J Med Ultrasonics (2005) 32:39–47
DOI 10.1007/s10396-005-0034-2© The Japan Society of Ultrasonics in Medicine 2005

ORIGINAL ARTICLE
Kazuhiro SUNAGAWA · Hiroshi KANAI

Measurement of shear wave propagation and investigation of estimation ofshear viscoelasticity for tissue characterization of the arterial wall

Received: August 20, 2004 / Accepted: November 16, 2004

Abstract
Purpose. The aim of this study was to find an array of frequency components, ranging from 0 Hz (direct current) to
several tens of hertz that comprise the small vibrations on
the arterial wall using noninvasive in vivo experiments.
These vibrations are caused mainly by blood flow. The viscoelasticity of the arterial wall was estimated from the frequency characteristics of these vibrations propagating fromthe intima to the adventitia.
Methods. Propagation of these frequencies in human tissue
displays certain frequency characteristics. Based on the
Voigt model, shear viscoelasticity can be estimated from thefrequency characteristics of the propagating vibrations.
Moreover, we estimated shear viscoelasticity from the measured frequency characteristics of shear wave attenuation.
Results. Shear wave propagation from the intima to theadventitia resulting from blood flow was explained theoretically based on the obtained measurements. Shearviscoelasticity was also estimated from the measured frequency characteristics of shear wave attenuation.
Conclusions. Based on the proposed method, shear viscoelasticity can be estimated from ultrasonographic
measurements. These results have a novel potential forcharacterizing tissue noninvasively.
Keywords phased tracking method · shear viscoelasticity ·shear wave · tissue characterization · ultrasoundK. Sunagawa · H. Kanai (*)
Department of Electronic Engineering, Graduate School ofEngineering, Tohoku University, Aramaki-aza-Aoba 05, Aoba-ku,
Sendai 980-8579, Japan
Tel. +81-22-795-7078; Fax +81-22-263-9444
e-mail: hkanai@ecei.tohoku.ac.jp
K. Sunagawa
Panasonic Mobile Communications Sendai R&D Laboratory, Sendai,Japan

Introduction
Changes in blood pressure are produced by cardiac pulses
propagated as pulse waves from the heart to the arterial
periphery, causing the arterial wall to vibrate at frequenciesof up to tens of hertz. Palpation can also be used to checkpulsation in the radial and other arteries. Because pulse
wave velocity varies with the elasticity and viscosity of thearterial wall, several methods for evaluating wall elasticity1,2
and viscosity3–5 based on pulse wave velocity have been
proposed.
The smooth muscles constituting the arterial wall contract or relax when stimulated by vasoactive substances.6
For example, sublingual administration of nitroglycerin, avasoactive agent, causes the smooth muscles of the arteries
to relax. Chronologic ultrasound analysis of changes in arterial wall thickness showed that smooth muscle response to
sublingual nitroglycerin appeared several tens of seconds
after the dose was administered, and that wall thickness
changed slowly over a period of several tens of seconds
after the first signs of response.
Pulsation of the heart also produces turbulent blood flowor eddies within the arterial lumen that express themselves
as murmurs at a frequency range higher than that of thepulse waves. We measured human carotid artery small
vibration on the atrial wall percutaneously using a phased
tracking method capable of precisely measuring small
vibration of the arterial wall with ultrasonography.7,8 Vibration of the arterial wall contained direct current and alternating current components at frequencies up to slightly
higher than 100 Hz.9,10
Local changes in stress on the surface of the arterial wall
produced by disturbances in blood flow or formation ofeddies appears to be a factor accounting for this small vibration. Vibration of the arterial wall also appears to propagate
from the intima to the adventitia, and local stress changes
on the arterial wall surface appear to produce vibration.
Similarly, the propagation characteristics of vibration fromthe surface of the arterial wall vary with viscoelasticity characteristics of the tissue constituting the wall.

40

Methods for evaluating viscoelasticity based on analysis
of vibration propagation characteristics through tissue after
vibration of the living tissue by external excitation havebeen proposed.11–14 However, because these methods
require an external source of vibration and a system formeasuring the internal vibration produced, they also expose
the subject to greater stress. Furthermore, these methods
introduce another problem by causing the entire bloodvessel to bend when the arterial wall is vibrated in this way.
To avoid these complications, we used a source of vibration
inherent in the living body and estimated the viscoelasticity of living tissue in a simple, noninvasive manner.
We propose a new method for estimating tissue viscoelasticity based on the assumption that arterial wall tissue
serves as a Voigt model in which Hooke’s law is applicable.
Tissue viscoelasticity is thus estimated based on the frequency characteristics of the attenuation of arterial wall
vibration, probably induced by blood flow as it propagatesfrom the intima to the adventitia. This frequency ranges
from direct current to tens of hertz.
This method does not require measuring the stressapplied to the elastic body, as do conventional methods of
estimating viscoelasticity. Furthermore, because it uses
vibration occurring naturally in vivo, it requires no externalsource of vibration and thus promises to allow distinction
and identification of tissue through noninvasive ultrasonicestimation of the viscoelasticity of arterial wall tissue.
Here we describe our attempt to use the phased tracking method7,8 to measure simultaneously the pulse wave
velocity on both the intimal and adventitial sides of theintact human carotid arterial wall ultrasonically. In this way,
we show that blood flow produces small vibration on thesurface of the arterial wall and that this vibration propagates from the intima to the adventitia. We also present theresults we obtained when attempting to estimate the shear
viscoelasticity constant of the human carotid artery wallartery from the frequency characteristics of attenuation
during the propagation of vibration.

Vibration caused by blood flow on the intima of thearterial wall
Cardiac pulsation produces changes in the internal pressure
on the surface of the arterial wall. Such factors as turbulent
flow and eddies caused by the shear stress produced byblood flow are known sources of small vibration at frequencies as high as tens of hertz.9,10
Using the phased tracking method7,8 to measure pulse
wave velocity on both the intimal and adventitial sides of
the intact wall of the human carotid artery simultaneouslywith ultrasonography, we found that blood flow produced
small vibration ranging from zero to several tens of hertz.
Subject A was a 28-year-old healthy male volunteer.
Ultrasound was applied in two alternating directions: one
perpendicular to the arterial axis, the other about 20° off
the arterial axis (Fig. 1). We thus attempted to measurewall vibration and blood flow velocity on both the intimal

Fig. 1. Cross-sectional B-mode image of the common carotid artery of
subject A, a 28-year-old man

and adventitial sides of the common carotid arterysimultaneously.
Figure 2 shows (1) data obtained on vibration velocity
patterns on the intimal side of the posterior wall of thecommon carotid artery during one cardiac cycle; (2) thevibration velocity pattern on the adventitial side; (3) patterns of blood flow along the axis; (4) patterns of change in
the inside diameter of the artery; and (5) the time course ofvibration velocity power on the intimal and adventitial sides
for each frequency.
When the time course of vibration velocity power foreach frequency was followed (Fig. 2d), the frequency was
analyzed while moving the 100-ms wide Hanning window
in increments of 10 ms. Figure 2 shows that blood flow along
the axis was first detected when the pulse wave arrived, andthat blood flow velocity increased until the pulse reached
the dicrotic notch formed by closure of the aortic valve.
Analysis of arterial wall vibration velocity patterns also
showed that vibration velocity power was greater from thearrival of the pulse wave (time A in Fig. 2) until the dicrotic
notch was formed by closure of the aortic valve (time D)
than during other periods.
The large variance in amplitude during the period frompulse wave arrival (time A) seen in Fig. 2 to formation of
the dicrotic notch resulting from closure of the aortic valve(time D) is attributable to the change in pressure producedin the artery when blood is ejected from the heart and theaortic valve closes. This change is accompanied by changes
in the inside diameter of the artery and distortion changes
in the thickness of the arterial wall. During the period B–C,
defined as the period between the arrival of a pulse andimmediately before the dicrotic notch was formed byclosure of the aortic valve, the internal arterial diameterchanged little; however, the arterial wall vibration velocity
power of the frequency range greater than around 40 Hz
was about 10 dB greater than during periods of slower blood
flow. Changes in the arterial inner diameter correlated
closely with changes in arterial pressure.3,15 Internal arterialpressure remained essentially constant during period B–C,

41

Fig. 3. Measurement of vibration propagation from the intima to theadventitia of the arterial wallin which the internal diameter of the artery remains almost
unchanged. Arterial wall vibration during period B–C may
thus be considered attributable solely to blood flow.
Such small vibration caused by blood flow appears toresult from both turbulence or eddies associated with theviscosity of blood flowing through the artery and the roughness of the arterial surface.16 As represented in Fig. 3, thevibration produced on the surface of the arterial wall produces elastic waves, the inner surface of the arterial wall
serving as a source of vibration; and this wave is propagatedfrom the intima to the adventitia of the arterial wall.

Measuring the propagation of small vibration from thewall of the human carotid artery
To confirm that the small vibration of frequencies ranging
from direct current to tens of hertz produced on the arterial wall is propagated along the axis of the arterial wall, we
used ultrasonography to measure small vibration on boththe intimal and adventitial sides of the arterial wall simultaneously. We then evaluated the relation between thevibrations recorded. Figure 3 shows two reference points set
along the ultrasound beam: one on the intimal side, theother on the adventitial side. The tracking method wasused to measure the phased wall vibration at both points
simultaneously.8

Fig. 2. Vibration of the intima of the posterior arterial wall during a
cardiac cycle in subject A. a, b Vibration velocity. c Axial blood flow. dChange in internal diameter of the artery. e, f Change in power spectraof vibration velocities

42

Vibration of the posterior wall of the carotid artery wasmeasured in a healthy 28-years-old male volunteer (subjectA) (Fig. 2). During the interval between the pulse wave
arrival and the formation of the dicrotic notch resulting
from aortic valve closure, the inside diameter of the arteryin segment B–C (Fig. 2) changed little, suggesting that arterial pressure remains almost constant and that the vibration
produced in this segment is attributable primarily to bloodflow.
Wall vibration power on the intimal side differed significantly from that on the adventitial side of the arterywhen the frequency exceeded 60 Hz, suggesting that thesmall vibration produced on the surface of the arterial wallis propagated as an elastic wave from the intima to theadventitia while undergoing attenuation through time. This
led us to evaluate the correlation between arterial wall
vibration on the intimal and adventitial sides after blood isejected from the heart. We used the amplitude squared
coherence function17,18 to confirm that the small vibration
produced on the surface arterial wall by blood flow is propagated from the intimal to the adventitial side.
The amplitude squared coherence function indicates theratio of power input-based components to output-based
components. It is defined from the input signal spectrum
Xi(k) and output signal spectrum Yi(k), as shown below,
where Ei denotes the averaging operation.
2g (k )

2

E1 È X i*(k )Yi (k )˘
ÎÍ
˚˙
=
2
2
˘
È
È
Ei X i (k ) Ei Yi (k ) ˘
˚˙ ÎÍ
˚˙
ÎÍ

(1)

For example, |g(k)|2 = 0.9 indicates that the power of inputbased components makes up 90% of the power of theoutput signal, and the remaining 10% is noise that cannot
be explained by linear propagation of input signals.
Figure 4a shows the data obtained using |g(f)|2 concerning the correlation between carotid artery wall vibration on
the intimal and adventitial sides for the period shown in Fig.
2, the Hanning window period, during which blood flow
alone seemed to account for the wall vibration velocity patterns observed. The time window interval was set at 100 ms,
and data for 10 cardiac beats were averaged in the frequency analysis. Figure 4a shows that coherence was high,in the range of 0 to about 70 Hz. We determined a propagation function for vibration from the intimal to the adventitial side of the arterial wall H(f) and evaluated amplitude
and phase characteristics to confirm that vibration produced on the surface of the arterial wall surface was propagated from the intima to the adventitia.
Figure 4b shows the amplitude characteristic |H(f)| of
H(f), a function of propagation of vibration from theintimal to the adventitial side of the arterial wall, for the
Hanning window period shown in Fig. 2, during which bloodflow alone appeared to account for formation of wall vibration velocity patterns. Figure 4c shows data concerning thephase characteristic –H(f) obtained in this way.
Figure 4 shows that attenuation of amplitude (Fig. 4b)
and delay in phase (Fig. 4c) occurred in the frequency range
between about 20 Hz and high coherence at 70 Hz. Here theFig. 4. Frequency characteristics of small vibration between the intima
and adventitia of the posterior arterial wall in subject A, a 28-year-oldmanphase was close to 0 when the frequency was less than about
40 Hz. The pattern of change in the inner diameter of theartery (Fig. 2d), however, showed that the internal diameter of the artery remained almost constant during the interval between the pulse wave arrival caused by ejection andthe dicrotic notch formation resulting from closure of theaortic valve, but that the internal diameter increased slowly
and slightly before the dicrotic notch was formed.
These findings combined with the vibration velocity patterns on the intimal and adventitial sides of the arterial wallshown in Fig. 2a,b confirm the production of low-frequency
vibration during the period from arrival of the pulse wave

43

produced by cardiac ejection to formation of the dicrotic
notch. Regarding the changes in vibration velocity poweron the intimal and adventitial sides of the arterial wall (Fig.
2e,f), we confirmed that the vibration power for the range
40–100 Hz changed little, although that at 20 Hz changed
markedly, by about 20 dB. These results suggest that small
vibration up to 40 Hz is primarily associated with changes
in the inner diameter of the artery resulting from a variation in blood pressure.
In Fig. 4c the calculated phase lag b is 15° at 50 Hz. Elastic
wave propagation velocity (c) can thus be obtained using
the following equation, assuming that the increase in timerelated variation wt is accompanied by a corresponding
increase in dislocation of bx to wt.1
c = dx dt = w b(2)

The vibration propagation velocity c at propagation distance d is equal to 1 mm, the thickness of the arterial wall,and can thus be calculated from the angular frequency w
and phase delay b using the equation c = w/b = 1.2 m/s. These
results suggest that the small vibration produced on thesurface of the arterial wall by blood flow in the human
carotid artery is propagated as shear elastic waves toward
the adventitia. They further suggest that the propagation
characteristics of the elastic wave transmitted throughtissue can be determined from the vibration velocities measured with ultrasonography at multiple points set across thedepth of the arterial wall, and that the viscoelasticity characteristics of tissue can be estimated from the propagation
characteristics.

2
Ï
rwb 2 a 2 - b 2
Ôm 1 =2ÔÔ
a 2 + b2
Ì
2rwab
Ô
2
Ôm 2 = 2
a + b2
ÔÓ

)

(

)

(

(

(4)

)

Furthermore if g = a + jb is applied to Eq. (3), both sides
are squared, the real and imaginary parts are rearranged,
and the quadratic equation is solved, we can calculate thedegree of attenuation a and phase b using the following
equations.11
1
ÏÊ rw 2 m 2 + w 2m 2 - m ˆ 2
Ô
1
2
1
˜
Ôa(w ) = Á
2
2 2
Á
˜
Ô
2 m1 + w m 2
Á
˜
Ë
¯
Ô
Ì
1
Ô
Ê rw 2 m 2 + w 2m 2 + m ˆ 2
1
2
1
Ô
˜
Ôb(w ) = ÁÁ22 2
˜2 m1 + w m 2
Ô
Á
˜
Ë
¯
Ó

(

(

)

(

)

(

)

(5)

)

Assuming that theshear elasticity constant m1 and shear viscosity constant m2
are constant irrespective of frequency, attenuation a andphase b in Eq. (5) are functions of angular frequency ofvibration w.

The propagation velocity of shear elastic wave cs can beobtained from the angular frequency w and phase b ofvibration as follows.
1

Estimation of the shear viscoelasticity constant fromthe frequency characteristics of attenuation of theshear elastic wave during propagationÊˆ2
2 m12 + w 2m 22w Á˜cs (w ) = =b ÁÁ rw 2 m + m 2 + w 2m 2 ˜˜
1
1
2
Ë
¯

The propagation characteristics of shear elastic waves offrequencies less than about 10 kHz are known to vary in frequency when the viscosity of living tissue is taken into
account.11,12 If the shear viscoelasticity constant m = m1 + jwm2of the Voigt model is applied to the wave function, whichtakes into account attenuation resulting from viscosity of anelastic body, the following relation is obtained11,12

Equation (6) indicates that the propagation velocity ofshear elastic wave cs(w) is also a function of angular frequency w.
Figure 5a–c shows the degree of elastic wave attenuation
during propagation a, phase b, and the frequency characteristic of propagation velocity cs(w), calculated using thereported data (m1 = 2.5 kPa and m2 = 15 Pa · s).10
The shear elasticity constant m1 and shear viscosity constant m2 of soft tissue in vivo can be obtained from theangular frequency w, the amount of attenuation a, and thephase b of vibration, using Eq. (4).
Because of the thinness of the intact human carotid
artery wall (approximately 1 mm), however, simultaneous
attenuation a and phase b of vibration during short-distance propagation are often difficult to measure precisely.
We therefore devised a method for an approximate estimation of the shear viscoelasticity constant of tissue based on
the degree of attenuation, a, during propagation, which iseasier to measure than the phase b. Equation (5) can be
developed as follows.

m = m1 + jwm 2 = -

rw
g2

(3)

where r denotes density; m1, shear elasticity constant; m2,
shear viscosity constant; and w, angular frequency of vibration. The wave number is indicated by g, taking attenuation
into account, and is expressed from the amount of attenuation a and phase b using the equation g = a + jb.
If g = a + jb is applied to Eq. (3) and the real and imaginary terms are rearranged, the shear elasticity constant m1
and shear viscosity constant m2 can be obtained using thefollowing equations.

(

(

)

)

(6)

44

2

a(w ) =

rw 2

( m +w m -m )
(

2
1

2

2
2

2
1

2

2
2

2 m +w m

1

)

1
-1
Ï
¸
m12 ˆ 2
m Ô
m12 ˆ
1 Ê
ÔÊ
1
= rwm 2 ÌÁ 1 + 2 2 ˜ - 1 ˝ ¥+Á˜
w m2 ¯wm 2 Ô 2m 22 Ë
w 2m 22 ¯ÔËÓ˛The following equation allows approximation of the highfrequency range, where w2m22 >> m21.
rw Ê
m12
m ˆÊ
m2 ˆ
2
- 12 ˜ Á 1 - 2 1 2 ˜â(w ) ª
Á1 +2 2
w m2 ¯2m 2 Ë
2w m 2 wm 2 ¯ Ë
ª

rw Ê
m1 ˆ
Á1 ˜
2m 2 Ë
wm 2 ¯(8)rmrw - 12ª2m 2
2m 2
Assuming that the shear elasticity constant m1 and the shear
viscosity constant m2 remain constant irrespective of
frequency, Eq. (8) is converted to a linear function â(w)2 =Aw + B, where the first term is the gradient A, and thesecond is the intercept B. The shear elasticity constant m̂1
and shear viscosity constant m̂2 can be estimated from coefficients A and B of the first term, w, using the following
equations.
Ï
2m 22BÔÔmˆ 1 = rÌÔmˆ = - r
ÔÓ 2
2A

(9)

Equation (5) can be developed as follows.

2a(w ) =

rw 2

( m +w m -m )
2
1

2

2
2

(

2 m12 + w 2m 22

1

)

1
2

-1
Ï
¸
1 Ê
w 2m 2 ˆ
w 2m 22 ˆÔÊÔ
1= rw ÌÁ 1 + 2 2 ˜ - 1˝ ¥
+
˜
2 Á
m1 ¯
m12 ¯
ÔË
Ô 2m 2 ËÓ˛(10)and becomes
ˆÊ
rw Ê
m12
w 2m 2 ˆ- 1˜ Á 1 - 2 2 ˜
Á1 +
2 2
m1 ¯
2m1 Ë
2w m 2¯Ëand becomesª0
2â(w ) ª(11)

when the angular frequency w0 at the point of inflection
from Eq. (11) to Eq. (8) can be obtained as follows using
Eq. (8)w0 =Fig. 5. Frequency characteristics of shear wave propagation: m1 =2.5 kPa, m2 = 15 Pa · s

m1
m2

(12)

which is the ratio of the shear elasticity constant m1 to theshear viscosity constant m2.
Figure 5d shows the frequency characteristic of thesquare of shear elastic wave attenuation calculated using

45

data reported by Oestreicher (m1 = 2.5 kPa, m2 = 15 Pa · s).11
The same parameter was estimated by our method using anapproximation with the linear function of angular velocity
w. Figure 5d shows that this method, using the approximation with a linear function of angular frequency w, is valid
for the frequency range in which w2m22 >> m21. The point of
inflection of the frequency characteristic of squared shear
elastic wave attenuation is shown to be close to the ratio of
the elasticity constant m1 to the shear viscosity constantm2 (i.e., f0 = 26.5 Hz).

Shear viscoelasticity constant estimated from the
propagation attenuation frequency characteristics ofhuman carotid artery wall vibration
Regarding the vibration on the intimal and adventitial sidesof the human carotid artery wall measured simultaneously
by ultrasonography (Fig. 2), the data obtained concerning
the amplitude and phase characteristics of the amplitude
squared coherence function and the propagation function(Fig. 4) show that vibration produced by blood flow is linearly propagated toward the adventitial side and is attenuated over time. This suggests that arterial wall tissue can bedeemed a Voigt model when analyzing the propagation
characteristics of the vibration produced on the surface of
the arterial wall. We thus attempted to estimate shear elasticity constant m1 and shear viscosity constant m2 from thefrequency characteristics of the attenuation of vibration
during propagation from the intimal to the adventitial sideof the human arterial wall using Eq. (8).
From DZmn, which denotes the distance between theintima m and the adventitia n, corresponding to the thickness of the arterial wall, the frequency characteristic amn(f)2
of vibration power per unit length between point m andpoint n can be obtained using the following equation.
2

a mn ( f ) =H( f )
DZmn

2

(13)

Then, to apply the approximation Eq. (8) to the high-frequency range (w2m22 >> m21), we selected a frequency range
over which vibration appears to be propagated from theintima to the adventitia of the arterial wall. Applying theamplitude squared coherence function for the period starting some time after cardiac ejection and ending immediately before closure of the aortic valve causes the dicrotic
notch to form (i.e., the period during which small vibration
appears to result from blood flow alone). Attenuation ofvibration during propagation over the selected range issquared and analyzed using the least-squares method to
obtain gradient A and intercept B of the linear function. We
then used Eq. (8) to estimate the shear elasticity constant
m1 and shear viscosity.
This method was applied to the carotid artery of ahealthy 28-year-old male volunteer. Figure 6 shows the data
we obtained concerning coherence of wall vibration velocity on the intimal and adventitial sides of the posterior wallFig. 6. Frequency characteristics of small vibration between the intima
and adventitia of the posterior arterial wall of subject Aof the carotid artery (Fig. 6a) and the squared attenuationof vibration during propagation from the intimal to theadventitial side of the posterior wall of the carotid artery(Fig. 6b).
Squared attenuation increased linearly with frequency
over the approximate range of about 30–100 Hz (Fig. 6b)
and was subjected to least-squares analysis (Fig. 6a) over
the range of 30–70 Hz, corresponding to the range with highcoherence of vibration on the intimal and adventitial sides.
The approximation line thus obtained gave m̂2 = 156 Pa · susing the shear viscoelasticity constant obtained from thisline by Eq. (8). Considering the ratio of the thus determined
shear elasticity constant m1 and the shear viscosity constantm2, the point of inflection of the frequency characteristic ofsquared attenuation was found to be close to 23 Hz.
We attempted to estimate the shear viscoelasticity constant in two other healthy male volunteers (subjects B andC, both 21 years old) in the same way for the period starting shortly after the pulse produced by cardiac ejection
arrived and ending immediately before the dicrotic notch
formed as a result of closure of the aortic valve – the period
during which blood flow alone appears to account for thevibration.
Figure 7 shows the data collected from subject B concerning wall vibration velocity coherence on the intimal andadventitial sides of the carotid artery (Fig. 7a) and thesquared attenuation of the vibration propagated from theintimal to the adventitial side of the posterior wall of

46

Fig. 7. Frequency characteristics of small vibration between the intima
and adventitia of the posterior arterial wall of subject B, a 21-year-oldmanFig. 8. Frequency characteristics of small vibration between the intima
and adventitia of the posterior arterial wall of subject C, a 21-year-old
mean

the carotid artery (Fig. 7b). Figure 7b shows that squared
attenuation increased linearly with a frequency of about
40–90 Hz. The frequency range of about 40–60 Hz with highcoherence of vibration on the intimal and adventitial sides
was subjected to least-squares analysis to determine theshear viscoelasticity constant, yielding m̂1 = 19 kPa and m̂2 =81 Pa · s. The point of inflection of squared attenuation wasclose to 37 Hz.
Figure 8 shows the data obtained from subject C, a 21year-old man, concerning coherence of wall vibration velocity on the intimal and adventitial sides of the carotid artery(Fig. 8a) and squared attenuation of vibration propagatedfrom the intimal to the adventitial sides of the posterior wallof the carotid artery (Fig. 8b). Coherence was low over thefrequency range of about 20–30 Hz (Fig. 8a). Analysis of thefrequency characteristics of squared attenuation revealed a
dip at about 30 Hz (Fig. 8b).
Equation (8) was applied to the frequency range of about
40–80 Hz, where the coherence of vibration on the intimal
and adventitial sides was high. The shear viscoelasticity constants thus obtained were m̂1 = 2.9 kPa and m̂2 = 223 Pa · s.
The point of inflection of the frequency characteristic ofsquared attenuation was around 2 Hz.
These results indicate that blood flow induces small
vibration on the arterial wall of the human carotid arteryand that this vibration is propagated from the intima to theadventitia of the arterial wall. The use of frequency characteristics of attenuation of vibration during propagation arelikely to facilitate estimation of the shear viscoelasticity
constant of arterial wall tissue. Also, when coherence is low
over part of the frequency range, as seen with subject C, we
may be able to estimate the shear viscoelasticity constant ofarterial wall tissue using the frequency characteristic ofattenuation of vibration for another frequency range withhigh coherence.
As shown in Fig. 8b, the linear approximation curve
dipped at about 30–40 Hz. When the curve was derived fromthe 50- to 80-Hz frequency range, however, the shear elasticity constant was m̂1 = 22 kPa, and the shear viscosity constant was m̂2 = 93 Pa · s. These results suggest that vibrationdiffers from the propagation of an elastic wave in that oscillation may occur around the 40-Hz region. We plan to use
these findings to analyze the mode of vibration of the arterial wall.

Conclusions
We used the phased tracking method to measure simultaneously the wall vibration on the intimal and adventitialsides of the human carotid artery with ultrasonography. We

47also conducted frequency analysis of wall vibration velocity
patterns, including an evaluation of the association between
the intimal and adventitial sides over specific ranges ofsmall vibration frequency. The analysis showed that small
vibration of up to about 100 Hz occurred on the surface of
the arterial wall, and that the vibration was propagatedfrom the intimal to the adventitial side of the artery.
We also attempted to estimate the shear viscoelasticity
constant of tissue from the propagation characteristics ofthis shear elastic wave and proposed a method for estimating the viscoelasticity characteristics on the basis of attenuation of the shear elastic wave alone by frequency
characteristics. We then attempted to use this method toestimate the shear elasticity and shear viscosity constants of
the arterial wall.
Our results suggest the possibility of distinguishing andidentifying tissue based on the propagation characteristics
of arterial wall vibration using percutaneous ultrasonography and an internal source of vibration inherent in vivo (i.e.,the vibration produced by the flow of blood through thearteries). This method requires no extracorporeal source ofvibration or other means of stress measurement requiredby conventional methods used to measure viscoelasticity.
Ultrasound measurement alone suffices. This method seems
to be particularly useful for studying the arterial wall, where
the propagation distance is short, and precise simultaneous
measurements of the propagation time and changes inphase and attenuation is difficult. We plan to continue tostudy the morphologic features of elastic wave propagation
through the arterial wall and to estimate the shear viscoelasticity characteristics in vivo.
This study was conducted within the framework of theresearch and development program of the Japan Society of
Ultrasonics in Medicine.

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