time from R−wave [s]

0.2
(3−b)
0

1.06 mm/s

−0.2
−0.4
−0.6

1.3 mmHg

94

−0.8
−1

92
90
0.6

−1.2
0.64

0.68

0.72
time from R−wave [s]

−1.4
0.6

1.13 mm/s

0.64

0.68
0.72
time from R−wave [s]Fig. 12. Blood pressure and velocity after 0.6 s from the R-wave ofelectrocardiogram. (1) 7.5 Hz. (2) 10 Hz. (3) 12.5 Hz. (a) Blood pressure.
(b) Velocities at the intimal side and the adventitial side.

respectively. In Fig. 12, it is shown that the amplitude ofvelocity at the intimal side is larger than that at theadventitial side. The changes in wall thickness were
calculated from the diﬀerences between the amplitudes ofvelocities at the intimal side and the adventitial side, which
can be measured from Figs. 12(1-b), 12(2-b), and 12(3-b).
From the amplitudes, p0 and h0 , of the change in internalpressure and the change in wall thickness measured from
Fig. 12, the elastic modulus, jEh ð fac Þj, at each actuation
frequency is obtained and plotted as a function of actuation
frequency, fac , as shown in Fig. 13. In Fig. 13, it is shownthat the elastic modulus, jEh ð fac Þj, increases with actuation
frequency, fac . From the measured jEh ð fac Þj, the static elastic
modulus, Es , and the viscosity constant, , were estimated tobe 100 kPa and 3.0 kPas, respectively.
The relationship between the mean internal pressure andthe elastic modulus of the human carotid artery is reported inelastic modulus [kPa]

Jpn. J. Appl. Phys., Vol. 43, No. 5B (2004)
500
Es =100 kPa
η =3.0 kPa·s

400

300

200

100

0

0

2

4

6

8

10
12
14
actuation frequency [Hz]Fig. 13. Elastic moduli, jEh ðfac Þj, of a carotid artery measured at multiple
frequencies (plot), and the estimated Voigt model (solid curve).

the literature.29) At a pressure of about 120 mmHg, whichcorresponds to the systolic pressure, the elastic modulus isabout 1.4 MPa. In diastole (blood pressure: about 60 mmHg),
it is reported that the elastic modulus has a similar value(about 200 kPa) in comparison with that measured in thispaper during diastole. Furthermore, the viscosity constant isreported to be about 5 kPas. The viscosity constantmeasured by the proposed method is in good agreementwith that reported in literature.
From these results, it is found that the viscoelasticity of
the arterial wall can be measured with transcutaneous
ultrasound using remote actuation.
6.

Conclusions

In this study, basic experiments were performed for theassessment of viscoelastic properties of the arterial wall. If
the wall is viscoelastic, the elastic modulus is changed by thefrequency of the applied stress. To investigate the frequency
characteristic of the elastic modulus, it is necessary to
generate changes in internal pressure at multiple frequencies.
By measuring the resultant minute change in wall thickness
by our phased tracking method, the frequency characteristicof the elastic modulus was obtained. We then assume the
Voigt model as a viscoelastic model of the wall, and thestatic elastic modulus and the viscosity constant wereobtained from the elastic moduli measured at multiple
actuation frequencies. Such a method for the noninvasive
measurement of the viscoelasticity has potential for thecharacterization of tissues in the arterial wall.

H. HASEGAWA and H. KANAI

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