◇Translation of Original Contribution◇

Simultaneous Measurement of Vibrations on Arterial Wall Upstream
and Downstream of Arteriostenosis Lesion and Their Analysis
Kazuhiro SUNAGAWA1,2 , Hiroshi KANAI1, EJSUM, Yoshiro KOIWA3, Keiko NITTA4, SJSUM,
and Motonao TANAKA4, SJSUM

Abstract
Acute myocardial infarction and cerebral infarction are generally known to be caused primarily by the ruptureof atherosclerotic plaques. It is thus necessary for clinical treatment to predict the rupture of these plaques. Bloodflow velocity around atherosclerotic plaques increases as the arteriostenosis lesion progresses, resulting in
turbulence downstream of the lesion. The resulting change in blood pressure produces shear stress, and change inthis stress affects the rupture of the atherosclerotic plaques. Cerebral ischemic paroxysm and cerebral infarction
have been reported to occur in a high percentage of cases in which inner vessel diameter has decreased to less than
70％ of its original diameter as a result of stenosis. This explains the use of standard ultrasonic diagnostic
equipment to measure blood flow in the screening of the carotid arteries. On the other hand, the noise signal
radiated from an aneurysm as a result of blood flow has been measured using the bruit sensor used to diagnose
cerebrovascular diseases. Many unsolved problems with regard to the relationship between noise and turbulencein blood flow remain, however. Here, small vibrations on the arterial wall were measured transcutaneously andanalyzed both upstream and downstream of the atherosclerotic plaque of a human carotid artery. Characteristicsof the resultant vibrations upstream of the stenosis clearly differed from those downstream of it. These results
should prove useful in predicting the rupture of atherosclerotic plaques.
J Med Ultrasonics 2001 ; 28 (Winter) : 157173.

Keywords
atherosclerosis, arteriostenosis, blood flow, small vibration on arterial wall, ultrasound1. Introduction
The rupture of atherosclerotic plaques is known tocause circulatory diseases like myocardial and cerebral
infarction1) . The clinician must be able to predictrupture or likelihood of rupture of these plaques.
Therefore, our research group proposed a method2) for
evaluating the elastic properties of the arterial wall bydetecting velocity of vibrations on the arterial wallusing ultrasonic diagnostic equipment to evaluate
atherosclerotic plaques. Increase in velocity of bloodflow around stenotic changes in artery resulting fromthese plaques causes downstream turbulence. The
resulting change in blood circulation is thought toaffect blood pressure and shear stress that can lead to
rupture of the plaques3). Some years ago the hot-film
flowmeter was used to detect turbulent blood flow
through stenotic areas4) ; today, however, turbulent
blood flow is easily detected using the FFT Doppler orcolor Doppler method with ultrasonic diagnostic
equipment. Cerebral ischemic paroxysm and cerebral
infarction have been reported to occur in a highproportion of cases in which stenosis has reduced the1

Department of Electronic Engineering, Tohoku University Graduate School of Engineering, Aramaki-aza-Aoba
05, Aoba-ku, Sendai 9808579, Japan, 2Matsushita Communication Sendai R&D Labs. Co., Ltd., Akedori 25,
Izumi-ku, Sendai 9813206, Japan, 3First Department of Internal Medicine, Tohoku University Graduate Schoolof Medicine, Seiryo-cyo 11, Aoba-ku, Sendai 9808574, Japan, 4Tohoku Welfare Pension Hospital, Fukumuroaza-Takasago 10, Miyagino-ku, Sendai 9830005, Japan
Original article is cited in Med Ultrasonics 2000 ; 27(1) : 1531.
J Med Ultrasonics Vol.28 Winter (2001)157

inner diameter of a vessel to less than 70％ of its
original diameter5). Carotid artery screening now uses
ultrasound (US) imaging to determine blood flow
velocity at stenotic sites of the arteries, and waveform
is used to determine stenotic rate, confirm occlusion of
the carotid artery or other stenotic lesions, anddistinguish between occlusion and stenosis6).
Acoustic analysis has been used in the attempt todetect blood-flow murmur using a blood-flow soundsensor and to diagnose arterial lesions7)8). Vibration of
the arterial wall was not detected directly, however,
and much remains to be learned about the effects of
turbulence on arterial wall vibration.
We therefore measured the wall vibration produced
at an artificially induced stenotic site in a silicone
rubber tube and in the carotid artery of anarteriosclerotic patient using a phased tracking
method9). This allowed us to measure vibrations on thearterial wall with US and to evaluate the effects ofblood flow on arterial wall vibration at the stenotic
site. Results obtained from this study provide usefulclues for predicting possible rupture of plaques.
2. Principles of arterial wall vibrations and in vivo
measurement system.
2.1 Principles of measuring the velocity of arterial
wall vibrations
Phase delay, which varies with total distance that
the US pulse travels in the body, occurs as thetransmitted US signal returns to the US probe after
being reflected by the arterial wall. When US pulses
with an angular frequency of ＝2 are repeatedlytransmitted to the arterial wall at time intervals of
, the phase 
of the pulses reflected from thetarget are described by the following equation, in
which with the sound velocity is , one-way
transmission time is , and distance to thereflecting object is .

 2 

 2  (1)

The phase difference 
 between two
detected waves 
 and 
 in theinterval of  can thus be obtained from thefollowing equation.

 




2 





(2)

In this equation, 
is the distance that theobject moves is the interval , and can be expressed
as follows.
 








2 

(3)

This 
is divided by  to obtain the158

average velocity in the interval .












 

2


 



 
(4)
 

2
2 
In the present study, received reflected waves weredetected by quadrature modulation, separated into real and imaginary signals, anddigitized. The phase 
of detected wave at thetime when the reflected waves were detected can beobtained from the following equation.


 






(5)

US pulses were transmitted almost simultaneously indirections on the arterial wall to measure vibration
at an arteriosclerotic lesion, and upstream anddownstream sites10) . When measuring simultaneously
in directions, pulse repetition frequency is 1/ th ofthat when measured in a single direction. Velocity ofin this case is obtained with thethe vibrations following equation.






 


 

 
2
2 





(6)
2.2 Determining the velocity of vibrations on thearterial wall using a phased tracking method
During the US examination, the distance between
the transducer and the artery changed several hundred
micrometers, varying with dilation of the artery.
These arterial changes included 100 to 200 m ofsimultaneous movement of the anterior and posteriorwall. Simultaneous movements were also measured
using the M-mode of the conventional US systems.
Because of cardiac contraction, however, it was
impossible to accurately measure changes in the innerdiameter of the artery. Instead, we used the phased
tracking method9), which allowed us to measure withhigh precision the vibration velocity on the
arterial wall that was included in simultaneous
movements, by accurate tracking of instantaneous
values of position from the surface of the body.
Accurate measurement of phase difference 
in  intervals was important. We therefore
determined the instantaneous position of theobject using the constraint least-squared approach9).
The position of the object at a given
time 
can be predicted by adding the change inthe position of the object, 
, obtained fromequation (3) to the position of the target, , at theprevious time .
 

(7)This is the tracking trajectory of the wall, and it
is possible to determine the vibration velocity withhigh accuracy by repeating this estimation while
J Med Ultrasonics Vol.28 Winter (2001)

Fig. 1 System for measuring in vivo.

tracking arterial wall motion.
2.3 In vivo measurement system
Fig. 1 shows a schematic diagram of the systemused to take measurements in vivo. Ultrasonic pulses
are transmitted to several sites arbitrarily selected on
the arterial wall from the 7.5 MHz linear US probe of
the US diagnostic equipment. A new beam address canbe assigned to each pulse by updating 8-bit data.
Ultrasonic pulses reflected by the arterial wall
return to the probe, detected by quarature modulation,, andand are separated into a real part signal an imaginary part signal, , and then digitizedusing a sampling frequency of 10 MHz. Sampled data
were transmitted to the workstation through the GPIB
cable and analyzed.
The spatial resolution when acquiring data in vivo isin the beam width of the ultrasound beam in the beam
focal plane, and recording with conventional US
diagnostic equipment at the spatial resolution in Mmode is possible. Minimum measurable vibration
velocity is 0.5 mm/s2) in the experimental setting. The
frequency of detectable vibration depends on the
Nyquist frequency of the pulse repetition frequency(PRF) in the two-way US signal. Vibration can bemeasured at frequencies of up to 3 kHz when the PRF
is 6 kHz.
3. Basic experiments with silicone rubber tubes.
3.1 Experimental system with a ventricular assist
device (VAD)
Fig. 2 shows a schematic diagram showing theexperimental system used here. The silicone rubber
tube is placed in a water bath and a pulsatile flow issent through the silicone rubber tube by theventricular assist device (VAD). The vibration
velocity on the wall of the tube is measured asdescribed in 2.3.
The inner diameter of the silicone rubber tube was
12 mm ; its wall thickness was approximately 1 mm.
The elastic modulus ( ) was obtained using thefollowing equation, in which an inner radius is andouter radius is , after  was obtained by theleast-squared approach using a measured result of the
J Med Ultrasonics Vol.28 Winter (2001)

Fig. 2 Experimental system using a ventricular assist device(VAD) to measure vibration signals on the wall of asilicone tube.

Fig. 3 Experimental results of relationship between applied
inner pressure and strain on silicone tube.

increased outer radius when the inner pressure
was changed by  .




3 



2  

(8)

Fig. 3 shows the inner pressure of the silicone rubber
tube and the strain on it. Elastic modulus () as
obtained by Equation (8), was approximately 8 MPa.
Using this silicone rubber tube, vibrations on the wall
produced by pulsatile flow were measured with andwithout stenosis in the tube. Stenosis was produced
artificially by constricting part of the tube by tying athread around it. Stenotic rate of the inner radius was
20％, and the liquid in the tube was tap water.
159

Fig. 4 (a) Measurement points on a silicone tube with stenosis.
(b) B-mode image of the silicone tube with stenosis.

Vibration
velocitywas
measuredalmostsimultaneously at four points on the wall : two points
on the anterior wall and two points on the posteriorwall approximately 7.5 mm upstream  anddownstream  of the stenosis. The PRF of ultrasonictransmission was set at 6 kHz. Ultrasonic transmission
was performed reciprocally (＝2) at beam positions
 and , and the PRF of ultrasonic transmission ineach direction is 3 kHz. Fig. 4 a shows measurement
points on a silicone rubber tube with stenosis ; andFig. 4 b, B-mode images of the silicone rubber tube
with stenosis.
3.2 Measurement of wall vibration on the silicone
rubber tube
Fig. 5 (1) shows signals driving the ventricularassist device (VAD) (a), vibration velocity signals on the anterior wall at an upstream siteof the stenosis  (b), vibration velocity signals on the posterior wall at an upstream site of
the stenosis, velocity signals of changes in the innerdiameter   
(d), andsignals of changes in the inner diameter ＝ . The FFT Doppler spectrum ofblood flow from upstream to downstream obtained160

using a conventional US system (f) is also shown.
Fig. 5 (2) also shows vibration velocity signals , 
on the anterior and posterior
walls downstream , velocity signals of changes in
the inner diameter 
, and signals of changes
in the inner diameter 
. Fig. 6 (1) and (2)similarly show the measured results of the same
parameters using the silicone rubber tube without
stenosis upstream  and downstream . The
following can be seen in these figures.
1) When the silicone rubber tube with stenosis is used,
it can be seen in Fig. 5 that high-frequency signals areincluded at a downstream site, while they are included
at an upstream site in vibration velocity signals both at
the anterior and posterior walls. Consequently, highfrequency signals are also included in the velocity
signals of changes in the inner diameter. These highfrequency signals are not included when the tube is notconstricted (Fig. 6).
2) Phase of velocity signals of change in the innerdiameter reverse upstream and downstream fromthe stenotic site immediately after VAD-generated
pulsatile flow. As a result, changes in the innerdiameter also reverse in phase, downstream from thestenosis in particular, and the anterior and posterior
walls are displaced toward the decreasing direction of
the inner diameter in the pulsatile flow phase. We
assume that there was negative pressure downstream.
3) With respect to measurement on a silicone rubber
tube with stenosis, Table 1 shows correlation
coefficients of velocity signals of vibration on theanterior wall at upstream and downstream sites ,  , velocity signals of vibration on
the posterior wall 
, 
, velocity signalsof changes in the inner diameter 
,
and their combinations between the times
from immediately after pulsatile outflow ＝0 s and＝0.6 s. Correlation coefficients can be obtained
from the following equation with respect to two
velocities , and .

 11
   

1























(9)
When a stenotic condition was created in the tube, thecorrelations between upstream and downstream fromthe stenosis decreased on the anterior and posterior
walls. It was also seen that the correlation between theanterior and posterior walls was slightly lower
downstream
fromstenosisthanupstream.
We consider that this resulted from simultaneous
movement of the silicone rubber tube and was not thesame upstream and downstream from the stenosis.
Velocity signals of inner diameter at the downstream
and upstream sites were opposite in phase.
J Med Ultrasonics Vol.28 Winter (2001)

Fig. 5 Experimental results obtained from a silicone tube with stenosis. (1) Measurement point  at an upstream location.
(2) Measurement point  at a downstream location. (a) Signal driving the ventricular assist device (VAD). (b)and  
on the anterior wall. (c) Small vibration signals 
andSmall vibration signals  
on the posterior wall. (d) Velocity signals 
and 
of inner diameter. (e) Change in inner
and 
. (f) FFT Doppler spectrum of blood flow obtained using ultrasonic diagnostic
diameter 
equipment.

Table 1

Correlation coefficients of small vibration signals measured on a silicone tube with stenosis

Small vibration signals on the anterior wall Upstream  
Small vibration signals on the posterior wall Upstream
 
Velocity signals of inner diameter
Upstream 
Upstream wall vibration signals
Anterior wall   
Downstream wall vibration signals
Anterior wall   

J Med Ultrasonics Vol.28 Winter (2001)

Downstream
Downstream
Downstream
Posterior wall
Posterior wall 
0.489

0.489
 −0.714

0.547

0.442

161

Fig. 6 Experimental results obtained from a silicone tube without stenosis. (1) Measurement point  at an upstream location.
(2) Measurement point  at a downstream location. (a) Signal driving the ventricular assist device (VAD). (b) Smalland  
on the anterior wall. (c) Small vibration signals 
and 
on thevibration signals  and 
of inner diameter. (e) Change in inner diameter
posterior wall. (d) Velocity signals 
and 
. (f) FFT Doppler spectrum of blood flow obtained using ultrasonic diagnostic equipment.


Table 2

Correlation coefficients of small vibration signals measured on a silicone tube with stenosis

Small vibration signals on the anterior wall Upstream  
Small vibration signals on the posterior wall Upstream
 
Velocity signals of inner diameter
Upstream 
Upstream wall vibration signals
Anterior wall   
Downstream wall vibration signals
Anterior wall  
 

162

Downstream
Downstream
Downstream
Posterior wall
Posterior wall 

0.963

0.967
 0.980
 −0.079

0.142

J Med Ultrasonics Vol.28 Winter (2001)

experiment. We also consider that these effects could
diminish when the tube was constricted, as a result of
the energy of pulsatile outflow mostly converted into
static pressure that affects the inner diameter. We thus
evaluated reproducibility of vibration velocity signals
at the anterior and posterior walls in the frequency
area, using the reproducibility function13) . The
reproducibility function can be obtained with 
the following equation.



 




(10)
 

   Where   is the spectrum of the velocity ofvibration andis the number of pulses. Fig. 7 (a)shows evaluation results produced by the
reproducibility function of vibration velocity signals
from the anterior and posterior walls of the silicone
rubber tube with stenosis. Fig. 7 (b) shows results
obtained when stenosis was not present. Correlation isshown either with or without stenosis, as there is highreproducibility between pulses in the component of
frequency that is less than 10 Hz, which is the main
component of the VAD pulse signals at the anterior
and posterior walls.
5. US Doppler waveform revealed turbulence andback flow downstream from stenosis. We think thatchanges in blood flow downstream from stenosis
strongly influence wall vibration in those sections of
the arteries.
Fig. 7 Reproducibility function of small vibration signals
from the wall of the silicone tube. (a) Silicone tube
with stenosis. (b) Silicone tube without stenosis.

4) Table 2, on the other hand, shows correlation
coefficients of velocity signals of vibration on theanterior wall of upstream and downstream sites ,  , velocity signals of vibration on
the posterior wall 
, 
, and velocity
signals of changes in the inner diameter 
,
between the times from immediately after
pulsatile outflow ＝0 s and ＝0.6 s. When stenosis
was not placed in the tube, the correlation of velocity
signals of the inner diameter was higher at both the
upstream and downstream sites and between theanterior and posterior walls. Correlation between
velocity signals of the inner diameter was lower
between the anterior and posterior walls  
 of the upstream site than between theanterior and posterior walls  
ofthe downstream site, however, probably because of a
subtle difference in axial tension between the anterior
and posterior walls that affected the vibration velocity
signals when the silicone rubber tube was fixed in the
J Med Ultrasonics Vol.28 Winter (2001)

4. Measurement of wall vibration on the human
carotid artery.
The wall vibration velocity was obtained from the
carotid artery, between the common carotid artery andthe carotid sinus, of a 40-year-old female patient witharteriosclerosis, and from the carotid artery, between
the common carotid artery and the carotid sinus, of a
25-year-old healthy male subject. Measurements weretaken at eight locations along the anterior andposterior walls at beam locations  and  at the
upstream sites, stenosis , and downstream site .
The PRF was set at 6 kHz. PRF at each measurement
point was 1.5 kHz, as measurement was performed ateach point in turn (＝4). Fig. 8, 9 show B-mode
images showing the points of measurement for thefemale patient with arteriosclerosis and the 25-yearold healthy male subject, respectively. Atherosclerotic
plaque was detected on the posterior wall of the
carotid artery in the 40-year-old female patient witharteriostenosis. The measuring function of the US
system used to analyze B-mode images showed theinner diameter  of the artery to be approximately
8.3 mm ; thickness of the plaque, 2.2 mm (theapproximate inner diameter at the stenotic site was
＝8.3 − 2.2＝6.1 mm) ; and the stenotic rate of
the inner diameter , approximately 27％12) , using
163

Fig. 8 B-mode image of arteriostenosis lesion of the
carotid artery of a 40-year-old female patientwith atherosclerosis.

Fig. 9 B-mode image of carotid artery of a 25-year-old
healthy male subject.

equation (11).
  100 [％](11)Fig. 10 (1) shows the electrocardiograms (a) of the
40-year-old female patient with arteriosclerosis,
vibration velocity signals  
(b) on the anteriorwall  at the beam site  on the carotid artery(upstream distal side from stenosis), vibration velocity
signals 
(c) on the posterior wall , velocity
signals 
of changes in the inner diameter(d), and signals 
of changes in the innerdiameter. Also shown is the FFT Doppler spectrum of
blood flow velocity at the point of measurement on thearterial wall (f). Similarly, Fig. 10 (2), (3), and (4)show results obtained from position  at measuring
164

point  (upstream proximal site from stenosis),measurement results of  at measuring point (stenosis), and measurement results of at measuring
point  (downstream).
Also, Fig. 11 (1), (2), (3), and (4) show results
at four points of measurement at upstream anddownstream sites on the carotid artery, between thecommon carotid artery and carotid sinus in the 25year-old healthy male subject.
These results would appear to justify the following
conclusions.
1) Vibration velocity signals from   to on the anterior wall of the carotid artery of
the 40-year-old female patient with arteriosclerosis
show no major change upstream from the stenosis,
although it is clear that the high-frequency
components are included markedly. Further,vibration velocity signals from 
to 
show that the high-frequency components are included
between the upstream and downstream sites.
2) The amplitude of the high-frequency components
increases downstream from stenosis, with respect toto 
of thevelocity signals from 
change in the inner diameter obtained from thedifference of vibration velocity between the anterior
and posterior walls as shown in Fig. 10. Although
upstream signal amplitude does not change markedly,
it decreases suddenly immediately after reaching thedownstream stenotic site. Changes in the innerdiameter were therefore smaller at the downstream sitethan at the upstream site, probably because staticpressure (blood pressure) decreases and dynamic
pressure increases when blood flow passes through astenotic site, and because static pressure takes longer torecover at the downstream from stenosis than at the
upstream site, and blood flow becomes turbulent
because of sudden channel dilation. FFT Doppler
spectra of blood-flow velocity measured by the US
system ate thought to behave similarly, because peak
blood-flow velocity at the downstream site
immediately after the stenosis changes less than at the
stenosis. Turbulent flow and back flow appear
downstream from stenosis, and it would appear thatflow changes caused by the stenosis markedly affectvibration of the wall, particularly at the downstreamsite. In addition, back flow appears upstream from thestenosis, probably because of stenotic changes
upstream of the point of measurement. The highfrequency components included in the vibration
velocity signals on the upstream wall have now been
confirmed.
3) Table 3 shows correlation coefficients of vibration
velocity signals measured between vibration velocity
signals from   through   of theanterior wall, vibration velocity signals measured
between vibration velocity signals from 
through 
of the posterior wall, and velocity
J Med Ultrasonics Vol.28 Winter (2001)

Fig. 10 In vivo experimental results obtained from the carotid artery of the patient with atherosclerosis shown in Fig. 8.
and(1) Measurement point . (2) Measurement point . (a) ECG signal. (b) Small vibration signals  
on the anterior wall. (c) Small vibration signals 
and 
on the posterior wall. (d) and 
of inner diameter. (e) Change in inner diameter 
andVelocity signals of 
. (f) FFT Doppler spectrum of blood flow obtained using ultrasonic diagnostic equipment. (3)
andMeasurement point . (4) Measurement point . (a) ECG signal. (b) Small vibration signals  
on the anterior wall. (c) Small vibration signals 
and 
on the posterior wall. (d) and 
of inner diameter. (e) Change in inner diameter 
andVelocity signals of 
. (f) FFT Doppler spectrum of blood flow obtained using ultrasonic diagnostic equipment.


showing changes in the inner diameter from
through 
at beam positions  to. The correlation of signals is lower both on theanterior and posterior walls between the upstream and the downstream . Correlation between theanterior and posterior walls is lower at downstream
J Med Ultrasonics Vol.28 Winter (2001)

location  than at the upstream location . These
results appear to support the view that turbulence
resulting from stenosis affects vibrations on thearterial wall.
4) Table 4, on the other hand, shows correlationcofficients between vibration velocity signals from165

Fig. 10 In vivo experimental results obtained from the carotid artery of the patient with atherosclerosis shown in Fig. 8.
and(1) Measurement point . (2) Measurement point . (a) ECG signal. (b) Small vibration signals  
on the anterior wall. (c) Small vibration signals 
and 
on the posterior wall. (d) and 
of inner diameter. (e) Change in inner diameter 
andVelocity signals of 
. (f) FFT Doppler spectrum of blood flow obtained using ultrasonic diagnostic equipment. (3)
andMeasurement point . (4) Measurement point . (a) ECG signal. (b) Small vibration signals  
on the anterior wall. (c) Small vibration signals 
and 
on the posterior wall. (d) and 
of inner diameter. (e) Change in inner diameter 
andVelocity signals of 
. (f) FFT Doppler spectrum of blood flow obtained using ultrasonic diagnostic equipment.


 through  
on the anterior wall, andvibration velocity signals from 
 through
 on the posterior wall, and velocity ofchanges in the inner diameter from 
through
 at the measurement positions from through between ＝0 s and ＝0.5 s, immediately
166

after pulsatile flow at the carotid artery of the 25-yearold healthy male subject. In the carotid artery of thissubject, there was a high correlation in the waveformsof the vibration both on the anterior and posterior
walls from the upstream to the downstream locations.

J Med Ultrasonics Vol.28 Winter (2001)

Fig. 11 In vivo experimental results obtained from the carotid artery of the healthy subject in Fig. 9.
(1) Measurement point . (2) Measurement point . (a) ECG signal. (b) Small vibration
and  
on the anterior wall. (c) Small vibration signals 
andsignals  
on the posterior wall. (d) Velocity signals 
and 
of inner
and 
. (f) FFT Doppler spectrum
diameter. (e) Change in inner diameter 
of blood flow obtained using ultrasonic diagnostic equipment. (3) Measurement point . (4)and  
onMeasurement point . (a) ECG signal. (b) Small vibration signals  and 
on the posterior wall. (d)the anterior wall. (c) Small vibration signals 
and 
of inner diameter. (e) Change in inner diameter
Velocity signals 
and 
. (f) FFT Doppler spectrum of blood flow obtained using ultrasonic
diagnostic equipment.

J Med Ultrasonics Vol.28 Winter (2001)

167

Fig. 11 In vivo experimental results obtained from the carotid artery of the healthy subject in Fig. 9.
(1) Measurement point . (2) Measurement point . (a) ECG signal. (b) Small vibration
and  
on the anterior wall. (c) Small vibration signals 
andsignals  
on the posterior wall. (d) Velocity signals 
and 
of inner
and 
. (f) FFT Doppler spectrum
diameter. (e) Change in inner diameter 
of blood flow obtained using ultrasonic diagnostic equipment. (3) Measurement point . (4)and  
onMeasurement point . (a) ECG signal. (b) Small vibration signals  and 
on the posterior wall. (d)the anterior wall. (c) Small vibration signals 
and 
of inner diameter. (e) Change in inner diameter
Velocity signals 
and 
. (f) FFT Doppler spectrum of blood flow obtained using ultrasonic
diagnostic equipment.

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J Med Ultrasonics Vol.28 Winter (2001)

Table 3 Correlation coefficients of small vibration signals measured on the arteriostenosis lesionof the carotid artery of a 40-year-old female patient with atherosclerosis
Small vibration signals on anterior wall
Upstream 1 

Upstream 2 
Stenotic portion 
Downstream 

Small vibration signals on posterior wall
Upstream 1

Upstream 2

Stenotic portion

Downstream

Velocity signals of inner diameter
Upstream 1

Upstream 2

Stenotic portion

Downstream
Vibration signals (Between anterior and posterior walls)
Upstream 1  

Upstream 2  

Stenotic portion  

Downstream  


Upstream 1

Upstream 2

Stenotic Portion

Downstream

1.000

0.538
1.000

0.369
0.187
1.000

−0.017−0.178
0.391
1.000

1.000

0.570
1.000

0.493
0.512
1.000

0.255
−0.051
0.195
1.000

1.000

0.412
1.000

0.372
0.438
1.000

0.274
0.238
0.242
1.000

0.397
0.539
0.255
0.463

Table 4 Correlation coefficients of small vibration signals measured on the carotid arteryof a 25-year-old healthy male subject
Small vibration signals on anterior wall
Upstream 1 

Upstream 2 
Stenotic portion 
Downstream 

Small vibration signals on posterior wall
Upstream 1

Upstream 2

Stenotic portion

Downstream

Velocity signals of inner diameter
Upstream 1

Upstream 2

Stenotic portion

Downstream
Vibration signals (Between anterior and posterior walls)
Upstream 1  

Upstream 2  

Stenotic portion  

Downstream  


J Med Ultrasonics Vol.28 Winter (2001)

Upstream 1

Upstream 2

Downstream 1

Downstream 2

1.000

0.984
1.000

0.970
0.984
1.000

−0.921−0.947
0.960
1.000

1.000

0.984
1.000

0.961
1.000
1.000

0.869
0.956
0.865
0.860

1.000

0.992
1.000

0.981
0.987
1.000

0.944
0.952
0.961
1.000

0.943
−0.956−0.907−0.854169

5. Frequency analysis of velocity signals of change in
the inner diameter.
5.1 Power spectrum of velocity signals of change
in form by change in the inner diameter
Fig. 12 a, b show the power spectra of velocity
signals of change in the inner diameter during theejection period (from immediately after ejection to＝0.6 s), with and without stenosis in the silicone
rubber tube, respectively. Fig. 13 a, b similarly show
power spectra of velocity signals of change in the innerdiameter during the ejection period (fromimmediately after ejection to ＝0.5 s) in the carotid
arteries of the patient with arteriosclerosis and thehealthy subject respectively.
Power spectra from the upstream and downstream
locations differ little when there is no stenosis in thesilicone rubber tube. When there is stenosis in thetube, however, the power of the high-frequency
component increases more downstream than upstream.
Behavior of the carotid artery resembles that of thesilicone rubber tube : the power of the high-frequency
component increases more at the downstream location
than at the upstream location. In the healthy subject,on the other hand, the high-frequency component at
the carotid sinus is quite powerful.
We consider that turbulent blood flow at the carotid
sinus markedly affects arterial wall vibration in thehealthy subject, because there was little difference in
S / N of the quadrature modulated US signals(approximately 30 to 40 dB) from the arterial wall.
In the silicone rubber tube, the power of the highfrequency component is large downstream fromstenosis. In the carotid artery of the patient witharteriosclerosis, however, the difference disappears in
the frequency range of over 250 Hz. This would
appear to be related to differences in elasticity : 8 MPain the silicone rubber tube against several hundred kPa
in the human carotid artery, and differences inviscosity in the carotid artery and silicone rubber tube.
These differences are also thought to be related to thefact that the power of the high-frequency componentof vibration is greater at the upstream location in thesilicone rubber tube with stenosis than in the one
without stenosis. High-frequency vibration generated
by turbulence downstream from stenosis appears to betransmitted to the upstream wall.

Fig. 12 Power spectra of small vibration signals on the walls of the silicone tube. (a) Silicone tube with stenosis.
(b) Silicone tube without stenosis.

Fig. 13 Power spectra of small vibration signals on the walls at the carotid artery. (a) Patient with atherosclerosis.
(b) Healthy subject.

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J Med Ultrasonics Vol.28 Winter (2001)

5.2 Evaluation of velocity signals of change in the
inner diameter using a reproducibility function
Reproducibility of amplitude and phase of velocity
signals of the inner diameter of the silicone rubber
tube and the carotid artery is evaluated between pulses.
Fig. 14, 15 show the reproducibility function of both
amplitude and phase and of amplitude of velocity
signals of the inner diameter alone in silicone rubber
tubes with and without stenosis, respectively, during
the ejection period(immediately after ejection until
＝0.6 s) in three pulses. Fig. 16, 17 similarly show
reproducibility functions of both amplitude and phaseand of amplitude of velocity signals of the innerdiameter alone in the carotid artery of the patient witharteriosclerosis and of the healthy subject, respectively,
during the ejection period (immediately after ejection
until ＝0.5 s).
Reproducibility function for amplitude and phase is
obtained from equation (10), as explained in 3.2.
Reproducibility function amplitude alone is obtained
from the following equation.
 









 






  


(12)

 

Fig. 14 Reproducibility function of velocity signals of inside
diameter of the silicone tube with stenosis. (a)Amplitude. (b) Amplitude and phase.

J Med Ultrasonics Vol.28 Winter (2001)

In both the silicone rubber tube with stenosis and thepatient with arteriosclerosis, reproducibility of
amplitude of velocity signals of the inner diameter
downstream from stenosis is high. When amplitude
and phase are evaluated at the same time, however,reproducibility between pulses decreases and has
frequency components higher than approximately 10
Hz. As shown in Fig. 12 a, 13 a, the high-frequency
component in the power spectrum between pulses was
low in reproducibility. This would appear to be
explained by the vibrations with low correlation
generated by turbulence being transmitted to the wall.
Furthermore, in the carotid sinus of the healthy
subject, reproducibility in frequency components
between pulses decreases when it exceeds
approximately 10 Hz. In this case also, this low
reproducibility between vibrations of low correlation
generated by turbulence would appear to be explainedby transmission to the arterial wall.
6. Conclusion
We measured vibrations around stenosis in asilicone rubber tube with a constriction and aroundstenosis in the common carotid artery of a patient witharteriosclerosis, and evaluated the effects of blood flow

Fig. 15 Reproducibility function of velocity signals of theinside diameter of the silicone tube without stenosis.
(a) Amplitude. (b) Amplitude and phase.

171

Fig. 16 Reproducibility function of velocity signals of inside
diameter of the carotid artery of the patient withatherosclerosis. (a) Amplitude. (b) Amplitude andphase.

Fig. 17 Reproducibility function of velocity signals of inside
diameter of the carotid artery of the healthy subject.
(a) Amplitude. (b) Amplitude and phase.

in stenosis on wall vibration. Small vibration of thearterial wall downstream of stenosis differed markedly
from that in a healthy subject. With respect tovibration on the arterial wall, the low-frequency
component, up to several tens of Hz and caused by thetransmission of pressure waves produced by cardiac
pulsatile outflow, was recorded. A high-frequency
component downstream from stenosis differed fromthe one described above. The high-frequency
component of the vibration observed downstream
from stenosis had low reproducibility between pulses.
FFT Doppler spectra showed turbulent flow and backflow downstream of stenosis. We therefore presume
that changes in blood flow markedly affect wall
vibration, particularly downstream from stenosis.
It is thus possible that we can evaluate the effects ofpulsatile blood flow on the local arterial wall bymeasuring and comparing vibrations on the arterial
wall. We believe this procedure has potential for
estimating the possibility of rupture of atherosclerotic

plaques.

172

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